Petroleum Experts REVEAL - FANARCO · 2 - 2 CHAPTER 1 – INTRODUCTION PETROLEUM EXPERTS LTD PC...

Petroleum Experts

REVEAL

October, 2003

USER GUIDE

The information in this document is subject to change as major improvements and/or amendments to the program are generated. When necessary, Petroleum Experts will issue the updated documentation. The software described in this manual is furnished under a licence agreement. The software may be used or copied only in accordance with the terms of the agreement. It is against the law to copy the software on any medium except as specifically allowed in the license agreement. No part of this documentation may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or information storage and retrieval systems for any purpose other than the purchaser's personal use, unless express written consent has been given by Petroleum Experts Limited. All names of companies, persons or third party products contained in the examples in this documentation are part of a fictitious scenario or scenarios and are used solely to document the use of a Petroleum Experts product. Address: Registered Office: Petroleum Experts Limited Petroleum Experts Limited Spectrum House Spectrum House 2 Powderhall Road 2 Powderhall Road Edinburgh, Scotland Edinburgh, Scotland EH7 4GB EH7 4GB Tel: (44 131) 474 7030 Fax: (44 131) 474 7031 Email: [email protected] Internet: www.petroleumexperts.com

REVEAL

1 Introduction .................................................................................................................. 1

1.1 System Requirements .............................................................................................. 1

1.1.1 Hardware and Software Requirements ............................................................... 1 1.2 Overview of REVEAL ................................................................................................ 1 1.3 Contacting Petroleum Experts Ltd..................................................................................... 2

2 Step by Step Examples................................................................................................ 1

2.1 Getting Started - Step by Step Example................................................................... 1

2.1.1 Step 1 - Initialise New Case ................................................................................ 2 2.1.2 Step 2 - Wizard Basics ........................................................................................ 3 2.1.3 Step 3 - Control Section ...................................................................................... 4 2.1.4 Step 4 - Reservoir Section .................................................................................. 6 2.1.5 Step 5 - Physical Section .................................................................................... 9 2.1.6 Step 6 - RelPerm Section.................................................................................. 11 2.1.7 Step 7 - Wells Section ....................................................................................... 14 2.1.8 Step 8 - Initialisation Section ............................................................................. 15 2.1.9 Step 9 - Schedule Section................................................................................. 16 2.1.10 Step 10 - Run Simulation .................................................................................. 17 2.1.11 Step 11 - View Results ...................................................................................... 18

3 Using the Input Wizard ................................................................................................ 1

3.1 Input Wizard.............................................................................................................. 1 3.2 Control Section ......................................................................................................... 2

3.2.1 Solver Options..................................................................................................... 2 3.2.1.1 Both Implicit Solvers - First Screen of Solver Options.............................. 4 3.2.1.2 Both IMPES Solvers - Second Screen of Solver Options......................... 5 3.2.1.3 IMPES Solver ........................................................................................... 5 3.2.1.4 Corant Flux Limit implicit solver................................................................ 5

3.2.2 Model Options ..................................................................................................... 6 3.2.3 Component List ................................................................................................... 7

3.3 Reservoir Section ..................................................................................................... 7

3.3.1 Geometry............................................................................................................. 7 3.3.2 Cartesian Geometry ............................................................................................ 9 3.3.3 Radial Geometry ............................................................................................... 10 3.3.4 Curvilinear Geometry ........................................................................................ 10 3.3.5 Grid Depth ......................................................................................................... 12 3.3.6 Porosity ............................................................................................................. 12 3.3.7 Permeability....................................................................................................... 13 3.3.8 Transmissibility Multipliers................................................................................. 13 3.3.9 Absolute Transmissibility................................................................................... 13 3.3.10 Net to Gross ...................................................................................................... 14 3.3.11 Pore Volume Multipliers .................................................................................... 14 3.3.12 Rock Type ......................................................................................................... 14 3.3.13 PVT Region ....................................................................................................... 15 3.3.14 Equilibration Region .......................................................................................... 15

PETROLEUM EXPERTS LTD

REVEAL

3.3.15 Non-Neighbour Connections ............................................................................. 15 3.3.16 Grid Refinement ................................................................................................ 16

3.4 Physical Section ..................................................................................................... 17

3.4.1 Fluid Properties ................................................................................................. 17 3.4.2 Rock Compressibilities ...................................................................................... 18 3.4.3 Miscellaneous.................................................................................................... 18

3.5 RelPerm Section..................................................................................................... 22

3.5.1 General Options ................................................................................................ 22 3.5.2 Residual Saturations ......................................................................................... 24 3.5.3 Relative Permeabilities...................................................................................... 27 3.5.4 Capillary Pressures ........................................................................................... 28 3.5.5 Endpoint Scaling ............................................................................................... 29

3.6 Aquifer Section ....................................................................................................... 30

3.6.1 Analytical Aquifer............................................................................................... 30 3.6.2 Cater Tracy model............................................................................................. 31

3.7 Mobility Section....................................................................................................... 33

3.7.1 Polymer and Gel................................................................................................ 33 3.7.2 Original Polymer Gel Model .............................................................................. 34 3.7.3 Carreau Polymer Model .................................................................................... 35 3.7.4 Kuparuk Polymer Gel Model ............................................................................. 36 3.7.5 Gelation and Degradation ................................................................................. 37 3.7.6 Inaccessible Pore Volume................................................................................. 38 3.7.7 Foam ................................................................................................................. 38

3.8 Phase Section......................................................................................................... 39

3.8.1 Introduction........................................................................................................ 39 3.8.2 Alcohol/Polymer Partitioning ............................................................................. 41 3.8.3 Surfactant Phase Model (Micro-Emulsion)........................................................ 43 3.8.4 Ternary Diagram ............................................................................................... 51 3.8.5 Surfactant Interfacial Tension............................................................................ 52 3.8.6 Surfactant Viscosity........................................................................................... 53

3.9 Adsorption Section.................................................................................................. 55

3.9.1 Adsorption Properties........................................................................................ 55 3.9.2 Adsorption Isotherms ........................................................................................ 56 3.9.3 Permeability Reduction ..................................................................................... 59

3.10 Water Chemistry Section ........................................................................................ 60

3.10.1 CO2 and H2S Partition Coefficients .................................................................. 62 3.10.2 H2S Souring ...................................................................................................... 63 3.10.3 Scale Inhibition .................................................................................................. 64

3.11 Wells Section .......................................................................................................... 65

3.11.1 Location and Properties .................................................................................... 65 3.11.2 Fracture Properties............................................................................................ 68 3.11.3 Geertsma deKlerk 1D Thermal Fracture ........................................................... 71 3.11.4 3D Thermal Fracture ......................................................................................... 72 3.11.5 Rock Stress and Elasticity................................................................................. 76

3.12 Well-bore Heating Section ...................................................................................... 78


REVEAL

3.13 Initialisation Section ................................................................................................ 79 3.13.1 PVT Initialisation................................................................................................ 79 3.13.2 Equilibration Initialisation................................................................................... 79 3.13.3 Trace Component Concentrations .................................................................... 80 3.13.4 Residual Saturations ......................................................................................... 80

3.14 Schedule Section.................................................................................................... 81

3.14.1 Well Schedule ................................................................................................... 81 3.14.2 Thermal Fracture Schedule............................................................................... 83

4 Grid Refinement ........................................................................................................... 1

4.1 Refinement Section .................................................................................................. 3 4.2 Reservoir Section ..................................................................................................... 5 4.3 Aquifer Section ......................................................................................................... 5 4.4 Wells Section ............................................................................................................ 5 4.5 Well-Bore Heating Section........................................................................................ 6 4.6 Initialisation Section .................................................................................................. 6

5 Menu Commands ......................................................................................................... 1

5.1 File ............................................................................................................................ 1 5.2 Options ..................................................................................................................... 2 5.3 Edit............................................................................................................................ 2 5.4 Input.......................................................................................................................... 3 5.5 Project....................................................................................................................... 3 5.6 Run Simulation ......................................................................................................... 4 5.7 Results...................................................................................................................... 4 5.8 View.......................................................................................................................... 5 5.9 Window..................................................................................................................... 5 5.10 Help .......................................................................................................................... 5 5.11 Playback ................................................................................................................... 5


REVEAL

6 External Data Import .................................................................................................... 1

6.1 Importing Overview................................................................................................... 1 6.2 Importing from ASCII ................................................................................................ 2 6.3 Importing from Eclipse (binary files) ......................................................................... 5

6.3.1 Data files Required.............................................................................................. 5 6.3.2 Rock Type Arrays and Compressibilities............................................................. 5

.......... 671.2414 Tm( )Tj/TT8 1 Tf56.3Tj10.98 0 0 10.98 211.19 >>BDCBT/TT8 1 Tf0 Tw 10.98 0 0 10.98 99.0005 ............

1 Introduction

1.1 System Requirements REVEAL supports all Windows-certified drivers that are shipped with Windows. The list of devices, software and hardware supported by Windows is included with the documentation of your copy of Windows.

1.1.1 Hardware and Software Requirements Minimum requirements recommended for REVEAL. Pentium III class PC (Windows 95, 98, NT, 2000 or XP) 500 MHz processor (2GHz recommended) 256 Mbytes of memory (1Gbytes recommended) 5 Gbyte hard disc space for temporary files 1280 by 1024 minimum display size with high colour (16 bit) resolution CD drive if the software is installed from a CD Licenses - REVEAL can be run using a single user (stand-alone) license or on a network. In either case, a special security key is needed. The security key is called Bitlock for stand-alone licenses, and Hardlock for network licenses. The security key is provided by Petroleum Experts. For a stand-alone license, the security key (Bitlock) must be attached to the parallel port of the PC. For a network installation, the security hey (Hardlock) can be attached to any PC communicating with the network. You should refer to the separate installation procedure for a network Hardlock sent with the Hardlock license.

1.2 Overview of REVEAL REVEAL is the fifth member of Petroleum Experts Integrated Production Management (IPM) suit of software. REVEAL is a full field reservoir simulator concentrating on modeling mobility and injectivity issues arising from injection of non-reservoir fluids at non-reservoir temperatures. Therefore thermal and chemical effects are widely integrated in the REVEAL models. In addition to standard simulator models, the features present within REVEAL include:

2 - 2 CHAPTER 1 – INTRODUCTION


PC Environment - runs on PC (Windows 95, 98, 2000, NT) with single

interface to all functionality. Wizard Data Input - simplified data entry, verification and visualisation prior

to calculation. 2D and 3D Graphics - may be viewed during simulations. OpenServer - full OpenServer functionality built in, for automation or

batch processing of runs or connection to third party software.

IPM Integration - PROSPER lift curves, Petroleum Experts PVT matching and GAP optimisation (GAP is able to control, through choke pressure drops, individual completions in REVEAL).

Thermal Fracturing - integrating thermo- and poro-elastic effects on reservoir stress with injection profile and fracture mechanics.

Hydraulic Fracturing - production fractures. Water Chemistry - chemical equilibrium of mixed waters predicting

precipitation and dissolution, including H2S souring and scale inhibition.

Chemical Adsorption - retardation and permeability reduction effects. Polymer and Gel - mobility changes for aqueous phase, including shear

thinning and permeability reduction Surfactant - 4th phase micro-emulsion model using ternary

diagrams. Well-bore Heating - microwave electrical heating of heavy viscous oils. Analytical Aquifer - Carter Tracy model. IMPES Solver - with flux corrected transport (fct) for models where

numerical dispersion is important (e.g. chemical additives), and material balance iterations.

Implicit Solver - for high mobility and large throughput models (e.g. coning).

Grid Refinement - general hexahedral refinement of master grid for IMPES and implicit solver options.

An import facility is available to import part data sets from ECLIPSE, VIP or ASCII. This will be extended to other simulators in due course.

1.3 Contacting Petroleum Experts Ltd We encourage feedback and if you have problems or questions using REVEAL, please send an e-mail to [email protected] with the following information.

1 Include the keyword 'REVEAL' in the e-mail subject.

2 REVEAL version and build number - use the menu option Help|About REVEAL... to obtain this information.

3 Description of the problem or question.

4 Include a REVEAL archive (*.rvl) file where possible. Check that this file is

not too large (>2MB). If it is large, then run the simulation for one timestep and save the file, this will eliminate potentially large quantities of graphical output data.

2 Step by Step Examples

2.1 Getting Started - Step by Step Example This section describes how to set up and run a very simple REVEAL (Build 111) model from scratch. The emphasis is on how the options and wizard can be used to enter basic information, rather than the engineering content of the model. The example is a simple 25 by 25 by 15 (X, Y, Z) grid reservoir, with one horizontal producing well at its centre. Step 1 initialise new case Step 2 wizard basics Step 3 control section Step 4 reservoir section Step 5 physical section Step 6 relperm section Step 7 wells section Step 8 initialisation section Step 9 injection schedule section Step 10 run simulation Step 11 view results

2 - 19 CHAPTER 2 – STEP BY STEP EXAMPLE

2.1.1 Step 1 - Initialise New Case Start REVEAL, and open a new project (File|New), or use the icon .

Select Options|Units and set the input and output units to Oilfield, then select OK.


CHAPTER 2 – STEP BY STEP EXAMPLES 3 - 19

Now is a good time to save the file using File|Save Project As..., and enter a file name (e.g. example1.rvl).

2.1.2 Step 2 - Wizard Basics The REVEAL input script is divided into several sections. These may be modified either by directly altering the text in the input script, or by using the project wizard. The wizard may be used for one section only, or run consecutively through all of the sections. The wizard is activated with a right click inside the input script window, or by selecting Input. Once the wizard ends normally (section(s) completed, or Finish selected), the output script is updated. To prevent the changes made in using the wizard from being written to the output script, select Cancel. Once the Wizard is exited, the only data stored internally by REVEAL is that written to the script and held in datablocks1. The Next and Previous buttons can be used to navigate forwards and backwards through the wizard screens. The Validation, Plot and Calculate buttons may be used on some screens to check data input. It is obviously advisable to save the REVEAL file archive (*.rvl) using File|Save Project or File|Save Project As... at regular intervals. The wizard cannot be running while a save is made. The REVEAL archive file contains the script and additional project files such as PVT, lift curve, output graphics etc. The archive files present may be viewed, added to or deleted using the option Project|Edit / View Project.... Start the wizard using Input|Script Wizard|Run All.

1Potentially large arrays of data (e.g. grid coordinates) held in the REVEAL archive but not displayed in the input script.

OCTOBER 2003 REVEAL MANUAL


2.1.3 Step 3 - Control Section This section sets the scope of the REVEAL model being created, and includes major solver options.


The next screen selects additional components (additional to water, oil & gas), including non-reservoir injection gases. Select Next. This completes the control section.



2.1.4 Step 4 - Reservoir Section This section enters the reservoir grid and some basic physical properties of the reservoir. On the first screen enter a Cartesian grid with X and Y dimension set to 25 and Z dimension set to 15, then select Next. We are going to enter a very simple grid with 300 ft square and 20 ft deep blocks. Enter the values as shown, then select Add to enter the Z direction depths. Select Plot to view a wire frame mesh. Close the plot screen to return to the ‘Reservoir Section: Cartesian grid input’ screen and select Next.

The next screen enters the reference depth at the top of the grid. Select Add, then All, to set all of the columns of blocks, then enter a value of 10000 ft. This data has been entered and can be checked using the Validate button. The list of data entered is not updated on the screen dynamically, but may be seen by clicking left over the list.



Select Next to enter the porosity data, select Add, then select All grid blocks, and enter a value of 0.2. Select Next to enter the X direction permeability, select Add, then select All grid blocks, enter a value of 100 mD. Select the Y Permeability tab at the bottom of the screen, and leave the Y direction permeability multiplier at 1, select Z Permeability tab and set the Z direction permeability multiplier to 0.1. Select Next to enter transmissibility multiplier data, used for permeability barriers etc. We won’t be using these so select Next to enter absolute transmissibility data. If this is entered (and the drop-down list at the top of the screen is changed to say 'Yes') REVEAL will not perform its own transmissibility calculations but will use these transmissibilities directly. These would normally be imported directly from the results of another simulator, so we won’t be using these, select Next. We won’t be setting net-to-gross ratios so select Next again. We won't be using pore volume multipliers so select Next again to define rock types. We won’t be setting net-to-gross ratios so select Next again. We won't be using pore volume multipliers so select Next again to define rock types. We will have only one rock type so select Add, then All. The same goes for PVT and equilibration regions on the next two screens. After completing the PVT and equilibration region screens select Next to enter non-neighbour connections, then Next again to enter grid refinement regions. We won’t be using either of these for this example. This ends the reservoir section and the data entered should be saved. Select Finish to end the wizard and write the data entered to the input script. Then select



File|Save Project to save the REVEAL archive. The data entered so far can be seen by scrolling up within the input script window. The on-context help can be invoked by selecting the icon shown below to view a simple description of the data entered in the script. Move the cursor over the script to view the on-context help and turn the on-context help off by de-selecting the icon shown.



2.1.5 Step 5 - Physical Section This section enters the fluid and rock physical properties, the most important of which are the PVT for water, oil and gas. Use the right mouse button from within the input script window to restart the wizard at the physical section by selecting Start Wizard|Physical. We are going to enter a simple (unmatched) black oil PVT for an oil that is undersaturated at 5000 psig and 200 F. Select New to enter a new PVT, then select Oil for the fluid type and enter a name (e.g. example1), then select OK to bring up the PVT entry screen. This is the same as other Petroleum Experts PVT entry and indeed previously created PVT files can be imported directly using the Import option. Do not do this now since we are creating PVT data from scratch and not importing an existing file. Enter the following black oil PVT data and then select Done to save the PVT data. We are not concerned with complexities of PVT matching and miscibility during this tutorial.

Thermal conductivity, diffusivity and dispersion data may be entered on this screen, but we are not including these effects in this model. Enter the following physical data using the default thermal properties button.



Note that units may altered dynamically by left clicking over the unit (highlighted above). Don’t alter the units now. Select Validate to check the data entered. Click right over any data entry cell and select Validation Range to change the minimum and maximum values. It is not necessary to alter the validation range for REVEAL to accept data input. Any changes made to the validation ranges are saved with the file. Select Next to enter the rock compressibility, enter a value of 1e-5 psi-1 for the uniform compressibility. Select Next to enter various (mostly optional) viscosity model parameters. No data entry is required so select Next to complete the physical data section.



2.1.6 Step 6 - RelPerm Section The relative permeability and capillary pressure data are entered in this section. Relative permeabilities may be direction and well dependent, but not for this case so select Next. This screen defines which residual saturation data will be applied to which rock type. This is simple in this case, since we are only going to enter one set of data. Select Add Region and make sure the Rock Coverage All checkbox is ticked. Enter the residual phase saturations as shown and select Next. Note that residual saturations for desaturation and gas hysteresis would be entered on this screen if these models were active.

Select Add Rel Perm, then tick the Directions(All) tickbox and set the Data Entry to Parametric. Enter the following data and select Plot to view the data entered. Select OK, then Next to enter the capillary pressure data.



We are going to have no capillary pressure in this model, so enter the following tabular data.



This completes the relative permeability section, so select Finish to write all of the data entered so far to the input script. Save the REVEAL archive and restart the wizard at the Wells section. Note that the Aquifer, Mobility, Phase behaviour, Adsorption and Water Chemistry sections are not required for this simple example.



2.1.7 Step 7 - Wells Section Start the wizard in the wells section if it is not already there. We are going to enter one horizontal well perforated at a depth of 10150 ft (centre of the reservoir). In the wells list select Create, to add the well, then select Multilateral description in the Enter well position by: selection box. Give the multilateral description an identifier name (e.g. horiz) and set the BHP reference to Fixed elevation and set a value of 10050 ft (remember the top of the reservoir is at 10000 ft and we have 5 vertical blocks of 20 ft each).

Select the Edit Multilateral button to enter the deviation survey for the well. Select the Change Reference button to set the first node of the well at coordinates (2000,3750,10150). Select OK once the reference position has been entered. Select Add tubing and then OK. Next, enter the deviation survey as shown below, note the internal diameter units have been change from feet to inches, and finally select OK to return to the wells input screen.



Select Plot to view the reservoir and completed well (the left mouse button rotates the reservoir and the CTRL and SHIFT keys in combination with the left and right mouse buttons all modify the display – if it gets too distorted use F5 to return to a default scaling). Return to the wizard and select Next to complete the Wells section.

2.1.8 Step 8 - Initialisation Section The first page of this section assigns a PVT description to each PVT region. Since we only have one PVT region and one PVT description the default assignment has been made already so select Next. The next page sets initial reservoir temperature and pressure, in addition to initial contact depths for each eqilibration region. We will simply set the temperature and pressure at the centre of the reservoir. Enter a reference depth of 10050 ft and reference pressure of 5000 psig. Enter an overburden and underburden temperature of 200 F and a 0 F/ft thermal gradient. Select Next to enter the last section.



2.1.9 Step 9 - Schedule Section This section sets the well constraints and time-step control data. We will run this case for 1000 days with a constant production rate of 10000 STB/d oil with a minimum Pwf of 2000 psig. Select Produce for the well type and Fix rate for the well control, and enter a rate of 10000 STB/d and set the Rate type to Total (oil+water). Select the green Constraints button to enter the minimum Pwf of 2000 psig. Set the initial time step size to 1 day. We recommend not using other time-step controls unless it is shown to be required. Set the schedule to run for 1000 days as shown. Finally select Next to complete the data input.

Save the REVEAL file using File|Save Project.



2.1.10 Step 10 - Run Simulation Select Run Simulation|Select Properties... to select which data and how often it should be saved. The grid data (arrays over active grid blocks) can be saved at different intervals to the tabular data (well, average reservoir properties, wellbore results). Modify this as appropriate and select OK when this has been done. Start the calculation ( ) and save the REVEAL archive once it has completed.



2.1.11 Step 11 - View Results Use the buttons to view the results. The results may also be viewed interactively during a calculation. The button provides average reservoir properties such as mean phase pressures, saturations and volumes. These data may be viewed, plotted and printed, or copied to the clipboard for import into another application. The button provides well results data, including instantaneous and cumulative rates, GOR, water cut and phase pressure and saturation data at well blocks. The button provides a three dimensional display of the fluid properties that were selected for display (Run Simulation|Select Properties...). It includes graphical representation of wells, completions and fractures. The following is a list of recommended control functions within the 3D display window. left mouse - rotates the image in wire-frame mode about the X and Y axes. Ctrl+right mouse - rotates the image in wire-frame mode about the Z axis. Shift+left mouse - pans the image. This may also be achieved by using the left

mouse button near the edge of the display window. Ctrl+left mouse - selects a region to be enlarged. F5 - returns the scaling to its original size. W key - sets the display to wire-frame mode. S key - sets the display to surface mode. The following is a list of recommended options available using the right mouse button within the 3D display window. right mouse|3D Options - set block shrink factors, surface transparencies and

select regions of blocks (usually a plane of blocks) to view.

right mouse|Scale - set the scale range for colour tables; set linear and logarithmic scaling and the end points (minimum and maximum values to scale between).

right mouse|Object Properties

- set visibility (presence or absence), transparency, wire-frame or surface mode for individual elements within the display (e.g. set fractures to be wire-frame). Some element types may be selected individually (wells, completions, fractures) by selecting the appropriate element type with the left mouse button in the Viewing Objects column of the table.

right mouse|View - set the variable to view. right mouse|Playback Options

- set the range, interval and speed of 3D playbacks. The forward and reverse playback is initiated and controlled using the buttons.

Once a view has been created, its properties may be saved and reopened later. Use Options|Preset Options|Save File and Options|Preset Options|Load File to achieve this. Enter a name for the view, select the properties to be saved (usually All) and




select OK. Note that the REVEAL archive2 must be saved for the view to be saved permanently. Many of the REVEAL example cases have default views saved. To view grid block properties evolving with time on a 2D plot, select the blocks to be viewed, either using Edit|Select Multiple Blocks, or by selecting the button to select and unselect individual blocks using a left mouse click. Deselect the button once the required blocks have been selected. Select Results|Results of Selected Cells to view the cell results. Use Edit|Unselect All Blocks to deselect all blocks.

2The REVEAL archive file (*.rvl) contains the script and additional project files such as PVT, lift curve, output graphics etc. The archive files present may be viewed, added to or deleted using the option Project|Edit / View Project....

3 Using the Input Wizard A REVEAL input data set is divided into several sections. These may be modified either by directly altering the text in the input script, or by using the project wizard. The wizard may be used for one section only, or run consecutively through all of the sections. The wizard is activated with a right click inside the input script window, or by selecting Input from the menu. Once the wizard ends normally (section(s) completed, or Finish selected), the output script is updated. To prevent the changes made in using the wizard from being written to the output script, select Cancel. Once the Wizard is exited, the only data stored internally by REVEAL is that written to the script and held in datablocks1. The Next and Previous buttons can be used to navigate forwards and backwards through the wizard screens. The Validation, Plot and Calculate buttons may be used on some screens to check data input. It is obviously advisable to save the REVEAL 2archive file using File|Save or File|Save As at regular intervals. The wizard cannot be running while a save is made.

3.1 Input Wizard The input wizard is divided into 13 sections, each containing several related pages. The sections and pages displayed are context sensitive and will depend on the options previously selected, the principal options are set in the control section. General help starting and using the input wizard is available, along with specific page-by-page help. Control section - Solver options, model options, component selection Reservoir section - Geometry, grid depth, porosity, permeability,

transmissibility multipliers, absolute transmissibilities, net to gross, pore volume multipliers, rock type, PVT region, equilibration region, non-neighbour connections and grid refinement

Physical section - Physical properties, rock compressibities and miscellaneous models (wax dropout, interfacial tension, miscibility, wettability, non-Newtonian oil)

Relperm section - Options, residual saturations, relative permeabilities, capillary pressures, endpoint scaling

Aquifer section - Analytical aquifer, Carter Tracy model Mobility section - Polymer/gel, original Carreau Kuparuk viscosity

models, gelation & degradation, inaccessible pore volume, foam, partition coefficients

Phase section - Introduction, alcohol/polymer partitioning, surfactant

1Potentially large arrays of data (e.g. grid coordinates) held in the REVEAL archive but not displayed in the input script. 2The REVEAL archive file (*.rvl) contains the script and additional project files such as PVT, lift curve, output graphics etc. The archive files present may be viewed, added to or deleted using the option Project|Edit / View Project....

2 - 84 CHAPTER 3 – USING THE INPUT WIZARD

micro-emulsion phase, ternary diagram, interfacial tension, surfactant viscosity

Adsorption section - Adsorption properties, permeability reduction Water chemistry section - Water chemistry options, H2S souring options, scale

inhibition options, chemical database Wells section - Location and properties, fractures, stress Well-bore heating section - Well-bore heating model Initialisation section - PVT initialisation, equilibration initialisation,

component concentrations, residual saturations Schedule section Well schedule, thermal fracture schedule

3.2 Control Section

3.2.1 Solver Options Four principal solver options are available, two IMPEC (implicit in pressure and explicit in concentration) solvers and two implicit solvers. The term IMPES (implicit in pressure and explicit in saturation) is equivalent to IMPEC in this context. Hints and tips - always start with the default options. Some experimentation is sometimes required for difficult cases. By checking the text debug output file, identify where cpu time is being spent (end of debug file). If the preconditioner and linear solver times are very different, then increase or decrease the power of the preconditioner appropriately. The more time spent in the preconditioner will speed the linear solve and vice-versa, so an optimum is usually when a simular cpu time is spent in the preconditioner and linear solver. To increase the preconditioner power, reduce the preconditioner drop and/or permulation tolerances. This increases the number of non-zero elements in the preconditioner. If the linear solver is having problems, then increase the preconditioner power or change the row/column ordering. Usually try ZD4 or D4Z orderings. If the newton steps are not converging, then this is often a consequence of problematic derivatives. Try using a known simple PVT, then simple relative permeability and capillary pressure curves. Sometimes the linear solver should be pushed further to improve Newton convergence. This is typically seen when the Newton convergence looks good for the first few iterations, then fails to converge. The linear solver may be pushed further by reducing the relative residual reduction. Also reduce the maximum saturation change on the solver screen. Check for very small blocks or very large permeability and gas flow. Implicit pressure explicit concentration - The IMPEC solvers solve each time-step faster than the implicit formulation and uses iterations to ensure material balance3. Its

3Material balance means that the mass and volume of components/phases within each grid block at the end of the time-step are consistent with the phase densities, following the volumetric Darcy flow during the time-step.


CHAPTER 3 – USING THE INPUT WIZARD 3 -84

time-steps are limited to the Courant limit4. It has various upstream weighting options to minimise numerical dispersion5 and reduce grid orientation6 effects. These are the only solver options available for micro-emulsion surfactant models, and should generally be selected for models where numerical dispersion of trace components is important (e.g. water chemistry) and the Courant time-step limit is acceptable. Implicit pressure and saturation - The implicit solvers are implicit in three phases and three components (water, oil and gas), using a one-point upstream weighting for mobilities. If more than the three principal components are present, then a Courant limit is required on the time-step size to update the additional component concentrations explicitly. Thermal models are not subject to the Courant time-step limit in the implicit formulation, but temperature may be subject to numerical dispersion at larger time-steps. These options should be selected for three component models where high velocities and small grid blocks are present (e.g. gas coning). Old IMPES - this is the original IMPES solver and has now been superceded by a more general IMPES solver (see next option). This option is required if the thermal fracture DLL is to be used, but does not support grid refinement. If neither grid refinement or a thermal fracture DLL are present then it should produce virtually identical results the default IMPES solver below. IMPES - this is the default IMPES solver, which will be maintained to include future models. It is effectively a subset of the fully implicit solver. Fully Implicit - this solver option should be used for three component systems (water, oil and gas) and other chemical models, where an implicit solver is required. It is not available for surfactant models, where the IMPES solver should be used. CFL Implicit - this is the fully implicit solver, where the Courant timestep limit is imposed to minimise numerical dispersion for chemical models. Depending on the solver option chosen, various solver options are available on two screens. Defaults are provided, and altering them must be performed with care. Some models may be significantly speeded up by careful choices.

4Courant Flux Limit (CFL) ensures that no more than one pore-volume throughput through any grid block occurs within a time-step. 5Spatial averaging (smearing out) within regions of high concentration gradients (e.g. flood front or trace component) due to linearisation of equations over the grid and in time. Made worse by using large grid blocks and large time-steps. Upstream weighting schemes are used to minimise the effect by extrapolating mobilities between grid blocks to maintain large concentration gradients where possible. Also known as numerical diffusion. 6Flow parallel and diagonal to the grid blocks' orientation may produce significantly different breakthrough times. This may be automatically minimised in REVEAL, using a method that alters the grid block phase transmissibilities to effectively increase diagonal flow and reduce parallel flow.



3.2.1.1 Both Implicit Solvers - First Screen of Solver Options Maximum variable changes - limits for pressure and saturation are entered. Generally the defaults should be applied. The saturation limit may be reduced to 0.1 to reduce time-steps and make the solve easier if convergence is slow. Convergence limits - convergence limits for pressure, saturation and relative rate for fixed rate wells. Generally the defaults should be applied. The saturation and implicit well limits may be reduced to 0.001 to increase the number of Newton iterations and reduce the material balance error, reducing oscillations. Row/Column ordering - this option is probably the most important and should be set appropriately. It includes various matrix ordering schemes, the cycling is from left to right (e.g. XYZ cycles the in the X direction, then Y direction, then Z direction, with the cycling fastest in X direction). Some D4 (chess board) ordering schemes are also included. In general the fastest ordering should correspond to the highest transmissibility direction (often Z) or the smallest bandwidth (direction with smallest number of blocks). For many areal models, ZD4 or ZYX would be good choices. Horizontal point scheme - either a 5 point or 9 point horizontal flow scheme is available for the fully implicit solver. The 9 point scheme is recommended since it significantly reduces grid orientation effects. Newton iteration options - these options should not be altered for most models. The maximum number of Newton iterations is entered. If a converged solution is obtained, but it took more than the ‘hold’ limit, then the next time-step will not be increased. If a converged solution is obtained, but it took more than the ‘reduce’ limit, then the next time-step will be reduced. A time-step is retaken with a reduced time-step if the current residual is lager than the divergence condition multiplied by the minimum residual calculated (i.e. detects Newton divergence). The maximum Newton step size is 1.0 for a full Newton step; for cases where Newton convergence is not occurring (oscillations or divergence) this value may be reduced to 0.5 to improve convergence at the expense of the number of Newton iterations required. Pre-conditioner options - the options for linear solver pre-conditioner should not generally be altered from the default values. The fill in parameter is the bandwidth of the pre-conditioning matrix, and may be increasedto help convergence of the linear solver; alternatively it may be lowered to reduce the size of the pre-conditioning matrix and hence memory requirements. The drop and permutation tolerances refer to the relative size of off-diagonal matrix elements included in the pre-conditioning matrix and column swapping. Solver options - the options for linear solver should not generally be altered from the default values. A stabilised bi-conjugate gradient (BCGSTAB) and generalised minimum residual solver (GMRES) are used. The residual reduction is a relative residual reduction defining convergence, and the residual maximum is an absolute residual limit. Sometimes reducing the residual maximum may help reduce oscillations between Newton iterations. The residual is defined as the r.m.s. mass rate error. The Krylov space size is used for the GMRES solver. If this value is increased, the solver may become more robust, but may require significantly more memory and become much slower, it may be reduced to a minimum value of 2 to minimise memory requirements.



3.2.1.2 Both IMPES Solvers - Second Screen of Solver Options Upstream weightings define how properties required at grid block faces are calculated, and are used to minimise numerical dispersion effects. Weightings are required for component concentration, temperature, permeability (mobility) and density. The permeability and density weightings are used prior to the implicit pressure solve, while the component concentration and temperature weightings are used during the explicit phase of the solve, after the implicit pressure solve has been performed. The phase velocities are determined by the implicit pressure solve. The component concentrations are the concentration of components within the phases present, and therefore component concentration weightings only effect trace components within the phases. 1-point - block face value is taken as the value in the centre of the upstream block. This is recommended for component concentration where trace components are not present, and also recommended for the surfactant micro-emulsion model, to ensure components are transported in the ratios present within the upstream block. 2-point - block face value is taken as a value extrapolated from the two upstream blocks. This method reduces numerical dispersion but generally not recommended. fct/2-point - similar to the 2-point scheme, but extended fct (flux corrected transport) algorithm [17] acts to minimise numerical dispersion. Recommended for temperature and component concentrations where trace components are present. fct/3-point - higher order, three block (two upstream and one downstream) fct method. This method should only be used when all blocks are identical cubes. Not generally recommended. Original - for mobility weighting, this method uses a 1-point upstream weighting for relative permeability and centred value for viscosity. Either this method or the 1-point upstream weighting are recommended for permeability weighting. Centred - for density weighting (used for gravitational term in implicit pressure solve), this method is a mean upstream/downstream value. Either this method or the 1-point upstream weighting are recommended for density weighting. Diagonal transmissibility - used to minimise grid orientation effects in the horizontal (constant Z) plane. A value of 0 turns this model off, while a value of 0.5 is recommended and is equivalent to allowing up to 1/3 of flow to be diagonal rather than parallel to block faces. This model only has significant effect near regions of large mobility variations (e.g. flood front).

3.2.1.3 IMPES Solver Row/Column ordering - See Section 3.2.1.1 Pre-conditioner options - See Section 3.2.1.1 Solver options - See Section 3.2.1.1

3.2.1.4 Courant Flux Limit implicit solver Concentration and temperature upstream weighting - see above.



3.2.2 Model Options This wizard page initialises the models that will be present, and consequently the subsequent sections and screens that will be displayed by the input wizard. Fracture model - includes thermal injection fractures and hydraulic production fractures. Aquifer model - is based on the Carter Tracy analytical model. Component models - include simple (water, oil and gas), surfactant (4th phase micro-emulsion), polymer/gel (various aqueous, oleic and gas phase mobility models) and water chemistry (aqueous phase precipitation model). The components that can be used later will depend on the component model selected on this screen, and as such these models are mutually exclusive. Chemically and physically inactive tracer components are available with all component models. Souring - H2S souring model, only available if the component model is water chemistry. Scale inhibition - precipitate scale inhibitor model, only available if the component model is water chemistry and the component Scale Inhibitor is included in the component list. Wettability, miscibility and well-bore heating - if these models are selected, then the various wizard screens for their data input will become active as the wizard is progressed. Transmissibility model - select 'normal' or 'extended'. The extended model is essentially that implemented in Eclipse as 'NEWTRAN'. In the normal model, the interface block area, rather than projections of mutual interface areas, is used in the transmissibility calculations. Reference conditions - The reference temperature is used for some correlations (e.g. adsorption or partitioning relations). The reference depth is used for reported reservoir average pressures and also used to reference all well Pwfs back to a common datum. Inactive block definition - there are two criterea that may be used to flag inactive blocks. 1. The porosity*net-to-gross is less than a defined limit, or 2. The grid cell pore volume is less than a defined limit. User Fracture DLL - a DLL (Dynamically Linked Library) may be supplied by a third party to perform thermal fracture calculations. Contact Petroleum Experts for more information on the DLL interface for this option.



3.2.3 Component List Reservoir components - the components to be included in the model are added by selecting the component and pressing Add, components may be deleted by selecting the component to be deleted in the list and using the Delete button. Water, oil and gas are always present. The components available will depend on the component model selected (previous wizard screen). Injected component - A non-reservoir gas for injection may be added. This gas will not modify the underlying oil PVT model and the mixing of the injection gas with reservoir gas is modelled approximately, since this is not a fully compositional model.

3.3 Reservoir Section

3.3.1 Geometry All REVEAL models consist of hexahedral grid blocks connected in a regular structure (topologically identical), with each block identified by its I,J,K numbers. I runs from 1 to NX, J from 1 to NY and K from 1 to NZ, where NX, NY and NZ are the number of grid blocks in each principal direction, with the Z direction being vertically down. NX must be greater than one. Select the grid coordinate system and the number of blocks in each principal direction NX, NY and NZ. The Update Globally button will update all other sections where possible to reflect changes made to NX, NY or NZ. The update globally option is only required when the grid size is being changed, and performs no function the first time a reservoir geometry is defined. Corner point grid - most large models will use the corner point grid coordinate system. The X, Y and Z coordinates of each block corner must be entered layer by layer (increasing Z) into a data array, by selecting the Data Array button. The data array must also be given a name. The X, Y and Z coordinate values should all be increasing in their respective positive directions. The corner point data may be copied and pasted from another application such as EXCEL, or imported directly from another simulator, where a filter is provided. See the Input option on the main bar for grid geometry import options. Once potentially large volumes of corner point data have been entered it is advisable to select Finish to leave the wizard and save the REVEAL archive7. Corner point (simplified) - in this scheme adjacent blocks share coordinates, there are therfore (NX+1) * (NY+1) * (NZ+1) coordinates in total. These are entered as X, Y and Z coordinates for each layer, with (NX+1) * (NY+1) enties per layer for each spatial direction. Corner point (full) - in this scheme ach block has 8 independent coordinates, there are therefore (2*NX) * (2*NY) * (2*NZ) coordinates in total. These are entered as X, Y and Z




coordinates for each layer, with (2*NX) * (2*NY) entries per layer for each spatial direction. Each block is considered in turn and its two corner point coordinates are entered before the next block data is entered. Map Axes - may be entered for cartesian or corner point grids. Three coordinates in the horizontal plane (X,Y coordinates only) defining an origin and directions for the X,Y axies of a map coordinate system are required. The coordinates are entered in the grid coordinate system and define a second coordinate (map) system that mey be used to enter well trajectories. Note that the map axes must be orthogonal (90 degrees between the axes). Cartesian grid - the Cartesian grid coordinate system generates a regular grid with constant grid spacing. Radial grid - the radial grid coordinate system generates a grid with radial grid blocks forming a sector away from a central well. For the radial grid option a central well radius must be input. The sector angles may be constant; if this is required then select the Uniform Sector Angle button and enter an angle. The units for the angle may be toggled between radians and degrees by clicking right within the angle data entry cell. Note that there is no flow between the grid blocks at Y=1 and Y=NY, even if the radial model is 360 degrees. Curvilinear grid - the curvilinear grid coordinate system generates a grid with 2 wells as one eighth of a repeated five-spot symmetry, reflecting the streamline flow between two wells, one injector and one producer. For the curvilinear grid option, the spacing between the well must be entered, and an excluded fraction. The excluded fraction is the fraction of the distance between the two wells excluded from the model, which prevents stability problems near the wells. It should typically be set to about 0.05. An additional page of data input is required for the Cartesian, radial and curvilinear grid options.



Cartesian grid Corner point grid

Radial grid Curvilinear grid

3.3.2 Cartesian Geometry Block sizes - the X and Y grid block dimensions should be entered for rows 1 to NX and columns 1 to NY. Consecutive rows or columns with the same grid block dimension may be entered as a group (e.g. if the first three dimensions are 100 ft and then next two dimensions are 50 ft, then only two rows of the table require to be entered). The Z dimension of the grid blocks is entered in one of three ways. Z range - the most common method, where the Z dimension of the grid blocks are entered for each layer (or groups of layers). Single layer range - for a single layer, the Z dimensions for blocks may vary in the X and Y directions. Care must be taken with this method to ensure that full coverage of the model is achieved (all blocks have a Z dimension). Layer n multiple - where one layer Z dimensions are a multiple of a previously defined layer. For each method of Z dimension entry, the range and Z dimension should be entered in the appropriate data entry cells and the Add button selected to add the data to a table of entries. An entry in the table may be modified by selecting and highlighting the required entry in the table and then modifying the data entered; the Add button should not be used to update modified data, since it will add another row to the table. The modified data can be viewed in the table by re-selecting the row in the table. Table entries may be deleted by using the Delete button.



Full coverage of the model may be checked by selecting the Validate button, and the resulting grid checked by selecting the Plot button.

3.3.3 Radial Geometry Block sizes - the X and Y grid block dimensions should be entered for rows 1 to NX and columns 1 to NY. Consecutive rows or columns with the same grid block dimension may be entered as a group (e.g. if the first three dimensions are 100 ft and then next two dimensions are 50 ft, then only two rows of the table require to be entered). The X grid block dimensions have units of length, while the Y grid block dimensions have units of angle. If constant angles were set on the previous wizard screen, then no Y dimensions are required. The Z dimension of the grid blocks is entered in one of three ways. Z range - the most common method, where the Z dimension of the grid blocks are entered for each layer (or groups of layers). Single layer range - for a single layer, the Z dimensions for blocks may vary in the X and Y directions. Care must be taken with this method to ensure that full coverage of the model is achieved (all blocks have a Z dimension). Layer n multiple - where one layer Z dimensions are a multiple of a previously defined layer. For each method of Z dimension entry, the range and Z dimension should be entered in the appropriate data entry cells and the I button selected to add the data to a table of entries. An entry in the table may be modified by selecting and highlighting the required entry in the table and then modifying the data entered; the Add button should not be used to update modified data, since it will add another row to the table. The modified data can be viewed in the table by re-selecting the row in the table. Table entries may be deleted by using the Delete button. Full coverage of the model may be checked by selecting the Validate button, and the resulting grid checked by selecting the Plot button.

3.3.4 Curvilinear Geometry Block sizes - the X grid block dimensions should be entered for rows 1 to NX. Consecutive rows with the same grid block dimension may be entered as a group (e.g. if the first three dimensions are 100 ft and then next two dimensions are 50 ft, then only two rows of the table require to be entered). The Y grid block dimensions are not required, since they are calculated by the model. The Z dimension of the grid blocks is entered in one of three ways. Z range - the most common method, where the Z dimension of the grid blocks are entered for each layer (or groups of layers). Single layer range - for a single layer, the Z dimensions for blocks may vary in the X and Y directions. Care must be taken with this method to ensure that full coverage of the model is achieved (all blocks have a Z dimension).



Layer n multiple - where one layer Z dimensions are a multiple of a previously defined layer. For each method of Z dimension entry, the range and Z dimension should be entered in the appropriate data entry cells and the Add button selected to add the data to a table of entries. An entry in the table may be modified by selecting and highlighting the required entry in the table and then modifying the data entered; the Add button should not be used to update modified data, since it will add another row to the table. The modified data can be viewed in the table by re-selecting the row in the table. Table entries may be deleted by using the Delete button. Full coverage of the model may be checked by selecting the Validate button.



3.3.5 Grid Depth For all grid geometries except corner point (where the coordinates of all blocks are entered explicitly), the depth of the top surface of the grid must be defined. The depth must cover the entire top layer (Z=1) of grid blocks, and is defined as the depth from a zero datum to the top of the grid blocks. For Cartesian grids, two methods are available, range/array and dip angles. For the radial and curvilinear grids, only the range/array method is available. Select Add to add an entry to the table of values. Range - each table entry may cover a range of blocks with a constant value (e.g. a flat top surface at 5000 ft would be achieved by selecting range, then the All button and entering a value of 5000). This data has been entered to the table, but the table display is not updated until an entry in the table is selected with the mouse. Several entries to the table may be added, modified or deleted. The coverage of the table entries must cover all blocks on the top layer (X=1,NX and Y=1,NY). The Validate button may be used to check coverage. Select entries in the table with the mouse to modify or delete them. Array - an array of depths are entered, one for the centre of each top surface grid block. The array must be given a unique name before data is entered. Data may be copied and pasted into the array from another application. Dip angles - the depth of the first block (X=Y=1) is entered, and the dip angles in the X and Y direction are entered.

3.3.6 Porosity The porosity of each grid block is required. This is the porosity at the reference pressure, with porosities being calculated as a function of rock compressibility for grid blocks with pressures below or above the reference pressure. A zero porosity is used to identify inactive grid blocks, which will take no part in the flow calculations. Two methods are available to enter porosities, range and array. Select Add to add an entry to the table of values. Range - each table entry may cover a range of blocks with a constant value. Click the right mouse button within the value entry cell to toggle between fraction and percentage porosity. Several entries to the table may be added, modified or deleted. The coverage of the table entries must cover all grid blocks. The Validate button may be used to check coverage. Select entries in the table with the mouse to modify or delete them. Array - an array of porosities are entered, one for each grid block, entered by layer with increasing depth (increasing Z). The array must be given a unique name before data is entered. Data may be copied and pasted into the array from another application. Use parent grid values - only available if the current grid is a refined grid (see grid refinement for general information on grid refinement and refined reservoir properties for information on entering refined grid reservoir properties), then use porosities defined for master (parent) grid.



The Plot button may be used to view the porosity distribution entered.

3.3.7 Permeability The permeability in the X, Y and Z directions is required for each grid block in the model. Use the tabs at the bottom of the screen to enter the Y and Z permeabilities, which can be entered explicitly, or as a multiple of the X direction permeabilities. See the porosity help screen for details of how to add ranges or arrays of permeabilities.

3.3.8 Transmissibility Multipliers This screen is optional and no data is required. The default transmissibility between two blocks is calculated using a harmonic average8 of the two adjacent grid block permeabilities. Transmissibility multipliers may be used to modify the transmissibilities between blocks to model transmissibility barriers (or enhancement). Transmissibility multipliers (default value of 1.0) may be given in the X, Y and Z directions for any or all grid blocks. e.g. an X direction transmissibility multiplier of 0.1 for grid block (3,4,2) reduces the transmissibility between grid blocks (3,4,2) and (4,4,2) by a factor of 10. See the porosity help screen for details of how to add ranges or arrays of transmissibility multipliers.

3.3.9 Absolute Transmissibility This screen is optional and no data is required. In normal use, the inter-block transmissibility is calculated internally by REVEAL from the block permeabilties, the block geometries (corner points), and the transmissibility multipliers. This screen can be used to overwrite those values with externally calculated values in the x-, y-, and z-directions. The values here will only be used if the 'Use external transmissibilities' option is set at the top of the screen. This data would normally be imported directly from an ASCII file or from another simulator. See the porosity help screen for details of how to add ranges or arrays of

8The harmonic average is the 'resisters in parallel' average. The following averages are defined for a variable x, with weightings w. arithmetic average harmonic average

∑∑=

i

ii

wwx

x

∑∑=

i

i

i

xww

x



transmissibilities.

3.3.10 Net to Gross This screen is optional and no data is required. The default horizontal permeabilities (XY plane) may be modified by entering a net to gross ratio for any or all grid blocks (default value of 1.0). e.g. a net to gross of 0.5 reduces the X and Y direction permeabilities by a factor of 2. See the porosity help screen for details of how to add ranges or arrays of net to gross ratios.

3.3.11 Pore Volume Multipliers This screen is optional and no data is required. The pore volume multipliers are multipliers for block volumes as calculated from the grid geometry. The porosity and inter-block transmissibilites are not affected by these multipliers. See the porosity help screen for details of how to add ranges or arrays of pore volume multipliers.

3.3.12 Rock Type A rock type must be assigned to each grid block in the model. Rock types are used to define regions of the model with the same physical or dynamic properties (e.g. relative permeability tables or rock heat capacity) later in the input wizard. To add a rock type select the Add button and define its coverage. To modify or delete a rock type select the rock type from the table and modify its coverage or select the Delete button. The coverage of a rock type is defined by a table of selected regions. Define a region by selecting ranges of X, Y and Z grid blocks, or the entire grid by using the All button. Multiple regions may be added, modified and deleted to define the coverage for each rock type. Check the coverage is complete by using the Validate button.



3.3.13 PVT Region A PVT region must be assigned to each grid block in the model. PVT regions are used to define regions of the model where different PVT may occur. Therefore different PVT regions must be non communicating. To add a PVT region select the Add button and define its coverage. To modify or delete a PVT region select the region from the table and modify its coverage or select the Delete button. The coverage of a PVT region is defined by a table of selected regions. Define a region by selecting ranges of X, Y and Z grid blocks, or the entire grid by using the All button. Multiple regions may be added, modified and deleted to define the coverage for each region. Check the coverage is complete by using the Validate button.

3.3.14 Equilibration Region An equilibration region must be assigned to each grid block in the model. Equilibration regions are used to define regions of the model where different equilibrations may occur. Equilibration includes initial pressure and reference depth and also include any contacts, these are defined in the initialisation section. Each equilibration region must only have one PVT region associated with it. To add an equilibration region select the Add button and define its coverage. To modify or delete an equilibration region select the region from the table and modify its coverage or select the Delete button. The coverage of an equilibration region is defined by a table of selected regions. Define a region by selecting ranges of X, Y and Z grid blocks, or the entire grid by using the All button. Multiple regions may be added, modified and deleted to define the coverage for each region. Check the coverage is complete by using the Validate button.

3.3.15 Non-Neighbour Connections This section is optional. Transmissibility connection between pairs of non-neighbour blocks may be entered. These connections can only be applied to blocks within the current refinement level. Enter the I,J,K coordinates of the blocks to be connected and a transmissibility. If the model has inactive (pinchout layers), then active vertical layers may be connected automatically for blocks separated by less than the 'maximum length between cells for auto-generation'. If this field is left empty, then no automatic non-neighbour connections will be set, unless the MinPV option is selected. Other options are available for pinch-outs as follows (the headings are the keywords that are written to the script): MinPV: this will generate a pinch out between blocks that have intermediate blocks removed because of their low pore volume (the pore volume is lower than the value set for 'minimum grid pore volume' in the Control section.



MinTz: the transmissibility multiplier in the z-direction for the topmost cell in a pinch out will be set to the minimum of the multipliers of the pinched out cells.

3.3.16 Grid Refinement This screen is optional and no data is required. Grid refinement is not available for radial or curvilinear grids, or using the original IMPEC solver. Refined regions within the main grid may be identified within this section. Only the scope and names of refined region(s) are entered at this stage. The scope of a refined region may contain any set of contiguous blocks within the main grid. Different regions of refinement must not overlap or be contiguous (contact neighbouring refined regions). Any well of fracture present within a simulation model must be either fully contained within the main grid (unrefined region) or fully contained within a refined region (i.e. no well or fracture may pass through a refinement boundary). To Add or delete a refined region use the New and Delete buttons, and enter a unique identifier name for the refined region. The coverage of a refined region is defined by one or more hexahedral sub-regions which are added or deleted using the Add and Delete buttons within the coverage section of this screen. Use the Validate and Plot buttons to check the coverage of refined regions. See the grid refinement section for more information.



3.4 Physical Section

3.4.1 Fluid Properties The physical properties of the fluids and reservoir rock are entered. These include the PVT for water, oil and gas components, density and compressibility for additional volumetric components and additional thermal data (heat capacity and thermal conductivity). PVT - the PVT for water, oil and gas are entered using the standard Petroleum Experts PVT screens, select the New or Edit buttons. If a new PVT is created it must be given a name and be either oil, gas or condensate. A previously generated PVT file (*.PVT generated by PROSPER) may be imported from the PVT screens using the Import facility. Matched PVT may be converted into tables (up to 5 temperatures) using the Calc Tables option from the PVT screens, speeding up most REVEAL calculations. If use tables is selected, then the tables must be complete (all columns completed) and have sufficient coverage over a range of temperatures and pressures to cover all expected values during the REVEAL simulation. Trace components - trace components are either volumetric or non-volumetric. The mass or volume of the non-volumetric trace components take no part in the pressure solve (for IMPEC or implicit formulations) so the density of trace components is only used to convert from mass to volume fractions. For this reason, non-volumetric component densities are set equal to the phase they are partitioned within (e.g. water chemistry components are partitioned in the aqueous phase). This means that component mass fractions within the phase are equivalent to volume fractions. The volumetric trace components (injected non-reservoir gas, surfactant and the two alcohol components) are included within the calculation of the phase densities and therefore take part in the pressure solve. For these components, a reference density and compressibility (c) are required to calculate the component densities.

( )( )refref PPc −= expρρ Thermal data - all REVEAL calculations are thermal, so heat capacity is required for all volumetric components. Non-volumetric components take no part in the heat transport equations. Scroll right on the component data form to enter heat capacities for water, oil and gas. Thermal conductivities are required for volumetric components if the thermal conductivity option is selected. Rock data - thermal data for each rock type is required. Over/underburden - the overburden/underburden rock density and thermal properties are also entered. Heat flux from the underburden and to the overburden is calculated using a model by Vinsome and Westerveld [10]. Diffusion and dispersion - select the options for component diffusivity and phase dispersivity if required. Additional data (diffusivity and dispersion lengths) will be required for these options. The diffusivity and dispersivity options are only available for the IMPEC solver formulation. Defaults - default thermal properties (specific heat capacity, thermal conductivity and rock



density) may be selected. These data are required even for nominally isothermal simulations, where no thermal gradient or thermal injection are present. Default aqueous component properties set the density and compressibility for additional aqueous volumetric components (surfactant and alcohols).

3.4.2 Rock Compressibilities The compressibility of each rock type is entered on this screen. Compaction and permeability reduction are also modelled on this screen. At least one rock compressibility should be entered, generally at the reference pressure (see control section). If the compaction option is not selected, then one rock compressibility is entered, then the porosity is calculated using the following equation.

( )refr PPcref e

−= φφ If the compaction model is active then a table of porosity and permeability multipliers should be entered as a function of pressure. The pressures and multipliers should increase mononically down the table. More than one entry should be made covering the entire range of predicted reservoir pressures to ensure rock compressibility.

3.4.3 Miscellaneous Several unrelated physical properties for various models are entered on this screen. The options available will depend on models selected in the control section. Wax dropout - this model is optional and no data entry is required. A rapid increase in oil viscosity at the wax drop-out temperature may be modelled. The oil phase viscosity is multiplied by the exponent of Bwax*(Twax-T)/(1+|Twax-T|), where T is the oil temperature. Interfacial tension - only required if the micro-emulsion surfactant model is selected in the control section. The initial oil/water interfacial tension is entered. A value of about 25 dyne/cm is reasonable for many oils. Wettability - only required if the wettability model is selected in the control section. This parameter controls the desaturation (interpolation between high and low tension relative permeability curves) as a function of adsorbed wetting agent. The initial reservoir wettability is set in the initialisation section; where a value of 1 represents high tension and -1 represents low tension. As the wetting agent is adsorbed from zero to its maximum value, the wettability is increased from the initial value (at zero adsorbed wetting agent) to the initial value plus twice the wettability change parameter entered on this page (at maximum adsorbed wetting agent). Therefore if the reservoir is initially high tension (wettability = 1) and a value of -1 is entered for the wettability change parameter, when the adsorbed wetting agent reaches its maximum value, the wettability will be 1+2*-1 = -1 (low tension). Similarly if the reservoir is initially low tension (-1) and a wettability change parameter of 1 is used, the wettability at maximum adsorbed wetting agent will be -1+2*1 = 1 (high tension).



Miscibility - only required if the miscibility model is selected in the control section. The miscibility pressure is entered as a linear function of temperature. Pmisc = P1+P2*(T-Tref), where T is the temperature and Tref is the reference temperature entered in the control section. If the block pressure rises above the miscibility pressure, then the oil and gas phase viscosities are modified by a quarter power mixing rule or the Todd Longstaff model [5] if this option is selected. A miscible hydrocarbon phase viscosity is calculated, where g is is the non water blocked gas fraction.

4

41

41

)1(−

−+= gogoh gg µµµµµ

owbgo

g

SSSS

g−+

=

ΩΩ−= hoo µµµ 1 ΩΩ−= hgg µµµ 1

nkγττ += 0

The Todd and Longstaff model modifies the oleic and gas phase viscosities using a user defined mixing parameter Ω.

The oil and gas phase viscosities approach each other as the mixing parameter (Ω) is increased, with a value of 1 leading to the gas and oil phase viscosities being equal (equivalent to the quarter power mixing rule). See the relperm section for more information on the wettability and miscibility models. Non-Newtonian fluid - entered within the PVT screens ('Visc Tables' button common to all Petroleum Experts software). The viscosity of heavy oils may be dependent on shear rate and this can be modelled by entering various rheological constants for the oil phase as a function of temperature and pressure. If this model is present, then the oil viscosity calculated from the standard PVT calculator will not be used. For a non-Newtonian fluid, the shear stress (τ) is related to shear rate (γ) by an exponential equation, where the rheological constants (τ0,k & n) are entered on this screen as functions of temperature and pressure.

µγτ =

In contrast, a Newtonian fluid has the simplified form, where µ is the Newtonian viscosity.

Note that if τ0=0 and n=1, then k is the viscosity. The internal units for shear stress are Pa, shear rate s-1, therefore k has units of Pa.s^n, and in the Newtonian limit k has units of Pa.s, where 1 Pa.s = 1000 cp. The effective (Newtonian) viscosity (µ) is obtained using the shear stress calculated for each grid block, see the polymer and gel mobility section for more information about shear. The block shear stress is obtained using the following equation.

SkrkP

φτ

98

∇=



If a grid block contains an injection well, then the well shear stress may be modified to reflect increased shear near the well. The well bore radius (rw) and Peaceman radius (r0) are used to estimate the increased potential gradient near the wellbore.

=

wrr0lnττ

The effective Newtonian viscosity to be used for oil mobility is calculated for an oil using the formula below, which is derived by comparison with laminar flow pressure drop calculations in tubing for non-Newtonian oils.

n

k

1

0

−

=ττ

τµ

Note that when τ0 is zero n is unity, it reduces to the Newtonian form where the viscosity is equal to k. A maximum cutoff viscosity is required (zero shear limit), since as the shear stress approaches zero, the model predicts the apparent Newtonian viscosity approaches infinity. The following is a rheological plot of oil viscosity and shear stress as a function of shear rate.

Corrected gas-phase viscosity for foam - The assumption is made that any gas present forms a homogenous bubbly mixture (foam) with the oil, modifying (increasing) the equivalent Newtonian viscosity (reducing the shear stress) for the foam mixture. Additionally, the gas phase viscosity is set equal to the oil phase (foam) viscosity to



reduce the mobility of the gas phase (bubbles within the oil phase).

n

nk

1

10

−

=

−εεττ

+= 0εττ

τµ

nnk −1εγwhere and f

o

ρρε =



3.5 RelPerm Section

3.5.1 General Options The first screen of the relperm section initialises various options that will affect the options and data required for the remaining relperm screens. Model - either Stone I or Stone II are available for three phase oil phase relative permeability. If the miscibility option is set and the pressure is above the miscibility pressure then the oil and gas phase relative permeabilities are calculated using the miscibility model. Stone I

)1)(1(* gwow

ogowoo SSkr

krkrSkr

′−′−

′=

−

−−=

ow

owwowow Sr

SrSrkrkr

11

*

( )mow

mwmww SrSrSr

SrSrSSS

−−−+−+

=′1 mow

ooo SrSrSr

SrSS

−−−−

=′1 mow

gg SrSrSr

SS

−−−=′

1

ogowo SrSrSr )1( αα −+= mogw

g

SrSrSrS

−−−−=

11α

Stone II

−−

+

+= gwg

ow

ogw

ow

owowo krkrkr

krkr

krkrkr

krkr**

*

10 ≤≤ okr

Hysteresis - may be applied to the water, oil and gas phases, see residual saturations for more information. Endpoint scaling - may be apllied to water, oil and gas phases, see endpoint scaling for more information. Directional relperms - more than one relative permeability may be defined per grid block. The relative permeability curve used will then depend on the direction of fluid flow. The default state for this option is off. The All faces option allows upto seven separate relative permeability curves for each grid block (one for each direction X-,X+,Y-,Y+,Z-,Z+ and one for connected wells). The Up,down,horizontal option allows upto four separate relative permeability curves for each grid block (one for horizontal flow X-,X+,Y-,Y+, one each for Z-,Z+ and one for connected wells). If the directional relperms option is set, then separate curves may be defined for wells, or defined to be one of the directional curves. Capillary desaturation - This option is set for models where surfactant (capillary desaturation9) is present. The surfactant model is enabled in the control section. When

9Capillary desaturation is parameterised by comparing the ratio of viscous and capillary/interfacial tension forces between phases. The capillary number (Nc) is defined for each phase.



the capillary desaturation option is set, two relative permeability curves will be required for low and high tension, with interpolation between the curves depending on the desaturation model. If capillary desaturation is set, when the surfactant model is not present then the capillary desaturation will vary only with the changing viscous forces since the interfacial tension between phases is constant. Capillary desaturation should be off when the wettability model is selected, since the interpolation between high and low tension relative permeability curves will be dependent on adsorbed concentration of wetting agent rather than by capillary desaturation. Gas miscibility - this option is only available when the gas miscibility option is selected in the control section. When the oil and gas phases are miscible (pressure above miscible pressure) the oil and gas relative permeabilities are modified using the Todd & Longstaff model [5] to calculate weighted means of the oil and gas phase relative permeabilities. The residual interpolation scheme uses an interpolated (between oil and gas phases) value for hydrocarbon phase residual saturation, while the simple model uses the oil and gas phase residual saturations. A residual saturation for the combined hydrocarbon phase is calculated, subject to water blocking. The water blocked hydrocarbon residual saturation is a function of water saturation and may be entered in tabular or parametric format on the capillary pressure screen. The parametric model takes the following form.

( )( )

1−

( )

1

+=

ww

wowwowowb Skr

SkraSrS

If capillary desaturation is present (see residual saturation page for definitions), then the water blocked oil saturation is modified.

( )( )SNcSSS log1 ++= oooowbowb 2101 The hydrocarbon phase residual saturation is then calculated using the gas fraction of non-blocked hydrocarbon phase (g).

owbgo

g

SSSg

++=

S

( ) ( )owbgoh SSrgSrgSr ++−= 1 The model calculates the relative permeability of the entire miscible hydrocarbon phase, using both the the oil/water and the gas data.

gowh gkrkrgkr +−= )1(

Mobile phase saturations (Sm) are calculated for the hydrocarbon phase using either a simple or interpolated model.

σ

ρ

−+∇⋅

=144h

PcPNc

pp

p

k



Simple model Interpolated model Oil and gas relative permeabilities

ogoow SrSSSm −+= hgoow SrSSSm −+= ( )owow Smkr

gowbgog SrSSSSm −−+= hgog SrSSSm

ho krgkr )1( −= gkr = hgkr

( )gg Smkr−+= The oil and gas relative permeabilities are then calculated.

3.5.2 Residual Saturations The residual saturations are entered for each rock type permeability curve. Note that the residual saturations are the same for all directional relative permeability curves for a given rock type. Separate residual saturations are required for high and low tension fluids if the desaturation model is present. Data are required for two phase water/oil and oil/gas relative permeability curves, and the micro-emulsion phase if the surfactant model is present. Gas hysteresis - the critical gas saturation (Srgc) is the saturation at which gas initially becomes mobile, while the maximum residual gas saturation (Srgm) is used to model gas hysteresis. The historical maximum gas saturation (Sgm) is used to estimate the current gas residual (Srg) saturation. The residual gas saturation will always be within the range defined by Srgc and Srgm, so if both values are identical no hysteresis will take place.

( )gcgmgcw

gcgmgcg SrSr

SrSrSrS

SrSr −−−

−+=

1 gmggc SrSrSr ≤≤ If the gas saturation is within the range [Srgc,Sgm], then the gas phase relative permeability is calculated by using a normalised gas saturation (Sg*) and the original gas relative permeability curve.

ll a

s 1 l 3 5 0 0 7 . 0 3 1 8 5 4 4 3 2 g B T / T T . 7 T m ( S r ) T j 1 2 . 0 9 8 5 0 n o r m a l i s e d g a s s a t u r a 4 3 2 g B m . p s e < 0 2 0 . 9 5 0 t c l


saturation. The residual oil saturation will always be within the range defined by Sroc and Srom, so if both values are identical no hysteresis will take place.

( )ocomocw

ocomoco SrSr

SrSrSrSSrSr −−−

−+=

1 omooc SrSrSr ≤≤ If the oil saturation is within the range [Sroc,Som], then the oil phase relative permeability is calculated by using a normalised oil saturation (So*) and the original oil/water relative permeability curve. For the oil/water relative permeability curve, the oil saturation used is that with no gas present, So=1-Sw.

( ) ( )ocooom

womoco SrSr

SrSSSSrSr −

−−−

+=1*

( )

( )ocSrS −−1 *

wow

owoco SrSr

SrSrSrS −−

−−+= 1

1 **

Water hysteresis - water phase hysteresis is controlled by altering the residual water saturation for the water/oil relative permeability curves. A similar interpolation scheme to the gas hysteresis option is employed for both the low (if desaturation is present) and high tension water residual saturations. The high and low tension water residual saturations are calculated first accounting for hysteresis, then interpolated to account for desaturation. The critical water saturation (Srwc) is the saturation at which water initially becomes mobile, while the maximum residual water saturation (Srwm) is used to model water hysteresis. The historical maximum water saturation (Swm) is used to estimate the current water residual (Srw) saturation. The residual water saturation will always be within the range defined by Srwc and Srwm, so if both values are identical no hysteresis will take place.

( )wcwmwc

wcwmwcw SrSr

SrSrSSrSr −

−−

+=1 wmwwc SrSrSr ≤≤

If the water saturation is within the range [Srwc,Swm], then the water phase relative permeability is calculated by using a normalised water saturation (Sw*) and the original water relative permeability curve.

( )wcwwwm

wwmwcw SrSr

SrSSSSrSr −

−−

+=*

( )wcw

wwwcw Sr

SrSrS −

−+= 1

1 ** SrS − *

The following plot demonstrates the hysteresis in relative permeability, for saturations below a historical maximum (Smax).



Desaturation - if a surfactant model is present, then desaturation parameters are required to control the interpolation between high and low tension values. The interpolation is a function of the capillary number10 (Nc) and defined for water(1), oil(2) and micro-emulsion(3) phases by two parameters each (S1 and S2).

( )( )[ ]21011 SNcLogSSS hrr ++=

Srl<Sr<Srh, where Srl and Srh are the low and high tension residual saturations. Wettability - if the wettability model is present, then the interpolation between high and low tension residual saturations is calculated as a function of the wettability. The wettability is initialised in the initialisation section and changes as the wetting agent is adsorbed. A wettability of -1 corresponds to low tension, while a wettability of 1 represents high tension, with linear interpolation for intermediate values of wettability. The change to the wettability as wetting agent is adsorbed is controlled by the wettability change parameter defined in the physical section.

10Capillary desaturation is parameterised by comparing the ratio of viscous and capillary/interfacial tension forces between phases. The capillary number (Nc) is defined for each phase.

σ

ρ

−+∇⋅

=144h

PcPNc

pp

p

k



3.5.3 Relative Permeabilities Relative permeability curves must be entered for each region defined in the previous residual saturation page. Select add or delete to create or delete relative permeability curves for each region, and select entries in the relative permeability list to modify the data entered. Directional relperms - relative permeability curves must be defined for each direction if directional relative permeabilities have been defined. However, directions with the same curves may be grouped to prevent excessive repetitive data entry. Tabular & parametric - for each relative permeability curve, either tabular or parametric entry may be used. The water/oil curves are for two phase water and oil, while the gas/oil curves are for two phase oil/gas in the presence of connate water. Therefore, for the gas/oil curves, the gas saturation range should be from Sgc to 1-Srw, and the corresponding oil saturation range should be from Srog to 1-Srw. Copy and paste may be used to enter or edit relative permeability tables. Use the Validate button to check coverage and the Plot button to view the relative permeability curves entered. The parametric relative permeabilities take the following form for high and low tension curves, where the end points (kr*) and exponents (n) are input.

nw

oww

wwww SrSr

SrSkrkr

−−

−=

1*

now

oww

owowow SrSr

SrSkrkr

−−−−

=11*

nm

m

mmmm Sr

SrSkrkr

−−

=1

*

nog

oggw

oggwogog SrSrSr

SrSSrkrkr

−−−

−−−=

11*

ng

gogw

gggg SrSrSr

SrSkrkr

−−−

−=

1*

The numerators represent the mobile phase fraction, while the denominators represent the maximum mobile fraction. Note that these correlations are based on the assumption of an oil reservoir initially containing connate water only. If the mobile phase fraction is exceeded (due to desaturation, aquifer or gas cap), then these correlations are not extrapolated and therefore tabular input should usually be used. For the oil in water relative permeability curves, So = 1-Sw, and for the oil in gas relative permeability curves So = 1-Srw-Sg. Surfactant - if the surfactant model is present, then in addition to the low and high tension water/oil curves and the gas/oil curves, a middle (micro-emulsion) phase curve is required as a function of mico-emulsion saturation. Desaturation - for the capillary desaturation and wettability models the interpolation between high and low tension relative permeability curves is parameterised by capillary number and wettability in a similar manner to the interpolation used to calculate residual saturations.



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1

Saturation

Rel

ativ

e pe

rmea

bilit

y

high tension

low tension

interpolated

interpolated residual saturation

3.5.4 Capillary Pressures Capillary pressure tables are required for oil/water and gas/oil. Oil/water capillary pressure (Pco) - Po = Pw+Pco At the residual (connate) water saturation the water/oil capillary pressure is a maximum, and should fall monotonically as the water saturation rises. A minimum value of zero should occur at a water/oil contact (Sw=1). If there is no water/oil contact, the maximum water saturation will be 1-Sro. If the J Leverett option is selected, then the dimensionless J function should be entered in the water/oil table. The water/oil capillary pressure for any block is then calculated (in oilfield units) by the following formula for each grid block.

kJPco φσ

84945.6=

where σ is the water/oil interfacial tension entered in the physical section, φ is the block porosity and k is the harmonic average block permeability. Gas/oil capillary pressure (Pcg) - Pg = Po+Pcg At zero gas saturation (gas/oil contact) the gas/oil capillary pressure is zero, and should rise monotonically to a maximum value at a gas saturation of 1-Srw. Water blocking - if the miscibility option is active then a hydrocarbon phase water-blocked residual saturation is required. This is a function of water saturation and may be constant, tabular or have a parametric form, parameterised by a wetting parameter. See



the relperm options page for the equation of the parametric form.

3.5.5 Endpoint Scaling Endpoint scaling is optional, and is only available if the option is selected on the relperm options page. Each relative permeability table has nominal endpoints defined as follows. 1] residual (connate) saturation is the minimum saturation entered 2] critical saturation is defined as the maximum saturation for which the relative permeability is zero 3] maximum saturation is the maximum saturation entered in the table If endpoint scaling is applied, then relative permeability and capillary pressure tables will be rescaled between the entered critical and maximum saturation endpoints. Endpoints are defined over the entire grid. Water scaled saturations - data for the critical and maximum water saturations may be entered. Oil scaled saturations - data for the critical water saturations for oil/water and oil/gas may be entered. Gas scaled saturations - data for the critical and maximum gas saturations may be entered. Scaled endpoints - the maximum endpoint relative permeability may be rescaled for the water, oil and gas phases.



3.6 Aquifer Section

3.6.1 Analytical Aquifer This section enters data to define an analytical aquifer model if the aquifer model was included in the control section. For more detailed information see Carter Tracy. Region list - several aquifers may be connected to the grid. Use the Add button to add an aquifer to the list and select an entry in the list to alter its properties. An aquifer may be deleted by selecting it in the region list and then selecting the Delete button. Boundary and connection area - for each aquifer the boundary region of the grid connected to the aquifer must be defined. Note that an aquifer connected to inactive blocks will not have any effect. Select the aquifer (grid) boundary (X-,X+,Y-,Y+,Z-,Z+) that the aquifer is connected to and enter the 2D range of blocks, the All button may be used to select an entire surface of the grid. General properties - four aquifer models (linear and radial with either finite or infinite acting) are available (Carter Tracy). The models are solutions to the constant terminate rate diffusivity equation with different geometries and boundary conditions. For all four models, some physical properties for the aquifer are required; porosity, permeability, compressibility, temperature and pressure at a reference depth. Geometry - depending on the aquifer model chosen, the physical extent of the aquifer is entered. The contact area is defined by the aquifer thickness (height) and encroachment angle, and either the aquifer width (linear) or inner radius (radial). The volume of the aquifer for the finite acting models are defined by the length (linear) and outer radius (radial). Component concentrations - the concentration of components in the aquifer are entered. This will usually be 1 for water and zero for other components.



3.6.2 Cater Tracy model The inflow to each grid block (IJK) connected to an aquifer is defined.

)))()((( aqaqaq tPtPBAQ −−= α 1 nijknijkijkijk +

where aIJK is the fractional area of grid block IJK connected to the aquifer

∑= ijk

ijk

AAαijk

Aaq and Baq are aquifer constants calculated for the aquifer model defined by the user, and are functions of the aquifer influence function φ(t) and the cumulative influx W(t).

tt

tt

B nnn

aqaq

∂∂′−

= ++

11 ϕϕ

C ′

( )

aqaq

naq B

tt

CWPA )(

′∂′∂

−∆=ϕ nn 1+

where a dimensionless time t' and an aquifer constant Caq are defined. faq are the encroachment angles. Finite linear aquifer Infinite linear aquifer Radial aquifer

2aqaqaqaq

aq

Lct

µφ=′

tk

aqaqaq

aq

ct

µφ=′

tk

2

aqaqaqaq

aq

Rict

µφ=′

tk

aqaqaqaq RiHfC 2 φπ=aqaqaqaqaqaqaq cWLHfC φ= aqaqaqaqaqaq cWHfC φ= aqaq c

2

The aquifer influence functions are calculated as solutions to a constant terminal rate diffusion equation.

ϕϕ 2∇=′∂t

∂

The aquifer influence function has unit gradient at the inner boundary and zero initial value. A zero gradient boundary condition is used for a finite aquifer at the outer boundary, or a zero solution boundary condition for an infinite aquifer. Approximate solutions to the influence function are obtained at the inner boundary and described below. The radial solutions are due to Hurst and van Everdingen [1]. Infinite linear aquifer

( )π

ϕ tt′

=′ 2

Finite linear aquifer

15.0≤′t 15.0≥′t



( )πtt′

2ϕ =′ ( ) ′′

( )tett ′−−+=2

20354.031 πϕ

Infinite radial aquifer

01.0≤′t 100001.0 ≤′≤ t 1000≥

( )π

ϕ tt′

= 2′ ( ) 222 asa

ct +++=′ϕ ( )b ( ) .0′t

( )

2ln80907 tt +

=′ϕ

′

15.3=a 2

tt ≤′ tt ≥′

5115.1

+=aab

bc −= 112.0

( )ts ′= ln

Finite radial aquifer

c c

( ) =′tϕ

( ) ( )tt ′=′ ∞ϕϕ

( )1−

+′∞

aq

aq

c

RiRo

tϕ

( )2 −′ tt

93.1

133.0

−=

aq

aqc Ri

Rot

( )t ′∞

ϕ is the infinite radial solution.



3.7 Mobility Section

3.7.1 Polymer and Gel The mobility section is rather complex, since it contains numerous models requiring a wide range of input data often consisting of correlation parameters with limited physical significance. Its scope is primarily to describe the modifications to pure phase viscosities (obtained from the PVT) arising from chemical additives including surfactants, polymers, gels etc. This screen initialises the polymer and gel model and sets the shear thinning parameters. Permeability reduction is implicitly included in the viscosity correlations, since it is used in the calculation of shear rate. Polymer/gel viscosity - three models are available for viscosity resulting from polymer and gel components (original, Carreau and Kuparuk). These models calculate a thickening factor (TF) for the aqueous and micro-emulsion (if surfactant is present) phases, subject to shear thinning near wells. The thickening factor is multiplied by the pure phase viscosity to obtain the modified phase viscosity. Details of the original and Kuparuk models (for polymer and gel) are given on subsequent pages of the mobility section, when additional data input is required. The Carreau model only applies to polymer (not available if gel is present) and requires no additional data. It is a correlation derived from a xanthan polymer that includes permeability reduction and shear thinning implicitly. Shear rate - the shear rate (γ) is defined for each rock type and is parameterised by a critical shear rate (γc) entered on this screen and the zero shear permeability reduction (R0) (see adsorption section). Original model Carreau and Kuparuk models

ww

wc

krSk

q

φγγ

89

=

08

9RkrSk

q

ww

wc

φγγ =

The mean permeability in the direction of flow is defined.

kzqqz

kyqqy

kxqqx

k w

w

w

w

w

w 1111222

+

+

=

If a grid block contains an injection well, then the well shear rate may be modified to reflect increased shear near the well. The default is for this model to be inactive, see the well section to activate the well shear model. The well bore radius (rw) and Peaceman radius (r0) are used to estimate the increased Darcy velocity near the well-bore.

=

wrr0lnγγ



3.7.3 Carreau Polymer Model This is a correlation model for polymer viscosity, including shear thinning and permeability reduction. It is based on a xanthan polymer with data over ranges 50-1000 ppm and 20-70 oC and shear 1-100 s-1. Note that the concentrations (cp) are in ppm and the temperature (T) is in K. The thickening factor (TF) is multiplied by the pure phase water viscosity to obtain the modified viscosity.

( ) 21

20 11

−

++=n

TF λγµ Zero shear specific viscosity

( )

−

= 1expexp 4

3210 Ta

acaca ppµ

reciprocal of critical shear rate

−

+−

=11

87

6

5 expaT

acaaTca

ppλ

shear thinning constant

−−=

6

910

expaTca

nap

The parameters a1 to a11 take the following values a1 = 0.001295 a2 = 0.001784 a3 = 0.01046 a4 = 1910.5 a5 = 0.01577 a6 = 275.0 a7 = 0.0002939 a8 = 2.67 a9 = 2.189 a10 = 0.4334 a11 = 195.3



3.7.4 Kuparuk Polymer Gel Model This model calculates a zero shear rate (and zero permeability reduction) thickening factor (TF0) that is modified by the shear rate (see shear rate) to obtain a total thickening factor (TF). This model applies to both polymer and gel. The final thickening factor is multiplied by the pure aqueous phase viscosity to obtain a modified water viscosity. Effective polymer salinity - the water component is clearly present in the aqueous phase, but may also be present in a micro-emulsion phase. Volumetric concentrations of polymer (cp), gel (cg), salt (cs) and divalent cations (cd) within the water component of the aqueous and micro-emulsion phases are calculated. Effective polymer salinity (cse) is defined for the Original and Kuparuk models with reference to three user input variables, a minimum threshold salinity (cs*), and two further coefficients, divalent cation dependence (β1) and dependence S (β2). The minimum threshold salinity is optional (default = 0.1). The divalent cation dependence is also optional (default = 1.0) and only applicable is the divalent cation component is present within the model.

[ ] 2β))1(*,max( 1β dssse cccc −−= Model interpolation temperatures - The Kuparuk model basically interpolates the correlation between high (TH) and low (TL) temperature limits. Polymer & gel viscosity parameters - the input parameters for both polymer and gel are identical. For the polymer the parameters are Ap1h (βp1H), Ap1l (βp1L), Ap2h (βp2H) and Ap2l (βp2L). For the gel the parameters are Ag1h (βg1H), Ag1l (βg1L), Ag2h (βg2H) and Ag2l (βg2L).

( ) ( )22021211 ggggppppse cccccTF αααα ++++=

( ) HpLpp ff 111 1

ββα −+= (Lpp f 22 1 ββα −+= Hp2 ( ) HgLgg ff 111 1 ββα −+= ( ) HgLgg ff 222 1 ββα −+=

)f

−H TT

−

=LH TT

f



3.7.5 Gelation and Degradation Reactions between polymer and cross-linker to form gel, and between de-chelation agent (chelated cross-linker) and cross linker is modelled by calculating mass reaction rates that are applied to the component mass concentration equations. Three models are available, depending on the components present. Note that in all of the models the temperatures may be input in any allowed units, but the correlations are expressed with absolute (R) temperatures. The concentrations are all volumetric fractions within the water phase. 2 component model - this model applies when only polymer and gel are present. The required data are rate coefficient (Rk), temperature coefficient (Bk), temperature threshold (Tr) and polymer volumetric concentration threshold (Pc0). If the temperature is greater than Tr and the polymer concentration is greater than Pc0 then a reaction between polymer and gel occurs with mass reaction rates per unit volume of water for polymer (Rp) and gel (Rg).

−−=

refkppkp TTBcRR 11expρ

−=

refkpgkg TTBcRR 11expρ

3 component model - this model applies when polymer, gel and cross-linker are present. The required data are rate coefficient (Rk), temperature coefficient (Bk), temperature threshold (Tr), polymer volumetric concentration threshold (Pc0), cross-linker volumetric concentration threshold (XLc0), polymer reaction rate multiplier (P0) and cross-linker reaction rate multiplier (XL0). If the temperature is greater than Tr, the polymer concentration is greater than Pc0 and the cross-linker concentration is greater than XLc0, then a reaction between polymer and cross-linker to produce gel occurs with mass reaction rates per unit volume of water for polymer (Rp), cross-linker (Rxl) and gel (Rg).

−−=

refkxlppkp TTBccPRR 11exp0 ρ

−−=

refkxlpxlkxl TTBccXLRR 11exp0 ρ

( )

−+=

refkxlpgkg TTBccXLPRR 11exp00 ρ

4 component model - this model applies when polymer, gel, cross-linker and chelated cross-linker are present. It is identical to the 3 component model, except that the chelated cross-linker can react to form cross-linker, before the polymer and cross-linker reaction occurs. The additional parameters for this model are de-chelation rate coefficient (Rk1), temperature coefficient (Bk1), temperature threshold (Tr1), chelated cross-linker concentration threshold (Cc0). If the temperature is greater than Tr1, the chelated cross-linker concentration is greater than Cc0, then a reaction between chelated cross-linker and cross-linker occurs with



mass reaction rates per unit volume of water for chelated cross-linker (Rc) and cross-linker (Rxl).

−−=

refkcckc TTBcRR 11exp 11ρ

−=

refkcxlkxl TTBcRR 11exp 11ρ

The 3 component reaction then occurs as described above, except that the cross-linker reaction rate is the sum of the two reactions involving cross-linker. Polymer and gel degradation - both polymer and gel may degrade at rates defined by rate (Rp0 and Rg0) and temperature coefficients (Bp0 and Bg0), reducing the reaction rates for these components.

−−=

refpppppp TTBcRRR 11exp 00 ρ

−−=

refgggggg TTBcRRR 11exp 00 ρ

3.7.6 Inaccessible Pore Volume The inaccessible pore volume is used to increase the apparent volumetric concentration of polymer and gel components. This will affect the mobility correlations using polymer and gel, and all other models that use polymer or gel concentrations. This is achieved by dividing the calculated polymer and gel volumetric concentrations by 1-ipv (inaccessible pore volume) entered on this screen. Inaccessible pore volumes may be entered for each rock type.

3.7.7 Foam This model is only available if the foamer component is present. It increases the gas phase viscosity, thereby reducing its mobility and modelling the production of foam in a heavy oil. The foamer model may be applied separately to each rock type, or all rock types. The concentration of foaming agent in the aqueous phase (cf) and five input parameters describe the modification to the gas phase viscosity. The input parameters include CRFK (βf1), foam threshold (βf2), ES (βf3), oil saturation threshold (βf4) and EO (βf5).

53 )0,1max()1,min(42

10ff

f

o

f

ffgg

S ββ

βββµµ −=

c

For information on natural foams associated with heavy oils, see the physical section.



3.8 Phase Section

3.8.1 Introduction The purpose of the phase section is to model the effect of adding a surfactant to the system. Surfactants emulsify oil and water into a new phase (an emulsion), causing desaturation and potentially enhanced recovery. Surfactants are generally used in conjunction with other chemicals, such as alcohols, which affect the phase behaviour, and polymers, which may also affect the phase behaviour and which are important for mobility control. Salinity and divalent ion concentration have a strong influence on phase behaviour, as does temperature and the equivalent alkane number (EACN) of the oil, which varies as the oil phase composition (Rs or GOR) varies. For surfactant flood simulations with REVEAL, up to six volumetric components may be present (water, oil, gas, surfactant and up to two alcohols). Non-volumetric components include salinity, and optionally polymer and divalent ions. Additionally tracer components may also be present. Alcohols are always assumed to be active in the phase behaviour; polymer may be active, or simply a mobility control agent. Adsorbed material is assumed to play no part in the phase behaviour calculation. Surfactant flood systems are described in many books on Petroleum Engineering; only an outline of the theory is given below. The phase calculations determine first the phases that are present in a given system, and from there determine those phase properties. The steps that are taken are: 1. Formation of psuedo-components - the components present are formed into three pseudo-components - aqueous/brine, oleic, and chemical. These then become the coordinates on a ternary diagram. All the water is placed in the aqueous pseudo-component, the oil in the oleic, and the surfactant in the chemical. Tracers, anions, and gels are placed in the aqueous pseudo-component. Alcohols and, optionally, polymers, are partitioned amongst all three pseudo-components as described in Alcohol and Polymer partitioning. 2. Creation of a ternary diagram - a ternary diagram is constructed to determine the phase behaviour of a system given a set of pseudo-component concentrations and a calculated effective salinity. A more complete discussion of effective salinity and phase behaviour is given in surfactant phase model. In brief, there are 4 possible systems (note the comment below about gas): a. Two phase oil/water (low/zero surfactant concentration) b. Two phase oleic/microemulsion (Type II(-) system) (low effective salinity) c. Two phase aqueous/microemulsion (Type II(+) system) (high effective salinity) d. Three phase aqueous/microemulsion/oleic (Type III system) (intermediate

effective salinities) The phase behaviour calculation is performed assuming all components throughout a gridblock are thoroughly mixed and in equilibrium. This assumption is retained when gas is present, even if the gas and oil are potentially immiscible; if the phase behaviour calculation results in an excess oil phase being formed (i.e. the upper phase in type II(-), type III, or no surfactant cases), then this phase is tested for immiscibility and split into



separate oil and gas phases if appropriate. Micro-emulsion phases containing both gas and oil (upper phase in type II(+) cases, middle phase in type III cases, or single phase cases) are always assumed to form a single miscible phase, regardless of whether the oil and gas are miscible. If the Todd and Longstaff model [5] is used, it is applied to all miscible upper phases (but not to middle phase or single phase micro-emulsions). The following table summarises the number and type of phases present, and those phases to which the Todd and Longstaff model is applied.

Phase behaviour

Single phase No surfactant Type III Type II(-) Type II(+)

P>Pcr 1 Phase 2 Phases 3 Phases 2 Phases 2 Phases Micro-emulsion Oil/gas† Oil/gas† Oil/gas† Micro-emulsion†

Water Micro-emulsion Micro-emulsion Water

Water

P>Pcr 1 Phase 3 Phases 4 Phases 3 Phases 2 Phases

Micro-emulsion Oil Oil Oil Micro-emulsion†

Gas Gas Gas Water

Water Micro-emulsion Micro-emulsion

Water

† Todd and Longstaff model is applied to these phases

The five phase regions identified are numbered from one to five, and may be plotted if 'Phase Region' is selected as a property to be stored during a calculation (Run Simulation|Select Properties...). Phase region number

Description

1 Micro-emulsion phase only 2 Water, oil/gas phases present - no surfactant 3 Water, oil/gas and micro-emulsion phases present (type III system) 4 Oil/gas and micro-emulsion phases present (type II(-) system) 5 Water and micro-emulsion phases present (type II(+) system)

3. Calculation of interfacial tension - the interfacial tension between emulsion and aqueous phases, and/or emulsion and oleic phases, is calculated using a correlation. See the interfacial tension section for more information. 4. Calculation of viscosity - the viscosity of the emulsion phase is calculated using a correlation. See viscosity for more information.



3.8.2 Alcohol/Polymer Partitioning See also: Introduction. This screen contains the data for partitioning alcohol and polymer components among the three pseudo-components. Press Plot to obtain a plot of the partitioning based on the data that you have entered. We introduce some symbols, definitions and identities. Vcp is the volume of component c in pseudo-component p Ccp is the volumetric concentration of component c in pseudo-component p cc is the total volumetric concentration of component c Vp is the volume of pseudo-phase p V is the total pseudo-phase volume vp is the volumetric concentration of pseudo-phase p Kcp is the partitioning constant for component c between pseudo-phase p and the aqueous pseudo-phase Define pseudo-phase subscripts for the aqueous (a), oleic (o) and chemical (c) pseudo-components, and component superscripts for the water (w), oil (o), surfactant (s), alcohol (x), salinity (n), polymer (p) and divalent ion (d) components. Component volumetric concentrations Total phase volume Volume identities

wa

xax

a VV

C =

oo

xox

o VV

C =

sc

xcx

c VV

C =

∑=p

pVV

1== ∑∑c

c

pp cv

Total component concentration Pseudo-phase volumetric concentration

VVcx

x = V

Vv pp =

Alcohol material balance Polymer material balance

sxc

oxo

wxa

x cCcCcCc ++= ( )spwpa

spc

wpa

p cKcCcCcCc +=+= Polymer partitioning - when the polymer is active in the phase behaviour, it is partitioned between the aqueous and chemical pseudo-components according to a partition coefficient Kp, which may vary linearly with temperature.

( ) pa

pc

refp

refpp

CC

TTKK =−+= δ

If a polymer is present but not active (i.e. it is simply a mobility control agent), polymer partitioning may be switched on, in which case the polymer is put in the aqueous pseudo-component, so that it partitions between phases in proportion to the amount of water in each phase, or polymer partitioning may be switched off, in which case the polymer is placed entirely in the aqueous phase at the end of the phase behaviour calculation, and thus is prevented from partitioning into any middle or upper phase that forms. Alcohol partitioning - alcohols are partitioned amongst all three pseudo-components, according to one of two partitioning models. Data for one or two alcohols is required, depending on the number of alcohol components in the model. 1. Hirasaki model - this is the default alcohol partitioning model. The alcohols are partitioned between the pseudo-components with partition coefficients that are constant



(at a given temperature). Partitioning constants relating partitioning of the alcohol components between the three pseudo components are defined. The left column of data input correspond to the aqueous/oleic partitioning and the right column corresponds to the aqueous/chemical pseudo-component partitioning. K are the Alc coefficients and δ are the Alc Temp Dep variables.

xa

xox

o CC

K =

xa

xcx

c CC

K =

The partitioning constants vary linearly with temperature.

( )refxoref

xo

xo TTKK −+= δ

( )refxcref

xc

xc TTKK −+= δ

2. Prouvost model [15,16] - this alternative partitioning model, due to Prouvost, allows for self-association of alcohols in the oleic pseudo-component and treats the chemical pseudo-component as an interfacial pseudo-component. The alcohol partition coefficients are calculated from more fundamental coefficients in each grid block at each time step, according to the overall composition in the grid block. No provision is made for these coefficients to be temperature dependent. For each alcohol, the model requires the input parameters: oil/water partition (ko(1)), chemical/water partition (ko(2)), oil/chemical partition (kc), equilibrium constant (k) and partition parameter (a). Salinity-dependent oil/water partition coefficient

+

+

=−=

xo

xo

xa

xa

w

nxo

xo

xo

CCCC

cckkk

1

1)2()1(

where w

n

cc

is the salinity, and xa

wa

xa

xa

xa

VVV

CC

+=

+1 is the volume fraction of alcohol in aqueous phase. ko is the ratio of the volume fraction of alcohol in the aqueous pseudo-component to the volume fraction of monomeric alcohol in the oleic pseudo-component. Oil/surfactant partition coefficient

+

+

=

xo

xo

xc

x

xc

xc

CCCa

C

k

1 kc is the ratio of the surface fraction of the alcohol in the chemical pseudo-component to the volume fraction of monomeric alcohol in the oleic pseudo-component. a is the ratio of the length of an alcohol molecule to the length of a surfactant molecule.



i-meric alcohol concentration ix

oxox

o

xix

o CCCkC ,1,1,

1+=+

where C is the ratio of the volume of i-meric alcohol in the oleic pseudo-component to the total volume of that pseudo-component.

ixo

,

k is a self-association equilibrium constant. These equations, together with the equation for the overall material balance of the alcohol, can be rearranged to express all quantities in terms of Co resulting in a cubic equation for Co. Thus the solution can be found analytically. When a second alcohol is present, similar input parameters are required for the second alcohol, and analogous equations apply. Simultaneous solution of both sets of equations then requires an iterative method. A quasi-Newton method is used; the user may set the convergence criterion (Alcohol threshold), and a limit on the number of iterations, which if exceeded produces an error message.

3.8.3 Surfactant Phase Model (Micro-Emulsion) See also: Introduction. This screen displays the data used to set up the ternary phase diagram. Press Plot to view a plot of the data. You can choose between a plot of effective salinity (against salinity) or a full ternary phase diagram. Pseudo-component concentrations - since only water, oil, gas, surfactant and alcohols are allowed to be volumetric in surfactant flood simulations, the volumetric concentrations (volume fractions) of the pseudo-components are given by (see Polymer/Alcohol partitioning for definitions):

( )211 == ++= xa

xa

wa CCcv

( ) gxo

xo

oo cCCcv +++= == 211

( )211 == ++= xc

xc

sc CCcv

These volumetric concentrations (which should sum to one) are used as the coordinates in the ternary diagram calculations. Effective salinity - the effective salinity is defined by:

( ) ( ) ( )( ) ( )( ) 11112211 1111 −−−−==== −+−++++= refE

refTp

cpx

cxx

cx

w

n

SE EETTfffccC βββββ

Where cn/cw is salinity and fc are volume fractions of components in the chemical pseudo-component. The β coefficients are user supplied and entered in the effective salinities table for alcohol-1, alcohol-2, temperature, polymer and EACN. Tref is the reference temperature defined in the control section.

211 == ++= x

cxc

xcx

c CCC

f



spw

pppa

ppc

pc cKc

cKCK


composition at CSEL or CSEU. Threshold for phase behaviour - in all phase environments, if the total amount of surfactant present in solution is less than a threshold value (Chem threshold) entered in the three-phase boundary section of this screen, two phases only are assumed to be present, one containing only the oleic pseudo-component, the other the aqueous and chemical pseudo-components. Binodal curve - in each diagram, only a single phase will be present if the overall composition lies above the binodal curve, which is assumed to be symmetric and to be given by the Hand equation:

oac vAvv =2

The Hand parameter A is related to the "height" of the curve, i.e. the maximum chemical concentration. At maximum chemical concentration, the hand parameter may be calculated since vc,max+va+vo=1 and va=vo at the maximum chemical composition.

2max,22

max, 21

−== c

ac

vAAvv

, therefore

2

max,

max,

12

−=

c

c

vv

A

It is found by linear interpolation in the effective salinity from values calculated at zero, optimal, and twice optimal effective salinity (denoted by subscripts j = 0, 1, 2 respectively):

SEOPSE CC < SEOPSE CC >

( )SEOP

SE

CC

AAAA 010 −+=

( )SEOP

SEOPSE

CCC

AAAA−

−+= 121

where the values Aj are found from the binodal curve heights at the three effective salinities:

2

max,

max,

12

−=

jc

jcj v

vA

which in turn are specified as (linear) functions of alcohol concentration, polymer concentration, temperature, and EACN:

( ) ( )refjBNErefjBNTpcjBNP

xcjBNX

xcjBNXjBNCjc EEHTTHfHfHfHHv −+−++++= ==

,,,2

,21

,1,max, The H parameters are entered in the Binodal parameters section of this screen for zero, optimal and twice optimal salinity, for a base value (HBNC), both alcohols (HBNX1 and HBNX2), temperature (HBNT), polymer (HBNP) and equivalent alkane number (HBNE). Three phase triangle - in the type III case, three phases exist if the overall composition point lies in the three phase triangle below the binodal curve. The compositions of the three phases are given by the vertices of the triangle, i.e. pure aqueous pseudo-component, pure oleic pseudo-component, and a middle phase containing all components, generally with a high chemical concentration but also with significant amounts of both oil and water, implying high solubilisation parameters (ratios of oil or water to surfactant). The position of the invariant or middle point (i.e. the apex of the



triangle) is assumed to move across the diagram from left to right as the effective salinity increases from CSEL to CSEU; to be precise, the value of the expression

221 oa vv −

+

increases linearly from 0 at CSEL to 1/2 at CSEOP to 1 at CSEU. Two phase regions (tielines) - when two phases only are present, either in a II(+) or II(-) phase environment, or if the composition point lies in one of the lobes between the three-phase triangle and the binodal curve of a type III phase diagram, the compositions of the two phases are given by the intersections with the binodal curve of the tieline passing through the overall composition point. The locus of the tieline is determined by the position of the appropriate plait point. This is the point on the binodal curve on which the pseudo-component compositions of emulsion and excess phase (aqueous or oleic) are identical - it is essentially a critical point. Two plait points are entered by the user in terms of a pseudo-oil concentration - a left hand plait point and a right hand plait point. In the case where the plait points are in the corners of the ternary diagram (0.0 and 1.0), the excess phases will consist of entirely the oil or water pseudo-component. In the type II(-) and type II(+) cases, the following Hand relation, known as the distribution function, relates the (pseudo-component) compositions of the two phases:

oo

sa

wa

so CECCC =

The Hand parameter E can be determined from the position of the plait point, the point on the binodal curve to which the tielines converge. At the plait point, both phases have the same composition (that of the plait point), and this composition lies on the binodal curve, so:

( ) ( )ooP

ooP

oo

ooP

ooP

ooP

ooP

waP

C

CACpACACC

CC

E

−++−−−

==14

211

2

where is the pseudo-oil concentration at the plait point. In type II(-) diagrams,

. Similarly, in type II(+) diagrams, C . The plait points are input in the binodal parameters section of the screen.

ooPCooPRC

ooPC = o

oPLooP C=

For the two phase lobes of a type III diagram, the distribution function is modified to reflect the fact that the base of the lobe is a side of the three phase triangle rather than the base of the ternary diagram, becoming:

oo

sa

wa

so CCECC ′′′=′′

where for the type II(+) lobe:

2

22

mo

mcmooa

oa C

CCCC

+=′

mo

mcoas

asa C

CCCC −=′

sa

oa

wa CCC ′−′−=′ 1



ooP

waP

CC

E′

′=′

where is the composition of the invariant point. Similar formulae apply for the type II(-) lobe. The position of the plait points is taken to vary linearly with effective salinity between the type II(-) and type II(+) values, so the pseudo-oil concentration of the plait point in the II(+) lobe is given by:

mkC

−

−=

SELSEOP

SELSEooPL

ooP CC

CCCC

21

for SEOPSE CC <

−−

+=SEOPSEU

SEOPSEooPL

ooP CC

CCCC 1

21

for C SEOPSE C>

and that in the II(-) lobe by:

( )

−

−−+=

SELSEOP

SELSEooPR

ooPR

ooP CC

CCCCC 1

21

for C SEOPSE C<

( )

−−

+−+=SEOPSEU

SEOPSEooPR

ooPR

ooP CC

CCCCC 11

21

for SEOPSE CC >

In addition to satisfying the distribution function equation, the compositions of the two phases must satisfy the binodal curve equation:

oa

wa

sa CACC =

2

and oo

wo

so CACC =

2

and the relations:

1=++ sa

oa

wa CCC and 1=++ s

ooo

wo CCC

aowoa

wa vSCSC =+ and C and oo

ooa

oa vSCS =+ 1=+ oa SS

which gives a total of 8 equations for the eight unknowns , C , , C , C , C ,

and . In the general case, these equations are solved for the pseudo-oil concentration in the micro-emulsion phase by an interval-halving iteration. In the special case where the plait point lies in the corner of the phase diagram, the composition of the excess phase is known (it is the pure pseudo-component), while the mico-emulsion phase has the same ratio of chemical pseudo-component to oleic (type II(+)) or aqueous (type II(-)) pseudo-component as the overall composition point; the equations can then be solved explicitly, and no iteration is necessary.

waC

oa

saC

wo

oo

so aS

oS

A ternary diagram generated with the data entered on this screen can be viewed by clicking the Plot button. Some examples that illustrate the above discussion are displayed below.



3.8.4 Ternary Diagram See also: Introduction. This plot is invoked from the surfactant phase behaviour screen. This screen can be used to view the data on the phase behaviour screen graphically. Properties such as alcohol and polymer concentration, as well as component concentrations of water and oil (for example) can be varied to see how the various phases develop with these properties. The screen itself is divided into several sections: Component Concentrations - these sliders can be used to set the relative concentrations of oil, water, and surfactant to determine in turn the pseudo-component concentrations. The values are normalised automatically - if you want to fix a value while changing another, check the 'fix' box next to the slider. Note that gas is not included in these basic calculations. The reason for this is purely to simplify the input parameters: if gas were included, a PVT calculation would need to be carried out at P,T, and the resulting gas concentration would depend on factors such as miscibility and whether or not the system were repressurised. In the simulation, gas forms part of the oleic pseudo-component as explained in the introduction to this section. The absence of gas means that the binodal curve and effective salinity will not depend on the EACN entered for the gas phase. Variable Parameters - the following input parameters can be varied: alcohol concentration, polymer concentration, salinity, and temperature. When the sliders are adjusted, the phase diagram will change accordingly. Calculation Results - the Hand parameter of the binodal curve and effective salinity for the input set are output. A description of the system at the overall concentration point is also given (e.g. 'two phase aqueous and oleic emulsion' for a type II(+) system). Pseudo-component concentrations in phases - this gives the pseudo-component concentrations of the resulting phases. In II(-) and II(+) systems, the phase concentrations are given by the intersections of the tieline with the binodal curve, as plotted. For the type III case, the concentrations are simply the vertices of the three phase triangle. Interfacial tensions - Interfacial tensions for the emulsion/aqueous interface and the emulsion/oleic interface are given, where applicable, if this input data has yet been entered. Plot Phase Composition - this presents a diagram with the relative phase saturations for the system at the overall composition point. Zoom - the chemical pseudo-component concentrations along the binodal curve are often quite small and this makes the detail of the plot quite difficult to see. Click on the 'zoom' arrows to effectively increase the chemical concentrations (note that this will distort the plot slightly as the concentrations still have to be normalised).



3.8.5 Surfactant Interfacial Tension The interfacial tension between aqueous, micro-emulsion and oleic phase are modified by the surfactant model, resulting in capillary desaturation. Once the phase compositions have bee calculated, the interfacial tension is calculated as a function of solubilisation parameters (X). For an interface between water and micro-emulsion (type II(+) environment or the II(+) lobe of a type III environment) the water/micro-emulsion interfacial tension (σwm) is calculated. Similarly for an interface between micro-emulsion and oil (type II(-) or the II(-) lobe of a type III environment) the oil/micro-emulsion interfacial tension (σom) is calculated. Water/micro-emulsion Oil/micro-emulsion

( )w

wm XGG

G13

111210 1

log+

+=σ

( )o

om XGG

G23

212210 1

log+

+=σ

cc

wc

w CC

X =

cc

oc

o CC

X =

In both cases, if the solubilisation parameter (Xw or Xo) is below a threshold Xmin (minimum solubilisation parameter, default = 1), a linear interpolation between the oil/water value (σow, entered in the physical properties section) and the the values given by the formulae above is used.

( ) ( ) ( )wmw

oww

wm XX

XX

σσσ 10min

10min

10 loglog)1(log +−= if X w minX<

( ) ( ) ( )omo

owo

om XX

XX

σσσ 10min

10min

10 loglog)1(log +−= if XX o min<

Additionally, the interfacial tension is forced to approach zero at the plait point by multiplying the calculated value of σ by

)2exp(1)exp(1

−−∆−−

( ) ( ) ( )2222 sq

sp

oq

op

wq

wp CCCCCC −+−+−=∆

where p and q denote the two phases between which the interfacial tension is being calculated. In the three-phase triangle of the type III phase diagram only, the interfacial tension may be made a function of overall surfactant concentration at concentrations below a specified threshold (ε), where the slope (S) is user defined.

( ) ( )

−+=ε

σσw

s

wmwmcc

S 1loglog 1010

( ) ( )

−+=ε

σσw

s

omomcc

S 1loglog 1010



3.8.6 Surfactant Viscosity If the surfactant model is being used, then the aqueous, oleic and micro-emulsion phase viscosities are calculated using one of two models, namely Pope and Barker (a variant of the Barker model is also available). See the mobility section for more information on viscosity models for polymer (thickening, shear thinning). At this stage, of a calculation, the aqueous, oleic and gaseous phase viscosities have been calculated, accounting for all additive except surfactant. Each of the three phases (p), aqueous, oleic and micro-emulsion are considered in turn. Within each phase, the volumetric component concentrations of water (Cwp), oil (Cop) and surfactant (Csp) are known. In addition to the model specific parameters required the user enters a thermal exponent factor Alpha6 (βmT). Note that this factor is used with absolute temperatures (R). Pope model - the user is required to enter the parameters Alpha1 to Alpha5 (βm1 to βm5). The volumetric concentration of hydrocarbon components (Chp) comprising oil+dissolved gas is calculated.

( ) ( )( ) (( +++++

−= CCCCCCCCTT

C wpmo

hp

sp

opmw

wp

opm

wpm

refmTm

spp expexpexp11exp 54321 βµβµββββµ

µw and µo are the water and oil viscosities calculated without surfactant being present. When the micro-emulsion phase is being considered, µo is modified to reflect any miscible free gas within this phase. Note that no free gas will be present within the oleic phase. The term ‘free gas’ is used here to mean excess gas (GOR-Rs) beyond that associated with the oil, that may be present within the micro-emulsion phase.

4

41

41

)1(−

−+= go

g

oo gg µµ

µµµ

where ∑∑

−

=g

g

cGORRsc

g1

The above sum is over all gaseous components (usually only one). Barker model - the user is required to enter the parameters Alpha1 to Alpha5 (βm1 to βm5). These are different from parameters entered for the Pope model. Aqueous phase viscosity Oleic phase viscosity

( )samwww CTF 10 βµµ += ( ) ( )

( )

−+−

+=TTTT

CRwax

waxwax

somRoo 1

exp20

0 βββµµ

The micro-emulsion phase viscosity depends on the phase present (i.e. region of ternary diagram). The phases present are controlled in REVEAL by the effective salinity (cse), which has values within a range extending from a minimum (cse,min) to a maximum (cse,max), with an optimal value (cse,opt) between the minimum and maximum values. Type II- (oleic and micro-emulsion phases only)

om µµ =



Type II+ (aqueous and micro-emulsion phases only) wm µµ =

Type III (aqueous, oleic and micro-emulsion phases)

( ) ( )( )

−

−−

−+=ref

mTseoptse

sesemmmm TTcc

cc 11expmin,,

min,343 ββββµ

for c ≤ optsese c ,

( ) ( )( )

−

−

−−+=

refmT

optsese

optsesemmmm TTcc

cc 11exp,max,

,454 ββββµ

for c > optsese c ,

For the type III micro-emulsion, the micro-emulsion viscosity is modified by the thickening factor calculated for the water present within the micro-emulsion phase. This modification is not applied if the variant Barker_x model is selected.

mmm TF µµ = The calculated micro-emulsion viscosity is then modified to reflect the presence of any ‘free gas’.

4

41

41

)1(−

−+= gm

g

mm gg µµ

µµµ

where ∑∑

−

=g

g

cGORRsc

g1



3.9 Adsorption Section

3.9.1 Adsorption Properties This screen sets the components that will adsorb onto rocks, and defines the isotherm describing the adsorption. Any component apart from water, oil and gas may be adsorbed. Adsorbed components are not transported with the fluid flow or subject to diffusion. Adsorbed minerals take no part in water chemistry equilibrations. Adsorbed surfactant takes no part in desaturation and micro-emulsion phase formation. Adsorbed components may reduce the permeability (e.g. polymer, gel or water chemistry minerals). Adsorbed wetting agent is used to model wettability desaturation. Data for rock types - adsorption data may be added for any or all rock types, with different data possible for different rock types. Select Add to add a new entry to the table, select an entry in the table to modify the adsorption data, or Delete to delete all of the adsorption data for the current rock type. Fluid list - this lists the components in the model that may be adsorbed. Select a component and use the Add or Delete buttons to add or delete adsorption data for that component. Some components must have adsorption data (e.g. surfactant, polymer, H+) if they are present, these components will have a red cross beside them and use the Add button to add adsorption data (which may be null if no adsorption is required). Adsorption isotherm - Four adsorption models are available, Langmuir, Linear, Stripping and Bright Water. Use the Plot button to view the isotherm. Permeability reduction - this is available for all adsorbed components apart from water chemistry minerals, which have their own permeability reduction model. The zero shear permeability reduction (R0) is a function of the adsorbed component concentration (Ca) and the input permeability reduction coefficient (RF). See the mobility section for more information on how the permeability reduction is used.

max

0 )1(1CaCaRR F −+=

The total permeability reduction is the sum of the permeability reductions of all adsorbing components. Adsorption initialisation - the initial adsorbed concentration is entered in units of mass per unit volume, where the volume is the total rock volume (including pore volume). This data is optional, with a default of zero. Data may be entered as a constant for each rock type, as a set of grid block ranges each with a constant value, or as a datablock11 with an entry for each grid block. For more information on using the range and array options see the reservoir section.

11Potentially large arrays of data (e.g. grid coordinates) held in the REVEAL archive but not displayed in the input script.



3.9.2 Adsorption Isotherms Four isotherm models are included, describing the adsorption profile as a function of concentration, temperature, permeability and salinity. Irreversible, reversible or partially reversible models are available, and the adsorption may also be rate dependent. All component concentrations have dimension of mass/volume. Mass fractions (c) in the aqueous phase are defined by the ratio of a given component concentration divided by the concentration of water (c=C/Cw). The partitioning of the total component concentration (C) between that adsorbed (Ca) and that remaining within the aqueous phase after adsorption (C*) is defined by the maximum adsorbed concentration (Camax,A[k]) and the isotherm parameter (b), which describes the shape of the isotherm. Langmuir isotherm The relation between adsorbed and aqueous component concentrations is characterised by the following equations, where a is defined below.

*1*bcacCa+

= wC

c =* CaC −

The maximum adsorbed concentration occurs when c* is large (i.e. Camax=a/b). If b is small, then Ca rises slowly, and if b is large then Ca rises quickly. In addition to Camax and b, the user enters the temperature (A[kt]), permeability (A[kx]) and salinity (A[ks]) coefficients used to calculate the parameter a (maximum adsorbed concentration at current conditions of temperature, permeability and salinity).

( ) ( )[ ] xarefTSSref kTTaCaaa −−++= maxbCaaref = 2

kykxk +=

22

b≤* *acCa

The effective salinity (CS) is calculated from the salts present, while the reference temperature (Tref) is input by the user in the control section. The mean permeability (k) is the mean horizontal permeability. Linear isotherm The linear isotherm is identical to the Langmuir isotherm, with the following modification. If c then =

b>* ab=If c then Ca Bright Water isotherm The Bright Water isotherm is identical to the Linear isotherm, with the following modification to the temperature dependence, requiring input parameters Tbw (A[kt]), abw (C[bw]) and ε (epsilon).

( ) ( )( )[ ] xakTTaCaaa −−++= tanhε bwbwSSref



Stripping isotherm The stripping isotherm adsorbs all available component to its maximum value, hence the isotherm parameter (b) is not required for this model.

),max( maxCaCCa = Reversibility Adsorption is always completely reversible for changes in salinity. Adsorption may be completely reversible, or completely irreversible for changes in temperature. If the irreversible option is selected, then the maximum historical thermal contribution to the adsorption parameter (a) is used. Adsorption may be completely irreversible, completely reversible, or partially reversible for changes in concentration for all isotherm models. Reversibility is controlled by entering an irreversible concentration limit (Cairrev). If Cairrev is not entered (cell left blank), then the model is assumed to be fully reversible. A Cairre value equal to Camax represents the fully irreversible case, while intermediate values model partially reversible isotherms. For a partially reversible isotherm, as the concentration of the adsorbing component increases, the adsorption level rises in accordance with the isotherm. The Langmuir curve is used as an example, where three points on the curve (Ca plotted as a function of C*) are identified. Point A is at the irreversible adsorption concentration (Ca = Cairrev). Point B is the point on the isotherm curve where a straight line passing through (0,Cairrev) has the same gradient as the isotherm curve (i.e. the tangent point). Additionally, point C is defined as the point (Cairrev,0) used to define point B. If the concentration falls before point A has been reached, then the adsorption does not reverse (irreversible). If the concentration starts to fall between point A and point B, then desorption occurs along a straight line from the maximum point reached on the isotherm curve to point C. If the concentration begins to increase again, adsorption moves back up the straight line until the isotherm is reached, and then continues moving up the isotherm. If the concentration starts to fall after point B, then desorption proceeds down the isotherm until point B is reached and then down the straight line connecting point B to point C.



Reversible Langmuir Isotherm

Concentration in solution (C*)

Ads

orpe

d co

ncen

trat

oin

(Ca)

A

B

C

Adsorption rate Adsorption may be assumed to take place instantly, or the time taken for adsorption to occur may be modelled using an input rate parameter (arate).

)(1 nrate

nn CaCataCaCa −∆+=+

where Ca is the newly calculated instantaneous adsorbed concentration, and Can and Can+1 are previous and current time step values.



3.9.3 Permeability Reduction Water chemistry permeability reduction - for adsorbed water chemistry minerals, both porosity (∆φ) and zero shear permeability reduction (R0) are functions of the adsorbed concentration, rock density (ρr), original porosity (φ0) and user defined permeability reduction coefficient (PN).

r

Caρ

φ =∆

NPR −∆−= )1(

0

0

φφ

Permeability reduction coefficients may be defined for each rock type or for all rock types. The total permeability reduction is the sum of the permeability reductions of all adsorbing components. See the mobility section for more information on how the zero shear permeability reduction is used. The porosity reduction is used as an equivalent inaccessible pore volume (ipv = -∆φ/φ), which increases the effective volumetric concentration of all trace components (i.e. water chemistry ions). Other permeability reduction factors - the shear dependence flag is available for viscosity correlations when polymer or gel components are present. It allows permeability reduction to be subject to shear thinning or not. See the mobility section for details of the shear model. By default permeability reduction only applies the aqueous phase, however, it may also be applied to oleic phase by selecting the Oil+water phase option and entering a fraction (PSPLIT) of the permeability reduction to be applied to the oleic phase. This option does not affect the permeability reduction applied to the aqueous phase.



3.10 Water Chemistry Section This section is only available for water chemistry calculations. The component model for water chemistry calculations is set in the control section. The water chemistry model predicts precipitation and dissolution of minerals within the aqueous phase. H+ (pH), e- (pe) are required species and should be included for all water chemistry models. Solid phase mineral concentrations are similarly input and tracked within the aqueous phase. PHREEQC The public domain water chemistry program PHREEQC is used to solve the chemical equilibrium within the water phase. It takes as input the aqueous master and mineral species’ molalities (mol/kgw), and returns their molalities following equilibration and mineral reaction. Redox reactions are possible, altering the electron activity, e.g. HS- <> SO4

2- + 9H+ + 8e- - 4H2O. Note that the redox reactions may have significant effect on the solution pH and pe. The reaction species and thermodynamic reactions are defined within a PHREEQC database. A default PHREEQC database is included with the REVEAL installation, and is written to the current data directory with the name 'phreeqc.dat'. The current data directory is set using the menu option File|Data Directory. To use a different chemical database, simply replace the 'phreeqc.dat' file in the current data directory, ensuring that the replacement database has the correct format for version 2.4.2 of PHREEQC. Partitioning - the PHREEQC model also returns the molality of dissolved CO2 and H2S. The CO2 and H2S may be partitioned between the aqueous and oil/gas phases. CO2 (oil/gas) <> CO3

2- + 2H+ - H2O (aq) H2S (oil/gas) <> HS- + H+ (aq) The change in pH can dramatically affect the precipitation/dissolution of mineral species. Adsorption - precipitated minerals may be adsorbed. Adsorbed minerals are not transported and take no part in the water chemistry equilibration. Output region - this defines are region of the grid that will have the results of the water chemistry equilibration output to the water chemistry results file. This file may be viewed by selecting Results|Debug|Debug water chemistry from the main REVEAL window. Calculation/output frequencies - the water chemistry equilibration may be performed every timestep or with a defined frequency in timesteps. Similarly, the water chemistry output may be output every timestep or with a defined frequency.



Electrical neutralisation - one species pair (anion and cation) is required to be internally adjustable to ensure precise electrical neutrality. This is usually chosen to be Cl- and Na+. Electrical neutrality of the mixture of ionic species (excluding free electrons, e-) should be ensured for both the reservoir and injected waters. This may be checked using the input wizard calculator in the initialisation and injection sections. New partition coefficient - if this option is set, then the water/oil partition coefficients for CO2 and H2S will be initialised using the initial components present, rather than using the value entered in the mobility section. See the mobility section for more information on the partitioning model. This will only affect water chemistry models where partitioning can take place (i.e. the components CO2oil/CO2gas or H2Soil/H2Sgas are present). Simplified equilibration - this flag is only available if there are no mineral precipitate components within the model. If this option is selected, then the PHREEQC chemical equilibrium program is not used, and therefore aqueous speciation of the tracked master species does not take place (i.e. the ionic master species do not associate to form aqueous dissolved species). However, H2S and CO2 partitioning and the H2S souring models are still available. These models calculate the aqueous dissolved CO2 and H2S using the PHREEQC database (for equilibrium constants and activity coefficients), assuming that all of the ionic master species (CO3-2 and HS-) are in ionic form (fully dissociated) and available to form aqueous dissolved CO2 and H2S. This approximation results in large cpu savings. Master species components - chemical components (ions) corresponding to a master set of reacting species are input and tracked. The water chemistry chemical components are defined to have the same density as the water present, therefore volumetric and mass concentrations are equivalent. Usually their concentrations are input as mass concentrations (e.g. ppm). Note that the H+ and e- concentrations are related to pH and pe with the following relations.

( )pHppmH −+ = 310][ and

( )peppme −−− = 310][

Seawater - a typical seawater composition is given below. Both sulphur valence states are included; this is a general requirement and all ions with multiple valence states should be included. Additional reservoir species (e.g. Ba+2) and possible minerals (e.g. Barite) should be included in the model. Ion Concentration (ppm) H+ 6E-6 (pH=8.22) e- 3.5E-12 (pe=8.45) Ca+2 412 Mg+2 1292 Na+ 10768 K+ 399 Cl- 19353 CO3-2 142 SO4-2 2712 HS- 0



3.10.1 CO2 and H2S Partition Coefficients This screen is present if the water chemistry model is active and partitioning of CO2 or H2S between aqueous and hydrocarbon phases is possible. For CO2 partitioning, the components CO2oil and CO2gas must be included in the model, and for H2S partitioning H2Soil and H2Sgas must be included (see control section for component selection). CO2 partitioning - Partition coefficients (PCwo and PCog) are defined for CO2 partitioning between aqueous and oleic phases, and between oleic and gas phases. The activity of CO2 in water is approximately equal to the molality (mole/kg water) of dissolved CO2. The partitioning is achieved by considering the CO2 dissolved in the hydrocarbon phases to be represented by an ideal gas in equilibrium with the aqueous phase. The ideal gas CO2 partial pressure is related to the mass concentration of CO2 within the hydrocarbon phase. PCwo = (Mole/litre of CO2 in oil) / (Activity of CO2 in water) PCog = (Mole/litre of CO2 in gas) / (CO2 concentration in oil) The partition coefficients are pressure dependant and take different forms depending on whether the pressure is above or below the partition reference pressure. If the pressure is above the partition reference pressure. PCwo = Partition coefficient + (Pressure-Partition reference pressure)*Kow above reference pressure PCog = 0 If the pressure is below the partition reference pressure. PCwo = Partition coefficient + (Pressure-Partition reference pressure)*Kow below reference pressure PCog = Gas/oil partition coefficient + (Pressure-Partition reference pressure)*Kgo below reference pressure H2S partitioning - this model has the same data input and form as the CO2 partitioning model above. Initial partition coefficients - if the New Partition Coefficient flag is checked in the water chemistry section, then the water/oil partition coefficients (Part Coefficient for both CO2 and H2S) are calculated from the initial conditions (i.e. initial value of CO2oil/H2Soil and initial equilibrated CO2/H2S in water).



3.10.2 H2S Souring The H2S souring model is only available if the water chemistry and souring options were selected in the control section. The souring model requires the components SO4-2, HS- and nutrient to be present. In addition, the H2S partitioning components H2S_oil and H2S_gas should usually be present within a souring model. HS- may also be an adsorbed component, modelling its retardation. The simplified equilibrium model may be used for souring calculations that do not contain precipitating minerals. The basis of the souring model is that SO4-2 reduces to HS- under the catalytic presence of sulphate reducing bacteria (SRB). The growth of SRB is controlled by the presence of the nutrient component within a suitable temperature range. As the nutrient is used up, the rate of SRB growth reduces, but the SRB remain present and available to reduce SO4-2 ions if they are present i.e. it is assumed that the SRB may metabolise at a constant concentration with no nutrient present due to remineralisation and resting cell metabolism. The SRB are assumed to not flow with the injected water, but remain and grow within grid blocks. The net result is that as the SRB grow, they are available to reduce SO4-2 ions within a cooled region near an injector, and the reduced HS- ions may then form aqueous and hydrocarbon phase (assuming partitioning) concentrations of dissolved H2S, which may then be transported in the aqueous and hydrocarbon phases. Temperature dependence - minimum and maximum temperature at which the SRB may grow. Concentration dependence - minimum and maximum SRB concentration. The minimum concentration is assumed to be present initially everywhere within the reservoir as a starting condition, in the form of SRB spores. The maximum concentration is the maximum concentration that the SRB can achieve, even it the conditions (temperature and nutrient availability) are otherwise favourable for SRB growth. SRB growth rate - half life for SRB concentration to double under favourable conditions (temperature within set bounds and nutrient available). Maximum SO4(-2) reduction rate - the sulphate reduction rate (molality/day) at maximum SRB concentration. The sulphate reduction rate at reduced SRB concentrations is a linear interpolation between zero and the maximum value entered here as a function of SRB concentration between its minimum and maximum values. The sulphate reduction rate is also limited by the sulphate ions present. Nutrient/SRB mass ratio - the mass ratio of nutrient to SRB, required to reduce the nutrient concentration as the SRB concentration increases (SRB growth).



3.10.3 Scale Inhibition The scale inhibition model is only available if the water chemistry option was selected in the control section, and there are precipitating minerals and the component Scale Inhibitor is present (see component selection). The scale inhibition model increases the solubility of minerals as a function of inhibitor concentration within the aqueous phase. The scale inhibitor may be adsorbed. Scale inhibition is based on the assumption that the scale inhibitor acts to provide nucleation centres for the precipitating mineral that prevents large particulate precipitation. The solubility of the minerals is controlled by a saturation index (SI). The default value is zero, and as the SI increases the soluble concentration of the mineral rises logarithmically, so that an SI of 1.0 allows the soluble concentration of the mineral to be ten times larger than the default value (defined by the PHREEQC database), before precipitation occurs. Scale inhibition can be applied to none, any or all precipitating minerals, but they all use the same scale inhibitor concentration to calculate the reduced solubility. Maximum effective inhibitor concentration - the maximum effective scale inhibitor concentration. Scale inhibitor concentrations above this maximum will not further increase solubility. Maximum saturation index - the maximum mineral saturation index (SI). The SI used will rise linearly from zero to the maximum SI entered as the scale inhibitor concentration varies between zero and the maximum effective value.



3.11 Wells Section

3.11.1 Location and Properties This section initialises the location and properties of wells. Use the Plot button to view the wells (green) and completions (red) over a wire-frame representation of the grid. Data for all wells - these switches are applied to all wells. The block or average well models define how the concentration of components within phases from producing wells are calculated. The default option (block) sets the component concentrations equal to the concentrations present within the producing block, and is generally recommended. The average option sets the component concentrations equal to a horizontal spatial average, which makes the assumption that component concentrations have a cubic form near the well.

( )24

28 ,1,,1,,,1,,1,, kjikjikjikjikji cccccc +−+− +++−

=

Etrapolate lift curves is generally not recommended, lift curevs should be generated over sufficient data ranges. The extrapolation may produce very erroneous results if the extrapolation is large. The shear model applies a shear thinning correction for water injection wells containing polymer and gel components. See the mobility section for more details. Well list - wells may be added using the Add button. Once a well has been added, its properties may be modified by selecting the well in the list. A well may be deleted by selecting it in the well list and using the Delete button. Well label - a name for the well that can be edited to identify the well. Enter well location - the method of defining the well completions can take three forms. Either a completion table containing the I,J,K coordinates of the completed blocks, or a vertical column of grid blocks identified by I,J block coordinates, or a general multi-lateral well may be defined. If a well is to be located within a refined region, then a fourth option (separate refinement) should be selected, and the refined region name entered. The extent of the refined region and its name should be entered in the reservoir section. The well location and completions within the refined region are defined in a separate refinement script. See the grid refinement section for more information. For radial and curvilinear geometries the first two wells are defined by the geometry and their location cannot be altered. Additional wells for these geometries are not recommended. Layer data & completion table - for the completion table or vertical column method of defining the well location, the data for each block associated with the well are entered. For the completion table, the I,J,K coordinates of the well must be entered for each block. A block may be set to be perforated by using the left mouse button within the table perforation column. For the completion table, the PI (Productivity Index) may be input



directly, or calculated using the Peaceman [13] model. For the vertical column method the perforated layers should be set and the data required by the Peaceman model entered. The well radius and skin are used to calculate a PI for anisotropic non square grid blocks using the Peaceman model. The fractional completion angle is a multiplier to the Peaceman calculated PI, modelling partially completed or deviated wells. It is up to the user to supply this data. For the well-bore heating model, the earth and electrode locations are identified in the final column of the completion or layer data table. Multilateral well [6] - if the well is a multilateral or defined by a deviation survey, then it must be given an identifier name. Select the Edit Multilateral button to enter a deviation survey. A reference location for the top of the well must be entered in either grid or map axes. A hierarchy of connected tubing sections (possibly consisting of several branches) can be added or deleted from the tubing list. For each tubing section a deviation survey is entered using either grid coordinates or deviation survey coordinates. Any interval on the tubing section may be completed and given a radius and skin. The well may be viewed using the View button at any time. Note that deviation surveys can be imported from previously exported files. REVEAL initially calculates the intersection of the completions with the matrix grid blocks. It then calculates the standard Peaceman connection [7,13] for a vertical well connected to each intersected grid block and correction factors accounting for the actual production to the intersected matrix blocks. The correction factor for each block intersected by a multilateral well is calculated using point-source solutions to the flow around the entire well, therefore including the interaction of well completions in different grid blocks. The point-source inflow to the block being considered is then compared to the block inflow calculated with a similar point-source solution obtained from a reference vertical well passing through the grid block centre. This approach effectively calculates a correction factor multiplier (skin) to each intersected block taking account of the non-radial flow, which is assumed by the Peaceman model. For example, the inflow at the ends of a completion will be greater than the inflow at the centre of the completion, and the interaction of multi-lateral completions will influence the production of neighbouring completions. The Peaceman well connection (PI) accounts for the logarithmic pressure distribution around a vertical well, and for a given rate (Q) and bottom hole pressure (Pwf) sets the appropriate mean block pressure (P) that will give the correct inflow (Q=PI(P-Pwf)) and total rate to surrounding grid blocks using the linear Darcy formula. The multilateral correction, essentially modifies the Peaceman connection factor to account for deviated, partially penetrating or multilateral completions. The reference Peaceman well is chosen to be vertical (even for horizontal wells), since the prevailing reservoir flow will most often be vertical pseudo-radial, following initial periods of horizontal radial and linear flow. This assumption is pessimistic with respect to PI calculation. Lift curve and well type - a PROSPER lift curve (*.tpd) may be imported. Generally it is recommended that the lift curve is imported and associated with a well in the schedule section rather than in the well section. Care should be taken to ensure that the imported lift curve is of the correct type (e.g. water injector or producer) for the well.



Pwf reference - the default (top of well tubing) location of the Pwf reference pressure depends on whether the well is defined by completion table, vertical column or a multilateral. For a completion table or vertical column, the Pwf is located at the top centre of the first block in the completion list, whether this block is completed or not. For a multilateral well the Pwf is located at the first (reference) node. Alternatively, a reference depth may be entered for each well. Non Darcy factor - a non-Darcy factor may be applied to the gas phase of any well. This factor is scaled for each completed block according to the Darcy connection factor (assumes equal drawdown for completed blocks) and applied as a rate dependent skin. The block geometrical connection factor (CF) prior to the non-Darcy effect is defined as

Srr

CF

w

eb

+

=

ln

kh2π

and is modified to include the non-Darcy skin as

bbw

e

nonDarcyb

QDSrr

CF++

=

ln, where b

bbwell

b CF

CFDD

∑=

kh2π

Note that if the well completion blocks are entered as a table with only the total connection factor, the nonDarcy skin will be applied with the denominator of the connection factor assumed to be unity. Wellbore friction - if this option is selected then an internal diameter and absolute roughness should be entered for every well segment, whether it is completed or not. This option is not available for curvilinear or radial grids, or for wells defined by a completion table. The wellbore friction model uses a simple no-slip frictional pressure drop model, taking into account a mean density and viscosity at each node within the wellbore. Cross Flow - a cross flow model is available for any well. It is recommended that crossflow is used for wells for which a trajectory and wellbore friction has been set, otherwise the crossflow fluid will be the combined produced or injected fluid not taking into account the local fluid within a wellbore. This model is not recommended to be used in conjunction with fractures, since cross flow within the fracture is not modelled.



3.11.2 Fracture Properties This screen is only active if fracture models is selected in the control section. It initialises the fracture type (producing or thermal injection), location and initial dimensions. All fractures have an origin at the centre of a grid block (with coordinates IJK), associated with a completed well. The fracture then has a two-dimensional shape running down the centre of adjacent blocks with constant (X, Y or Z) coordinate. Fracture list - use the Add button to add fractures to the model. Select a fracture in the fracture list to alter its properties or use the Delete button to delete the fracture. Fracture position - give the fracture a label name or use the default and select a well to be associated with the fracture. Every fracture must be associated with a well. For both injection and producing fractures more than one fracture (multi-layer fractures) may be associated with a well. The location of the fracture origin is then defined. For wells with a completion list or vertical wells, the completed block number for the fracture is entered. For a multi-lateral well the coordinates of the fracture centre are input; use the Calculator button to select a completion and interpolate a position along the completion (using either an X,Y or Z coordinate). Note that for multi-lateral wells, the fracture origin will be moved from the input position to the centre of the block containing the input position when the calculation is run. This is because the fracture origin must be defined at a block centre, since the connection of the well to the block is defined by reference to the block centre. Fracture model - three fracture models are available, a 1D analytical thermal fracture model (Geertsma deKlerk), a finite-element thermal fracture model (3D model) and producing fracture model. The first two models are thermal injection fractures, where the shape of the fracture evolves as the fracture propagates, while the producing fracture model has a static fracture shape, assumed to be sustained by propant or acid treatment. For all three fracture models the initial dimensions of the fracture are required; a half height above and below the fracture origin and a half length. For the injection (thermal) fractures, this data is used to describe the initial fracture dimensions arising from formation damage or naturally occurring fractures. The propagation of a fracture starts when the well Pwf is large enough to generate a stress intensity at the fracture tip greater than the critical stress intensity. Prior to propagation initiation, no inflow from the fracture is assumed. A smaller initial fracture size will require a larger initiating Pwf and hence longer Darcy (well completion only) inflow time before the fracture is initiated. For the 3D fracture and producing fracture, a two dimensional finite-element grid is used and explicitly models the fluid flow and pressure drops within the fracture. For these fracture models, the permeability (k) within the fracture must be defined. Three models are available, including constant permeability, Fcd (dimensionless fracture constant) and parallel plate. The latter two models depend on the fracture width (w), fracture half length (L1/2) and X-direction reservoir permeability (kx) for the Fcd model, and are defined below.

wk xcd 2/1=

LkF



12

2wk =

An Fcd value of 500 to 1000 represents the infinite conductivity approximation. Geertsma deKlerk - this model is basically a volume balance model based on a leakoff correlation. The leakoff and spurt coefficients are the only additional data required for this model. This model is a single wing model and the fracture origin should be positioned in the first row of the grid (I=1 or J=1) so that the wing may propagate in the X+ or Y+ direction. The propagation direction depends on the minimum principal stress direction.

Minimum principal stress direction Fracture propagation direction (length) Fracture height direction X Y+ Z (vertical) Y X+ Z (vertical) Z X+ Y (horizontal)

3D fracture - this model calculates the fracture shape including effects of stress changes due to injected fluids, elastic fracture opening, propagation depending on rock strength, flow within the fracture, leakoff rate balancing the well injection rate and Pwf. The propagation direction is dependent on the minimum principal stress direction.

Minimum principal stress direction Fracture propagation plane X YZ plane Y XZ p

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ETei(a)(24( )452r5n 3900201 Tf67ioe 0 9.02.2a2hx33n>>B r9627p467i67ioe 0 9.02.787 452r5n 393 T2 601te444( Tm(i76 455.9o87 9.02.2a2hx33n>>B r9i2 T2 601te444( T4 Tm2o8 T21 19 467.4264 Tm(aga2i 5ea.In4396670TjTf9179.4 Tm2o8 T21 19 9ea.In4396670TjTf9179.4 Tm2o8 T21 19 9ea.In4396670TjTf9gd10.0201.18re0.0201.18r9063 3 Th.810.0201 0 0 10.0201 379.47ea.01.h.810.0201 0 0 136670TjTf9gd10.0201.18re0.01.1s7h4TjTf9gd10.0201.18re0.0201510.0201 0 0 10.43n8390l4257ea.In4396670TjTf9179.4 Tm23 r96201 379.47272r624 0 0 T2120.510e88e 427850e44672575(X)Tj10.02010dY Tm13ana3 Th935 Tm( )Tj0 0ne446.97i89j 9e9x3 Tm(a)Tj10.0201 0 r22 r96Y049B3390662.7829 455.90l5Tm23 r96201 379.47272r624u01 0 201 Tf91j10.0.01.1s7h4T.0201 0 r22 r9610d8r9063 3 Th.82o1 3s10.02if10.0201 0 0ne446e9x3 Tm(a)9i2 T2 601te444( T4 Tm683l1201o8eldETei2733n>>B r96201 1446n-sT3)ne4402if10.0201 0 10.9801 89.43.4725h5.h.7R 4279 455.901 0 0 10.9801 89.43.02hc.18re0.01.1s7h6n-s(a)T4xe5m.02h5.t)Tj3n8l34j10.0201 0 01516e9x38 0 001.1s7h6n-s(a)Th95o50.4 .1.242m(201 r Tm v3ec904r62.7829 455.90601 0 020484)ne4446n-inr93 17393 T2 601te444( Tm(i76 4 n5ea.095.l stre) r0.0Jn667e40r96Y0p1 0.1s201 37 455.h.7R 40.08h1ei676 4 n50.0Jn667eE4p5329>>B r96200t1 0.694( Tm8lw25h5.h.76746n-inr93 17393 T2 601te444( Tm(i76 4 n5ea.095.l stre) r0.0Jn667e40r96Y0p1 0.1s201 37 455.8.90.0201.18re0.01.14 n50.0Jn667eE4p5329>>B49.501 8>B48020F6946n-s7hd10.0201.18re0.0201510.02p53E4p5329>>B49.501 8>B4802007R 40.08h1ei68b3oe5m55.h.7R 40.08h1ei676 4 .18re0R 40.08h10 0 10.46r1r96200t1 0.6939667e0R n5ea.095.l str.Tm( )713)ne4446n-sT3)ne4446n-sT3)ne4446n-sT T212010.5644 455.906e44482eael1.46r1r96200t1 0.6939667e0R 6oe6e4444aeaee4446n1j10.0.01.1s7h7R 40.08h1ei68b3oe5mee7n6 4 n5ea.062002p53E4p5329>>B49.501 8>Bni3359 9ea.In4396670TjTf9gd10.mee7n6 4 n5ea.062002p53E4p5329 9ea.l6.08)ne4446n-s 0 T2120.510e88e 42785001.9.43.02hc.18re0.01.1s7h6nm.02h5.t)Tj3n8l3-sTh935 Tm( )TjEToP01 0 0 10.9801 5( )35 1e34 4 n50.0Jn667eE4p5329>>B r9623e102h5.t)P013u(a)74p5329 9ea.l6.08)ne4446nh20201t9lai9623e102h5.t)P013u(a)74p7)74p1.9801 5( )30.02035r31t9lai943gd10R 40.08h1ei6776742pi.501 8>B53)ne4446n-sT3)ne55.h.7R 405o5329 9ea.l7272r624 0 0 T2120.510e88e 42788kea.In4396670br.l7229 455.90601 0 ,4o7cr( )3002hc.181172r5m2l.901 0 0 10.9801 89.43.02hc.18re0.01.1s7h6n-s(a)T4xe5m.02h5.t)Tj3n8l34ja0689.43.02hc.180Jn6u lh6n-s(a)T4xe5m.02h5.t)Tj.02h5.t


The shape of the fracture plane may be rectangular or elliptical. The width at the fracture origin is entered, and the width profile defined to be either constant (=central value) or decrease with an elliptical cross-section towards the fracture boundaries. A fracture skin may be included for this model, reducing productivity with a positive value. Thermal fractures - the stress near the fracture is reduced if injection water at a temperature below the reservoir temperature is used. Similarly the stress rises if the pressure rises above the initial reservoir pressure (pressure at which the in-situ stress is defined). The 1D Geertsma de Klerk model only uses the stress at the fracture tip, and therefore this model is not greatly influenced by the stress reduction parameters. All fracture models may use constant pressure, constant rate, or injection curves for the well from which the fracture propagates. The resulting fracture will have the following properties. Pressure and rate consistent with the injection well constraints. Leakoff rate from the fracture to the rock matrix consistent with the fracture size and leakoff model. Stress intensity at the fracture tip equal to the rock critical stress intensity. Various iterations are performed to ensure that the fracture shape (lateral and width), pressure and leakoff rate are consistent with the well performance, current stress and reservoir conditions.



3.11.3 Geertsma deKlerk 1D Thermal Fracture This is a simple model that only allows a single-wing fracture to be modelled. It requires a leakoff and spurt coefficient to be supplied, defining the leakoff rate as a function of fracture area. It is most applicable in cases where the rock is fairly elastic and relatively large fracture volumes may be present. Fracture opening and propagation criteria - this model assumes a rectangular vertical fracture with half-length (Lf) and a constant pressure (Pf) within the fracture. If this pressure is greater than the rock stress (σ), then the fracture can open. The criterion for fracture propagation is that Pf generates a stress intensity at the tip greater than the critical stress intensity, KIc. Propagation stops when the stress intensity at the tip is equal to the critical stress intensity. Open condition Propagation condition

σ>fP f

Icf L

KP

πσ +>

Width and length equations - the width of the fracture at its widest point (ww) (injection site) and the fracture half-length are related to the total fracture injection rate (Qf), leakoff rate (QL), leakoff (C) and spurt (SP) coefficients, time (t), half-height (h), and history of the evolving fracture area (A(t)). Basically, this model is a material balance model, where the changing volume of the fracture is the difference between the injected and leakoff rates. The volume of the fracture is a function of its length and central width, which in turn are related to the elasticity and tensile strength of the rock for a given internal pressure. Elastic strain relation describing fracture shape Material balance equation

)()1(2 συ−

−= ffw PL

Gw

tASQQ

tV

pLf ∆∆

−−=∆∆

Fracture volume and area Leakoff equation

wf whLV2π

= and hLA f4= ∫ −

=t

L dddA

tCQ

0

τττ

G is the shear modulus and defined by Young's modulus (E) and Poisson's ratio (ν).

( )υ+=

12EG

These equations are solved for the fracture pressure and leakoff rate for an input total fracture injection rate. The result depends on whether the fracture is propagating or not. The fracture pressure is then coupled to the injection lift curve, finally after iterations returning a consistent total injection rate Q=Qf+Qw.



3.11.4 3D Thermal Fracture Both single-wing and complete (double-wing) fractures are possible using this model. A finite-element grid is introduced, with triangular internal elements and quadrilateral boundary elements. The fracture is therefore approximated by a 2D plane with fracture widths defined over this plane.

A skin (S) may be defined for the fracture. The mobility connection factor (M) for a grid block intersecting the fracture with an area of intersection (A) and pressure drop (∆P) between the fracture and grid block is calculated assuming linear flow in the a normal direction (Y direction in equations below) away from both sides of the fracture.

PS

MAQ ∆

+=

1 ∑∆

=p

py krYK

Mµ

8

Internal pressure width equation – the pressure and width within the fracture are related by the following equation.

∫ ′′∇⋅∇−

=− AdwR

GzxP )1()1(4

),)((υπ

σ

22 )()( zzxxR ′−+′−= G is the shear modulus and defined by Young's modulus (E) and Poisson's ratio (ν).

( )υ+=

12EG

Singularities are dealt with analytical expressions on the internal triangular elements. On

the outer quadrilateral elements, it is assumed that aw∝ , where a is the distance from the tip and w=0 on the outermost boundary. The critical width (wc) at which the fracture will just propagate is defined at a small fixed distance (a) from the fracture tip such that the stress intensity at the tip is equal to the critical stress intensity for the rock (KIc).

( )π

υ2

14 aG

Kw Icc

−=



Incompressible fluid fracture flow equation - the flow and pressure within the fracture are related to the fracture leakoff rate.

0)()144

(12

022

=−∆

−+−+−∇− ∫∫∫ f

f

mat Qt

VdAwdAPPMdVhPw ρ

µ Qf is the total fracture injection rate, added at the central node of the finite-element grid. Volumetric storage rate within the fracture is included, reflecting the volume increase

of the fracture since the previous fracture update 0VdAw −∫ ft∆ . Finite-element equation - the fracture width and leakoff equations are written in finite-element form. Finite-element width equation Finite-element leakoff equation

iijij PwW σ−= 0)()

144( 0 =−

∆

−+−+− i

f

ijijj

matjjij

jjij Q

tVwL

PPMLh

PFρ

Solution method - the finite-element equations are combined and solved iteratively for the fracture widths using the Newton Raphson method.

jijiiji FJwwwF 10)( −−=′⇒= λ

where j

iij w

FJ

∂∂

= is the Jacobian and λ is a scale factor found using a line-search

algorithm. The finite-element fracture width solver is supplied with a total rate (Qf), and the shape of the fracture is iterated on until a consistent shape is found with the stress intensity at the fracture tip equal to the critical stress intensity (KIc) for the fracturing rock. The pressure at the centre of the fracture (Pf) is returned and a top level of iteration is performed to ensure that Qf and Pf are consistent with the total well rate (including flow directly from the well into the rock matrix) and the bottom hole flowing pressure (Pwf). Note that for a single wing fracture only the flow from the well completions and one wing of the fracture are injected into the grid. However, the total well rate and Pwf must be defined for both wings of the fracture. The result is that the reported injection rate (well and one fracture wing) may be as little as 50% of the total well injection rate entered in the schedule. Stress calculation - the stress on the fracture surface is calculated from the in-situ stress field (σinsitu) and poro/thermo-elastic stress reductions (∆σP & ∆σT). The in-situ stress is defined by the user as a function of depth or by horizontal layer. The poro and thermo stress reductions take a similar form and the equations used were obtained from Koning [18].

yyinsituTPinsitu σσσσσσ ∆−=∆−∆−= The Goodier (χ) displacement potential is first calculated over the entire FD (finite difference) grid by solving Laplace’s equation.

( ) ( )TAPAE Tp ∆+∆+

−=∇υχ 12



where PPP initial −=∆ and TTT reference −=∆ AP and AT are poro-elastic and thermo-elastic constants. The displacement potential could be used to calculate any component of the stress reducing tensor. The Y direction stress reduction (perpendicular to fracture surface) is then calculated. Similar forms for the stress reduction are performed if the principal stress direction is in the X or Z direction.

( ) TAPAy

ETpyy ∆+∆+

∂∂

+=∆ 2

2

1χ

υσ

This method is effective for thermal fracturing only once the cooled region is at least the same size as the grid blocks being used. An analytical model for fracture initiation and propagation within the fracturing block is used. The simplified model was derived from references [9, 12, 14, 22]. An estimate of the cooled and flooded region radii are calculated from the total downhole volume of injected water (W). Cooled region radius Flooded region radius

ρρ

CpCp

WV wwcooled =

, 3

43

πcooled

cooledV

r = ( )∑−

=r

flood SWV

1φ , 3

43

πflood

flood

Vr =

The pressure and temperature distribution within the cooled and flooded regions are estimated as a function of radial distance (r) from the fracture centre. These simple approximations assume that the temperature and pressure are at a mean between the injection and reference/initial conditions at their respective cooled/flooded radii. Cooled region temperature Flooded region pressure

( )cooled

refinjinjcooled rrTTTT 2

2

2−−=

( ))ln(2

)ln(

w

flood

winitinjinjflood

rrrr

PPPP −−=

The thermo-elastic and poro-elastic stress reductions on the fracture surface within the fracturing block are then calculated, ssuming a ‘circular’ shape function of 0.5. a

( ) ( )[ ]floodinitialPcooledreferenceTyy PPATTA −+−=∆ 5.0σ As the fracture extends beyond its initial block, the stress reductions calculated using the Goodier displacement potentials are interpolated onto the 2D fracture surface. For this interpolation, the stress reduction for the fracturing block is calculated using the simple model above with the cooled temperature set equal to the injection temperature (Tcooled=Tinj), and the flooded pressure set equal to the block average pressure (Pflood=Pblock). Note that this stress reduction is only applicable once the fracture has grown beyond its initial block. Implementation - the two-dimensional finite-element (FE) fracture grid described above is coupled to the three-dimensional finite-difference (FD) main grid. The FE grid is located down the centre-line (constant Y) of the FD grid. The origin of the fracture is located at the centre of a FD grid block. The FE grid has internal triangular and quadrilateral elements on its boundary. The size of the elements may vary as the fracture propagates, although their topology remains constant. Variables are defined at the nodes of the grid. These variables include the fracture width, internal fracture temperature and pressure, fracture surface stress, and derived quantities such as injection water density and viscosity.



The FD grid has hexahedral elements, which have fixed size. Variables are defined at the centre of the grid blocks and represent volume average properties, and therefore are dependent on the grid block dimensions (especially near an injection source, where the spatial variation of physical properties such as pressure and temperature are far from linear). Relevant variables include pressure, temperature, permeability and phase mobilities. Some variables are required on both the FD and FE grids and linear interpolation is used to transfer properties from one grid to the other. The FE grid basis functions are used to interpolate to the FD grid, while interpolation from the FD to the FE grid is performed using bilinear interpolation of four values at FD grid block centres. The temperature within the FE fracture grid is set using the following formula (Meyer).

( ) matrixinj TTT αα −+= 1

( )( )( ) ( )

Ω

−++

+−=

2

21221

211

x

xα

where x is the fractional distance from the centre of the fracture to its tip, and Ω is a user specified heat flux coefficient. Note that the temperature at the FE grid nodes is not a function of the grid shape or area, since x remains constant as the grid grows. The displacement mobility (Σ(kr/µ)) of fluids within the FD grid is calculated using the FD grid temperature, pressure and phase saturations. These are merely the mobilities used for the flow within the FD grid. The previously injected water displacement mobility (calculated as a water blocking fracture skin) uses the internal fracture temperature (FE grid) and FD grid pressure to calculate the water viscosity with the water phase relative permeability end-point. The thickness of the water blocking layer is calculated from the total volume of water injected. Finally, once the fracture shape, pressure and total rate have been calculated, the resulting fracture is connected to the FD grid as a set of ‘connection factors’ and a constant rate injection. The connection factors are calculated by considering the total flow from the FE fracture grid to each FD grid block intersected by the fracture. Once the volumetric rate into each FD grid block is calculated, the connection factor for that block is simply the rate divided by (Pf-Pi), where Pf is the internal fracture pressure and Pi is the FD grid block pressure. Several FD grid time-steps may be taken before the fracture is updated again. The connection factors (and rate) remain constant during these time-steps, resulting in the Pwf increasing until the fracture shape is updated again.



3.11.5 Rock Stress and Elasticity This screen is only available if thermal fractures are present and defines the mechanical properties of the rock to be fractured and the initial in-situ stress. Stress - an initial reference stress and reference temperature are input. All thermal fractures have the same minimum principal stress direction and these fractures will propagate with a plane normal to this direction. The inactive block stress, is the stress that will be applied if the fracture propagates into inactive blocks or outside of the gridded region - this value should be chosen to be large enough to confine the fracture within the grid. Stress properties per layer - the elastic coefficients (young's modulus and Poisson's ratio), elastic stress reduction parameters (poro and thermo-elastic stress reduction) and the critical rock stress intensity (rock strength) are entered layer by layer. The poro-elastic stress coefficient is defined as:

( )υα

−=

1EA PP

and

( )

Ecb

g

P

υα

21−

=

c1−

E is Young's modulus υ is Poisson's ratio Pα is the linear poro-elastic expansion coefficient gc is the matrix grain compressibility bc is the bulk matrix compressibility

The thermo-elastic stress coefficient is defined as:

( )υα

−=

1A TT

E

Tα is the linear thermal expansion coefficient

Select the variable to entered, then select Add to enter data. Different data may be entered for different vertical layers (Z increasing with depth), or the All button may be used to enter the same data for all layers. Select a layer from the layer summary table to modify the data or Delete the layer. The variable will turn from red to green when all of the data is entered, or use the Validate button to check all required data has been input. Stress layering - a term may be added to the reference stress as a function of layer or depth. Enter a top and bottom stress increment at the top and bottom limit of each layer range entered. This may be used to define stress barriers or a vertical stress gradient. The increments need not be continuous (i.e. the bottom of one layer need not be the same at the top of the layer immediately below). Note that if layer stress variations are used, then data for each layer should be included if there are inactive blocks within the grid.



A fracture will tend to propagate from its origin into low stress regions. To minimise large distortions to the finite-element grid the in-situ stress field should be reasonably smooth (and not a high stress barrier) at the fracture origin.



3.12 Well-bore Heating Section This section is only active if the well heating model is selected in the control section. The location of the electrodes (electrode and earth) are defined in the wells section and the voltage to be applied is set in the schedule section. The heating model applies a microwave frequency voltage across two points on a well and calculates the heating effect within the reservoir, which in turn will reduce the viscosity of heavy oils. The voltage generated (V) within the reservoir is calculated on the finite difference grid used for the flow equations by solving Laplace's equation with boundary conditions V=V0 on the electrode, V=0 on the earth electrode and no voltage flux on the boundary of the grid.

( ) 0=∇⋅∇ Vσ The heat supplied to the grid (W) is then calculated from the voltage field.

( )2VW ∇= σ Resistivity - Rw is the water resistivity and is calculated using Arp's law, or input as a table of values as a function of temperature.

( )( )CT

CTRR refrefw +

+=

where C is Arp's constant 6.77F Lithology, saturation and tortuosity - the conductivity of the reservoir (σ) is calculated from Archie's law.

w

nw

m

aRSφ

σ =

where φ is the porosity, a is the lithology coefficient, m is the tortuosity (cementation) coefficient and n is the saturation exponent. The lithology coefficient, tortuosity coefficient and saturation exponent may be entered for multiple regions of the grid, defined by ranges of blocks. See the reservoir section for information on how to add range data. Use the Validate button to check coverage is complete. Archie's law is applied up to the boiling point of water defined by T=0.08329742*P+458.76 (F); once this temperature is reached, the conductance is set to zero and the lithology coefficient set to 1E6 to make the loss of conductance virtually irreversible.



3.13 Initialisation Section

3.13.1 PVT Initialisation This section initialises the PVT for each region defined within the reservoir section. Each PVT region must be non communicating, so that different PVT fluids do not mix within the reservoir. Region List - selects the region to be initialised. All regions must be initialised. PVT Files - select the PVT file to be associated with the current region. The PVT files may be added to or viewed. Generally, the PVT files are entered within the physical section. RS - Gradient - This section is optional and can only be entered if the miscibility option has been set for the PVT. The miscibility option provides the possible for multiple saturated oil tables and a variable initial RS. The initial RS versus depth should be entered within this table. The table is not extrapolated so sufficient depth range should be entered.

3.13.2 Equilibration Initialisation This section initialises the reservoir for each equilibration region specificed within the reservoir section. Each equilibration region must have only one PVT, i.e. equilibration regions must be a subset of the PVT regions. The equilibration includes pressure and contact (oil/gas water/oil or water/gas) depths. The pressure and contact depths are use during the initial reservoir equilibration to assign initial pressures and saturations to all grid blocks. Region List - selects the region to be initialised. All regions must be initialised. Reference depths - one reference pressure is required at a reference depth for each equilibration region. If a gas/oil contact is to be defined then the reference pressure will be the bubble point pressure and does not require to be entered. If an oil/water or gas/water contact depth is defined, then the reference pressure is only required if there is no gas/oil contact. If no contacts are present, then a reference pressure and depth should be entered. Although the reference depth can take any value, it should generally lie within the reservoir. If a GOC is then calculated during equilibration then a gas cap will be present. Thermal gradient - the thermal gradient must be entered for each equilibration region. The reference temperature is the temperature at the temperature reference depth, and the gradient is the initial thermal gradient (increasing with depth). Miscellaneous Thermal Initialisation - the overburden and underburden temperature should also be input, they are not required to be input for each equilibration region. For



an isothermal model the temperatures input should all be the same and the thermal gradient should be zero. Initial wettability - the initial wettability is only required for models with relative permeability desaturation controlled by adsorbed wetting agent. This model is enabled in the control section. A value of -1 corresponds to initial low tension relative permeability, while a value of +1 corresponds to initial high tension relative permeability. Intermediate values are possible and correspond to intermediate (interpolated) desaturation.

3.13.3 Trace Component Concentrations This screen is only available if more than three components (water, oil and gas) are present. The initial concentrations of the trace components in their initial phase (aqueous phase for most components) in mass fraction (component mass per unit mass of host phase). The default is zero concentration. Select a component and enter its initial concentration. The concentration may be defined over a number of range regions or for each grid block. See the reservoir section to get information on how to use the range and array selection methods. Use the right mouse button within the concentration input cell to toggle units between kg/kg and ppm. Electrical neutrality - only used for water chemistry models, where electrical neutrality is required (all ions except e-). Neutrality will be maintained internally by adding or removing the ion pair defined in the water chemistry section, but the electrical neutrality of the initial concentrations of ions entered may be tested and modified (usually by adding or removing Na+ or Cl- ions) using the Calculate button. Alter the tolerance parameter to view the grids with charge imbalances greater than a defined limit. Generally the electric neutrality should be better than 0.05 charge/mole for all grid blocks.

3.13.4 Residual Saturations This section is optional and residual (connate) saturations may be entered. If data is not entered, then the connate saturations will be the minimum saturation entered in the relative permeability section. This data is used during equilibration to set connate saturations and as end points for the capillary pressure tables.



3.14 Schedule Section

3.14.1 Well Schedule This section defines the schedule of well control (production and injection) and the timestep control. It is characterised by a sequence of schedules, that run sequentially until a termination (exit condition) is met, when the next schedule is started. Schedule list - this lists the schedules that will be applied in chronological order. Schedules my be Added, Deleted or Inserted. The Clear button deletes all of the schedules. All of the remaining data entered on this screen is applied separately for each schedule entered. Restart file - a restart file may be generated at regular intervals or not generated at all. If a restart file is generated it may overwrite the previous restart file or be added to a list of restart files. Two types of restart files are possible. The default restart file stores only the data required to perform a restart and should be used under most circumstances. A debug restart file stores all current data structures (including workspace) and may be very large and slow to write; the debug restart files should only be used for the fracture IPR calculations or for diagnostic reasons if requested by Petroleum Experts. It is recommended that for most models the restart files are suppressed. A restart file may generated interactively at any time during a calculation by pausing the simulation and using the menu option Run Simulation|Generate restart step. If the simulation pauses before the current timestep is completed and the restart option is unavailable, use the Run Simulation|Do One step command to complete the timestep. The list of restart files may viewed or deleted using the menu option Project|Edit view project. Timestep size - this section sets the initial timestep control and data entered is dependant on the solver options (IMPEC or implicit) used. The first schedule must have an initial timestep size, this should generally be set to a small value, that will increase as the simulation progresses, this prevents a potentially large number of retrys at the start of the simulation where transient behaviour may be severe. Subsequent schedules may also have initial timesteps set, but this is not necessary. The volumetric error should be set. This is the principal timestep control parameter for the IMPEC solver. It is recommended that a value 1E-4 with 3 iterations or 1E-5 with 5 iterations is used. The material balance volumetric error is defined as the fractional volumetric error at the end of the timestep (i.e. difference between porosity and total volume fraction of fluids present within a gridblock calculated using the pressure and temperature at the end of the timestep). A smaller tolerance for the volumetric error may result in smaller timesteps and require more solver iterations. Material balance iterations are not used with the implicit solver, which only generates material balance errors as a result of explicit thermal effects and incomplete convergence. A a value of 1E-4 is recommended for the implicit solver volumetric error. The saturation overflow limit is only required for the IMPEC solver, and limits saturation



changes near the residual saturations of fluids, preventing undershoot in saturation (saturations below the residual saturation). The default value is 0.01 and may be reduced to 0.001 in cases where very mobile phase saturations are oscillating near the residual saturation (e.g. production below the bubble point). A reduction of this limit will result in smaller timesteps being used and slow the simulation to improve stability. The limit dC option only applies to the IMPEC solver and sets a limit on the fractional change in trace component concentrations within a timestep. This option should generally not be used. It may be applied to reduce timesteps near large concentration gradients to limit numerical dispersion in some models. The maxdt and mindt are minimum and maximum timestep sizes and should not generally be set. Sometimes the maximum timestep size may be set to increase temporal resolution. The limdT and limdP options are limits on temperature and pressure change during a timestep. Again these options should not generally be set, except in cases where rapid changes in temperature or pressure are generating instability in the solutions obtained (e.g. large oscillations in thermal fracture behaviour). Well schedule - data is entered for each well by selecting the well in the list and selecting the well to be shut-in, producing or injecting. For producing or injecting wells, three control mechanisms are available, constant Pwf, constant rate (oil+water, oil, water or gas for producer) or constant Pws (well head pressure). For injection wells, a voidage replacement option is available, where a fraction of the total production voidage for a group of producing wells is specified. For any control mechanism (required for Pws control) a lift or injection curve may be associated with the well. Use the Import button to import the lift curve. Ensure that the curve type (e.g. Oil - naturally flowing for an oil producer or Water injector for a thermal fracture well) matches the well. A label name may also be given to the lift curve. The lift curve should cover the full range of possible condition (GOR, water cut, rate etc.) for the model being investigated. For an injection well, the bottom hole temperature and composition must be entered. If an injection curve generated by PROSPER has bottom hole temperature data, then this may be used by selecting the Use TPD Temp option. Use the Injection button to set the injector as water or gas and set the concentration of any trace components in the injection fluid. Electrical neutrality for ions present in the injection water for water chemistry calculations can be checked. See the initialisation and water chemistry sections for more information. In addition, the relative permeability model for the injection must also be set. The options are: 1. Standard (the default model). In this case, the fluid mobility for a connected grid block is given by the sum over phases of the rel perm for that phase divided by its viscosity. 2. End point. The relative permeability used will be the end point of the rel perm curve for the injected phase. 3. Fixed. Enter a fixed value for the relative permeability that will be used in injection. Note that options 2 and 3 are not available if wellbore friction or well cross-flow are being modeled due to the possibility of multi-component injection.



Use the Well control button to enter constraints on the well. For wells that have completions defined by completion table or vertical well (not multilateral) use the Perforations button to enable/disable or modify the perforation properties. If a wellbore heating model is present, then the heating can be turned on and an electrode voltage applied. If the heating is turned off, then no heating will take place. Exit conditions - the schedule will run until an exit condition is met. If several exit conditions are entered, then the first to be met will end the schedule and the next schedule (if there is one) will be started. Use the left mouse button to select options in the exit condition table. Usually an exit condition will simply be until a given time in days. Cycling of Schedules / Loops - it is possible to set the simulation to cycle over existing schedule entries in the list for a given amount of time or until a constraint is breached. This is potentially useful for applications such as WAG injection or polymer treatments. To create a cycle, select the Add or Insert Sched./Cycle button. If there is more than one schedule prior to this in the list, you will be given the option to create the new schedule as a cycle. Select from the list boxes the start and end points of the cycle. REVEAL does not allow nested cycles, or cycles over schedule entries that have conditional exit conditions (e.g. exit when water cut exceeds a certain value). This is reflected in the validation of the list box entries. You may, however, enter a conditional exit condition on the cycle itself.

3.14.2 Thermal Fracture Schedule This screen sets the thermal fracture update options, and is only displayed if a thermal fracture is present. The update options are applied separately to each schedule and each thermal fracture. The 3D thermal fracture calculation is cpu intensive and the fracture shape should not generally be updated every timestep. If the fracture update is set to off, then no fracture calculation will take place for the current schedule. If it is set to on, then three update criteria are provided. The first criteria to be met will cause the fracture shape to be updated. If an update criteria is left blank then that criteria will not be used. The fracture is automatically updated every time a new schedule is started. If more than one fracture is associated with a well, then a fracture update will be performed including all fractures associated with the well every time any of the fracture update criteria are met. Days - the fracture will be updated at a constant frequency. Timesteps - the fracture will be updated every given number of timesteps. Often recommended to ensure the fracture is updated with some regularity (say every 10 timesteps). Pressure - the fracture will be updated when the pressure at the centre of the fracture changes by a fixed amount. The fracture model calculates the fracture size, grid connection factors, central pressure and injection rate every time it is updated. The well




constraint was used during the fracture update to calculate the fracture pressure, injection rate and connection factors. Therefore, after subsequent normal iterations (without fracture update using the same connection factors), a change in the fracture pressure reflects changes in the reservoir arising from the injection and is a good measure of when the fracture should be undated. This option is recommended with an update pressure of about 50 psi. If the well connected to the fracture is controlled by a constant Pwf, then this update parameter will not result in fracture updates.

4 Grid Refinement This section describes the grid refinement available within REVEAL. The following image is of a grid with five refined regions.

Grid refinement is not available for radial or curvilinear grids, or using the original IMPES solver. Grid refinement is incorporated directly into the solvers with no additional iterations required. Every REVEAL simulation has a master grid, which consists of a topologically regular hexahedral grid, with NX, NY and NZ blocks in the X, Y and Z directions. Therefore a total of NX.NY.NZ grid blocks are defined and may be identified by three integer indices (I,J,K). Some of the master grid blocks may be inactive (reference porosity set to zero). Grid refinement is achieved by defining a set of contiguous (touching) master grid blocks, and then defining refinement parameters for the refined regions. More than one refined region is possible. A maximal range is defined for each refinement, it includes all of the master grid blocks contained within a region (Imin,Jmin,Kmin) to (Imax,Jmax,Kmax), where subscripts min and max are the minimum and maximum master grid indices in each principal direction for the refined region. The following graphic provides an example. Refinement (yellow blocks) is defined for

2 - 6 CHAPTER 4 – GRID REFINEMENT

(1,3,4) to (4,4,4) and (3,5,4) to (7,5,4). The maximal range is (1,3,4) to (7,5,4), (outlined in red).

The following is a list of limitations applied to the selection of refined regions. 1 Refined blocks must consist of a connected (contiguous) selection of master grid

blocks. 2 The boundary of each refined region must either be coincident with the master

grid boundary or be surrounded by master grid blocks, not other refined regions i.e. refined regions must not touch each other. This limitation is currently extended to preclude any two refined regions that have any overlap in their maximal range.

3 Any well or fracture (thermal or producing) present within a refined region must

be completed entirely within the refined region. Wells or fractures may not cross the boundary between refined and unrefined regions.

4 It is best (minimises memory requirements) to specify the refined region in as few

contiguous regions as possible. For example, the above example could have been inefficiently defined block by block as (1,3,4) to (1,3,4) and (2,3,4) to (2,3,4) and (3,3,4) to (3,3,4) and (4,3,4) to (4,3,4) etc.

The extent of the refined region is defined within the reservoir section of the main input script. Any wells or fractures present within a refined region are identified in the wells section of the main input script, and their properties assigned in a separate refinement script. The well control (fixed Pwf, Pws or rate and constraints) for all wells is controlled within the schedule section of the main input script. Once the extent of the refined region and any wells within the refined region are identified within the main input script, the refinement script may be initialised. This is achieved by selecting Project|Create a refinement file... from the main dropdown menu and selecting the refinement to be edited. The refinement input script has the same form as the main input script, using a script generating wizard, except that fewer sections are required. The following pages detail the input options required to be entered in the refinement script. refinement section - defined the degree of refinement reservoir section - initialise physical properties for the refined region aquifer section - add aquifer to refined region


CHAPTER 4 – GRID REFINEMENT 3 - 6

wells section - initialise well location and completion properties within the refined region voltage section - physical properties for well-bore heating model initialisation section - initial component concentrations within refined region

4.1 Refinement Section This section contains two screens and initialises the degree of refinement for a refined region previously defined in the reservoir section of main input script. The first screen is used to enter a label for the refinement. Generally it is best to use a separate label for each refinement datablock. Enter a unique label name and select Edit Refinement. Once the refinement has been entered use the Plot and Validate buttons to check the refinement coverage. The second screen defines the grid refinement. The coverage section at the top of the screen identifies the maximal range for the refinement. The maximal range is listed for each principal direction (X,Y and Z) and covers blocks on the master grid. Only some of the blocks implied by the maximal range may actually be refined (e.g. if the refined region is not a complete hexahedral). The refinement is defined separately in the X, Y and Z directions. Select the direction for data to be entered. X, Y and Z direction data must all be entered. For each direction, data must be entered for each master grid block listed in the coverage, regardless of whether refinement is actually required. Use the Add and Delete buttons to add data for each master grid block in the maximal range. The refinement data is therefore entered for each master grid block in each of the three principal directions. Refinement data takes the form of normalised ratios to subdivide the master grid block. A value of 0.5 will subdivide the master grid block into two equal blocks, values of 0.2, 0.4, 0.6 and 08 will divide the master grid block into five equal blocks, and if no data is entered, then no refinement is recorded. In this last case a warning will be applied, but the simulation may be run. In the following example, the master grid is 15 by 15 by 1 (NX by NY by NZ) and the refined region is identified as including master grid blocks (9,10,1) to (10,10,1) and (9,9,1) to (9,9,1) representing a simple 'L' shape. Therefore, the maximal range in the X, Y and Z directions are (9 to 10), (9 to 10) and (1 to 1). The following refinement data was entered. direction master block refinement X 9 0.5 X 10 0.3 and 0.7 Y 9 0.5 Y 10 0.3 and 0.7 Z 1 0.2, 0.4, 0.6 and 0.8 The table entry for X direction, master grid block 10 is shown below.



This results in a refined grid with NX = 5, NY = 5 and NZ = 5, in an 'L' shape.


CHAPTER 4 – GRID REFINEMENT 5 - 6

4.2 Reservoir Section This section contains five screens and initialises the required reservoir properties for the refined region (porosity, permeability, transmissibility multipliers, net to gross ratio and rock type). Use the Plot and Validate buttons where available to check coverage. See the reservoir input script for the master grid input script for more information entering data on these screens. Porosity - either enter porosities for the refined grid using the same input method as was used for the master grid, or select the Use parent grid values button, which will copy the values from the master grid into the refined grid variables. Permeability - either enter permeabilities for the refined grid using the same input method as was used for the master grid, or select the Use parent grid values button, which will copy the values from the master grid into the refined grid variables. Note that if parent grid properties are required, then these should be set for each of the X, Y and Z directions separately using the tab at the bottom of the screen. Transmissibility - this is optional, the default being unit transmissibility multipliers. Any transmissibility multiplies set for the master grid will be used automatically for refined grid blocks on the boundary of the refined region, but transmissibility multipliers required internally within the refined region should be entered explicitly on this screen. Net to gross - this is optional, the default being unit net to gross ratios. Either enter net to gross ratios for the refined grid using the same input method as was used for the master grid, or select the Use parent grid values button, which will copy the values from the master grid into the refined grid variables. Rock type - enter the coverage of each rock type within the refined grid. Rock types are defined within the main grid script and will be listed in the rock list. Ensure full coverage of the refined region.

4.3 Aquifer Section This section contains one screen and is only available if an aquifer model is specified in the control section of the main input script. See the aquifer input screen in the main input script for more information on the data entry required.

4.4 Wells Section This section contains one screen for well description, and optionally two screens for fracture and mechanical rock properties. The well(s) and fracture(s) (if present) will have already been identified within the wells section for the main grid. The position and properties of the wells/fractures are entered in this section in a similar manner to wells/fractures within the main grid. See the wells section in the main input script for more information on the data entry required.




4.5 Well-Bore Heating Section This section contains one screen and is only available if a well-bore heating model is specified in the control section of the main input script. See the voltage screen in the main input script for more information on the data entry required.

4.6 Initialisation Section This section contains one screen and is only available if more additional components (other than water, oil and gas) are present within the model. The initial component concentrations are entered in a similar way to those within the main grid. See the initialisation screen in the main input script for more information on the data entry required.

5 Menu Commands

This section describes the dropdown menu items on the main REVEAL bar. These options are available when a REVEAL archive has been loaded. If the current window is the 3D graphics window, then the Options, Edit and Results menus are different. The additional dropdown menus Playback and Multi views are also available if the current window is the 3D graphics window (see the graphics help for more information on the 2D and 3D displays). File Options Edit Input Project Run Simulation Results View Window Help Playback (3D only) 5.1 File New open a new REVEAL archive. Open... open an existing REVEAL archive. Close close the current REVEAL archive. Save Project save the current REVEAL archive. Save Project As... save the current REVEAL archive with a new name. Save Scripts save changes made to the input script to the current REVEAL

archive, does not save result data. Import import a script file (*.bpi), PVT or lift curve. It is recommended

that the PVT or lift curve are imported into the required sections (physical and injection schedule) as data is entered.

Print... print the input script or 3D display, depending on which window is active.

Print Preview preview and print the image to printed. Print setup... initialise the printer and associated options. Data Directory set the default directory tree that will be used for Open and

Save operations. (files) list of the previous 10 REVEAL archives, select one to open it. Exit end the REVEAL session.

2 - 5 CHAPTER 5 – MENU COMMANDS

5.2 Options Units set or change the units system to be used, all data in the input

script and wizard will be changed to reflect changes to the units.

Memory Allocation maximum memory before REVEAL swaps refinement grid data to disk. This should generally be left at the default value of 4GB corresponding to the maximum memory allocatable on the windows 32 bit architecture. The operating system will automatically swap data to the disk as required, if the model is larger than the RAM available.

If the current REVEAL window is the 3D graphics then the following menu options are

available. General select variable to be displayed, use cell (recommended) or

point data (only for regular grids) interpolation. Viewing Properties various options to select part of a grid to view, alter

transparency, shrink grid blocks, view wireframe. Scale alter the colour table end points manually, exact end points or

rounded end points, also set linear or logarithmic range. Playback movie playback settings, frequency, range and speed. Preset Options save or load previously saved 3D settings. Reset View rescale the view to show the entire grid. 5.3 Edit Undo undo last change made while editing the input script. Cut delete selected text in the input script. Copy copy selection to clipboard, from any text (input script, debug

etc.). Paste paste clipboard (input script only). Clear delete selected text in the input script. Select All select entire text (input script, debug etc.) Find... find text in an text file (input script, debug etc.). Find Next repeat previous find. Replace... find and replace text in the input script. Goto Section scroll the input script to the selected section. If the current REVEAL window is the 3D graphics then the following menu options are

available. Select Multiple Blocks select some blocks using IJK coordinates to view 2D plot of

variables (against time). Use Results to view the selected blocks.

Unselect All Blocks deselect all blocks selected.


CHAPTER 5 – MENU COMMANDS 3 - 5

5.4 Input Script Wizard start the input wizard, for a single section

or multiple sections. Control start the wizard at a selected screen in

the control section. Reservoir start the wizard at a selected screen in

the reservoir section. Physical start the wizard at a selected screen in

the physical section. Relperm start the wizard at a selected screen in

the relperm section. Aquifer start the wizard at a selected screen in

the aquifer section. Mobility start the wizard at a selected screen in

the mobility section. Phase start the wizard at a selected screen in

the phase section. Adsorption start the wizard at a selected screen in

the adsorption section. Water Chemistry start the wizard at a selected screen in

the water chemistry section. Wells start the wizard at a selected screen in

the wells section. Well-bore Heating start the wizard at a selected screen in

the well-bore heating section. Initialisation start the wizard at a selected screen in

the initialisation section. Schedule start the wizard at a selected screen in

the schedule section. Import from simulator or ASCII file ... import basic geometry and physical

properties. See importing for more details.

Water Chemistry Equilibration Calculation water chemistry calculator - requires water chemistry data to be present in input script

Thermal Fracture IPR Calculation thermal fracture IPR calculator - requires thermal fracture calculation to have saved (debug) restart files

View System Geometry view the entire model topology, including wells and refined regions.

5.5 Project Edit / View Project... view, delete or reimport various files contained in the REVEAL

4 - 5 CHAPTER 5 – MENU COMMANDS

5.6 Run Simulation Select Properties... select the properties and frequency of variables to

be stored for visualisation during and after the calculation.

Start/Resume start a calculation, or resume after a calculation has been paused.

Do One step do one timestep and pause the calculation. Run until run the calculation until a specified runtime is

reached. Pause pause a calculation. Stop stop a calculation, a stopped calculation cannot

be restarted. Restart Simulation... restart a simulation from a restart file. Generate a Restart Step manually generate a restart file, pause (do not

stop) a calculation before using this option. When a simulation is paused, it may not pause at the end of a timestep, to complete the current timestep and allow the restart file to be generated, use the 'Do One step' command. The restart file contains just the data required to restart a simulation.

Generate a Debug Restart Step manually generate a debug restart file, pause (do not stop) a calculation before using this option. The debug restart file contains every data structure (including workspace) used by REVEAL and may be very large: in general the first restart option (above) should be used.

Show Output show/hide the calculation summary window. Show Input show/hide the input script window. 5.7 Results Average Reservoir Results display and plot average and total reservoir properties. Well Results display and plot well properties. Reservoir Graphics start the 3D graphics display. Debug view the debug or water chemistry debug files. These

text files contain diagnostic information not displayed elsewhere.

If the current REVEAL window is the 3D graphics then the following menu options are

available. Results of Selected Cells display and plot the results (2D variable v time) of

selected data cells in the 3D display.


CHAPTER 5 – MENU COMMANDS 5 - 5


5.8 View Toolbar enable/disable the run/graphics toolbar towards the top of the

main REVEAL window. Statusbar enable/disable the status bar at the bottom of the REVEAL

window. Navigator enable/disable the HelpViewer and Navigator window on the

left of the REVEAL window. 5.9 Window Cascade cascade the REVEAL windows. Tile tile the REVEAL windows, best viewed with four windows. Arrange Icons arrange any iconified windows. (windows) bring a selected window to the foreground. 5.10 Help Help Index Start the online help at the first page (Contents). Help Search Start the online help. Script On-Context Brief description of keyword in input script, move the mouse

over the script to view the on-context help. About REVEAL REVEAL version and Petroleum Experts contacts. 5.11 Playback Forward move forward (in time) through previously run case. Backward move backward (in time) through previously run case. Stop stop the 3D movie or stop the 3D update during a calculation. Pause pause the 3D movie or pause the 3D update during a

calculation. Resyncronise after pausing the 3D update during a calculation, reconnect to

the calculation. Goto Timestep goto the 3D results for an input timestep.

6 External Data Import

6.1 Importing Overview This section describes how data can be imported into REVEAL from other simulators or ASCII files. In general, there is no one-to-one correspondence between REVEAL data and that of other simulators, and so a certain amount of post-import manipulation may be required. See the individual sections below for more information. Enter the import facility by invoking Input|Import from simulator or ASCII file. The import procedure consists of an Import Wizard of three screens to take you through the import process. The three steps are: 1. Load the simulation or ASCII case into REVEAL 2. Specify the properties that you wish to import 3. View the import results to check for errors. 1. Loading the case to import Select from the top the format that the data is in. At the moment the following formats are supported: ASCII, Eclipse binary, Eclipse ASCII, VIP MAP, and VIP VDB (split or non-split). The details of this screen obviously depend on the format selected - for more information go to the specific sections in the help. 2. Specifying the import properties Regardless of the import format, the second screen presents the following options: Geometry/Reservoir property data - if you import any of these, you must also import the grid nx, ny, nz dimensions. The sections are as follows: Corner point geometry - this data represents the (xyz) corner points of each vertex of each grid hexahedron, and so specifies the topography of the reservoir system. Data sets are always imported in corner point geometry, regardless of how they were originally generated (for example, as a Cartesian or Radial grid). Porosity - this imports the porosity reference value for each grid block. X-/Y-/Z-Permeability - this imports the directional permeability data for each grid block. Net To Gross This imports the net-to-gross value for each grid block. X-/Y-/Z-Transmissibility multiplier - this imports the directional transmissibility multiplier for each grid block. X-/Y-/Z-Transmissibility - this imports the absolute inter-block transmissibilities for each grid block (in the positive direction, i.e. X+, Y+, Z+)

2 - 9 CHAPTER 6 – EXTERNAL DATA IMPORT

Non-Neighbour Connections - this imports non-neighbour connection data. PV Multiplier - this imports the multiplier applied to the pore-volume. Tabular data - this includes the relative permeability and PVT data tables. See the individual sections on Eclipse or VIP for more information. Rock data - this imports the rock type array and, where possible, rock compressibilities. See the individual sections on Eclipse or VIP for more information. PVT/Equilibration region data - this imports regional data. Restart Data - solution data. It is possible to restart REVEAL from an Eclipse or VIP restart file. Select the required date from the drop down lists. 3. Completing the import A status screen will be displayed: this tells you whether the import of each section has been successful or not. If any section has failed to import, highlight that section in the list and press Details. A message box will be displayed with the reason for the failure. On the right hand side of the status screen are some notes on the data that has been imported. See the individual sections on the data source in question for more information.

6.2 Importing from ASCII A single text file is required for the ASCII data import option. The text file to import should be entered on the first screen in the import wizard. The units for the data should be those currently selected for the REVEAL case. The following keywords and data are required: DIMENSION - followed by the grid dimensions NX, NY and NZ. Either NODES or NODES_8PT keywords are required. NODES - followed by the node coordinates X,Y,Z for each node. There will be a total of (NX+1).(NY+1).(NZ+1) nodes, and they will be ordered cyclically in the X, Y then Z directions with the X direction cycling fastest. NODES_8PT - followed by the node coordinates X,Y,Z for each node. There will be a total of (2*NX).(2*NY).(2*NZ) nodes, a total of 8 corner nodes per block. The 8 nodes for each block are entered sequentially, and the blocks are ordered cyclically in the X, Y then Z directions with the X direction cycling fastest. Therefore there will be 24 coordinates entered for each block. The 8 corner nodes should be ordered as shown below.


CHAPTER 6 – EXTERNAL DATA IMPORT 3 - 9

Z

Y

X

5 6

78

1 2

34

END - marks the end of the file. The following keywords and data are optional for grid block data. For each case there will be NX.NY.NZ entries, and they will be ordered cyclically in the X, Y then Z directions with the X direction cycling fastest. POROSITY - followed by the grid block porosities (inactive blocks have a zero porosity). PERMX - followed by the grid block permeabilities in the X direction. PERMY - followed by the grid block permeabilities in the Y direction. PERMZ - followed by the grid block permeabilities in the Z direction. NETTOGROSS - followed by the grid block net to gross ratios. TRANSX - followed by the grid block transmissibility multipliers in the X direction. The transmissibility multipliers are applied to the block face in positive direction. TRANSY - followed by the grid block transmissibility multipliers in the Y direction. TRANSZ - followed by the grid block transmissibility multipliers in the Z direction. ABSTRANSX - followed by the absolute grid block transmissibility values in the X direction ABSTRANSY - followed by the absolute grid block transmissibility values in the Y direction ABSTRANSZ - followed by the absolute grid block transmissibility values in the Z direction ROCKTYPE - followed by the grid block rock types (integers > 0). PVTREG - followed by the grid block PVT region identifier (integers > 0). EQLREG - followed by the grid block equilibration region identifier (integers > 0). PVMULTIPLIER - followed by the grid block pore volume multipliers.



NNC - followed by the number of non-neighbour connections, followed by the connections themselves in the format: (x1,y1,z1)-(x2,y2,z2), T. See below for an example. A trivial example file is listed below. DIMENSION 2 2 2 NODES 0 0 0 100 0 0 200 0 0 0 100 0 100 100 0 200 100 0 0 200 0 100 200 0 200 200 0 0 0 100 100 0 100 200 0 100 0 100 100 100 100 100 200 100 100 0 200 100 100 200 100 200 200 100 0 0 200 100 0 200 200 0 200 0 100 200 100 100 200 200 100 200 0 200 200 100 200 200 200 200 200 POROSITY 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 PERMX 100 100 100 100 100 100 100 100 NETTOGROSS 1 1 1 1 1 1 1 1



TRANSZ 100 100 100 100 100 100 100 100 NNC 1 1 1 1 2 2 2 0.3 END

6.3 Importing from Eclipse (binary files) There is no one-to-one correspondence between an Eclipse data set and a REVEAL data set. This section describes the special processing carried out by REVEAL to import Eclipse cases.

6.3.1 Data files Required To import the geometrical and physical data (including tabular data), the Eclipse files required are the binary output grid geometry (*.grid or *.grd or *.egrid) file and initialisation file (*.init or *.ini). Formatted version of these files can also be read (.fgr and .fin). See the Eclipse manual if these files have not been generated. To import the restart data (solution and well data) restart file(s) will be required (*.rst or *.unrst). These may be in individual or unified format (this must be specified on the load screen).

6.3.2 Rock Type Arrays and Compressibilities There is no direct analog to the REVEAL rock type within Eclipse. Rock type arrays can be imported optionally from the SATNUM, PVTNUM, or EQLNUM arrays. Rock compressibilities can only be imported if a rock type array is imported from the PVTNUM data in Eclipse. (This is because there should be a rock compressibility value defined for each individual value in the PVTNUM table). The rock compressibility is only available if the rock compaction facility is not being used in the Eclipse data set. Note also that the rock compressibilities are set at a given reference pressure. This reference pressure is not imported into the REVEAL data set and should be set manually if required. This is because the REVEAL reference pressure is used in calculations other than that for rock compression.

6.3.3 Relative Permeabilities In REVEAL, residual saturations, relative permeabilities, and capillary pressures are all dependent on a defined rock type. Each rock type has a set of residual saturations for all phases, and for each set of residual saturations there will be a set of capillary pressure tables and relative permeability tables. There may be more than one set of rel perm tables for each set of residual saturations - indeed, this would be required if you were using directional rel perms. In Eclipse, there is no direct analog to the REVEAL rock type. Arrays such as SATNUM and PVTNUM have similar meanings but are used in different ways within Eclipse (for example, SATNUM is used to specify rel perm tables, PVTNUM is used



to specify separate PVT areas and, optionally, rock compressibility values). For this reason, no attempt is made to assign the imported rel perm data to any particular rock type regardless of whether the rock regions have been defined or not. Each rel perm table (of which there may be several) is assigned to All Rock Types, and it is up to the user after the import has been carried out to assign the rel perms to the required rock region. See the Relperm section on the input wizard for more information on how to do this. For Eclipse two phase systems, REVEAL will generate dummy rel perm tables for the phases that are not present in the simulation. These, of course, will not affect the calculation if the phase in question remains absent.

6.3.4 PVT REVEAL imports oil or gas PVT data from Eclipse. It is not currently possible to import an Eclipse condensate PVT. The Petroleum Experts black oil PVT module consists of two sections: a correlation data set and a tabular data set. If both sets are present, the tabular data is used in preference: the correlations are used to fill in 'GAPs' in the tabular data. When a PVT table is imported from Eclipse, it is expected that all the required tabular data will be present and so there will be no need for the correlation data. Dummy correlation data is generated by the import process: this should not affect the PVT calculations. The REVEAL PVT is always three phase (water, oil, and gas). It is nevertheless possible to import Eclipse 'dead oil' (i.e. no gas phase or no dissolved gas) cases: in these situations a nominal low value for Rs is provided for the saturated tables and no undersaturated tables are generated. When undersaturated tables are used by REVEAL, a controlled miscibility setting must be provided by the user. This determines the rate at which gas will dissolve in the oil if the reservoir is pressurised. The import process sets this value to zero (i.e. gas does not redissolve once liberated): the user is free to change this value after the import. Eclipse PVT tables are isothermal - REVEAL tables are not. It is possible in REVEAL to generate several saturated tables (each with up to 5 undersaturated tables 'hanging' from each) for various temperatures. When the import is carried out, only one saturated table will be generated. The temperature for this table will be the reference temperature for the simulation if specified, or 100 degrees F if not. Eclipse may contain several PVT tables (corresponding to the PVT NUM array). REVEAL only uses one black oil PVT. After the import the status screen will display the PVT files that have been generated by REVEAL. Select the PVT file that you would like to use in subsequent REVEAL simulations. The other PVT files will remain within the archive and can be swapped into the simulation at a later date. When a 'live' oil PVT is imported, you must tell REVEAL the initial bubble point pressure for the reservoir. The is used to calculate the initial Rs from the saturated curves that have been imported.



6.3.5 EndPoint Scaling The enpoint scaling saturation arrays corresponding to the Eclipse keywords SWL, SWCR, SWU, SOWCR, SOGCR, SGL, SGCR and SGU may be imported. Additionally, the relative permeability endpoint scale factors KRW, KRO and KRG may be imported.

6.3.6 Well Data This is imported as a table over completed blocks (ijk) with connection factors as calculated by Eclipse.

6.3.7 Solution Data A REVEAL format restart file will be generated from which simulation restarts can be run. See the Run Simulation menu item for more information.

6.4 Importing from Eclipse (ASCII files) It is currently possible to bring the corner points of an Eclipse grid into REVEAL directly from the Eclipse ASCII deck. Specifically, REVEAL can read the COORD and ZCORN cards and translate the data into a REVEAL datablock. The units for the data should be those currently selected for the REVEAL case. On the first import wizard screen select the Eclipse (ASCII) option from the drop down list. On the resulting screen you must specify the dimensions of the grid that you are about to import, as this data may not be present in the grid file that you specify later on. The table on the lower part of the screen allows you to enter several ASCII files that contain the data for different areas of the grid. The columns of the table are as follows: Box definition - x1, y1, z1, x2, y2, z2, 'all grid': These define the sub-region of the total grid that is to be imported from the ASCII files that follow. Alternatively, click 'all grid' if the ASCII files contain coordinates over the entire grid. ACTNUM file (optional): If you wish, you may specify a file which contains the ACTNUM array for the grid so that only coordinates of active blocks are imported COORD file: This file contains the COORD card of the Eclipse deck. ZCORN file: This file contains the ZCORN card of the Eclipse deck.



6.5 Importing from VIP There is no one-to-one correspondence between a VIP data set and a REVEAL data set. The logic applied during the import process is the same as that applied for Eclipse - see the Eclipse import page for more information. Note that the VIP analogues of PVTNUM, SATNUM, and EQLNUM are IPVT, ISAT, and IEQL.

6.5.1 Data Files Required Two different VIP formats are supported. For any format the import process starts be selecting 'Input | Import from simulator or ASCII file' from the main menu. 1. MAP data In this case the files required are: 1. Core data - .map file (binary) and i.dat file (text) 2. Exec data - .map file and r.dat file - only required for the import of restarts The core data contains the grid properties (topography, petro-physical properties) and tabular data (PVT and relative permeabilities). The exec data contains the solution (restart) data. To load data of this format, select 'VIP MAP format' from the drop down list at the top of the screen. Enter the root directory for the case under 'Directory'. Enter the files to read: the 'core file name' is the ASCII file ending 'i.dat' (the 'i.dat' will be appended automatically). The 'core file MAP name' is the binary file ending '.map'. If you choose to import restart/solution data then check the box marked 'Load Solution/Restart data'. You will then have to fill in equivalent fields to those above for the 'exec' data. 2. VDB data This format can appear in two different but equivalent forms - VDB files from VIP are either 'flat' (the data is archived into a single .vdb file) or 'split' (the vdb file is actually a separate directory under Windows). First determine whether you have a flat or split format VDB file and check the 'Split VDB file' box if it is necessary. In this case the files required are: 1. Study data - .vdb file (binary) 2. Core file - ending i.dat (as above) 3. Exec file - ending r.dat (as above) - only required for the import of restarts To load data of this format, select 'VIP VDB format' from the drop down list at the top of the screen. Enter the root directory for the case under 'Directory'. Enter the vdb file name (the extension .vdb will be appended automatically) and click 'Load'. The cases in the archive will be listed in the box. You must now select the studies from the list for the core data (grid properties) and exec data (solution data). Enter the i.dat (and optionally the r.dat) file name in the fields at the bottom of the




screen. The 'i.dat' and 'r.dat' are appended automatically. Important Note Much of the array data (such as ISAT, IPVT etc) is not placed in the map file by default. To ensure that all the required data is present, include the instruction 'MAP ALL' in the VIP input deck. See the VIP manual for more information.

7 Graphics

7.1 Visualisation Overview Use the P,WR,3D, and Xflow buttons to view the results. The results may also be viewed interactively during a calculation. The P button provides average reservoir properties such as mean phase pressures, saturations and volumes. These data may be viewed, plotted and printed, or copied to the clipboard for import into another application. The WR button provides well results data, including instantaneous and cumulative rates, GOR, water cut and phase pressure and saturation data at well blocks. The 3D button provides a three dimensional display of the fluid properties that were selected for display (Run Simulation|Select Properties...). Note that the variables and frequency with which they are to be stored must be set before a calculation is run. It includes graphical representation of wells, completions and fractures. The Xflow button provides a three dimensional schematic of the wellbore with the intersected grid blocks. If a wellbore model has been set up in the input deck this view will display the results of the wellbore calculations, i.e. the calculated properties at the nodes and in the tubing. It also provides information on any crossflow that may be occurring. The 3D graphics requires the display driver to be operating with a screen area of at least 1280*1024 pixels and 16 bit (high colour) resolution. If the current window is the 3D graphics window, then the dropdown menus Options, Edit and Results are specific to 3D graphics. The additional dropdown menu Playback is also available if the current window is a 3D graphics window .

7.1.1 Interaction with the 3D Visualisation Windows Rotation - to rotate the view, click the left button of the mouse and drag the mouse in the direction that you would like to rotate. The rotation axis is perpendicular to the direction of mouse movement and in the current focal plane of the view. - to rotate the view about an axis normal to the screen and passing through the current focal point, press the ctrl key with the right mouse button. The speed of rotation is proportional to the distance from the centre of the screen to the mouse position. Zooming - area ('rubber band') zooming can be achieved by holding down the ctrl key while dragging the mouse with the left mouse button depressed. - alternatively, click on the magnifying glass icon (+) in the toolbar and then click and drag across the area to be zoomed into. - a single click with the magnifying glass icon (+) selected will perform a zoom in of a fixed ratio, centred on the position at which the mouse was clicked.

2 - 4 CHAPTER 7 - GRAPHICS

- similarly, a single click the the magnifying glass icon (-) selected will perform a zoom out of a fixed ratio, centred on the position at which the mouse was clicked. Panning - panning can be achieved by holding the shift key while dragging the mouse with the left button depressed. Essentially, the viewing position is shifted parallel to the focal plane of the view, although the effect is to 'drag' the objects from one position to another. Other controls - F5 will reset the display to the initial size, such that the entire system is visible. - W acts as a shortcut to present a wireframe mode view of the entire system. - S acts as a shortcut to present a surface mode view of the entire system. 3D visualisation preferences To invoke the preferences screen from any 3D view, select Options | Preferences... from the main menu. This is also accessible from a right click. The screen is divided into two tabs: Lookup tables - the colour tables for different view properties can be changed. The default is for a basic RGB graduation for pressure and default properties, with phase saturations represented by a single colour with a graduation in colour saturation. To change a lookup table, adjust the palette at the top of the screen to the starting (low value) colour and click on the button at the left hand side of the lookup table that you are changing. The table will change to reflect the selection. Then perform the same action for the ending (high value) colour. The lookup table is calculated by interpolating HSV values between the top and bottom of the table. View properties: - the perspective mode determines whether the view is generated with parallel rays or by applying a false (but perhaps more visually pleasing) perspective based on a view position. - the background colour can be changed by adjusting the sliders on the colour palette. - the mouse rotation sensitivity governs how quickly the view is rotated for a unit movement of the mouse position. Main 3D View Functions The graphics toolbar (below the main toolbar at the top of the REVEAL screen) contains most of the functions that are available from the visualisation window. Some functions are different depending on whether the current view is a 3D view or a wellbore (Xflow) view - these differences are detaield below. Going from left to right across the toolbar: Animation buttons:

Advance the view by one step

Animate the view results from the current step

Advance to the last step

Stop an animation ... with similar buttons performing the reverse procedures...


CHAPTER 7 – GRAPHICS 3 - 4

If a simulation is currently being run, this pauses the graphics (i.e. disengages the graphics from the current run)

If a simulation is currently being run, this re-synchronises the graphics with the run (if the graphics had previously been paused)

Selection buttons:

(3D) Allows cells to be selected. As the mouse is moved over the view, the grid cells below the mouse pointer are highlighted. Click on the required cell to select it - 2D results for this cell can then be viewed by invoking Results | Results of selected cells. Many cells can be selected at once.

(Xflow) Allows results for an item in the view to be displayed at an instant in

time. Move the mouse over the item in question and a window will appear giving the current timestep results for the item. If the view contains grid blocks and wellbore items (tubing and nodes) it can be difficult to select a tubing node rather than a grid block. To get round this, invoke the 'Object Properties' screen (either from the toolbar or Options | Viewing properties) and change the 'pick mode' selections.

(3D only) Unselects all cells.

(3D only) Invokes a screen to allow cells to be selected from IJK lists.

Zoom buttons: These allow the view to be zoomed in or out, as described above. Results:

(3D) Invokes a screen with the time dependent results for the currently selected set of cells.

(Xflow) Invokes a screen with time dependent results for all the items in the

system (grid blocks, calculation nodes, and tubing) Property buttons:

(3D) Invokes a screen allowing you to change the variable that is currently displayed. It also allows you to view point scalar data rather than cell data. The point data is interpolated from the grid block corners and weighted by the inverse square of the distance to the corners.

(Xflow) Invokes a screen allowing you to change the variable that is currently

displayed for the different object categories. The tubing variable can be set to the calculated fluid rate, or alternatively can be set to display simple interpolated values between the end nodes.

(3D) Invokes a screen that allows the properties of the objects in the view to be altered, e.g. the transparancies or visibilities of the grid objects, and whether to display surface or wireframe data. It is also possible, from this screen, to display subsets of grid cells (normally a plane of blocks in X, Y, or Z) and to change the z scale factor.

(Xflow) In addition to setting general object properties, the 'pick mode' can be

changed. The pick mode determines those objects that are candidates for


4 - 4 CHAPTER 7 - GRAPHICS


picking when 'selection mode' is entered. It may be desirable, for example, to remove grid blocks from the pick mode to allow easier picking of nodes and inflow objects.

Scale. Sets the ranges of values that are mapped to the colour tables.

Playback. Sets various playback / animation options. The next field is the Xflow view well selection list box. Select from the drop down list the well data that you wish to view.

This is equivalent to pressing F5, i.e. the view is reset to the maximum zoom. Other functions Once a view has been created, its properties may be saved and reopened later. Use Options|Preset Options|Save File and Options|Preset Options|Load File to achieve this. Enter a name for the view, select the properties to be saved (usually All) and select OK. Note that the REVEAL archive1 must be saved for the view to be saved permanently. Many of the REVEAL example cases have default views saved.


8 DeBug Output The debug output is contained within the REVEAL archive1 as a text file. It may be viewed during or once a simulation has been completed using the menu command Results|Debug|Debug Simulation. Note that the menu command Results changes its function when the active REVEAL window is the 3D display. Additional debug output is created during a water chemistry calculation and can be view using the menu command Results|Debug|Debug Water Chemistry. The finite element fracture variables are also output in detail to the debug output file. The debug output file contains much general model information not displayed elsewhere. The most useful information it contains falls into three categories. Initialisation data - including the analytical well PI calculation results and post equilibration saturations and pressures for each block. Runtime data - includes timestep data which gives information on the number of iterations (IMPES and implicit formulations), what variable is controlling the timestep, maximum volumetric error and maximum variable changes. See the table at the end this page for information on the timestep control summary (8 digit summary at the end of each completed timestep). Additionally, fracture data for the finite element grid is output in detail for each thermal fracture calculation. Completion data - includes error and warnings at the end of a calculation, total runtime statistics and some information on the final state of the calculation.

Digit Meaning Character Description 1 Retake & ‘on-hold’ -

# * h

OK Timestep to be reduced Timestep to be retaken Timestep to be unchanged

2 Timestep limited - r v t c p i f d e

None Max growth rate Volumetric flow limit Temperature constraint Concentration constraint Pressure constraint Injection schedule Fracture update Implicit solver (diverging Newton steps) Implicit solver (estimated next timestep)

3 Cause of retake - n v m p t

No retake Negative concentrations Volumetric flow limit Material balance constraint Pressure constraint Temperature constraint


2 - 2 CHAPTER 8 – DEBUG OUTPUT


c d

Concentration constraint Implicit solver (diverging)

4 Cause of ‘on-hold’ - m p t c d

Not ‘on-hold’ Material balance constraint Pressure constraint Temperature constraint Concentration constraint Implicit solver (diverging)

5 Limit reached - l u

Not limited Minimum timestep limit Maximum timestep limit

6 Volumetric flow c s w

Total volume inflow (Courant) Mobile phase saturation undershoot Total well inflow/outflow

7 Implicit solver i l d c p s

Pre-conditioner failure Linear solver failure Newton steps diverging Newton steps not converged Pressure change too large Saturation change too large

9 Engineering

9.1 Introduction This section provides descriptions of the reservoir engineering models and solution methods provided by REVEAL that are not described elsewhere in detail. It concentrates on the underlying physical processes and the numerical approximations used to model them. Phases and components definitions of phases and components within REVEAL Transport equations flow equations applied for IMPES and implicit solver

options Dispersion and diffusion trace component flow Thermal equations heat transport applied for IMPES and implicit solver

options

9.2 Phases and Components Phases - a phase is a distinct (immiscible with other phases) fluid. The three phases aqueous, oleic and gaseous are always possible, but may not be present. Phases are characterised by their saturations (volume fraction of pore volume), which sum to one. If the surfactant component is present, then a middle (micro-emulsion) phase may be present between the aqueous and oleic phases. The transport equations are formulated on the basis of phase properties (saturation, density, relative permeability, viscosity and capillary pressure). Components - a component is a chemical species (or mixture of chemicals) that forms the basis of the fluids present. The components water, oil and gas are always present within all models. Components are partitioned within phases. For an oil reservoir, the water component is present within the aqueous phase, the oil component present within the oleic phase and the gas component present within the oleic and gaseous phases. For a condensate reservoir, the gas component is only present within the gaseous phase, while the oil component is partitioned between the oleic (dropout) and gaseous phases. For a dry gas reservoir, both oil and gas components are partitioned within the gaseous phase (no oleic phase). If a 4th micro-emulsion phase is present, then the water, oil and gas components will be partitioned between their original phase and the micro-emulsion phase. Only components that affect the phase densities are considered volumetric. These components include water, oil, gas, non-reservoir injected gas, surfactant, and the two possible alcohol components. All other components are non-volumetric, they only contribute to the transport equations by modifications to phase mobilities, or not at all for tracer components.

2 - 5 CHAPTER 9 - ENGINEERING

9.3 Transport Equations Transport equations - laminar flow through a porous medium is assumed, and quantified by Darcy's equation in oilfield units for each phase (p).

−+∇−=

144.

6.3266h

PcPkrk

q ppw

p

pp

ρµ

where qp is the Darcy velocity (ft/d) k is rock permeability (D) krp is phase relative permeability µp is the phase viscosity (cp) ρp is the phase density (lb/ft3) h is the depth (ft) Pw is the water phase pressure (psi) Pcp is the phase capillary pressure (psi) The accumulation of mass (mp) of a phase into a control volume (V) is then defined by a summation of fluxes over the the surface area (A).

( )Aqm ppp ρ⋅−∇= The accumulation of mass into volume Vp is then subject to phase compressibility (cp) and rock compressibility.

PPV

Vc p

p

p

pp ∂

∂=

∂

∂−=

ρρ11

( )t

Vm ppp ∂

∂=

ρ

pp VSV φ= Equating these accumulation terms leads to a material balance equation.

( ) ( ) 0=⋅∇−∂

∂Aq

tS

V pppp ρ

φρ

1=∑ pS This differential equation is non-linear and also requires to be discretised both spatially and temporally before it can be solved numerically. For all solution methods, a harmonic average1 permeability (k) is used at grid block faces, while different upstream weightings for face mobilities (Mp) are available for the implicit/explicit solver options. A face volumetric transmissibility (Tp) is also defined, resulting in a final version of the transport equation. 1The harmonic average is the 'resisters in parallel' average. The following averages are defined for a variable x, with weightings w. arithmetic average harmonic average

∑∑=

i

ii

wwx

x

∑∑=

i

i

i

xww

x


CHAPTER 9 – ENGINEERING 3 - 5

p

pp

krM

µ=

pp AkMT 3266.6= ( )

0144

=

−+∇⋅∇+

∂

∂ hPcPT

tS

V ppwpp

pp ρρ

φρ

Implicit solution - for this solver option, the transport equation is solved with respect to the oil phase pressure (Po) and the three phase saturations (Sp). A single point upstream weighting is applied for mobility and density. IMPES solution - for this solver option, the transport equation is solved in two steps using a total volumetric implicit pressure (explicit transmissibility and capillary pressure) solution to calculate the water phase pressure (Pw) and an explicit concentration (saturation) update using the calculated phase Darcy velocities. The implicit pressure solution uses a total compressibility term (c) including rock and fluid phase compressibilities.

0144

2 =

−+∇+

∂∂ ∑

p

ppwp

w hPcPT

tP

Vcρ

−+∇−=

144h

PcPAT

q ppw

pp

ρ

The explicit nature of this formulation allows more sophisticated upstream weightings for phase transmissibility, trace component concentrations and density, reducing numerical dispersion, but more severe limitations on the time-step size are required to ensure stability. Trace component concentrations are updated using the phase Darcy velocities and upstream weightings for component volume fractions. For more information on the solver options see the control section of the input wizard help.

9.4 Dispersion and Diffusion The dispersion and diffusion of trace components within phases is optionally available in the physical section, and is only possible using the IMPES solver option. The IMPES solver, first solves an implicit pressure model, resulting in phase Darcy velocities (qp) between neighbouring grid blocks. The transport of trace components in the explicit phase of the solve, is calculated by calculating mass fluxes of the trace components (Fc). If dispersion and diffusion are not present, then the trace component mass fluxes are calculated using upstream weighting of component concentrations within associated phases (Ccp) and the phase Darcy velocities.

∑=p

cppcc CqF ρ

If dispersion or diffusion are present, then the trace component mass fluxes are modified by calculating a dispersive flux (Gcp), dependent on the component


4 - 5 CHAPTER 9 - ENGINEERING

concentration gradient. Note that trace components are only partitioned within one phase (unless a middle phase micro-emulsion is present) and the component density is equal to its host phase density (i.e. volumetric and mass fractions of component within phase are equivalent).

( )∑ −=p

cp

cppcc GCqF ρ

( ) ( )( )cppTpLpp

pcpTpp

cpp

cp Cq

q

qCqDSG ∇⋅−+∇+= αααφ

where Dcp are component diffusion coefficients, and αLp and αTp are longitudinal and transverse phase dispersion lengths. Numerical dispersion may be minimised by selecting the fct/2-point upstream weighting for component concentration in the control section of the input script.

9.5 Thermal Equations For both the IMPES and implicit formulations, the thermal heat transport equations within REVEAL are applied after the pressure and component concentrations have been updated. Therefore, the phase Darcy velocities between grid blocks is known and the heat transport is calculated explicitly with respect to the flow and pressure. Convective heat transport (heat flowing with the fluid) and optionally conductive heat transport (heat flowing with thermal gradient) are included. The accumulation of heat (J) into a control volume (V) is defined by a summation of conductive and convective fluxes over the surface area (A). The thermal conductivity is a harmonic average2 between adjacent blocks, and includes contributions from the rock and all phases present. The phase heat capacities (Cpp) are those calculated at the end of the timestep. In oilfield units, J has dimensions of (BTU/d).

( ) ( )∑∇−∇⋅−∇=p

ppp ATCpqTAkJ ρ

The accumulation of heat into volume V then results in a temperature change (heat transport equation). ( ) 0=−∂

∂ JtHT

2The harmonic average is the 'resisters in parallel' average. The following averages are defined for a variable x, with weightings w. arithmetic average harmonic average

∑∑=

i

ii

wwx

x

∑∑=

i

i

i

xww

x


CHAPTER 9 – ENGINEERING 5 - 5


where H is the total heat capacity (BHU/F) of the control volume V (grid block), calculated before and after the flow is updated (beginning and end of timestep). For the IMPES formulation, or the implicit formulation when the CLF3 limit is selected, the heat transport equation is solved explicitly for temperature (T) i.e. J is first calculated, then T is updated. This has the advantage that upstream weighting models (fct/2-point recommended) may be used for convective thermal fluxes, reducing numerical dispersion. The upstream weighting is the method used to estimate the heat capacity (ρp.Cpp) at the interface between adjacent blocks. For the implicit formulation, the CLF limit is not observed, and the explicit method used for the IMPES formulation is unstable. Therefore, the temperature is calculated by implicitly solving the heat transport equation in one step, a 1 point upstream weighting is used for calculating convective thermal fluxes. Heat source terms are also added for well-bore heating, well inflow/outflow and overburden/underburden heat flow.

3Courant Flux Limit (CFL) ensures that no more than one pore-volume throughput through any grid block occurs within a time-step.

Appendix A - References

A.1 References 1 Van Everdingen A.F., Hurst W., The Application of the Laplace

Transformation to Flow Problems, Trans. AIME 156, 1949. 2 Carter R.D., Tracy G.W., An Improved Method for Calculating Water Influx,

SPE 1626-G, 1960, 3 Geertsma J., deKlerk F., A Rapid Method of Predicting Width and Extent of

Hydraulically Induced Fractures, SPE 2458, 1969. 4 Wiliams B.B., Fluid Loss from Hydraulically Induced Fractures, SPE 2769,

1970. 5 Todd M.R., Longstaff W.J., The Development, Testing and Application of a

Numerical Simulator for Predicting Miscible Flood Performance, SPE 3484, 1972.

6 Cinco-Ley H., Ramey H.J., Miller F.G., Pseudo-skin Factors for Partially-

Penetrating Directional-Drilled Wells, SPE 5589, 1975. 7 Peaceman D.W., Interpretation of Well-Block Pressures in Numerical

Reservoir Simulation, SPE 6893, 1978. 8 Clifton R.J., Abou-Sayed A.S., On the Computation of the Three-Dimensional

Geometry of Hydraulic Fractures, SPE 7943, 1979. 9 Zolotukhin A.B., Analytical Definition of the Overall Heat Transfer Coefficient,

SPE 7964, 1979. 10 Vinsome P.K., Westerveld J., A Simple Method for Predicting Cap and Base

Rock Heat Losses in Thermal Reservoir Simulators, J. Can. Pet. Tech., 1980. 11 Clifton R.J., Abou-Sayed A.S., A Variational Approach to the Prediction of the

Three-Dimensional Geometry of Hydraulic Fractures, SPE 9879, 1981. 12 Perkins T.K., Gonzalez J.A., Changes in Earth Stress Around a Wellbore

Caused by Radially Symmetrical Pressure and Temperature Gradients, SPE 10080, 1984.

13 Peaceman D.W., Interpretation of Well-Block Pressures in Numerical

Reservoir Simulation with Nonsquare Grid Blocks and Anisotropic Permeability, SPE 10528, 1983.

14 Perkins T.K., Gonzalez J.A., The Effect of Thermoelastic Stresses on

Injection Well Fracturing, SPE 11332, 1985. 15 Prouvost L.P., Pope G.A., Rouse B., Microemulsion Phase Behaviour: A

Thermodynamic Modeling of the Phase Partitioning of Amphiphilic Species,

2-2 APPENDIX A - REFERENCES


SPE 12586, 1985. 16 Prouvost L.P., Satoh T., Sepehrnoori T., Pope G.A., A new Micellar Phase-

Behaviour Model for Simulating Systems with up to Three Amphiphilic Species, SPE 13031, 1984.

17 Christie M.A., Bond D.J., Multidimensional Flux-Corrected Transport for

Reservoir Simulation, SPE 13505, 1985. 18 Koning E.J.L., Fractured Water Injection Wells - Analytical Modelling of

Fracture Propagation, SPE 14684, 1985. 19 Vandamme L., Jeffrey R.G., Curran J.H., Pressure Distribution in Three-

Dimensional Hydraulic Fractures, SPE 15265, 1986. 20 Meyer B.R., Heat Transfer in Hydraulic Fracturing, SPE 17041, 1989. 21 Clifton R.J., Wang J-J., Multiple Fluids, Propant Transport, and Thermal

Effects in Three-Dimensional Simulation of Hydraulic Fracturing, SPE 18198, 1988.

22 Detienne, J-L., Creusot M., Kessler N., Sahuquet B.,Bergerot J-L., Thermally

Induced Fractures : A Field Proven Analytical Model, SPE 30777, 1995. 23 Parkhurst D.L., User's Guide to PHREEQC-a Computer Program for

Speciation, Reaction-Path, Advective-Transport, and Inverse Geochemical Calculations, US Geological Survey, 1995.

Appendix B – Sample Files

B.1 Sample Files The following is a brief description of the sample files included with the installation. Depending on where REVEAL was installed, they may be found in C:\Program Files\Petroleum Experts\IPM #\Samples\reveal, where # is the IPM (Integrated Production Management) release version number. Fracture examples thermal_fracture.rvl producing_fracture.rvl Water chemistry examples water_chemistry.rvl watchem_curvilinear.rvl - simple Barite production example using curviliear grid. souring.rvl - simple souring example with Barite precipitation. souring_simple.rvl - simple souring example without minerals. scale_inhibitor.rvl - simple souring example with Barite scale inhibition. Chemical additive examples surfactant.rvl - surfactant micro-emulsion phase created. foam.rvl - simple foamer treatment to reduce gas coning. gel.rvl - simple isothermal gel/polymer injection affecting mobilities. Grid geometry examples radial.rvl - radial grid. curvilinear.rvl - repeated 5 point well curvilinear grid. corner.rvl - simple corner point example with analytical multi-lateral well. Aquifer examples aquifer_radial.rvl - simple grid with a radial aquifer. Gas-Condensate examples condensate.rvl - example with a condensate PVT description. dry_gas.rvl - example with a dry gas PVT description. Thermal examples wb_heating.rvl - example heating a heavy oil to reduce viscosity. Openserver examples Well_control.xls - example of the use of the OpenServer to automate well control

(THP and injection temperature). Batch_matching.xls - example of the use of the OpenServer to automate batch

calculations for sensitivity/matching analysis. Well_production.xls - example of the use of the OpenServer to report block by block

well production rates. Step-by-step examples example1.rvl - step by step example creating a simple model from scratch.

2-2 APPENDIX B – SAMPLE FILES


Implicit solver examples producing_fracture.rvl Grid refinement examples producing_fracture_refine.rvl

Appendix C – FQA’s

C.1 Frequently Asked Questions Q1 Data lost when wizard ended.

Q2 Oscillations in results.

Q3 Copy and paste between wizard screens and other applications.

Q4 Which files do I require to import an Eclipse data set.

Q1: Data lost when wizard ended.

A1 Data is held in temporary files until the archive is saved using the Save menu option. The temporary files in the archive may be viewed using the menu option Project|Edit / View project, or by opening the REVEAL archive (*.rvl) using winzip. The principal temporary file is the input script, which contains the changes made using the wizard.

Changes made using the wizard will be updated to the input script if the wizard is ended using Finish, or if the wizard ends because Next was selected and no more wizard screens are available (either the end of the schedule section or the end of the current section is only one section is being edited with the wizard). In this case, the data in the input script is over-written and previous data will be lost.

If the wizard is ended using the Cancel button, then the changes made using the wizard are not saved to the input script (these changes are lost).

Q2: Oscillations in results.

A2 Oscillations are generally caused by incomplete convergence of solutions (material balance errors) or time-steps that are too long.

To improve convergence, use the implicit solver option where possible (especially for cases with only 3 components, water, oil and gas). Using the implicit solver, the convergence criteria may be tightened by reducing the pressure, saturation and implicit well limits from 0.01 (default) to 0.001.

Using, the IMPES solver, material balance may be improved by reducing the volumetric error from 0.0001 to 0.00001. More iterations may be required to achieve the reduced material balance error so also increase the number of iteration from 3 to 5. Also, the saturation underflow limit may be set to 0.001 to minimise oscillation in gas flow near its residual saturation.

Also using the IMPES solver, under some circumstances, the timestep may also be controlled by setting a maximum limit on pressure, temperature or component concentration change.

2 - 2 APPENDIX C – FREQUENTLY ASKED QUESTIONS


If tabular PVT data is being used, check that it covers the full range of pressures and temperatures, and has no discontinuities. If a matched (or unmatched) correlation PVT data is being used, it may be useful to convert it to tabular format using the option Calc Tables found on the PVT input screen (see physical properties section).

Check relative permeability and capillary pressure data are reasonable (smoothly monotonic).

Q3: Copy and paste between wizard screens and other applications.

A3: Data may be copied and pasted between the REVEAL wizard screens and other applications such as EXCEL. To copy from REVEAL, select the region to be copied and use Control+C to copy and Control+V to paste the selection. Alternatively, entire sections may be copied using options obtained using a right mouse click. To paste data into REVEAL, the size (number or columns) of the region to be pasted must match that required by REVEAL. The simplest way to check the column format required is to select and copy a blank region from REVEAL into EXCEL (for example).

Q4 Which files do I require to import an Eclipse data set.

A4 See the external data import section.

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