Bilinear pressure diffusion and termination of bilinear flow in a vertically fractured well injecting at constant pressure

Abstract

Abstract. This work studies intensively the flow in fractures with finite hydraulic conductivity intersected by a well injecting or producing at constant pressure, either during an injection or production well test or the operation of a production well. Previous investigations showed that for a certain time the reciprocal of flow rate is proportional to the fourth root of time, which is characteristic of the flow regime known as bilinear flow. Using a 2D numerical model, we demonstrated that during the bilinear flow regime the transient propagation of isobars along the fracture is proportional to the fourth root of time. Moreover, we present relations to calculate the termination time of bilinear flow under constant injection or production well pressure as well as an expression for the bilinear hydraulic diffusivity of fractures with finite hydraulic conductivity. To determine the termination of bilinear flow regime, two different methods were used: (a) numerically measuring the transient flow rate in the well and (b) analyzing the propagation of isobars along the fracture. Numerical results show that for low dimensionless fracture conductivities the transition from bilinear flow to another flow regime (e.g., pseudo-radial flow) occurs before the pressure front reaches the fracture tip, and for high dimensionless fracture conductivities it occurs when the pressure front arrives at the fracture tip. Hence, this work complements and advances previous research on the interpretation and evaluation of well test analysis under different reservoir conditions. Our results aim to improve the understanding of the hydraulic diffusion in fractured geologic media, and as a result they can be utilized for the interpretation of hydraulic tests, for example to estimate the fracture length. Highlights. The reciprocal of flow rate is proportional to the fourth root of time. The migration of isobars in the fracture is proportional to the fourth root of time. For low dimensionless fracture conductivities, bilinear flow ends before the pressure front reaches the fracture tip. For high dimensionless fracture conductivities, bilinear flow ends when the pressure front reaches the fracture tip. Isobars accelerate when they approach the fracture tip.

Closed-Loop Systems for Geothermal Energy Exploitation from Hydrocarbon Wells: An Italian Case Study

“…The pipe equivalent surface (S eq ) can be calculated by following the approach proposed in [38], considering the sum of the areas S gg and S p as indicated in Figure 4. Consequently, D eq is obtained by following Equation (18).…”

“…Although geothermal open-loop systems in sedimentary formations may provide a sustainable solution where the geothermal potential and heat demand coincide [14,15], these technologies are subject to some technical problems, including groundwater recession, corrosion and scaling. Further important issues are represented by the reinjection of fluids [16,17] and by the complex additional exploration activities [18].…”