Vertical Integration of Three-Phase Flow Equations for Analysis of Light Hydrocarbon Plume Movement

摘要

Groundwater contaminatioon due to surface spills or subsurface leakage of hydrocarbon fuels, organic solvents, and other immiscible organic liquids is a widespread problem. Numerical models for phase-separated hydrocarbon migration in the vadose zone and groundwater have been presented recently by various researchers. Most analyses have been restricted to consideration of two-dimensional domains involving a vertical slice through unsaturated and/or saturated zones. In the report a mathematical model is derived for areal flow of water and light hydrocarbon in the presence of gas at atmospheric pressure. Vertical integration of the governing three-dimensional, three-phase flow equations is performed under the assumption of local vertical equilibrium to reduce the dimensionality of the problem to two orthogonal horizontal directions. Independent variables in the coupled water and hydrocarbon areal flow equations are specified as the elevation of zero gauge hydrocarbon pressure (air-oil table) and the elevation of zero gauge water pressure (air-water table). Constitutive relations required in the areal flow model are vertically integrated fluid saturations and vertically integrated fluid conductivities as functions of air-oil and air-water table elevations. Closed-form expressions for the vertically integrated constitutive relations are derived based on a three-phase extension of the Brooks-Corey saturation-capillary pressure function. Reduction in dimensionality combined with dimished nonlinearity, makes the vertically integrated water and hydrocarbon model an efficient formulation for analyzing field-scale problems involving hydrocarbon spreading or recovery under conditions for which the vertical equilibrium assumption is expected to be a satisfactory approximation.