Analytical Solutions for Predicting Fracture Outlet Temperature of ProducedFluid from Enhanced Geothermal Systems with Different Well-CompletionConfigurations

摘要

Enhanced Geothermal Systems(EGS)are those in which advanced drilling and fracturing technologies arerequired to extract heat energy from the earth's crust in areas where higher heat flow than average and naturalpermeability and/or fluid content are lacking.In order to make an EGS project successful,extensive studiesshould be conducted,especially for the purposes of evaluating and predicting future thermal performance ofsubsurface system.The main objective of this study is to present novel analytical models and their analyticalsolutions for predicting the temperature and heat recovery behaviors of four different hydraulically fracturedwell configurations of EGS created in a hot dry rock formation.The configurations considered are a single-vertical-planar fracture intersecting a horizontal-well doublet system orienting in a horizontal plane,multi-vertical-planar fractures intersecting a horizontal-well doublet system orienting in horizontal plane,a single-vertical-planar fracture intersecting a horizontal-well doublet system orienting in a vertical plane,andmulti-vertical planar fractures intersecting a horizontal-well doublet system orienting in a vertical plane.In developing these analytical solutions,basic concepts of conservation of heat due to convection andconduction have been applied.The partial differential equations describing and coupling convective heattransfer in hydraulically fractured wells with conductive heat transfer in the matrix system,which is assumedto be homogenous,for each well completion type were solved subject to the appropriate initial,interfaceand outer boundary conditions by using the method of Laplace transformation and inverted numerically byusing the Stehfest inversion algorithm(Stehfest,1970).The solutions presented in this study treat hydraulicfractures as porous media.The analytical solutions derived were validated by using the existing solutionsavailable in the literature for the single-fracture and multiple-fractures intersecting a horizontal-well doubletsystem,given by Arpaci et al.(1966)and Gringarten et al.(1975)who both treat hydraulic fractures 100%porous,respectively.The solutions developed for each of the well completion type were used to performparametric studies to investigate the effect of parameters on temperature of produced fluid and in return onfeasibility of a given EGS completion.Main conclusions obtained from the extensive parametric studiesare: Geothermal gradient has substantial effect on fracture outlet temperature of the produced fluid in EGSmodels having vertical flow in fractures especially for low injection volumetric flow rates,hydraulic fracture porosity has substantial effect on determining intrinsic velocity of fluid within pores of fracture,and in EGSmodels having vertical flow,downward flow case is observed to have better performance in terms of heatrecovery factor than upward flow case of the same model.