Temperature Behavior During Multistage Fracture Treatments in Horizontal Wells

Downhole temperature measured by distributed-temperature sensors (DTSs) shows distinct response to injection and shut-in during multistage fracture treatments in horizontal wells. A thermal model predicting temperature distribution along the wellbore is essential to use the DTS technology to quantitatively diagnose fracture treatments. 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 predicts temperature distribution in a system that contains reservoir, wellbore, and fractures during fracture propagation and after well shut-in. 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 models, which are derived from the energy-conservation equations. A sequential simulation method is then applied for multistage fracture treatments by considering the treatment schedule. The full model has three modes: no fracture, fracture propagation, and warm back for shut-in. The full model is used to simulate the stage that is under fracturing. Once the fracture pumping is finished, warm back of the entrained fracture fluid during shut-in periods is simulated by removing the convection term and implementing the corresponding boundary conditions. Numerical solutions are necessary for time-dependent fluid loss and complex nonlinear heat exchange. Mass- and energy-conservation equations are solved by use of the fully implicit finite-difference approach for the conjoint 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 by use of the integrated model. The influences of fluid distribution, fluid loss caused by natural and induced fractures, DTS-deployment locations, and reservoir-heat-transfer parameters on temperature behavior are investigated. At the creation and propagation of fractures, injection flow rate (convection) plays an important role on fracture propagation and leakoff front movements. Heat conduction is the dominant mechanism governing temperature response during shut-in. By use of the algorithm for single-stage treatment, a work flow for multistage fracture simulation is created by performing a single-stage stimulation, shutting in the stage, and moving to the next stage along the wellbore. For a shale reservoir, the time frame to reach thermal equilibrium is on the order of weeks, and this gives the possibility to identify the flow-rate distribution from temperature measurements. Sensitivity of fluid distribution, fluid loss, DTS fiber-cable locations for different completion methods, and reservoir parameters is examined, which helps us to understand temperature behavior for fracture diagnosis by use of DTS data during stimulation operations. The methodology developed in this work can be a complementary component to a model that predicts temperature behavior during production to provide better boundary conditions, and it can also be a standalone tool to analyze fracturing-fluid distribution.