An analytical solution for modeling thermal energy transfer in a confined aquifer system

A mathematical model is developed for simulating the thermal energy transfer in a confined aquifer with different geological properties in the underlying and overlying rocks. The solutions for temperature distributions in the aquifer, underlying rock, and overlying rock are derived by the Laplace transforms and their corresponding time-domain solutions are evaluated by the modified Crump method. Field data adopted from the literature are used as examples to demonstrate the applicability of the solutions in modeling the heat transfer in an aquifer thermal energy storage (ATES) system. The results show that the aquifer temperature increases with time, injection flow rate, and water temperature. However, the temperature decreases with increasing radial and vertical distances. The heat transfer in the rocks is slow and has an effect on the aquifer temperature only after a long period of injection time. The influence distance depends on the aquifer physical and thermal properties, injection flow rate, and injected water temperature. A larger value of thermal diffusivity or injection flow rate will result in a longer influence distance. The present solution can be used as a tool for designing the heat injection facilities for an ATES system.     

The flow and heat transfer characteristics of compressed air in high-pressure air injection wells

High-pressure air injection (HPAI) is a significant enhanced oil recovery (EOR) technology of light oils especially in deep, thin, low-permeability reservoirs. The flow and heat transfer behaviors of compressed air in wellbore is essential to maximize performance of air in EOR. Due to strong compressibility of air and high injection pressure, wellbore temperature and pressure are greatly affected by friction and gas compression. However, the available models of wellbore flow and heat transfer are only accurate for thermal fluid, such as saturated steam and superheated steam, injected at relatively low pressure and high temperature. In this paper, a novel model is proposed to characterize wellbore pressure and temperature distribution for HPAI wells with consideration of dynamic behaviors of injected air. Flow and heat transfer in depth direction are coupled with air properties by iterative technique, and heat transfer in radial direction is treated as steady state in wellbore and transient state in formation. The mathematical model is solved by employing finite difference method and it is validated by field data. Then, integrated analyses of flowing pressure, heat transfer mechanism, and interaction between pressure and temperature are conducted. Results indicate that (1) as well depth increases, temperature difference between formation and air tends to become constant, and the radial heat transfer tends to reach an equilibrium state. The higher the flow rate is, the deeper the equilibrium depth is. (2) Air temperature is dominated by heat transmission from formation at low flow rates and dominated by frictional heat and gas compression effect at high flow rates. Fictional heat begins to affect air temperature at an injection rate beyond the critical value, while gas compression effect can increase air temperature in the whole calculated injection rate range. (3) Interaction between wellbore temperature and pressure is mainly achieved by altering air density. The effect of injection pressure on air temperature can be negligible, while the influence of injection temperature shows strong dependency on injection rate.     

Cyclic Thermo-Mechanical Analysis of Wellbore in Underground Compressed Air Energy Storage Cavern

The compressed air energy storage (CAES) method is a viable method of storing surplus energy underground when there is a mismatch between energy generation and demand. Wellbores embedded in rock are an integral part of energy storage structures, and are used for injecting and extracting the compressed air. During injection and production cycles, the storage reservoir and wellbore are subjected to cyclic change in external pressure and temperature, which may cause failure of the wellbore. In this paper, cyclic thermo-mechanical analysis of a horizontal wellbore in an underground CAES cavern is performed using finite element analysis. The rock behavior is simulated using the Mohr-Coulomb constitutive law. The reduction in the yield strength of rock with increase in the number of loading cycles is taken into account in the analysis. Parametric sensitivity studies are carried out to study the effects of dilation and friction angles of rock, the ratio of in situ horizontal and vertical stresses, loading frequency, and the magnitude of the temperature cycles in the cavern on the wellbore performance for different types of rock. The thermo-mechanical cyclic behavior leads to plastic strains that are greater than those obtained by performing mechanical analysis only. Significantly large deformation is generated in rock for large dilation angle and high loading frequencies.     

An Analytical Solution for Mechanical Responses Induced by Temperature and Air Pressure in a Lined Rock Cavern for Underground Compressed Air Energy Storage

Mechanical responses induced by temperature and air pressure significantly affect the stability and durability of underground compressed air energy storage (CAES) in a lined rock cavern. An analytical solution for evaluating such responses is, thus, proposed in this paper. The lined cavern of interest consists of three layers, namely, a sealing layer, a concrete lining and the host rock. Governing equations for cavern temperature and air pressure, which involve heat transfer between the air and surrounding layers, are established first. Then, Laplace transform and superposition principle are applied to obtain the temperature around the lined cavern and the air pressure during the operational period. Afterwards, a thermo-elastic axisymmetrical model is used to analytically determine the stress and displacement variations induced by temperature and air pressure. The developments of temperature, displacement and stress during a typical operational cycle are discussed on the basis of the proposed approach. The approach is subsequently verified with a coupled compressed air and thermo-mechanical numerical simulation and by a previous study on temperature. Finally, the influence of temperature on total stress and displacement and the impact of the heat transfer coefficient are discussed. This paper shows that the temperature sharply fluctuates only on the sealing layer and the concrete lining. The resulting tensile hoop stresses on the sealing layer and concrete lining are considerably large in comparison with the initial air pressure. Moreover, temperature has a non-negligible effect on the lined cavern for underground compressed air storage. Meanwhile, temperature has a greater effect on hoop and longitudinal stress than on radial stress and displacement. In addition, the heat transfer coefficient affects the cavern stress to a higher degree than the displacement.     

跨季节蓄热型地源热泵热传递规律研究

基于有限元分析法,建立了准三维非稳态传热模型。在试验验证的基础上,分析了跨季节蓄热型地源热泵蓄热过程中土壤温度、单位井深换热量、热作用半径随热泵运行时间的变化规律,讨论了土壤结构、入口水温、入口质量流量、热泵运行模式等对土壤传热规律的影响,并研究了土壤热平衡问题。结果表明:同一半径不同深度处,土壤温度增长幅度随土壤热扩散率的增加而增大;土壤热作用半径随热泵运行时间及入口水温的升高而增加,并逐渐趋于稳定;间歇运行模式下,地埋管附近土壤温度及换热量均呈波动式变化,且当径向距离大于0.3 m时,与连续模式一致;在满足换热量的情况下,流体质量流量不宜过大;系统运行一个周期（360 d）后土壤温度基本可以恢复,且流体入口温度不宜低于40 ℃。     

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。     

反循环气体钻井非线性温度模型

在反循环气体钻井中,循环介质与地层之间不断进行着热交换,因此井内温度分布是影响气体反循环钻井流体动力学参数的重要因素。基于反循环钻井技术特点,考虑循环介质与地层间热量的交换,沿钻孔径向取传热平衡微分单元作为研究对象,建立中心通道内流体和环状间隙内流体热平衡方程。通过求解线性非齐次方程推出反循环气体钻井非线性温度模型,并给出了模型求解的边界条件。通过算例可知,按照自然地层温度计算的井底温度比采用该模型计算的井底温度高21.14 K,这是因为随井深增加,热量由温度较高的地层向温度较低的气体传递,但是热传递并不完全,考虑地层与井眼流体热交换的反循环气体钻井非线性温度模型符合井内温度分布。     

Geothermal energy exploitation from depleted high-temperature gas reservoirs by recycling CO2:The superiority and existing problems

CO2 can be used as an alternative injectant to exploit geothermal energy from depleted high-temperature gas res-ervoirs due to its high mobility and unique thermal properties.However,there has been a lack of systematic anal-ysis on the heat mining mechanism and performance of CO2,as well as the problems that may occur during geothermal energy exploitation at specific gas reservoir conditions.In this paper,a base numerical simulation model of a typical depleted high-temperature gas reservoir was established to simulate the geothermal energy exploitation processes via recycling CO2 and water,with a view to investigate whether and/or at which condi-tions CO2 is more suitable than water for geothermal energy exploitation.The problems that may occur during the CO2-based geothermal energy exploitation were also analyzed along with proposed feasible solutions.The re-sults indicate that,for a depleted low-permeability gas reservoir with dimensions of 1000 m × 500 m × 50 m and temperature of 150℃using a single injection-production well group for 40 years of operation,the heat mining rate of C02 can be up to 3.8 MW at a circulation flow rate of 18 kg s-1 due to its high mobility along with the flow path in the gas reservoir,while the heat mining rate of water is only about 2 MW due to limitations on the injectivity and mobility.The reservoir physical property and injection-production scheme have some effects on the heat mining rate,but CO2 always has better performance than water at most reservoir and operation condi-tions,even under a high water saturation.The main problems for CO2 circulation are wellbore corrosion and salt precipitation that can occur when the reservoir has high water saturation and high salinity,in which serious salt precipitation can reduce formation permeability and result in a decline of CO2 heat mining rate(e.g.up to 24％reduction).It is proposed to apply a low-salinity water slug before CO2 injection to reduce the damage caused by salt precipitation.For high-permeability gas reservoirs with high water saturation and high salinity,the supe-riority of CO2 as a heat transmission fluid becomes obscure and water injection is recommended.     

Cylindrical probe with a variable heat flow rate: A new method for the determination of formation thermal conductivity

The thermal conductivity of a geological formation is one of the important petrophysical parameters which are preferable to study in situ in geophysical well logs. A new technique for the determination of formation thermal conductivity has been developed. We assumed that formation dry density, porosity, and pore fluids saturations could be determined from core samples or cuttings. In this case the specific heat and density of a formation can be quantitatively estimated. It is also assumed that the instantaneous heat flow rate and time data are available for a cylindrical probe with a variable heat flow rate placed in a wellbore. A semi-theoretical equation describing the temperature of the probe’s wall is used to determine in situ the formation conductivity as a function of the temperature increase. The formation thermal diffusivity is also calculated. A field example is presented.     

Analytical solutions for transient temperature distribution in a geothermal reservoir due to cold water injection

An analytical solution to describe the transient temperature distribution in a geothermal reservoir in response to injection of cold water is presented. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. Results show that heat loss to the confining rock layers plays a vital role in slowing down the cooling of the reservoir. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be profound on the results.     

珊瑚砂热物理参数测试与预测模型对比分析

在我国“海洋强国”建设下,南海岛礁建设顺利推进,以浅层礁坪为介质的地源热泵技术、能量桩等,实质是与礁砂介质能量交换的过程,需进一步掌握珊瑚砂导热性能的演变规律。以南海岛礁珊瑚细砂为研究对象,测定并探讨在不同干密度和含水率下对3大热物理参数的影响,并选用12种砂土热物理参数模型的预测数据与实测数据进行类比分析,提出适宜预测珊瑚细砂导热性能的经验模型。结果表明,珊瑚细砂导热系数和体积比热容、热扩散系数均与干密度呈正相关关系,导热系数和体积比热容与含水率的相关系数高于干密度,而热扩散系数与含水率呈“凸”形增长关系,与干密度的相关系数远高于含水率。基于试验实测数据进行线性回归分析,修订Cote-Konrad模型与Gangadhara Rao模型,显著提高模型对珊瑚细砂导热系数预测准确性;通过De Vries模型与Xu模型的线性修正,大幅缩小珊瑚细砂体积比热容预测值与实测值的差异,在Dai模型相关系数的二元拟合分析基础上,建立表征珊瑚细砂热扩散系数预测模型,为岛礁隔热、控温工程设计以及珊瑚砂热物理特性研究提供参考。     

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.     

Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low-permeability formations

The coupled heat-fluid-stress problem of circular wellbore or spherical cavity subjected to a constant temperature change and a constant fluid flow rate is considered. Transient analytical solutions for temperature, pore pressure and stress are developed by coupling conductive heat transfer with Darcy fluid flow in a poroelastic medium. They are applicable to low permeability porous media suitable for liquid-waste disposal and also simulating reservoir for enhanced oil recovery, where conduction dominates the heat transfer process. A full range of solutions is presented showing separately the effects of temperature and fluid flow on pore pressure and stress development. It is shown that injection of warm fluid can be used to restrict fracture development around wellbores and cavities and generally to optimize a fluid injection operation. Both the limitations of the solutions and the convective flow effect are addressed. Copyright © 1999 John Wiley & Sons, Ltd.     

饱和稀疏裂隙岩体三维水流-传热过程中位移和应力的一种半解析计算方法

针对高放射核废深地质处置库近场环境,建立分布热源作用下饱和裂隙岩体三维水流-传热过程中位移和应力的一种半解析计算方法：采用Goodier热弹性位移势和Laplace变换计算由温度梯度产生的温梯位移和应力;考虑单一裂隙的情况,利用经典弹性力学的Boussinesq解和Cerruti解计算为满足边界条件的约束位移和应力,与温梯位移和应力叠加,可得总体热位移和应力;把裂隙面离散为矩形单元集合,采用极坐标系下的解析法计算包含奇点的单元积分,采用数值法计算与分布热源有关和不含奇点的单元积分。与基于裂隙面法向一维热传导假设的一种解析解对比,结果表明,半解析法与解析法的计算结果基本一致,但由于半解析法考虑岩石的三维热传导,因温度时空分布和演变的不同而导致不同的温梯应力。针对一个假想单裂隙岩体三维水流-传热过程,计算温梯位移和应力、约束位移和应力、总体位移和应力;结果表明,裂隙水流-传热可能对位移和应力的分布和演变有显著影响,距离分布热源较近的岩石因升温膨胀受到约束而出现压应力,而距离分布热源较远的岩石则可能因协调收缩受到约束而出现拉应力。     

与海洋天然气水合物微纳米尺度赋存和开采储存技术有关的研究进展

天然气水合物是一类潜在的储量巨大的清洁能源.近年来,水合物的研究已经逐渐拓展至纳米、介观层面.纳米科学贯穿了水合物研究的全过程,包括上游天然气水合物成藏、开采和下游的储运、分离等水合物应用技术,其核心在于研究水合物在纳米材料表面、内部、间隙中生长和分解的传质传热过程.将以第九届国际水合物大会（ICGH9）为切入点,从水合物成藏、开采和下游技术应用几个方面综述近年来水合物研究中的纳米研究进展.目前对水合物的研究尺度并未做到全覆盖,水合物在纳米材料间隙中的传质传热过程研究较少,纳米材料的累积放大效应研究也存在空白.这正是水合物成藏、开采研究中的瓶颈问题.未来的研究应该着眼于水合物在纳米材料中生成和分解的传质传热作用,以此为主线将水合物技术和水合物成藏、开采研究中的核心问题进行统一协同研究.      

Influence of geologic layering on heat transport and storage in an aquifer thermal energy storage system

A modeling study was carried out to evaluate the influence of aquifer heterogeneity, as represented by geologic layering, on heat transport and storage in an aquifer thermal energy storage (ATES) system in Agassiz, British Columbia, Canada. Two 3D heat transport models were developed and calibrated using the flow and heat transport code FEFLOW including: a “non-layered” model domain with homogeneous hydraulic and thermal properties; and, a “layered” model domain with variable hydraulic and thermal properties assigned to discrete geological units to represent aquifer heterogeneity. The base model (non-layered) shows limited sensitivity for the ranges of all thermal and hydraulic properties expected at the site; the model is most sensitive to vertical anisotropy and hydraulic gradient. Simulated and observed temperatures within the wells reflect a combination of screen placement and layering, with inconsistencies largely explained by the lateral continuity of high permeability layers represented in the model. Simulation of heat injection, storage and recovery show preferential transport along high permeability layers, resulting in longitudinal plume distortion, and overall higher short-term storage efficiencies.     

不同土壤类型与含水率对水平埋管换热性能影响数值分析

为揭示地源热泵系统水平埋管换热器在不同土壤类型中的换热性能,基于土壤毛管水理论知识,结合数值模拟的研究手段,探讨了蓄能不同类型土体内(砂土、壤土、黏土)三相组成的差异对水平埋管换热器换热特性的影响规律。结果表明,在通入308.15 K制冷工况下,水平管在壤土中的出水温度降低至303.3 K,进出口水温差为4.9 K,埋管单位延米换热量37.1 W/m,水平管在壤土中的制冷换热效益显著;不同土壤(砂土、壤土、黏土)在经历相同制冷周期下,水平管的换热过程对壤土的温度场分布影响最小,管体在壤土中运行时热堆积风险系数最低。研究表明,水平管与土壤的换热性能同时受土壤比热容与土壤导热系数的影响,提高土壤导热系数比提高土壤比热容获得的效益更加显著。可以通过压实回填、减少土壤孔隙率、提高固相回填材料导热系数、加大布管深度以提高回填材料含水率等方法来强化埋管的换热性能。      

Sinusoidal oscillations radiating from a cylindrical source in thermal conduction or groundwater flow: Closed‐form solutions

The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, we study the two‐dimensional radial propagation of a sinusoidal perturbation radiating from a cylindrical source within an infinite slab of homogeneous material. The solution of this problem has several applications. For instance, it can be used to determine the hydraulic diffusivity of the subsurface based on measurements of the hydraulic head around a vertical well during its development. For thermal problems, it can be used to determine the thermal diffusivity based on measurements of the temperature distribution around a cylindrical heat source generating a sinusoidal power per unit length. In this paper, we present a comprehensive analytical solution of this problem and we compare these solutions with numerical solutions. Two approximate analytical solutions, which can be relevant in practice, are also presented. Finally, we give an upper bound for the survival time of the transient part of the solution and we provide an estimate of the radius of influence of the sinusoidal solicitation. Copyright © 2010 John Wiley & Sons, Ltd.     

不同注热水温度下水合物开采实验研究

天然气水合物(NGH)是目前备受关注的新型洁净优质能源,注热法是其有效开采方式之一。为了经济有效地进行注热开采,采用自制的一维天然气水合物开采模拟实验装置,在填砂模型中生成相同初始条件的天然气水合物藏, 然后注入热盐水进行开采模拟实验,分析不同注热水温度对开采动态的影响。结果表明：注热水温度越高,水合物开始分解的越早,注热阶段的平均产气速率也越大;不同注热水温度下,热前缘的移动接近于线性,注热温度从40 ℃到100 ℃时,平均热前缘移动速度从015 cm/min增加到02 cm/min,说明注热水温度对热前缘的移动影响不大。注热前期,注热水温度越高,能量效率越高,但注热后期,注热水温度越高,能量效率反而越低。在本组实验条件下,注热水温度从40 ℃增加到100 ℃时,注热开采的能量效率由67减小到24,而平均热前缘移动速度并没有明显降低。因此,为保证注热开采的经济有效,建议在注热前期注高温水,在中后期采用低温水驱替。