Pressure Transient Solutions for Multifractured Enhanced Geothermal Systems

Abstract This study investigated a semianalytical solutions for the pressure and rate transient response for multifractured enhanced geothermal systems. A multifractured enhanced geothermal system is composed of two media, namely the rock matrix (low permeability with a large volume) and the fractures (high permeability with minimal volume). We can model the fluid flow inside both fractures and rock matrix as a coupled partial differential equation (PDE). Based initially on Green's functions, we then formulated a linear system of equations composed of the pressure transient response from the PDE, the fracture-rock matrix connection for pressure and flux constraint, and the well control condition under pressure or flux constraint, for the pressure and flux at all sources representing wells and fracture-rock matrix connections. This is a time-domain solution as the convolution is expressed as a linear operator in a linear system of equations. There are four key behaviors in a multifractured horizontal well which are radial flow inside the fracture, bilinear flow, linear flow inside the rock matrix, and radial flow inside the rock matrix. For multiple wells intersecting the same fractures, the superimposed response from both producer and injector creates a constant pressure boundary on a line of symmetry at late time with negative one slope. Depending on fracture conductivity, the pressure transient solution can vary from hydraulically connected mainly through the rock matrix to hydraulically connected mainly through the fractures. Moreover, we showed that the flux contribution, a proportion of fluid flow between injector and producer through fractures or the rock matrix, is directly correlate to fracture conductivity. This is essential for heat transfer as it is indicative of whether the multifractured enhanced geothermal system is conductive or convective. Finally, the one-month circulation test in the Utah FORGE project, a multifractured enhance geothermal system with one producer and one injector, was interpreted. From pressure transient analysis, we discovered a radial flow inside fractures behavior with a product of fracture permeability and fracture aperture in the range of 501.78 to 2336.56 md-ft. Due to the limited duration transient of less than 20 hours, there are no clear indications of bilinear flow, linear flow inside rock matrix, radial flow inside the rock matrix, or constant pressure boundary. Nevertheless, we could still reconstruct pressure and rate transient responses from a simplified injection rate history and constant pressure-controlled production that resemble actual measurement.