Mathematical Geology

, Volume 34, Issue 4, pp 435–456

Three-Dimensional Modeling of Mass Transfer in Porous Media Using the Mixed Hybrid Finite Elements and the Random-Walk Methods


  • H. Hoteit
    • Institut de Mécanique des Fluides et des SolidesUniversité Louis Pasteur de Strasbourg
  • R. Mose
  • A. Younes
    • Département Physique et MécaniqueFaculté des Sciences et Techniques
  • F. Lehmann
  • Ph. Ackerer

DOI: 10.1023/A:1015083111971

Cite this article as:
Hoteit, H., Mose, R., Younes, A. et al. Mathematical Geology (2002) 34: 435. doi:10.1023/A:1015083111971


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.

mass transport modelingadvection–dispersion equationrandom-walk methodlaboratory model

Copyright information

© International Association for Mathematical Geology 2002