Downhole temperature measurements is one of the solutions to understand downhole flow conditions, especially in complex well/reservoir domains such as multi-stage fractured horizontal wells. In the past, models and methodologies have been developed for fracture diagnosis for multiple-stage fractured horizontal wells. They are based on either semi-analytical approach for simplicity or reservoir simulation for generality. The challenges are that semi-analytical models are not robust enough to describe complex fracture systems, while numerical simulation is computationally expensive and impractical for routine inversion. To develop a comprehensive approach to translate temperature to flow profile, we adopted Fast Marching Method in simulating both heat transfer and velocity/pressure field in the domain of interest (heterogeneous reservoir with multiple fractured horizontal wells). Fast Marching Method (FMM) is a relatively new approach which 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 reservoir only happens near hydraulic/natural fractures. FMM can be used to efficiently track the heat front that is associated with flow field.
In this study, we solve the thermal model in porous media by transforming the general energy balance equation into a 1-D equation with a ‘diffusive time of flight’ as the spatial coordinate system. Besides the diffusive heatpropagation, Joule-Thomson effect and viscous dissipation are also 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 a 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.