An analytical solution on spontaneous imbibition coupled with fractal roughness, slippage and gravity effects in low permeability reservoir

Abstract

Spontaneous imbibition (SI) refers to displacement of non-wetting phase by wetting phase fluids in porous media which driven by capillary force. Spontaneous imbibition plays an important role in terms of increasing hydrocarbon recovery in low-permeability and tight reservoirs. In this study, we derived a new analytical model of spontaneous imbibition height in low-permeability reservoir considering effective viscosity, surface roughness, slip and gravity effects in a single tortuous capillary tube. Firstly, analytical solutions of imbibition height are derived in a single tortuous rough capillary tube with and without gravity effects. Moreover, our analytical model shows satisfactory match with experimental results from literatures in typical low-permeability core samples. Finally, sensitivity studies are conducted to discuss the effect of surface fractal dimension, effective viscosity, contact angle, interfacial tension, pore sizes and slip length on imbibition height, respectively. The results show that imbibition height inversely proportional to surface fractal dimension, effective viscosity, and contact angle on rough surface. Higher surface fractal dimension, effective viscosity and contact angle decrease imbibition height significantly. On the contrary, the imbibition height is proportional to pore radius, IFT, and slip length. Neglecting the slip effect results in underestimation of imbibition height in nanopore sizes, and insignificant changes are observed for micro-pore sizes. The presented models have clear physical meaning in every parameter on the imbibition height performance.