A Unified Pore Network Model for Evaluation of Permeability, Relative Permeability, and Sealing Capacity From Mercury Intrusion Measurement
Authors: Yang Yunlai 
Published: October 2022

This paper presents a new 3D mathematical pore network model for evaluating some important, but hard-to-measure physical properties, including permeability, relative permeability, recovery factor, and sealing capacity from easy-to-measure mercury intrusion data. A 3D pore network is constructed by mimicking the penetration process of mercury based on an idealized pore shape. The pore shape is two frustra of cones connected at their base. A pore orientates in 3D space with an alignment angle to the bedding, which is a function of deformation of the sedimentary rock. Since mercury intrusion measures a 3D pore network and intrudes pores from largest to smallest, a pore size distribution measured by mercury intrusion is itemized into individual pores; a 3D pore network model is then formed by adding pores, one by one from the largest to the smallest, to the pore network. In the process, pores are connected into pore strings along the three orthogonal directions. The properties are derived by modeling fluid flow in the pore strings in a particular direction. Sealing capacity is simply the capillary pressure of the smallest pore of the first three largest orthogonal pore strings of the 3D pore network. Permeability is modeled by applying the modified Hagen-Poiseuille equation, Darcy’s law, energy and mass conservation, and the effect of eddy formation and flow direction change in the pores to the constructed 3D pore network model. Relative permeability is modeled for the imbibition process for two-phase flow based on the below imbibition theory proposed in this paper. Initially, the nonwetting phase exists in large pore strings, and the wetting phase occupies small pore strings. There are always some pores in a large pore string connected with pores of the small pore strings. In the imbibition process, under the differential pressure and capillary pressure, the wetting phase in some small pores invades some large pores filled with the nonwetting phase at the contact to form interfaces. As a result, in these pore strings, the effective pressure drop, which drives the movement of the fluids, is reduced by the capillary pressure of the interfaces. The constructed relative permeability model is a function of viscosity, interfacial tension (IFT), and contact angle of the fluids, and also pressure gradient, which is often overlooked. The developed model has been applied to some mudstone and limestone samples. The modeled sealing capacities of 29 mudstone samples show that a mudstone with a clay content greater than 40% and porosity less than 0.2 would be an effective caprock to oil. The modeled permeabilities of 29 limestone samples show that the model is able to predict limestone permeability within a factor of two in nearly four orders of magnitude range. The modeled relative permeabilities of two limestone samples demonstrate the effect of IFT, contact angle, and pressure gradient on the relative permeability and recovery factor and the capability of the model to simulate a special phenomenon—permeability jail.