Flow through the fracture is usually estimated by cubic law, which assumes flow to occur between two parallel plates. The cubic law is valid to represent the flow through the fracture system if the matrix permeability is very low to provide any significant flow contribution. However, in high permeability rocks, the flow occurs through both fracture and matrix systems. Flow through matrix may sometimes exceed that through the fractures under increased stress acting on the reservoirs. Under these circumstances, the cubic law should be modified by combining the weighted average of the permeabilities in order to account for flow through matrix. In this paper we present the amount of flow through fracture and matrix system based on modified cubic law equations by conducting a series of laboratory experiments on fractured cores under different stress conditions. The flow rate through fracture and matrix system and the pressure drop were matched using simulation. X-ray CT was used to determine the fracture aperture and saturation distributions. In addition, the saturation distributions from simulation results were compared to X-ray CT Scan results.
The first comprehensive work on flow through open fractures was done by Lomize1, in which he used parallel glass plates and demonstrated the validity of cubic law for laminar flow. He modeled fluid flow with different fracture shapes and investigated the effects of changing the fracture walls from smooth to rough. Later, comprehensive fluid flow studies were conducted through a single fracture to investigate the validity of cubic law2,3. Idealized fracture models were constructed by assuming that the fracture planes had contact area and roughness.
The flow in a fracture is usually characterized by the classical cubic law equation4
Equation (1) (Available in full paper)
This equation neglects the matrix permeability compared to the fracture permeability. As a result, the classical cubic law does not account for any flow occurring through the matrix and assumes that the flow occurs entirely through the fracture. This assumption holds for low permeability reservoirs. However, in high permeability reservoirs the classical cubic law is no longer valid and has to be modified by considering the effect of matrix permeability5. Flow might also be diverted from the fracture to matrix due to the decrease in the fracture aperture size with the increase in the stress conditions6 The cubic law equation is valid only for steady-state laminar flow between two parallel plates. This equation assumes that the walls of the fracture are smooth. Witherspoon et a.l4 conducted laboratory experiments to validate parallel plate theory and they showed that the parallel plate approximation tends to break down at higher normal stress (>10 MPa) across the fracture. Alfred5 also confirmed that parallel plate assumption is not valid to adequately model the fluid flow experiments when overburden pressure is significant. The flow in a single fracture does not progress uniformly as assumed by parallel plate theory; rather, it flows through a limited number of channels7,8,9. Several authors7,9,10 measured fracture aperture directly without any applied stresses and found that fracture apertures follow log-normal distribution.