Abstract
Relating the macroscopic properties of porous media such as capillary pressure with saturation is an on-going problem in many fields, but examining their correlations with microstructural traits of the porous medium is a challenging task due to the heterogeneity of the solid matrix and the limitations of laboratory instruments. Considering a capillarity-controlled invasion percolation process, we examined the macroscopic properties as functions of matrix saturation and pore structure by applying the throat and pore network model. We obtained a relationship of the capillary pressure with the effective saturation from systematic pore network simulations. Then, we revisited and identified the microstructure parameters in the Brooks and Corey capillary pressure model. The wetting phase residual saturation is related to the ratio of standard deviation to the mean radius, the ratio of pore radius to the throat length, and pore connectivity. The size distribution index in the Brooks and Corey capillary pressure model should be more reasonably considered as a meniscus size distribution index rather than a pore size distribution index, relating this parameter with the invasion process and the structural properties. The size distribution index is associated with pore connectivity and the ratio of standard deviation to mean radius (σ0/r¯), increasing with the decline of σ0/r¯ but the same for networks with same σ0/r¯. The identified parameters of the Brooks and Corey model might be further utilized for correlations with other transport properties such as permeability.
Highlights
Invasion percolation (IP), introduced by Wilkinson and Willemsen [1], provides a realistic description of the slow biphasic fluid displacement processes in porous materials
We explored the influence of the morphology and topology of pore network on the macroscopic parameters of the Brooks and Corey capillary pressure model
The entry pressure decreases with expanding pore size distribution, as well as at pore connectivity above six
Summary
Invasion percolation (IP), introduced by Wilkinson and Willemsen [1], provides a realistic description of the slow biphasic fluid displacement processes in porous materials. IP is relevant to various applications (such as secondary oil recovery) and was generally used to model a drainage process during which a wetting fluid is displaced by a non-wetting fluid [2]. IP was used to model imbibition, where a wetting fluid invades a porous medium originally saturated by a non-wetting fluid [3]. Invasion percolation is driven by the capillary pressure Pc , which can be modeled with the normalized or effective wetting phase saturation as proposed by Brooks and Corey [5]: Se = 1 (Pc ≤ Pe ). Where entry pressure Pe and Se denote the entry pressure and effective saturation, respectively
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