Permeability Estimation of Porous Rock by Means of Fluid Flow Simulation and Digital Image Analysis

Abstract

Permeability plays an important role to determine the characteristics of how fluids flow through a porous medium which can be estimated using various methods. Darcy's law and the Kozeny-Carman equation are two of the most utilized methods in estimating permeability. In Darcy's law, permeability can be calculated by applying a pressure gradient between opposing sides of inlet-outlet of a certain direction. The permeability then depends on the fluid viscosity and the flowrate. The Kozeny-Carman equation is an empirical equation which depends on several parameters such as shape factor of the pore, tortuosity, specific surface area, and porosity to determine the permeability. For both methods, digital image obtained by means of Micro CT-Scan is used. In this research, the permeability estimation using the Darcy's law was conducted by simulating fluid flow through the digital image using Lattice Boltzmann Method (LBM). As for the Kozeny-Carman equation, digital image analysis was used to obtain the required parameters. Two Kozeny-Carman equations were used to calculate the permeability of the samples. The first equation (KC1) depends on pore shape factor, porosity, tortuosity, and specific surface area while the second equation (KC2) only depends on pore radius, porosity, and tortuosity. We investigate the methods by first testing on three simple pipe models which vary in the radii. By using the result from Darcy's law as a reference, we compare the results from the Kozeny-Carman equations. From the calculation, KC2 yield smaller difference to the reference. The three methods were then applied to the Fontainebleau sandstone to verify the previous result.