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.     

Effects of regional groundwater flow on the performance of an aquifer thermal energy storage system under continuous operation

Numerical investigations and a thermohydraulic evaluation are presented for two-well models of an aquifer thermal energy storage (ATES) system operating under a continuous flow regime. A three-dimensional numerical model for groundwater flow and heat transport is used to analyze the thermal energy storage in the aquifer. This study emphasizes the influence of regional groundwater flow on the heat transfer and storage of the system under various operation scenarios. For different parameters of the system, performances were compared in terms of the temperature of recovered water and the temperature field in the aquifer. The calculated temperature at the producing well varies within a certain range throughout the year, reflecting the seasonal (quarterly) temperature variation of the injected water. The pressure gradient across the system, which determines the direction and velocity of regional groundwater flow, has a substantial influence on the convective heat transport and performance of aquifer thermal storage. Injection/production rate and geometrical size of the aquifer used in the model also impact the predicted temperature distribution at each stage and the recovery water temperature. The hydrogeological-thermal simulation is shown to play an integral part in the prediction of performance of processes as complicated as those in ATES systems.     

Thermal performance and heat transport in aquifer thermal energy storage

Aquifer thermal energy storage (ATES) is used for seasonal storage of large quantities of thermal energy. Due to the increasing demand for sustainable energy, the number of ATES systems has increased rapidly, which has raised questions on the effect of ATES systems on their surroundings as well as their thermal performance. Furthermore, the increasing density of systems generates concern regarding thermal interference between the wells of one system and between neighboring systems. An assessment is made of (1) the thermal storage performance, and (2) the heat transport around the wells of an existing ATES system in the Netherlands. Reconstruction of flow rates and injection and extraction temperatures from hourly logs of operational data from 2005 to 2012 show that the average thermal recovery is 82 % for cold storage and 68 % for heat storage. Subsurface heat transport is monitored using distributed temperature sensing. Although the measurements reveal unequal distribution of flow rate over different parts of the well screen and preferential flow due to aquifer heterogeneity, sufficient well spacing has avoided thermal interference. However, oversizing of well spacing may limit the number of systems that can be realized in an area and lower the potential of ATES.     

Predicting the risk of saltwater contamination of freshwater aquifers during aquifer thermal energy storage

Aquifer thermal energy storage (ATES) is an underground thermal energy storage technology with a large potential to decarbonise the heating and cooling of buildings. ATES installations typically store thermal energy in aquifers that are also exploited for potable water, so a major consideration during development is ensuring that system operation will not lead to groundwater pollution. In this study, the risk of contamination due to upconing of a shallow freshwater/saltwater interface during ATES operation is investigated. Fluid flow, and heat and salt (chloride ion) transport are simulated in a homogeneous aquifer during ATES operation via a well doublet. The impact of geological, hydrological and operational parameters is investigated in a sensitivity analysis. Two new dimensionless numbers are proposed to characterise salt upconing and redistribution during ATES operation and provide a close match to simulated concentrations: C_R,w characterises the contamination risk at the ATES installation, and C_R,d characterises the risk at locations downstream of the ATES installation with respect to background groundwater flow. ATES systems with C_R,w and C_R,d < 10 introduce low risk of contamination in a homogenous aquifer, with chloride concentration at, and downstream of, the ATES system, remaining below the World Health Organisation’s advised limit. ATES installations with C_R,w and C_R,d > 10 cause a rapid increase in aquifer chloride concentration. The results are used to estimate an exclusion distance beyond which ATES system operation will not cause contamination in a homogenous aquifer. The dimensionless parameters proposed allow rapid assessment of the potential for saltwater contamination during ATES operation.

     

壁面局部接触裂隙岩体水流-传热的一种理论模型及计算分析

核废物地质处置、地热开发、石油开采等工程领域都可能涉及稀疏裂隙岩体中的水流-传热过程。现有的裂隙岩体水流-传热理论模型和计算方法基本上都是以平行光滑壁面裂隙模型为基础的,没有考虑裂隙的壁面局部接触对水流、水-岩热交换以及岩体传热的影响。针对粗糙壁面裂隙水流过程,阐述了基于Stokes方程的Reynolds润滑方程及Hele-Shaw裂隙模型,采用MATLAB软件中的PDE工具求解,并与Walsh的等效水力开度公式进行对比;分析壁面局部接触裂隙水流-传热与填充裂隙水流-传热的相似性,提出了瞬时局部热平衡假设的适用条件,并在裂隙局部接触体传热满足Biot数条件的前提下,计算分析裂隙局部接触体与水流之间的局部热平衡时间及其影响因素;在裂隙局部接触体与水流之间满足瞬时热平衡假设的前提下,利用填充裂隙水流-传热的解析解,计算了壁面局部接触裂隙水及两侧岩石的温度分布,并分析了裂隙局部接触面积率、裂隙开度、裂隙水平均流速对岩石温度和裂隙水温度的影响特征,结果表明：（1）在设定条件下,由于裂隙局部接触体与裂隙水流之间的热交换,裂隙水流对其两侧岩石温度的影响范围随接触面积率的增大而减小,裂隙两侧岩石对裂隙水流温度的影响程度随接触面积率的增大而增大;（2）裂隙开度和裂隙水流速对岩石温度和裂隙水温度的影响方式的影响是一致的,即由于裂隙水流量随裂隙开度和裂隙水流速的增大而增大,裂隙水流对其两侧岩石温度的影响范围随裂隙开度和裂隙水流速的增大而增大,裂隙两侧岩石对裂隙水流温度的影响程度随裂隙开度和裂隙水流速的增大而减小。     

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.     

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。     

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。     

地热储层单裂隙岩体渗流传热数值模拟研究

研究地热储层裂隙岩体中的渗流传热过程对干热岩地热资源的开采具有重要的意义。本文以干热岩地热工程为背景,采用COMSOL Multiphysics数值模拟软件对地热储层单裂隙岩体中渗流传热机理进行了研究,并分析了流体注入速度和温度对岩体温度场的影响及其对干热岩地热工程的影响。研究发现流体参数对岩体温度场的影响主要体现在两个方面：一方面是对岩体温度场受扰动区域以及幅度的影响,另一方面是对岩体温度场达到稳态所需要时间的影响。流体注入速度的提升会降低系统的寿命和寿命期的出口法向总热量值,当考虑出口法向总热通量时,存在最佳流体注入速度,本研究中最佳流体注入速度为0.011m/s。流体注入温度的提升会增加系统的寿命和系统的出口法向总热通量和总热量。研究为干热岩自热资源的开发与利用提供了理论依据,为工程运行参数的设计提供了参考依据。     

The influence of paleoclimatic events on the functioning of an alpine thermal system (France): the contribution of hydrodynamic–thermal modeling

Numerical models of the Aix-les-Bains thermal aquifer (France) were used to investigate the influence of Quaternary paleoclimatic events on the current thermal state of the groundwater. Initial numerical tests were successful in that present-day fluid flows (heads and flow rates) and the resulting velocities were compatible with residence time data. Water flowing through an aquifer cools the rock mass; therefore, the rate of water flow governs the outlets temperature. For the Aix-les-Bains aquifer, applying present-day flow rates to the entire history of the aquifer leads to much more substantial cooling of the rock mass than is indicated by the outlets temperature (i.e. present-day flow rates are 10 times too high). This suggests that the aquifer may have gone through alternating functioning phases, during which the rock mass cooled, and blocked phases, during which the aquifer reheated. Other results indicate that the main parameters affecting thermal behavior during a functioning phase are the total inflow volume, rather than individual inflow rates, and the initial heat field. As phenomena linked to glaciation can lead to the blocking of infiltration zones and aquifer outlets, the findings suggest that the hypothesis of intermittent aquifer functioning related to glaciations is compatible with the current thermal field.     

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。      

FDEM-TH3D: A three-dimensional coupled hydrothermal model for fractured rock

This paper proposes a three-dimensional coupled hydrothermal model for fractured rock based on the finite-discrete element method to simulate fluid flow and heat transport. The 3D coupled hydrothermal model is composed of three main parts: a heat conduction model for the rock matrix, a heat transfer model for the fluid in the fractures (including heat conduction and heat convection), and a heat exchange model between the rock matrix and the fluid in the fractures. Four examples with analytical solutions are provided to verify the model. A heat exchange experiment of circulating water in a cylindrical granite sample with one fracture is simulated. The simulation results agree well with the experimental results. The effects of the fracture aperture, fluid viscosity, and pressure difference on the heat exchange between the fluid and rock are studied. Finally, an application concerned with heat transport and fluid flow in fractured rock is presented. The simulation results indicate that the 3D fully coupled hydrothermal model can capture the fluid flow and temperature evolution of rocks and fluids.     

含水层热量输运中自然热对流和水-岩热交换作用的研究

本文对含水层热量输运过程中存在的自然热对流和水-岩热交换作用进行了深入研究, 目的是为了弄清两种作用对热量输运的影响。首先针对普通水流方程和热量输运方程的局限性, 给出了能够描述这两种作用的新的数学方程, 并通过建立一个非线性三维含水层热量输运模型加以实现。然后利用上海第二承压含水层的群井储能试验资料, 根据不同的条件进行计算。计算结果与实测数据的对比分析表明, 自然热对流通常对含水层的热量输运有明显作用, 定量研究时不应忽略；水-岩热交换作用持续时间短, 对整个热量输运过程影响较小。     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响，选取甘肃北山地区的花岗岩，制作了稀疏非正交裂隙岩体模 型，采用河砂填充裂隙后进行模型试验；并对模型试验进行离散元数值模拟，分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力，无填充时岩体温度和热应力比填砂时低；模 型试验和离散元模拟均表明，岩体温度和岩体应力随裂隙水流速度增大而减小，但是系统达到稳态所需要的时间变短；模 型试验中斜裂隙水流对温度场起主要作用；由于现有3DEC软件不能考虑水的热物性参数随温度的变化，进而产生自然对 流换热，斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响,选取甘肃北山地区的花岗岩,制作了稀疏非正交裂隙岩体模 型,采用河砂填充裂隙后进行模型试验;并对模型试验进行离散元数值模拟,分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力,无填充时岩体温度和热应力比填砂时低;模 型试验和离散元模拟均表明,岩体温度和岩体应力随裂隙水流速度增大而减小,但是系统达到稳态所需要的时间变短;模 型试验中斜裂隙水流对温度场起主要作用;由于现有3DEC软件不能考虑水的热物性参数随温度的变化,进而产生自然对 流换热,斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

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.     

Impact of groundwater withdrawals on the interaction of multi-layered aquifers in the Viterbo geothermal area (central Italy)

The impact of groundwater withdrawals on the interaction between multi-layered aquifers with different water qualities in the Viterbo geothermal area (central Italy) was studied. In this area, deep thermal waters are used to supply thermal spas and public pools. A shallow overlying aquifer carries cold and fresh water, used for irrigation and the local drinking-water supply. Starting with a conceptual hydrogeological model, two simplified numerical models were implemented: a steady-state flow model of the entire groundwater system, and a steady-state flow and heat transport model of a representative area, which included complex interactions between the aquifers. The impact of increased withdrawals associated with potential future development of the thermal aquifer must be considered in terms of the water temperature of the existing thermal sources. However, withdrawals from the shallow aquifer might also influence the discharge of thermal sources and quality of the water withdrawn from the shallow wells. The exploitation of the two aquifers is dependent on the hydraulic conductivity and thickness of the intervening aquitard, which maintains the delicate hydrogeological equilibrium. Effective methods to control this equilibrium include monitoring the vertical gradient between the two aquifers and the residual discharge of natural thermal springs.     

稀疏不规则裂隙岩体模型三维水流-传热对温度和应力影响的试验研究

选取高放射核废物处置库重要预选场区甘肃北山地区的花岗岩,制作750 mm（宽）×300 mm（厚）×1 000 mm（高）的稀疏不规则裂隙岩体模型,该模型由18块花岗岩和竖向与斜向各两条裂隙组成,在裂隙及岩石内部埋置温度传感器、水压计、直角应变花,并在模型一侧设置局部热源,研究热源温度和裂隙水流速对岩石温度和应力的影响。结果表明,竖裂隙水主要从顶部进水口流向底部出水口,斜裂隙水主要从侧部进水口流向侧部出水口,竖裂隙与斜裂隙在交汇处存在微小流量交换;由于热源处在两条斜裂隙进水口之间,并且斜裂隙长度小于竖裂隙,岩石热传导与斜裂隙水流对岩石温度分布起控制作用,竖裂隙水流对岩石横向热传导起阻滞作用;由于热传导和水流传热的不规则性,上层岩石形成从左向右为主的传热路径,中层和下层岩石形成从上向下为主的传热路径;由于上、下层岩石温度梯度较小,岩石收缩受热拉应力,而中层岩石温度梯度较大,岩石膨胀受热压应力,大主应力的方向大致垂直于斜裂隙面与竖裂隙面的交线,岩石应力增量随斜平面方向的温度梯度增大而增大;热源温度越高,裂隙水流速越低,岩石温度越高、岩石应力越大,系统达到稳态需要的时间越长。     

The Pliocene Yafo Formation in Israel: Hydrogeologically inert or active?

For several decades the “Saqiye beds” (later renamed Yafo Formation) underlying the Coastal Plain aquifer (Kurkar Group) aquifer of Israel, were regarded as an extremely thick, tectonically undisturbed, and absolutely impervious aquiclude. Following intensive groundwater exploitation from the overlying Kurkar Group aquifer, brackish and saline waters were locally encountered in the lower parts of this aquifer and always at the contact with the underlying Yafo Formation aquiclude. The present study revealed that this aquiclude is not a uniform and impervious rock unit, but rather an alternation of pervious and impervious strata within the Yafo Formation containing highly pressured fluids of different — mostly high — salinities. The permeable beds are at an angular unconformity and in direct contact with the overlying Kurkar Group aquifer. The Yafo Formation and the underlying and overlying rock units are dislocated by numerous fault systems, which facilitate accessibility of brines into the Kurkar Group aquifer. The mobilization of the saline fluids and their injection into the Kurkar Group aquifer could be due either to diffusion of saline fluids occurring in the permeable horizons of the Petah Tiqva Member through the clays of the Yafo Formation or to their upconing following intensive pumping in the Coastal Plain aquifer. It could have also been caused by up-dip movement of saline water as the result of overpressure generated by major accumulation of gas in the permeable horizons. Another possible mechanism could be hydraulic contact with pressurized brines up-flowing along fault zones from deep-seated Jurassic or Cretaceous reservoirs. The squeezing of saline interstitial water from the clays of the Yafo Formation into the overlying Kurkar Group aquifer, is of secondary importance for groundwater salinization (its input is comparable with salt input from rain).     

地铁隧道围岩内温度分布规律的模型试验及其热导率反算研究

为能精确计算地铁隧道围岩内的传热量,模拟了地铁隧道围岩内的热传导,研究了地铁围岩内的温度分布规律,并通过试验结果对土体热导率进行反算。分析表明：同一时刻,距隧道壁面不同距离处的温度以指数形式进行变化,距离越远,温度越小;时间越久,隧道内流体的温度影响范围越大。除隧道外壁面外,距隧道壁某距离处的温度,随时间的增长而逐渐增长,距隧道壁较近处土体温度较高,温度增长速率随时间的增长而逐渐减小;距隧道壁面距离较远处温度较低,其增长速率随时间的增长而逐渐增大。传热时间超过某一值后,围岩内温度增长率逐渐平稳趋于一定值。根据模型试验结果能较精确得到土样的热导率数值。