Study of the Heat Transfer in the Wellbore During Acid/Hydraulic Fracturing Using a Semianalytical Transient Model

Bottomhole-temperature variations have a significant influence on the rheological properties of fracturing fluid and the reaction rates of rock and acid in the operations of acid/hydraulic fracturing. In this work, a semianalytical model is developed for calculating the heat transfer in a wellbore under transient state. In the model, transient heat conduction in the cement sheath and forced convection in the tubing under different flow regimes are considered. Also in this model, calculation methods of heat-transfer coefficients of forced convection in the tubing and natural convection in the annulus are improved in relation to the existing methods. The semianalytical model is verified by monitoring the data of acid and hydraulic fracturing; it is accurate enough to estimate the physical properties of the fracturing fluid and perform simulations in the reservoirs. We studied transient heat conduction in a cement sheath, the influence of flow regimes on tubing, the variation of thermal properties in the wellbore, and the influence of vertical variations of rock type. Simulation results show that the influence of different heat-transfer states of the cement sheath on bottomhole temperature is much more significant under the injection rate of fracturing. Laminar flow is activated by extremely low injection velocity or low temperature in shallow layers. However, such low velocity can never be attained in the fracturing operation. Also, the high heat resistance caused by laminar flow in shallow layers cannot affect the bottomhole temperature significantly because of the low temperature difference between fracturing fluid and formation rock. We also found that the complex vertical variation of rock type and shale and sandstone interbedding could be approximated by the average temperature of simple models that are computationally faster and have an acceptable range of errors.