【机械类毕业论文中英文对照文献翻译】地源热泵系统的现状分析及与其它热力方式的比较
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【机械类毕业论文中英文对照文献翻译】地源热泵系统的现状分析及与其它热力方式的比较,机械类毕业论文中英文对照文献翻译,机械类,毕业论文,中英文,对照,文献,翻译,源热泵,系统,现状,分析,其它,热力,方式,比较
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毕业设计(论文)外文资料翻译学 院： 机械电子工程学院 专 业： 热能与动力工程 姓 名： 赵 龙 学 号： 080504110 外文出处： Applied Energy 35 （2011）3256-3264 附 件： 1.外文资料翻译译文；2.外文原文。 指导教师评语： 签名： 年 月 日附件1：外文资料翻译译文地源热泵系统的现状分析及与其它热力方式的比较Stuart J. Self *, Bale V. Reddy, Marc A. RosenFaculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, Canada L1H 7K4摘要 在很多地区供热在生活中是必不可少的，且不断增长的能源需求和污染物的排放使传统的加热技术受到挑战，包括地热。对地源热泵系统的评估包括热泵技术、接地情况、当今世界上的地位和近期的发展。对地源热泵和传统加热方式在成本、二氧化碳排放及其它参数方面进行比较。当电价较低的时候用地源热泵是经济实惠的。当电力生产利用能源率较高时选择地源热泵机组有着最低的污染排放量。关键词 热力 地热能 热泵 蓄能 效率 经济1 引言全球的大部分能源供应被用来发电和对特定空间的供热，这些能源多数来自化石燃料。化石燃料的总量有限而且它的燃烧对环境是有害的：排放导致气候变化的温室气体和其它污染物。我们对能源的需求正在不断增长而且完全可以预见到未来化石燃料的短缺1。Hammond2认为伴随化石燃料的燃烧产生的全球变暖和污染物排放对于构建可持续发展的能源系统是一个不容忽视的因素。这种担心对于降低整个社会对化石燃料的依赖有着积极的影响，它使人们有意识的降低对能源的需求并且努力寻找替代能源。寻找对环境更加友好且经济的能源来替代传统化石燃料燃烧。除化石燃料以外，地球表面下储存着丰富的热能。由于污染物的排放远远低于传统的化石燃料燃烧能源系统，所以说地热能源系统是非常环保的3,4。地热能源的利用主要通过三种方法：发电、直接供热、通过地源热泵间接的供热或制冷。这三种利用方法分别用到了地热的高、中、低三个不同温度的资源。高温和中温的能源通常来源于由熔化的地壳产生的热流体，从大面积的水或者熔浆中聚集。低温能源接近周围的环境温度而且大多源于地表和周围空气对太阳能的吸收。高、中温热力能源一般都在地球深处5，而由于钻孔和其它开发方法在极深地方的费用会变得很高，所以深度对开发高、中温热力能源的经济性有很大的影响。低温地热资源丰富而且在全世界大多数地区都可以开发和利用。由于深度较小涉及问题少，提取这种能源相当的简单。热泵提高低温热源的温度使之达到实际应用的需求。地源热泵可以使空间加热变得环保和经济，并且可以应用于一定空间的制冷。本文审视地源热泵系统并且把它和其它的热力系统进行比较，以提高对地源热泵的认识并且提高它在合适情况下的利用率。2 地源热泵地源热泵能够经济高效的提供热量，并且排放的污染物很少6。热泵的概念自1800年被人所认可，至今已经商用约六十余年。类似于冰箱，热泵将较低温度热源中的热量转移到温度较高的介质中7。热泵提供的热量是可利用的，通常应用于适宜的温度环境下来保持一定空间的舒适性。热泵最有吸引力的一个特点是，热泵所传输的热量会多于运行过程本身所需求的能量4,8。地源热泵（GHPs），也被称作土壤源热泵、地热能量系统、地下耦合热泵、地面耦合热泵9,10，是由三个主要系统：l 地源热泵：使热量在地面和建筑间转移并改变热量的温度11。l 接地系统：通过换热器促进热量从地面的吸收，供给地源热泵11。l 室内供热系统：调整和输送适度的热量到特定空间11,12。2.1 热泵系统热泵系统以电为动力驱动压缩机，来保持工质必要的浓度同时传递热能4,8。基本的热泵系统用于运行蒸汽压缩制冷循环。热泵内的工质通常是使用制冷剂，制冷剂的选择由地源热泵的整体特点和要求所决定6,13。地源热泵系统通过控制工质的压缩和膨胀来改变其压力和温度，从而实现热量在地源和供热空间之间的传递4,8,11。热泵主要包括五个组件(图1) 10,11,14：压缩机、膨胀阀、换向阀、两个热交换器。当然还有很多小型的组件和配件，例如：风机、管道和辅助控制系统。图1 地源热泵系统及减温器基本布局地源热泵的加热流程如下12：l 从地源吸收热能并输送到蒸发器。l 热泵机组内制冷剂占主导地位的工质进入蒸发器，热量从接地系统转移到工质中从而引起制冷剂升温沸腾成为压力较低的蒸汽；温度略有增加。l 蒸发器中产生的蒸汽进入电动压缩机，压缩之后成为高温高压蒸汽。l 高温蒸汽进入冷凝器。此时制冷剂高于外部空间，从而促使热量热量从制冷剂传递到建筑空间中。制冷剂降温凝结，成为高温高压液体。l 热液体通过膨胀阀，压力降低从而使温度下降。制冷剂再次进入蒸发器，开始下一个循环包括制冷系统在内的许多系统是要把特定空间中的热量转移释放到土地中去。在制冷模式下，四通阀作用于流体，使工质在循环中按照相反的方向流动。换热器的功能反转，与地源相连的热交换器成为冷凝器，建筑空间中的热交换器成为蒸发器8,12。有一些系统，包括减温器(图1)，作为辅助换热器将热量传递到一个热水箱。减温器安装在压缩机出口处，将压缩气体所产生的热量通过热水箱传递到水循环中，这样一来能够降低甚至消除加热水所需的热量。能源利用效率优劣的评价，一般是用系统产出的能量比上运行系统所消耗的能量。热泵所能产出的热量多于输入热泵的能量，也就是说，按照能效比的定义，热泵的能效比是大于100%的。为了避免这种尴尬，定义系统所实现的制冷或制热量与输入功率的比值为用长期性能系数(COP)，以此评价热泵性能9。地源热泵的COPs通常在3到6之间，取值依赖于系统与地连接设置、系统大小、地源特点、安装深度、当地气候等特点10,15。2.2 热量输送系统热泵系统的供热系统将热量由热泵输送到整个空间。输送系统主要有两种：水-空气传热与水液体传热。水空气传热系统将能量有地源转移到空气，由空气作为向空间传热的传输介质，水液体供热系统是由水和另外一种作为介质的液体进行换热。在北美，最常见的地源热泵系统是水空气换热的，热泵的冷凝器加热空气线圈，热空气从其中通过。热空气通过空调管道和通风口进入建筑12,16。水液体加热系统俗称液体循环系统，在此系统中，能量由接地线圈从地源吸收，接着被热泵加热并传递至水中，由水作为介质传递至建筑中。系统中的水通过地源热泵系统冷凝器吸取热量。之后水由泵驱动环绕建筑转动，将热量由地面辐射供热、散热器或局部空气线圈等供热方式方式传递至空间中。这种系统相对于传统的强制对流系统需要较低的温度。室内温度最高的空气在加热炉中被强迫向天花板上升，形成一个凉爽舒适的居住空间。为了能使生活空间更加接近于期望的温度，进入空间气体的温度必须高于空间本身温度。地板辐射供热的空间温度由地板到天花板都会很均匀，提供舒适的生活温度需要的能量更低8, 15,16。也有混合的动力系统，它结合了两种系统的供热方法，能够更加有效灵活的控制空间温度。2.3 接地系统空气源热泵使用周围环境作为热源，地源热泵使用地面作为热源。环境空气温度一年四季以及每天的差异相对地面都更加大17。浅于0.8米的地面每天的温度会有波动，而更深的地方温度基本没有变化。地面温度随季节的变化比较明显，每天的变化比较小。图2显示了地面温度在一年内加拿大渥太华的地表温度一年内的变化。随着深度的增加，极端高温和极端低温开始大范围出现。地面以下的温度取决于很多因素，如太阳辐射、积雪、气温、降水和地面的热性能。在加拿大每年持续观察深于十米的水温18。如图3显示了渥太华不同深度随季节变化的温度变化情况。地面下深度（m）图1 加拿大渥太华，地面温度与深度的变化关系。Ref修正12。地源热泵利用了地面温度相对恒定，而且在冬天温度高于环境空气温度，在夏天低于环境空气温度17的特性。地面温度仍然接近建筑环境所期望的温度值。当内部和外部的温度出现剧烈的变动时，空气源热泵如要提供相同程度的热量需要做更多的工作，这会导致能效比的降低14。如果存温差大小出现变化，热泵系统不需要额外操作。接地系统或者接地环路热交换器由使流体在热泵系统和地面间传输的一束管路组成。两种主要的回路设计方法是：双回路和单回路构造。温度（C）图3 加拿大渥太华一年内不同时期地表温度变化。Ref修正12。2.3.1 双回路构造双回路配置是最常见的系统配置，包含一个独立于热泵系统之外的接地系统。热泵机组由地面获取的热量通过热交换器由水或水/防冻剂混合物转移到制冷剂。目前标准管道规格是由聚乙烯或聚丙烯制造，内径19mm(3/4英寸)，作为中小型规模应用。有两种双回路构造：闭环式和开放式。2.3.1.1 闭环式系统闭环式系统的应用很常见，其中传热流体存在于循环线圈中，不与地面产生直接接触；热量在地面和管道之间进行传递20。闭环系统分作四类：纵向、横向、螺旋等。垂直闭环系统由垂直方向的热交换管道组成。有一个深入地面的孔道，一般深度在4575m，面积较大的建筑和工业使用可能会超过150m。建筑底部有一个U形连接器，与两个管道连接接入孔中（图4）21。为了强化传热，管道和井壁之间充满了一种可用泵吸收的浆状材料20,22。为了确保在多重多样的钻孔中流动顺利进行，需要采用歧管系统，这种系统可以安置在系统内部或者循环区域内部。垂直循环的一个优势是降低了安装面积，使它更适用于土地面积有限的情况。另一个促进它使用的因素是它不会破坏周围环境，因为钻孔相对挖沟来说影响较小17,23。此外，由于地下深处的温度一年四季接近恒定，将管道定位在那里使地源热泵有着稳定的热性能并能降低整个回路的长度20,23。使用这种系统最大的缺点是安装成本较高，因为钻孔比挖沟要昂贵的多。因此，垂直闭环系统更多应用于大规模工程9。在地面面积充足的地方常见的是水平闭环系统，接地回路铺于沟中后埋入地下。根据传热要求和土地情况，循环的安排方式可能有所差别。三种最常见的布局形式是基本回路（图5）、连续回路（图6）、并行回路（图7）。相对于连续式和并列式回路，基本回路布局通常需要占用较大的面积。连续回路降低了对面积的要求而且简单易安装，所以也很常见9。连续回路和并列回路可以结合使用，能够提高安装使用的灵活性。对于住宅设施来说，水平式比垂直式更加具有经济性，因为挖沟的成本远小于钻孔9。放置管道的沟深度一般不超过几米，但在会出现霜冻的地区，应当在冻土层以下。随着深度降低，土壤和周围环境的相互作用增强，这将导致不同时间段和不同季节地面温度出现变化，进而影响传热和系统性能。影响传热的其它因素包括雨水、降雪、植被情况和阴影等9。这些因素都会导致水平系统比垂直系统需要安排更多的管路。水平系统需要水/防冻液混合，作为寒冷气候下的防冻保护9。图4 垂直闭环热交换的地热热泵系统图5 地源热泵水平闭环基本回路图6 地源热泵水平闭环连续回路图7 地源热泵水平闭环并列回路闭式螺旋循环的排布类似传统的水平循环，因为它也是水平的放置于浅沟内。但是，螺旋循环的管道在沟内是圆形放置的，每个螺旋有管道直接通向热泵9,24。螺旋循环相对于水平循环占用的面积较小，而且对沟的要求也更低，但对于固定的负载它需要更长的管路。有的螺旋循环是将管道放置于垂直的窄沟中。这种垂直排布的主要优势是降低了对水平面积的需求，也允许了很多种类挖沟设备的使用，有时有利于降低成本17。需要注意的是，在挖沟花费构成地源热泵系统的主要成本时，螺旋循环能够降低初始成本，在材料花费更大时是不会提高经济性的21。螺旋循环相对于水平循环的其它缺点包括：更低的传热量和更大的传热面积需求。由于螺旋循环管道长度增加，因此相对于其它水平排布循环对泵有着更大的需求，这就降低了系统COP。闭环式池塘循环是闭式循环中最少见的热交换系统，基本上是淹没在水体中的螺旋式闭环系统。盘绕的管道接入框架并用混凝土固定。框架通常在池塘底部以上2348cm，以便管道周围流体形成对流21。循环管道位置一般要超过1.8m深，这对于保证水质环境较低情况下，热质的稳定是必不可少的，并且能够确保在寒冷的季节管道周围水温不会低于水的冰点。由于河流的水文情况不是很稳定，因此不适合应用此系统，例如洪水或碎石可能会使管道损坏9,24。池塘循环正在日益普及，部分原因是因为相比于其它系统需要更少的管道，而且有着优越的传热特性，既不需要钻井也不需要挖沟。这个系统的主要缺点是需要一个足够到的水体，而且对水体有着诸多限制，例如禁止划船。2.3.1.2 开环式系统开放式热交换系统直接与地面进行热交换。这些系统都使用当地的地下水或地表水，如湖泊、池塘，作为直接传热媒介。水抽出后流过热泵热交换器，之后流回地下或者用于灌溉9。目前，对废弃矿井中丰富水源的利用越来越广泛，因为充满热水的废矿井可以使地源热泵技术的应用变得非常廉价。开放式系统更加倾向应用于大型热泵系统。目前应用开环系统的最大的地源热泵系统，为宾馆和办公楼提供10MW的热量9。常见的开环式系统有三种：提取井、回灌井和地表水系统（图8）。水从一个达到地下水位的生产井抽取，之后流经热泵热交换器，之后流回距离生产井有一段距离的地下，这段距离足以让热量由地表传递到水中9。回灌可以排除；开放引流价格便宜，但需要有丰富的水源供应热泵，有一个切实够大的容量以备长期使用14。热泵机组水流量一般在5.711.4L/m。图8 开放式热泵换热系统及地源热泵生产井和注水井。开环系统的好处是水源温度基本保持不变。因为避免了地源热泵系统额外的与地连接的热交换器，这就提高了COP18。由于不同的抽取方法，开环式系统可以承担很高的载荷而且有着很高的COPs，并能降低成本9。此外，开环式系统相对于闭环式垂直系统需要的钻孔较少，有着简单的对地链接设计，并能降低运行成本。地源热泵需要抽取一定量的水，这有可能受到当地水资源保护法则的限制。开环式系统的主要缺点是需要保护水质，由于通常使用干净的地下水或地表水，开环式系统有时是被禁止的18。开环系统和地源热泵系统之间的热交换器很容易受到腐蚀、污染和结垢，因此水应该处于中性并且含有一些微量矿物质，例如铁24。如果水的化学性质不接近于中性，那么使用者的维修次数可能会大大提高9。2.3.2 单回路配置单回路配置也被称作直接交换系统，热泵工作流体流经地面换热器，从而避免了接地环路对热交换器的需要。在供热过程中，接地环路基本上成为热泵蒸发器。单回路配置还排除了接地环路循环泵，而不是依靠增大压缩机。这些措施都增加了地源热泵的COP18。由于铜管优越的传热性能，经常应用于这些系统中以减少需要的排布面积。直接换热的压力较大，需要良好的施工以避免因管道破裂对系统运行的影响。如果管道破裂，整个系统可能需要挖出来进行维修。另一个缺点是涉及增加接地回路容纳制冷剂的体积，这会增加系统成本9。尽管如此，由于具有较高的COPs，单回路配置系统的应用越来越普及，而且一些国家（法国和奥地利）正在研究与蒸发器直接换热加上一些设施直接冷凝来进行地板式供热9。2.4 全球地位地源热泵的主要优势是能够利用温度在5-30的土壤和地下水，而这个温度范围在全世界各地的一定深度都会存在15。如，在2004年约30个使用地源热泵系统的国家，领先的国家有美国、瑞典、德国、瑞士、加拿大和奥地利等。表1列出了有安装地源热泵能力的几个国家。截止2004年全球安装的地源热泵热能力12万千瓦左右，每年的能源使用需求在20亿千瓦时。该技术在法国、荷兰、中国、日本、俄罗斯、英国、挪威、丹麦、爱尔兰、澳大利亚、波兰、罗马尼亚、土耳其、韩国、意大利、阿根廷、智利、伊朗、英国和挪威15逐渐兴起。自1994年以来的年均增长率一直在10左右，目前大约是170万的应用12。美国和欧洲的领导人，目前也出于经济增长考虑发展该技术。表1 2004年热泵技术使用领先的国家国家热装机容量（MW）每年能源使用（GWh）地源热泵安装数量美国瑞典德国瑞士加拿大澳大利亚630020005604404352756300800084066030037060000020000040000250003600023000地源热泵技术的增长一直比其他可再生能源与常规能源技术慢一些。增长受限可以归因于诸多因素，包括非标准化的系统设计、相对于其它系统较高的成本、人们对于GHPs安装知识有限、政府政策的限制、经济规模和地区经济的限制6,18。尽管有这些问题存在，但是却正在不断的被解决，提高了人们对该技术的接受程度15。3 近期发展近期有很多关于地源热泵系统各个方面发展的报告。3.1 辅助冷却组件由于压缩机和泵都不是100%的效率，它们运行过程中产生的热量直接被释放浪费掉。压缩机和泵产生的废热可用于预热循环泵中的制冷剂。将制冷剂通入一个密封的外壳，覆盖于泵和压缩机外面，由它们的电动机驱动能够实现将热量传递出去。预热能够提高组件性能，提高整个地源热泵系统的COP，以及降低接地回路换热器的热负荷8。3.2 地面霜冻循环在多年冻土地区地源热泵的使用也逐步开始。建筑地基传热可能使永久冻土层融化并危及结构的完整性。通过安装一个紧邻地基的地面循环，冻土融化的现象可能降低甚至消失。从地基散发的热量被循环系统抽取，以确保建筑不会大幅度影响当地地表温度。抽取的热量用于补充建筑所需的热量，通常占建筑所需总热量的2050%。该系统不应当使地面冻结的时间超过自然周期内冻结的时间，不应当扰乱当地的生态环境。热交换回路应当时安全可靠的，以防出现故障影响到建筑的稳定性12。3.3 单井回灌热交换系统单井回灌某些方面结合开放式和封闭式水热交换系统。它们本质上是地下水源热泵系统，使用来自于半开放式循环安排的井水。在这样的系统中，一个垂直钻孔深入来自深岩井底部温水中，用潜水泵抽取供给热泵机组。冷水被引止抽水井口附近。冷水深入地下过程中吸取土壤中的热量，从而避免了单独建造一个注水井。单井回灌系统最近越来越被人所接受，因为在合适的地区它们有着良好的整体性能。该系统被安装在地表有4560m石床的地点。国内作为饮用水源的井很容易被改造应用于该系统。该系统还可以应用于充满水的矿井和隧道9。4 供热系统的分析比较在以下供暖系统间进行比较：地源热泵、空气源热泵、电动基板、热水器、天然气炉（中、高效率）。加拿大三个省份（阿尔伯塔省、安大略省和新斯科舍省）进行效率、成本和排放量评估。结果列于表2、3。在欧洲的发展也进行了探讨。4.1 效率地源热泵具有高效率，反映在他们的COPs。典型的等效于COP的系统有以下这些：地源热泵：3-5、空气源热泵：2.3-3.5 、踢脚线电热水器：1、中间效率天然气炉： 0.78-0.82、高效率天然气炉：0.88-0.97 。4.2 经济性相比于传统供热系统，地源热泵系统初始成本大幅提高，主要因为地源热泵机组和接地装置（包括钻井和挖沟的成本）等资金的投入。但是，地源热泵能够高效的降低运行成本。4.2.1 在加拿大的经济性趋势对于在加拿大的情况分析是，假设所有条件相同的情况下初始投资成本的评估。在天然气特定的省份，每年供热成本为基础的电力成本。假设20年的寿命和平均COP 4的地热系统。典型地热泵有20-25年的保证，但存在有超过30年运行的系统。假定系统安装不需要新的管道安装。表2总结了评估成本。结果表明地热热泵的经济可行性很大程度上取决于位置。电力、天然气的价格和其他取暖燃料价格具有区域性。在阿尔伯塔省和新斯科舍地源热泵是最经济竞争力的选择。在安大略省的空气源热泵有决心20年后极大降低成本。艾伯塔省和新斯科舍省比安大略省有较高的电力价格，直接影响到了这一调查结果。高电价促进了空气源热泵和电动地板的推广使用。研究还发现，当天然气的价格较低时，使用天然气和地源热泵供暖花费之间的差距缩小。当天然气或其它燃料价格较低时，使用地源热泵可能并非最经济的选择18。在特定的地区地源热泵空调系统表现出渐增的经济优势，因为地源热泵在反向工作时使它们能够从建筑中吸收能量传递至地面。而传统的供热系统需要一个单独的空间制冷空调，地源热泵系统避免这种初始成本24。地源热泵系统的投资回收期通常是6至20年之间，根据资金成本、能源价格和能源价格不断上涨18。另一个没在研究中量化的优势是，设备本身的价值。GHPs倾向于增加属性值，能够实现建设和土地投资的高回报，并促进更理想的抵押贷款评估18。请注意，地源热泵系统是最具成本效益的，如果安装在建筑施工中，或者当一个老的供暖系统需要更换时。购买和安装地源热泵，作为一个工作系统的选择，很少是值得从能源和经济的角度考虑的14。4.2.2 在欧洲的经济性趋势表4说明了欧盟各国家的天然气和电力价格。该分析假设所有国家具有稳定的热负荷且系统有20年的寿命。比较空气源热泵、电加热器、天然气炉（中、高效率）的成本（包括初始成本）。为简单起见，初始成本假设为与加拿大的比较中使用的相同。欧洲的天然气和电力成本较高，但是高于加拿大的投资花费看起来是相对的。在大多数欧盟国家看来，地源热泵系统想对于传统供热方式更具经济性，而安装成本的增高相对于20年的使用寿命来说是微不足道的。在德国、爱尔兰、卢森堡、西班牙和英国发现，使用高效率的天然气炉更加经济，这是由于电力的价格要高于可燃气体。表2在几个地点的各种供暖系统的经济参数比较供热系统投资成本($)阿尔伯塔安大略省新斯科舍省年花费($)现值($)年花费($)现值($)年花费($)现值($)地源热泵空气源热泵电热板天然气炉a天然气炉b90004900155015001900601813225712761109210202116046690270202408032844412312344104915560137802617048380228806498772432188516532723027940501904475040460单位为2009年加元。现值指一个20年期间。a代表中间效率。b代表高效率。表3 在几个地点各种供热系统的二氧化碳排放量比较供热系统每年燃料使用（kWh）阿尔伯塔安大略省新斯科舍省排放强度排量排放强度排量排放强度排量地源热泵空气源热泵电热板天然气炉a天然气炉b608082142228028475246551.121.121.120.1900.1906826922225015541046840.1880.1880.1880.1900.190114315444188541046841.041.041.040.1900.190634685732325554104684排放强度单位为(kgCO2/kWh)。排量单位为（kg）。表4欧盟几个国家天然气、电力价格，以及与电力相关的二氧化碳排放量27,28。国家天然气价格($/kWh)电力价格($/kWh)排放强度国家天然气价格($/kWh)电力价格($/kWh)排放强度澳洲0.080.270.239拉脱维亚0.050.150.443比利时0.080.280.311立陶宛0.060.170.307赛福斯N/A0.270.974卢森堡0.070.250.307捷克0.070.190.922荷兰0.100.250.419丹麦0.150.390.680挪威N/AN/A0.015爱沙尼0.050.141.015波兰0.070.201.108芬兰N/A0.200.403葡萄牙0.090.240.630法国0.080.180.108斯洛伐克0.060.230.382德国0.080.350.626斯洛尼亚0.090.200.392希腊N/A0.170.882西班牙0.070.260.493匈牙利0.070.220.695瑞典0.120.260.076爱尔兰0.020.270.706瑞士N/AN/A0.041意大利0.100.270.565英国0.060.210.558欧盟0.080.230.486该研究提供了一个在欧洲国家地源热泵实施的一般概述。不同的国家之间，热负荷有所差别，这项研究中引入了不同的表达词汇。在对供热要求较低的地区引入地源热泵可能不够经济，因为地源热泵机组的初始投入是较大的。此外，在气候较温暖的地区，通过降低设备大小能使安装地源热泵的初始成本降低。地源热泵设备的细节问题，要在深入研究分析欧洲特定国家的气候情况下决定。4.3 二氧化碳排放该评估比较了不同供暖系统的二氧化碳排放量。尽管其它污染物的排放也是不可忽视的，但此处集中考虑二氧化碳的排放，因为它是最常见的温室气体而且被认为是影响气候变化的重要因素18。地源热泵不直接排放二氧化碳，排放源于生产电力的发电厂。当电力生产过程中二氧化碳的排放较高时，地源热泵系统排放的二氧化碳也相应的增高。地源热泵是否环保取决于地源热泵所使用的电力生产过程中产生的二氧化碳，它的COP和其它供暖系统的效率25。4.3.1 加拿大二氧化碳排放趋势加拿大地区二氧化碳排放情况的确定，考虑了设备消耗的电量或者天然气的量和燃料排放强度（每kWh电力生产所产生的二氧化碳）。再次审视前面提到的三个省。假设天然气成分是相同的阿尔伯塔省，安大略省和新斯科舍省，每单位气体消耗时的排放量是固定的。每个省的平均排放强度使用碳监测行动（CARMA）在线数据库。不同省份，各种供暖系统的二氧化碳气体排放量列于表3。由于安大略省具有新一代低排放设备，超过50%的电力生产来源于核能，其余部分来源于火力发电厂和水力发电厂，应用地源热泵有利于环保。在阿尔伯塔省和新斯科舍省超过80%的电力生产来自化石燃料，包括煤、天然气发电厂16。相对高效率（95%）的天然气锅炉，当生产每kWh电力的排放强度小于0.76kg时，使用地源热泵能够降低二氧化碳排放18。一般情况下，如果地源热泵使用的电力来源于环保的生产方式，地源热泵相对于传统的电加热设备和天然气燃烧设备能够最大程度的降低排放。在电力生产时排放的二氧化碳较多的地区，使用度源热泵系统所能带来的减排有限。当应用可再生能源进行发电时，地源热泵所产生的二氧化碳排放仅仅来源于运行过程，排量很小甚至接近于零。总体而言，地源热泵通常提供最大（或近乎最大）的排放量的减少。4.3.2 欧洲二氧化碳排放趋势表4列出了欧盟不同国家电力生产过程中的二氧化碳排放强度。使用与电力生产相关设施的碳排放门槛，由Dowlatabadi和Hanova确定18为0.76kg/kWh，由表可以看出，所列出的大多数国家使用地源热泵取代传统供热系统都能够取得降低排放的效果。在一个国家内使用地源热泵机组能显着减少国家整体的二氧化碳排放量。例如，耦合地面地源热泵连接当前英国电网，考虑到英国电网目前的发电组合，使用地源热泵系统相对于传统供热系统能够降低超过50%的二氧化碳排放15。5 结论地源热泵是一种高效的供热技术，能够减少二氧化碳的排放量，潜在的避免了化石燃料的燃烧而且具备一定的经济性优势。对于加热特定的建筑空间，相对于其它供热方式，地源热泵系统显著的减少了能源的使用。随着环境的变化，地源热泵系统可以进行许多变化，而且在世界大部分地区适合使用地源热泵。在选择供热模式时，考虑地源热泵系统是非常重要的，如效率、排放量、经济性等方面。参考文献（见原文）附件2：外文原文The importance of axial effects for borehole design of geothermalheat-pump systemsD. Marcottea,b,c,*, P. Pasquiera, F. Sheriffb, M. BerniercaGolder Associates, 9200 lAcadie, Montreal, (Qc), H4N 2T2 CanadabCANMET Energy Technology Centre-Varennes, 1615 Lionel-Boulet Blvd., P.O. Box 4800, Varennes, (QC), J3X 1S6 CanadacDe partement des ge nies civil, Ge ologique et des mines, Ecole Polytechnique de Montre al, C.P. 6079 Succ. Centre-ville, Montre al, (Qc), H3C 3A7 Canadaa r t i c l e i n f oArticle history:Received 13 May 2008Accepted 18 September 2009Available online 23 October 2009Keywords:Infinite line sourceFinite line sourceGround loop heat exchangersHybrid systemsUnderground water freezinga b s t r a c tThis paper studies the effects of axial heat conduction in boreholes used in geothermal heat pumpsystems. The axial effects are examined by comparing the results obtained using the finite and infiniteline source methods. Using various practical design problems, it is shown that axial effects are relativelyimportant. Unsurprisingly, short boreholes and unbalanced yearly ground loads lead to stronger axialeffects. In one example considered, it is shown that the borehole length is 15% shorter when axialconduction effects are considered. In another example dealing with underground water freezing, theamount of energy that has to be removed to freeze the ground is three times higher when axial effectsare considered.? 2009 Elsevier Ltd. All rights reserved.1. IntroductionGeothermal systems using ground-coupled closed-loop heatexchangers (GLHE) are becoming increasingly popular due togrowing energy costs. Such a system is presented in Fig. 1.The operation of the system is relatively simple: a pump circu-lates a heat transfer fluid in a closed circuit from the GLHE to a heatpump (or a series of heat pumps). Typically, GLHE consistsof boreholes that are 100150 m deep and have a diameter of1015 cm. The number of boreholes in the borefield can range fromone, for a residence, to several dozens, in commercial applications.Furthermore, several borehole configurations (square, rectangular,L-shaped) are possible. Typically, a borehole consists of two pipesforming a U-tube (Fig.1). The volume between these pipes and theborehole wall is usually filled with grout to enhance heat transferfrom the fluid to the ground. In some situations it is advantageousto design so-called hybrid systems in which a supplementary heatrejecter or extractor is used at peak conditions to reduce the lengthof the ground heat exchanger.Given the relatively high cost of GLHE, it is important to designthem properly. Among the number of parameters that can bevaried, the length and configuration of the borefield are important.There are basically two ways to design a borefield. The first methodinvolves using successive thermal pulses (typically 10-years1month6 h) to determine the length based on a given configura-tion and minimum/maximum heat pump entering water temper-ature 8,3. There are design software programs that perform thesecalculations. Some use the concept of the g-functions developed byEskilson 5. The g-functions are derived from a numerical modelthat, by construction, includes the axial effects. The other approachis to perform hourly simulation. This last approach is essential fordesign of hybrid systems in which supplemental heat rejection/injection is used. There are several software packages that canperform hourly borehole simulations. For example, TRNSYS 9 andEnergyPlus 4 use the DST 6 and the short-time step model 5,respectively. Even though these packages account for axial effects,they necessitate a high level of expertise. Furthermore, it is noteasily possible to obtain ground temperature distributions like theones shown later in this paper. In this paper hourly simulations areperformed using the so-called finite and infinite line sourceapproximations where the borehole is approximated by a line witha constant heat transfer rate per unit length. These approximationspresent, in a convenient analytical form, the solution to the tran-sient 2-D heat conduction problem. Despite their advantages,hourly simulations based on the line source approximation are* Corresponding author. De partement des ge nies civil, ge ologique et des mines,Ecole Polytechnique de Montre al, C.P. 6079 Succ. Centre-ville, Montre al, (Qc),H3C 3A7 Canada. Tel.: 1 514 340 4711x4620; fax: 1 514 340 3970.E-mail address: denis.marcottepolymtl.ca (D. Marcotte).Contents lists available at ScienceDirectRenewable Energyjournal homepage: /locate/renene0960-1481/$ see front matter ? 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.renene.2009.09.015Renewable Energy 35 (2010) 763770rarely used in routine design due to the perceived computationalburden.The major difference between the finite and infinite line sourcelies in the treatment of axial conduction (at the bottom and top ofthe borehole) which is only accounted for in the former. Thetheoretical basis of the finite line source, although more involvedthan for the infinite line source, was first established by Ingersollet al. 7. It has been rediscovered recently by Zeng et al. 15 whoimproved the model by imposing a constant temperature at theground surface. Lamarche and Beauchamp 11 have made a usefulcontribution to speed up the computation of Zengs model. Finally,Sheriff 13 extended Zengs model by permitting the borehole topto be located at some distance below the ground surface. She alsodid a detailed comparison of the finite and infinite line sourceresponses, but did not examine the repercussion on borefielddesign.At first glance, the axial heat-diffusion is likely to decrease(increase) the borehole wall temperature in cooling (heating)modes respectively. Therefore, designing without consideringaxial effects appears to provide a safety factor for the design. But,is it really always the case? Moreover, are the borehole designsincorporating axial effects significantly different from thoseneglecting it? Under which circumstances are we expected tohave significant design differences? These are the main questionswe seek to answer. The main contribution of this research is todescribe, using synthetic case studies, the impact of consideringaxial effects on the GLHE design. Our main finding is that formany realistic circumstances the axial effects cannot be neglec-ted. Therefore, design practices should be revised accordingly toinclude the axial effects.We first review briefly the theory for infinite and finite linesource models. Then, we present three different design situations.The first two situations involve the sizing of geothermal systemswith and without the hybrid option, under three different hourlyground load scenarios. The last design problem examines theenergy required and ground temperature evolution in the contextof ground freezing for environmental purposes.2. Theoretical backgroundThe basic building block of both infinite and finite line sourcemodels is the change in temperature felt at a given location andtime due to the effect of a constant point source releasing q0units ofheat per second 7:DTr;t q04pksrerfc?r2ffiffiffiffiffiatp?(1)where erfc is the complementary error function, r the distance tothe point heat source, andais the ground thermal diffusivity.The line is then represented as a series of points equally spaced.In the limit, when the distance between point sources goes to zero,Fig. 1. Sketch of a GLHE system.NomenclatureaThermal diffusivity (m2s?1)A, B, C, D Synthetic load model parameters (kW)br/HCsGround volumetric heat capacity (Jm?3K?1)erfc (x)Complementary error function(erfcx 12ffiffiffippRNxe?t2dtEWTTemperature of fluid entering the heat pump (K or?C)FoFourier number, Foat/r2ksVolumetric ground thermal conductivity (Wm?1K?1)HBorehole length (m)HPHeat Pumpq0Radial heat transfer rate (W)qRadial heat transfer rate per unit length (Wm?1)SBorehole spacing (m)rDistance to borehole (m)rbBorehole radius (m)RbBorehole effective thermal resistance (KmW?1)tTimeDT (r, t)Ground temperature variation at time t and distance rfrom the borehole (K or?C)TfFluid temperature (K or?C)TgUndisturbed ground temperature (K or?C)TwTemperature at borehole wall (K or?C)uH2ffiffiffiffiatpx, ySpatial coordinates (m)zElevation (m)D. Marcotte et al. / Renewable Energy 35 (2010) 763770764the combined effect felt at distance r from the source is obtained byintegration along the line.2.1. Infinite line sourceIn an infinite medium, the line-integration gives the so-called(infinite) line source model 7:DTr;t q4pksZNr2=4ate?uudu(2)2.2. Finite line sourceIn the case of a finite line source, the upper boundary isconsidered at constant temperature, taken as the undisturbedground temperature 15. This condition is represented by addinga mirror image finite line source with the same load, but oppositesign, as the real finite line. Then, integrating between the limits ofthe real and image line, one obtains 15,13:DTr;t;z q4pksZH00erfc?du2ffiffiffiffiatp?du?erfc?d0u2ffiffiffiffiatp?d0u1Adu(3)where du ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 z ? u2qand d0u ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 z u2q, z is theelevation of the point where the computation is done. The left partof the integrand in Equation (3) represents the contribution by thereal finite line, the right part, the contribution of the image line.Fig. 2 shows the vertical temperature profile obtained withEquation (3) at radial distance r2 m, after 200 days, and atr1 m, after 2000 days of heat injection. The correspondinginfinite lines-source temperature is indicated as a reference. In thisexample, the borehole is 50 m long, the groundthermal parametersare ks2.1 Wm?1K?1and Cs2e06 Jm?3K?1. The ground is inti-tially at 10oC. The applied load is 60 W per m for a total heatingpower of 3000 W. As expected, the importance of axial effects andthe discrepancy between infinite and finite models increases withthe Fourier number (at/r24.54 and 181.4 for these two cases).In hourly simulations, the fluid temperature (Tfin Fig. 1) isrequired. This necessitates knowledge of the borehole thermalresistance Rb(i.e. from the fluid to the borehole wall), and of theborehole wall temperature (Twin Fig. 1) 2. The average boreholewall temperature it obtained by integrating Equation (3) along z.However, this is computationally intensive due to the doubleintegration. Lamarche and Beauchamp 11 have shown, using anappropriate change of variables, how to simplify Equation (3) toa single integration. Accounting for small typos in 11 and 15 asnoted by Sheriff 13, the average temperature difference, betweena point located at distance r from the borehole and the undisturbedground temperature, is given by:DTr;t q2pks0BBBZffiffiffiffiffiffiffiffiffib21pberfcuzffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiz2?b2qdz ? DA?Zffiffiffiffiffiffiffiffiffib24pffiffiffiffiffiffiffiffiffib21perfcuzffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiz2?b2qdz ? DB1CCCA(4)wherebr/H, r is the radial distance from the borehole center,uH2ffiffiffiffiatpand DA, and DBare given by:DAffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 1qerfc?uffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 1q?berfcub? e?u2b21? e?u2b2uffiffiffipp!andDBffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 1qerfc?uffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 1q? 0:5?berfcubffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 4qerfc?uffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 4q? e?u2?b21? 0:5?e?u2b2 e?u2?b24?uffiffiffipp!10121416182022240102030405060Temperature ( oC)Depth (m)Vertical temperature profile Infline, r=2, t=200 dFline, r=2, t=200 dFline average, r=2, t=200 dInfline, r=1, t=2000 dFline, r=1, t=2000 dFline average, r=1, t=2000 dFig. 2. Vertical ground temperature profile at radial distances r1 m and r2 m afterrespectively 2000 days and 200 days, Fo(r 1, t2000)181.4 and Fo(r 2,t200)4.54.Constantheatinjectionof3000 W.Thermalparameters:ks2.1 Wm?1K?1,Cs 2e06 Jm?3K?1.010002000300040005000024681012Days T (oC) InfiniteFiniteFEMFig. 3. Comparison of Finite and Infinite line source model with finite element model(FEM) for a 30 m borehole. Average temperature variation computed at 0.5 m from theborehole axis, over the borehole length. Constant heat transfer rate of 1000 W.Thermal parameters: ks2.1 Wm?1K?1, Cs2e06 Jm?3K?1.D. Marcotte et al. / Renewable Energy 35 (2010) 763770765The particular case rrbin Equation (4) gives the borehole walltemperature.2.3. Numerical validationFig. 3 compares the variation in temperature over timecomputed with finite and infinite line source to the numericalresults of a finite element model (FEM) constructed withinCOMSOL?. The finite element model is 2-D with axial symmetryaround the borehole axis. The ground is represented bya 50 m longand 50 m radius cylinder. The borehole is represented by a 30 mlong and 0.075 m radius cylinder delivering 1000 W. The axis ofrevolution is located at the borehole center and constitutesa thermal insulation boundary whereas all external boundaries areset to the undisturbed ground temperature. Over 6000 triangularelements equipped with quadratic interpolating functions are usedto discretize the model. The agreement between the FEM modeland the finite line source is almost perfect, the maximum absolutedifference in temperature over the 5000 days period being only0.019oC.Fig. 4 compares the temperature obtained with the infiniteand finite line source models, at r 1 m and r 0.075 m (atypical value for rb), with the thermal parameters specifiedabove. A 1oC temperature difference between the infinite andfinite models is obtained after 2.5 y and 2 y, at 1 m and 0.075 mrespectively. Note that the temperature reaches a plateau for thefinite line source model indicating that a steady-state conditionhas been reached. In contrast, the infinite line source modelexhibits a linear behavior.Fig. 5 shows the ground temperature, computed at a distance of1 m from the borehole, for increasing values of the borehole length.As expected, the finite line source solution reaches the infinite linesource solution for long boreholes.0.001 0.01 0.111010010001020304050607080r=0.075 mr=1 mGround temperatureTime (y)Temperature (oC)Fig. 4. Comparison of Finite (solid) and Infinite (broken) line source model, computedat distance 1 m and 0.075 m from the borehole. Constant heat transfer rate per unitlength of 100 W/m. Thermal parameters: ks2.1 Wm?1K?1, Cs2e06 Jm?3K?1.010020030040050060070080090010001212.51313.5Borehole length (m)Temperature (oC)Average temperature vs borehole length Infinite linesourceFinite linesourceFig. 5. Infinite vs finite line source average temperature along a vertical profile. The loadis 20 W/m, thermal parameters: ks2.1 Wm?1K?1, Cs2e06 Jm?3K?1. Temperaturecomputed after one year at r1 m from the borehole.1234561000100Cooling (+) Heating () load Time (h)Load (kw)1234562001000100Load decompositionLoad (kw)Fig. 6. Principle of temporal superposition for variable loads.0510152025303533.544.555.566.577.5COP vs EWTEWTCOP CoolingHeatingFig. 7. COP as a function of EWT.D. Marcotte et al. / Renewable Energy 35 (2010) 7637707663. Design of complete geothermal systemsIn this section we compare the design length of borefieldsobtained with the finite and infinite line source models for givenhourly ground load scenarios. These calculations imply that singleborehole solutions will need to be superimposed spatially. We havealready seen an instance of this principle of superposition whilecomputing the line source solution from a series of constant pointsources along a line 7, see Equations (1 and 2). The additivity ofeffects (variation in temperature) stems from the linear relationbetween q andDT, and the fact that energy is an extensive andadditive variable. The temporal superposition also follows the samegeneral principle of addition of effects as described by Yavuzturkand Spitler 14 and illustrated by Fig. 6. When the load is varyinghourly, a new pulse is applied each hour. It is simply the differencebetween the load for two consecutive hours. More formally, for theinfinite line source as an example, with a single borehole, we have:DTr;t Xi; ti?tq?i4pkZNr2=4at?tie?uudu(5)where: q*1q1, and q*iqi?qi?1, i2.I, tI?t, is the incrementalload between two successive hours. With multiple boreholes,DTx0;t Xnj1Xi; ti?tq0i4pkZNkxj?x0k2=4at?tie?uudu(6)where: n is the number of boreholes, xjand x0are the coordinatevectors of borehole j and point where temperature is computed,respectively. Note that for long simulation periods, the computa-tional burden becomes important.In the test cases that follow we assume that all of the buildingheating and cooling loads are to be provided by the GLHE system,i.e. there is no supplementary heat rejection/injection. Syntheticbuilding loads are used to enhance the reproducibility of ourresults. These building loads are simulated using:Qt A ? B cos?t87602p? C cos?t242p? D cos?t242p?cos?2t87602p?(7)In Equation (7), t is in hours, A controls the annual loadunbalance, B the half-amplitude of annual load variation, C and D4030201001020304040302010010203040 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225Borehole location and priority numberCoord. x (m)Coord. y (m)Fig. 8. Borehole grid and priority number. Number indicates order of inclusion in the design when required.Table 1Number of boreholes required, complete geothermal system. Constant T assumesa constant ground surface temperature of 10oC, Periodic T assumes a periodicground surface temperature with an amplitude of ?20oC in phase with the heatload.ScenarioBorehole length Infinite line Finite lineConstant T Periodic TBalanced (A?17)100 m333334Balanced50 m767480Cooling dominant (A17) 100 m393637Cooling dominant50 m937981Heating dominant(A?30)100 m575356Heating dominant50 m134115124Table 2Number of boreholes required, hybrid system. HP capacity represents 40% ofmaximum building load. The last two column represent the percentage of thebuilding load supplied by the HP for each mode.ScenarioBoreholelengthNumber ofboreholes% EnergyInfiniteFiniteCooling Inf.(Fin.)Heating Inf.(Fin.)Balanced100 m191969 (69)77 (78)Balanced50 m373767 (67)72 (73)Cooling dominant100 m242469 (69)86 (86)Cooling dominant50 m413970 (69)90 (88)Heating dominant100 m373767 (67)83 (86)Heating dominant50 m555372 (70)70 (73)D. Marcotte et al. / Renewable Energy 35 (2010) 763770767the half-amplitude of daily load fluctuations. D/C controls therelative importance of the damped component used to simulatelarger daily fluctuations in winter and summer. Coefficients A to Dare in kW.We consider three different load scenarios, each with B100,C50, and D25. One is approximately balanced (A?17), one isa cooling dominated load (A17) and the other is a heating domi-natedload(A?30).Conversionofbuildingloadstogroundloadsisdone with: qgroundqbuilding(1?1/COP). The heat pump COP variesas a function of entering water temperature as depicted in Fig. 7.For all scenarios, we consider a unique set of possible locationsfor the boreholes. The locations are at the nodes of a regular grid ofmesh S6 m. The boreholes are assigned a priority number (lowernumber / highest priority), moving excentrically from the gridcenter to the fringes (see Fig. 8). The system is simulated with100 m and then, 50 m long boreholes. The borehole heads arelocated at the ground surface.For each scenario and given number of boreholes, we simulatethe hourly fluid temperature for a 10-year period. We repeat thissimulation for different number of boreholes and finally keep thelowest number of boreholes ensuring that the fluid temperature atthe HP entrance never exceeds the HP limit specifications. We dothis computation using both the infinite and finite line sourcemodels.Thermal parameters of the ground are: thermal conductivityks2 Wm?1K?1, volumetric heat capacity Cs3.4e06 Jm?3K?1and borehole thermal resistance Rb0.1 mKW?1. The ground isinitially at 10oC and all the boreholes have a radius of rb0.075 m.Table 1 gives the number of boreholes required for a specificscenario and model. The choice of model does not have a strongimpact on the balanced load scenario. However, for cooling andheating dominant scenarios, the finite line source model indicatesa reduction in the number of boreholes of approximately 7% and15% for the 100 m and 50 m borehole length. As expected, theshorter the borehole length, the greater are the discrepanciesbetween both models.3.1. Seasonal effectsThe finite line source model assumes a constant temperature atthe ground surface equal to the undisturbed ground temperature.This hypothesis would more or less correspond to the case ofgeothermal boreholes located under a building slab. However, inmany cases, the boreholes are located outside the building areawhere the ground surface temperature varies in phase with theheat load. One can expect the axial effect at the ground surface willbe less than under the constant temperature assumption. Theinfluence of ground surface temperature variation on the groundtemperature, at any depth and time, can be computed for a periodicsignal 7. Using the principle of superposition, the influence on thedesign can be assessed.Last column of Table 1 gives the number of boreholes requiredwhen the ground surface temperature is periodic, in phase with theheat load, and shows a yearly variation of ?20oC. The boreholeheads are located at the ground surface, a feature that maximizesthe seasonal effects on the design. As expected, the designs withperiodic ground surface temperature require more boreholes thanwithconstantgroundsurfacetemperature.Forunbalancedscenarios, the periodic ground surface temperature solutionsobtained are intermediate between the infinite and the finite linesource designs.05101520253064202468Time (year)oTemperature ( C)Rock temperature at x=(13,5,12.0) Infinite linesourceFinite linesource1510505101515105051015Control pointx (m)y (m)Fig. 9. Vertical average rock temperature at point x(13.5, 12.0). Thermal parameters: ks2 Wm?1K?1, Cs3.4e06 Jm?3K?1.05101520253010009008007006005004003002001000Time (year)Load (W)Ground cooling load / borehole Infinite linesourceFinite linesourceFig. 10. Evolution of average load per borehole.D. Marcotte et al. / Renewable Energy 35 (2010) 7637707684. Design of hybrid geothermal systemsThe design situation borrows its essential features (boreholegrid, thermal parameters, heat load scenarios) from the previouscomplete geothermal system example. The main difference is thatthe HP and auxiliary system power are respectively selected at 40%and 60% of the maximum building load. The simulation works thesame wayas previously with the following modification. Each hour,the fluid temperature at the HP entrance (EWT) is computed. IfEWT, at any hour, exceeds the HP specification limit, it is assumedthat the HP cycles to keep the EWTat its limit value, the excess loadbeing taken by the auxiliary system. We keep track of all the loadsprovided by the auxiliary system. At the end of the 10-year simu-lation, we verify that the load to the auxiliary system never exceedsits capacity. If exceeded, we add more boreholes. The final design isobtained with the smallest number of boreholes compatible withthe auxiliary system capacity.Table 2 shows the number of boreholes for a specific scenarioand computation model. The proportion of energy provided by thegeothermal system, relative to the total building energy requiredfor the 10-year period, is also given. Unbalanced scenarios withshort boreholes display reduction of only 6% for the number ofboreholes required. However, comparison of Tables 1 and 2 revealsstriking reduction in numberof boreholes. The hybrid systemsneedonly between 46% and 70% of the number of boreholes for thecomplete geothermal system. Yet, the geothermal components ofhybrid systems are able to supply between 67% and 70% of thecooling load and between 73% and 88% of the heating load for thevarious scenarios examined. As the borehole construction costrepresents the main investment in a geothermal system, it indi-cates that hybrid systems can be economically advantageous.Even though hourly simulations are computationally moreinvolved, efficient methods exist to speed up the computations1,10,12. For example, a hybrid system 10-years hourly simulationfor a 45 boreholes field is computed in less than 2 min on a stan-dard laptop.5. Comparing performances for a rock freezing problemIn some environmental problems, like those involving DNAPL(dense non-aqueous phase liquid), the contaminants reach thebedrock and then can propagate through the rock fractures. In suchX coordinate (m)Y coordinate (m)Infinite line: Temperature after 5 years 15105051015151050510151210864202X coordinate (m)Y coordinate (m)Finite line: Temperature after 5 years 15105051015151050510151210864202X coordinate (m)Y coordinate (m)Infinite line: Temperature after 20 years151050510151210864202X coordinate (m)Y coordinate (m)Finite line: Temperature after 20 years 1510505101515105051015151050510151210864202Fig. 11. Ground temperature after 5 years (top) and 20 years (bottom). Infinite line source model (left) and finite line source model (right).D. Marcotte et al. / Renewable Energy 35 (2010) 763770769circumstances, remediation can be extremely difficult and expen-sive. One solution is to catch and treat all the contaminants flowingthrough the fractures. This requires designing a series of wellsforming an hydraulic trap. The pumping and treatment is expensiveand it has to be maintained typically for hundreds of years. More-over, the flow of water to treat could be relatively important. Analternative is to permanently freeze the liquid within the fracturesto avoid any movement of the contaminant.In the following example, we consider the problem of freezingwater inside rock fractures, in a domain 30 m by 30 m by 30 m, forthe purpose of long term confinement of toxic DNAPLs. A 10 ?10borefield is considered (see Fig. 9). Thermal parameters of the rockare: thermal conductivity ks2 Wm?1K?1and volumetric heatcapacity Cs3.4e06 Jm?3K?1. The borehole thermal resistance isRb0.1 m KW?1. The rock is initially at 10oC. The rock porosity issmall enough so as to neglect the latent heat of water and theincrease of rock thermal conductivity occurring when waterfreezes. The total HP capacity is 100 kW (one kW per borehole)and the EWT limit is ?8oC. The mass flow of the circulating fluid is19 l/s (or 0.19 l/s for each borehole). The simulation is run for 30years. The HP capacity is kept at its maximum until the EWT hasreached the limiting value of ?8oC. Then, the HP cycles tomaintain the EWT at this temperature. The performance of thesystem is monitored by computing rock temperature at a controlpoint located at the borefield periphery at (x, y) (13.5,12) m (seeFig. 9).Fig. 9 shows the rock temperature obtained at this control pointusing the infinite and finite line source models. Fig. 10 shows thecorresponding average hourly load per borehole. In both figures,the rugged nature of the load curves is due to intermittent opera-tion of the HP. As shown in Fig. 9, the rock becomes permanentlyfrozen after 10 months and 2.2 years for the infinite and finitemodels, respectively. The temperature difference between bothmodels increases steadily with time, to reach approximately 2oCafter 30 years. The finite line source model predicts that about150 W per borehole are required compared to only 50 W perborehole for the infinite line source model (Fig. 10). Thus, despitea higherheat transfer rate per borehole, the finite line source modelpredicts a higher rock temperature at the control point.In this next example, the same 10?10 borefield is cooled ata rate of 10 W/m (300 W/borehole) for the first year and then3.33 W/m (100 W/borehole) permanently. The temperature distri-bution in the ground is computed using the infinite and finite linesource models after 5 and 20 years. Results are presented in Fig.11.The proportion of the domain with temperature below freezing is79% and 100% after 5 and 20 years for the infinite line sourcecalculation whereas it is only 10% and 52% with the finite linesource model. Therefore, a design based on the use of the infiniteline source would have wrongly predicted ground freezing. Thus,contrary to the two previous examples, the infinite model does notprovide a conservative design.6. ConclusionThis paper studies the effect of axial heat conduction in bore-holes used in geothermal heat pump systems. The axial effects areexamined by comparing the results obtained using the finite andinfinite l
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