Modeling of underground water contamination by non aqueous liquids

Mathematical Simulation of the Behavior of Spent Organic Extracting Agent in the Near-Well Region in the Case of Deep Burial

“…The system of equations describing the dynamics of the pressure P, temperature T, and the reduced density ρ i φ of the ith component in the part of the system φ, can be written in the form where u φ , µ φ are the rate of filtration and the viscosity of the liquid phase part φ (u 3 = u 4 = 0); k is the permeability of the medium; S φ is the degree of saturation of the part of the system φ; ƒ φ (S φ ) is the relative phase permeability of the part φ; m is the porosity; t is the time; (J κ ) i φ*φ is the flux density of the ith component from the part φ * into the part φ as a result of capillary imbibition; J i ψφ is the mass flux density of the ith component from the part ψ into the part φ; J i φ*φ is the flux density of the ith component from the part φ * into the part φ as a result of convective flow, caused by mass transfer of the macrocomponents between the parts of the system; J i φφ+4 is the flux density of the ith component from the part φ to the surface of the rock; J φ i is the density of sources of the ith component in the part φ as a result of radioactive decay or radiation-chemical and thermochemical decomposition of the organic components; J i fφ is the effective flux density of the ith component from the part f into the part φ as a result of a change in the degree of saturation of the liquid parts of the system; c is the volume heat capacity of the medium, determined by the heat capacity and volume fraction of the parts; c φ is the volume heat capacity of the part φ, determined by the heat capacity and the reduced density of the constituents of its macrocomponents; β is the thermal conductivity of the medium; W is the specific power of heat release; F is the thermal flux through the top and bottom of the bed; the symbol "*" denotes the replacement of the mobile part of a phase by the immobile part and vice versa (1 ↔ 3, 2 ↔ 4); and the symbol "~" denotes a replacement of the organic phase by a water phase with the same mobility and vice versa (1 ↔ 2, 3 ↔ 4, 5 ↔ 6, 6 ↔ 7) [9,10].…”