Determination of Permeability–Porosity–Stresses Dependence for Loose Media Based on Inverse Problem Solution by Lab Test Data

Abstract

The process, justified by theory and physical modeling, enables to establish dependence of poroperm properties of loose geomaterials versus fluid pressure and stresses. The laboratory unit designed and manufactured by researchers, comprises a measurement cell filled with a loose material, a hydraulic press, and a recorder of pressure, flow rate, and stress $\sigma_{m}$, stepwise applied to the cell. At each loading stage the permeability test was carried out at different input gas pressures $p_{n}$. The stationary measured flowrate data $Q_{mn}$ and the back analysis were employed to establish the empirical permeability–effective stress dependence, followed with approximation by two-parameter exponential function. The measurement cell was vacuumized at fixed $\sigma_{m}$ the cell was connected to a vessel, filled with air of a preset mass. Porosity $\varphi_{m}$ was calculated based on the equilibrium pressure gained in “cell–vessel” system. The experiments performed with the medium-grained sand revealed that the exponent factor characterizing the relationship between permeability and effective stress is something like 0.02 bar⁻¹; the permeability–porosity relation can be described by a power function; thereto, Kozeny–Carman equation is fulfilled with good precision as well.