![]() ![]() By solving the Navier-Stokes equations (or its linear approximation for small Reynolds numbers, called Stokes flow or creeping flow) on the microscale geometry, the porosity and permeability of the porous medium can be extracted. Numerical experiments via simulation can also be used to analyze the fully resolved geometry, which includes voids and solid particles. If the porosity and permeability are not known, experimental results are necessary to quantify these material properties. As for the superficial velocity, it is the equivalent velocity through the homogenized domain - as if the microscopic flow through the pore space were distributed evenly at the macroscopic scale. Porosity, which is defined as the volume fraction of the pore space, determines the superficial average velocity. Permeability characterizes the resistance to flow through the pores. The macroscale approach assumes that the behavior of the pore space is quantified by two averaged quantities: This difficulty is due to the large difference between the length scales of the microscopic and macroscopic systems found in application areas such as oil and gas, civil engineering, and biological and medical engineering.Ī sponge is one example of a porous material. Solving for Darcy’s law can provide insight into many different physical systems where it is practically impossible to simulate the fully resolved microscale system. In a previous blog post, we discuss interfaces available for simulating macroscale flow in porous media, including the Darcy’s Law interface. Using a Macroscale Approach to Model Porous Media Flow But what if we don’t know what the effective macroscopic properties are? Here, we look at how to extract the macroscopic flow properties of porosity and permeability from a fully resolved microscale submodel. ![]() When simulating flow in porous media, it can be efficient to simplify the geometric complexity of the real porous material using a homogenized macroscale approach. ![]()
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