Initial water imbibition of gas-saturated natural reservoir rock: A generalized multifactor geometry model with capillary bundles

Abstract

The spontaneous imbibition in porous medium is of interest for many engineering problems particularly in the reservoir exploitation over several decades. So far, various analytical or numerical models have been proposed to simulate the imbibition, but none of them can fully take into account real microscopic geometry characteristics of pore structure. Therefore, assuming quasi-steady and completely developed laminar flow with no-slip boundary conditions when capillary bundles imbibe an incompressible Newtonian liquid, a generalized spontaneous imbibition model is proposed based on a fractal pore structure consisting of tortuous and nonuniform capillaries with different sizes and noncircular cross-sections. A theoretical analysis and experimental contrast demonstrate that the derived formulas enable the unification of several traditional and newly developed models available from the literature and have the better predicted trend with the relative error controlled within 100% in comparison to them. The obtained model is evaluated against previously reported data of water imbibition measured for various natural porous rocks in multiple directions. The validation results show that the generalized model can be utilized to characterize the imbibition behavior of porous rocks with little clay and even extend to other natural and engineering porous materials, including consolidated and unconsolidated media, and that the interconnected pores cannot always be assumed to be cylindrical or uniform. Moreover, the present model is applied to inversely estimate the pore size as a result of good agreement with experimental measurements. Simultaneously, in accordance with the new theoretical model, the difference in water imbibition is newly revealed for selected rock samples from the literature.