The Brooks and Corey Capillary Pressure Model Revisited from Pore Network Simulations of Capillarity-Controlled Invasion Percolation Process

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.

Effects of Relative Humidity and Paper Geometry on the Imbibition Dynamics and Reactions in Lateral Flow Assays

“…where S w and S wr represent the saturation level (moisture content in the wetted paper substrate) and residual saturation level of paper (equilibrium moisture content of dry paper), respectively. 39 The twophase modeling approach of BCM also permits us to independently define relative permeabilities of water (k w ) and air (k a ).…”

“…A narrow range of pore sizes (i.e., uniform pore diameters) corresponds to small λ p , resulting in a sharp transition across the imbibition interface separating the wetting phase and dry phase, whereas a wide range of pore sizes (i.e., non uniform pore diameters) corresponds to large λ p , resulting in smeared fluid front. Consequently, the effective capillary pressure ( P c ) at the diffuse imbibition interface is reduced from entry capillary pressure ( P ec ; used in the LW framework) as described in eq . where S w and S wr represent the saturation level (moisture content in the wetted paper substrate) and residual saturation level of paper (equilibrium moisture content of dry paper), respectively . The two-phase modeling approach of BCM also permits us to independently define relative permeabilities of water ( k w ) and air ( k a ). …”

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

“…We use the values s cw = 0.25 , s or = 0.2 and the exponent W = 4 in the case of water and W = 2 when dealing with oil and = 1 . See [21] for details…”

Dewatering Optimization of Coal Seam Gas Production Wells: A Review and Future Perspectives

“…The capillary pressure change during CSG production can be characterized by the capillary pressure curve, , as illustrated in Figure . Three experimental methods are widely used to measure the capillary pressure, namely, the porous plate method, − the centrifuge method, − and the mercury injection method. − …”