The aim of this project has mainly been to study the variation of hydraulic conductance with geological factors, such as porosity, for different pore models. For all cases the hydraulic conductances have been calculated by assuming a Darcy law relation between the flow rate and the pressure gradient. The actual liquid flow has been determined by solving different versions of the Navier-Stokes equations in the pores.

One task has been the calculation of hydraulic conductance in a 3-dimensional pore model (one-phase). In this case the pore has been described by dividing it into nodes and channels. That is, large openings in the pore are defined as nodes, and each node is connected to a different number of other nodes by channels. Each of the channels are descbribed by a different number of cross-sections. The figure shows a very simplified illustration of one such pore network. The lines that connect the nodes are pore channels, for instance described by four cross-sections as in the figures below.

The flow model is simplified by applying a so-called parabolized Navier-Stokes formulation for each of the channels. We then end up with solving a 2-dimensional Poisson type equation for each of the cross-sections in each of the channels, and a linear system connecting the nodes in order to have mass conservation.

Another task has been the calculation of hydraulic conductance of water and oil in different multiphase domains (water-oil-gas), where the domains have been 2-dimensional cross-sections of flow channels. The actual size and shape of the domains depend on the various boundary conditions between the phases.

The figures below show the contour lines of the velocity for a triangular pore, with water in the corners, oil in the centre. Left figure shows the velocity with pressure drop in the water phase (only velocity in water phase). Right figure is with pressure drop in the oil phase (velocity in both phases because of large oil viscosity).

The programming in the project is based on the Diffpack software library.