A heat loss analytical model for the thermal front displacement in naturally fractured reservoirs

• A model for the injection of cold water into a naturally fractured reservoir (NFR).
• The NFR is modeled as two interconnected homogeneous systems, matrix and fracture.
• Heat and mass balances are established for the water flow in the NFR.
• Solutions for thermal and non thermal equilibrium between the water and the rock.
• Type-curves are presented for the rate of advance of the thermal front.

A theoretical study of the injection of separated cold water into naturally fractured hot geothermal reservoir rock is presented. The hot geothermal reservoir is assumed to be initially at a uniform temperature. The fractured system is modeled as two interconnected homogeneous systems, one for the matrix and the other for the fractures. Heat and mass balances are established for the interconnected system, when the cold injected fluid travels through the fractures in close contact with a hot matrix. Solutions to this problem are presented for two cases: one in which instantaneous thermal equilibrium takes place between the injected cold fluid and the rock, and the second considers a non equilibrium thermal condition, for which solutions are derived for the cases when heat transfer occurs under pseudo-steady state and transient conditions. Heat interchange with underlying and overlying impermeable formations is also considered. Type-curves are presented for the rate of advance of the thermal front with dimensionless injection time. A sensitivity analysis was performed to investigate the effect of several parameters on the rate of advance of the thermal front.