New model of Single-Well Push-Pull thermal test in a Fracture-Matrix system

Single-well push pull (SWPP) thermal tests have been widely used to characterize fracture-matrix systems for storing and/or exploring geothermal energy. Two important assumptions in previous mathematical models of the SWPP thermal test are found to be problematic: the thermal mixing effect in the wellbore is ignored and the fracture thermal conductance is omitted. These two assumptions are not correct in many applications and have to be revoked. Meanwhile, solutions associated with previous three-stage (injection, resting and extraction) models of SWPP tests are computationally very expensive to obtain and need improvement for practical usage. In this study, a new three-stage model is developed considering both the wellbore thermal mixing effect and the fracture thermal conductance, and an analytical solution has been developed using Laplace transform method and Green's function method. To test the new model, a high-resolution finite-difference numerical solution is established, and the results show that the analytical and numerical solutions agree with each other very well. Comparing with previous three-stage analytical solution, the computational cost is much less for the new solution of this study. We find that breakthrough curves (BTCs) in the wellbore for the extraction stage are not only dependent on the values of the injecting and pumping rates, but also on the ratio between them. The new model is most sensitive to fracture aperture, and least sensitive to flow velocity in the fracture. The previous models of ignoring the thermal mixing effect and/or the fracture thermal conductance may cause great errors and should be avoided.