Rate decline analysis for finite conductivity vertical fractured gas wells produced under a variable inner boundary condition

This paper presents a new approximate semi-analytical method for predicting performance of a finite conductivity vertical fractured gas well produced at a variable production system. The proposed solution is based on the gas diffusivity equation with a variable inner boundary condition. The variable inner boundary condition in this study represents that the type of the inner boundary conditions changes from constant rate to constant pressure during the production time. The calculations of the two-stage performance for a finite vertical fractured gas well are accomplished. The two-stage performance is influenced by the limiting bottom-hole pressure, the initial rate and the fracture conductivity. A high initial rate reduces the extents of both the constant-rate period and the total production life. However, the initial rate has no effect on the cumulative gas production when the production period is sufficiently long. Moreover, the initial rate may be appropriately adjusted to achieve the optimum cumulative gas production in a specific production period. The cumulative gas production can be effectively improved by establishing a lower limiting bottom-hole pressure. The higher the fracture conductivity is, the longer the constant rate period elapses, and the shorter the constant pressure period remains. A higher fracture conductivity is helpful to achieve a larger cumulative gas production in a shorter production period. Thus, the operation can be optimized by setting a low limiting bottom-hole pressure, a suitable initial rate and fracture conductivity. The proposed method may be applied to other typical well performance prediction in a variable production system.