Determination of the nanodarcy gas permeability and other parameters of naturally and hydraulically fractured shale formations by pressure-pulse transmission testing of core plugs, drill cuttings, and crushed samples is discussed. The methods available for interpretation of pressure tests are reviewed and modified with emphasis on difference between the intrinsic and apparent permeability. Improved formulations and analysis methods which honor the relevant physics of fluid and transport, and interactions with shale are presented. Better design and analysis of experiments for simultaneous determination of several unknown parameters that impact the transport calculations, including deformation, adsorption, diffusion, and deviation from Darcy flow are described. The permeability and other parameters of shale samples are recommended to be determined by simultaneous analysis of multiple pressure tests conducted under different conditions to accommodate for temporally and spatially variable conditions. The inherent limitations of the methods relying on the analytical solutions of the diffusivity equation based on the Darcy's law are explained.
The permeability measured using a Darcy-like equation is not the intrinsic permeability but the apparent permeability which depends on the prevailing conditions of fluid, transport, and shale. The intrinsic permeability of shale depends on the temperature and effective stress conditions and therefore the conditions of a particular intrinsic value should also be specified. The primary reason for the contradictory values of permeability measured by application of the analytical models is explained by dependence of measured permeability of shale on particular testing conditions over which only a certain average permeability value is obtained from most analytical solutions.
Crushed samples have different size particles. The permeability of a particle depends on its size. Large particles are likely to have both the matrix porosity and fracture porosity. Consequently, it is not correct to assume all the particles of different sizes to have the same permeability. Whereas, most attempts in calculating the permeability using the pressure tests on crushed samples assume the same permeability for all particles. This assumption can only be applicable for samples of uninform particle sizes.
