A new volumetric source mathematical model for pressure behavior around horizontal wells in dual media reservoirs

A new mathematical model is presented to describe the pressure behavior around a horizontal well in dual media heterogeneous reservoirs. An exact solution of the model is derived by means of orthogonal transformation, methods of images and the theory of matrix differential equations. Through comparison of the results of this model with those of the areal source models, it is shown that the new model presented here can be used to characterize pressure behavior more precisely than other models, especially when the formation thickness is small, or heterogeneity is severe.