An optimization method for equivalent bulk permeability of gas shale matrix with crushed samples and re-recognition of the influence of pressure and particle size

The pressure decay (or gas expansion) test with crushed samples has been used to evaluate the matrix permeability of shale and other low-permeability rock for many years. However, there still exist uncertainties relating to particle size and equilibrium pressure. The existing late-stage curve fitting method has the advantage of easy calculation, but the assumption that gas enters particles with a single permeability value is not generally applicable for shale samples, and late-stage analysis may lead to underestimation. This study proposes an optimization method to determine the equivalent bulk permeability that ensures the smallest sum of squares of errors between the forward-predicted pressure decay curve and the measure one. Both the optimization and curve fitting method are applied to two shale samples from the Ordovician Wufeng Formation of two wells in the Sichuan Basin, China with improved apparatus and testing procedures. The optimization method is superior to the curve fitting method in the repeatability and regularity on the change of apparent permeability with pressure. A strong linear relationship between apparent permeability and coefficient of compressibility is established between 3 and 12 bars. The variation of permeability with particle size is more diverse than that is commonly understood and might be nonmonotonic, depending on the change of pore structure during crushing. Change of apparent permeability with pressure (non-Darcy feature) is proposed as a criterion of whether pore structure has changed significantly. It is suggested to measure the variation of permeability with pressure and particle size to obtain a more comprehensive understanding of matrix permeability and pore structure.