Mass Conservation Equations Sample Clauses

Mass Conservation Equations. The assumptions imposed when developing the flow equations are local thermodynamic equilibrium except for tracers and dissolution of organic component, immobile solid phases, slightly compressible soil and fluids, Fickian dispersion, ideal mixing, and Xxxxx'x law. The boundary conditions are no flow and no dispersive flux across the impermeable boundaries. The continuity of mass for component κ in association with Xxxxx'x law is expressed in terms of overall volume of component κ per unit pore volume (C˜ κ ) as ∂ .  np . .  1) A ∂t  =1  where the overall volume of component κ per unit pore volume is the sum over all phases including the adsorbed phases:  ncv  np C˜ κ =  1− ∑Cˆ κ  ∑SACκA + Cˆ κ for κ = 1,..., nc (2.2)  κ =1  A=1 κ ncv is the total number of volume-occupying components. These components are water, oil, surfactant, and air. np is the number of phases; Cˆ κ is the adsorbed concentration of species κ; and ρκ is the density of pure component κ at a reference phase pressure PR relative to its density at reference pressure PR0, usually taken at the surface condition of 1 atm. We assume ideal mixing and small and constant compressibilities Co . κ R R0 ρκ = 1 + Co (P P ) (2.3) The dispersive flux is assumed to have a Fickian form: D˜ κA,x = φ . SA K κA ⋅ ∇C κA (2.4) αTA φ SA The dispersion tensor KκA including molecular diffusion (DkA) are calculated as follows (Bear, 1979): . DκA . (αLA − α TA) uAi uAj