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COMSOL Modeling of Non-linear Transport Properties in Low Permeability Samples


This paper presents the results of modeling of five different plug based measurement protocols, and discusses their strength and weaknesses. The necessity of using the full nonlinear flow equation for the interpretation of the data is also discussed. Five different protocols are modeled: steady state, unsteady state, pulse decay, sinusoidal pressure and moving boundary conditions. These differ by the addition of reference chambers to the steady state apparatus and the pressure boundary conditions applied. Our implementation of the nonlinear equation includes the assumption of constant viscosity, rock compressibility, and pressure dependent permeability, i.e. the gas slippage effect (Klinkenberg corrections). We find that variable (pressure dependent) density increases the average pressure in the sample due to the nonlinear pressure profile induced. This leads to the estimation of permeability that is too small compared to an assumption of a linear profile. In contrast, the Klinkenberg effect causes an increased estimated permeability. It is difficult to separate these two effect, as a result, modeling the full nonlinear behavior of the transport properties is necessary. From the results of the modeling, we believe plug scale measurements are practical, and grinding of samples is not necessary. We recommend using unsteady state measurements, supplemented with sinusoidal pressure and pulse decay to calibrate the magnitude of the nonlinear effects, and the impact of diffusion and absorption.