Modification of the CRM material balance model for three-phase flow conditions

About the authors:

Airat A. Galeev, Chief Specialist of the Process Automation and Data Management Division, RN-Geology Research Development, Tyumen, Russia; aagaleev@rn-gir.rosneft.ru, https://orcid.org/0009-0005-2582-2400

Tatyana I. Sinitsyna, Cand. Sci. (Tech.), Head of the Production Engineering Division, RN-Geology Research Development, Tyumen, Russia; tisinitsyna@rn-gir.rosneft.ru, https://orcid.org/0009-0007-4986-9486

Abstract:

Capacitance Resistance Models (CRM) are a series of simplified material balance models that use production and injection data to evaluate downhole interactions and estimate production. The field of application covers optimization of well operation conditions, assessment of flooding performance and reservoir pressure management. The use of such models does not require significant computational and time costs, which allows them to be applied in conditions requiring prompt decision-making. Despite the large number of publications devoted to improving CRMs and expanding their range of applicability, there are still some limitations and unaffected areas of research in these models. Such limitations include disregarding the multiphase flow in a reservoir, which leads to a decrease in the predicting quality in conditions of significant changes in the water cut. The appearance of free gas in a reservoir due to a decrease in pressure below the bubble-point pressure results in significant changes in the flow pattern, which is not taken into account in a CRM model. This paper describes a modified CRM-based model for three-phase flow conditions (oil, water, gas). The results of numerical experiments in real wells are shown, demonstrating the best predicting quality in comparison with a classical CRMP model.

References:

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, 5(3), 164–185. https://doi.org/10.21684/2411-7978-2019-5-3-164-185 [In Russian]

Bekman, A. D. (2023). A new two-phase capacitance-resistance proxy model of the oil field development process. Mathematical Modeling, 35(5), 47–61. https://doi.org/10.20948/mm-2023-05-04 [In Russian]

Bekman, A. D., & Zelenin, D. V. (2021). Application of advanced CRMP for reservoir pressure mapping. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 7(4), 163–180 https://doi.org/10.21684/2411-7978-2021-7-4-163-180 [In Russian]

Stepanov, S. V., Bekman, A. D, Ruchkin, A. A, & Pospelova, T. A. (2021). Supporting Oil Field Development Using CRM Models. Express. [In Russian]

Shevtsov, N. O., & Stepanov, S. V. (2022). Improving the material balance model to account for changes in the well productivity index. Mathematical modeling, 34(2), 3–16. https://doi.org/10.20948/mm-2022-02-01 [In Russian]

Brooks, R., & Corey, T. (1964). Hydraulic Properties of Porous Media. Hydrology Papers. Colorado State University.

Brown, K. E. (1977). Technology of Artificial Lift Methods. Vol. 1. PennWell Books.

Brown, K. E. (1984). Technology of Artificial Lift Methods. Vol. 4. PennWell Books.

Cao, F. (2014). Development of a Two-Phase Flow Coupled Capacitance Resistance Model. PhD Dissertation. University of Texas, Austin, TX, USA.

Guo, Z., Reynolds, A. C., & Zhao, H. (2018). Waterflooding optimization with the INSIM-FT data-driven model. Computational Geosciences, 22, 745–761. https://doi.org/10.1007/s10596-018-9723-y

Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.

Holanda, R. W. d., 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, 11, 3368. https://doi.org/10.3390/en11123368

Jamali, A., & Tavakkol, A. E. (2017). Application of capacitance resistance models to determining interwell connectivity of large-scale mature oil fields. Petroleum Exploration and Development, 44(1), 132–138 https://doi.org/10.1016/S1876-3804(17)30017-4

Kianinejad, A., Chen, X., & DiCarlo, D. A. (2015). The effect of saturation path on three-phase relative permeability. Water Resources Research, 51(11), 9141–9164. https://doi.org/10.1002/2015WR017185

Mallipeddi, R., & Suganthan, P. N. (2009). Differential evolution algorithm with ensemble of populations for global numerical optimization.  OPSEARCH, 46, 184–213. https://doi.org/10.1007/s12597-009-0012-3

Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045

Raissi, M., Yazdani, A., & Karniadakis, G. E. (2020). Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 367, 1026–1030. https://doi.org/10.1126/science.aaw4741

Salehian, M., & Çınar, M. (2019). Reservoir characterization using dynamic capacitance–resistance model with application to shut-in and horizontal wells. Journal of Petroleum Exploration and Production Technology, 9, 2811–2830. https://doi.org/10.1007/s13202-019-0655-4

Sayarpour, M. (2008). Development and Application of Capacitance-Resistive Models to Water/CO2 Floods. PhD Dissertation. University of Texas, Austin, TX, USA.

Vogel, J. V. (1968). Inflow performance relationships for solution gas drive wells. Journal of Petroleum Technology, 20(1), 83–92.

Weber, D., Edgar, T. F., Lake, L. W., Lasdon, L., Kawas, S., & Sayarpour, M. (2009). Improvements in capacitance-resistive modeling and optimization of large scale reservoirs. SPE Western Regional Meeting, San Jose, California. SPE-121299-MS. https://doi.org/10.2118/121299-MS

Willhite, G. P. (1986). Waterflooding. Vol. 3. Textbook Series, SPE.

Yousef, A., Gentil, P., Jensen, J., & Lake, L. (2005). A capacitance model to infer interwell connectivity from production and injection rate fluctuations. SPE Annual Technical Conference and Exhibition, Dallas, Texas. SPE-95322-MS. https://doi.org/10.2118/95322-MS

Zhao, Hui, Kang, Zhijiang, Zhang, Xiansong, Sun, Haitao, Cao, Lin, & Reynolds, A. (2015). INSIM: A data-driven model for history matching and prediction for waterflooding monitoring and management with a field application. SPE Reservoir Simulation Symposium. SPE-173213-MS. https://doi.org/10.2118/173213-MS