NON-DARCY LIQUID FLOW IN SHALE: THEORY AND LABORATORY EXPERIMENT RESULTS

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’s law is not always adequate for describing liquid flow process in a shale formation. This non-Darcy flow behavior (characterized by nonlinearity of the relationship between liquid flux and hydraulic gradient), 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 propose a phenomenological model for liquid flow in shale (in which liquid flux is a power function of pressure gradient) and developed 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 results and observations from different research groups. Furthermore, based on the developed analytical solution, we also developed a laboratory test methodology using nuclear magnetic resonance imaging to estimate parameters for the phenomenological model from spontaneous imbibition tests. The relative importance of this non-Darcy liquid flow for hydrocarbon production in unconventional reservoirs remains an issue that needs to be further investigated.