Unconventional Spontaneous Imbibition into Shale Matrix: Theory and a Methodology to Determine Relevant Parameters

Abstract

Spontaneous imbibition of fracturing fluids into a shale formation has many practical applications for shale gas recovery. Because of the strong solid–liquid interaction in low-permeability media, Darcy law is not always adequate for describing liquid flow process in a shale formation. This unconventional (non-Darcian) flow behavior, however, has not been given enough attention in the shale gas community. The current study develops a systematic methodology to address this important issue. We first review related studies in the literature on relationship between liquid flux and hydraulic (or pressure) gradient in low-permeability media; the unconventional flow behavior is characterized by nonlinearity of the relationship. Then, we propose a phenomenological model for liquid flow in shale (in which liquid flux is a power function of pressure gradient) and develop an analytical solution to a one-dimensional spontaneous imbibition problem that obeys the model. The validity of our model is verified by satisfactory comparisons of theoretical and observed relationships between cumulative imbibition and time. The potential mechanisms of the unconventional flow are discussed. Furthermore, based on the developed analytical solution, we propose a laboratory test methodology to estimate parameters for the phenomenological model from spontaneous imbibition tests.