花岗岩单裂隙渗流传热特性试验

基于岩石裂隙渗流传热试验系统,以蒸馏水为换热工质,针对预制平滑裂隙与粗糙裂隙的花岗岩岩样,开展不同试验温度与水流条件下的单裂隙对流换热特性试验研究。试验结果表明：①同一温度水平下,对流换热系数的量值与流量呈正相关关系,但对流换热系数的增幅大于流量的增幅,随岩石基质温度的升高,相同流量水平下的对流换热系数呈增大趋势;②与平滑裂隙试验结果相比,粗糙裂隙面的对流换热强度有所提高,但增幅不大;③沿渗流路径,裂隙面局部对流换热强度的演化呈现多波峰的非线性特征,其中粗糙裂隙的非线性更加强烈。但二者均存在由进水口至出水口,换热强度逐渐减弱的特征。④努塞尔数与普朗特数1/3次方的商与雷诺数较好地满足幂指数关系,随着试验温度的升高,这种关系逐渐向线性转变。     

Application of the Fourier method to the numerical solution of moving boundary problem in heat conduction

An algorithm for the solution of a nonlinear problem of phase boundary movement and evolution of temperature distribution due to the perturbation in the basal heat flux has been discussed. The reduction of the problem to a system of nonlinear ordinary differential equations with the help of a Fourier series method leads to a stiff system. This stiffness is taken care of by the use of a modified Euler’s method. Various cases of basal heat flow variation have been considered to show the performance and stability of the technique for such a nonlinear system. The first case of step-wise function is taken to analyse the performance of the technique, and the study has been extended to other general cases of linear increase, periodic variation, and box and triangular function type variations in the heat flux. In the step-wise case the phase boundary attains a constant position rapidly if the supplied heat flux is sufficiently large. The effect of periodicity in the heat flow is clearly depicted in the phase boundary movement, where the phase boundary oscillates about the mean position at large times. The absence of any constant level in the case of linear increase in heat flux is due to a very large value of heat flux. In the cases of box car and triangular heat flux the boundary starts moving downward after the cessation of excess heat flux but does not immediately return to its original preperturbation state, instead approaches it at large times. This technique may be applied to more general cases of heat flow variation.     

胶东半岛不同构造单元深部热流分流聚热模式

中生代、新生代时期地壳剧烈运动将胶东半岛划分为胶北隆起、胶莱凹陷、胶南-威海隆起三大构造单元,其中隆起山地区广泛分布花岗岩、变质岩,凹陷盆地区主要分布砂岩沉积地层,胶北隆起区与威海隆起区相对于胶莱凹陷盆地区具有更高的大地热流值.为系统分析胶东半岛大地热流值分布特征及其形成机理,本文在分析胶东半岛构造-热发展史、地热地质背景、地温场分布、岩石热导率、钻孔岩性与测温数据、地热流体化学成分等基础上,发现胶东半岛地热资源均为断裂构造控制类型的中低温对流型,其热源主要为三元聚热:导热断裂带水热对流、大地热流传导、地下水运移传导-对流;构造分布、岩石热物性、地热热储分布、地下水活动等是影响地温场分布的主要因素.针对胶东半岛地温场特征及其控制因素,提出了适合该地区的隆起-凹陷分流聚热模式与概念模型,即隆起山地区岩性以导热率、渗透率相对较高的侵入岩、变质岩为主,凹陷盆地区岩性以导热率、渗透率相对较低的砂岩为主,低导热率、低渗透率的凹陷区底部更像是一个相对隔热、隔水的顶板,使得来自地壳深部的大地热流及携带热量的流体、气体等在上涌的过程中在凹陷区的底部发生折射与再分配,从而导致热流在隆起山地区的底部形成一个温度相对更高的聚热区,反映在地表即是隆起山地区相对凹陷盆地区具有更高的大地热流值,特别隆起山地区轴部位置为热流值最高的区域,高热流值区域分布形态呈NE、NNE向分布,基本与胶东半岛NE、NNE向的深大断裂走向一致,该模式的提出可以更好地为胶东地区的地热资源勘探提供指导方向.     

On the heat transfer coefficient between rock fracture walls and flowing fluid

Two analytical solutions are derived to model the heated flow-through experiments for granite fractures in the literature. The first model, which assumes an identical/continuous temperature between the bulk fluid and fracture surfaces, represents an upper bound solution of water temperature in rock fractures. The second model including the empirical parameter of heat transfer coefficient is used to calculate the average heat transfer coefficient based on the available experimental data. The obtained heat transfer coefficients are smaller than that from the thermal boundary layer theory for flat plates, but larger than the previous estimates. A power function is fitted to describe the relation between heat transfer coefficient and flow velocity. Both models show that water temperature increases non-linearly along fracture plane.     

Role of radiogenic heat generation in surface heat flow formation

Heat generation due to decay of long-lived radioactive isotopes is considered in the Earth’s crust of the Archean–Proterozoic and Paleozoic provinces of Eurasia and North America. The heat flow that forms in the mantle is calculated as the difference between the heat flow observed at the boundary of the solid Earth and radiogenic heat flow produced in the crust. The heat regime in regions with anomalously high radiogenic heat generation is discussed. The relationship between various heat flow components in the Precambrian and Phanerozoic provinces has been comparatively analyzed, and the role of erosion of the surfaceheat- generating layer has been estimated.     

分布热源作用下单裂隙岩体三维水流-传热的半解析计算方法

针对高放射性核废物地下处置库近场饱和裂隙岩体环境,提出一种由分布热源、饱和单裂隙和两侧无限大岩石构成的三维水流-传热简化模型,建立了控制微分方程和基于拉氏变换域格林函数的积分方程;采用矩形单元把裂隙面域离散化,利用极坐标下的解析方法计算包含奇点的单元积分,利用数值方法计算分布热源和不包含奇点的单元积分,建立拉氏变换域的线性代数方程组,求解后,利用拉氏数值逆变换,计算任意时刻裂隙水和岩石的温度分布。对两个无内热源、流场确定的计算模型进行了计算,与仅考虑岩石沿裂隙面法向一维热传导的解析解进行了对比。计算分析了分布热源作用下饱和单裂隙岩体的三维水流-传热特征及其对裂隙水流速、岩石热传导系数和热源热流集度的敏感度。计算结果表明：与直接采用高斯数值积分相比,提出的解析法奇异积分精度较高;就裂隙水温度而言,单裂隙岩体三维水流-传热半解析计算方法与解析法得到的结果基本一致,但由于半解析计算方法考虑了岩石的三维热传导,使得裂隙水的上游温度较低,而下游温度较高;无分布热源作用时,岩石热传导系数越大,裂隙水温度越低;裂隙水流速越大,裂隙进水温度对裂隙水和岩石温度分布的影响越明显;由于受到裂隙水流动传热的作用,分布热源对裂隙水温度和岩石温度的影响在裂隙水流的下游区域比较显著。     

Estimate of heat flux at the ice-water interface in Lake Baikal from experimental data

An original system for measuring temperature in the ice cover and subglacial water and an increase in the ice thickness provides data necessary for calculation of the heat flux at the ice-water interface. Successive freezing of 1-mm temperature sensors during the ice growth allows us to measure temperature gradients in the vicinities of the ice-water interface for the first time. An analytical equation derived from the Stefan condition allows calculations of the heat flux at the phase boundary on the basis of the experimental data, which agree with independent estimates that have been made on the basis of the subglacial temperature gradients and are within the 4–39 W/m² range. The flow at the ice-water interface is comparable with the heat flux inside the ice depth and significantly affects the dynamics of the ice cover thickness.     

镜质体成烃反应动力学模型的标定及其在热史恢复中的应用

镜质体反射率（Ｒｏ）与其生烃率有关，因此，由Ｒｏ应可求取其生烃率；同时，在求取了镜质体成烃反应动力学参数之后，若已知其受热史，则可计算出镜质体的生烃率；反过来，若已知镜质体的生烃率，应可反推其受热史。基于这一基本原理，本文在建立和标定镜质体成烃反应动力学模型的基础上推导了可将其应用于存在着抬升、剥蚀和古地温非线性变化等复杂地质条件下热史恢复的原理模型，结合海拉尔盆地海参７井的实测Ｒｏ值，有效地恢复了其古热史     

Heat extraction from aquifer geothermal systems

This study aims to model temperature distributions in an aquifer thermal extraction (ATE) system that contains a single extraction well in a thin confined aquifer. The aquifer is bounded by hot dry rocks with different thermomechanical properties and thicknesses. Based on the heat convection–conduction equation, a mathematical model is developed to describe the spatial and temporal temperature distributions of the ATE systems. The mechanisms of heat transfer in the model involve horizontal convection and thermal conduction in the aquifer, and vertical thermal conduction in both rocks. A semi‐analytical solution in dimensionless form is developed using the Laplace transform technique and its corresponding time‐domain result is computed by the modified Crump method. In addition, the steady‐state solution is obtained by applying the final value theorem. The simulation results from the semi‐analytical solution indicate that the aquifer temperature distributions are affected by aquifer thickness, the thermomechanical properties of the aquifer and rocks, geothermal gradient, outer boundary temperatures of the rocks, extraction rate, and operating time. The present solution can be used as a preliminary tool for assessing heat extraction efficiency in ATE systems. Copyright © 2010 John Wiley & Sons, Ltd.     

基于Levenberg-Marquardt算法的填埋场中降解产热参数反演研究

填埋场中垃圾降解产热参数是研究填埋场温度变化及热资源利用的基础。基于室内试验得到的峰值产热模型、填埋场中热传导理论以及Levenberg-Marquardt(LM)算法,提出了填埋场中降解产热参数的反演分析方法。结合填埋场实际工况,建立了填埋场热传导一维模型并得到了温度的解析解。基于某一深度的温度数据,采用LM算法反演得到了填埋场的降解产热参数,采用反演得到的降解产热参数可以计算填埋场任意深度的温度。基于产热参数可以计算得到填埋场的峰值产热速率、峰值产热时间和总产热量。以中国无锡桃花山填埋场和美国密歇根填埋场为例,分别反演得到了降解产热参数,采用反演得到的降解产热参数计算反演点之外测点的温度并与实测值进行对比,验证了反演模型的合理性和适用性。对比发现,与实际填埋场相比,室内试验的降解产热峰值更大,且峰值时间更短。与密歇根填埋场相比,无锡桃花山填埋场的前期产热速率更大,到达降解产热峰值的时间更短。     

Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Presentation of an analytical solution

The thermoelastic response due to a time-dependent rectangular heat source in a semi-infinite medium is analyzed. The problem originates from studies of nuclear waste repositories in rock. Canisters containing heat-emitting nuclear waste are deposited over a large rectangular area deep below the ground surface. The solution for a time-dependent heat source is obtained from the corresponding instantaneous heat source by superposition. The thermoelastic problem for the instantaneous rectangular heat source in a infinite surrounding is solved exactly. An important step is the introduction of so-called quadrantal heat sources. The solution for the rectangle is obtained from four quadrantal solutions. The solution for the quadrantal heat source depends on the three dimelasionless coordinates only. Time occurs in the scale factors only. The condition of zero normal and shear stresses at the ground surface is fulfilled by using a mirror heat source and a boundary solution. The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple solution is obtained. The final analytical solution is quite tractable considering the complexity of the initial problem. The solution may be used to test numerical models for coupled thermoelastic processes. It may also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three-dimensional global process.     

地埋管换热器动态热负荷下地层温度场的解析解

垂直地埋管换热器（borehole heat exchanger,BHE）是利用浅层地热能的主要换热装置,如何确定合理的地埋管间距对地源热泵系统（ground source heat pump system,GSHPs）的传热性能与经济性影响很大。以往工程应用中未考虑地埋管热负荷的动态变化,常采用最大延米热/冷负荷（即最不利情况下）的影响半径作为设计依据,使设计参数趋于保守,很难实现地源热泵系统的技术和经济优化,而考虑负荷变化的数值模拟方法耗时复杂,不便于工程应用。文章提出了一种在地埋管实际热冷负荷动态变化条件下,计算地埋管换热器影响半径的简单数学方法。该法首先推导了地埋管换热器在周期性热流边界条件下,井筒周围地层温度场的解析解,在此基础上将地面建筑物全年周期下的实际波动热冷负荷进行傅里叶级数近似展开,最后通过线性叠加每个周期函数对应的解析解,得到建筑物实际动态热冷负荷下的地层温度动态分布。提出的解析解实时耦合了地面建筑动态热冷负荷,计算结果接近实际应用,具有计算精度高、简单方便快捷的优点,便于在工程实际中推广应用。     

Thermal stresses in borehole heat exchangers

The backfilling materials of borehole heat exchangers (BHE), particularly the grout material, must provide a suitable thermal contact and ensure durability to the induced thermal stresses because of the heat loading. In this paper, the thermal stresses that occurred in BHEs because of heat injection or extraction is investigated with an analytical solution of a hollow cylinder model that is adapted for time‐dependent heat loading, the geometry of a BHE, and the thermo‐mechanical properties of surrounding ground conditions. Firstly, the hollow cylinder model is solved with the considered boundary conditions in 2D plane stress. Secondly, the temperature differences at the inner and outer circles of the cylinder are evaluated with the heat line source models for continuous and discontinuous loading to observe the impact of the heat loading schedule. The developed analytical solution for thermal stress investigation is validated with numerical models. It is demonstrated that the analytical solutions agree well with numerical results for two types of BHE configurations (co‐axial and single U‐shaped pipes). Furthermore, the calculated maximum stresses are compared with the tensile strength of grout materials obtained from Brazilian tests. It is predicted that the thermal contraction of the grout, partially constrained by the surrounding rock, generates tensile stresses that may lead to cracking in the BHE. According to the results, the stiffness of rock has a primary role on the developed tensile stresses, and the relationship between the thermal conductivity of the ground and of the grout induces a proportional impact on the magnitude of thermal stresses. Copyright © 2015 John Wiley & Sons, Ltd.     

分布热源作用下裂隙岩体渗流-传热的拉氏变换-格林函数半解析计算方法

以裂隙岩体高放射性核废物地下处置库性能评估为目标,提出了分布热源作用下单裂隙岩体渗流-传热的简化概念模型、控制微分方程和拉氏变换-格林函数半解析法,为进一步采用半解析法计算分布热源作用下多裂隙岩体的渗流-传热问题奠定了基础。针对单裂隙岩体的渗流-传热问题,建立考虑岩石内热源和二维热传导的控制微分方程,利用拉氏变换域微分方程的基本解建立格林函数积分方程,采用解析法处理其中的奇点,通过数值积分和拉氏数值逆变换求解,计算任意时刻裂隙水和岩石的温度分布。通过算例,与基于岩石一维热传导假定的解析解进行了对比,并计算分析了分布热源作用下单裂隙岩体的渗流-传热特征及其对裂隙开度、岩石热传导系数和热流集度的敏感度。算例表明,（1）就裂隙水温度而言,由于考虑了岩石的二维热传导,拉氏变换-格林函数半解析解小于基于岩石一维热传导假定的解析解;（2）裂隙水温度和岩石温度对裂隙开度和热流集度的敏感度较大,对岩石热传导系数的敏感度较小。     

米尺度裂隙岩体模型水流-传热试验的数值模拟分析

为了研究高放射性核废物地下处置库近场的水流-传热耦合问题,采用国内高放废物地下处置库预选场址--甘肃北山地区的花岗岩石块体,加工组合成米尺度的规则裂隙岩体模型,设置边界热源和裂隙水流,试验模拟裂隙水水流与传热之间的相互作用。作为该室内模型试验的前期理论研究,采用等效孔隙介质数值模型,着重分析了裂隙开度、裂隙流量和热源功率对流场和温度场的影响。在设定条件下,计算分析表明：热传导和裂隙水水流由热源作用初期的不耦合很快转化为耦合;不流动的裂隙水主要表现为热存储和热传导,而流动的裂隙水还引起流动传热和水与岩石之间的对流换热,使岩体温度场明显不同于单纯热传导的情况;如果保持裂隙水流量不变,则裂隙开度的变化对水流-传热影响不大;如果保持裂隙水流速不变,则裂隙开度的变化对水流-传热影响显著;热源功率越大,通过裂隙水的热流量越大,裂隙水压强越大,而当温度超过100 ℃时,裂隙水会因汽化而压强显著增大;加热7 d时,热量的输入和输出几乎相等,裂隙水流带走的热量接近热源供给的热量,模型系统基本达到了热平衡。     

镜质体成烃反应动力学模型的标定及其在热史恢复中的应用

镜质体反射率（Ｒｏ）与其生烃率有关，因此，由Ｒｏ应可求取其生烃率；同时，在求取了镜质体成烃反应动力学参数之后，若已知其受热史，则可计算出镜质体的生烃率；反过来，若已知镜质体的生烃率，应可反推其受热史。基于这一基本原理，本文在建立和标定镜质体成烃反应动力学模型的基础上推导了可将其应用于存在着抬升、剥蚀和古地温非线性变化等复杂地质条件下热史恢复的原理模型，结合海拉尔盆地海参７井的实测Ｒｏ值，有效地恢复了其古热史。     

套管式地埋管换热器热短路及换热性能

套管式地埋管换热器是深层地源热泵系统常用的换热装置。基于流体流动换热方程,建立套管式地埋管换热器与周围岩体之间的传热模型。以第一个供暖季为例,分析内管导热系数和循环水流量对换热性能的影响,并引入换热器效能对热短路现象进行评估,研究结果显示:内管导热系数越大,热短路现象越显著;热短路使内外管中循环水温差降低,管内出现热堆积,导致换热器换热功率降低;套管式地埋管换热器的换热功率随循环水流量的增大逐渐增大;内外管之间存在热短路时,出口水温随循环水流量的增大先升高后降低,随着流量增大,换热器效能增大。研究成果可为深层地源热泵系统中地埋管换热器的设计提供借鉴。      

传导-对流型热流的计算模拟

本文对8个初始模型和7个组合模型中沿断层的水热对流、断层产状、山体地形和沉积盆地与基岩热导率反差等四个影响因素对传导型地表热流分布的影响进行了计算机模拟研究。模型设计和参数的选值以西藏中北部一些地热区实测的传导-对流型热流为主要参考依据,但不直接涉及对流组分的校正,而着眼于更广泛的单因子和多因素的模型研究。分析中采用无量纲参数:α=(K₁)/(K₂)(K₁和K₂分别为基岩和沉积盆地的热导率),β=(q₁)/(q₂)(q₁和q₂分别为地表热流的垂向分量和模型的底部热流)以及γ=L/H(L和H分别为离模型左侧边界的距离和山体的高度),以求更广的普适性。对模拟结果的分析表明,上述四项影响因素依其重要性可排序为对流强度—断层倾角—介质热导率反差—地形效应。     

冻土温度状况研究方法和应用分析

分析讨论了冻土温度状况研究中相关问题,包括构成多年冻土层的岩性、含水量、结构和构造,决定多年冻土温度状况动态变化的地面温度与气温间的关系,地中热流,研究区域的确定以及取决于地层的岩性、含水量、结构和构造、容重的热量在地层内传播过程的热物理参数.在分析物理学、地学和气候学等学科研究结果的基础上,笔者认为:1)在研究冻土温度状况问题中,研究区域应根据所研究问题的时间尺度确定,由于多年冻土层内不同深度上的温度和热流(或温度梯度)随时间的不同影响深度也不同,研究数十年时间尺度的多年冻土温度状况问题,一般应取多年冻土下限处的地中热流(或温度梯度)作为问题的下边界条件;2)以气温积温(或气温)与地面温度积温(或地面温度)比值所定义的N系数不仅存在年变化、季节变化和日变化,并在求解时必须已知地面冻结(或融化)的持续时间,而在目前对于不同地面条件缺乏定量描述气温与地面温度间关系的实验基础.因此,在缺乏比较严格的地面条件定量描述的情况下,应用气温与地面温度之差描述二者间的关系可能更为简单;3)在青藏高原地区,由于不同区域地形、地面条件、地层岩性以及地中热流等存在着很大差异,因而,不同区域多年冻土的热状况也不同.所以,不能简单地以气温等值线进行多年冻土制图,更不能以此年冻土变化预报的基础.     

地埋点热源作用下层状半空间的热-力耦合响应

采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发,利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元;然后结合有限单元法原理组装得到总刚度矩阵,结合边界条件,得到其在变换域内的解答,最后应用拉普拉斯-傅里叶积分逆变换技术,得到物理域内的解。编制了相应的计算程序,算例分析表明：该结果与已有文献吻合较好,该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度;层状岩土介质体系中,热扩散系数对温度及地表隆起的变化过程影响显著,但对其初始值和最终稳定值影响不明显;分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。