Hydrocarbon-bearing ultra-tight formations generally exhibit heterogeneous, anisotropic, and pressure-dependent petrophysical properties. Consequently, various laboratory measurements on separate core plugs and crushed rock samples from tight formations tend to generate inconsistent petrophysical estimates. These inconsistencies are further escalated by the existence of varied pressure- and pore-size-dependent fluid flow mechanisms in the nanopores of ultra-tight formations. We circumvent such discrepancies in petrophysical estimates by simultaneously estimating six petrophysical parameters from laboratory-based pressure-step-decay measurement on a single ultra-tight rock sample. The proposed method involves nitrogen gas injection into an ultra-tight rock sample at multiple stepwise pressure increments, high-resolution pressure-decay measurement at the outlet, 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.
This work is performed with an aim to improve the petrophysical estimates previously obtained from pressure-step-decay measurements using only a Klinkenberg-type gas slippage model. We implement a transitional transport model that can handle both slip and diffusion. The proposed 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-Knudsen diffusion weight factors parameters. Accuracy of the estimates depends on the physical models incorporated in the forward model and on the error minimization algorithm implemented in the inversion scheme. The estimation results are independent of initial guess of intrinsic permeability, effective porosity pore-volume compressibility, and pore throat diameter in the range of 3 nd to 300 nd, 0.01 to 0.15, 10-2 to 10-6 psi-1, and 60 nm to 500 nm, respectively. The average estimated values of intrinsic permeability, effective porosity, pore-volume compressibility, and pore throat diameter of the nine ultra-tight samples are 86 nd, 0.036, 2.6E-03 psi-1, and 195 nm, respectively. Notably, the two inverted slippage-Knudsen diffusion weight factors indicate that the gas transport mechanism in the nine ultra-tight pyrophyllite samples is completely dominated by slip flow without any Knudsen diffusion or transitional flow even though the Knudsen numbers across the samples during the entire duration of the pressure-step-decay measurements are in the range of 0.01 to 1.