Applying Statistical Methods to Assess Fractured Reservoirs Relying on Field Data

   The presence of fractures in reservoirs can have both a negative and a positive impact on the technical and economic indicators of field development and thus an early classification of fractures is an important requisite. Identifying the type of a fractured reservoir at the initial stages of development is a clue to selecting an optimal type of model and field development system. The paper evaluates the applicability of the cumulative production indicator and the productivity index of wells to determine the type of fractured reservoir with the help of a statistical method for analyzing the Lorenz curve and the Gini coefficient (as applied to determine the impact of fractures) with small data samples and at the initial stages of development. A method of mathematical statistics namely the bootstrap method is used in this paper in order to study the fracture impact coefficient for a small number of wells. This method is based on the repeated generation of random samples multitude from the original data set and their subsequent statistical analysis. Modeling of samples was carried out by means of a random number generator available in spreadsheets. The results of a research proved that the use of indicators such as cumulative production and productivity index to identify fractured reservoirs with a small number of wells produced the comparable results. To increase the reliability of classification for a small number of wells, a data sample is required that will most fully describe the field. It is possible to obtain a representative sample of data for an objective analysis of the distribution and influence of fracture systems by placing wells covering the entire area of the field. In the early stages of development, due to the low production volumes and short periods of well operation, it is recommended to use the productivity index for the analysis.

1. Aguilera R. (1995). Naturally fractured reservoirs. Tulsa, Oklahoma: PennWell Publishing Company, p. 521.

2. Ahr Wayne M. (2011). Geology of carbonate reservoirs: the identification, description, and characterization of hydrocarbon reservoirs in carbonate rocks. John Wiley & Sons, Inc, p. 296.

3. Akhkubekov A. E., Vasilyev V. N. (2010). Acid Tunneling Technology: Application Potential in Timan-Pechora Carbonates. SPE Russian Oil and Gas Conference and Exhibition. Moscow, Russia. doi: 10.2118/135989-MS

4. Allan Jack, Sun S. Qing. (2003). Controls on Recovery Factor in Fractured Reservoirs: Lessons Learned from 100 Fractured Fields. SPE Annual Technical Conference and Exhibition. Denver, Colorado. doi: 10.2118/84590-MS

5. Baker Richard O., Kuppe Frank (2000). Reservoir Characterization for Naturally Fractured Reservoirs. SPE Annual Technical Conference and Exhibition. Dallas, Texas. doi: 10.2118/63286-MS

6. Bourbiaux B. (2010). Fractured Reservoir Simulation: a Challenging and Rewarding Issue.Oil and Gas Science and Technology, 65(2), pp. 227–238. doi: 10.2516/ogst/2009063.

7. Dixon Philip M., Weiner Jacob, Mitchell-Olds Thomas, Woodley Robert. (1987). Bootstrapping the Gini Coefficient of Inequality. Ecology, 68(5), pp. 1548–1551. doi: 10.2307/1939238

8. Lorenz John C., Cooper Scott P. (2020). Applied Concepts in Fractured Reservoirs. John Wiley & Sons, Ltd, p. 240.

9. Manrique E., Thomas C., Ravikiran R., Izadi M., Lantz M., Romero J., Alvarado V. (2010). EOR: Current status and opportunities. SPE Symposium on Improved Oil Recovery. Tulsa, Oklahoma, USA, pp. 1584–1604. doi: 10.2118/130113-MS

10. Marchal D., Gonzalez I., Benito J., Balseiro P. (2005). Technologies and Exploitation Strategies Applied to the Development of a Naturally Fractured Carbonate Reservoir: The Cretaceous Cogollo Group in La Concepción Field, Maracaibo Basin, Venezuela. SPE Latin American and Caribbean Petroleum Engineering Conference. Rio de Janeiro, Brazil. doi: 10.2118/97384-MS

11. Martyushev D.A. (2014). Evaluation of fracture porosity of carbonate reservoir using probabilistic-statistical methods. Neftyanoe khozyaystvo, (4), pp. 51–53. (In Russ.)

12. Mélard G. (2014). On the accuracy of statistical procedures in Microsoft Excel 2010. Computational Statistics, 29(5), pp. 1095–1128. doi: 10.1007/s00180-014-0482-5

13. Narr Wayne, Schechter David S., Thompson Laird B. (2006). Naturally Fractured Reservoir Characterization. Society of Petroleum Engineers, p. 112.

14. Nelson Ronald A. (1985). Geologic Analysis of Naturally Fractured Reservoirs. Gulf Publishing Company, Book Division, p. 320.

15. Nelson Ronald A. (2001). Geologic analysis of naturally fractured reservoirs. Gulf Professional Publishing, p. 352.

16. Nelson Ronald A. (2020). Static Conceptual Fracture Modeling: Preparing for Simulation and Development. John Wiley & Sons Ltd. doi: 10.1002/9781119596875.index

17. Shchekin A.I., Vasiliev V.A., Nikolaychenko A.S., Kolomiytsev A.V. (2021). Field classification of fractured reservoirs of crystalline basement. Georesursy = Georesources, 23(3), pp. 90–98. (In Russ.) doi: 10.18599/grs.2021.3.12

18. Spence Guy H., Couples Gary D., Bevan Tim G., Aguilera Roberto, Cosgrove John W., Daniel Jean-Marc, Redfern Jonathan (2014). Advances in the study of naturally fractured hydrocarbon reservoirs: A broad integrated interdisciplinary applied topic. Geological Society Special Publication, 374(1), pp. 1–22. doi: 10.1144/SP374.19

19. Sun S. Qing, Sloan Rod (2003). Quantification of Uncertainty in Recovery Efficiency Predictions: Lessons Learned from 250 Mature Carbonate Fields. SPE Annual Technical Conference and Exhibition. Denver, Colorado. doi: 10.2118/84459-MS

20. Sun Shaoqing, Pollitt David A. (2021). Optimising Development and Production of Naturally Fractured Reservoirs Using a Large Empirical Dataset. Petroleum Geoscience, 27(2). doi: 10.1144/petgeo2020-079

21. Tiab D., Donaldson E.C. (2015). Petrophysics. Gulf Professional Publishing. doi: 10.1016/C2014-0-03707-0

22. Toledo-Piña R., Leon-García A., Padilla-Sixto R. (2014). Water Injection in Offshore Naturally Fractured Reservoirs Associated to a Common Aquifer. SPE Latin America and Caribbean Petroleum Engineering Conference. Maracaibo, Venezuela. doi: 10.2118/169275-MS

23. Yitzhaki S., Schechtman E. (2013). The Gini methodology. A primer on a statistical methodology. New York: Springer, p. 548. doi: 10.1007/978-1-4614-4720-7

24. Zakrevskiy K.E., Kundin A.S. (2016). Features of geological 3D modeling of carbonate and fractured reservoirs. Moscow: OOO «Belyy Veter», 404 p. (In Russ.)