井筒与地层非稳态换热数值计算方法

NUMERICAL CALCULATION METHOD OF TRANSIENT HEAT TRANSFER BETWEEN BOREHOLE AND FORMATION

在计算井筒与地层换热时,常规非稳态换热公式由于假设了井筒温度不发生变化,计算结果与实际情况有较大误差。考虑到井筒温度变化,提出了一种井筒与地层非稳态———瞬态换热的数值计算方法。该方法先由能量平衡方程、初始条件和边界条件建立数学模型,再引入无因次量进行无因次化,从而得到井筒与地层换热的微分方程。然而由于井口压力等参数发生变化,井筒温度也随之不断发生变化,使该微分方程不能直接运用。文中先将时间离散,分别求解出每一时间段内地层与井筒的热交换量,然后采用叠加原理得到热交换总量。经实例验证,该方法得出的解与实际测试结果能很好吻合。

It is assumed the borehole temperature is a constant in the conventional transient heat transfer formula when calculating the heat transfer between borehole and formation. So the calculating results have big errors comparing with the real cases. Considering the variation of the borehole temperature, a numerical calculation method of transient heat transfer between borehole and formation is developed. At firstt the method will establish the mathematical model according to the energy balance equation, the original conditions and the boundary conditions. Then the model is simplified with dimensionless parameters to derive the differential equation of heat transfer between borehole and formation. But the differential equation can't be used directly because the borehole temperature will change constantly due to the parameters such as wellhead pressure etc. change. Therefore, the time is segmented into several small intervals first. Then the heat transfer between borehole and formation is calculated for every interval respectively. With stack principle, the total heat transfer between borehole and formation is obtained. With real cases to verify, the results obtained from the method can couple with the really measured results very well, which provides more reliable basis to take proper measures for the jobs of well drilling, completion and stimulation etc.