Capillary force driven primary and secondary unidirectional flow of wetting liquid into porous medium

The flow dynamics of a unidirectional, spontaneous capillary flow of a wetting liquid into porous medium is investigated numerically and experimentally. With respect to whether the sessile liquid is present or absent at the porous medium surface, the flow within porous medium is referred to as primary and secondary flow, respectively. The primary flow ends once the sessile liquid is imbibed by porous medium, while the secondary flow ceases once the equilibrium liquid distribution in porous medium is achieved. Hence, the wetted volumes of porous medium at the end of the primary and secondary flow can differ significantly. Both primary and secondary flow are solved numerically using a dynamic capillary network model with a micro-force balance, which utilizes the general definition of liquid potential at the liquid free interface. The instantaneous liquid flow quantities, including saturation, flow rate, pressure and capillary pressure at the network pores, are calculated numerically and later averaged to obtain the macroscopic flow characteristics. Three distinct pairs porous medium/liquid: (i) and (ii) flow of two different liquids into the same porous medium, and (iii) flow of one of the previously used liquids into a new porous medium are studied experimentally, and the spatial and time saturation profiles are measured. The capillary network structure is adjusted such that the corresponding numerical and experimental saturation profiles agree. From the numerical solution, the multiphase flow parameters: capillary pressure and relative permeability dependences on the liquid saturation are deduced and referred to as intrinsic properties of the secondary flow. Throughout the secondary flow duration time, each pair of porous medium/liquid shows unique dependences of both capillary pressure and relative permeability as functions of the saturation. Finally, the changes in capillary pressure and relative permeability are compared for distinct pairs of porous medium/liquid.

The secondary spread is defined as an internal flow of a wetting liquid within porous medium, once there is no liquid present at any of the porous medium boundaries. The dynamics of such flows is measured experimentally and later reproduced numerically using the capillary network model. From the numerical solution, capillary pressure and relative permeability for the secondary spread are determined.Figure optionsDownload as PowerPoint slideHighlights
► Wetted volume of the porous medium can increase significantly due to the secondary spread.
► Dynamic numerical solution is used to predict the wetting liquid distribution.
► Numerical liquid distribution is matched with experimental measurements.
► Capillary pressure and relative permeability are found from numerical solution.