Table 5 List of models predicting residual oil saturation.

No	Models	References
1	\({S}_{or}={S}_{or1}^{high}+\frac{{S}_{or1}^{low}-{S}_{or1}^{high}}{1+{T}_{1}{N}_{T}^{\tau }}\)	Delshad¹⁹²
2	\({S}_{or1}={S}_{or1}^{high}+\frac{{S}_{or1}^{low}-{S}_{or1}^{high}}{1+{T}_{1}{N}_{T}}\) \({S}_{or2}={S}_{or2}^{high}+\frac{{S}_{or2}^{low}-{S}_{or2}^{high}}{1+{T}_{2}De}\) \({S}_{or}=\mathrm{min}({S}_{or1},{S}_{or2})\)	Lotfollahi et al.¹⁹³
3	\({S}_{or}^{*}=\left\{\begin{array}{l}1 \,if \,De<1 \\ 1-0.133logDe \,if \,De\ge 1\end{array}\right.\)	Qi et al.¹³⁹
4	\({S}_{or}=\left\{\begin{array}{l}-0.009\mathrm{ln}\left({N}_{ce}\right)+0.3348\, if\, {N}_{ce}<{N}_{crt} \\ 0.287\mathrm{exp}\left(-3.42{N}_{ce}\right) \,if\, {N}_{ce}>{N}_{crt}\end{array}\right.\) \({N}_{ce}=\frac{V{\mu }_{pore}}{{\sigma }_{ow}}\)	Azad and Trivedi¹²⁸

Where \({S}_{or}\) is the residual oil saturation, \({T}_{1}\) is the trapping fitting parameter, \(\tau \) is the model parameter dependent on the rock pore size distribution, \({S}_{or1}^{low}\) and \({S}_{or1}^{high}\) are the residual oil saturations at critical and total desaturation trapping numbers, respectively;\({S}_{or1}\) and \({S}_{or2}\) are the residual oil saturations determined by trapping and Deborah numbers, respectively, \(De\) is the Deborah number, \({T}_{2}\) is the viscoelastic fitting parameter (usually taken as 0.3–0.5 in sandstones), \({S}_{or2}^{low}\) and \({S}_{or2}^{high}\) are the residual oil saturations at low Deborah numbers (waterflooding \(De\)) and high Deborah numbers (viscoelastic polymer flow \(De\)), respectively,\({S}_{or}^{*}\) is the normalized residual oil saturation that is the ratio of residual oil saturation after polymer flooding to the one before polymer injection,\({N}_{ce}\) is the extensional capillary number, \({N}_{crt}\) is the critical capillary number,\(V\) is the interstitial velocity, \({\sigma }_{ow}\) is the interfacial tension between oleic and aqueous phases, and \({\mu }_{pore}\) is the pore-apparent viscosity that is calculated using extensional parameters.

Search