An analytical model for cleanup of yield-stress fluids in hydraulic fractures

The retention of fracturing fluid in a proppant pack reduces the dimensionless fracture conductivity, F-ed, resulting in poor well productivity regardless of fluid type (gelled oil, crosslinked polymers, viscoelastic surfactants, or foams). Analytical expressions derived in this paper can be used to calculate the extent of fracture cleanup under a set of production conditions. Several dimensionless parameters describing the fluid, fracture, and reservoir properties are introduced that affect the equilibrium cleanup. A second, transient, fracture-cleanup model is also proposed and is used to estimate the dimensionless-parameter values. The equilibrium model predicts that cleanup increases greatly with decreasing dimensionless yield stress of the fracturing fluid. The magnitude of cleanup is also greater for cases in which the permeability ratio of the clean portion of the,fracture to the fouled portion is high. The cleanup is expected to increase with an increase in the ratio of reservoir and fracture mobility until an optimum is reached, and then decrease with increasing the mobility ratio. The critical process of parameter estimation is achieved by making experimental measurements and by history matching published fracture flowback data using the transient model.