Abstract
Enhanced Geothermal Systems (EGS) are those in which advanced drilling and fracturing technologies are required to extract heat energy from the earth's crust in areas where higher heat flow than average and natural permeability and/or fluid content are lacking. In order to make an EGS project successful, extensive studies should be conducted, especially for the purposes of evaluating and predicting future thermal performance of subsurface system. The main objective of this study is to present novel analytical models and their analytical solutions for predicting the temperature and heat recovery behaviors of four different hydraulically fractured well 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, and multi-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 and conduction have been applied. The partial differential equations describing and coupling convective heat transfer in hydraulically fractured wells with conductive heat transfer in the matrix system, which is assumed to be homogenous, for each well completion type were solved subject to the appropriate initial, interface and outer boundary conditions by using the method of Laplace transformation and inverted numerically by using the Stehfest inversion algorithm (Stehfest, 1970). The solutions presented in this study treat hydraulic fractures as porous media. The analytical solutions derived were validated by using the existing solutions available in the literature for the single-fracture and multiple-fractures intersecting a horizontal-well doublet system, 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 perform parametric studies to investigate the effect of parameters on temperature of produced fluid and in return on feasibility of a given EGS completion. Main conclusions obtained from the extensive parametric studies are: Geothermal gradient has substantial effect on fracture outlet temperature of the produced fluid in EGS models 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 EGS models having vertical flow, downward flow case is observed to have better performance in terms of heat recovery factor than upward flow case of the same model.
