Improved Waterflood Analysis Using the Capacitance-Resistance Model Within a Control Systems Framework
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AbstractThe Capacitance Resistance Model (CRM) is a fast way for modeling and simulating gas and waterflooding recovery processes, making it a useful tool for improving flood management in real-time. CRM is an input-output and material balance-based model, and requires only injection and production history, which are the most readily available data gathered throughout the production life of a reservoir. In this work, the CRM input-output relationship is explored by representing the CRM with state-space (SS) equations. The linear system SS equations define the relationship between inputs, outputs and states to completely describe system dynamics. The SS-CRM is a multi-input/multi-output (matrix) representation, which provides more insight into reservoir behavior than analyzing performance on a well-by-well basis. Thus, it is computationally faster and easier to apply in fields with large numbers of wells. The CRM parameters are estimated using a grey-box system identification algorithm. The matrix form of the CRM history matching and a sensitivity analysis to the CRM parameters estimates are presented. Minimal realizations and reduced order models are easily obtained with the SS-CRM approach. The performance of three CRM representations are analyzed: integrated (ICRM), producer based (CRMP) and injector-producer based (CRMIP). The methodology developed here is tested in two reservoir systems, homogeneous with flow barriers and channelized. We find that the ICRM does not reproduce the rate fluctuations as well as the CRMP and CRMIP. The CRMP works well for wells in low heterogeneity regions but not as well as the CRMIP in more heterogeneous areas, e.g. near the flanks of channel deposits. This new approach facilitates closed-loop reservoir management by enabling CRM's use for linear control algorithms, which can improve tracking performance and predictability, and is amenable to real-time optimization.
