The multiple continuum framework for fluid flow in fractured porous media typically employs matrix to fracture transfer functions. Historically, transfer functions were developed from rather oversimplified assumptions such as pseudosteady state flow and a fracture network that is instantly and completely filled with water. This approach results in constant, time independent shape factors and pessimistic predictions of recovery. This paper presents a study designed to measure and interpret multiphase matrix-fracture transfer in two geometries: i) small-cubic matrix blocks with an external fracture and ii) large-cylindrical core samples with intersecting fractures. Water is injected into the fractures to observe the physical process of imbibition and flow through fractures in multidimensions. X-ray computerized tomography is employed to measure in-situ water-phase saturation and observe the progress and pattern of imbibition. Results are classified as either filling-fracture or filled-fractured depending on the fracture aperture and injection flow rate.

A new methodology arising from dimensional analysis is used to interpret the time dependence of the shape factor. Significant time dependence is found. Interestingly, plots of shape factors versus dimensionless time display similar characteristic behavior despite the much different experimental geometry. The time-dependent portion decreases linearly with a slope determined by the fracture aperture, fracture width normal to the flow direction, and the flow rate in the fracture. At a dimensionless time of roughly 0.1, shape factors became constant for all cases. The methodology proposed is promising for obtaining the shape factor for any fracture geometry, length and dimension, as well as water rate. No upscaling of the shape factor functions is required because they are obtained from dimensional analysis.

You can access this article if you purchase or spend a download.