Numerical Simulation For Multiphase Flow And Transport In Groundwater System

The problem of groundwater organic contamination has been given widespread regarddue to using a great deal of oil production in industry, agriculture and daily life, in whichsurface spills or subsurface leakage of Light Non-aqueous Phase Liquids(LNAPL, forexample, gasoline and diesel oil) which poses a serious threat to soil-groundwater system. It'sa nonlinear physical and chemical process composed of water-oil-gas three phases flow andcoupling multi-physical factors. Aiming at this kind of organic contamination problem, it isnecessary to analyze and simulate the kinetic process of such materials and forecast theirpollution range and component concentration in the subsurface in order to provide evidencesfor the treatment and risk evaluation.In this paper, the kinetic mechanism of water-oil-gas three phase liquids and the lastconstitutive relation of pressure-saturation-relative permeability were summarized. Under theisothermal condition and other hypothesizes, using theories of the petrophysics and reservoirnumerical simulation and groundwater numerical simulation for references, applying theconservation of mass and the continuum medium mechanics method, we established thewater-oil-gas three phases flow mathematic model, which made the formation process ofmathematic model more integrate and legible. Secondly, we transformed the control equationsto the pressure head. Finally, applying the research results of J.C.Parker and his workmates,transforming the saturation to pressure head, the flow equations were unified to the pressurehead, which is a nonlinear partial differential equations system. In the numerical calculus, starting from the generalized Galerkin variation principle, wegot the variation forms of the multiphase flow equations. Therefore, we can apply generalizeddifference methods to solve the above water-oil-gas three phases flow equations andconcentration equations. Finally, the semi-discrete generalized difference scheme and the fullydiscrete generalized difference scheme were established. It's necessary for us to linearize the implicit nonlinear ordinary differential equationssystem which were derived from the generalized difference scheme. Based on the classicNewton-Raphson method, we introduce damp parameters Newton descending method toresolve that equations system. As a result, the new method can escape the shortcoming thatthe iteration was broken down when the Jacobi matrix is singularity or morbidity, and extendthe local convergence to the global convergence. We applied Krylov subspace projectionmethod to resolve the sparse linear algebra system of equations derived from the abovemethod.In order to validate the mathematic model and the computation method, we applied theabove mentioned methods and process to simulate a real model. The basic seepage rule in theporous medium is: after the leakage accident took place, the leak oil seep vertically by thegravity and spread horizontally along the surface at the same time. A small quantity of leak oilwas hold almost in the upper porous medium of capillary zone, and the horizontal extendrange is narrow. Under this condition, though little oil entered the capillary zone, pollutioncomponents diffuse horizontally along the upper edge of capillary zone. The capillary zonewas contaminated, and held the bulk of pollution components by the capillarity. So thecapillary zone is the main enrichment zone for the leak oil. When a great deal of oil wasleaked out, except a little oil is hold by the upper porous medium of the capillary zone, theleakage oil can overcome the entry pressure of the interface between oil and water to enter thecapillary zone, and seep vertically by the gravity. At the same time, the leakage oil spreadhorizontally along the upper edge of the capillary zone. Lastly, it penetrates through thecapillary zone, then float on the table of groundwater. If groundwater table has hydraulicgradient, the floating oil will flow along with the groundwater, and forms a lens. The pollutionarea contaminated by the leakage oil extends gradually.The paper emphasizes particularly on the numerical method. It can enrich numericalmethod for the equation of evolution, and accelerate mathematic theory research on themultiphase flow.