ResSimCh1

CONTENTS

1 WHAT IS A SIMULATION MODEL? 1.1 A Simple Example of a Simulation Model 1.2 A Note on Units

2 WHAT IS A RESERVOIR SIMULATION MODEL? 2.1 The Task of Reservoir Simulation 2.2 What Are We Trying To Do and How Complex Must Our Model Be?

3 FIELD APPLICATIONS OF RESERVOIR SIMULATION 3.1 Reservoir Simulation at Appraisal and in Mature Fields 3.2 Introduction to the Field Cases 3.3 Case 1: The West Seminole Field Simulation Study (SPE10022, 1982) 3.4 Ten Years Later - 1992 3.5 Case 2: The Anguille Marine Simulation Study (SPE25006, 1992) 3.6 Case 3: Ubit Field Rejuvenation (SPE49165,1998) 3.7 Discussion of Changes in Reservoir Simulation; 1970s - 2000 3.8 The Treatment of Uncertainty in Reservoir Simulation

4 STUDY EXAMPLE OF A RESERVOIR SIMULATION

5 TYPES OF RESERVOIR SIMULATION MODEL 5.1 The Black Oil Model 5.2 More Complex Reservoir Simulation Models 5.3 Comparison of Field Experience with Various Simulation Models

6 SOME FURTHER READING ON RESERVOIR SIMULATION

APPENDIX A - References

APPENDIX B - Some Overview Articles on Reservoir Simulation

1. Reservoir Simulation: is it worth the effort? SPE Review, London Section monthly panel discussion November 1990.

2. The Future of Reservoir Simulation - C. Galas, J. Canadian Petroleum Technology, 36, January 1997.

3. What you should know about evaluating simulation results - M. Carlson; J. Canadian Petroleum Technology, Part I - pp. 21-25, 36, No. 5, May 1997; Part II - pp. 52-57, 36, No. 7, August 1997.

11Introduction and Case Studies

2 Institute of Petroleum Engineering, Heriot-Watt University 3


LEARNING OBJECTIVES:

Having worked through this chapter the student should:

Be able to describe what is meant by a simulation model, saying what analytical models and numerical models are.

Be familiar with what specifically a reservoir simulation model is.

Be able to describe the simplifications and issues that arise in going from the description of a real reservoir to a reservoir simulation model.

Be able to describe why and in what circumstances simple or complex reservoir models are required to model reservoir processes.

Be able to list what input data is required and where this may be found.

Be able to describe several examples of typical outputs of reservoir simulations and say how these are of use in reservoir development.

Know the meaning of all the highlighted terms - or terms referred to in the Glossary - in Chapter 1 e.g. history matching, black oil model, transmissibility, pseudo relative permeability etc.

Be able to describe and discuss the main changes in reservoir simulation over the last 40 years from the 60's to the present - and say why these have occurred.

Know in detail and be able to compare the differences between what reservoir simulations can do at the appraisal and in the mature stages of reservoir development.

Have an elementary knowledge of how uncertainty is handled in reservoir simulation.

Know all the types of reservoir simulation models and what type of problem or reservoir process each is used to model.

Know or be able to work out the equations for the mass of a phase or component in a grid block for a black oil or compositional model.



BRIEF DESCRIPTION OF CHAPTER 1

A brief overview of Reservoir Simulation is first presented. This module then develops this introduction by going straight into three field examples of applied simulation studies. This is done since this course has some reservoir engineering pre-requisites which will have made the student aware of many of the issues in reservoir development. In these literature examples, we introduce many of the basic concepts that are developed in detail throughout the course e.g. gridding of the reservoir, data requirements for simulation, well controls, typical outputs from reservoir simulation (cumulative oil, watercuts etc.), history matching and forward prediction etc. After briefly discussing the issue of uncertainty in reservoir management, some calculated examples are given. Finally, the various types of reservoir simulation model which are available for calculating different types of reservoir development process are presented (black oil model, compositional model, etc.).

PowerPoint demonstrations illustrate some of the features of reservoir simulation using a dataset which the student can then run on the web (with modification if required) and plot various quantities e.g. cumulative oil, watercuts etc.

This module also contains a Glossary which the student can use for quick reference throughout the course.

1 WHAT IS A SIMULATION MODEL?

1.1 A Simple Example of a Simulation Model

A simulation model is one which shows the main features of a real system, or resembles it in its behaviour, but is simple enough to make calculations on. These calculations may be analytical or numerical . By analytical we mean that the equations that represent the model can be solved using mathematical techniques such as those used to solve algebraic or differential equations. An analytic solution would normally be written in terms of well know equations or functions (x2, sin x, ex etc).

For example, suppose we wanted to describe the growth of a colony of bacteria and we denoted the number of bacteria as N. Now if our growth model says that the rate of increase of N with time (that is, dN/dt) is directly proportional to N itself, then:

dN

dtN

= . (1)

where is a constant. We now want to solve this model by answering the question: what is N as a function of time, t, which we denote by N(t), if we start with a bacterial colony of size N

o. It is easy to show that, N(t) is given by:



N t N eot( ) . .= (2)

which is the well-known law of exponential growth. We can quickly check that this analytical solution to our model (equation 1), is at least consistent by setting t = 0 and noting that N = N

o, as required. Thus, equation 1 is our first example of a

simulation model which describes the process - bacterial growth in this case - and equation 2 is its analytical solution. But looking further into this model, it seems to predict that as t gets bigger, then the number N - the number of bacteria in the colony - gets hugely bigger and, indeed, as t , the number N also . Is this realistic ? Do colonies of bacteria get infinite in size ? Clearly, our model is not an exact replica of a real bacterial colony since, as they grow in size, they start to use up all the food and die off. This means that our model may need further terms to describe the observed behaviour of a real bacterial colony. However, if we are just interested in the early time growth of a small colony, our model may be adequate for our purpose; that is, it may be fit-for-purpose. The real issue here is a balance between the simplicity of our model and the use we want to make of it. This is an important lesson for what is to come in this course and throughout your activities trying to model real petroleum reservoirs.

In contrast to the above simple model for the growth of a bacterial colony, some models are much more difficult to solve. In some cases, we may be able to write down the equations for our model, but it may be impossible to solve these analytically due to the complexity of the equations. Instead, it may be possible to approximate these complicated equations by an equivalent numerical model. This model would commonly involve carrying out a very large number of (locally quite simple) numerical calculations. The task of carrying out large numbers of very repetitive calculations is ideally suited to the capabilities of a digital computer which can do this very quickly. As an example of a numerical model, we will return to the simple model for colony growth in equation (1). Now, we have already shown that we have a perfectly simple analytical solution for this model (equation 2). However, we are going to forget this for a moment and try to solve equation 1 using a numerical method. To do this we break the time, t, into discrete timesteps which we denote by t. So, if we have the number of bacteria in the colony at t = 0, i.e. N

o, then we want to calculate the

number at time t later, then we use the new value and try to find the number at time t later and so on. In order to do this systematically, we need an algorithm (a mathematical name for a recipe) which is easy to develop once we have defined the following notation:

Notation: the value of N at the current time step n is denoted as Nn

the value of N at the next time step, n+1 is denoted as Nn+1

Clearly, it is the Nn+1 that we are trying to find. Going back to the main equation that defines this model (equation 1), we approximate this as follows:

N N

tN

n nn

+ 1

.

(3)

where we use the symbol, "", to indicate that equation 3 is really an approximation, or that it is only exactly true as t 0. Equation 3 is now our (approximate) numerical



model which can be rearranged as follows to find Nn+1 (which is the unknown that we are after):

N t Nn n+ = +1 1( . ). (4)

where we have gone to the exact equality symbol, =, in equation 4 since, we are accepting the fact that the model is not exact but we are using it anyway. This is our numerical algorithm (or recipe) that is now very amenable to solution using a simple calculator. More formally, the algorithm for the model would be carried out as shown in Figure 1.

Set, t = 0

Choose the time step size, tSpecify the initial no. of bacteria at t = 0

i.e.No and set the first value (n=0) of Nn to No

No = No

Print n, t and N (Nn)

Set Nn+1 = (1 + .t). Nn

Set Nn = Nn+1

n = n+1

t = t + t

Time to stop ?e.g. is t > tmax mn ax or n >

No

Yes

End

The above example, although very simple, explains quite well several aspects of what a simulation model is. This model is simple enough to be solved analytically. However, it can also be formulated as an approximate numerical model which is organised into a numerical algorithm (or recipe) which can be followed repetitively. A simple calculator is sufficient to solve this model but, in more complex systems, a digital computer would generally be used.

Figure 1

Example of an algorithm to

solve the simple numerical

simulation model in the

text



1.2 A Note on UnitsThroughout this course we will use Field Units and/or SI Units, as appropriate. Although the industry recommendation is to convert to SI Units, this makes discussion of the field examples and cases too unnatural.

EXERCISE 1.Return to the simple model described by equation 1. Take as input data, that we start off with 25 bacteria in the colony. Take the value = 1.74 and take time steps t = 0.05 in the numerical model.

(i) Using the scale on the graph below, plot the analytical solution for the number of bacteria N(t) as a function of time between t = 0 and t = 2 (in arbitrary time units).

(ii) Plot as points on this same plot, the numerical solution at times t = 0, 0.5, 1.0, 1.5 and 2.0. What do you notice about these ?

(iii)Using a spreadsheet, repeat the numerical calculation with a t = 0.001 and plot the same 5 points as before. What do you notice about these?

Time0

500

1000

1 2

N(t)

(i)

(ii)



2 WHAT IS A RESERVOIR SIMULATION MODEL?

In the previous section, we introduced the idea of a simulation model applied to the growth of a bacterial colony. Now let us consider what we want to model - or simulate - when we come to developing petroleum reservoirs. Clearly, petroleum reservoirs are much more complex than our simple example since they involve many variables (e.g. pressures, oil saturations, flows etc.) that are distributed through space and that vary with time.

In 1953, Uren defined a petroleum reservoir as follows: ... a body of porous and permeable rock containing oil and gas through which fluids may move toward recovery openings under the pressure existing or that may be applied. All communicating pore space within the productive formation is properly a part of the rock, which may include several or many individual rock strata and may encompass bodies of impermeable and barren shale. The lateral expanse of such a reservoir is contingent only upon the continuity of pore space and the ability of the fluids to move through the rock pores under the pressures available.

L.C. Uren, Petroleum Production Engineering, Oil Field Exploitation, 3rd edn., McGraw-Hill Book Company Inc., New York, 1953.

This fine example of old fashioned prose is not so easy on the modern ear but does in fact say it all. And, whatever it says, then it is precisely what the modern simulation engineer must model!

2.1 The Task of Reservoir Simulation

Let us consider the possible magnitude of the task before us when we want to model (or simulate) the performance of a real petroleum reservoir. Figure 2 shows a schematic of reservoir depositional system for the mid-Jurassic Linnhe and Beryl formations in the UK sector of the North Sea. Some actual reservoir cores from the Beryl formation are shown in Figure 3. It is evident from the cores that real reservoirs are very heterogenous. The air permeabilities (k

air) range from 1mD to

almost 3000 mD and it is evident that the permeability varies quite considerably over quite short distances. It is common for reservoirs to be heterogeneous from the smallest scale to the largest as is evident in these figures. These permeability heterogeneities will certainly affect both pressures and fluid flow in the system. By contrast, a reservoir simulation model which might be used to simulate waterflooding in a layered system of this type is shown schematically in Figure 4. This model is clearly hugely simplified compared with a real system. Although the task of reservoir simulation may appear from this example to be huge, it is still one that reservoir engineers can - and indeed must - tackle. Below, we start by listing in general terms the activities involved in setting up a reservoir model.

One way of approaching this is to break the process down into three parts which will all have to appear somewhere in our model:

(i) Choice and Controls: Firstly, there are the things that we have some control over. For example:



Where the injectors and producer wells are located The capability that we have in the well (completions & downhole equipment) How much water or gas injection we inject and at what rate How fast we produce the wells (drawdown)

We note that certain quantities such as injection and production rates are subject to physical constraints imposed on us by the reservoir itself.

(ii) Reservoir Givens: Secondly, there are the givens such as the (usually very uncertain) geology that is down there in the reservoir. There may or may not be an active aquifer which is contributing to the reservoir drive mechanism. We can do things to know more about the reservoir/aquifer system by carrying out seismic surveys, drilling appraisal wells and then running wireline logs, gathering and performing measurements on core, performing and analysing pressure buildup or drawdown tests, etc.

(iii) Reservoir Performance Results: Thirdly, there is the observation of the results i.e the reservoir performance. This includes well production rates of oil, water and gas, the field average pressure, the individual well pressures and well productivities etc.

Barrier

Fluvia

l/Flood

plain

Estuar

ine Ba

ySSWFluvial

mud/sandsupply

Fluvial/FloodplainFacies AsociationFC: Fluvial channel sandstonesCRS: Crevasse channel/splay sandstonesOM/L: Overbank/lake mudstoneCS: Coal swamp/marsh mudstone and coal

Estuarine Bay-FillFacies AssociationTC: Tidal channel sandstonesTF: Lower intertidal flat sandstonesTS: Tidal shoal sandstoneSM: Salt marsh/upper intertidal flat mudstonesBM: Brackish bay mudstonesFTD: Flood tidal delta

Tidal Inlet-Barrier ShorelineFacies AssociationTCI: Tidal inlet/ebb channel sandstonesSS: Barrier shoreline sandstoneETD: Ebb tidal delta

Block diagram illustrates the gradual infilling of theBeryl Embayment by fluvial/floodplain (Linnhe l),estuarine-bay fill (Linnhe ll) and tidal inlet-barriershoreline facies sequences (Beryl Formation).

Shorefa

ce

CoalFluvial/crevasse channel-fillsTidal channel-fillsTidal inlet-fillsShoal/barsFlood-oriented currentsEbb-oriented currentsLongshore currents

FC

CRS

OM/CS

OM/CS

TC

TC

TC TC

TFTF

TF

TSSM

SMSM

SM

BMFTD

TCI

SS

SS

SS

ETD

L L

L

12.15

km

Figure 2

Conceptual depositional

model for the Linnhe and

Beryl formations from the

middle Jurassic period (UK

sector of the North Sea).

(G. Robertson in Cores

from the Northwest

European Hydrocarbon

Provence, edited by C D

Oakman, J H Martin and

P W M Corbett, Geological

Society, London. 1997).



Medium-grainedCarbonate cemented

sandstone ( =14%, ka = 2mD)- some thin clay and

carbonate rich lamination

Medium-grainedripple-laminated and

bioturbated carbonatecemented sandstone

( =10%, ka = 1mD)

Pyritic mudstone (pm)fine-grained bioturbated

sandstone( =16%, ka = 29mD)

Medium to coarse-grainedcross-stratified

sandstone( =21%, ka =1440mD)

- in fining-up units

Coarse-grainedcarbonaceous sandstone( =20%, ka =2940mD)

- in cross-stratified,fining-up units

1 m

Slab 1Top

15855 ft

Slab 2Top

15852 ft

Slab 3Top

14591 ft

Slab 4Top

14361 ft

Slab 5Top

14358 ft

15858 ftBase

15855 ftBase

14594 ftBase

14364 ftBase

14361 ftBase

yx

zInput:, c

rock, net to gross

kx, k

y, kz,

Swi, k

rw(Sw), k

rw(Sw),

Pc(S

w)

Water Injector

Producer

Approximate Size of Core vs. Grid Size

Figure 3

Cores from the mid-

Jurassic Beryl formation

from UK sector of the North

Sea. is porosity and ka is

the air permeability. (G.

Robertson in Cores from

the Northwest European

Hydrocarbon Provence,

edited by C D Oakman, J H

Martin and P W M Corbett,

Geological Society, London.

1997).

Figure 4

A schematic diagram of a

waterflood simulation in a

3D layered model with an

8x8x5 grid. The information

which is input for a single

grid block is shown.

Contrast this simple model

with the detail in a

geological model (Figure 2)

and in the actual cores

themselves (Figure 3).



2.2 What Are We Trying To Do and How Complex Must Our Model Be?

Therefore, at its most complex, our task will be to incorporate all of the above features (i) - (iii) in a complete model of the reservoir performance. But we should now stop at this point and ask ourselves why we are doing the particular study of a given reservoir? In other words, the level of modelling that we will carry out is directly related to the issue or question that we are trying to address. Some engineers prefer to put this as follows:

What decision am I trying to make? What is the minimum level of modelling - or which tool can I use - that

allows me to adequately make that decision?

This matter is put well by Keith Coats - one of the pioneers of numerical reservoir simulation - who said:

The tools of reservoir simulation range from the intuition and judgement of the engineer to complex mathematical models requiring use of digital computers. The question is not whether to simulate but rather which tool or method to use. (Coats, 1969).

Therefore, we may choose a very simple model of the reservoir or one that is quite complex depending on the question we are asking or the decision which we have to make. Without giving technical details of what we mean by simple and complex, in this context, we illustrate the general idea in Figure 5 which shows three models of the same reservoir. The first (Figure 5a), shows the reservoir as a tank model where we are just concerned with the gross fluid flows into and out of the system. In Chapter 2, we will identify models such as those in Figure 5a as essentially material balance models and will be discussed in much more detail later. The particular advantage of material balance models is that they are very simple. They can address questions relating to average field pressure for given quantities of oil/water/gas production and water influx from given initial quantities and initial pressure (within certain assumptions). However, because the material balance model is essentially a tank model, it cannot address questions about why the pressures in two sectors of the reservoir are different (since a single average pressure in the system is a core assumption). The sector model in Figure 5b is somewhat more complex in that it recognises different regions of the reservoir. This model could address the question of different regional pressures. However, even this model may be inadequate if the question is quite detailed such as: in my mature field with a number of active injector/producer wells where should I locate an infill well and should it be vertical, slanted or horizontal ? For such complicated questions, the model in Figure 5c would be more appropriate since it is more detailed and it contains more spatial information. This schematic sequence of models illustrates that there is no one right model for a reservoir. The simplicity/complexity of the model should relate to the simplicity/complexity of the question. But there is another important factor: data. It is clear that to build models of the types shown in Figure 5, we require increasing amounts of data as we go from Figure 5a5b5c. It is also evident that we should think carefully before building a very detailed model of the type shown in Figure 5c, if we have almost no data. There are some circumstances where we might build quite



a complicated model with little data to test out hypotheses but we will not elaborate on this issue at this point.

The simplicity/complexity of the model should relate to the simplicity/complexity of the question, and be consistent with the amount of reliable data which we have.

So, Sw and Sg

Average Pressure =Average Saturations =

Wells Offtake(a) "Tank" Model of the Reservoir

(b) Simple Sector Model

(c) Fine Grid Simulation Model of a Waterflood

Aquifer

Oil Leg

Aquifer

Producer - West Flank Producer - East Flank

Injector Producer

200ft

2000ft

P

We are now aware that various levels of reservoir model may be used and that the reservoir engineer must choose the appropriate one for the task at hand. We will assume at this point that building a numerical reservoir simulation model is the correct approach for what we are trying to achieve. If this is so, we now address the issue: What do we model in reservoir simulation and why do we model it ? There are, as we have said, a range of questions which we might answer, only some of which require a full numerical simulation model to be constructed. Let us now say what a numerical reservoir simulation model is and what sorts of things it can (and cannot) do.

Definition: A numerical reservoir simulation model is a grid block model of a petroleum reservoir where each of the blocks represents a local part of the

Figure 5

Schematic illustrations of

reservoir models of

increasing complexity.

Each of these may be

suitable for certain types of

calculation (see text).



reservoir. Within a grid block the properties are uniform (porosity, permeability, relative permeability etc.) although they may change with time as the reservoir process progresses. Blocks are generally connected to neighbouring blocks are fluid may flow in a block-to-block manner. The model incorporates data on the reservoir fluids (PVT) and the reservoir description (porosities , permeabilities etc.) and their distribution in space. Sub-models within the simulator represent and model the injection/producer wells.

An example of numerical reservoir simulation gridded model is shown in Figure 6, where some of the features in the above definition are evident. We now list what needs to be done in principle to run the model and then the things which a simulator calculate, if it has the correct data. To run a reservoir simulation model, you must:

(a) Gather and input the fluid and rock (reservoir description) data as outlined above;

(b) Choose certain numerical features of the grid (number of grid blocks, timestep sizes etc);

(c) Set up the correct field well controls (injection rates, bottom hole pressureconstraints etc.); it is these which drive the model;

(d) Choose which output (from a vast range of possibilities) you would like to haveprinted to file which you can then plot later or - in some cases - while thesimulation is still running.

The output can include the following (non-exhaustive) list of quantities:

The average field pressure as a function of time The total field cumulative oil, water and gas production profiles with time The total field daily (weekly, monthly, annual) production rates of each

phase: oil, water and gas The individual well pressures (bottom hole or, through lift curves, wellhead)

over time The individual well cumulative and daily flowrates of oil, water and gas

with time Either full field or individual well watercuts, GORs, O/W ratios with time The spatial distribution of oil, water and gas saturations throughout the

reservoir as functions of time i.e. So(x,y,z;t), S

w(x,y,z;t) and S

g(x,y,z;t)

Some of the above quantities are shown in simulator output in Figure 7. This field example is for a Middle East carbonate reservoir where the structural map is shown in Figure 7(d). Figure 7(a) shows the field and simulation results for total oil and water cumulative production over 35 years of field life. Figure 7(b) shows the actual and modelled average field pressure. The type of results shown in Figures 7(a) and 7(b) are very common but the modelling of the RFT (Repeat Formation Tester) pressure shown in Figure 7(c) is less common. The RFT tool measures the local pressure at a given vertical depth and, in this case, it can be seen that the reservoir comprises of three zones each of ~ 100 ft thick and each is at a different pressure. This indicates that



pressure barriers exist (i.e. flow is restricted between these layers). This is correctly modelled in the simulation. This is an interesting and useful example of how reservoir simulation is used in practice.

Note that a vast quantity of output can be output and plotted up and the post-processing facilities in a reservoir simulator suite of software are very important. There is no point is doing a massively complex calculation on a large reservoir system with millions of grid blocks if the output is so huge and complex that it overwhelms the reservoir engineers ability to analyse and make sense of the output. In recent years, data visualisation techniques have played on important role in analysing the results from large reservoir simulations.

Observed Water

Observed Oil

Modelled Water

Observed DataModelled Data

Modelled Oil

00

100

200

300

400

500

600

700

5 10 15 20 25 30 35

Year of Production

Cum

ulat

ive

Pro

duct

ion

(MM

B)

01500

2000

2500

3000

3500

5 10 15 20 25 30 35

Year of Production

Ave

rage

Pre

ssur

e (p

sia)

1000 1500 1000 2500 3000

-300

-200

-100

Datum

Dep

th (f

t.)

(a) Full field history match of cumulative oil and water production

(b) Full field history match of volume weighted pressure

(c) Match of RFT pressure data by reservoir simulation model at Year 30

Observed Modelled

Figure 6

An example of a 3D

numerical reservoir

simulation model. The

distorted 3D grid covers

the crestal reservoir and a

large part of the aquifer

which is shown dipping

down towards the reader.

Oil is shown in red and

water is blue and a vertical

projection of a cross-section

at the crest of the reservoir

is shown on the x/z and

y/z planes on the sides of

the perspective box. Two

injectors can be seen in the

aquifer as well as a crestal

horizontal well. Two faults

can be seen at the front

of the reservoir before the

structure dips down into the

aquifer. The model contains

25,743 grid blocks.

Figure 7 (a) to (d)

Example of some typical

reservoir simulator output.

From SPE36540,

Reservoir Modelling and

Simulation of a Middle

Eastern Carbonate

Reservoir, M.J. Sibley,

J.V. Bent and D.W. Davis

(Texaco), 1996.



Observed Water

Observed Oil

Modelled Water

Observed DataModelled Data

Modelled Oil

00

100

200

300

400

500

600

700

5 10 15 20 25 30 35

Year of ProductionC

umul

ativ

e P

rodu

ctio

n (M

MB

)

01500

2000

2500

3000

3500

5 10 15 20 25 30 35

Year of Production

Ave

rage

Pre

ssur

e (p

sia)

1000 1500 1000 2500 3000

-300

-200

-100

Datum

Dep

th (f

t.)

(a) Full field history match of cumulative oil and water production

(b) Full field history match of volume weighted pressure

(c) Match of RFT pressure data by reservoir simulation model at Year 30

Observed Modelled

1 Mile C

DrilledNew LocationInjector LocationConvert to Injector

C

C

C

CC

A Lower CretaceousCarbonate Reservoir in theArabian Peninsula

Most wells drilled in 1955-1962

> 600 MMBO produced byearly 1980s

-this study 1992

(d) Field structural map with 50' contour interval

Figure 7b

Figure 7c

Figure 7d



How some of this output might be used is illustrated schematically in Figure 8. This is an imaginary case where the reservoir study is to consider the best of four options in Field A: Option 1 - to continue as present with the waterflood; Option 2 - upgrade peripheral injection wells; Option 3 - upgrade injectors and drill six new injectors; Option 4 - drill four new infill wells. Clearly, it is much cheaper to model these four cases than to actually do one of them. The important quantities are the oil recovery profiles for each case compared with the scenario where we simple proceed with the current reservoir development strategy (Option 1). Of course, we do not know whether the forward predictions which we are taking as what would happen anyway, are actually correct. Likewise, we may be unsure of how accurate our forward predictions are for each of the various scenarios. In fact, an important aspect of reservoir simulation is to assess each of the various uncertainties which are associated with our model. This would ideally lead to range of profiles for any forward modeling but we will deal with this in detail later. We discuss the handling of uncertainties in rather more detail in Section 3.8. of this Chapter.

In the schematic case shown in Figures 8(a) - 8(g) we note that:

(i) The areal plan of the reservoir is given showing injector and producer well location in Figure 8(a);

(ii) The corresponding stratification/lithology of the field is shown along the well A-B-C-D transect in Figure 8(b);

(iii) Figures 8(c) and 8(d) show the areal grid and the vertical grid, respectively;

(iv) The forward predictions of cumulative oil for the various options are shownin Figure 8(f). Note that Option 3 produces most oil (but it involves drillingsix additional injection wells);

(v) The economic evolution of each option using the predicted oil recovery profiles in Figure 8(f) is shown in Figure 8(g) (where NPV = Net Present Value; IRR = Interval Rate of Return: these are economic measures explained in the economics module of the Heriot-Watt distance learning course). Note that option 4 emerges in the most economic case although it produces rather less oil than option 3.

A

B

C

D

InjectorProducer

(a) Field A areal plan showing injector and producer well locations; lithology is given from wells A, B, C and D

Figure 8

Schematic example of how

reservoir simulation might

be used in a study of four

field development options

(see text).



A

BC

D

Sand 1

Sand 2Sand 3

Sand 4

(b) Schematic vertical cross-section showing the lithology across the field through 4 wells A, B, C and D

A

B

C

D

A

B

C

D

A B CD

NZ = 8

(c) Reservoir simulation (areal) grid showing current well locations.

A

B

C

D

A

B

C

D

A B CD

NZ = 8

(d) Reservoir simulation vertical cross-sectional grid showing current well locations.

Figure 8 (c)

Figure 8 (d)

Figure 8 (b)



The grid has 8 blocks in the z- direction representing the thickness of theformation as shown below; NZ = 8. Note that the vertical grid is not uniform.

Time

Infill Wells

Periferal Injectors

Option 3

Option 4

Option 2

21

34

Continue as at present (do nothing) Option 1Cum

ulat

ive

Oil

Option

NP

V o

r IR

R

A

B

C

D

(e) Option 1- continue as at present; Option 2 - upgrade peripheral injection wells; Option 3- upgrade injectors + add 6 new injectors; Option 4 - drill four new infill wells.

Time

Infill Wells

Periferal Injectors

Option 3

Option 4

Option 2

21

34


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Option

NP

V o

r IR

RA

B

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D

(f) Simulated oil recovery results for various options

Time

Infill Wells

Periferal Injectors

Option 3

Option 4

Option 2

21

34


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Option

NP

V o

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R

A

B

C

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Figure 8 (e)

Figure 8 (f)

Figure 8 (g)



(g) Economic evaluation of options - NPV or IRR

Now consider what we are actually trying to do in a typical full field reservoir simulation study. There is a short answer to this is often said in one form or another: it is that the central objective of reservoir simulation is to produce future predictions (the output quantities listed above) that will allow us to optimise reservoir performance. At the grander scale, what is meant by optimise reservoir performance is to develop the reservoir in the manner that brings the maximum economic benefit to the company. Reservoir simulation may be used in many smaller ways to decide on various technical matters although even these - for example the issue illustrated in Figure 8 - are usually reduced to economic calculations and decisions in the final analysis as indicated in Figure 8(g).

3 FIELD APPLICATION OF RESERVOIR SIMULATION

3.1 Reservoir Simulation at Appraisal and in Mature FieldsUp to this point, we have considered what a numerical reservoir simulation model is and we have touched on some of the sorts of things that can be calculated. Rather than continue with a discussion of the various technical aspects of reservoir simulation one by one, we will proceed to three field applications of reservoir simulation. These studies will raise virtually all of the technical terms and concepts and many of the issues that will be studied in more detail later in this course. The important terms and concepts will be italicised and will appear in the Glossary at the front of this chapter.

Reservoir simulation may be applied either at the appraisal stage of a field development or at any stage in the early, middle or late field lifetime. There are clearly differences in what we might want to get out of a study carried out at the appraisal stage of a reservoir and a study carried out on a mature field.

Appraisal stage: at this stage, reservoir simulation will be a tool that can be used to design the overall field development plan in terms of the following issues:

The nature of the reservoir recovery plan e.g. natural depletion, waterflooding,gas injection etc.

The nature of the facility required to develop the field e.g. a platform, a subsea development tied back to an existing platform or a Floating Production System (for an offshore fileld).

The nature and capacities of plant sub-facilities such as compressors forinjection, oil/water/gas separation capability.

The number, locations and types of well (vertical, slanted or horizontal) to bedrilled in the field.

The sequencing of the well drilling program and the topside facilites.



It is during the initial appraisal stage that many of the biggest - i.e. most expensive - investment decisions are made e.g. the type of platform and facilities etc. Therefore, it is the most helpful time to have accurate forward predictions of the reservoir performance. But, it is at this time when we have the least amount of data and, of course, very little or no field performance history (there may be some extended production well tests). Therefore, it seem that reservoir simulation has a built-in weakness in its usefulness; just when it can be at its most useful during appraisal is precisely when it has the least data to work on and hence it will usually make the poorest forward predictions. So, does reservoir simulation let us down just when we need it most? Perhaps. However, even during appraisal, reservoir simulation can take us forward with the best current view of the reservoir that we have at that time, although this view may be highly uncertain. As we have already noted, if major features of the reservoir model (e.g. the stock tank oil initially in place, STOIIP) are uncertain, then the forward predictions may be very inaccurate. In such cases, we may still be able to build a range of possible reservoir models, or reservoir scenarios, that incorporate the major uncertainties in terms of reservoir size (STOIIP), main fault blocks, strength of aquifer, reservoir connectivity, etc. By running forward predictions on this range of cases, we can generate a spread of predicted future field performance cases as shown schematically in Figure 9. How to estimate which of these predictions is the most likely and what the magnitude of the true uncertainties are is very difficult and will be discussed later in the course.

Time (Year)

Most Probable Case

"Pessimistic" Case

"Optimistic" Case

Cum

ulat

ive

Oil

Rec

over

y (S

TB)

2005 2010 2015

For example, scenarios for various cases may involve:

Different assumptions about the original oil in place (STOIIP; Stock Tank Oil Originally In Place).

Different values of the reservoir parameters such as permeability, porosity,net-to-gross ratio, the effect of an aquifer, etc..

Major changes in the structural geology or sedimentology of the reservoir

e.g. sealing vs. leaky faults in the system, the presence/absence of majorfluvial channels, the distribution of shales in the reservoir etc..

Figure 9

Spread of future predicted

field performances from a

range of scenarios of the

reservoir at appraisal.



Mature field development: we define this stage of field development for our purposes as when the field is in mid-life; i.e. it has been in production for some time (2 - 20+ years) but there is still a reasonably long lifespan ahead for the field, say 3 - 10+years. At this stage, reservoir simulation is a tool for reservoir management which allows the reservoir engineer to plan and evaluate future development options for the reservoir. This is a process that can be done on a continually updated basis. The main difference between this stage and appraisal is that the engineer now has some field production history, such as pressures, cumulative oil, watercuts and GORs (both field-wide and for individual wells), in addition to having some idea of which wells are in communication and possibly some production logs. The initial reservoir simulation model for the field has probably been found to be wrong, in that it fails in some aspects of its predictions of reservoir performance e.g. it failed to predict water breakthough in our waterflood (usually, although not always, injected water arrives at oil producers before it is expected). By the way, if the original model does turn out to be wrong, this does not invalidate doing reservoir simulation in the first place. (Why do you think this is so?)

At this development stage, typical reservoir simulation activities are as follows:

Carrying out a history match of the (now available) field production historyin order to obtain a better tuned reservoir model to use for future field performanceprediction

Using the history match to re-visit the field development strategy in termsof changing the development plan e.g. infill drilling, adding extra injectionwater capability, changing to gas injection or some other IOR scheme etc.

Deciding between smaller project options such as drilling an attic horizontalwell vs. working over 2 or 3 existing vertical/slanted wells

It may be necessary to review the equity stake of various partner companiesin the field after some period of production although this typically involvesa complete review of the engineering, geological and petrophysical data priorto a new simulation study

The reservoir recovery mechanisms can be reviewed using a carefully historymatched simulation model e.g. if we find that, to match the history, we must reduce the vertical flows (by lowering the vertical transmissibility), we maywish to determine the importance of gravity in the reservoir recovery mechanism.(Coats (1972) refers to this as the educational value of simulation modelsand it is a part of good reservoir management that the engineer has a goodgrasp of the important reservoir physics of their asset.)

There are many reported studies in the SPE literature where the simulation model is re-built in early-/mid-life of the reservoir and different future development options are assessed (e.g. see SPE10022 attached to this chapter).

Late field development: we define this stage of field development as the closing few years of field production before abandonment. A question arises here as to whether the field is of sufficient economic importance to merit a simulation study at this stage.



A company may make the call that it is simply not worth studying any further since the payback would be too low. However there are two reasons why we may want to launch a simulation study late in a fields lifetime. Firstly, we may think that, although it is in far decline, we can develop a new development strategy that will give the field a new lease of life and keep it going economically for a few more years. For example, we may apply a novel cheap drilling technology, or a program of successful well stimulation (to remove a production impairment such as mineral scale) or we may wish to try an economic Improved Oil Recovery (IOR) technique. Secondly, the cost of field abandonment may be so high - e.g. we may have to remove an offshore structure - that almost anything we do to extend field life and avoid this expense will be economic. This may justify a late life simulation study. However, there are no general rules here since it depends on the local technical and economic factors which course of action a company will follow. In some countries there may be legislation (or regulations) that require that an oil company produces reservoir simulation calcualtions as part of their ongoing reservoir management.

3.2 Introduction to the Field CasesThree field cases are now presented. We reproduce the full SPE papers describing each of these reported cases. In the text of each of these papers there are margin numbers which refer to the Study Notes following the paper. We use these to explain the concepts of reservoir simulation as they arise naturally in the description of a field application. In fact, you may very well understand many of the term immediately from the context of their description in the SPE paper.

The three field examples are as follows:

Case 1: The Role of Numerical Simulation in Reservoir Management of a West Texas Carbonate Reservoir, SPE10022, presented at the International Petroleum Exhibition and Technical Symposium of the SPE, Beijing, China, 18 - 26 March 1982, by K J Harpole and C L Hearn.

Case 2: Anguille Marine, a Deepsea-Fan Reservoir Offshore Gabon: From Geology Toward History Matching Through Stochastic Modelling, SPE25006, presented at the SPE European Petroleum Conference (Europec92), Cannes, France, 16-18 November 1992, by C.S. Giudicelli, G.J. Massonat and F.G. Alabert (Elf Aquitaine)

Case 3: The Ubit Field Rejuvenation: A Case History of Reservoir Management of a Giant Oilfield Offshore Nigeria, SPE49165, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA, 27-30 September 1998, by C.A. Clayton et al (Mobil and Department of Petroleum Resources, Nigeria)

These cases were chosen for the following main reasons:

They are all good technical studies that illustrate typical uses of reservoirsimulation as a tool in reservoir management (we have deliberately taken all cases at the middle and the mature stages of field development since muchmore data is available at that time);

They introduce virtually all of the main ideas and concepts of reservoirsimulation in the context of a worked field application. As these concepts



and specialised terms arise, they are explained briefly in the study notes althoughmore detailed discussion will appear later in the course. Compact definitions of the various terms are given in the Glossary at the front of this module;

They are all well-written and use little or no mathematics;

By choosing an example from the early 1980s, the early/mid 1990s and the late 1990s, we can illustrate some of the advances in applied reservoir simulation that have taken place over that period (this is due to the availability of greater computer processing power and also the adoption of new ideas in areas such as geostatistics and reservoir description).

How you should read the next part of the module is as follows:

Read right through the SPE paper and just pay particular attention when there is a Study Note number in the margin;

Go back through the paper but stop at each of the Study Notes and read through the actual point being made in that note.

As noted above, all the main concepts that are introduced can also be found in the Glossary which should be used for quick reference throughout the course or until you are quite familiar with the various terms and concepts in reservoir simulation.

See SPE 10022 paper in Appendix

3.3 Case 1: The West Seminole Field Simulation Study (SPE10022, 1982)Case 1: The Role of Numerical Simulation in Reservoir Management of a West Texas Carbonate Reservoir, SPE10022, presented at the International Petroleum Exhibition and Technical Symposium of the SPE, Beijing, China, 18 - 26 March 1982. by K J Harpole and C L Hearn.

Summary: This paper presents a study from the early 1980s where a range of re-appraisal strategies for a mature carbonate field are being evaluated using reservoir simulation. For example, possible development strategies include the blowdown of the gas cap or infill drilling. They explicitly state in their opening remarks that their central objective is to optimise reservoir performance by choosing a future development strategy from a range of defined options. The structure of the study is very typical of the work flow of a field simulation study, viz Introduction; Reservoir Description; Simulation Model; History Matching; Future Performance; Conclusions and recommendations. Although this paper is almost 20 years old, it introduces the reader in a very clear way to virtually all the concepts of conventional reservoir simulation.

Location maps and general reservoir structure shown in Figures 1 and 2 of SPE 10022.



Study Notes Case 1: 1. States explicitly that the objective of the study is to optimise reservoir performance as discussed in the introductory part of this module.

2. Raises the issue of an accurate reservoir description being required and this is emphasised throughout this paper.

3. An interesting point is raised comparing the carbonate reservoir of this study broadly to sandstone reservoirs. It notes that the post-depositional diagenetic effects are of major importance in the West Seminole field in that they affect the reservoir continuity and quality i.e. the local porosity and permeability. In contrast, it is noted that sandstone reservoir are mainly controlled by their depositional environment and tend to show less diagenetic overprint. However, a point to note is that the broad outline and work flow of a numerical reservoir simulation study are quite similar for both carbonate and sandstone reservoirs.

4. Carbonate diagenetic processes include dolomitisation (dolomite = CaMg(CO3)

2),

recrystallisation, cementations and leaching. This geochemical information is not directly used in the simulation model but it is important since it leads to identification of reservoir layer to layer flow barriers (see below).

5. Strategy: Previous gas re-injection into the cap + peripheral water injection => not very successful. They want to implement a 40 acre, 5-spot water flood; see Fig. 3. A 5-spot is a particular example of a pattern flood which is appropriate mainly for onshore reservoirs where many wells can be drilled with relatively close spacing (see Waterflood Patterns in the Glossary).

6a. They raise the issue of vertical communication between the oil and gas zones. This is an excellent example of an uncertain reservoir feature that can be modelling using a range of scenarios from free flow between layers to zero interlayer flow + all cases in between. Therefore, we can run simulations of all these cases and see which one agrees best with the field observations (which is what they do, in fact).

6b. The vertical communication - or lack of it - will affect flow between the oil and gas zones which may lead to loss of oil to the gas cap; see Figure 4.

7. States the structure of the simulation study work flow: Accurate reservoir description - Develop the simulation model (perform the history match - see below - use model for future predictions - evaluate alternative operating plans). A history match is when we adjust the parameters in the simulation model to make the simulated production history agree with the actual field performance (expanded on below).

8a. A lengthy geological description of the reservoir is given where the depositional environment is described - reference is made to extensive core data (~7500 ft. of core).

8b. The impact of the geology/diagenesis in the simulation model is discussed here. There is evidence of field wide barriers due to cementation with anhydrite which may reduce vertical flows. This is important since it gives a sound geological interpretation to the existence of the vertical flow barriers. Therefore, if we need to include this to



match the field performance, we have some justification or explanation for it rather than it simply being a fiddle factor in the model.

9. Figure 5 shows the 6 major reservoir layers where the interfaces between the layers are low , low k anhydrite cement zones. Again, these may be explained from the depositional environment and the subsequent diagenetic history of the reservoir.

10. 7500 ft. of whole core analysis for the W. Seminole field was available which was digitised for computer analysis (not common at that time, late 1970s). This is very valuable information and is often not available.

11. Permeability distributions in the reservoir are shown in Fig. 6 and these data are vital for reservoir simulation. Dake (1994; p.19) comments on this type of data: What matters in viewing core data is the all-important permeability distribution across the producing formations; it is this, more than anything else, that dictates the efficiency of the displacement process.

12. They note that no consistent k/ correlation is found in this system (which is quite common in carbonates). Often some approximate k/ correlation can be found for sandstones (e.g. see k/ Correlations in the Glossary).

13. The W. Seminole field does exhibit a distinctly layered structure and the corresponding permeability stratification in the model is shown in Fig. 7.

14a. Pressure transient work - again gives important ancillary information on the reservoir. The objectives of this work were to determine whether there was (i) directional permeability effects, directional fracturing or channelling; (ii) the degree of stratification in the reservoir; (iii) evaluation of the pay continuity between the injectors and producers

14b. No evidence of channelling or obvious fracture flow system

14c. Distinct evidence was seen for: (a) the presence of a layered system; (b) restricted communication between layers (P 200 - 250 psi between layers). This is vital information since it gives an immediate clue that there is probably not completely free flow between layers i.e. there are barriers to flow as suspected from the geology.

14d. Finally on this issue, there is pressure evidence of arithmetically averaged permeabilities. This is again typical of layered systems.

15. Native state core tests are referred to from which they obtained steady-state relative permeabilities. These could be very valuable results but no details given here. NB it appears that only one native state core relative permeability was actually measured. This is probably too little data but reflects the reality in many practical reservoir studies that often the engineer does not have important information; however, we just have to get on with it.

16. In this study the reservoir simulator which they used was a commercial Black Oil Model (3D, 3 phase - oil/water/gas). Modelling carried out on the main dome portion of the reservoir. This is done quite often in order to simplify the model and to focus



on the region of the field of interest (and importance in terms of oil production). A no flow boundary is assumed in the model on the saddle with the east dome (justified by different pressure history). Again, this is supported by field evidence but it may also be a simplifying judgement to avoid unnecessary complication in the model.

17a. The grid structure used in the simulations is shown in Fig 8. The particular grid that is chosen is very important in reservoir simulation. An areal grid of 288 blocks ( 16 x 18 blocks) - about 10 acre each is taken along with six layers in the vertical direction; i.e. a total of 1728 blocks. This would be a very small model by todays standards and could easily be run on a PC - this was not the case in late 1970s.

17b. They refer to changing the transmissibilities between grid blocks in order to reduce flows. (See Glossary for exact definition of transmissibility.)

18. The following three concepts are closely related (see Pseudo-isation and Upscaling in the Glossary):

18a. Grid size sensitivity: Refers to the introduction of errors due to the coarsness of the grid known as numerical dispersion.

18b. The very important concept of pseudo--relative permeability is introduced here (Kyte and Berry, 1975). Pseudos are introduced in order to control numerical dispersion and account for layering. In essence, the use of pseudos can be seen as a fix up for using a coarse grid structure.

18c. Corresponding coarse and fine grid reservoir models are shown in Fig. 9. They note that the fine grid model uses rock relative permeabilities while the coarse grid model uses pseudo relative permeabilities.

19. History Matching: The basic idea of history matching is that the model input is adjusted to match the field pressures and production history. This procedure is intended as being a way of systematically adjusting the model to agree with field observations. Hopefully we can change the correct variables in the model to get a match e.g. we may examine the sensitivity to changes in vertical flow barriers in order to find which level of vertical flow agrees best with the field (indeed, this is done in this study). See History Matching in the Glossary.

20a. Early mechanism identified as solution gas drive and assistance from expansion. Some initial discussion of field experience and numerical simulation conclusions is presented and developed in these points.

20b. They note some problems with data from early field life. (i) Complicated by free gas production; (ii) channelling due to poor well completions; (ii) no accurate records on gas production for the first 6 years. 20c. The actual field history match indicates that approx. 8 - 10 BCF of gas must have been produced over this early period in order to match the field pressures. This is a use of a material balance approach in order to find the actual early STOIIP (STOIIP = Stock Tank Oil Initially In Place).



21a. They present a description of some adjustments to the history match - but overall it is very good (which they attribute to extensive core data).

21b. Some highlighting of problems with earlier water injection .

21c. The actual history match of reservoir pressure and production is shown in Fig. 10. This is a good history match but think of which field observable - gas production, water production or average field pressure - is the easiest/most difficult to match?

22. A good description of their study of the sensitivity to vertical communication is given at this point. This is examined by adjusting the vertical transmissibilities. They look at the following cases: (i) no barriers; (ii) moderate barrier; (iii) strong barriers and (iv) no-flow barriers. Most of the sensitivties are for the moderate and strong barrier cases.

23a. Results showed that => strong barrier case is best but some problem high GOR wells are encountered randomly spaced through the field. They diagnosed and simulated this as behind the pipe gas flow in these wells to explain the anomalies in the field observations. This is quite a common explanation that appears in many places.

23b. Layer differential pressures up to 200 - 250 psi can only be reproduced for the strong barrier case. In simulation terms, this is probably the strongest evidence that this is the best case match.

24. The strong barrier case was chosen as the base case and this was used for the predictive runs. The base case predictions refer to the cases which essentially continue the current operations and these are shown in Fig. 11.

25. The strategies looked at for the future sensitivities are listed as follows: (i) change rate of water injection; (ii) management of gas cap voidage i.e. increase of gas and blowdown at different times; (iii) infill drilling.

26a. Outlines the problems/issues for various strategies as follows: (i) shows vertical communication is very importance - it has a major impact on predicted reservoir performance; (ii) shows that can avoid high future P between gas cap and oil zone by high water injection or early blowdown; (iii) shows better development strategy is to keep low P e.g. increase gas injection or infill drill. Finally, shows infill drilling is the most attractive option and the forward prediction for this case is shown in Figure 12.

26b. Table showing some alternatives in text.

27a. A brief summary of the best future development option is given which is: (i) infill drilling as the best option; (ii) water injection increased concurrently with the drilling program to maintain voidage replacement (but prevent the over-injection of water).

27b. For completeness, it is explained why other plans are not as attractive; i.e. blowdown of gas cap before peak in waterflood production rate would significantly reduce oil recovery.



28. A reasonably good initial forward prediction from 1978 - 1981 is shown in Figs. 13 and 14.

29. Conclusions are given which, in summary, are as follows:

1. Detailed reservoir description essential for numerical modelling.

2. Carbonate - both primary and post-depositional diagenetic factors are important.

3. Waterflood in W. Seminole very sensitive to vertical permeability.

4. Vertical permeability is broadly characterised using 3D numerical simulation.

5. Understanding of reservoir response (mechanism) essential to good management.

6. Management of W. Seminole field best if minimum _P between oil zone and gas cap (lower losses of oil --> gas cap) by: (i) infill drilling; (ii) controlling water injection rates to maintain voidage replacement - dont over-inject; (iii) careful management of voidage replacement into gas cap.

Important terms and concepts introduced in SPE10022:

Specific to Reservoir Simulation: history match, permeability distribution, black oil model, grid structure, transmissibility, numerical dispersion, pseudo--relative permeabilites.

General terms: 5-spot water flood, permeability distribution, k/ correlation, steady-state relative permeability, rock relative permeabilities, solution gas drive, material balance, infill drilling, voidage replacement.

3.4 Ten Years Later - 1992An interesting snapshot of where reservoir simulation technology had reached 10 years after the West Seminole study can be seen in the following papers:From the proceedings of the SPE 67th Annual Technical Conference, Washington, DC, 4-7 October 1992:

SPE24890: From Stochastic Geological Description to Production Forecasting in Heterogeneous Layered Systems, K. Hove, G. Olsen, S. Nilsson, M. Tonnesen and A. Hatloy (Norsk Hydro and Geomatic)Summary: This paper describes the transfer of data from a detailed gridded stochastic geological model to a more coarsely gridded reservoir simulation model. It is essentially a field application of a methodology described in a previous paper from the same company (Damsleth et al, 1992; Damsleth, E., Tjolsen, C.B., Omre, H. and Haldonsen, H.H., A Two Stage Stochastic Model Applied to a North Sea Reservoir, J. Pet. Tech., pp. 402-408, April 1992). The two step procedure involves a first step of constructing the geological architecture of the reservoir followed by a



second stage where the petrophysical values are assigned to each building block in the geological model. The consequences of making various assumptions in the gridding are evaluated for water, gas and WAG (water-alternating-gas) injection. They note that is it very important to represent the main geological features in the gridded model. It was also noted that, when a regular coarse grid was used, the contrast in properties of this heterogeneous reservoir were smoothed out by the averaging process and in most cases led to a more optimistic predicted production performance. That is, the more stochastic models led to a reduction in predicted recovery compared with conventional coarse gridded models.

In the proceedings of the SPE European Petroleum Conference, Cannes, France, 16-18 November 1992. A session at this conference produced the following selection of reservoir simulation papers:

SPE25008: Reservoir Management of the Oseberg Field After Four Years, S. Fantoft (Norsk Hydro)

Summary: The Oseberg Field (500x106 Sm3 oil; 60x106 Sm3 gas) comprises of seven partly communicating reservoirs. Both water and gas are being injected and modelled in this study and results indicate over 60% recovery in the main reservoir units. The modelling results indicate that the plateau production will be extended by the use of horizontal wells. The objective of the simulation study was exactly this - i.e. to maximise the plateau and improve ultimate oil recovery. This is a very competent simulation study and - although details are not given - it is stated that the geological model is updated annually based on information from new wells. It establishes several aspects of the reservoir mechanics and makes a number of recommendations for operating practice in the future. In other respects, this is quite a conventional study.

SPE25057: The Construction and Validation of a Numerical Model of a Reservoir Consisting of Meandering Channels, W. van Vark, A.H.M. Paardekam, J.F. Brint J.B. van Lieshout and P.M. George (Shell)Summary: This study focuses on a reservoir which has low sandbody connectivity and which is interpreted as a meandering channel fluvial system. Two years of depletion data is available and one of the aims of the study was to evaluate the possibility of performing a waterflood in this field. They identified a problem in that the sandbody connectivity was lower than might be expected from the sedimentology alone and it was conjectured that this might be due to minor faulting with throws of a few meters. This study again emphasises the importance of the reservoir geology and tries to relate the performance back to this. The geological model is also an early practical example of using a voxel representation of the system - approx. 128,000 voxels were used in the model. They noted that the original (sedimentological) models gave over optimistic connectivity. An acceptable match to observed field pressures by including some level of smaller scale faulting.

SPE25059: Development Planning in a Complex Reservoir: Magnus Field UKCS Lower Kimmeridge Clay Formation (LKCF), A.J. Leonard, A.E. Duncan, D.A. Johnson and R.B. Murray (BP Exploration Operating Co.)Summary: This simulation study was carried out on the geologically complex, low net to gross LKCF (rather than on higher net to gross Magnus sands studied



previously). The objective was to formulate a development plan for the LKCF which would accelerate production from these sands. Stochastic modelling techniques were integrated into more conventional deterministic models and various options were screened for inherent uncertainty and risks. The study concluded that a phased water injection scheme was the best way forward with the phasing being used to manage and offset the considerable geological risks. Ranges of expected recovery were generated and an incremental recovery of 60 MMstb was predicted increasing the total reserve of the LKCF by a factor of x2.4. This study also demonstrated the importance of inter-disciplinary team work to overcome the previously inhibiting high risks involved.

The proceedings of Europec92 also included the following paper:

SPE25006: Anguille Marine, a Deepsea-Fan Reservoir Offshore Gabon: From geology Toward History Matching Through Stochastic Modelling, C.S. Giudicelli, G.J. Massonat and F.G. Alabert (Elf Aquitaine)This paper is such a good example of contemporary studies at that time, that this is chosen as our Case 2 example and is presented in some detail in the next section.

3.5 Case 2: The Anguille Marine Study (SPE25006,1992)Case 2: Anguille Marine, a Deepsea-Fan Reservoir Offshore Gabon: From geology Toward History Matching Through Stochastic Modelling, SPE25006, presented at the SPE European Petroleum Conference (Europec92), Cannes, France, 16-18 November 1992, by C.S. Giudicelli, G.J. Massonat and F.G. Alabert (Elf Aquitaine)


Summary: The Anguille Marine Field in Gabon has 25 years of production history. The waterflood performance indicated severe sedimentary heterogeneity as the field is known to have been deposited in a deep water fan sedimentary environment. This paper is one of the first to refer to the multi-scale nature of the heterogeneity (5 scales were studied) and to refer this back to the sequence stratigraphy of the depositional environment. The sequence stratigraphic approach allowed the field to be divided into the main types of turbiditic geometries (channels, lobes, slumps, laminated facies). Fine scale models (> 2 million grid blocks) were generated using geostatistical techniques and several issues were raised concerning both the geological model and the upscaling process itself. This is a very good example of an early integrated geology(sedimentology)/engineering study in reservoir simulation. The multi-scale nature of the heterogeneity is well related back to the geology.

Study Notes Case 2: 1. Depositional environment: the Anguille Marine field is a deep sea fan environment (i.e a turbidite) with a low sand/shale ratio. This geological description opens the discussion (unusual for previous simulation studies) and the geology features heavily in the flow properties and hence in the geological and reservoir models of this field.

2. Sequence stratigraphy: A more modern feature of reservoir simulation is that the five identified scales of heterogeneity are recognised and some attempt is made to



incorporate them into the 3D simulation model. These scales are also firmly linked to the geology (sedimentology) through the principles of sequence stratigraphy.

3. Geostatistics: Reference is made to how the geological features constrain the fine scale 3D models (of > 2 million blocks - which was large for the time) using geostatistical techniques. By the early 90s, the use of geostatistical methods was becoming more widespread and how it has been applied in this case is covered better by Refs. 1 - 5 in this paper.

Location and structure maps of Anguille Marine are given in Figures 1 - 4.

4. Brief field facts: Discovery 1962; primary depletion commenced in 1966 but reservoir pressure fell rapidly over the next 2 - 3 years and GOR increased; waterflooding from 1971 restored pressure support but channelling led to early water breakthrough; infill drilling not very successful due to lack of current understanding of complex reservoir geology; new approach in 1990 focused more strongly on the reservoir geology of this heterogeneous low sand/shale ratio system recognising the characteristic geometries of a tubditic fan - lobes channels, levees, slumps, laminated facies etc.

5. The approach: It is important in all reservoir simulation studies to have a clear logic to how we approach the simulation of a large complex reservoir system. Here they describe their general methodology although details are in Refs. 1 - 4 at the end of the paper. Basically they: describe and model upper reservoir/ extend to the whole reservoir/ try to translate the geological model to a practical simulation model. On the latter issue they describe the use of partial models where just a smaller sector of the reservoir is studied but lessons are taken back into the full model.

6. Reservoir description: Section 2 of the paper gives a sedimentological description of the reservoir as a slope-apron fan of complex lithology (depositional model Figure 3) in which 14 (simplified) facies were retained; criteria of composite log recognition of various facies shown in Figure 5. Some contradictory water breakthrough observations were noted. Table 1 gives sedimentary body dimensions (lengths and widths) for channels, lobes. levees/crevasse-splay, slumps, channels (Upper Anguille); Table 2 gives mean petrophysical characteristics. A very important final result for reservoir simulation is the identification of five scales of heterogeneity - Figures 6 and 7; this makes the geological analysis and information numerically useable.

7. Sedimentary history: In earlier reservoir simulation studies, and indeed up to the present time, it is rare to see sedimentary history discussed in terms of a sequence stratigraphic analysis (even mentioning the pioneering work on sea level changes of P. R. Vail et al, Seismic stratigraphy and global changes of sea level, in Seismic Stratigraphy, Applications to Hydrocarbon Exploration, AAPG Memoir 26, pp. 49-212, 1977). Chronostratigraphic correlations refer to the timelines of simultaneous deposition. This analysis underpins much of the reservoir description but we will not elaborate on it here.

8. Geostatistical modelling: Mainly discussed in Refs. 1 and 2 of this paper. Firstly, focus on geostatistical modelling of the 3D distributions of the major flow units (channels and lobes) and barriers (laminated facies or slumps) for the entire reservoir. This is done as a conditional simulation where the distribution is constrained



(or conditioned) to the observed facies and reservoir quality observed at the wells. Secondly, the smaller scale heterogeneities are unconditionally simulated (synthetically) to yield average properties within the major flow units (see Ref. 2 in paper). The geostatistical simulation method used was indicator simulation (Refs. 1 and 8) which require the average frequency and variogram information.

9. Reservoir zonation: Six unit vertical reservoir zonation shown in Figure 10. Simulations of lateral continuity within each of the units (five - not Middle Anguille, Figure 10) performed independently since they correspond to separate sedimentary phases. For horizontal zonation, Figure11 shows lateral zonation on LA2 and UA2 units showing directional trends and thus variograms with spatially variable anisotropy direction used in final model. Figures 12 - 15 show resulting correlation structures of the various units. Ends up with >2 million grid blocks in the full field 3D model.

10. Flow simulations: Discusses details of upscaling from fine grid stochastic model (>2 million blocks) to coarse grid simulation model (11,000 grid blocks). 11 vertical layers are retained to represent the reservoir layering with more blocks being used in the best reservoir units. Upscaling of absolute permeability at some aggregation rate (e.g. 4x4) is applied leading to areal block sizes of 200m x 200m - see Figure14. Relative permeabilitiees were upscaled on a typical block configuration (details in Refs. 2 and 4). Additionally: Three major zero-transmissibility faults included in model; some WOC variation across field; depth varying bubble points assigned; 25 years of injection/production for history matching.

11. Simulation results: Initial pressure depletion results shown in Figure 16 - where 14 out of 17 wells show satisfactory pressure behaviour. Pressure behaviour and water breakthrough are poorly predicted during injection stage - Figure 17; water saturations around injectors shown in Figure18 - upscaling has washed out the finer scale strong anisotropy.

12. Model changes: Table 8 lists a number of sometimes quite radical changes to the model in order to achieve a better fit to observed field performance - Figure 15 shows differences in upscaled permeability maps. Continuing problems with injection predictions => - is geological model correct? - what is the real effect of upscaling?

13. Partial models: Thin model - Figure 19 shows the thin partial field model to verify reservoir geology; well AGM18 good water breakthrough match (Figure 20) - early breakthrough for well AGM29 (Figure 21). When thin model upscaled as in full field model (abs. k upscale + rel perm as before) - results in Figures 21 and 22 - breakthrough delayed in both wells but shape of BSW is satisfactory. Conclusions: Thin model partly validates geological model; Some problems with upscaling not supressing breakthrough, making reservoir too connected and eliminating strong anisotropy. Test model - (50 x 20 x 56) model extracted from full field model. Figure 23 shows that an optimum upscaling aggregation rate (2 x 2 x 7) is found - they warn caution on this point. We note that if very reliable and general upscaling techniques were available, then this should be eliminated (more work has been done on this issue since 1992 - much of it at Heriot-Watt!).



14. Conclusions: Sedimentology controls heterogeneity analysis when very wide variation in

sandbody geometries is found (as in this case)

Link understanding of reservoir history to sequene stratigraphy

Litho-interpretation of seismic cant give paleo-direction when there is techtonic activity during sedimentation

Multi-scale heterogeneity analysis essential to quantify sub-grid petrophysical properties

Geostatistical indicator simulation is a good tool for modelling this multi- scale heterogeneity - trends can also be included

Stochastic model for Anguille Marine constrained by geology gives hopeful first results

If aggregation rate in upscaling is optimised, history matching is possible with the use of strictly controlled geological parameters

3.6 Case 3: Ubit Field Rejuvenation (SPE49165,1998)Case 2: The Ubit Field Rejuvenation: A Case History of Reservoir Management of a Giant Oilfield Offshore Nigeria, SPE49165, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA, 27-30 September 1998, by C.A. Clayton et al (Mobil and Department of Petroleum Resources, Nigeria)


Summary: This is another good example of where integrated reservoir management has greatly contributed to the success of a field redevelopment plan. In particular, a clearer understanding of the reservoir structural geology has been central to this process. The reinterpretation of the structural geology of the field (the fault blocks, compartments and slump blocks) was achieved using seismic data in a range of complementary ways. The Ubit reservoir is a prograding shallow marine system which has been tectonically disturbed. The downslope movements of the youngest sand sequences resulted in large scale slumping and block sliding although reservoir quality in these sediments is good to excellent. Important facts on the Ubit reservoir and this study are: STOIIP = 2.1 billion bbl oil; 37API black oil, B

o = 1.38, GOR 612

scf/stb, o = 0.64 cp and

g = 0.16 cp; production from a relatively thin oil column

(160 ft.) and a fairly thick gas cap (50 - 550 ft.). Previous average production = 30 MBD; after implementation of study recommendations (many horizontal wells etc.), expected production 140 MBD. The notes on this SPE paper will not be very extensive and only a few of the main novel points will be discussed below.

Study Notes Case 3: 1. New data and techniques: The study is a very good example of the close integration of (especially) 3D seismic data used in several ways, computer mapping



and reconstruction of the slump blocks, advanced reservoir simulation procedures, visualisation etc.

2. Recommendations: These have been quite clearly established and stated. The study shows that the key strategies are

Implement horizontal well drilling (approx. 57 wells). Full field simulation defining drilling placement and timing. Balancing a non-uniform gas cap. Maintaining a stable gas cap (gravity stable displacement) and pressure. Establish field plateau rate. Minimising free gas production.

3. Uncertainties: there was an initially erroneous view of certain aspects of the reservoir geology and the key uncertainties at the start of the study were

Geological complexities in reservoir architecture, particularly structural deformation.

Sandbody geometries. Petrophysical rock and fluid properties. Distribution of flow units.

4. Structural reinterpretation: Figures 2a and 2b show both the original and current interpretations of the structure. The original rubble beds are reinterpreted as being techtonically disturbed downslope movements of the youngest sand sequences resulting in large scale slumping and block sliding. The older interpretation saw these facies as being essentially chaotic whereas they are now thought to be more ordered and predictable. 3D seismic data is of central importance in the definition of the structural geometries where the bedded and disturbed strata are shown on a seismic section in Figure 4. Several seismic techniques were applied including attribute analysis, rock physics and amplitude analysis, seismic facies analysis of time slices and conventional reflector mapping. The resulting 70 internal slump and fault blocks are shown in Figure 7.

5. Petrophysics-based facies: Seven flow controlling depositional facies were identified as shown in Figure 8 with rock properties related to grain size (lithology, typical log response, net/gross, k vs. , P

c and k

ro-k

rw). Depositional facies types

present are - marine turbidites and debris flow sands; lower delta plain tidal channels and lagoonal sands; shallow marine upper shoreface and lower shoreface sands and shelf shales (best are turbidites, shoreface and channel sands - comprise 80% pore volume in oil column).

6. Layering and Reservoir Simulation Model: Vertical layering is shown schematically in Figure 9 and the areal grid is given in Figure 12, with a set of rock property maps for a single simulation layer given in Figure10. Grid is N

x x N

y x N

z = 93 x 40 x 18 (67,000 blocks) with most oil leg cells being z = 10ft.

to resolve the gravity stable gas front. Rock property slices were loaded into the 3D modelling software to connect up the stratigraphic layers (using new but unclear developments by authors) as shown in Figure 11.



7. Relative permeability: An interesting point is made concerning the oil relative permeability (k

ro) close to its end point - see Figure 14. Although k

ro is low in this

region (kro ~10-6 - 10-7), it significantly affects the tail of the reservoir oil production

profile - see Figure 15. The adjusted curve in Figure 14 is used to get more realistic longer time recoveries (Figure 15). This is important because gravity stable gas cap expansion and downward displacement is the principal oil recovery mechanism - see schematic view in Figure 9.

8. History match and forward prediction: Average field pressure and GOR are history matched - see Figures 15 and 16. Matching field pressure is not so difficult since Ubit shows good pressure communication (high k - lack of sealing faults). Some discussion of field management is presented. Figure 22 shows the initial part of the improved productivity (up to 140 MBD from 37 horizontal wells) and future predictions. See Recommendations (point 2 ) above.

3.7 Discussion of Changes in Reservoir Simulation; 1970s - 2000From the above field examples (Cases 1 -3), there is clearly

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