“…where K w is water permeability, mD; μ w is water viscosity, Pa s; P c is capillary force, Pa; ⌀ is porosity; A c is imbibition crosssectional area, cm 2 ; S wf is the water saturation of the imbibition front; S wi is the initial water saturation; V imb is the volume of imbibed water, cm 3 ; and t is the imbibition time, s. Shale formation has a tremendous capacity for imbibition of water that is injected during MHF stimulation. 60,61 You et al 62 summarized the factors that promote imbibition, including well-developed bedding and natural fractures, ultralow initial water saturation, high content of clay mineral, high capillary pressure, dual-wettability (water and hydrocarbon), and high content of soluble salt. The initial water saturation, S wi , in the main shale gas production layer is usually less than 30−45% and much less than the irreducible water saturation (64− 80%).…”