Carbonate reservoirs are usually strongly fractured, with very high permeability contrasts between matrix blocks and fractures. Normally, a simulation of fluid flow with a dual porosity model is used, which is based on a fluid-exchange term where the dimensionless time is a key factor. Besides traditional reservoir rock and fluid parameters, the scaled dimensionless time must include the influence of capillary and gravitational forces. A very recent publication [Li and Horne, SPE Paper No. 77544, 2002] examined an "analytical" model that involved all these effects. In the present paper, we have tested the model for spontaneous imbibition of aqueous surfactant solution into preferential oil-wet carbonate cores. A chemical reaction occurs between the surfactant and adsorbed polar organic components/carboxylates at the carbonate surface, ahead of the fluid displacement process, as has been discussed previously [Standnes and Austad, J. Pet. Sci. Eng., 28, 123, 2000]. It was of great interest to determine if this new analytical model could handle such a process. The ranges for the scaling parameters were as follows: interfacial tension (IFT), 0.3-0.8 mN/m; permeability, 3-350 mD; initial water saturation (S-wi), 0-0.5; core height, 5-30 cm (but with the same diameter); diameter, 2.5 and 3.5 cm (but with the same core height); temperature, 40-70 degreesC; and sulfate concentration, 0-1.7 g/L. Temperature change has a great influence on the imbibition rate, because of changes in IFT, critical micelle concentration, and fluid viscosity. Sulfate, being a potential-determining ion toward CaCO3 [according to Pierre et al., J. Dispersion Sci. Technol., 11, 611, 1990] was observed to have catalytic effects on the wettability alteration process in chalk at low temperature [according to Strand et al., Energy Fuels, 17, 1133, 2003]. When the characteristic length (La) is used as the shape factor of the cores, all the parameters scaled very well, except for the height of the core and the diameter of the core at low IFT (low temperature). However, when just the height of the cores was used as the shape factor, all the parameters scaled quite well when the normalized oil recovery was plotted versus dimensionless time. The fit of the scaling, using the height of the core as the shape factor, suggested that gravitational forces were very active in the oil recovery mechanism.