Analytical model for fluid flow distribution in an Enhanced Geothermal Systems (EGS)

Enhanced geothermal system (EGS) is often envisioned to consist of at least two wells spaced sufficiently apart and connected by hydraulic fractures that serve as flow paths. All the flow paths must be utilized efficiently to ensure the system is operated at its highest potential. However, building an efficient and sustainable EGS is a complicated process as the fluid always chooses the path of least resistance, which can lead to uneven flow distribution. This study focuses on several critical parameters related to well designs, which can potentially allow for optimized flow distribution. An analytical model (written in Python) is developed based on Kirchhoff's law to calculate the flow distribution in any doublet EGS. Wellbore perforations, the completed wellbores and the fractures are simulated as resistance while the fluid is simulated as a current analog. The model solves the pressure at each node, analogous to voltage, using pipe flow equations and Darcy's law. Three different doublets EGS designs (parallel, anti-parallel and non-parallel) were simulated using the model, and a detailed sensitivity study was performed. Anti-parallel doublet systems perform the best in terms of better fluid distribution and at a lower frictional loss. It was also observed that the flow distribution in a doublet system can be affected by fracture permeability, perforation size and flow rate. Higher permeability fracture leads to poor fluid distribution. Smaller perforation size improves the fluid distribution, but it leads to huge frictional losses. Low flow rates also help with optimized fluid distribution but would eventually lead to low heat output.