390 水动力学研究与进展 2002年第3期 4结论 通过本文的研究我们可以得到以下的结论 (I)可以用解析或半解析(Laplace变换及Laplace数值反变换)方法给出多孔介质中的 热传导问题的解，但时间较小(to≤D)时Laplace数值反变换得到的结果不准确； (2)研究多孔介质地层温度分布可以忽略垂直方向的热传导： (3)流量是影响多孔介质地层温度分布及井筒温度最主要的参数，因此，可以通过分析 井筒中温度随深度的变化曲线或产层处的温度随时间变化的曲线来反求注入（或产出）流量 以及地层热力学参数 参考文献 [I IESSEM L.B et al.A method of cakulating the distribution of temperature in flowing gasw.Trans..AMME 19572(10):169172. MOS J T.et a.How to temperature proiles in a water injection wel.Oil &GaJ..1959.57(11) 7年178 4.m.196144:427-435 A and PA MA 1981 5102 11 10013 Analytical solution of temperature in wellbore and formation in multi-laver LU De-tang,ZENG Yi-shan,GUO Yong-cun (University of Science and Technokgy of China.Hefei 230026.China) The mathematical model for wellbore and fom tod in muti-lacer The ed as lay s.The Laplace tained in both the Lplace and real spaces Key words: 1994-2016 China Academic Joural Electronic Publishing House.All rights reserved.http://www 4 结论 通过本文的研究我们可以得到以下的结论 (1) 可以用解析或半解析 (Laplace 变换及 Laplace 数值反变换)方法给出多孔介质中的 热传导问题的解 ,但时间较小 (tD ≤zD )时 Laplace 数值反变换得到的结果不准确 ; (2) 研究多孔介质地层温度分布可以忽略垂直方向的热传导 ; (3) 流量是影响多孔介质地层温度分布及井筒温度最主要的参数 , 因此 ,可以通过分析 井筒中温度随深度的变化曲线或产层处的温度随时间变化的曲线来反求注入 (或产出)流量 以及地层热力学参数 。 参 考 文 献 : [ 1] LESSEM L B, et al.A method of calculating the distribution of temperature in flowing gas wells[ J] .Trans., AIME, 1957, 2(10):169-172 . [ 2] MOSS J T, et al .How to calculate temperature profiles in a water injection well[ J] .Oil &Gas J ., 1959 , 57(11): 174-178. [ 3] RAMEY H J JR.Wellbore heat transmission[ J] .JPT , 1962, 14(4):427-435 . [ 4] BARELLI A and PALAMA A.A new method for evaluation formation equilibrium temperature in holes during drilling [ J] .Geothermics, 1981, 14(4):95-102 . [ 5] WOOLEY G R.Computing downhole temperatures in circulation , injection, and production wells[ J] .JPT, 1980 , 32 (12):1509-1522. [ 6] STEHFEST H .Numerical inversion of Laplace transforms[ J] .ACM, Communications, 1970, 13(1):47-49 . Analytical solution of temperature in wellbore and formation in multi-layer LU De-tang , ZENG Yi-shan , GUO Yong-cun (University of Science and Technology of China , Hefei 230026 ,China) Abstract: The mathematical model for wellbore and formations heat transmission were presented in multi-layer.The vertical non-homogeneous formations were approximated as layed formations with different physical properties.The Laplace transformation was used to the dimensionless equations of heat transmission.The closed-form analytical solutions were ob￾tained in both the Laplace and real spaces. Key words : dimensionless temperature ;multi-porous ;heat transmission ;Laplace transformation ; analytical inversion of Laplace transforms 390 水 动 力 学 研 究 与 进 展 2002 年第 3 期