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A Realistic Transport Model with Pressure-Dependent Parameters for Gas Flow in Tight Porous Media with Application to Determining Shale Rock Properties

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Abstract

A nonlinear transport model for single-phase gas flow in tight porous media is developed. The model incorporates many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption into and out of the rock material, and a correction for high flow rates. This produces a nonlinear advection–diffusion type of partial differential equation with pressure-dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. A key finding is that all model parameters should be kept pressure dependent for the best results. An application is to the determination of rock properties, such as porosity and permeability, by history matching of the simulation results to data from pressure-pulse decay tests in a rock core sample (Pong et al. in ASME Fluids Eng Div 197:51–56, 1994).

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Acknowledgements

The authors would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the National Science, Technology and Innovation Plan (NSTIP), and through the Science Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No. 14-OIL280-04.

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  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhahran, 31261, Saudi Arabia

    Iftikhar Ali & Nadeem A. Malik

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  1. Iftikhar Ali
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  2. Nadeem A. Malik
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Correspondence to Nadeem A. Malik.

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Ali, I., Malik, N.A. A Realistic Transport Model with Pressure-Dependent Parameters for Gas Flow in Tight Porous Media with Application to Determining Shale Rock Properties. Transp Porous Med 124, 723–742 (2018). https://doi.org/10.1007/s11242-018-1092-4

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