基于双层非稳态导热过程的井筒温度场半解析模型

A semi-analytic model of wellbore temperature field based on double-layer unsteady heat conducting process

在油气井酸化、压裂增产施工中,温度控制着入井工作液的流变性和酸岩反应速度,是影响裂缝几何形态、酸蚀导流能力和措施后产能的重要因素。但目前的井筒温度场模型还缺乏对非稳态过程的严密推导和精确描述。为此,首先在物性分析的基础上,建立了轴向上离散、径向上解析的双层非稳态导热井筒温度场半解析模型,并通过拉普拉斯变换和Stehfest数值反演方法进行了求解;其次,分析了不同水泥环导热过程处理方法对井筒温度分布的影响,认为假设水泥环具有稳态热阻,模拟输出的误差过大且难以修正;最后,对地层和施工参数进行了敏感性分析,认为岩性、施工排量和注入温度变化对井筒温度分布具有显著的影响,而油管腐蚀的影响则可以忽略。现场实际应用效果表明,该数学模型精度较高,模拟结果与监测结果吻合良好。该成果对于提高单井酸化压裂成功率、增加措施后的产能和油气田采收率具有重要意义。

In the process of well acidizing and fracturing, downhole working fluid rheology and acid-rock reaction rate are controlled by temperature, which is an important factor affecting fracture geometry, acid etching conductivity and stimulated productivity. At present, however, the well bore temperature field model lacks strict deduction and fine description of the unsteady process. In this paper, a semianalytic model was established for temperature field of double-layer （axial discretion and radial analysis） unsteady heat conducting wellbores and solved by means of Laplace transformation and Steh lest numerical inversion. Then, analysis was conducted of the effect on wellbore temperature distribution by cement-sheath heat conducting treatment methods. It is believed that the errors of analog outputs are too large to be corrected when cement sheath is assumed to have steady state thermal resistance. Finally, sensitivity analysis was performed on formation and operation parameters. It is regarded that wellbore temperature distribution is remarkably influenced by lithological change, operational discharge capacity and injection temperature, but the effect of tubing corrosion can be neglected. Field application shows that this mathematical model is higher in precision and the simulation results fit monitoring results. Therefore, this research result is of great importance in increasing the success ratio of single-well acid fracturing and improving productivity and recovery factor after stimulation.