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Knowledge of reservoir heterogeneity in waterfiooding is key to achieving a better sweep efficiency in a waterfiooding process. However, a high degree of spatial variation in reservoir properties and a limited number of measurements make heterogeneity quantification difficult. Furthermore, the contributions of heterogeneities to waterfiooding efficiency are unknown. We present a multiphase reservoir network model that can not only approximate interwell heterogeneity, but that can also be used to improve the performance of the waterflood.

We develop the network model by dividing the reservoir into a number of node volumes, each of which contains a well. Flow between the node volumes is obtained by solving for the pressure field in the diffusivity equation. A network of pseudo-streamlines connecting wells (producer-injector and injector injector) is then generated in order to map the saturation between the wells. Instead of grid properties, flow area and interwell Dykstra-Parsons coefficients for time of flight characterize flow arid saturation along the streamlines. The model parameters are estimated by a history matching of the fractional-flow data. A derivative-free optimization algorithm is then used to minimize the objective function (the sum of the squared differences between the simulated and actual producer fractional flow).

The approach that we present uses only injection and production rates, well positions, and well fractional-flow values, which are the most accessible data in a field. The method was tested using several reservoir models with different synthetic permeability distributions and geologic features. Results show that as interwell heterogeneity increases, Dykstra-Parsons coefficients increase, and flow areas decrease. Furthermore, frontal shock, which is a characteristic of displacement of immiscible incompressible phases, is prevented by the introduction of Dykstra-Parsons coefficients.

Flow area and the time-of-flight Dykstra-Parson coefficient can be used to improve waterflood sweep efficiency. Resulting parameters also help in decision making regarding injected water reallocation, but only through a study of injection and production rates. (C) 2017 Elsevier B.V. All rights reserved.