压裂过程中瞬态井简-地层耦合温度场半解析模型

压裂过程中,井筒温度的变化会影响压裂液到达井底时的流变性以及在地层中的滤失性,准确预测井筒及地层温度分布可以指导施工方案的设计.关于压裂过程井筒温度场的研究主要集中在数值模型方面,目前还没有合适的解析模型.文中在Hasan采气井筒瞬态传热解析模型的基础上建立了压裂过程井筒瞬态传热方程,通过Laplace变换进行求解,消除了Hasan采用稳态假设求解温度梯度所引起的高排量时的误差,使之能够准确地模拟压裂过程的瞬态井筒温度.通过与Hasan模型和数值模型的对比,验证了该方程的准确性.结果显示,在相同精度下Hasan模型计算效率远高于数值模型.之后,通过将井筒瞬态解析解与地层二维瞬态传热数值解结合,建立了压裂过程瞬态井筒-地层耦合温度场半解析模型,并应用该模型分析了排量及注入温度对压裂井筒-地层温度场的影响.

Transient semi-analytic model for wellbore-formation temperature of fracturing management

The rheological and filtration properties of the fracturing fluid could be affected heavily by the variation of the wellbore temperature during fracturing.Accurate prediction of wellbore and formation temperature can be used to guide the scheme of fracturing.Nowadays,the research is focused on the numerical aspects and there is still a lack of an appropriate transient analytical method to model the temperature variation of the fracturing process.In this paper,a transient heat transferring model for production process established by Hasan was modified into a model for fracturing process.And the Laplace method is used here to solve the model,which eliminates the error of the Hasan's model in light of the removal of the steady assumption when solving the gradient of temperature.The validation of the model is verified by comparing Hasan's model with numerical model.The results also show that the efficiency of our model is much better than numerical method under the same accuracy.A semi-analytical temperature prediction model for fracturing process is established based on our wellbore analytical model and two-dimensional transient heat transfer equation of formation.Then the effects of the injection rate,injection temperature and thermal-storage parameter on the temperatures of wellbore and formations are analyzed by the semi-analytical model.