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本文基于井筒与地层间能量平衡原理,将井筒钻井液划分成不同径向单元网格,建立了考虑径向温度梯度条件下钻井液层间温度模型;同时引入钻井液轴向导热项,建立了钻井液轴向导热温度模型,将数学模型应用隐式有限差分法离散与求解.计算结果表明:钻井液径向温度梯度对井筒径向与轴向温度产生的误差分别为0.15℃和0.2℃左右;而钻井液轴向导热对井筒温度分布几乎不产生影响.因此,通过建立的数学模型进行系统分析表明,在建立井筒-地层耦合瞬态传热模型时可忽略两者对井筒温度分布的影响.基于数学建模方法验证了以前学者模型假设条件的正确性,为油气井与地热井井下温度分布规律深入研究奠定了可靠的理论基础.
Based on the principle of energy balance between wellbore and formation, this paper divides the wellbore drilling fluid into different radial unit grids, and establishes the interlayer temperature model of drilling fluid considering the radial temperature gradient. At the same time, the axial thermal conductivity of drilling fluid is introduced to establish The axial thermal conductivity model of drilling fluid is established and the mathematical model is discretized and solved by implicit finite difference method.The calculated results show that the error of the radial temperature gradient of drilling fluid on the radial and axial temperature of the wellbore is 0.15 ℃ and 0.2 ℃ respectively , And the axial thermal conductivity of the drilling fluid has little influence on the wellbore temperature distribution.Accordingly, the system analysis through the established mathematical model shows that when the wellbore-formation coupling transient heat transfer model is established, the difference between the wellbore temperature distribution The correctness of the assumptions of the previous scholar model is verified based on the mathematical modeling method, which lays a solid theoretical foundation for further research on the temperature distribution rules of oil and gas wells and geothermal wells.