MODELING OF LOW SALINITY EFFECTS IN SANDSTONE OIL ...

6 OMEKEH, EVJE, AND FRIISBeta Cabeta Cax 10 −34.543.532.521.510.50.10.20.30.40.5Mg2+ (mole/liter)0.60.70.20.410.80.6Ca2+ (mole/liter)1.21.4Figure 1. Plot showing β ca as a function of varying C ca and C mg concentrations,and with C na = 0.15 (moles per liter). Other parameters in (12) like K cana ,K mgna , and CEC, are listed in Appendix A.(12) β ca (C na , C ca , C mg ) =and(13) β mg (C na , C ca , C mg ) =K cana√γca C ca CEC2K cana√γca C ca + 2K mgna√γmg C mg + γ na C na,K mgna√γmg C mg CEC2K cana√γca C ca + 2K mgna√γmg C mg + γ na C na.We note that the equations (11), (12) and (13) are equivalent to a Langmuir-type adsorptionisotherm. Fig. 1 illustrates how the β ca function depends on the concentrations C na , C ca , C mg .At high magnesium concentration, the amount of calcium ion adsorbed on the rock, β ca , becomesquite low.3. Coupling of wettability alteration to changes on the rock surfaceThis section discusses aspects concerning the flow functions. Since we only consider flows withoutcapillary pressure in Section 6, we limit the discussion to the relative permeability functions.The following ideas are also employed in [14, 15], however, in the context of spontaneous imbibitionon chalk cores where capillary forces are the driving forces in oil recovery. It also partially followsideas employed in previous works in [22, 41, 45].3.1. Relative permeability functions. As a basic model for relative permeability functionsthe well-known Corey type correlations are used [12]. They are given in the form (dimensionlessfunctions)(14)k(s) = k ∗( s − s)wrNk,swr ≤ s ≤ 1 − s or ,1 − s or − s wr( 1 −k o (s) = ko∗ sor − s) Nko,swr ≤ s ≤ 1 − s or ,1 − s or − s wrwhere s wr and s or represent critical saturation values and Nk and Nk o are the Corey exponentsthat must be specified. In addition, k ∗ and k ∗ o are the end point relative permeability values thatalso must be given. Now, we define two extreme relative permeability functions corresponding tothe wetting state of the rock for high salinity and low salinity conditions.