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

Ultra-tight formations generally exhibit heterogeneous, anisotropic, and pressure-dependent petrophysical properties. Conventional core analyses tend to generate inconsistent petrophysical estimates when the physical measurements are performed on different core samples extracted from ultra-tight formations. The discrepancies in petrophysical estimates are further escalated due to pressure-and pore-size-dependent fluid flow mechanisms in the nanopores of ultra-tight rocks. In the first part of this two-paper series publication, a method is proposed to simultaneously estimate four petrophysical properties by inverting laboratory-based pressure-step-decay measurement on a single ultra-tight rock sample; thereby, circumventing the petrophysical inconsistencies due heterogeneity and anisotropy. In this second part, an inversion algorithm is developed to simultaneously estimate six petrophysical parameters by processing the laboratory pressure-step-decay measurements. Similar to the first part, the laboratory step-decay measurement involves nitrogen gas injection into an ultra-tight rock sample at multiple stepwise pressure increments and high-resolution pressure-decay measurement at the outlet, which is followed by a deterministic inversion of the measured downstream pressure data based on numerical finite-difference modeling of nitrogen gas flow in the ultra-tight rock sample. Unlike the first part, the forward model of the nitrogen flow through the nanoscale pores of the ultra-tight rock samples accounts for not only the gas slippage but also transitional flow and Knudsen diffusion. 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 2cm-long, 2.5-cm-diameter core plugs extracted from a 1-ft(3) ultra-tight pyrophyllite block. We estimated the intrinsic permeability, effective porosity, pore-volume compressibility, pore throat diameter, and two slippagediffusion 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.