Analysis of oil recovery rates for spontaneous imbibition of aqueous surfactant solutions into preferential oil-wet carbonates by estimation of capillary diffusivity coefficients

Spontaneous imbibition (SI) is a very important oil recovery mechanism from low-permeability fractured reservoirs. However, this process will not take place if the reservoir rock is preferential oil-wet. Recently, it was discovered that SI into preferential oil-wet carbonate is possible if the porous medium is exposed to a water-phase containing cationic surfactants of the type CnTAB. Estimation of SI rates for aqueous surfactant solutions into preferential oil-wet carbonates based on the diffusion equation approach have been performed in this work. Capillary diffusivity coefficients (CDCs) were calculated for SI tests into preferential oil-wet carbonates and compared to corresponding data for imbibition of water into strongly water-wet chalk (reference wettability state). The diffusion approach is especially suitable for SI driven by a foregoing wettability alteration process induced by surfactants due to problems to measure dynamic flow parameters accurately during the wettability alteration process. The solution to the three-dimensional diffusivity equation describing oil recovery as a function of time is expressed by an infinite series. Approximating the solution using only one term in each spatial direction makes it possible to calculate CDCs after performing a least square fit on experimental data. The results show that CDCs for SI into preferential oil-wet carbonates are in the range (1.7–14) × 10−11 m2/s, which are approximately three orders of magnitude lower than for SI of water into strongly water-wet chalk. However, CDCs for imbibition into preferential oil-wet carbonates are still larger than what is observed for cores having mixed-wettability of which have the exponential decay parameter λ reduced up to four orders of magnitude compared to imbibition into strongly water-wet core material [N.R. Morrow, G. Mason, Curr. Opin. Colloid Interf. Sci. 6 (2001) 321–337]. The calculated CDC for imbibition into strongly water-wet chalk shows good agreement with other values published in the literature.