Dispersion in Flow through Porous Media

Abstract

Dispersion in Flow through Porous Media Muhammad Sahimi; Muhammad Sahimi U. of Minnesota Search for other works by this author on: This Site Google Scholar Adel A. Heiba; Adel A. Heiba U. of Minnesota Search for other works by this author on: This Site Google Scholar Barry D. Hughes; Barry D. Hughes U. of Minnesota Search for other works by this author on: This Site Google Scholar H. Ted Davis; H. Ted Davis U. of Minnesota Search for other works by this author on: This Site Google Scholar L.E. Scriven L.E. Scriven U. of Minnesota Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 1982. Paper Number: SPE-10969-MS https://doi.org/10.2118/10969-MS Published: September 26 1982 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Sahimi, Muhammad, Heiba, Adel A., Hughes, Barry D., Davis, H. Ted, and L.E. Scriven. "Dispersion in Flow through Porous Media." Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 1982. doi: https://doi.org/10.2118/10969-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search nav search search input Search input auto suggest search filter All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Annual Technical Conference and Exhibition Search Advanced Search AbstractDispersion is a consequence of flow. It results from the different paths and speeds and the consequent range of transit times available to paths and speeds and the consequent range of transit times available to tracer particles convected across a permeable medium. The kinematic mechanism stems from the connectivity structure of porespace; the dynamic mechanism, from the effect of pore shape and size on flow. Molecular diffusion can modify both. In many circumstances these mechanisms lead to distributions of macroscopic average solute or tracer concentration that are diffusive, i.e. that can be modeled by the convective diffusion equation, dispersion coefficients taking the role of diffusivity.For cases of diffusive mixing locally at pore junctions and no appreciable diffusion between, a simple network approximation is appropriate. Square and simple cubic networks of variable pore segments, with average flow in one of the pore directions, are useful idealizations. Dispersion in one-and two-phase flow through these networks is studied here by the Monte Carlo strategy of replicated computer experiments. This strategy combined, with considerable computational savings, with the percolation theory of fluid distributions in two-phase flow. Network percolation theory of fluid distributions in two-phase flow. Network topology and pore geometry and thus the two basic mechanisms are precisely controlled.The results show that dispersion is diffusive in the cases simulated. Longitudinal (mean flow direction) dispersivity is an order of magnitude greater than dispersivity in transverse directions. In two-phase flow, longitudinal dispersivity in a given phase rises greatly as the saturation of that phase approaches residual, i.e. its percolation threshold; transverse dispersivity also increases, but more slowly. As the threshold is neared, the backbone of the sub-network occupied by the phase becomes increasingly tortuous, with local mazes spotted along it that are highly effective dispersers.All of the findings accord qualitatively with most available data, except that dispersivities in reality are not constant but increase slowly with macroscopic average flow rate, which may stem from molecular diffusion that is lost from the network approximation used. Keywords: dispersion coefficient, dispersivity, machine learning, tracer particle, fraction, imbibition, simulation, percolation threshold, upstream oil & gas, square network Subjects: Reservoir Fluid Dynamics, Flow in porous media This content is only available via PDF. 1982. Society of Petroleum Engineers You can access this article if you purchase or spend a download.