conceptual framework for using system identification in...

Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, March 8-10, 2016

Conceptual Framework for Using System Identification in Reservoir Production Forecasting Berihun Mamo Negash1, Lemma Dendena Tufa2, Ramasamy Marappagounder3 and Mariyamni Bt. Awang4

Universiti Teknologi PETRONAS Petroleum Engineering Department1,4 Chemical Engineering Department 2,3

32610 Bandar Seri Iskandar Perak Darul Ridzuan, Malaysia

[email protected], [email protected] [email protected] and [email protected]

Abstract-Defining a reliable forecasting model in petroleum reservoir management has always been a challenge. In cases where reservoir description is limited and when fast decision with an acceptable accuracy is required, current methods have significant limitations and restrictions. System identification, which is based on historical data and statistical methods could be promising. However, the complexity of a petroleum reservoir system and the availability of numerous model structures in system identification make it challenging to adapt this method effectively. In this paper, a conceptual framework for using system identification is proposed. Based on a reservoir’s recovery mechanism, the conceptual framework will help to systematically select an appropriate model structure from the various model structures available in system identification. The results show that system identification polynomial models can provide very accurate models, in a very short time, to predict performance of reservoirs under primary and secondary recovery mechanisms. These models have also the potential to be established as a practical, cost-effective and robust tool for forecasting reservoir fluid production.

Keywords-System identification; production forecasting; conceptual framework; reservoir modeling

I. INTRODUCTIONOne of the most important jobs of reservoir engineers, in principal collaboration with production engineers, is to

forecast future fluid production rates. Forecasting is an integral part of reservoir management. It allows estimation of the upcoming production profile and meet numerous objectives, some of which include: • Evaluating the economics of developing the reservoir[1].• Planning the required equipment and facilities[2].• Planning each well’s completions and the regularity of work-over processes [3].• Evaluating strategies to boost production[4].• Evaluate well performance and effectiveness of operations.• To help understand the reservoir behavior better.

II. LITERATURE REVIEWThe most established methods for reservoir performance forecasting are Decline curve analysis (DCA) and reservoir

simulation (RS) [5-9]. Each of these methods has strengths, limitations and restrictions [10]. The application of DCA is limited to early production stage of a well, where production is at steady state and the reservoir is under boundary-dominated flow. In addition, rock and fluid compressibility must be low and constant. In cases such as gas reservoir and solution gas derive oil production, where compressibility is higher, the decline is less severe and hence none of the curtailment trends will fit.

On the other hand, numerical reservoir simulation provides a more accurate and robust solution to the task of forecasting reservoir performance. Reservoir models are often used to analyze, optimize and forecast both pressure and saturation dependent terms. Geological, geophysical and petrophysical data are inputs required to describe the reservoir and build a simulation model. However, development of an accurate and representative geological and geophysical model is extremely challenging. Moreover, a reservoir is a gigantic subsurface system that is both heterogeneous and anisotropic. Due to the relatively large size, samples of rock and fluid are collected from only a few locations within the boundary of the reservoir. Statistical techniques are then employed to populate and infer rock and fluid properties for the remaining portion. Thus, reservoir property data used in modelling and forecasting are only best estimates and will not be exact representatives of the reservoir at large. Besides, the history matching stage by which the inferred reservoir properties are adjusted until the numerical simulation model reasonably mimics the actual reservoir, is a formidable task and has substantial limitations [6, 8].

1387© IEOM Society International


In practice, it is common to implement more than one method to reduce uncertainty and increase precision. Here system identification which is popular in downstream oil and gas industry is proposed. There are numerous examples where system identification is utilized to model complex engineering systems [11-18]. Recent studies also investigated the use of mostly artificial neural network in oil and gas industries [10, 19-23].

Artificial neural network is the most investigated SI technique for prediction in the oil and gas industry. However, system identification has many model structures beyond artificial neural network. An important characteristics of system identification is that it is flexible in a sense that there are various model structures which can be altered on the polynomials defining the structures [24-26]. There has been no attempt to map the large variety of SI modelling techniques to the numerous reservoir drive mechanisms for the purpose of production forecasting. In other words, system identification has not been investigated as much in the oil and gas industry as it is for downstream industries such as refineries and process industries.

This study describes and classifies reservoirs into distinguishable recovery mechanisms and associate system identification models to each drive mechanism. It also evaluates the efficacy of the proposed system identification method by quantifying the deviations of model output and validation data set. The working data came from synthetic benchmark reservoir models.

III. METHODOLOGY

A. System identificationSystem identification is the concept of utilizing statistics to describe a dynamic system. This is achieved by inferring a

statistical model (SI) based on the observations (the inputs and outputs) of the dynamic system and/or based on a prior knowledge of the system [27]. There are numerous SI models available and selecting the most suitable model to describe the system would require experimentation and engineering knowledge of the system.

System identification is still a new concept in petroleum engineering. Literature review shows that it has previously been used by researchers to predict water cuts [28]as well as optimize production rates [29]. However, these studies only focused on a certain recovery mechanism and are particular cases. This is because there is a limitation to system identification, which is that the system has to be in the in the same state during the course of the observations, i.e. no variations in operating conditions [28]. Additionally, in direct contrast to reservoir simulation, system identification treats the system under study as either a grey box model or a black box model. A possible input signal for reservoirs is injection rate of displacing fluid while a possible output signal could be fluid production rate or any other production parameter. Typically, inputs are linked to outputs through functions and not by considering physical phenomena. Even though the true physics of the system is not being considered, system identification can be an efficient method for prediction, especially when the reservoir is not well understood and time for decision is short.

B. Validation criteria: Normalized root mean squared errorThe identification process has several stages, one of which is the validation stage. A criterion must be defined to measure how good the fit is between the observed output and predicted values from the SI models. In this study normalized root mean squared error (NRMSE) is used to quantify the deviations. The Equation for NRMSE is given in Eqn. (1) [30]: 1 :, :,:, :, (1) Where:

• ‖ indicates the 2-norm of a vector.• fit is a row vector of length N• i = 1,...,N, where N is the number of channels.

C. Reservoir recovery mechanismsThere are five key primary drive mechanisms [31]for pushing fluids to the production well:• Expansion of the reservoir rock and the reservoir fluids• Expansion of solution gas escaping out of the oil phase• The pressure exerted from a gas cap• The pressure exerted from an aquifer• Gravity causing a segregation effect that separates liquids of different densities. Oil tends to travel downwards and

gas travel upwards.A reservoir under primary drive can be represented by the block diagram in Fig. 1. It is immediately obvious that

since there are no injection wells, the reservoir does not have any input. Outputs from systems of this kind are called time series and identification falls under a special branch of system identification called time series analysis, or Output-only models[26].



Figure 1: Block Diagram of primary recovery

Secondary drive mechanisms involve injection of fluids to maintain or increase the reservoir pressure in addition to displacing the reservoir fluids with the injected fluid [32]. The main injection fluids are water and gas that is not miscible with the reservoir hydrocarbons. The block diagram for this drive mechanism can be seen in Fig. 2.

Figure 2: Block Diagram of secondary recovery

Tertiary drive mechanisms: This involves the use of special injection fluids and materials that can alter the properties of the reservoir fluids to achieve a combination of the following objectives: (1) make it easier for oil to flow, (2) to limit water flow and (3) to cause a more effective displacement by the injection fluid compared to secondary recovery methods. The diagram for this recovery method can be seen in Fig. 3. It should be noted that, although the inputs and outputs of tertiary drive seem similar to the secondary drive mechanism, the injection fluids are affecting the system in a different way (alters reservoir properties). This may cause the relationship between inputs and outputs to become non-linear and hence making the system non-linear.

Figure 3: Block Diagram of tertiary recovery

D. Data Gathering: description of ReservoirsThe process of collecting simulation models for each recovery scenario comprises of creating suitable models from

existing template models. These template models are heavily modified by the authors and are only considered suitable once they clearly reflect the drive mechanism under investigation. The final models should also have enough complexity, which is measured through the following criteria:

• Total number of grid-blocks in the model. Generally, higher number of grid blocks indicate complexity in themodel.

• Heterogeneity of rock properties, such as permeability and porosity. Large heterogeneities are required.• The presence of faults makes the reservoir more complex.

Reservoir Systems under Teritiary

Recovery

Input Output

Unmeasured Disturbances

Reservoir Systems under Secondary

Recovery

Input Output

Unmeasured Disturbances

Reservoir systems under

primary recovery

Measurement Noice

Output data


Proceedings of the 2016 International CKuala Lumpur, Malaysia, March 8-10, 2

These models are then modified to ruan optimized constant bottom-hole pressuoil recovery but also taking into accouninjection wells) and the lowest BHP thaproduction wells). The CMG simulatorsmechanism there are around 3653 data pcases. Appendix A describes the list of th

E. The System identification procedureThe cross-validation division method ussecond half used for validation. The authpapers that have references to cross-validthe data. The authors also believe that thwhatever the period of data we have, say

The model structures available for primarI. Autoregressive (AR)

II. Autoregressive Integrated III. Autoregressive Moving AvIV. Autoregressive Integrated M

The model structures available for the secI. Autoregressive with exogen

II. Autoregressive Integrated wIII. Autoregressive Moving AvIV. Autoregressive Integrated MV. Box-Jenkins (BJ)

VI. Box Jenkins Integrated (BJThe MATLAB toolkit calculates the besof zero indicates that the model does notgraph of Fit percent vs. model order is pbest model is chosen by looking at the grto plateau. In other words, the best modaccuracy when order is increased. An exa

A. Analyzing prediction performance ofTable 1 summarizes the best order o

and drive mechanism. For all five privalidation data sets (5 years production porders. These are excellent results becausthat time series analysis can be a veryforecasting methods. However, it shoulddata. Noise here means measurement erFurthermore, for most of the model stru

Perc

enta

ge F

it

Conference on Industrial Engineering and Operations M2016

un for a total period of 10 years and the wells in each ure (BHP) constraint. BHP is optimized by selecting th

nt the restrictions of the reservoir, i.e. fracture pressurat can support production without having to resort tos are set to record data every day for 10 years. This

points for each input and output. Furthermore, a black ohe cases utilized in building the conceptual frame work

sed is 50:50. This means that the first half of data whors decided on this ratio after looking at MATLAB mdation. A prominent paper [24] established that this ishis is the easiest method to visualize for the readers. T

y 1 year, we can make prediction of the exact same peri

ry drive mechanisms (time series models) are:

(ARI) verage (ARMA) Moving Average (ARIMA) condary drive mechanisms are: nous inputs (ARX) with exogenous inputs (ARIX) verage with exogenous inputs (ARMAX) Moving Average with exogenous inputs (ARIMAX)

JI). st fit of the models using Normalized Root Mean Squat predict values better than the mean value of the data. plotted in order to be able to pick the best order for a raph and seeing where the increase in accuracy with incdel order is the lowest order after which there is no mample is shown in Fig. 4.

Figure 4: Choosing the best model order

IV. RESULTS AND DISCUSSION

f system identification of the defining polynomials as well as the fit percentaimary drive mechanisms, all polynomial models havprofiles) extremely well. The fit percentage is well ovese rarely are predictions this accurate, even using reser

y reliable forecasting tool and that it can establish itd be noted that the data sets used in this work assume rrors due to method of sampling as well as limitationuctures, the model order for the best fit is of order 3

0

50

100

1 2 3 4 5 6 7 8 9 10 11

Order

ARIMAX

Management

model are set to operate on he one that results in highest re of the reservoir rock (for o artificial lift methods (fors means that for each drive oil fluid model is used in all

k.

will be used for training and manual examples and several s the classic way of splitting This is because, considering od with the SI models.

are (NRMSE). A percentage For each model structure, a given model structure. The

creasing order number starts more significant increase in

age for each model structure ve managed to predict the r 97% for all the best model rvoir simulation. This shows tself among the established that there is no noise in the

ns of measurement devices. or less. This is also a good



result because it means that we do not need overly complex polynomial models that have large number of parameters in order to get more than satisfactory levels of prediction.

However, for the secondary recovery cases, the prediction performances of most the model structures do not show results that are as good as the results for primary production. What is most evident is that for the oil rate and GOR curves of water injection case as well as the oil rate curve of the gas injection case, there are no model structures that could predict with a fit percentage greater than 90%. This could indicate that the relationship between the input (displacing phase injection rate) and these output curves are not linear and this may be why these linear models cannot adequately model the relationship. However, for the remaining three parameters, the results show that good prediction (above 90% fit) can be obtained from one or more model structures. It seems that more studies need to be done for the cases of gas and water injection. Research could be done into investigating if changing the orders of the poles, zeros and delays of the model independently of each other can yield better fit results. Research could also be done to investigate if single input-multiple output (SIMO) models can yield better fit results because the output parameters would have each other to benchmark themselves to. If all that does not help to improve prediction accuracy, then research can be done into using non-linear SI models for the purpose of modelling gas and water injection.

Tables 2 shows the conceptual framework, which is derived from the results of Table 1. The table ranks the different system identification model structures according to the percentage fit exhibited during cross validation. The numbers, 1 to 4 for primary drive and 1 to 6 for secondary drive, show the accuracy of the model, with 1 being most accurate and increasing number being less accurate. This framework will provide a good starting point for engineers so that they do not have to test so many different model structures with many different order numbers when they want to use system identification for forecasting their reservoir production.

TABLE I. RESULTS TABLE

Recovery Mechanism

Model Structure

Best Model Order : Fit percentage Recovery Mechanism

Model Structure

Best Model Order : Fit percentage

OIL RATE WATER CUT

GAS:OIL RATIO

OIL RATE

WATER CUT

GAS:OIL RATIO

Rock & Liquid

Expansion Drive

AR 5 : 99.28 3 : 99.68 2 : 99.92 Combined Drive

AR 3 : 99.95 3 : 100 3 : 99.99

ARI 2 : 99.92 1 : 99.46 1 : 99.93 ARI 2 : 99.96 1 : 100 2 : 100

ARMA 5 : 99.49 2 : 99.83 1 : 99.96 ARMA 3 : 99.96 2 : 100 3 : 99.99

ARIMA 1 : 99.74 1 : 99.79 1 : 99.93 ARIMA 2 : 99.94 1 : 100 2 : 100

Solution Gas Drive

AR 3 : 99.54 1 : 97.87 1 : 99.79 Water Injection

drive

ARX N/A N/A 5 : 0.765

ARI 1 : 99.06 1 : 98.27 1 : 99.8 ARIX 1 : 51.42 8 : 35.84 2 : 6.427

ARMA 2 : 99.46 1 : 97.89 2 : 99.77 ARMAX N/A N/A 4 : 14.14

ARIMA 1 : 99.54 2 : 98.86 1 : 99.8 ARIMAX 1 : 58.46 4 : 92.13 3 : 10.33

Gas Cap Drive

AR 2 : 98.95 7 : 95.95 2 : 99.55 BJ 9 : 56.36 8 : 88.41 N/A

ARI 2 : 99.75 1 : 97.29 1 : 99.8 BJI 6 : 42.04 9 : 88.5 1 : 10.5

ARMA 2 : 98.97 2 : 97.34 4 : 99.74 Gas Injection Drive

ARX N/A 1 : 94.68 1 : 75.51

ARIMA 1 : 99.72 1 : 97.49 1 : 99.97 ARIX 2 : 35.95 10 : 17.5 9 : 43.95

Aquifer Drive

AR 3 : 99.06 2 : 99.96 3 : 99.57 ARMAX N/A 1 : 92.03 9 : 95.71

ARI 3 : 99.96 1 : 99.97 3 : 99.76 ARIMAX 1 : 41.79 4 : 32.57 4 : 95.61

ARMA 3 : 99.72 2 : 99.96 3 : 99.41 BJ 3 : 70.61 9 : 51.99 4 : 97.38

ARIMA 3 : 99.88 1 : 99.97 3 : 99.73 BJI 2 : 68.87 10 : 90.48 3 : 96.96



TABLE II. CONCEPTUAL FRAMEWORK

OIL RATE

AR

AR

I

AR

MA

AR

IMA

AR

X

AR

IX

AR

MA

X

AR

IMA

X

BJ

BJI

Rock & Liquid Expansion Drive 4 1 2 3

Solution Gas Drive 2 4 3 1

Gas Cap Drive 4 1 3 2

Aquifer Drive 4 1 3 2

Combined Drive 3 1 2 4

Water Injection 5 3 6 1 2 4

Gas Injection 5 4 6 3 1 2

WATER CUT

AR

AR

I

AR

MA

AR

IMA

AR

X

AR

IX

AR

MA

X

AR

IMA

X

BJ

BJI








GAS-OIL-RATIO

AR

AR

I

AR

MA

AR

IMA

AR

X

AR

IX

AR

MA

X

AR

IMA

X

BJ

BJI










B. Practical considerationsActual reservoir production data have some unfavorable characteristics. These unfavorable characteristics are missing

data, data outliers, drifting data, and data co-linearity. Missing data is when a single or series of the data at different times are not recorded and not made available for the modeler. This could happen for a number of reasons including downtime due to hardware failure. When this happens a traditional way of remedy is replacing the missing data with the mean value. However, other efficient interpolation techniques such as spline and Lagrange interpolating polynomials could be utilized. Maximum-likelihood, Bayesian multiple imputation [33] and iteratively reweighted least square [34] have also been applied to replace missing data in the downstream industries. Outliers are measurements that noticeably deviate from the meaningful data. The 3σ rule, whereby data which are three standard deviations away from the mean are considered outliers, is most commonly employed for detection of outliers [35]. On cases where data outliers are detected the corresponding values must be treated in the same way as missing data. Presence of drifting data is a common problems in time series data analysis. Data drifting could happen because of mechanical wear of the flow meters or environmental changes around the wellheads and surfaces where measurements are conducted. The most popular approach to deal with such problems is through the application of moving window techniques. Here the models are updated periodically using only a defined number of the most recent samples [35]..

V. CONCLUSIONThe purpose of this study was to create a framework that connects various drive mechanism and most suitable

forecasting model. This framework will serve as a reference to engineers and assist to speed up the identification process when modelling a reservoir using system identification.

The results show that System identification polynomial models can provide an excellent model to predict oil rate, water cut and GOR curves for any type of reservoir. Time series models can predict production parameters of reservoirs under primary drive mechanisms with up to 99% accuracy. Meanwhile, reservoirs under secondary drive mechanisms can also make use of system identification models, with some models having prediction accuracy well above 90%. However, more research needs to be done to improve the prediction accuracy for secondary drive mechanisms. This is due to the increased complexity of the models and the presence of exogenous input data.

System identification based reservoir models can be established as a practical, cost effective and robust tool for forecasting reservoir fluid production. The procedures described in this paper as well as the final conceptual model can serve as a framework or guide to reservoir engineers if they wish to implement system identification for production forecasting.

REFERENCES 1. Spencer, J.A. and D.T. Morgan. Application of forecasting and uncertainty methods to production. in SPE

Annual Technical Conference and Exhibition. 1998: Society of Petroleum Engineers.2. Tompkins, J.A., et al., Facilities planning. 2010: John Wiley & Sons.3. Kingsman, B.G., Modelling input–output workload control for dynamic capacity planning in production

planning systems. International Journal of Production Economics, 2000. 68(1): p. 73-93.4. Kaplan, R.S., Measuring manufacturing performance: a new challenge for managerial accounting research.

1992: Springer.5. Arps, J., Analysis of decline curves. Transactions of the American Institute of Mining, Metallurgical and

Petroleum Engineers, 1945. 160: p. 228-247.6. Cancelliere, M., F. Verga, and D. Viberti, Benefits and limitations of assisted history matching. Offshore

Europe, 2011.7. Fetkovich, M., Decline curve analysis using type curves. Journal of Petroleum Technology, 1980. 32(6): p.

1065-1077.8. Tavassoli, Z., J.N. Carter, and P.R. King, Errors in history matching. SPE Journal, 2004. 9(03): p. 352-361.9. Tomomi, Y. Non-Uniqueness of History Matching. in SPE Asia Pacific Conference on Integrated Modelling for

Asset Management. 2000: Society of Petroleum Engineers.10. Olominu, O. and A.A. Sulaimon, Application of Time Series Analysis to Predict Reservoir Production

Performance, Society of Petroleum Engineers.11. Brabec, M., M. Paulescu, and V. Badescu, Tailored vs black-box models for forecasting hourly average solar

irradiance. Solar Energy, 2015. 111: p. 320-331.12. Prada, L., et al., A novel black-box simulation model methodology for predicting performance and energy

consumption in commodity storage devices. Simulation Modelling Practice and Theory, 2013. 34: p. 48-63.13. Logar, V., Ž. Kristl, and I. Škrjanc, Using a fuzzy black-box model to estimate the indoor illuminance in

buildings. Energy and Buildings, 2014. 70: p. 343-351.14. Papadopoulos, T.A., et al., Simplified measurement-based black-box modeling of distribution transformers using

transfer functions. Electric Power Systems Research, 2015. 121: p. 77-88.



15. Grancharova, A., J. Kocijan, and T.A. Johansen, Explicit output-feedback nonlinear predictive control based onblack-box models. Engineering Applications of Artificial Intelligence, 2011. 24(2): p. 388-397.

16. Haley, T.A. and S.J. Mulvaney, On-line system identification and control design of an extrusion cookingprocess: Part II. Model predictive and inferential control design. Food control, 2000. 11(2): p. 121-129.

17. Angarita-Jaimes, N., et al., Optimising the assessment of cerebral autoregulation from black box models.Medical engineering & physics, 2014. 36(5): p. 607-612.

18. Hickman, T.S., A rationale for reservoir management economics. Journal of Petroleum Technology, 1995.47(10): p. 886-890.

19. AlAjmi, M.D., et al., Profiling Downhole Casing Integrity Using Artificial Intelligence, Society of PetroleumEngineers.

20. Shahkarami, A., et al., Artificial Intelligence (AI) Assisted History Matching, Society of Petroleum Engineers.21. Enyioha, C. and T. Ertekin. Advanced Well Structures: An Artificial Intelligence Approach to Field Deployment

and Performance Prediction. in SPE Intelligent Energy Conference & Exhibition. 2014: Society of PetroleumEngineers.

22. Anifowose, F.A., et al. Improved permeability prediction from seismic and log data using artificial intelligencetechniques. in SPE Middle East Oil and Gas Show and Conference. 2013: Society of Petroleum Engineers.

23. Chen, H., H. Klie, and Q. Wang. A Black-Box Interpolation Method To Accelerate Reservoir SimulationSolutions. in SPE Reservoir Simulation Symposium. 2013: Society of Petroleum Engineers.

24. Nelles, O., Nonlinear system identification. 2002, IOP Publishing.25. Ljung, L., System identification toolbox: user's guide. 1995: Citeseer.26. Ljung, L., System identification. 1998: Springer.27. Keesman, K.J., System identification: an introduction. 2011: Springer Science & Business Media.28. Renard, G., et al. System Identification Approach to Watercut Analysis in Waterflooded Layered. in SPE/DOE

Improved Oil Recovery Symposium. 1998: Society of Petroleum Engineers.29. Elgsaeter, S., O. Slupphaug, and T.A. Johansen. Production optimization; system identification and uncertainty

estimation. in Intelligent Energy Conference and Exhibition. 2008: Society of Petroleum Engineers.30. Cheung, G.W. and R.B. Rensvold, Evaluating goodness-of-fit indexes for testing measurement invariance.

Structural equation modeling, 2002. 9(2): p. 233-255.31. Ahmed, T., Reservoir engineering handbook. 2006: Gulf Professional Publishing.32. Satter, A., G.M. Iqbal, and J.L. Buchwalter, Practical enhanced reservoir engineering: assisted with simulation

software. 2008: Pennwell Books.33. Graham, J.W., Missing data analysis: Making it work in the real world. Annual review of psychology, 2009. 60:

p. 549-576.34. Chen, J.-M. and B.-S. Chen, System parameter estimation with input/output noisy data and missing

measurements. Signal Processing, IEEE Transactions on, 2000. 48(6): p. 1548-1558.35. Kadlec, P., B. Gabrys, and S. Strandt, Data-driven soft sensors in the process industry. Computers & Chemical

Engineering, 2009. 33(4): p. 795-814.



APPENDIX A: RESERVOIR DATA US

1) Rock & Liquid Expansion Drive (Fig. A1 shows that the obtained reservoirreservoir pressure rapidly declines in theshows the field oil production rate and fithe reservoir. The key characteristics of t

• Total number of grid-blocks: 286• Rock properties: Porosity varies i

each block from 0 to greater than 3• Relative permeability curves are p• Initial average reservoir pressure i• There are 10 producer wells, all

below the bubble point. This allow• No aquifer support.

Figure A1: Identification of drive mechan

Figure A2: Production performance parameters

2) Solution Gas Drive (SGD)Fig. A5 shows that the obtained rese

Similarly, average reservoir pressure alsois more compressible than live oil. The below bubble point and getting producedbecause the gas production rate eventualwater production, it is very negligible (ldrive.

This model is based on the expansionfield oil cumulative production curves wmechanism with only the following diffe

• Initial average reservoir pressure i


USED IN BUILDING THE CONCEPTUAL FRAME

(RLD) r model follows the typical trend of reservoirs under exe first two years of production and the total producingield oil cumulative production curves with time and Figthe reservoir are:

in each block, from 0 to 0.17. Absolute permeability 300 mD, while Kv/Kh ratio is 0.5. Sw also varies from

provided in Fig A4. is 4000 psi and bubble point (Pb) is 2000 psi. operating at constant BHP of 2050 psi only in order

ws for rock and fluid expansion to be the only drive me

nism – RLD

s (Output) – RLD

Figure A3: 3D view

Figure A4: Relative perm

ervoir model follows the typical trend of reservoirs uno rapidly declines, though not as fast as the previous drtotal producing GOR increased rapidly at first due to

d in large amounts very quickly due to it being more mly reduces as there is less and less gas in the reservoir.less than one barrel), which shows that the main drive

n drive model obtained previously. Fig. A6 shows the with time. The key characteristics of the reservoir are serences: is 2561 psi and Pb is 2000 psi.

Management

EWORK

xpansion drive[31]. Average g GOR is constant. Fig. A2 g. A3 shows the 3D view of

in I & J direction varies in m block to block.

to deplete the reservoir not echanism.

of reservoir– RLD

meability curves – RLD

nder solution gas drive [31]. rive mechanism because gas o gas coming out of the oil

mobile. Later on, GOR drops . As for the field cumulative e mechanism is solution gas

field oil production rate and similar to the previous drive



• There are 10 producer wells, all operating at constant BHP of 500 psi in order to deplete the reservoir below thebubble point.

Figure A5: Identification of drive mechanism – SGD Figure A6: Production performance (Output) – SGD

3) Gas Cap drive (GCD)Fig. A7 shows that the obtained reservoir model follows the typical trend of reservoirs under gas cap drive [31]. Average reservoir pressure declines continuously but much slower than that of solution gas drive or expansion drive. Water production is very small, as shown by the water rate almost being zero at all times, and hence water production can be ignored when compared to oil production rates and cumulative volumes produced. Lastly, GOR will slowly increase with time due to the expanding gas cap. Fig. A8 shows the field oil production rate and field oil cumulative production curves with time and Fig. A9 shows the 3D view of the reservoir. The key characteristics of the reservoir are:

• Total number of grid-blocks: 1400• Rock properties: Porosity varies in the vertical direction with values ranging between 0.15 to 0.27. Absolute

permeability in I & J direction varies in the vertical direction with values ranging between 45 to 350 mD, whileKv/Kh ratio is 1. Kv/Kh ratio is set to a high value in order to promote gravity segregation effect, so that thesolution gas that comes out of the oil will go upwards to the gas cap and the oil downwards towards the producers.Also, Sw varies from block to block.

• Relative permeability curves are provided in Fig. A10.• Initial average reservoir pressure is around 10576 kPa and Pb is 9570 kPa.• There are 5 producer wells, all operating at constant BHP of 7000 kPa. The reason for the high BHP is that gas cap

drive is very sensitive to the production rate and hence lower rates is better in the long run because it will allow thegas cap to displace the oil more evenly (piston like manner) and result in higher recovery.

• No aquifer support.

Figure A7: Identification of drive mechanism – GCD Figure A8: Production performance parameters (Output) – GCD



4) Aquifer drive (AQD)Fig. A11 shows that the obtained res

particular reservoir has a bottom aquifedecline is very gradual or almost non-exrapidly due the water encroaching into tconstant for most of the production perio

Fig. A12 shows the field oil producthe 3D view of the reservoir. The key cha

• Total number of grid-blocks: 2500• Rock properties: Porosity varies in

varies in each block from 30 to 30block.

• The relative permeability curves a• Initial average reservoir pressure i• There are 6 producer wells, all ope



Figure A9: 3D view


servoir model follows the typical trend of reservoirs uner drive support. As can be seen from the average rexistent after just a brief period of steep decline. Waterthe oil zone, but this is expected of an aquifer drive.

od due to the reservoir pressure being maintained. ction rate and field oil cumulative production curves waracteristics of the reservoir are: 0 n each block, ranging mainly 0.2 to 0.3. Absolute perm

00 mD, while absolute J permeability=I permeability. S

are provided in Fig. A14. is around 5490 kPa and Pb is 5570 kPa. erating at constant BHP of 1000 kPa.

nism – AQD Figure A12: Production performa

Management

of reservoir – GCD

meability curves – GCD

nder aquifer drive [20]. This eservoir pressure curve, the r production increases quite Lastly, GOR stays roughly

with time and Fig. 13 shows

meability in I & K direction Sw also varies from block to

ance parameters (Output) – AQD



Figure A13: 3D view of reservoir –

5) Combined drive (COD)Fig. A15 shows that the obtained re

This particular reservoir has a combinatiaverage reservoir pressure curve, the decnot strong. This is also shown from the v(the cumulative water production curve increasing as the gas cap continues to exp

Fig. A16 shows the field oil productithe 3D view of the reservoir. The key cha

• Total number of grid-blocks: 3888• Rock properties: Porosity varies

direction varies in each block frofrom block to block.

• There are 4 different rock types these relative permeability sets are

• Initial average reservoir pressure i• There are 21 producer wells, all op


AQD Figure A14: Relative perm

eservoir model follows the typical trend of reservoirs ion of solution gas drive, gas cap drive and aquifer drivcline is very fast because the pressure support from botvery slow encroachment of water, which result in only looks like it is constantly very close zero). Lastly, th

pand and more solution gas comes out of the oil. ion rate and field oil cumulative production curves witaracteristics of the reservoir are: 8. This reservoir has several faults.in each block, ranging between 0.156 to 0.17. Abso

om 4 to 10 mD, while Kv/Kh ratio is 0.3. Also, Sw a

in the reservoir, each with their own set of relative pe provided in Fig. A18. is around 10716 psi and Pb is 30000 psi. perating at constant BHP of 1500 psi

Management

meability curves – AQD

under combined drive [20]. ve. As can be seen from the th the gas cap and aquifer is very little water production

e GOR curve is continually

th time and Fig. A17 shows

olute permeability in I & J and Net-to-gross ratio varies

permeability curves. One of



Figure A15: Identification of drive mechanism – COD

Figure A16: Production performance parameters (Output) – COD

Figure A17: 3D view of reservoir – COD

Figure A18: Relative permeability curves – COD

6) Water Injection (WAI)Fig. A19 shows a comparison of two cases:

i) The reservoir is only being depleted by 25 producer wells.ii) The reservoir has 25 producer wells and 10 injector well injecting water into the aquifer.

As can be seen from the average reservoir pressure curves of the two cases, the water injection case provides very good pressure support and maintains the reservoir pressure at a much higher pressure than the case with no injection. Moreover, the case with water injection provides higher levels of both oil and water recoveries. Cumulative oil recovery increases by around 25% due to the higher reservoir pressure. Understandably the water production also increases significantly due to injected water bypassing the oil. This proves that case (ii) is a good representation of secondary recovery by water injection and it can used to provide input-output data for the system identification process. Fig. A20 shows the field oil production rate and field oil cumulative production curves with time for the output data. That figure also shows the field water injection rate and field cumulative water injected curves with time for the input data. Also, Fig. A21 shows the 3D view of the reservoir. The key characteristics of the reservoir are:

• Total number of grid-blocks: 9000• Rock properties: Porosity varies for each block in the K direction, ranging between 0.8 to 0.17. Absolute

permeability in I & J direction varies in each block and their distributions were made using geo-statisticaltechniques, varying mainly in the range between 20 mD to 700 mD. Meanwhile Kv/Kh ratio is 0.01. Also, Swvaries from block to block.

• The relative permeability sets are provided in Fig. A22.• Initial average reservoir pressure is around 4566 psi and Pb is 3600 psi.• There are 25 producer wells, all operating at constant BHP of 2000 psi. There are also 10 injector wells, all

operating at constant BHP of 4543.39 psi.




Figure A20: Production performance parameters WAI

7) Gas Injection (GAI)Fig. A23 shows a comparison of two cas

i) The reservoir is only being depleteii) The reservoir has 5 producer wellsAs can be seen from the average re

pressure support and maintains the reservthe case with gas injection provides higaround 86% due to the higher reservoirinjected gas bypassing the oil. This proveit can used to provide input-output data fmodel obtained previously. Fig. A24 shtime for the output data. The figure alsotime for the input data. The only additionwell, operating at constant BHP of 25,00


nism – WAI

(Input & Output) –

Figure A21: 3D view


ses: ed by 5 producer wells. s and 1 injector wells injecting gas into the gas cap. eservoir pressure curves of the two cases, the gas invoir pressure at a much higher pressure than the case wgher levels of both oil and gas recoveries. Cumulativr pressure. Understandably the gas production also ines that case (ii) is a good representation of secondary refor the system identification process. This model is baows the field oil production rate and field oil cumula

o shows the field gas injection rate and field cumulatin in this model compared to the gas cap drive model is0 kPa.

Management

w of reservoir – WAI

meability curves – WAI

njection case provides good with no injection. Moreover, ve oil recovery increases by ncreases significantly due to ecovery by gas injection and ased on the gas cap reservoir ative production curves with ive gas injected curves with s the addition of one injector



Figure A23: Identification of drive mechanism - GAI Figure A24: Production performance parameters (Input & Output) –

GAI


conceptual framework for using system identification in...

Documents