Reservoir characterization using dynamic capacitance–resistance model with application to shut-in and horizontal wells

Abstract

Capacitance-resistance model (CRM) is a nonlinear signal processing approach that provides information about interwell communication and reservoir heterogeneity. Several forms of CRM have been introduced; however, they would deliver erroneous model parameters if production history involves shut-in period. To address this issue, this study presents a dynamic capacitance-resistance model (D-CRMP), a comprehensive formulation that is capable of handling multiple shut-in periods in different producers. CRM model parameters are representative of the geological information. Accordingly, two geologically identical synthetic examples are used to validate D-CRMP; one including shut-in periods in historical production data of some producers and the other one with all continuously operating wells. Obtaining the same model parameters and the high quality of fitting in both cases proved the reliability of D-CRMP, which allows the utilization of historical data to characterize the reservoir behavior in real cases. Investigation of uncertainty on the fitted model parameters was also performed to demonstrate that confidence intervals are affected mostly by two aspects; permeability distribution and interwell distance. It is shown that though the confidence intervals in the heterogeneous fields are relatively higher than the homogeneous examples, higher permeability and lower producer-injector distance reduce the uncertainty of model parameters in both cases. This study also applies the proposed model in reservoirs with horizontal wells and further examines the impact of well direction and length of the productive interval on the connectivities between wells. Keywords Capacitance-resistance model • Reservoir characterization • History matching • Waterflood • Shut-in well • Horizontal well Abbreviations BHP Bottom-hole pressure CMG Computer modeling group Ltd. CRM Capacitance-resistance model CWI Cumulative water injection D-CRMP Dynamic capacitance-resistance model ICRM Integrated capacitance-resistance model IMEX Implicit-explicit black oil simulator IWC Interwell connectivity MLR Multivariate linear regression MSHW Multi-segmented horizontal well List of symbols L, F, t Mean length, force, and time, respectively c t Total compressibility (L 2 /F) f ij Interwell connectivity between injector i and producer j , dimensionless I Water injection rate (L 3 /t) J Productivity index (L 5 /F − t) N p Cumulative liquid production rate (L 3 /t) n P Total number of producers n T Total number of historic time periods n I Total number of injectors P wf Well bottom-hole pressure (F/L 2) q Total liquid production rate (L 3 /t) R 2 Correlation coefficient Time constant, t

Data-driven approach for evaluation of formation damage during the injection process

“…By assuming different control volumes, different forms of the CRM can be developed, including CRMT, CRMP, and CRMIP (Sayarpour 2008;Weber et al 2009;Salehian and Çınar 2019). CRMT (CRM Tank) is used for a system of one injector and one producer.…”

“…There are several methods for understanding the quality of connection between injectors and producers of a field, including tracers, traditional reservoir simulators and datadriven approaches (Moghadam et al 2011;Rong et al 2016;Suleymanov et al 2016;Salehian and Çınar 2019). A datadriven approach uses the injection and production data of a field in order to find the quality of connection between the wells.…”

Reservoir Management Through Characterization of Smart Fields Using Capacitance-Resistance Models

“…From these, accounting for well intervention during the lifetime of the reservoir presents a major challenge [10]. Shut-ins especially results in re-allocation of streamlines between the injector and producer, which leads to a difficulty in determining the injection weights for CRM [11]. Recently, Salehian and Soleimani [12] developed a comprehensive mathematical formula for CRM to predict waterflood performance and match the history of either vertical or horizontal wells including shut-in periods.…”

Multi-solution well placement optimization using ensemble learning of surrogate models

“…Surrogate models (SMs, also known as proxy models) are employed as an approximation method in the optimization process to reduce the cost of objective function evaluations when the underlying fullphysics model is expensive to simulate. Three main types of surrogate modeling approaches are commonly employed in the field development and control optimization problems: (1) physics-based approaches such as reduced order modeling (Van Doren et al, 2006;Cardoso and Durlofsky, 2010;Durlofsky, 2010;He and Durlofsky, 2014;Trehan and Durlofsky, 2016) or streamline-based simulation methods (Thiele and Batycky, 2003;Park and Datta-Gupta, 2011;Salehian and Çınar, 2019;Ushmaev et al, 2019), (2) Machine Learning (ML) techniques such as support vector machine (SVM) (Drucker et al, 1997;Guo and Reynolds, 2018;Panja et al, 2018;Zhang et al, 2021), Artificial Neural Network (ANN) (Jain et al, 1996;Güyagüler et al, 2002;Yeten et al, 2003;Golzari et al, 2015;Rahmanifard and Plaksina, 2019;Sabah et al, 2019;Sun and Ertekin, 2020;Enab and Ertekin, 2021;Gouda et al, 2021), Gaussian Process Regression (GPR) (Knowles, 2006;Zhang et al, 2009;Horowitz et al, 2013) methods, and (3) Deep Learning (DL) methods such as Convolutional Neural Network (CNN) (LeCun et al, 1998;Glorot et al, 2011;Hinton et al, 2012;Chu et al, 2020;Kim et al, 2020;Kim et al, 2021). Physics-based approaches can approximate the original reservoir behavior with lower-order equations to reduce the computational cost.…”