A new algorithm for finding CRM-model coefficients

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

2019, Vol. 5. №3

Title: 
A new algorithm for finding CRM-model coefficients


For citation: Bekman A. D., Stepanov S. V., Ruchkin A. A., Zelenin D. V. 2019. “A new algorithm for finding CRM-model coefficients”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 5, no 3, pp. 164-185. DOI: 10.21684/2411-7978-2019-5-3-164-185

About the authors:

Alexander D. Bekman, Cand. Sci. (Math), Senior Manager, Tyumen Petroleum Research Center; ORCID, adbekman@tnnc.rosneft.ru

Sergey V. Stepanov, Dr. Sci. (Tech.), Professor, Department of Applied and Technical Physics, University of Tyumen; Senior Expert, Tyumen Petroleum Research Center; eLibrary AuthorID, svstepanov@tnnc.rosneft.ru

Alexander A. Ruchkin, Cand. Sci. (Tech.), Expert, Tyumen Petroleum Research Center; eLibrary AuthorID, aaruchkin@tnnc.rosneft.ru

Dmitry V. Zelenin, Senior Expert, Tyumen Petroleum Research Center; eLibrary AuthorID, ORCID, dvzelenin@tnnc.rosneft.ru

Abstract:

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example — the ambiguity of the solution as the result of data inaccuracy.

The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

References:

  1. Ruchkin A. A., Stepanov S. V., Knyazev A. V., Stepanov A. V., Korytov A. V., Avsyanko I. N. 2018. “Applying CRM model to study well interference”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no 4, pp. 148-168. DOI: 10.21684/2411-7978-2018-4-4-148-168 [In Russian]
  2. Stepanov S. V., Sokolov S. V., Ruchkin A. A., Stepanov A. V., Knyazev A. V., Korytov A. V. 2018. “Considerations on mathematical modeling of producer-injector interference”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no 3, pp. 146-164. DOI: 10.21684/2411-7978-2018-4-3-146-164 [In Russian]
  3. Artun E. 2016. “Characterizing reservoir connectivity and forecasting waterflood performance using data-driven and reduced-physics models”. SPE Western Regional Meeting (23-26 May, Anchorage, Alaska, USA). SPE-180488-MS. DOI: 10.2118/180488-MS
  4. Fletcher R. A.1971. “A general quadratic programming algorithm”. IMA Journal of Applied Mathematics, vol. 7, no 1, pp. 76-91. DOI: 10.1093/imamat/7.1.76
  5. Holanda R. W., Gildin E., Jensen J. L., Lake L. W., Kabir C. S. 2018. “A state-of-the-art literature review on capacitance resistance models for reservoir characterization and performance forecasting”. Energies, vol. 11, no 12, art. 3368. DOI: 10.3390/en11123368
  6. Jamali A., Ettehadtavakkol A. 2017. “Application of capacitance resistance models to determining interwell connectivity of large-scale mature oil fields”. Petroleum Exploration and Development, vol. 44, no 1, pp. 132-138. DOI: 10.1016/S1876-3804(17)30017-4
  7. Valko P. P., Doublet L. E., Blasingame T. A. 2000. “Development and application of the multiwell productivity Index (MPI).” SPE Journal, vol. 5, no 1. SPE-51793-PA. DOI: 10.2118/51793-PA
  8. Weber D., Edgar T. F., Lake L. W., Lasdon L. S., Kawas S., Sayarpour M. 2009. “Improvements in capacitance-resistive modeling and optimization of large scale reservoirs”. SPE Western Regional Meeting (24-26 March, San Jose, California). SPE-121299-MS. DOI: 10.2118/121299-MS
  9. Yousef A. A., Gentil P. H., Jensen J. L., Lake L. W. 2005. “A capacitance model to infer interwell connectivity from production and injection rate fluctuations”. SPE Annual Technical Conference and Exhibition (9-12 October, Dallas, Texas). SPE-95322-MS. DOI: 10.2118/95322-MS