Mechanism of fluid flow along a dynamic conductivity fracture with pressure-dependent permeability under constant wellbore pressure

Abstract

With the production of hydrocarbons from reservoirs, fractures will gradually close, resulting in dynamic conductivities along the fracture. The main objective of this study is to develop a new semi-analytical model in Laplace domain to reveal the mechanism of fluid flow in a dynamic conductivity fracture with pressure-dependent permeability under constant wellbore pressure condition. A new model of dynamic conductivity fracture with pressure-dependent permeability has been established, which has the same form as the model of dynamic conductivity fracture with non-Darcy flow. Thus, the solution procedure of a dynamic conductivity fracture with non-Darcy flow can be introduced to obtain the distributions of dimensionless pressure, flow rate and fracture conductivity along the fracture. Results show that the fracture conductivity is a function of pressure, which varies along the fracture dynamically. During the production, the flow rate will change along the fracture as a function of the fracture conductivity and production time. With the increase of initial conductivity, the dimensionless flow rate increases dramatically, but increasing rate will slow down. For the same initial conductivity, as the dimensionless fracture permeability modulus increases, pressure difference drops along the fracture, which results in the reduction of production rate.