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We simulate a method of measuring the relative permeabilities known as the steady-state method. In this method a predefined fractional flow of both fluid phases is injected into the pore space at constant flow rates, while the pressure drop across the sample is constant. Steady-state is reached when downstream and upstream fractional flows are equal. We mirror the input geometry and impose periodic boundary conditions along the flow direction as well, in order to allow both fluid phases enter and exit the model smoothly. A body force is applied to each fluid phase to achieve the same pressure drop and avoid capillary-end effects. To ensure that steady state has been reached, various quantities, such as the flow rates, should be tracked in check whether they have to converge steady-state values, which are then used for relative permeability calculation at the set target saturation
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I was a fluid mechanic researcher. I studied the interaction fluid-solid (dissolution) in the porous media. If you explain me more about your project : need analytical solution or programming ??