We propose a proxy model to separate oil and water production total predicted liquid rate. This is essential to optimal waterflooding management. The proxy models studied here are widely used to estimate parameters in the field of petroleum engineering due to their low computational cost and do not require prior knowledge of reservoir properties. The approach uses production history and the producer-based capacitance and resistance (CRMP) model, together with the combination of two fractional flow models, Koval ( ) and Gentil ( ). We will henceforth call Kogen this combined model.

The combined fractional flow model can be formulated as a constrained nonlinear curve fitting. The objective function to be minimized is a measure of the difference between calculated and observed water cut values (Wcut) or net present values (NPV). The constraint limits the difference in water cuts of the Koval and Gentil models at the time of transition between the two. The problem can be solved using gradient-based method the sequential quadratic programming (SQP) algorithm. In this study, the gradient is computation by finite differences. The parameters of the CRMP model are the connectivity between wells, time constant, and productivity index. These parameters can be found using a Nonlinear Least Squares (NLS) algorithm. With these parameters, it is possible to predict the liquid rate of the wells. The Koval and Gentil models are used to calculate the Wcut in each producer well over the concession period which in turn allows to determine the accumulated oil and water productions.

Two synthetic models, Brush Canyon Outcrop and Brugge model are used to validate the proposed strategy. Then we compare the solutions obtained with the three fractional flow models (Koval, Gentil, and Kogen) with results obtained directly from the simulator.

It has been observed that the proposed combined model, Kogen, consistently generated more accurate results. In addition, CRMP/Kogen proxy model has demonstrated its applicability, especially when the available data for model construction is limited, always producing satisfactory results for production forecasting with a low computational cost.


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