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Governing equations: For this isothermal process, the number of moles, N_i, of each species are characterized as a function of the gradients in terms of advective-dispersion transfer, chemical reaction rate variables analogous to the various reactions given in previous section and external sources/sinks given by the rate of change in the number of moles of species added or subtracted. Hence, the rate of change in the number of moles of each species must satisfy the general conservation equation for all components, N_t, written as:

V_b (∂N_i)/∂t-V_b ∇ ⃗∙[∑_(j=o,g,aq)▒(ξ_j y_ij (u_j ) ⃗-y_ij (D_ij ) ⃗ ⃗ ) ]-V_b (∂σ_(i,aq))/∂t-V_b (∂σ_(i,m))/∂t-q_i=0 for i=1,…..,N_t (20)

Total flux according to Darcy’s law is represented by:

(u_j ) ⃗=k ⃗ ⃗λ_ij (∇P_j-γ_j ∇Z) for j=o, g, aq

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Detailed explanation can be found in Nghiem et al. (2004a) and Nghiem et al. (2011). The discretized equation for mineral components is:

V_b/∇t (〖N_i〗^(n+1)-〖N_i〗^n )-V_b 〖r_(i,m)〗^(n+1)=0 for i=1,…..,N_m (27)

It is crucial to ensure that the sum of phase volumes equal to the pore volumes by employing the volume constraint equation

∑_(j=o,g,aq)▒[〖N_j〗^(n+1)/〖ρ_j〗^(n+1) ] -ϕ^(n+1)=0 (28)

Numerical Solution Approach: Elimination of the equilibrium reactions term from equation 25 using ERA matrix reduced the discretized equation to only primary aqueous component. Then, the number of all conservation equations including hydrocarbon and aqueous components becomes N_ia+N_c. There are N_tot=N_ia+3N_(c )+5+ R_aq+N_m equations that can be used to find solution to the same number of unknown variables as summarized