Analytical modeling of acceleration-induced conductivity damage in a propped hydraulic fracture of a high-pressure gas well

The compressible pseudoradial and pseudosteady state flow in a well intersected by a finite-conductivity vertical fracture is analyzed. A modified dimensionless fracture conductivity reflecting the acceleration effect is introduced from a comparison of the mass rate of an accelerating flow and that of a Darcy flow at the same pressure drawdown. It is shown that a gas flow with the acceleration effect can be choked at a moderate drawdown pressure. The damage to the dimensionless fracture conductivity caused by the acceleration effect is significant when the fracture permeability is greater than 20D, the reservoir permeability is greater than 5mD, the fracture length is less than 200 m or the reservoir pressure is higher than 100 MPa. In a low permeability reservoir (<1 mD), the Forchheimer drag is significant, while the acceleration effect is negligible.