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The Application of Stefan Problem in Calculating the Lateral Movement of Steam Chamber in SAGD

机译：Stefan问题在计算SAGD蒸汽室横向运动中的应用

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摘要

It is extremely important to monitor the development of steam chambers in reservoirs in the process of SAGD (Steam Assisted Gravity Drainage). By analyzing the temperature data of monitoring wells, the extending velocity and direction of steam chamber can be obtained, which helps to regulate and improve production effectively. Based on Stefan's inverse problem, a mathematical model is established in this paper for acquiring the extending velocity of steam chamber by using the temperature data of monitoring wells. Mathematical methods are utilized to solve the model such as Fourier transformation as well as an analytic solution using the moving velocity of steam chamber's edges. Finally, sensitivity analyses concerning some factors such as the formation heat transfer coefficient, the temperature of steam chamber, and the rate of temperature rise of monitoring wells are made. Field application showed that the model can be used to calculate the moving velocity in real time and determine the boundary scope of the steam chambers easily.
机译：在SAGD（蒸汽辅助重力排水）过程中，监测储层中蒸汽室的发育极为重要。通过对监测井的温度数据进行分析，可以获得蒸汽室的延伸速度和方向，有助于有效调节和提高产量。基于Stefan的反问题，建立了一个数学模型，通过利用监测井的温度数据来获取蒸汽室的扩展速度。利用数学方法来求解模型，例如傅立叶变换以及使用蒸汽室边缘的移动速度的解析解。最后，对地层传热系数，蒸汽室温度，监测井温升率等因素进行了敏感性分析。现场应用表明，该模型可用于实时计算运动速度并容易确定蒸汽室的边界范围。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第18期|372581.1-372581.11|共11页
  • 作者

    Chen Xiong; Nie Ren-Shi; Jia Yong-Lu; Sang Lin-Xiang;

  • 作者单位

    Southwest Petr Univ, State Key Lab Oil & Gas Reservoir Geol & Exploita, Chengdu 610500, Sichuan, Peoples R China.;

    Southwest Petr Univ, State Key Lab Oil & Gas Reservoir Geol & Exploita, Chengdu 610500, Sichuan, Peoples R China.;

    Southwest Petr Univ, State Key Lab Oil & Gas Reservoir Geol & Exploita, Chengdu 610500, Sichuan, Peoples R China.;

    Chinese Petr Corp, Feng Cheng Oilfield Operat, Karamay 834000, Xinjiang, Peoples R China.;

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