超深井井筒温度数值模型与解析模型计算精度对比研究

A Comparative Study on the Calculation Accuracy of Numerical and Analytical Models for Wellbore Temperature in Ultra-Deep Wells

准确预测钻井过程中的井筒温度是科学评价井筒中流体流动安全与压力控制的关键。为此,基于井筒–地层各区域能量守恒原理,建立了井筒–地层传热数值模型和井筒–地层传热解析模型,分别用全隐式有限差分法和解析法对数学模型进行了求解;并结合顺北油田某超深井井身结构与钻井参数,从传热机理上分析了2种模型的井筒温度计算精度及其影响因素。分析认为:钻进时,下部井段环空流体温度低于原始地温,而上部井段流体高于原始地温;解析模型应用简化的无因次时间函数表示从远处地层传至近井壁的拟稳态热交换方式,并用综合传热系数表征地层–环空、环空–钻柱内总的热交换量,减少了井筒与地层间的热交换量,导致其计算出的环空和钻柱内流体温度低于数值模型。研究结果表明,数值模型计算结果与实测值吻合程度高,数值模型和解析模型的计算误差分别为1.46%和6.94%,两者计算结果差值为13.15℃。研究结果为深入认识钻进中井筒-地层传热机理和准确评价温度场提供了理论依据。

The accurate prediction of wellbore temperature during drilling is the key factor in the scientific evaluation of wellbore fluid flow safety and pressure control.Therefore,based on the principle of energy conservation between wellbore and formation in each area,the numerical and analytical models for wellbore-formation heat transfer were built.The fully implicit finite difference method and the analytical method were adopted to solve the mathematical models,respectively.Given the wellbore structure and drilling parameters of an ultra-deep well in Shunbei Oilfield,calculation accuracy of the above two models on the calculation results and the influencing factors were analyzed from the aspect of the heat transfer mechanism.The analysis showed that during drilling,the annular fluid temperature in the lower well section was lower than the original ground temperature,while the fluid temperature in the upper well section was higher than it.In the analytical model,a simplified dimensionless time function was used to represent the quasi-steady state heat exchange mode from distant formations to near well walls,and the comprehensive heat transfer coefficient was employed to characterize the total heat exchange between the formation and annulus,and between the annulus and the interior of the drill string.As a result,the wellbore-formation heat exchange was reduced,and thus the calculated fluid temperature in the annulus and drill string was lower than the result from numerical simulations.The results revealed that the calculated results of the heat transfer model were highly consistent with the downhole measurements,while the errors of the numerical solution and analytical solution were 1.46%and 6.94%,respectively,with a difference of 13.15℃.The research results provide a theoretical basis for an in-depth understanding of the wellbore-formation heat transfer mechanism and the accurate evaluation of the temperature field during drilling.