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首页> 外文期刊>International Journal of Heat and Mass Transfer >Heat flow rate at a bore-face and temperature in the multi-layer media surrounding a borehole
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Heat flow rate at a bore-face and temperature in the multi-layer media surrounding a borehole

机译：钻孔表面的热流量和钻孔周围多层介质中的温度

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摘要

Assessment of the heat either delivered from high temperature rocks to the borehole or transmitted to the rock formation from circulating fluid is of crucial importance for a number of technological processes related to borehole drilling and exploitation. Normally the temperature fields in the well and surrounding rocks are calculated numerically by finite difference method or analytically by applying the Laplace-transform method. The former approach requires tedious and, in certain cases, non-trivial numerical computations. The latter method leads to rather bulky formulae that are inconvenient for further numerical evaluation. Moreover, in previous studies where the solution is obtained analytically, the heat interaction of the circulating fluid with the formation was treated on the condition of constant bore-face temperature. In the present study the temperature field in the rock formation disturbed by the heat flow from the borehole is modeled by a heat conduction equation, assuming the Newton model for the convective heat transfer on the bore-face, with boundary conditions that account for the thermal history of the borehole exploitation. The problem is solved analytically by the generalized heat balance integral method. Within this method the approximate solution of the heat conduction problem is sought in the form of a finite sum of functions that belong to a complete set of linearly independent functions defined at the finite interval bounded by the radius of thermal influence and that satisfy the homogeneous boundary conditions on the bore-face. In the present study first and second order approximations are obtained for the composite multi-layer domain. The numerical results illustrate that the second approximation is in a good agreement with the exact solution. The only disadvantage of this solution is that it depends on the radius of thermal influence, which is an implicit function of time and can only be found numerically by iterative algorithms. In order to eliminate this complication, in this study an approximate explicit formula for the radius of thermal influence and new close-form approximate solution are proposed on the basis of the approximate solution obtained by the integral-balance method. Employing the non-liner regression method the coefficients for this simplified solution are obtained. The accuracy of the approximate solution is validated by comparison with the exact analytical solution found by Carslaw and Jaeger for the homogeneous domain.
机译：评估从高温岩石传递到井眼或从循环流体传递到岩层的热量对于与井眼钻探和开采相关的许多技术过程至关重要。通常情况下，井和围岩中的温度场通过有限差分法进行数值计算，或者通过应用拉普拉斯变换法进行分析。前一种方法要求乏味，并且在某些情况下需要非平凡的数值计算。后一种方法导致相当庞大的公式，不便于进行进一步的数值评估。此外，在以前的研究中，通过解析获得溶液，在恒定的井壁温度条件下处理了循环流体与地层的热相互作用。在本研究中，假设井壁对流传热采用牛顿模型，且边界条件考虑了热量，因此通过热传导方程来模拟受井眼热流干扰的岩层温度场。钻孔开采历史。通过广义热平衡积分法解析地解决了该问题。在这种方法中，以有限函数之和的形式寻求热传导问题的近似解，这些函数属于以热影响半径为边界的有限区间内定义的，完全独立的线性独立函数集，并且满足齐次边界孔面上的条件。在本研究中，获得了复合多层结构域的一阶和二阶近似值。数值结果表明，第二近似值与精确解非常吻合。该解决方案的唯一缺点是，它取决于热影响半径，它是时间的隐式函数，只能通过迭代算法在数值上找到。为了消除这种复杂性，本研究在积分平衡法获得的近似解的基础上，提出了热影响半径的近似显式公式和新的闭式近似解。使用非线性回归方法，可以获得该简化解的系数。通过与Carslaw和Jaeger针对齐次域找到的精确解析解进行比较，验证了近似解的准确性。

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