Downhole temperature measured by distributed temperature sensors (DTS) shows distinct response to injection and shut-in during a multi-stage fracture treatment in horizontal wells. A thermal model predicting temperature distribution along the wellbore is essential to use the technology quantitatively diagnose the treatment. With inversion, the model can be used to translate downhole temperature measurement to downhole flow distribution, and therefore to estimate fracture efficiency.
In this paper, we present a thermal/flow model that predict temperature distribution in a system that contains reservoir, wellbore, and fractures during fracture propagation and after shut-in the well. We coupled a wellbore flow model with a simple fracture propagation model to predict fracture half-length, and fluid distribution. For a single-stage fracture treatment, a transient wellbore thermal model is coupled with the fracture and formation thermal model, which are based on the energy conservation equation. A sequential simulation method is then applied for multi-stage fracture treatments by introducing a time control factor. Warm back of the entrained fracture fluid during shut-in periods is simulated while other stages are run by removing the fluid injection term and implementing corresponding boundary conditions. Numerical solutions are necessary for time dependent fluid-loss and complex non-linear heat exchange. Mass and energy conservation equations are solved by fully implicit finite difference approach for the conjointly gridding system. The results of the fracture and formation model are verified by analytical solutions for simplified cases.
This paper provides synthetic case studies in a low-permeability reservoir using the integrated model. The influences of fluid distribution, fluid-loss due to natural and induced fractures, DTS deployment locations, and reservoir heat transfer parameters on temperature behavior are investigated for single-stage fracture treatment. At initiating and propagating of fractures, injection flowrate plays an important role on fracture half-length and leak-off front movements. Heat conduction is the dominant mechanism governing temperature response during shut-in. Using the algorithm for single-stage treatment, a work flow for multi-stage fracture simulation is created by performing a single-stage stimulation, shutting in the stage, and moving to the next stage along the wellbore. Large temperature signal change occurred at fractured locations during the injection period, and warm back behavior is observed after shut-in of the well due to the large temperature difference between the injection fluid and the formation. For a shale reservoir, the time scale to reach thermal equilibrium is on the order of weeks. Observed sensitivity to fluid distribution, fluid-loss, DTS fiber cable locations, and reservoir parameters in proposed examples allow for fracture diagnosis using distributed temperature data during stimulation operations.
The methodology can be a complimentary component to a model that predict temperature behavior during production to provide better boundary condition, and it can also be a stand-alone tool to analyze fracture injection fluid distribution.