Rate transient analysis of multiple wells system producing at constant bottomhole pressures

This paper presents rate transient analysis of multiple wells system producing at constant bottomhole pressures during boundary-dominated flow period in a closed rectangular reservoir. The proposed algorithm is based on an analytical model with numerical approximation, and production decline is predicted through a series of mathematical methods such as the Laplace transform, the Dirac Delta function, convolution, the Green’s function and the superposition principle. The proposed model is validated by the Computer Modeling Group (CMG) simulation, the results show that the proposed model is accurate enough to predict the production performance of multi-well system producing under constant bottomhole pressures during boundary-dominated flow period in a closed rectangular reservoir. We conclude that at a given time, the flow rate of a well decreases as the total number of wells increases and the bottomhole pressures of adjacent wells decrease, while the total reservoir production increases as the bottomhole pressures of reservoir wells decreases. And at a given time, the greater distance between the observation well and adjacent wells, the larger the flow rate and cumulative production the observation well. In terms of the decline rate of the flow rate, it depends on the number of wells, the bottomhole pressures of adjacent wells, and the size of reservoir. The conventional models presented in the literature are mostly empirical or semi-analytical, which are not grounded in fundamental theory. Our proposed model has a solid theoretical basis, it provides a computationally efficient, accurate and convenient method for predicting transient flow rates of multiple wells producing at constant bottomhole pressures in a closed rectangular reservoir. 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