7 decision making under uncertainty in petroleum engineering · pdf file- 3 - 7 decision...

WORKSHOP PROCEEDINGS

7 Decision making under uncertainty in petroleum engineering

7.4. Stochastic model for characterizing oil production data

Elizabeth Santiago and Leonid Sheremetov


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7 Decision making under uncertainty in petroleum engineering 7.4. Stochastic model for characterizing oil production data


Stochastic Model for Characterizing Oil Production

Elizabeth Santiago, Leonid Sheremetov

Instituto Mexicano del Petróleo, Av. Eje Central Lázaro Cárdenas Norte, 152 Col. San Bartolo Atepehuacan, Mexico-city, Mexico CP 07730

{esangel, sher}@imp.mx

Abstract. This paper presents a strategy for designing a stochastic model for forecasting the oil production, which analyzes the production data by consider-ing statistical measurements. These measurements are obtained for different reservoir formations for variables associated with oil production. This charac-terization leads to a set of patterns or states associated with the behavior of pro-duction data which are used for designing a stochastic model. The proposed strategy consists of three main modules. The first one is the preprocessing of data which involves the analysis of the production data, and the comparison be-tween two blocks of production data: the historical production and the produc-tion tests, both of them for each well. The second module involves the charac-terization and pattern recognition by formation. This module applies statistical tools to the features associated with the well production data, improving the forecasting of the production behavior. Finally, the third module generates a repertory of states with different patterns which are used for defining a set of meaningful states of all the wells. The resultant model helps to identify different profiles of production series which is crucial in the decision making. Further-more the model presents a general framework for the forecasting of the future production by adding other types of data, for both green and brown fields.

Keywords. stochastic model, forecasting, well characterization

1 Introduction

The reservoir characterization of hydrocarbons for forecasting the oil production is a challenge. The problem lays in the conjunction of different characteristics obtained from a wide spectrum of data sources. Conventional reservoir characterization starts with the modeling of the geology, and is followed by adding petrophysical and geo-physical information in order to obtain a relatively complete (the best possible at the time of development) geological perception of the reservoir. Furthermore, the uncer-tainty is a factor which needs to be considered in any prediction model [2, 9]; it is mainly in data that evolve in time. Engineering principles of fluid flow are then added so as to arrive at a dynamic reservoir model, which is tuned using the production his-tory of multiple wells. On the contrary, Top-Down modeling approaches the reservoir modeling from an opposite angle and direction when compared to conventional pro-


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cess by attempting to build a model of the reservoir, starting with the well produc tion behavior (history) [11].

The analysis of the forecasting of the oil production began with the works on the decline curve analysis (DCA) which are based on Arps equations [1], the equation of the Darcy’s law [10], and the identification of type curves [7]. Currently, many works have been developed by improving the analysis of the production curves [4, 6, 8, 11, 12, 13], including the application of the DCA in fractured reservoirs with fractal ge-ometry [3]. Also the DCA has been used with the probabilistic approaches to evaluate the uncertainty in the reserves estimates. It is important due to the fact that historical data usually possess significant amounts of noise [5]. However, in most of the models (except [11]) the partitioning of the production series, in particular, taking into ac-count geological formations, is not considered. Joining together partial results ob-tained with such partitioning, a general description of the well’s profile is obtained.

This work presents a strategy for designing a stochastic model for forecasting the oil production, which analyzes the production data by considering statistical measure-ments. These measurements are obtained for different reservoir formations for varia-bles associated with oil production. For illustrative purposes in this paper these varia-bles are limited to gas and water productions. This characterization leads to a set of patterns or states associated with the behavior of production data which are used for designing a stochastic model. The proposed strategy consists of three main modules. The first one is the preprocessing of the data which involves the analysis of the pro-duction data, and the comparison between two blocks of production data: the produc-tion history and the production tests, both of them for every well. The second module involves the characterization and pattern recognition by formation. This module ap-plies statistical tools to the features associated with the well production data, improv-ing the forecasting of the production behavior. Finally, the third module generates a repertory of states with different patterns which are used for defining a set of mean-ingful states of all the wells. The proposed approach is applied to Jujo-Tecominoacan oilfield of the Bellota-Jujo asset located in the south-east part of Mexico. Jujo-Tecominoacan is a naturally fractured reservoir (NFR).

The rest of the paper is organized as follows. The following section describes the proposed methodology. In Section, 3 conducted experiments are described and their results are analyzed. Finally the proposed approach is compared with the related works followed by the concluding remarks.

2 Proposed methodology

The proposed methodology is grounded in the fact that the behavior of time series describing production data of a well depends upon different conditions in different time periods. These conditions range from different lift mechanisms to different for-mations or layers, characterized by different petrophysical properties and recovery


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factors. For NFR, preferential source of oil (fracture or matrix) should be also taking into consideration. The problem is that usually it is very difficult to identify and con-sider all these factors. The approach proposed in this paper is based on the statistical analysis of wells behavior and identification of temporal patterns for future produc-tion. These patterns can be used along with other forecasting methods based both on local and global metrics.

The flow chart of the statistical well characterization model using dynamic data is presented in Fig. 1. This methodology consists of three modules which are described as follows. The input data are the series of monthly historical production data. This information requires a preprocessing analysis for validating the series, which is car-ried out in module 1. Once the information is validated, this module realizes the sepa-ration of the series of monthly oil production. At the same time the association with other features is done, in particular gas and water production. Later the characteriza-tion module 2 computes the basic statistics such as media, standard deviation, and variance for each formation. The results obtained are analyzed for each formation by associating the statistical metrics; then multiple wells are evaluated and transition probabilities are obtained. These probabilities are used for generating the probabilistic model of the oilfield wells (module 3).

Fig. 1. General schema of the statistical characterization of a well

3 Results of experiments

To illustrate the characterization module let us consider one of the wells of Jujo-Tecominoacan oilfield. The general description of this well is shown in Table 1. The well derive its production from Upper Jurassic Kimmeridgian (UJKim), Upper Juras-sic Tithonian (UJTit), and Lower Cretaceous (LC) formations. Some wells also pro-


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duce from Upper Cretaceous Agua Nueva (UCAN) formation. According to this in-formation, in Table 2, 3, and 4, the total and percentage of every variable are obtained for each formation. The first and the second column of each table indicate the initial and final date of the production from the formation, the third column presents the months of production, and the fourth and fifth columns show the total production and the contribution for each formation (allocation factor). Finally, the last column points out the formation of each period.

Table 1. General data of the well

Total records 278 Initial date 01/02/1986 Final date 01/03/2009 Total production (Bls.) 9719944.34 Total gas 11423.975 Total Water 389656.433

Table 2. Total historical oil production obtained for each formation

Date_I Date_F # Months T Oil_F % Prod Formation

01/02/1986 01/10/1989 41 6436833 16.19% UJKIM

01/05/1990 01/04/1992 24 739659.8867 8.63% UJKIM

01/02/1998 07/10/2004 81 1493786.944 29.14% LC

01/11/2004 01/03/2009 53 1049664.509 19.06% UJTIT

Table 3. Total gas obtained for each formation

Date_I Date_F # Months T Gas_F % Gas Formation

01/02/1986 01/10/1989 41 7002.372976 61.29% UJKIM

01/05/1990 01/04/1992 24 914.9753237 8.01% UJKIM

01/02/1998 07/10/2004 81 1858.100492 16.26% LC

01/11/2004 01/03/2009 53 1648.526742 14.43% UJTIT

Table 4. Total water obtained for each formation

Date_I Date_F # Months T Water_F % Water Formation

01/02/1986 01/10/1989 0 172559 44.28% UJKIM

01/05/1990 01/04/1992 12 38214.23547 9.80% UJKIM

01/02/1998 07/10/2004 81 66307.29305 17.01% LC

01/11/2004 01/03/2009 53 112575.9046 28.89% UJTIT


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The statistics metrics for historical oil, gas, and water productions are obtained and presented in Figures 2, 3 and 4 respectively. In each figure the states (S1 to S4) are associated with the formations UJKIM, UJKIM, LC, and UJTIT. In Fig. 2, the per-centage shows the fraction of total well oil production obtained from the formation; for example, the formation LC contributes with 15.37 % of the total production (9719944.34 Bls.) of the well.

Fig. 2. Transition model and statistical metrics obtained for oil production history in the 4 formations

Fig. 3. Transition model and statistical metrics obtained for the gas production in the 4 for-mations

Fig. 4. Transition model and statistical metrics obtained for the water production in the 4 formations

State S1

S2

S3

S4

% PROD 66.22%

7.61%

15.37%

10.80%

AV_P 156995.927

30819.162

18441.8141

19804.9907

Var_P 6350648297

76904255.2

37604539.7

100904587

DS_P 79690.9549

8769.50713

6132.25405

10045.1275

Formation UJKIM

UJKIM

LC

UJTIT

State S1

S2

S3

S4

% GAS 61.30%

8.01%

16.26%

14.43%

AV_G 170.7895848

38.12397182

22.93951225

31.10427815

Var_G 9920.137064

236.0616326

178.0812649

1981.212351

DS_G 99.59988486

15.36429734

13.34470925

44.51081162

Formation UJKIM

UJKIM

LC

UJTIT

State S1

S2

S3

S4

% WATER 44.28%

9.80%

17.01%

28.89%

AV_W 28759.83333

3184.519

818.608

2124.073

Var_W 311074320

1513739.659

1698563.974

60589172.290

DS_W 17637.29

1230.341

1303.289

7783.904

Formation UJKIM

UJKIM

LC

UJTIT


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The resulting statistical metrics are presented for each state. For example in S2, the average AV_P=30819.162, the variance Var_P=76904255.2, and standard deviation DS_P=8769.50713. These operations are applied to gas and water productions. The results obtained for this well are shown in Fig. 3 and Fig. 4.

This procedure is repeated for all the wells. Once all the wells have been analyzed, the next step is the association among all the resultant states. The simplification of all the states is done for the design of the stochastic general model. This model is pre-sented in Fig 5 which consists of 7 states. The probabilities associated with them are shown in Table 5.

Fig. 5. Transition model among formations for Jujo-Tecominoacan oilfield

Table 5. Transition Matrix of probabilities among formations (states)

UJTIT UJKIM LC UJTIT LC

UJKIM, UJTIT

UCANLC

UCAN, LC, UJTIT

UJTIT 0.6875 0.125 0.0625 0.0625 0 0 0.0625 UJKIM 0.353 0.412 0.059 0.059 0.117 0 0 LC 0.5 0 0.5 0 0 0 0 UJTIT, UJKIM 0.25 0.5 0 0 0.25 0 0 UJTIT, LC 0 0 0 0.5 0 0.5 0 UCAN, LC 1 0 0 0 0 0 0 UCAN, LC, UJTIT 1 0 0 0 0 0 0


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The model obtained from the analysis of associations among the wells provides a general profile of the reservoir. It leads to support an outlook when any current state is known; even this model shows a historical schema of the reservoir. It is important to comment that the transition probabilities among formations are generated from the wells that produced from various formations. In this analysis, some wells remained in the same formation along all the production period On the other hand, the statistical metrics of oil, gas and water productions in the characterization module allows us knowing the behavior of the data of each formation, and to compare the statistical relations among the transitions of the states. In Table 6, a comparison of the statistical metrics is shown for another well; in this case the transition is UJKIM to LC.

Table 6. Comparison of statisical characteristicas of the transition UJKIM to LC

Well

Initial date 01/01/1986 01/11/2002 End date 01/11/2002 01/04/2012 No. of records 304 304 Total production 7623310.37 7623310.37 Effective months 198 86 T_Prod_F 6564290.82 1060110.86 % PROD 86.11% 13.90% AVG_P 33152.984 12326.8705 Var_P 378310146 73318471.8 DS_P 19450.1966 8562.62062 Formation UJKIM LC

With the statistical model of the reservoir behavior we can predict the pattern of the future behavior of the wells and, considering the statistical characteristics of this pat-tern, the main parameters of oil production. The model in Fig. 5 allows forecasting any state considering the probabilities obtained for the wells of the oilfield. However, it is clear that for a new set of wells with other properties of the reservoir, the model needs to be adapted.

4 Conclusions

In the literature, most of the works use the pressure in combination with oil produc-tion for prediction, based on the empirical Arps equation. However, the use of DCA models has some limitations. One of them is the difficulty to foresee which equation


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will follow. In addition, each type of curves has some disadvantages, for example, the exponential decline curve tends to underestimate reserves and production rates; the harmonic decline curve has a tendency to overpredict the reservoir performance [14]. In some cases, production decline data do not follow any model but crossover the entire set of curves.

The resultant model helps to identify different profiles of production series which is crucial in the decision making. Furthermore the proposed model presents a general framework for adding other types of data to improve the forecasting for any future production, for both green and brown fields. The application of Markov chains can be easily adapted to the forecasting problem associating the transition matrix with oil production.

5 Acknowledgments

Partial support for this work was provided by CONACYT-SENER-Hidrocarburos projects 146515 and 143935.

6 References

1. Arps J. J. Analysis of Decline Curves. Trans. AIME, 160 (1945), pp. 228-247 2. Barker J. W., Cuypers M., and Holden L., Quantifying uncertainty in production forecasts:

Another look at the PUNQ-S3 problem, Tech. Rep, SPE 62925, 2000. 3. Camacho-Velázquez R., Fuentes-Cruz G., Vazquez-Cruz M. Decline-Curve Analysis of

Fractured Reservoirs With Fractal Geometry. Society of Petroleum Engineers. SPE Reser-voir Evalution & Engineering (2008).

4. Chan C. W., Nguygen H. H., and Li X. Data Analysis for Oil Production Prediction. Ener-gy. Volume 35, Issue 7, July 2010, Pages 3097–3102.

5. Cheng, Y., Wang, Y., McVay, D.A., and Lee, W.J. 2010. Practical Application of a Proba-bilistic Approach to Estimate Reserves Using Production Decline Data.SPE Econ & Mgmt 2 (1): 19-31. SPE-95974-PA. doi: 10.2118/95974-PA.

6. Darwis S., Ruchana B. N., and Permadi A. K. Robust Decline Curve Analysis. J. Indones. Math. Soc. (MIHMI). Vol. 2 (2009), pp. 105-111.

7. Fetkovich M. J. Decline curve analysis using type curves. Journal of Petroleum Technolo-gy, 1980, 32(6):1065-1077.

8. Fetkovich M. J., Vienot M.E., Bradley M.D., Kiesow U.G. Decline-Curve Analysis Using Type Curves-Case Histories. SPE Formation and Evaluation, (1987).

9. Hegstad B. K., and More H. Uncertainty assessment in history matching and forecasting: Geostatistics Wollongong’96, E.Y.Baafi and N. A. Schofield, Eds., V.1, Kluwer Academic Publishers, p.p. 585–596.

10. Kim H. Mathematical Characteriztion of Petroleum Reservoir and Prediction of Future Oil Production. Journal Appl. Math. & Computing. Vol. 21(2006), No.1-2, pp.509-523

11. Mohaghegh, S. D., Gaskari, R. and Jalali, J., New Method for Production Data Analysis to Identify New Opportunities in Mature Fields: Methodology and Application, SPE 98010, 2005.

WORKSHOP PROCEEDINGS7 Decision making under uncertainty in petroleum engineering

7.4. Stochastic model for characterizing oil production data Elizabeth Santiago and Leonid Sheremetov

12. Li K., Horne R. N.: A Decline Curve Analysis Model Based on Fluid Flow Mechanisms. SPE, Stanford University. SPE 83470. (2003)

13. Palacios J. C., Blasingame T. A.: Decline-Curve Analysis Using Type Curves-Analysis of Gas Well Production Data. SPE 25909. (1993)

14. Xie C., Guan Z., Luo G., Li X. Decline Analysis of Oil Well Stimulation Rule Using Matlab. Proc. 2010 Int. Conference on Web Information Systems and Mining, IEEE Com-puter Society, pp. 231 – 234.

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