An analytical model on production performance of multiple wells producing at constant bottomhole pressures

Original Manuscript Submitted: 4/1/2018; Final Draft Received: 9/7/2018 This paper presents an analytical model with numerical approximation on production performance of multiple wells producing at constant bottomhole pressures during boundary-dominated flow period in a closed rectangular reservoir. It is obtained through a series of mathematical methods such as Laplace transform, Dirac delta function, convolution, Green's function, and superposition principle. Computer Modeling Group Ltd. (CMG) simulation is used to validate the new proposed model and it is found that the model is accurate enough to predict the production performance of multi-well system producing under different 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 well numbers increases and bottomhole pressures of adjacent wells decrease, while the total reservoir production increases as the bottomhole pressure of reservoir wells decreases. And, at a given time the greater distance between the observation well and adjacent wells, the bigger flow rate and cumulative production the observation well has. In terms of the decline rate of flow rate, it depends on well numbers, bottomhole pressures of adjacent wells, as well as the size of the reservoir. Compared with the empirical or semi-analytical models in the literature, our proposed model is fully analytical which has solid theoretical basis; it is accurate enough to predict the production performance of multiple wells under constant bottomhole pressures.