software for reservoir performance prediction

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SPE-178288-MS

Software for Reservoir Performance PredictionOkotie Sylvester, Federal University of Petroleum Resources; M.O. Onyekonwu, University of Port Harcourt

Copyright 2015, Society of Petroleum Engineers

This paper was prepared for presentation at the Nigeria Annual International Conference and Exhibition held in Lagos, Nigeria, 46 August 2015.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents

of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect

any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written

consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may

not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Predicting the performance of reservoirs helps engineers to estimate reserve, development planning which

requires detailed understanding of the reservoir characteristics and production operations optimization and

more importantly, to develop a mathematical model that will adequately depict the physical processes

occurring in the reservoir such that the outcome of any action can be predicted within reasonable tolerance

of errors. In this paper, software REPAT was built based on material balance and an expansion of

Tarners method by incorporating water influx and time concept to the material balance equation. The

history matching process consists of modifying the aquifer parameters until an acceptable match was

obtained within engineering accuracy. Example 9.2 in L.P. Dake was used as a case study. A STOIIP

value of 311.48 STB was obtained with an error of 0.00195 and R value of 0.99999 which is an indication

of a good fit, while the STOIIP obtained from MBal gave an error of 0.00253. The reservoir is supported

by a combination of water drive and fluid expansion drive and Hurst Van Everdingen radial aquifer model

was selected as the most likely case. The parameters used to obtain the history match and the STOIIP

compare favourably with the expected values from L.P Dake and MBal. A good pressure and historical

production simulation match was obtained.

Introduction

One of the roles of a reservoir engineer is to continuously monitor the reservoir, collect relevant data and

interpret these data to be able to determine the present conditions of the reservoir, Estimate future

conditions and control the flow of fluids through the reservoir with an aim to increase recovery factor and

accelerate oil recovery. It therefore implies that the ability of a Reservoir Engineer to predict the behaviorof petroleum reservoirs depends solely on his ability to predict the flow characteristics of the fluids in the

reservoir. Thus, the main concern of the engineer to carry out a study on the reservoir is to adequately

simulate the reservoir with the minimum effort. In the real life scenario, the knowledge of a reservoir is

not accurately known since the reservoirs are large complex systems with irregular geometries that are

found in subsurface formations with several uncertainties, limited information about the reservoir

structure and behavior (Holstein 2007).

In this paper, a software was developed based on material balance and an expansion of Tarners method

by incorporating water influx and time concept to the MBE to predict the performance of oil reservoir

since simulation method of prediction is very complex, requiring a geologic model, populating the model


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with rock, fluid, historical production data and all events that have occurred in the reservoir. Though the

simulation method is a more accurate technique but a rigorous exercise which requires carrying out a

material balance on each of the grid blocks.

Tarek (2010) stated that material balance equation, MBE plays a major role in most reservoir

engineering calculations. It helps reservoir engineers to constantly seek for ways to optimize hydrocarbon

recovery by predicting the future performance of the reservoir. We should note that the MBE simply

provides performance as a function of average reservoir pressure without the fluid flow concepts.Combining the MBE and fluid flow concepts would enable the engineer to predict the reservoir future

production performance as a function of time.

Odeh & Havlena (1963)rearrange MBE into different linear forms. This method requires the plotting

of a variable group against another variable group selected depending on the reservoir drive mechanism

and if linear relationship does not exist, then this deviation suggests that reservoir is not performing as

anticipated and other mechanisms are involved which were not accounted for; but once linearity has been

achieved, based on matching pressure and production data then a mathematical model has been achieved.

This technique is referred to as history matching. Therefore, the application of the model enables

predictions of the future reservoir performance.

There are several methods which have appeared in literatures for predicting the performance of

solution-gas behaviour relating pressure decline to gas-oil ratio and oil recovery. Tarner (1944) andMuskat (1945) proposed an iterative technique to predict the performance of depletion (solution-gas)-

drive reservoirs under internal gas drive mechanism, using rock and fluid properties. The assumptions of

both methods include negligible gravity segregation forces. These authors considered only thin, horizontal

reservoirs. Both methods use the material balance principle (static) and a producing gas-oil ratio equation

(dynamic) to predict reservoir performance at pressures. A more detailed description of both methods

appears inCraft and Hawkins (1991).

Tracy (1955) In the model developed for reservoir performance prediction, did not consider oil

reservoirs above the bubble-point pressure (undersaturated reservoir). It is normally started at the

bubble-point pressure or at pressures below. To use this method for predicting future performance, it is

necessary to choose the future pressures at which performance is desired. This means that we need to

select the pressure step to be used. Furthermore, among these methods of reservoir performance

prediction, none considered aquifer in the MBE, hence, the software developed for this study incorporated

aquifer into Tarners method of reservoir performance prediction for solution gas drive. Three aquifer

models such as Hurst Van Everdingen (1947), Carter-Tracy (1960) and Fetkovich (1971) were pro-

grammed to allow for flexibility.

Classic analytical models of aquifers are relatively easy to program in computer spreadsheets, provided

that equation discretization is correctly done. With the exception of the van Everdingen & Hurst, the

models do not demand much computer power. In the van Everdingen & Hurst, calculations of the previous

steps are redone at each time-step added to the behaviour, which represents a bigger computational effort.

The equation that rules the van Everdingen & Hurst model is based on the superposition principle. Any

numerical calculation method for this model requires more computing power than other models. Despite

this drawback, it is the ideal model for comparisons, because it faithfully represents the hydraulic

diffusivity equation. Other proposed models, such as Carter & Tracy, Fetkovich, and Leung, sought to

eliminate the disadvantage of the required computing power, and thus became more popular in commer-

cial flow simulators. The error of this model in computing the accumulated influx is insignificant when

compared to the base model (van Everdingen & Hurst).

Reservoir Characterization

An accurate description of reservoir rock, fluid contents, rock fluid systems, fluid description and flow

performance are required to provide sound basis for reservoir engineering studies. Hence, proper reservoir

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characterization is important to analyse the effects of heterogeneity on reservoir performance due to

primary, secondary, and/or enhanced oil recovery operations. Porosity and permeability are important

flow properties; an accurate reservoir characterization requires accurate porosity and permeability de-

scription as function of space.

Reservoir characterization is a process to reduce geological uncertainties by quantitatively predicting

the properties of a reservoir and define reservoir structural changeability. It is a process ranging from the

discovery phase of a property to the management phase of the reservoir. Prior to performing a reservoirsimulation, accurate characterization is the first key step to undertake which helps to identify uncertainty

range inherent in reservoirs. Here we try to assess the range of reservoir performance from an under-

standing of the subsurface uncertainties. This concept is a limitation and it is not considered in the material

balance method used in developing the tool for predicting performance of reservoirs in this paper. At this

point, we need not to border ourselves with a thorough review of literature in reservoir rock character-

ization which would not be practically possible because of the wide nature of this discipline.

Describing the Pvt

To appropriately estimate the reservoir pressure and saturation changes as fluid is produced throughout the

reservoir, requires a precise description of the reservoir fluid properties. To accurately describe theseproperties, the ideal process is to sample the reservoir fluid and perform a laboratory studies on the fluid

samples. This is not always possible to continuously take fluid sample for analysis as the reservoir

pressure declines, hence, engineers have resorted to correlations to generate the fluid properties. There-

fore, REPAT offers several options for calculating the required properties as the reservoir pressure

declines. The program uses traditional black oil correlations, such as Petrosky and Fashad (1993),

Standing (1947),Ikiensikimama et al (2008)andGlaso (1980)etc. where only basic PVT data is available.

Besides, where detailed PVT laboratory data is provided, the developed tool uses this data instead of

generating PVT properties from correlations. The data is inputted in the required table format (PVT

tables), there is flexibility with the software whereby the data can be entered manually or imported from

Microsoft excel in the accepted format. Figure 1shows the PVT input screen of REPAT.

Figure 1PVT Data Analysis Output Screen

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History Matching

The update of a model to fit the actual performance is termed history matching. Clearly speaking,

developing a model that cannot accurately predict the past performance of a reservoir within a reasonable

tolerance of error is not a good tool for predicting the future of the same reservoir. To history match a

given field data in MBE, we have to state clearly the known parameters to match and the unknown

parameters to tune in order to get field production data with minimum tolerance of error and these are

presented inTable 1.

The general approach by the engineer whose production information is already available is to

determine the production rates for the given period of production. The value calculated is use to validate

the actual rates and if there is agreement, the rate is assumed to be correct. This rate is used to predict the

future production rates. On the contrary, if there is no agreement between the calculated and the actual

rates, the calculation is repeated by modifying some of the key parameters. This process of matching the

computed rate with the actual observed rate is called history matching.

It therefore implies that history matching can simply be put as a process of adjusting the key properties

of the reservoir model to fit or match the actual historic data. One of these parameters that is vital in

history matching is the aquifer parameters which are not always known. Hence, modification of these

parameters to obtain an acceptable match within reasonable engineering tolerance of error or engineering

accuracy is history matching. The tool developed in this study tries to modify one or several aquifer

parameters and return the calculations until a satisfactory match is obtained (Donnez, 2010).

The Problem Definition

One of the problems faced today in the industry in making predictions of the reservoir behavior is to

adequately take into account the knowledge about geological trends and some set of constraints whether

quantified or not that are essential in making a good simulation study. The engineer should bear in mind

a list of designated limits of all is variables. It can be argued very effectively that there is really no unique

set of descriptive parameters which fit a reservoir.

Material balance equation makes use of pressure in the prediction; Tarner and Muskat method which

are widely used do not considered time in their prediction performance. Also, neither water influx nor

gravity segregation was considered. Thus, this paper incorporate aquifer and time scale to the equation in

making predictions. The time history will be inferred from the reserves and well production rates. Though

it does not consider reservoir geometry, heterogeneity, fluid distribution, the drainage area, the position

and orientation of the wells.

Table 1History match and prediction parameters

Known Parameters

History Matching Parameter Symbol

Production data Np, Gp, Wp and Rp

Hydrocarbon Properties Boi, Bo, Bg, Bgi, Rsi, Rs

Reservoir Properties Sw, cw, cf, m

Pressure drop P

Unknown Parameters

Reserves N

Water Influx We

Prediction Reserves, Water influx, Hydrocarbon properties, Reservoir properties

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Technical Objectives

The technical objectives of this study are to:

Develop a simple tool that will predict future reservoir performance based on material balance

equation and also find means of increasing ultimate recovery and compare result with MBal

predicting tool.

Estimate the hydrocarbon volume in-placeDetermine the type of energy in the system and evaluate the strength of the aquifer if present

Determine the most likely aquifer model and properties

Determine the probable limits of the reservoir

Potential Benefits of Repat

User friendly

It can serve for academic purpose

REPAT can be used as a stand-alone tool or a pre-processing tool for reservoir simulation study to

infer in place volume and best aquifer model.

Minimize cost of foreign commercial software

Modeling Approach/ Methodology

The workflow used in the development of REPAT is given inFigure A2ofappendix Aand the data

used to valid the tool was obtained from fundamentals of reservoir engineering by L.P Dake (Elsevier,

1978),chapter 9, example 9.2. This data was analysed as oil reservoir. The pressure and production data

used in the analysis are as provided by the author. The production history spans a period of 10 years

(August 1994- August 2004). The PVT, the reservoir (tank) and production history data used in the

analysis are shown intable A1,table A2andtable A3ofappendix Arespectively. Below are some of the

mathematical equations coded in REPET.

(1)

(2)

(3)

(4)

(5)

Description of the tool used in the study

The reservoir performance analysis tool (Repat 8.5) is a package designed to help engineers to gain a

better understanding of reservoir behaviour, infer hydrocarbon in place, determine the best aquifer model,

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history match production history and perform prediction run. The tool is setup in a way that user can go

from left to right on the options menu and from each option, user can navigate top to bottom. Thus, this

tool is broken down into various components and these are:

Setting the system/model options

Entering PVT data and perform correlation match to select the best model

Entering reservoir, relative permeability and aquifer dataEntering production history data

Performing a history match

Performing prediction run

Generation of report

help

Results from Repat and Mbal

Material balance analysis has been carried out on example 9.2 of L.P Dake reservoir. The Reservoir

Prediction Analysis tool, REPAT of this study was used for the analysis and compare with MBAL, of

Petroleum Experts Limited. The program uses a conceptual model of the reservoir to predict the reservoirbehavior and reserves based on the effects of fluids production from the reservoir. Besides, the in-place

volumes calculated from this study can be subjected to static and dynamic simulation toll for validation.

The reservoir pressure, PVT and production data, after careful review, served as input data into the

REPAT and MBAL program. The summary of the results obtained from L.P Dake Example 9.2 analyses

are as shown in table 2.

Table 2Summary of L.P Dake Example 9.2 Analysis Results

Parameter REPAT MBAL L.P DAKE

Aquifer model Hurst-Van Everdingen Hurst-Van Everdingen-Dake Hurst-Van Everdingen

Reservoir Thickness (ft) 100 100 100

Reservoir Radius (ft) 9200 9200 9200

Outer/Inner Radius 5.0761 5.1 5.00

Encroachment Angle 140 140 140

Aquifer Permeability (md) 200 327.19 200

OIIP (MMSTB) 311.48 312.79 312

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The Hurst-Van Everdingen model was selected as the most likely case for example 9.2 in L.P Dake.

The parameters used to obtain the history match and the OIIP from Hurst-Van Everdingen radial aquifer

compare favourably with the expected values. The inferences from the Material Balance Analysis of this

example using REPAT are as follows:

The OOIP is 311.48MMSTB from the diagnostic (F/EtVs W

e/E

t) plot as shown in figure 3.

Table 3Summary of Input Data for the Aquifer model of L.P Dake Example 9.2

Parameter Value Source

Aquifer Permeability (md) 327.19 Regression in REPAT and MBAL

Encroachment Angle (deg.) 140 Fault Polygon

Reservoir Radius (ft) 9200 Estimated from seismic map

Outer/Inner radius (Ratio) 5.00 Estimated from seismic map

Reservoir Thic kness(ft) 100 Logs

Figure 2History-Prediction pressure plot

Figure 3Graphical estimate of STOIIP

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The example 9.2 reservoir is influenced by a combination of water drive and fluid expansion drive

mechanism as revealed by the energy plot (figure 4)

Results from the analytical cumulative oil produced match as shown in figure 5indicates a Hurst

Van Everdingen radial water drive behavior, encroaching at an angle of 140. A good production

simulation match was obtained

The Results of the analysis indicates that the HurstVan Everdingen radial aquifer Influx model

incorporated into the (F/EtVs W

e/E

t) straight line method is the most likely aquifer model.

Figure 6shows the dimensionless aquifer plot and the red line indicates example 9.2 plot

Figure 4 Energy plot

Figure 5History match plot

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The plot from MBal, the graphical, energy, analytical and aquifer is shown in figure A1inappendix

A.

The volume obtained with REPAT using example 9.2 reservoir compares favourably with the volume

reported by L.P. Dake as depicted in table 2.

Constraints

Unknown aquifer characteristics and properties

Prediction ResultFigure 7shows the prediction result obtained from example 9.2 after careful analysis and history match.

The predicted result match perfectly well with the historical data and extrapolated to a future pressure as

the reservoir declines to abandonment. REPAT has a user defined option of prediction to control the start

and end of prediction result. Hence, since the tool gave a close value of STOIIP as compared with the base

case of example 9.2 and also able to match the historical data, it is there assure good prediction results.

Figure 6Aquifer plot

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Conclusions

The result obtained from the analysis of example 9.2 from fundamentals of reservoir engineering by L.P

Dake using this study software REPAT, the following conclusion can be drawn:

The Hurst-Van Everdingen radial aquifer model was selected as the most likely case. The

parameters used to obtain the history match and the OIIP compare favorably with the expected

values from L.P. Dake and MBal as shown intable 2above.The error in STOIIP obtained from REPAT is 0.00195 and R value of 0.99999 which is a good fit,

while MBal is 0.00253 using the STOIIP in example 9.2 in L.P Dake as base case.

The reservoir is supported by a combination of water drive and fluid expansion drive

The result of STOIIP obtained after regression on aquifer-reservoir radius ratio converges at 5.0761

from Hurst-Van Everdingen radial aquifer model.

A good pressure and historical production simulation match was obtained from REPAT

Recommendations

Results from REPAT should be compared with result from other means of oil in place estimate such

as static (geology) and simulation (eclipse).

Prediction of cumulative water produced should be model.

REPAT can be used as a pre-processing tool for reservoir simulation/study to infer in place volume

and best aquifer model.

It can be used as a stand alone for reservoir performance

REPAT can also be used in academic environment.

ReferencesCarter, R. D., and Tracy, G. W., (1960): An Improved Method for Calculations Water InfluxTrans.

AIME

Figure 7Result from REPAT

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Craft, B., Hawkins, M., Terry, R., (1991): Applied Petroleum Reservoir Engineering,2nd ed. Prentice

Hall

Dake, L. P., (1978): Fundamentals of Reservoir EngineeringAmsterdam Elsevier Scientific Publish-

ing Company

Donnez, Pierre, (2010): Essential of Reservoir Engineering, Editions Technip, Paris. Pp. 249272

Fetkovich, M. J., (1971): A Simplified Approach to Water Influx Calculations- Finite Aquifer

Systems, JPT, pp. 814828Glaso, O., (1980): Generalized Pressure-Volume-Temperature Correlations, JPT,May, pp. 785795

Havlena, D., and Odeh, A. S., (1963): The Material Balance as an Equation of a Straight Line,

Trans. AIME, Part 1: 228 I-896; Part 2: 231 I-815

Ikiensikimama, S. S., Effiong E. U and Ogbaja O. (2008): Undersaturated Oil Forrmation Volume

Factor and Viscosity Bellow Bubblepoint Correlations, SPE 119723, rpesented at the 32nd

Annual International Conference of the SPE Nigerian Council, Abuja, Nigeria

Petrosky, G. E., and Farshad, F. (1993): Pressure-Volume-Temperature Correlations for Gulf of

Mexico Crude Oils, SPE Paper 26644, presented at the 68th Annual Technical Conference of the

SPE in Houston, Texas, 36 October

Standing, M. B. (1947), Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, pp.

125126 Dallas: Society of Petroleum EngineersTarek Ahmed (2010): Reservoir Engineering Handbook. 3rd Ed., Amsterdam: Elsevier Scientific

Publishing Company

Tarner, J. (1944). How different size gas caps and pressure maintenance affect ultimate recovery.Oil

Wkly, June 12, 3236

Tracy, G. (1955). Simplified form of the MBE. Trans. AIME, 204, 243246

Van Everdingen, A., and Hurst, W. (1949) The Application of the Laplace Transformation to Flow

Problems in Reservoirs, Trans. AIME, pp. 186305

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Appendix A

Table A1PVT data for L.P Dake Example 9.2

PVT data Time (day)

Pressure

(psia)

Solution

GOR

(scf/STB)

Oil FVF

(rb/STB)

Gas FVF

(rb/STB)

Oil

Viscosity

(cp)

Gas

Viscosity

(cp)

Parameter L.P Example 9.2 0 2740 650 1.404 9E-04 0.54 0.0148

GOR (Rs) 650 365 2500 592 1.374 1E-03 0.589 0.01497

Oil Gravity 40 730 2290 545 1.349 0.001 0.518 0.01497

(Yg) 0.7 1096 2109 507 1.329 0.001 0.497 0.01497

Salinity 14000 1461 1949 471 1.316 0.001 0.497 0.01497

1826 1818 442 1.303 0.001 0.497 0.01497

2191 1702 418 1.294 0.002 0.497 0.01497

2557 1608 398 1.287 0.002 0.497 0.01497

2922 1535 383 1.28 0.002 0.497 0.01497

3287 1480 381 1.276 0.002 0.497 0.01497

3652 1440 364 1.273 0.002 0.497 0.00182

Table A2Reservoir and Aquifer data

Aquifer data Reservoir data

Par ameter L .P Exampl e 9.2 Parameter L .P Exam pl e 9.2

Reservoir thickness 100 Temperature 115

Reservoir radius 9200 Initial Pressure 2740

Aquifer radius 46000 Porosity 0.25

Emcroachment angle 140 Swc 0.05

Aquifer permeability 200 Cw 3.00E-06

Cf 4.00E-06

Relative Permeability Data

Residual Sat End Point Exponent

Krw 0.25 0.039336 0.064557

Kro 0.15 0.8 10.5533

Krg 0.05 0.9 1

Table A3Production data of L.P Dake Example 9.2

Time (dd/mm/yyyy) Reservoir Pressure (psia)

Cum oil Produced

(MMSTB)

Cum Gas Produced

(MMSCF)

Cum Water Produced

(MMSTB)

1/8/1994 2740 0 0 0

1/8/1995 2500 7.88 5988.8 0

1/8/1996 2290 18.42 15564.9 0

1/8/1997 2109 29.15 26818 0

1/8/1998 1949 40.69 39672.8 01/8/1999 1818 50.14 51393.5 0

1/8/2000 1702 58.42 62217.3 0

1/8/2001 1608 65.39 71602.8 0

1/8/2002 1535 70.74 79228.8 0

1/8/2003 1480 74.54 85348.3 0

1/8/2004 1440 77.43 89818.8 0

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Figure A1Result from MBal

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Figure A2Work flow in developing REPAT 8.5

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Figure A2Continued

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software for reservoir performance prediction

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