Water flow modeling in bounded gas-bearing fractured geological strata: A semi-analytical and experimental study

Abstract

Underground water disposal is a technique for wastewater management, enhanced oil recovery (EOR), or artificial groundwater/aquifer recharge. Host layers might be naturally or even hydraulically fractured which can significantly increase the permeability of the medium where a linear flow geometry around the vertical fractures intersecting the wells is expected. In fact, each of flow from wellbore (injection point) to fracture as well as fracture-matrix flow may be linear in different conditions of fracture conductivity. When both are linear it is named “bilinear flow” in hydraulic fracture appications equivalent to “fully linear flow” in this study. In this paper, a semi-analytical solution is presented for transient saturation of injected water in naturally/hydraulically fractured gas-bearing rocks with linear flow in both wellbore-fracture and fracture-matrix spacings. The solution is general and can be used for either unsaturated soils or depleted reservoirs which are defined with no-flow boundaries. To do so, proposed semi-analytical model was validated with experimental results, based on waterflood testing apparatus in an artificially fractured core-plug which showed a very good matching. In addition to introducing new sets of type curves to delineate water saturation in both matrix and fracture in both constant terminal rate and saturation (CTR and CTS) inner boundary conditions, we defined the average water velocity ratio (AWVR), a conceptual criterion, to assess if CTS and CTR water storage can be logically compared. Results derived based on this concept are: 1) more speedy movement of water front along the last four-fifth of the fracture length by CTR and 2) higher matrix blocks storativity neighboring the first half of the straight fracture plane by CTS. Solutions from our model can directly simulate the unsteady behavior of saturation variations along the fracture and across the rock matrix versus time for an underground water injection problem. Ultimately, this can assist engineers to have an easy spatiotemporal estimation of water storage in the matrix of the host formation.