Downhole-temperature measurement is one of the solutions to understanding downhole-flow conditions, especially in complex well/reservoir domains such as multistage-fractured horizontal wells. In the past, models and methodologies have been developed for fracture diagnosis for multiple-stage-fractured horizontal wells. They are based either on a semianalytical approach for simplicity or on reservoir simulation for generality. The challenges are that semianalytical models are not robust enough to describe complex fracture systems, whereas numerical simulation is computationally expensive and impractical for inversion. To develop a comprehensive approach to translate temperature to flow profile, we adopted the fast marching method (FMM) in simulating both heat transfer and the velocity/pressure field in the interested domain (heterogeneous reservoir with multiple-fractured horizontal wells). FMM is a new approach that is efficient in front tracking. Previous studies show a significant success in the investigation of pressure-depletion behavior and shale-gas production-history match. By the nature of heat transfer in porous media, the thermal-front propagation would lag behind pressure, and the noticeable temperature change in the reservoir only happens near hydraulic/natural fractures. FMM can be used to efficiently track the heat front that is associated with the flow field.
In this study, we solve the thermal model in porous media by transforming the general energy-balance equation into a 1D equation, with the diffusive time of flight (DTOF) as the spatial coordinate system. Besides the diffusive heat conduction, the convection, Joule-Thomson effect, and viscous dissipation are considered in the model. The inner boundary of the model is carefully handled, and the drainage volume of each fracture is calculated to identify different inflow temperature related to flow rate at perforation locations. The model was validated by the finite-difference approach. Examples are presented in the paper to illustrate the application of the new method. The approach can be used to quantitatively interpret temperature measurements to fracture profiles in horizontal wells.