Gravity drainage caused by density difference between fluids in the fractures and in the matrix rock can be an effective mechanism for recovering oil from naturally fractured reservoirs (NFRs). This process has been studied in the past, and oil-recovery-rate scaling laws that depend inversely on matrix block height have been developed.
In this work, we show that these scaling laws are only valid for one-dimensional flow where fracture spacing is small compared to matrix block height. We use single-element mechanistic fracture models and discrete-fracture-matrix (DFM) models of realistic systems to develop new scaling relationships that better capture 3D gravity drainage in weakly wetting realistic NFRs. The single-element models reveal that the gravity drainage rate scales as a function of both fracture spacing and matrix block height, and not only on the inverse of matrix block height as previous investigations suggested. This has implications for maximum gravity-drainage rates that are possible in fractured reservoirs—either through the geological distribution of heterogeneities or through operational control of the fluid-height difference in the fractures and matrix. We also create detailed DFM models for geologically realistic fracture networks that result in a spatially variable distribution of fracture spacing and matrix block height, and describe how to scale gravity drainage in such systems.