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2013 IHS. All Rights Reserved. All trademarks belong to IHSor its affiliated and subsidiary companies, all rights reserved. www.ihs.com

IHS

PERFORM v8.0Technical Reference Manual

July 2013

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PERFORM v8.0 Technical Reference Manual

July 2013

201 3, IHS and its affiliated and subsidiary companies, all rights reserved. All other trademarksare the property of IHS and its affiliated and subsidiary companies.

This product, including software, data and documentation are licensed to the user for its internal business purposes only and may not be disclosed, disseminated, sold, licensed, copied,reproduced, translated or transferred to any third party.

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July 2013 i

Contents

Table of Figures ............................................................................................................................................................i

System Analysis Overview .......................................................................................................................................... 1 Using System Analysis ................................................................................................................................................. 5

General Analysis Procedure ..................................................................................................................... 5

Applying System Analysis ................ ................. .................. ................. .................. ................. .................. 7

Modeling Worst-Case Discharge Scenarios ............................................................................................. 9

Introduction ........................................................................................................................................... 9

Setup .................................................................................................................................................... 9

Fluid Properties .................................................................................................................................... 9

Reservoir Data .................. ................. ................. .................. ................. ................. .................. ............ 9

Completion Data ................................................................................................................................... 9

Pressure/Temperature Calculation Control Process .......................................................................... 10

Wellbore Data ..................................................................................................................................... 10

Flowline .............................................................................................................................................. 10

Sensitivity Analysis ............................................................................................................................. 10

Final Steps .................. ................. .................. ................. ................. .................. ................. ................ 11

Reservoir Skin......................................................................................................................................... 11

Completion Effects .................................................................................................................................. 12

Differential Graph ............................................................................................................................... 13

Perforation Shot Density .................................................................................................................... 14

Perforation Interval ............................................................................................................................. 15

Tubing Size ............................................................................................................................................. 16

Surface Pressure .................................................................................................................................... 18

Fluid Property Calculations ..................................................................................................................... 19

Reservoir Component ................................................................................................................................................ 21

Vertical IPR Types .................................................................................................................................. 22

User Enters PI .................................................................................................................................... 22

Vogel/Harrison (1968) ........................................................................................................................ 23 Vogel corrected for water cut ............................................................................................................. 26

Darcy .................................................................................................................................................. 26

Jones et al. (1976) .............................................................................................................................. 32

Jones 4-Point Test and Jones Enter a and b ................................................................................ 34

Back Pressure Eq (1930) and Back Pressure 4-Point Test ............................................................ 35

Backpressure Four-Point Test (gas wells only) ................. ................. ................. .................. ............. 36

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Transient Flow Equation ..................................................................................................................... 36

Fractured Well .................................................................................................................................... 38

Fractured Well Rueda et al (2005) .................................................................................................. 43

Fractured Well Chase et al (1993) .................................................................................................. 45

Datafile 2 Col ASCII ......................................................................................................................... 48 Guo-Schechter (1997) ........................................................................................................................ 48

Darcy Frack Pack (1996) ................................................................................................................. 49

Guo (2001) - Wellhead Test ............................................................................................................... 51

Chase et al. (1993) - 1pt test .............................................................................................................. 53

Future IPR curves............................................................................................................................... 54

Horizontally Completed Wells ................................................................................................................. 56

Horizontal IPR Types .............................................................................................................................. 60

Giger et al. (1984)............................................................................................................................... 61

Economides et al. (1991) ................................................................................................................... 64 Joshi (1988) ........................................................................................................................................ 66

Renard and Dupuy (1991) .................................................................................................................. 69

Kuchuk (1988) .................................................................................................................................... 71

Babu and Odeh (1989) ....................................................................................................................... 74

Goode and Thambynaya (1987) ........................................................................................................ 78

Guo & Evans (1993) - Horizontal well with multiple fractures ............................................................ 81

Coalbed Methane (CBM) - Thungsuntonkhun and Engler (2001) .......................................................... 84

Coning/Cresting ...................................................................................................................................... 87

Total Skin Factor ..................................................................................................................................... 93

Partial Penetration Skin Factor ................ ................. .................. ................. ................. .................. .... 94

Geometrical Skin Factor ..................................................................................................................... 94

Acid Treatment.......... .................. ................. ................. .................. ................. ................. .................. .... 95

Completion Stimulation Performance Evaluation After Acid Treatment ................. .................. .......... 95

Correlations ........................................................................................................................................ 96

Correlations To Calculate Bottomhole Pressure (When Not Given) ............................................................................... 96

Correlations To Calculate Simulated Pressure (From Reference 3) ................................................................................ 97

Correlations To Calculate Skin Factor (From Reference 1) ............................................................................................ 98

Completion Component .......................................................................................................................................... 101

Open Hole Completion ......................................................................................................................... 101

Open Perforation Completion ............................................................................................................... 102

Stable Perforation Completion .............................................................................................................. 104

Collapsed Perforation Completion ........................................................................................................ 108

Gravel Pack Completion ....................................................................................................................... 110

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Gravel Pack Beta Turbulence Factor ............................................................................................... 113

Gravel Pack Open Hole Completion ..................................................................................................... 114

Gravel Pack Open Perforation Completion .......................................................................................... 115

Gravel Pack Stable Perforation Completion ......................................................................................... 115

Flux Calculation .................................................................................................................................... 115 Gravel Pack Collapsed Perforation Completion ................................................................................... 117

Perforation Gun Database .................................................................................................................... 117

Sand Production Prediction .................................................................................................................. 120

Wellbore and Flowline ............................................................................................................................................ 122

Oil Well Vertical Flow ............................................................................................................................ 123

Category A .................. ................. .................. ................. ................. .................. ................. .............. 124

Category B .................. ................. .................. ................. ................. .................. ................. .............. 124

Category C ....................................................................................................................................... 124

Gas Well Vertical Flow .......................................................................................................................... 127 Oil Well Horizontal Flow ........................................................................................................................ 128

Gas Well Horizontal Flow ..................................................................................................................... 130

Pressure changes in Compressors and Pumps ................................................................................... 132

Downhole Pumps .................................................................................................................................. 133

Performance Curve Method ............................................................................................................. 133

Electrical Submersible Pumps ESP ............................................................................................................................ 133

Progressing Cavity Pumps PCP ................................................................................................................................. 134

Horsepower Conversion Method ...................................................................................................... 136

Electrical Submersible Pumps ESP ............................................................................................................................ 136 Progressing Cavity Pumps PCP ................................................................................................................................. 136

User Added Pumps ..................................................................................................................................................... 137

How Gas Separation Works for Downhole Pumps in PERFORM? ................................................. 137

Flow Through Restrictions .................................................................................................................... 138

Critical Flow ...................................................................................................................................... 138

Subcritical Flow ................................................................................................................................ 139

API 14B ........................................................................................................................................................................ 139

Critical and/or Subcritical Flow ......................................................................................................... 141

Perkins .......................................................................................................................................................................... 141 Ashford and Pierce ........................................................................................................................................................ 144

Sachdeva et al. .............................................................................................................................................................. 146

Maximum Erosional and Minimum Unloading Velocity......................................................................... 148

Maximum Erosional Rate ................................................................................................................. 148

Minimum Unloading Rate ................................................................................................................. 149

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Guo et. al. (2005).............................................................................................................................. 149

Calculation Control and Heat Transfer ................................................................................................. 152

Quick and Detailed Pressure Traverse Calculation ......................................................................... 152

Linear Temperature Gradient ........................................................................................................... 153

Temperature Survey ................. .................. ................. .................. ................. ................. ................. 153 Heat Transfer Correlation ................................................................................................................. 154

User-Entered Heat Transfer Coefficients ......................................................................................... 154

Model Calibration Using Production Data ............... .................. ................. ................. .................. ........ 154

Step 1: Production Data Selection ................................................................................................... 155

Step 2: Calibration Of Fluid, Temperature And Wellbore Models .................................................... 155

Step 3: Inflow Parameter Adjustment (Well Deliverability Adjustment) ............................................ 155

Step 4: Update Calculation And Comparison Chart ......................................................................... 156

Step 5: Update Base Model With Adjusted Parameters .................................................................. 156

Flow Assurance .................................................................................................................................... 156 Inhibitor ............................................................................................................................................. 157

Wellbore Deviation ................................................................................................................................ 158

Gas Lift Designs and Optimization ........................................................................................................................ 161

The Process of Gas Lift ........................................................................................................................ 161

Valve Mechanics .............................................................................................................................. 162

Gas Lift Valves ............................................................................................................................................................. 162

Valve Opening and Closing Forces ............................................................................................................................... 163

Unbalanced Pressure Operated Valves: ........................................................................................................................ 164

Production Pressure Operated Valves ........................................................................................................................... 167 Continuous Flow Unloading Sequence ......................................................................................................................... 171

Properties of Injection Gas and Applications ................................................................................................................ 172

Continuous Flow Gas Lift ................................................................................................................. 175

Pressure Gradients ........................................................................................................................................................ 175

Gas Lift Feasibility Studies ........................................................................................................................................... 175

Computer Design Procedure (Pressure Operated Method) ............... ................. .................. ........... 177

Bracketing Criteria ............................................................................................................................ 180

Bracket Spacing ............................................................................................................................... 181

Gas lift optimization .......................................................................................................................... 182 Downhole Network .................................................................................................................................................. 184

Maximization ........................................................................................................................................................... 187

References ................................................................................................................................................................ 189

Index ......................................................................................................................................................................... 195

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Table of FiguresFigure 1.1: Producing System ........................................................................................................................................ 1

Figure 1.2: Nodal Plot ................................................................................................................................................... 3 Figure 2.1: System Analysis Plot with Multiple Conditions ................. .......... .......... ........... .......... ........... ........... ......... 6

Figure 2.2: Gradient Curves .......................................................................................................................................... 8

Figure 2.3: Effect of Formation Skin ........................................................................................................................... 11

Figure 2.4: Inflow Sensitivity on Skin ......................................................................................................................... 12

Figure 2.5: Differential Graph ..................................................................................................................................... 13

Figure 2.6: Effect of Perforation Shot Density (SPF) .................................................................................................. 14

Figure 2.7: Inflow Sensitivity on Perforation Shot Density (SPF) .......... .......... ........... .......... .......... ........... .......... ...... 14

Figure 2.8: Effect of Perforation Interval ........... ........... .......... .......... ........... .......... .......... ........... .......... ........... ........... 15

Figure 2.9: Inflow Sensitivity on Perforation Interval ................................................................................................. 16

Figure 2.10: Effect of Tubing Size .......... ........... ........... .......... .......... ........... .......... ........... .......... .......... ........... ........... 17

Figure 2.11: Outflow Sensitivity on Tubing Size ........................................................................................................ 17

Figure 2.12: Effect of Wellhead Pressure .................................................................................................................... 18

Figure 2.13: Outflow Sensitivity on Wellhead Pressure .............................................................................................. 19

Figure 3.1: Reservoir Component ................................................................................................................................ 21

Figure 3.2: User Enters PI ........................................................................................................................................... 22

Figure 3.3: Vogel Solution Gas Drive with Flow Efficiency ........... .......... ........... .......... .......... ........... .......... ........... .. 25

Figure 3.4: Square Reservoir ....................................................................................................................................... 38

Figure 3.5: Horizontally Completed Well ................................................................................................................... 57

Figure 3.6: Schema for Giger, Joshi, Renard & Dupuy, and Economides correlations .................. ........... ........... ....... 61

Figure 3.7: Schema for Kuchuk and Babu & Odeh correlations .............. ........... .......... .......... ........... .......... ........... .... 71

Figure 3.8: Schema for Goode & Thambynaya correlation ......................................................................................... 78

Figure 4.1: Open Hole Completion ........................................................................................................................... 101

Figure 4.2: Open Perforation Completion ................................................................................................................. 102

Figure 4.3: Open Perforation ..................................................................................................................................... 102

Figure 4.4: Collapsed Perforation (Spherical Flow Model) ....................................................................................... 108

Figure 4.5: Gravel Pack Schematic............................................................................................................................ 111 Figure 4.6: Example concrete target (API 19B) .......... .......... ........... .......... ........... .......... .......... ........... .......... ........... 118

Figure 4.7: Full view of the concrete target ............................................................................................................... 118

Figure 4.8: Effective stress induced penetration changes. ....................................................................................... 120

Figure 5.1: Cross section of a Progressing Cavity Pump ........................................................................................... 137

Figure 6.1: Reduction in fluid column weight by formation and injected gas ........... .......... ........... .......... ........... ..... 161

Figure 6.2: A typical gas lift system ........... ........... .......... .......... ........... .......... ........... .......... ........... .......... ........... ..... 162

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Figure 6.3: Bellows Type Gas Lift Valve .................................................................................................................. 163

Figure 6.4: Injection pressure operated valves .......... ........... .......... .......... ........... .......... .......... ........... .......... ........... .. 164

Figure 6.5: Production Pressure Operated Valves ..................................................................................................... 168

Figure 6.6: Production Pressure Operated Valve with a Spring providing the closing force .................. ........... ....... 168

Figure 6.7: Continuous Gas Lift Unloading Sequence .............................................................................................. 171 Figure 6.8: Gas throughput chart ............................................................................................................................... 174

Figure 6.9: Pressure Versus Depth Plot Illustrating Continuous Flow Operations .................................................... 176

Figure 6.10: Flowing Gradient Traverse Below the Point of Injection ........... .......... ........... .......... .......... ........... ....... 177

Figure 6.11: Point of Injection Determination ........................................................................................................... 177

Figure 6.12: Correlation for Bracket Spacing ............................................................................................................ 181

Figure 6.13: Pressure Operated Design Method ........................................................................................................ 182

Figure 7.1: Multilayer ................................................................................................................................................ 184

Figure 7.2: Multilateral .............................................................................................................................................. 185

Figure 8.1 : Sensitivity has vertical mixing of variables ......................................................................................... 187 Figure 8.2: Maximization has both vertical and diagonal mixing of variables ........... .......... ........... .......... ........... ..... 188

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System Analysis OverviewThe primary objective of the system analysis technique is to maximize well productivity byanalyzing and optimizing the complete producing well system. The analysis can lead to increased

profitability from oil and gas investments by improving completion design, increasing well productivity, and increasing producing efficiency.System analysis is essentially a simulator of the producing well system. The system, illustrated inFigure 1.1, includes flow between the reservoir and the wellhead (separator if a flowline isincluded), and contains the following components:

Flow through the reservoir to the sandface Flow through the completion Flow through the bottomhole restrictions Flow through the tubing Flow through the surface flowline restrictions Flow through the flowline into the separator

Figure 1.1: Producing System

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As system analysis simulates the entire system, it models each component within the systemusing equations or correlations to determine the pressure loss through the component as afunction of flow rate. The total pressure loss through the system for a given flow rate is thesummation of the pressure losses through all components. Minimizing pressure loss in individualcomponents within the system results in less overall pressure loss and increased flow rate from a

well.The total pressure loss is ultimately realized as the overall difference between average reservoir

pressure, P r , and the outlet pressure (wellhead/top of tubing or flowline outlet). The averagereservoir pressure and outlet surface pressure constitute the endpoints of the system (inlet andoutlet), and are the only pressures in the system, which do not vary with flow rate.

System analysis analyzes the entire system by focusing on one point within the series ofcomponents. This point generally is referred to as a node, hence the term Nodal Analysis . Thefinal solution is independent of the location of the node.

For manual calculations, the primary interest of the application generally dictates the location ofthe node. For example, if the main interest is an investigation of the effects of the componentsnear the surface (such as flowline or surface choke), then, the node is chosen at the wellhead orflowline outlet. If the effects of the downhole components are the primary interest (such as the

bottomhole flowing pressure), then the node is chosen at downhole.

In PERFORM, you can use a sensitization technique that allows you to see the effects ofchanging parameters. In this way, you can usually choose the node at a point inside the wellboredirectly adjacent to the perforations. This point is designated as wellbore flowing bottomhole

pressure, P wf .

The producing system is divided into two segments at the node. The upstream, or inflow,segment is comprised of all components between the node and the reservoir boundary. Thedownstream, or outflow, segment consists of the components between the node and the

separator.After isolating the node in the system, both of the following fundamental requirements at thenode must be met:

Only one pressure exists at the node at any given flow rate (P inflow = P outflow ) Only one flow rate exists through the node (Q inflow = Q outflow )

Because the producing system consists of interacting components that each contributes pressureloss independently as a function of flow rate, the procedure necessary to find the unique flowrate that satisfies the two requirements at the node is iterative. To simplify the procedure, thesystem analysis approach uses a graphical solution in which the pressure at the node is shown asa function of the producing rate for both the inflow and outflow segments.

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The system analysis plot, or nodal plot, illustrated in Figure 1.2 contains both the inflow andoutflow relationships.

Figure 1.2: Nodal Plot

The inflow curve bends downward. This illustrates that as flow rate increases through the inflowsegment, pressure loss increases so that there is less pressure available at the node (or thedownstream side of the inflow segment).

The outflow curve bends upward. This illustrates that for a fixed separator pressure, the pressurerequired at the node (inlet to the outflow segment) increases as flow rate increases.

Although each segment is exclusive of the other at varying flow rates, the two requirementslisted previously (only one pressure and flow rate exist at the node) dictate that only one solutionexists for the system at a particular set of conditions. On the nodal plot, this solution is theintersection of the inflow and outflow curves. This intersection indicates the producing capacityof the system and provides both the flow rate, Q, and the corresponding bottomhole pressure,Pwf .

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Using System Analysis

General Analysis ProcedureA general procedure for solving most cases involves the following steps:

1. Make a specific objective for the case, such as determining the size of tubing to use in awell.

2. Determine the type of analysis needed to solve the problem, such as a Systems Analysis.3. Determine the components needed (reservoir, wellbore, completion, and flowline) and

the correlations desired.4. Find all required data, make educated guesses for unknown values, and enter the data for

each component.

5. Calculate the case and check the output graphically.6. Interpret the output based on the type of case. Test the results for confidence bycomparing the results with the data you have found.

7. Adjust the input and calculate again to improve the output results as needed.8. Repeat from step 1 for the next objective of the case.

You can use a general analysis procedure to determine the producing capacity of a well systemfor a set of well conditions. More importantly, you can use the procedure to determine thequantitative effect and importance of each variable within the system on the overall system

performance. The system components use the variables in either equations or correlations.

Although some values generally do not change during the well's life (for example, reservoirthickness, permeability, and total depth), many values are variable. The ability to change thevalues that directly affect system performance and well productivity allows you to achievecomplete well optimization.

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One of the underlying advantages of system analysis is its ability to predict the result caused bychanges in the design variables. The alteration in well performance is seen directly on thesystems plot through multiple inflow or outflow curves (each at a different set of conditions) andmultiple intersection points. The Q and P wf values at each intersection represent the producingstatus at that particular condition. The simplified systems plot in Figure 2.1 illustrates a typical

scenario with multiple inflow curves at different reservoir pressures and multiple outflow curvesat various tubing diameters.

Figure 2.1: System Analysis Plot with Multiple Conditions

As mentioned, the primary node used in most system analysis applications is the node at the bottom of the wellbore. Furthermore, although the system is comprised of many interactingcomponents, it usually is simplified to four primary components:

Flow through the reservoir Flow through the completion Flow up the tubing and any restrictions (vertical flow) Flow through the flowline and any restrictions (horizontal flow)

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Applying System AnalysisSystem analysis can be applied in both new and existing wells. In new wells, the technique can

be used to simulate anticipated conditions and plan the optimum completion and well design. Inexisting wells, the technique is used first to model existing conditions, then to evaluate areas of

potential improvement.To use system analysis on new wells, you must estimate data from offset wells, regionalexperience, and common sense. Because you do not have measured test data for comparison, thesystem analysis solution should cover the entire range of input variables. For example, you canselect a preliminary tubing size for a new well by calculating a system analysis solution for awell using a broad range of inflow curves generated with "most pessimistic," "most likely," and"most optimistic" values of formation permeability. Although this type of solution is not meantto be entirely accurate, it provides a general idea of anticipated conditions.

Although using system analysis for existing wells can be slightly more complex than for proposed wells, the results obtained are more complete and accurate. The primary difference between the two cases is the ability in existing wells to model current conditions using actualdata so that you can adjust input variables accordingly to better predict system performance.After reliably matching existing conditions, the effect of varied well conditions can be predictedwith a higher degree of confidence.

In both cases, you must completely understand each component in the system to fully use thesystem analysis technique. In order to understand a particular component, you must have aquantitative description of each of the variables used to model the component. The pressure lossthrough the component is a direct function of the magnitude of these variables. In the design andimplementation of an efficient producing well system, you can alter many of the variables thatdirectly affect the producing capacity of the well. This flexibility is the basis of well optimizationthrough system analysis.

Existing producing conditions in a well can be modeled by matching either a producing rate or pressure. If no producing bottomhole pressure is known, the well system could be modeled bysimply calculating both a rate and a pressure, and comparing the rate to the known conditions. Inthe event that a producing bottomhole pressure is known, either through a single pressure or aflowing gradient survey, the tubing performance can be modeled directly. This procedure isespecially beneficial in an oil well case, where there are many different correlations available butonly one provides the best solution for the well. The use of an improper correlation in a systemanalysis solution can cause serious error.

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In addition to correlation selection, the gradient match is also helpful in confirming input datathat may not be exact. Figure 2.2 is an example illustrating the use of the gradient curve to matchactual well data for an oil well by varying wellhead pressure.

Figure 2.2: Gradient Curves

As mentioned earlier, the system analysis approach can be understood as simulation of the producing system. Once the data is entered to create a base case of the well system (andconfirmed through matching, if possible), the technique can be used to simulate variedconditions and solve a "what if" scenario. The effect of design and completion variables on totalsystem performance can be predicted. Many variables can be simulated and optimized. Theimportance of each depends on specific well conditions. The items used most often in system

analysis to optimize oil and gas wells include the following: Reservoir Skin

Completion Effects

Tubing Size

Wellhead or Separator Pressure

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July 2013 9

Modeling Worst-Case Discharge Scenarios

Introduction

With recent events in the Gulf of Mexico, the US BOEMRE has tightened regulations regarding

the issuing of offshore drilling permits. The BOEMRE now requires a worst-case dischargereport outlining how an operator will respond to a worst-case discharge (WCD) scenario,including estimates of the maximum flowrate. PERFORM can be used to generate theseestimates with some slight modifications to a standard nodal analysis case.

Setup

Generally, the setup for a WCD scenario should be similar to a regular nodal analysis for anoffshore producing well. Select System analysis for a Producing well and set the Node Positionto bottomhole. The fluid type should be set according to the target fluid of the well. If you have amultilayered or multilateral well, check the Downhole Network box to indicate this. Examples ofmultilayered and multilateral well setups can be found in the EXAMPLES folder in the

PERFORM install directory.You will also need to set the maximum Flow Rate under the Calculation Limit. This is themaximum flowrate that PERFORM will calculate inflow and outflow curves for. In some WCDscenarios, the flowrate of the well will be higher than the maximum limit allowed byPERFORM. If this is the case, you can override the minimum and maximum input values byturning off Range Checking in Expert Mode (Options > Expert Mode. Check Expert Mode,uncheck Perform Range Checking). After turning off range checking, you will be able to enter amuch larger calculation limit.

F lu id Proper ties

Here, you must enter oil and gas gravities, a gas-oil or gas-liquid ratio, and a water cut. Thesewill be used to calculate the various fluid parameters PERFORM needs to run a nodal analysis,such as viscosity and density. After you enter the parameter, click on the PVT correlations tab toselect which industry correlations will be used to calculate each of these fluid properties. Foroffshore use in the Gulf of Mexico, select the Petrosky (GOM) correlation wherever available.

Reservoir Data

The Reservoir Data dialog should be completed exactly the same for a WCD scenario as anyother. In general, it is better to stick to simpler Inflow models as the data inputs for the morecomplex models (such as detailed wellbore geometry and reservoir information) are not knownfor wells being drilled.

Completion Data

Usually, the Completion type is left as Open Hole/Not Calculated for WCD scenarios. This is because a WCD scenario typically occurs while the well is being drilled, before any completiontechnique is used. If you would like to model a WCD scenario that occurs during a completion orworkover process, you can select a different completion type.

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Pressur e/Temperatur e Calcul ation Contr ol Pr ocess

This dialog should be filled out exactly the same as for a regular nodal analysis. Enter a wellheadand reservoir temperature and select the temperature calculation option. For offshore gas wells,the temperature calculation controls are more important, as the temperature represents a large

portion of the total energy of the system, and the frequent temperature changes that can occur inan offshore environment can affect calculated results.

Well bore Data

The Wellbore Data dialog is the key to properly setting up a WCD scenario. First, you mustchoose a wellbore correlation. Generally, IHS recommends well established industry correlationfor WCD scenarios, such as Hagedorn and Brown, although mechanistic models will sometimes

be appropriate as well. You can click on the Smiley Face icon next to the drop -down to viewIndustry Best Practices for each correlation.

Typically, we assume that no tubing is present in the wellbore during a WCD, and only entercasing strings. Casing strings should be representative of the status of the wellbore during theWCD scenario. To simulate the open hole portion of a wellbore, you can use a casing string witha diameter equal to the drill bit and a higher roughness factor. Open wellbore roughness varywidely, but are typically much higher than a casing or tubing roughness. If the known data aboutthe well is insufficient to determine the roughness, a search on SPE.org or another professionalwebsite may be helpful. Typically, the effect on the total system from the open hole portion ofthe well is quite small compared to the rest of the casing. If the well is deviated, a directionalsurvey must be entered.

Finally, you will assign the wellhead pressure, top of perfs, and water depth. The wellhead pressure is typically set to one of two values, the first being atmospheric pressure, and the second being equal to the hydrostatic pressure from the water column at that depth. Assuming that theWCD scenario occurs on the sea floor, the well will be producing with a back pressure equal tothe hydrostatic column of water. This pressure will serve to stifle the flow of the well to a degree.The other value often used is 0 psig, or atmospheric pressure. This generates a true worst -casemodel, as the flowrates generated are as pessimistic as possible. Only good engineering

judgment can determine which of these two values should be used for the wellhead pressure. Thetop of perfs should be set as the upper limit of the topmost perforation interval, and the waterdepth at well location should be entered.

Flowline

Typically, flowlines are not included in WCD scenarios. However, you can optionally includerisers or other flowline components in your model, and they will be represented by an additional

pressure loss in the outflow curve.

Sensitivity A nalysis

This screen allows you to answer what if questions about your well by entering sensitivities.When you do a sensitivity analysis, you are running multiple PERFORM cases simultaneously,often with one small change between each case. Calculated case results can be viewed from thegraphs and reports of PERFORM.

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July 2013 11

F inal Steps

After the sensitivity analysis screen, you are finished setting up your WCD scenario. At this point, you will need to run the calculation by clicking the Calculate button on the top toolbar.Then, you will want to view the various reports and graphs available in PERFORM. Specificallyof interest will be the new Worst Case Discharge Report. This report was specifically developedto be in compliance with the requirements of the BOEMRE for WCD modeling and contains allof the information available in PERFORM that the BOEMRE will want. You can include thisreport with other materials to be submitted to the BOEMRE. Please note that additional dataitems are required related to volumetric and geologic analysis (see www.boemre.gov for moreinformation.)

Reservoir SkinThe reservoir skin is a deviation from Darcy flow, which assumes laminar, radial flow in a

homogenous formation. The skin is typically caused by damage near the wellbore from drilling

and completion fluids or from enhancement through stimulation, but is caused also by othersources such as partial penetration and restricted flow through perforations. Thus, the effect ofaltering skin is generally associated with the effect of removing damage through stimulation. Insystem analysis, you can do this by reviewing several inflow cases, each at an improved skinvalue. Figures 2.3 and 2.4 illustrate this case, where a highly damaged formation with a skin of32 is analyzed after stimulation with skins of 20, 5, 0, -3, and -6.

Figure 2.3: Effect of Formation Skin
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Figure 2.4: Inflow Sensitivity on Skin

Please be aware, that the total skin is made up of several terms, including mechanical (damage)effect, so the well may still have a positive skin after a stimulation treatment.

Completion EffectsThe following items induce a similar response in the system performance and are variables in thecompletion design that are generally subject to change and optimize:

Perforation shot density

Perforation size

Perforation diameter

Perforation length

Perforation interval

Gravel pack size

Gravel pack permeability

Damaged zone radius and permeability Perforation crushed zone effects

Perforated interval

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Di ff erential Graph

The differential graph, Figure 2.5, is especially helpful in emphasizing the completion effects ofa well. The differential graph has two main curve types. The first type, shown bendingdownward to the left, represents the difference between the pressure remaining after flowing

through the reservoir (P ws) and the pressure needed to flow through the outflow segment. Thedifference is the pressure available to produce through the completion. The curves shown

bending upward to the left are the actual pressure losses through the completion as a function ofrate.

Figure 2.5: Differential Graph

Similar to the standard system analysis graph, the intersection of these two curves dictates the producing capacity of a well for a given set of conditions. Although both example plots in thissection illustrate the effect of varied perforation shot density, you can vary and display any of thecompletion variables listed in the same manner.

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14 July 2013

Per for ation Shot D ensity

A typical analysis applied to completion design is shown in Figures 2.6 and 2.7, which illustratethe effect of perforation shot density.

Figure 2.6: Effect of Perforation Shot Density (SPF)

Figure 2.7: Inflow Sensitivity on Perforation Shot Density (SPF)

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July 2013 15

Per foration I nterval

The perforation interval is the measured length of formation interval that is actually perforated.In many completions, the perforation interval is somewhat less than the formation thickness.This can be the result of:

Well problems that result in the inability to completely penetrate the producing formation Reduced perforation interval aimed at lowering completion cost Altered perforation intervals to accommodate subsequent stimulation treatments

A reduced perforation interval affects the inflow segment in two ways. First, if reservoirturbulence is taken into account (i.e., Jones equation), the reduced interval increases the pressureloss encountered as the flow converges in the reservoir into the perforation interval. Second, thereduced perforation interval reduces the number of actual perforations available for flow into thewellbore, thereby increasing pressure loss through the completion. Both of these effects result inless productivity from a well, as illustrated in Figures 2.8 and 2.9.

Figure 2.8: Effect of Perforation Interval

Perform can be used to estimate the pseudo skin factor corresponding to the partial penetrationwith the Skin factor option available for System analysis cases.

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16 July 2013

Figure 2.9: Inflow Sensitivity on Perforation Interval

Tubing SizeProperly sized tubing is very important in an efficiently designed well system. In an oil well,

pressure loss through the tubing can constitute the majority of the pressure loss through the entiresystem. If the tubing size is too small, friction loss will become excessive. If the tubing size istoo large, additional pressure loss will be encountered due to liquid loading. In some cases, thisloading can prevent the well from flowing at all. Incorrectly sized tubing can result in lessavailable production from a well and possibly reduced flowing periods.

Figures 2.10 and 2.11 show the effect of tubing size in an oil well. The reversal effect in thelargest diameter as it actually crosses the next smaller diameter indicates less available

production due to liquid loading. The tubing sizes sensitized are 2 3/8", 2 7/8", 3 1/2", 4", and 41/2" respectively.

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Figure 2.10: Effect of Tubing Size

Figure 2.11: Outflow Sensitivity on Tubing Size

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Figure 2.13: Outflow Sensitivity on Wellhead Pressure

Fluid Property CalculationsPetrosky and Ghetto & Villa methods are added in version 6.0. Both methods providecalculations for viscosity (including saturated, under saturated and dead oil), bubble point

pressure, solution gas oil ratio, and oil compressibility. In addition, Petrosky method provides acorrelation to calculate formation volume factor.

Petrosky is based on 90 data points from the Gulf of Mexico oil samples. They have alsoconsidered standing correlation as the basis for their correlations. The ranges of variables used todevelop this correlation are:

Pb, psia 1574 to 6523

T, deg F 114 to 288oAPI 16.3 to 45

g (air=1) 0.58 to 0.85

R s (scf/STB) 217 to 1406

Ghetto & Villa method maybe used as a general method for heavy oil. The correlations have been evaluated against a set of 195 crude oil samples collected from the Mediterranean Basin,Africa, the Persian Gulf and the North Sea. About 3700 measured data points have beencollected and investigated. For all the correlations, the following statistical parameters have beencalculated a) relative deviation between estimated and experimental values, b) average absolute

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20 July 2013

percent error c) standard deviation. Oil samples have been divided into the following fourdifferent API gravity classes:

Extra-heavy oils for oAPI< 10

Heavy oils for 10< oAPI 31.1

This correlation is recommended as a general choice for extra heavy oils (up to 6 API). Theranges of variables used to develop the correlations are given in the following table:

TABLE 2: AGIP'S RANGE FOR PVT PROPERTIES SAMPLE

Tank- oil gravity (API) 6 to 56.8

Reservoir pressure (psia) 242.22 to 15304.62

Reservoir temperature (F) 80.6 to 341.6

Solution GOR (scf/STB) 8.61 to 3298.66

Bubblepoint pressure (psia) 107.33 to 6613.82

Separator pressure (psia) 14.5 to 868.79

Separator temperature (F) 59 to 194

Separator GOR (scf/STB) 8.33 to 2985.87

Stock-tank GOR (scf/STB) 4.39 to 527.43

Total surface m gravity (air=1) 0.624 to 1.789

Separator gas gravity (air=1) 0.605 to 1.530

Mole fraction of CO 2 in total gases (% mol.) 0 to 98.8

Mole fraction of N 2 in total gases (% mol.) 0 to 63.32

Mole fraction of H 2S in total gases (% mol.) 0 to 5.65

Oil formation volume factor (bbl/STB) 1.034 to 2.887

Isothermal compressibility (psia -1 x 10 6) 3.02 to 43

Dead-oil viscosity (cp) 0.46 to 1386.9

Gas-saturated oil viscosity (cp) 0.07 to 295.9

Under saturated oil viscosity (cp) 0.13 to 354.6

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July 2013 21

Reservoir ComponentThe reservoir component, illustrated in Figure 3.1, of the system is composed of the flow

between the reservoir boundary and the sandface. This component is always upstream of thenode and, in this discussion, is combined with the completion component to form the entireinflow segment.

Figure 3.1: Reservoir Component

The flow through the reservoir is often referred to as the inflow performance relationship (IPR)of a well. It is a measure of the reservoir's ability to produce fluid as a result of a pressuredifferential. This ability depends on many factors, including reservoir type, producing drivemechanism, reservoir pressure, formation permeability, and fluid properties.

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Reservoir Component PERFORM v8.0 Technical Reference Manual

22 July 2013

Vertical IPR Types

User Enter s PI

The inflow performance relationship for an oil well is often simplified as a constant inflow or

productivity index (PI), where inflow is directly proportional to drawdown, in the form of:Constan t Produ ct iv i ty Index

wf r PPQ

=PI

where:

PI = Productivity index (stb/d/psi)

Q = Total liquid flow rate (stb/d)

Pr = Average reservoir pressure (psi)Pwf = Bottomhole flowing pressure (psi)

Figure 3.2: User Enters PI

The constant productivity index is expressed on the system analysis plot as a straight line between P r and Q max (at P wf = 0) with a slope of 1/PI. The Vogel equation can be used to correctthe flow below the bubblepoint pressure with the user-entered PI to calculate the IPR above the

bubblepoint pressure.

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PERFORM v8.0 Technical Reference Manual Reservoir Component

July 2013 23

Vogel/H arr ison (1968)

The productivity index concept relies on the assumptions that reservoir and fluid propertiesremain constant and are not a function of pressure. Although these assumptions are true in somecases, especially in single-phase liquid flow, wells that produce both oil and gas will beoverestimated below the bubblepoint if you use the user-entered PI relationship.

In 1968, Vogel presented an IPR solution for wells producing both oil and gas from saturatedreservoirs. 5 Using the reservoir model proposed by Weller 35, Vogel used a computer to calculateIPR curves for several fictitious solution gas drive reservoirs that covered a wide range of oilPVT properties and reservoir permeability characteristics. He plotted these IPR curves asdimensionless IPR curves with each pressure value divided by the maximum shut-in pressure,and each flow rate divided by the maximum rate (Q max at P wf = 0). He combined thesedimensionless curves into a general reference curve in the following form:

Vogel Equat ion 2

r

wf

r

wf

max PP

8.0PP

2.00.1QQ

where:


Qmax = Maximum flow rate at P wf = 0 (stb/d)

Pwf = Bottomhole flowing pressure (psi)

Pr = Average reservoir pressure (psi)

The Vogel relationship can be regarded as a general equation for solution gas drive reservoirs producing below the bubblepoint. Above the bubblepoint, the standard Darcy equation or user-entered straight line PI is considered adequate. In cases of undersaturated reservoirs wherewellbore pressure may be above or below the bubblepoint, the Vogel equation can be used as acorrection below the bubblepoint pressure in combination with the user-entered PI, Darcy,transient, and fractured well correlations. In this case, the selected correlation is used betweenreservoir pressure (P r ) and bubblepoint pressure (P b), followed by the Vogel relationship belowthe bubblepoint pressure.

The Vogel equation is differentiated with respect to P wf to give a secondary equation for Q max .

Secondary Vogel Equat ion fo r Q max

1.8PPI

+Q=Q b

bmax

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24 July 2013

where:


Q b = Flow rate at bubblepoint (stb/d)

PI = Productivity index (stb/d/psi)P b = Bubblepoint pressure (psi)

The final form of the Vogel equation for wells producing above the bubblepoint is:

Comb inat ion Vogel equat ion P w f > P b

wf r PPPI=Q where:


PI = Productivity index (stb/d)


Pwf = Bottomhole flowing pressure (psi)

The final form of the Vogel equation for wells producing below the bubblepoint is:

Comb inat ion Vogel equat ion P w f < P b

wf r max b P'PPIQ+Q=Q where:

Q' = Flow rate below bubblepoint (stb/d)

Q b = Flow rate at bubblepoint (stb/d)


P b = Bubblepoint pressure (psi)

P'wf = Bottomhole flowing pressure below bubblepoint (psi)

The Vogel equation was developed with the assumption that there is no skin effect or that flowefficiency (FE) equals one. Standing 6,7 proposed a method to correct the Vogel relationship to

account for non-unity flow efficiencies.

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In this correction, test pressures used in the Vogel equation are first modified as follows:

wf r wf wf PPFE1+P='P where:

P'wf = Equivalent undamaged flowing pressure

FE = Flow efficiency, 0.5 to 1.5

This correction alters the bottomhole flowing pressure due to additional pressure loss through thedamaged area around the wellbore. For damaged wells, FE value is less than 1.0. For stimulatedwells, FE is greater than 1.0.

Figure 3.3: Vogel Solution Gas Drive with Flow Efficiency

The previous equation presents a problem with high flow efficiencies and low flowing

bottomhole pressures. The value of P' wf can calculate as a negative value, which cannot be usedin the Vogel equation. A correction to the Vogel solution is to account for either positive ornegative values of P' wf in the following equation.

)/P(1.792P')0.1FEmax(

r wf e2.02.1Q/Q

This equation is only used if the P' wf is negative, otherwise the normal Vogel equation is used.

Est imat ion of FE

If two stabilized tests are available and reservoir pressure is accurately known, FE can beestimated with the following equation:

) A A21( C ) A A21( ) A1( C ) A1( 25.2 FE 2

222

11

12

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where:

A1 = Pwf 1/PR

A2 = Pwf 2/PR

C = Q 1/Q2 Q1 = Test rate 1, STB/day

Q2 = Test rate 2, STB/day

Pwf 1 = Test BHP 1, psia

Pwf 2 = Test BHP2, psia

PR = Reservoir pressure, psia

Vogel corr ected for water cut

The Vogel corrected for water cut (composite) IPR method calculates an IPR for any water cut.If the water cut (fraction of water phase of the total oil plus water phase) is zero, the compositemethod matches exactly to the Vogel method. If the water cut is 100%, the composite methodmatches the PI method. When the Vogel method is selected, PERFORM uses the compositemethod equations with the water cut set to 0%. If you want the water cut considered in the IPRand it is not 0%, you must use the composite method; otherwise the water cut is ignored.

A complete discussion and derivation of the equations used in calculating the PI, Vogel, andVogel correct for water cut IPR methods is detailed in "The Technology of Artificial LiftMethods," Volume 4, pages 30-35 by Kermit E. Brown 1984 PennWell Publishing.

DarcyThe basic equation used to describe the flow of fluid through a reservoir is the radial form of theDarcy equation. Henry Darcy originally developed the equation in 1856 to describe the flowthrough sand filter beds used in water purification. The basic Darcy concept describes flowthrough porous media as a function of pressure differential, cross-sectional area, fluid viscosity,flow distance, and permeability (the measure of the media's ability to transmit fluid). Hedeveloped the equation under the assumptions that only single-phase, laminar flow existed, andthe fluid was essentially incompressible.

Although the original Darcy equation was developed for linear flow in the vertical direction, theequation has been modified to predict radial flow. The general Darcy equation for an oil well is:

Darcy equation : Oil Well

DQ+S+43

(x)lnB

)P(Pkh(0.00708) =Q wsr

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July 2013 27

where:


k = Effective permeability (md)

h = Net formation thickness (ft)Pr = Average reservoir pressure (psi)

Pws = Flowing sandface pressure (psi)

= Average liquid viscosity (cp)

B = Average formation factor (rb/stb)

x = Drainage area factor r e/r w or from area and shape factor

S = Skin effect

D = Non-Darcy turbulence factor (1/stb/d)

r e = Reservoir radius (ft)

r w = Wellbore radius (ft)

The Darcy equation for a gas well is slightly different because of the dynamic behavior of gas properties as a function of rate and pressure, where pseudopressure, is used and is:

Darcy equat ion : Gas Wel l

DQ+S+43 xlnT

hk 0.000703 =Q

g

wsr gg

where:

Qg = Gas flow rate (Mscf/d)

k g = Effective gas permeability (md)

h = Net formation thickness (ft)

r = Avg. reservoir pseudopressure (psi 2/cp)

ws = Flowing sandface pseudopressure (psi2

/cp)T = Average reservoir temp ( R)


S = Skin effect

D = Non-Darcy turbulence factor (1/Mscf/d)

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28 July 2013



The Vogel equation can be used to correct the Darcy equation below the bubblepoint pressure. PIis calculated from the following equation and is used in the Vogel equation described earlier.

Product iv i ty Index Darcy

S+43

xlnB

hk0.00708 =PI

where:

PI = Productivity Index (stb/d/psi)






S = Skin effect



Non-Darcy Turbu len t Term

The non-Darcy turbulent term, D, in the Darcy equation is used to account for inflow turbulence.This term is sometimes referred to as the Ramey Turbulence, or Ramey D, term. The non-Darcyterm is applied as an effective rate-dependent skin, shown as the DQ or DQ g term in thedenominator of the Darcy equation. The term is usually obtained through multi-rate testing ofwells where skin is calculated as a function of rate.

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Skin Effect

Skin can be defined as a correction to account for non-Darcy or non-homogeneous flow behavior. In many discussions, skin is defined as a total skin that is comprised of severalindividual components.

DQ)t,q(SS'S where:

S' = Total skin

S = Physical skin caused by damage near the wellbore or enhancementthrough stimulation

S(q,t) = Rate- and time- dependent skin, generally caused by permeabilityalteration due to changing gas saturation near the wellbore

DQ = Rate-dependent skin, described as the non-Darcy flow term

The physical skin, S, is understood to be caused by a physical alteration to the reservoir,generally near the wellbore. This can be in the form of damage from the penetration of drillingand/or completion fluids, causing a positive skin. Conversely, this skin can be represented as anegative value, caused by stimulation of the well through fracturing or acidizing.

The rate- and time-dependent skin, S(q,t), is induced by two-phase fluid behavior at or near thewellbore. This skin can give the appearance of non-Darcy flow behavior. In general, this skin is a

permanent condition (unless fluid conditions change), and cannot be altered with stimulation.

The non-Darcy term, DQ, is simply a representation of the energy loss due to turbulent behaviorin the reservoir. The value can be determined by isochronal testing.

System analysis accounts for the total skin effect in several ways. Most inflow equations allowfor a skin entry, which generally is the physical skin, S. If the skin entry is positive, it indicatesdamage. If the skin entry is negative, it indicates stimulation. The rate-dependent non-Darcy termis available for use in the Darcy equation. Because system analysis is an isochronal procedure,the rate- and time-dependent skin, S(q,t), becomes a function of rate only and logically can beincluded with the non-Darcy skin.

Note : In a system analysis solution, be sure not to include turbulent or physical skin more thanonce. If the skin effect is measured including the completion by transient testing within thewellbore, this skin takes into account completion effects. If this skin is used subsequentlyin the reservoir segment as a physical skin, S, or as a rate-dependent skin, DQ, or as both,additional pressure loss through the completion segment will cause an underestimated

inflow curve. This situation exists for the four-point test (Jones and back pressure) for oilwells and gas wells and Vogel for oil wells.

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July 2013 31

Shape Shape Factor Shape Shape Factor

0.564 0.966

0.571 1.444

0.565 2.206

0.605 1.925

0.610 6.590

0.678 9.360

0.668 1.724

1.368 1.794

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32 July 2013

Jon es et al . (1976)

Turbulent flow in the reservoir, generally occurring near the area of wellbore convergence, cancause significant additional pressure loss. This is especially prevalent in high rate gas wells.

The basic Darcy equation was generated with the assumptions that only laminar flow existed

through the porous media. As wells produce at relatively high rates, this assumption becomesinvalid as turbulent flow begins to develop. The overall effect of this turbulence is added energyloss, which results in a lower flow rate for a given pressure differential. This turbulent flow isoften referred to as non-Darcy flow behavior.

An equation suggested by Jones, Blount, and Glaze 8 in 1976 accounts for turbulence in a producing oil or gas well. The equation, referred to as the Jones equation, is written in thefollowing forms:

Jon es Equat ion : Oi l Wel l

bQ+aQ=PP 2wsr

where:

r h

B102.30 =aw

2 p

2-14

; turbulent term

kh0.00708

S+0.472xlnB = b

; laminar term

and where:


Pws = Flowing sandface pressure (psi)Q = Total liquid flow rate (stb/d)

= Turbulence coefficient (1/ft)


= Fluid density (lb/ft 3)

h p = Perforated thickness (ft)




S = Skin effect



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July 2013 33


Jon es Equat ion : Gas Wel l

g2gwsr bQ+aQ=

where:

gw

2 p

g2-1

r h

T 103.16 =a ; turbulent term

hk

S+0.472xlnT1424 = b

g

; laminar term

and where:

r = Average reservoir pressure (psi2/cp)

ws = Flowing sandface pressure (psi 2/cp)


= Turbulence coefficient (1/ft)

g = Gas specific gravity

T = Average reservoir temperature (R)

h p = Perforated thickness (ft)


g = Gas viscosity (cp)


S = Skin effect

k g = Effective permeability (md)



For oil wells, you can also obtain the turbulent term, a, and the laminar term, b, by plotting (P r -Pwf )/Q versus Q. For gas wells, plot (P r 2 - P wf 2) / Q g versus Q g. The resulting slope will be theturbulent term and the intercept will be the laminar term.

The laminar term is simply the Darcy equation. The turbulent term is the turbulent portion of theJones equation and is shown as a function of rate. The contribution of this turbulent term tends toreduce the available flow rate from a well as rate increases. The term accounts for additionalwellbore convergence effects caused by partial penetration or a limited perforated interval. This

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July 2013 35

Back Pressur e Eq (1930) and Back Pressur e 4-Poin t Test

The effects of reservoir turbulence can also be modeled using the backpressure equation:

n2ws2r PPC=Q where:

Q = Flow rate (stb/d or Mscf/d)

C = Backpressure coefficient

Pr = Reservoir pressure (psi)

Pws = Sandface pressure (psi)

n = Turbulence coefficient

The turbulence coefficient, n, can be obtained from stabilized test data where (P r 2 - P ws2) is

plotted versus Q on a log-log scale. This method requires at least three and usually four flowing bottomhole pressure and flow rate data pairs (thus called a four-point test). The turbulencecoefficient is determined from the inverse slope of the line, and is a measurement of the turbulentcondition of the well.

Turbulent flow yields values of n between 0.5 (completely turbulent flow) and 1.0 (completelylaminar flow). In some solution gas drive reservoirs, the 'n' value can be larger than 1.0. 45 The

backpressure equation is considered a valid inflow representation if turbulence is a factor and testdata are available and suitable for confident prediction of n. Solve for the backpressurecoefficient, C, using a point on the backpressure line. The Backpressure Four-Point Test methodcalculates the best fit of the four-point test data points to arrive at the n and C values.

The Backpressure equation is used to calculate the IPR from a known n and C value based on theresults of a plot of (P r 2 - P ws2) versus Q for both oil and gas wells. The Backpressure 4-Pt TestIPR method involves the computer calculation of the backpressure n and C values based on user-entered test data. The results for oil wells and gas wells will be very different because

pseudopressure is used in the gas well cases so that the equation becomes:

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36 July 2013

Backpr essur e Four -Poin t Test (gas well s only)

nwsr CQ where:

Q = Flow rate (stb/d or Mscf/d)C = Backpressure coefficient

r = Reservoir pseudopressure (psi2/cp)

ws = Sandface pseudopressure (psi2/cp)

N = Turbulence coefficient

Note : For gas wells, do not use the resulting n and C values from this equation in the user-entered Backpressure equation. This restriction does not apply to oil wells because bothmethods use the difference in the pressure squared and not pseudopressure.

Tr ansient F low Equation

In many cases, an inflow is desired for a new well that has not reached pseudosteady state and isstill producing in a transient condition. Both the Darcy equation and its derivative, the Jonesequation, were developed under the assumption that the producing well has reached

pseudosteady state. During the transient period, use the transient equation to predict the inflow performance for a well. Use the Vogel equation below the bubblepoint pressure to correct thetransient equation for oil wells with a solution gas drive.

Transien t equat ion : o i l w el l

0.87S+3.2275r c

k tlogB162.6

P Pkh=Q

2wt

wsr

where:


K = Effective permeability (md)

H = Net formation thickness (ft)


Pws = Flowing sandface pressure (psi)



T = Producing time (hrs)

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July 2013 37

= Porosity

ct = Total system compressibility (1/psi)


S = Skin effect

Transien t equat ion : gas w el l

0.87S+3.2275

r c

tk logT1638

)h(k = Q

2wtg

g

wsr gg

where:


k g = Gas effective permeability (md)


r = Average reservoir pseudopressure (psi 2/cp)

ws = Flowing sandface pseudopressure (psi2/cp)

T =

t = Producing time (hrs)

= Porosityg = Average gas viscosity (cp)

ct = Total system compressibility (1/psi)


S = Skin effect

The pressure behavior of a reservoir during the transient period is essentially the same as that ofan infinite acting reservoir. Use the following equation to estimate the length of time required tosurpass this transient period and reach pseudosteady state:

Time to pseud osteady s ta te

k 0.001005r c =(hrs)Time

2et

where:

= Porosity

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38 July 2013

= Viscosity (cp)

ct = Total compressibility (1/psi)

r e = Drainage radius (ft)


F ractured Well

PERFORM uses a digitized, constant rate, finite-conductivity, closed square, fractured well type-curve to calculate the effect of a vertically drilled well that has been hydraulically fractured. Thetype curve requires a dimensionless time, dimensionless fracture conductivity, and fracture

penetration ratio to calculate a dimensionless pressure drop for a known wellbore pressure andtime. The well is assumed to be in the center of a square reservoir with an aspect ratio 1:1.

Figure 3.4: Square Reservoir

Reservoir conductivity is calculated as:

Oil well

Bhk0.00708

= R ct

Gas well

460Thk0.000703

= R ct

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July 2013 39

where:

R ct = Reservoir conductivity

K = Reservoir permeability (md)

H = Reservoir thickness (ft) = Fluid viscosity (cp)

B = Formation volume factor (rb/stb)

T = Reservoir temperature ( F)

The fracture penetration ratio is determined by the following formula and must evaluate to between 0.0 and 1.0 or an error message appears. Note that r e is normally evaluated as a reservoirradius but in this case, it is the length of one side of a square reservoir divided by 2.

Fracture penet rat ion ra t io

e

f pr r

x = F

where:

F pr = Fracture penetration ratio

xf = Fracture half length (ft)

r e = Length of one side of square reservoir divided by 2 (ft)

The dimensionless fracture conductivity is calculated as follows and must evaluate between 0.01and 500.0 or PERFORM displays an error message:

Dimension less f racture con duct iv i ty

f

f cd k x

wk = F

where:

Fcd = Dimensionless fracture conductivity

k f = Fracture permeability (md)

W = Fracture width (ft)


xf = Fracture half width (ft)

The dimensionless time is calculated as follows and must be between 0.00001 and 1000.0 orPERFORM displays an error message:

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40 July 2013

Dimension less t ime

2f t

Dxf xc

k t0.000264 =t

where:

tDxf = Dimensionless time


T = Production time (hr)

= Porosity (pore volume/ bulk volume)

= Fluid viscosity (cp)

ct = Total compressibility (1/psi)

xf = Fracture half length (ft)The type curve function interpolates the type curve to arrive at the dimensionless pressure dropin the fracture and reservoir as:

pr cdf DxD F,F,tf = p

The flow rate is calculated as follows:

Flow rate: oi l well

D

wf rct

pPP R

= Q

Flow rate: gas well

D

wf r ctg p

R = Q

where:

Q = Flow rate at P wf (stb/d or Mscf/d)

R ct = Oil or gas reservoir conductivity

Pr = Reservoir pressure (psia)Pwf = Wellbore pressure (psia)

pD = Dimensionless pressure

r = Reservoir pseudopressure (psi2/cp)

w = Wellbore pseudopressure (psi2/cp)

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July 2013 41

f

The flow rate above assumes that the well is in non-turbulent flow. To account for turbulence inthe fracture that may occur, a non-Darcy flow rate adjustment is made to the flow rate accordingto the size of the proppant in the fracture itself as follows:

Non-Darcy flow factors

Proppant size A-term B-term

8 - 12 mesh 1.24 17423.61

10 - 20 mesh 1.34 27539.48

20 - 40 mesh 1.54 110470.39

40 - 60 mesh 1.60 69405.31

A turbulence beta factor is calculated as:

af

7

k

b 103.088386 =

where:

= Turbulence factor

b = b term from the previous Non-Darcy Flow Factors table


a = a term from the previous Non-Darcy Flow Factors tableA flow velocity and Reynold's number is determined to calculate a revised fracture conductivityas follows:

Oil well veloci ty

whB Q10x249.3

V oo5

Gas wel l veloci ty

wh

B Q10x.7875V

gg3

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42 July 2013

Reynold ' s num ber

f -11

RE

k V101.5808 = N

Non-Darcy d imension less f racture condu ct iv i ty

REf f

cd N1k x wk

F

where:

V = Fracture flow velocity

Q = Liquid flow rate (stb/d)

Bo = Liquid volume factor (rb/stb)

h = Formation thickness (ft)

w = Fracture width (ft)


Bg = Gas volume factor (scf/stb)

NRE = Reynold's number

= Fracture turbulence factor

= Fluid density (lbm/ft 3)


= Fluid viscosity (cp)

k = Formation permeability (md)

An iteration technique is used to converge on a dimensionless pressure and flow rate using thetype curve to arrive at a final non-Darcy flow rate at a given wellbore pressure. The sameequations used above to calculate Q and R ct are used in the iteration until a convergence with theflow rate, Q, used in the above velocity equations gives the same flow rate from the type curvecalculation. PERFORM allows a maximum of 20 iterations and displays an error message ifunable to converge.

Oil well cases can also be adjusted for the Vogel relationship below the bubblepoint pressureusing the Vogel equations. An instantaneous productivity index is calculated for the Vogelequation as:

Product iv i ty Index

wf r

o

P PQ

=PI

Perf Tech

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