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Transport of Immiscible Fluids Within and Below the Unsaturated Zone: A Numerical Model
Author(s) -
Faust Charles R.
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i004p00587
Subject(s) - vadose zone , porous medium , capillary pressure , mechanics , fluid dynamics , saturation (graph theory) , nonlinear system , multiphase flow , relative permeability , flow (mathematics) , two phase flow , partial differential equation , aquifer , mathematics , groundwater , geology , geotechnical engineering , porosity , mathematical analysis , physics , combinatorics , quantum mechanics
A numerical model is developed that describes the simultaneous flow of water and a second immiscible fluid under saturated and unsaturated conditions in porous media. The governing equations are a simplified subset of the three‐phase flow equations commonly used in petroleum reservoir simulation. The simplification is analogous to that used to derive the Richard's equation for flow of water in the unsaturated zone. The assumption that pressure gradients in the air phase are negligible leads to two partial differential equations. The proposed formulation is posed in terms of volumetric water saturation and fluid pressure in the immiscible fluid. The two‐dimensional equations for flow in a vertical plane are approximated by finite differences. The fully implicit equations are solved by a direct matrix technique and Newton‐Raphson iteration on nonlinear terms. The resulting numerical model is potentially applicable to many problems associated with immiscible contaminants in groundwater. Unfortunately, data such as relative permeabilities and capillary pressures for the types of fluids and porous materials present in hazardous waste sites are not readily available. As this type of data becomes available and field investigation techniques improve, applications of this type of model will become more practical. Examples are used to demonstrate the potential application of the model and the sensitivity of results to fluid properties.