Three-dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random-walk methods.

*(English)*Zbl 1107.76401Summary: A three-dimensional (3D) mass transport numerical model is presented. The code is based on a particle tracking technique: the random-walk method, which is based on the analogy between the advection-dispersion equation and the Fokker-Planck equation. The velocity field is calculated by the mixed hybrid finite element formulation of the flow equation. A new efficient method is developed to handle the dissimilarity between Fokker-Planck equation and advection-dispersion equation to avoid accumulation of particles in low dispersive regions. A comparison made on a layered aquifer example between this method and other algorithms commonly used, shows the efficiency of the new method. The code is validated by a simulation of a 3D tracer transport experiment performed on a laboratory model. It represents a heterogeneous aquifer of about 6-m length, 1-m width, and 1-m depth. The porous medium is made of three different sorts of sand. Sodium chloride is used as a tracer. Comparisons between simulated and measured values, with and without the presented method, also proves the accuracy of the new algorithm.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76M10 | Finite element methods applied to problems in fluid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |