Petrophysical interpretation of laboratory pressure-step-decay measurements on ultra-tight rock samples. Part 2 - In the presence of gas slippage, transitional flow, and diffusion mechanisms

This work improves the petrophysical estimates previously obtained from the inversion of pressure-step-decay measurements modeled based on only a Klinkenberg-type gas slippage as proposed in the first part. A transitional transport model is implemented to account for the separate and simultaneous occurrence of gas slippage and diffusion across an ultra-tight rock sample during a pressure-step-decay measurement performed in the pore pressure range of 5 psi to 500 psi at room temperature. The proposed interpretation method was applied to nine 2-cm-long, 2.5-cm-diameter core plugs extracted from a 1-ft3 ultra-tight pyrophyllite block. We estimated the intrinsic permeability, effective porosity, pore-volume compressibility, pore throat diameter, and two slippage-diffusion coefficients of each sample. Estimation accuracy relies on the forward model of the fluid flow in ultra-tight rock sample and on the error minimization algorithm implemented in the inversion scheme. For the nine ultra-tight samples, on an average, the estimated intrinsic permeability, effective porosity, pore-volume compressibility, and pore throat diameter are 86 nd, 0.036, 2.6E-3 psi−1, and 195 nm, respectively. Notably, the two slippage-diffusion coefficients indicate that the gas transport mechanism in the nine ultra-tight pyrophyllite samples during the pressure-step-decay measurement is completely dominated by slip flow without any Knudsen diffusion or transitional flow, despite the Knudsen numbers across each sample during the entire duration of the pressure-step-decay measurements were determined to be in the range of 0.01-1. This observation contradicts the widely accepted qualitative classification of gas transport mechanism based on the Knudsen numbers and mandates an inversion-based approach to identify the fluid flow mechanism and an appropriate fluid flow model for nanoscale pores.