“…On the basis of the imbibition length from eq , to obtain the imbibition weight, it is assumed that the pore volume in shale is composed of multiple capillaries [capillary( i ), where i = 1, 2, 3, ..., n ], shown as Figure . In the multiple capillary model, we assume that each capillary has the same average pore diameter (λ a ) and tortuosity (τ), thus having the same imbibition length [ L s ( i ) and L t ( i ), where i = 1, 2, 3, ..., n ] and sectional area of each capillary [ A p ( i ), where i = 1, 2, 3, ..., n ], shown as Additionally, on the basis of the rock physics theory, it gives two traditional assumptions that the total sectional area of the pore ( A p ) is equal to the sum of A p (1), A p (2), A p (3), ..., and A p ( n ) and the porosity of the sectional area is approximately equal to the porosity of the volume, meaning that ϕ = V p / V = A p / A . Then, the volume of imbibition liquid at any given time [ V i ( t )] can be calculated, expressed as Finally, when the volume and density of the liquid in the shale sample are combined, we can obtain the imbibition amount, shown as where w ( t ) is the imbibition amount (%), W ( t ) is the weight of the shale sample at t (g), and W o is the weight of the original shale sample (g).…”