Breakthrough Investigation of Advective and Diffusive Transport in a Porous Matrix with a Crack

Fluid flow and transport processes in fractured porous media are of particular interest for geologists and in the material sciences. Here a systematic investigation is presented, dealing with a generic geometric set-up of a porous matrix with a crack. In such a combined porous medium/free fluid system flow patterns have been examined frequently, while the resulting transport patterns have attracted less attention. Using numerical modeling with finite elements the problem is approached using a dimensionless formulation. With a reduced number of dimensionless parameter combinations (Darcy-, Peclet- and Reynolds-numbers) solution dependencies are examined in parametric sweeps. Breakthrough curves are fitted in comparison to those of 1D model approaches, yielding effective diffusivities and velocities. The computations reveal highest sensitivity concerning the angle between crack axis and flow direction, followed by the Peclet number and the crack axes ratio. As a dimensionless representation is used the results are scale independent. Thus, they deliver estimations concerning effective heat and solute transport parameters that can be relevant in all application fields.