Integral transforms for flow and transport in discrete and continuum models of fractured heterogeneous porous media

摘要

The Generalized Integral Transform Technique (GITT) is employed in combination with a single domain reformulation strategy and a coupled eigenvalue problem expansion base to construct analytical or hybrid numerical-analytical solutions for flow and transport in fractured porous media. The problem formulation and provided formal solutions encompass both continuum (multi-porosity/multi-permeability) and discrete (fracture-matrix interaction) models for heterogeneous porous media. The single domain representation is written with the aid of space variable coefficients, that account for the abrupt physical properties and source terms transitions across the different subregions. The aim is to provide an unified formalism that includes a wide class of problems in fluid flow, heat and mass transfer in heterogeneous media, with the integral transformation process for the potentials (pressure, velocities, temperature, or concentrations) being applied over the whole physical domain at once, thus markedly reducing the mathematical manipulations. The space variable coefficients are then carried on to the eigenvalue problem formulation which provides the base for the eigenfunction expansion. In addition, a coupled eigenvalue problem alternative is proposed, which is particularly useful in dealing with multi-porosity/multi-permeability flow and transport models, collapsing the multiple coupled potentials equations into one single integral transformation process. Two representative applications are briefly considered, one dealing with contaminant transport with discrete fracture-matrix interaction in layered porous media and the other related to dual porosity/dual permeability model of flow in unsaturated soils.