Modeling flow in porous media with rough surfaces: Effective slip boundary conditions and application to structured packings

- An upscaling methodology is proposed to characterize fluid flow in porous media with rough surfaces.
- The no-slip condition on the rough surface is replaced with a tensorial slip condition on a fictive smooth surface.
- The permeability decreases significantly, even for small amplitudes of the roughness.
- The pressure drop is accurately predicted for structured packings used in separation processes.
- Different regimes are identified in the transition from creeping flow to the onset of unsteady inertial flow.

Understanding and modeling flows in columns equipped with structured packings is crucial to enhance the efficiency of many processes in chemical engineering. As in most porous media, an important factor that affects the flow is the presence of rough surfaces, whether this roughness has been engineered as a texture on the corrugated sheets or is the result of hydrodynamic instabilities at the interface between a gas and a liquid phase. Here, we develop a homogenized model for flows in generic porous media with rough surfaces. First, we derive a tensorial form of an effective slip boundary condition that replaces the no-slip condition on the complex rough structure and captures surface anisotropy. Second, a Darcy-Forchheimer model is obtained using the volume averaging method to homogenize the pore-scale equations with the effective slip condition. The advantage of decomposing the upscaling in these two steps is that the effective parameters at the Darcy-scale can be calculated in a representative volume with smooth boundaries, therefore considerably simplifying mesh construction and computations. The approach is then applied to a variety of geometries, including structured packings, and compared with direct numerical solutions of the flow to evaluate its accuracy over a wide range of Reynolds number. We find that the roughness can significantly impact the flow and that this impact is accurately captured by the effective boundary condition for moderate Reynolds numbers. We further discuss the dependance of the permeability and generalized Forchheimer terms upon the Reynolds number and propose a classification into distinct regimes.