Experimental and analytical study of multidimensional imbibition in fractured porous media

Capillary imbibition is an important mechanism during water injection and aquifer influx in fractured porous media. Better understanding of matrix–fracture interaction and imbibition in general is needed to model effectively these processes. Using an X-ray computerized tomography (CT) scanner and a novel CT-compatible core holder, a series of experiments to study air and oil expulsion from rock samples by capillary imbibition of water in a three-dimensional (3-D) geometry were conducted. The air–water system was useful because a relatively large number of experiments could be conducted to delineate physical processes. Different injection rates and fracture apertures were utilized. Two different fracture flow regimes were identified. The “filling fracture” regime shows a plane source that grows in length due to relatively slow water flow through fractures. In the second regime, the “instantly filled fracture” regime, the time to fill the fracture is much less than the imbibition time and the imbibition performance scales as the square root of time. In the former regime, the mass of water imbibed scales linearly with time. A new analytical model is proposed for filling fractures incorporating implicit matrix/fracture coupling. Good agreement is found between experiments and calculation. This analytic coupling was obtained by solving the saturation diffusion equation with appropriate initial and boundary conditions. The solution provides the location of the wetting phase front in the fracture and the saturation distribution in the matrix. The solution is analogous to that obtained by Marx and Langenheim [Trans. AIME 216 (1959) 312] for the areal extent of an equivalent heated zone in thermal recovery methods. Analogous terms among flow and heat transfer in porous media were found and are also presented.