SPONTANEOUS IMBIBITION of A WETTING FLUID into A FRACTURE with OPPOSING FRACTAL SURFACES: THEORY and EXPERIMENTAL VALIDATION

Spontaneous imbibition (SI) is a capillary-driven flow process, in which a wetting fluid moves into a porous medium displacing an existing non-wetting fluid. This process likely contributes to the loss of fracking fluids during hydraulic fracturing operations. It has also been proposed as a method for an enhanced recovery of hydrocarbons from fractured unconventional reservoirs. Numerous analytical and numerical approaches have been employed to model SI. Invariably, these idealize a fracture as the gap formed between parallel flat surfaces. In reality, rock fracture surfaces are rough over multiple scales, and this roughness will influence the contact angle and rate of fluid uptake. We derived an analytical model for the early-time SI behavior within a fracture bounded by parallel impermeable surfaces with fractal roughness assuming laminar flow. The model was tested by fitting it to experimental data for the SI of deionized water into air-filled rock fractures. Twenty cores from two rock types were investigated: a tight sandstone (Crossville) and a gas shale (Mancos). A simple Mode I longitudinal fracture was produced in each core by compressive loading between parallel flat plates using the Brazilian method. Half of the Mancos cores were fractured perpendicular to bedding, while the other half were fractured parallel to bedding. The two main parameters in the SI model are the mean separation distance between the fracture surfaces, x', and the fracture surface fractal dimension 2 ≤ D < 3. The x' was estimated for each core by measuring the geometric mean fracture aperture width through image analysis of the top and bottom faces, while D was estimated inversely by fitting the SI model to measurements of water uptake obtained using dynamic neutron radiography. The x values ranged from 45μm to 190μm, with a median of 93μm. The SI model fitted the height of uptake versus time data very well for all of the rock cores investigated; medians of the resulting root mean squared errors and coefficients of determination were 0.99mm and 0.963, respectively. Estimates of D ranged from 2.04 to 2.45, with a median of 2.24. Statistically, all of the D values were significantly greater than two, confirming the fractal nature of the fracture surfaces. Future research should focus on forward prediction through independent measurements of D and extension of the existing SI model to late times (through the inclusion of gravity) and fractures with permeable surfaces.