using fast and reliable proxies instead of sophisticated an time-consuming reservoir simulators is of great importance in reservoir management. The capacitance-resistance model (CRM) as a fast proxy has been widely used in this area. However, the inadequacy of this proxy for simplifying complex reservoirs with a limited number of parameters has not been addressed appropriately in related works in the literature. In this study, potential uncertainties in the modeling of the waterflooding process in the reservoir by the producer-based version of CRM (CRMP) are formulated, leading to embedding a new error-related term into the original formulation of the proxy. Considering a general form of the model error to represent both white and colored noises, a system of a CRMP-error equation in introduced analytically to deal deal with any type of intrinsic model imperfection. Two approaches are developed for the problem solution including the following: tuning the additional error-related parameters as a complementary stage of a classical history matching procedure, an updating these parameters simultaneously with the original model parameters in a data-assimilation approach over model training time. To validate the model and show the effectiveness of both solution schemes, the injection and production data of a water-injection procedure in a three-layered reservoir model are used. Results show that the error-related parameters can be matched successfully along with the model original variables either in a routine model calibration procedure or in a data-assimilation approach by using the ensemble-based Kalman filter (EnKF) method. comparing the average of the obtained range for the liquid rate as the problem output with true data demonstrates the effectiveness of considering model error. this leads to substantial improvement of the results compared with the case of applying the original model without considering the error term

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