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Appendix ENumerical discretization of modelA one-dimensional grid is defined with N grid blocks of size ∆z. The mobility parameterand phase density are weighed upstream. The time step of integration is given by ∆t. Theoil pressure is solved for using a discretized scheme in the following form (see Valiollahi2005 [140] for details):aP n+1 n+1o,i+1 + bPo,i + cP n+1o,i−1 = d,(E.1)where P n o,i represents the oil pressure in grid block i at time step n. The coefficients inEq. E.1 for the regular grid blocks (1 < i < N) are given by (the sub- and superscript ofU T w are omitted)( )a = − λ n o,i + λn w,i ,(b =c = −d = ϕ∆z2∆t−(Swρw) ni−λ n w,iλ n o,i + λn w,i + ρn o,i−1ρ n o,i( ρ no,i−1ρ n o,i)λ n o,i−1 + ρn w,i−1ρ n λ n w,i−1 + ϕ∆z2w,i)λ n o,i−1 + ρn w,i−1ρ n λ n w,i−1w,i[( ) n(S o c o + S w c w ) n i P o,i n − Soρ o i)](∑J ϱJ,n iw J,nw,i − wJ,n−1 w,i)(P n c,i+1 − P n c,i+ ρn w,i−1ρ n λ n w,i−1w,i,∆t(S o c o + S w c w ) n i ,()∑I ϱI,n iw I,no,i − wI,n−1 o,i() ( )Pc,i n − P c,i−1n + ∆z 2 1ρ n − 1w,i ρ n Ui n.o,i(E.2)Hence, the pressure is updated by solving the following matrix equationMP n+1 = d,(E.3)where M is a tri-diagonal matrix comprising the defined terms a, b and c.The inlet boundary condition is taken into account through the equationa 1 P n+1o,2 + (b 1 + c 1 )P n+1o,1 = d 1 − c 1q o ρ o,sc ∆zAρ o λ o, (E.4)where ρ o,sc is the oil density at standard conditions, q o is equal to Q in the injection step155