A Mathematical Model of Surfactant Spontaneous Imbibition in a Tight Oil Matrix with Diffusion and Adsorption

Surfactants can significantly improve the oil recovery of spontaneous imbibition (SI) in unconventional oil reservoirs, but mathematical modeling of surfactant SI for displacing oil in a tight matrix is challenging because of its complex mechanism. Considering the mechanisms of surfactant diffusion and adsorption, the flow equation for the SI of surfactant solution into an oil-saturated capillary is derived, and the dynamic capillary pressure and surfactant concentration during the SI process are characterized. Then, based on the pore size distribution of the pores in a tight matrix, a core-scale mathematical model for SI of surfactant solution into an oil-saturated tight matrix is developed and validated with experimental data from the literature. The results show that surfactant adsorption can increase the product of interfacial tension and the cosine of the contact angle, and the increased capillary pressure in pores leads to a faster imbibition rate. A surfactant with a high adsorption and desorption rate on the water-solid interface and diffusion ability will lead to a higher oil production rate by SI in unconventional oil reservoirs. The proposed model is beneficial for modeling the dynamic process of surfactant SI and screening suitable surfactants for enhanced oil recovery in unconventional reservoirs.