Analytical modelling of the water block phenomenon in hydraulically fractured wells

Hydraulic fracturing is a key technology which has enhanced the economic viability of the unconventional low permeability reservoirs by increasing their productivity. However, the high capillary forces associated with low permeability reservoirs can trap water near to the fracture face and impair the production of gas or oil. This phenomenon is commonly referred to as water block. In order to estimate how water blocking impairs well productivity, the model for well inflow performance must account for two phases, gas compressibility, gas-water capillary pressure, wettability, inertial flows, and pressure-dependent gas viscosity. In this paper, we derive an exact solution for the inflow performance of a fractured gas well during non-inertial flow. For inertial flow, an approximate analytical solution is obtained using the streamline method. The solutions account for immobile water, gas compressibility, gas-water capillary pressure, wettability, inertial flows, and pressure-dependent gas viscosity. A sensitivity analysis shows the essential role played by the Leverett J function, the relative permeability curves and the ratio between the capillary, viscous and inertial forces. The derived solutions are applied in a case study to determine that water block is a likely contributor to skin.