Non-Darcy flow of gas in propped fractures

Abstract

This research was performed to find the effect of non-Darcy flow of gas in fractures on reducing well productivity. The concept of Wright utilizing four flow regimes to describe flow in porous media was applied in this study. These flow regimes are laminar, steady inertial, turbulent transition and turbulent. For the turbulent transition regime, a non-Forchheimer equation was derived and used for the analysis of the experimental data. A series of experiments were performed to determine the permeability, k, the inertia factor, β, the fracture conductivity, kh, and the three coefficients, a, b, and c, of the non-Forchheimer equation. With the permeability and the inertia factor of the steady inertial regime, a straight line can be constructed on the Forchheimer x-y plot. With the three coefficients of the non-Forchheimer equation, a second power curve can be obtained on the same Forchheimer plot for the turbulent transition regime. These two curves can be combined to reconstruct the experimental results of this study. The coefficients, b and c, are identified as the inertia factor and wake factor, respectively, in the turbulent transition regime. These six parameters were determined for forty-two runs on twenty sandstone samples. The properties varied in the analysis were hardness of the sandstone, frac sand particle size, frac sand concentration and confining pressure.