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International Journal of Mining, Reclamation andEnvironment

ISSN: 1748-0930 (Print) 1748-0949 (Online) Journal homepage: http://www.tandfonline.com/loi/nsme20

A study into extraction of geothermal energy fromtailings ponds

S.A. Ghoreishi-Madiseh , F.P. Hassani , A. Mohammadian & P.H. Radziszewski

To cite this article: S.A. Ghoreishi-Madiseh , F.P. Hassani , A. Mohammadian & P.H.Radziszewski (2013) A study into extraction of geothermal energy from tailings ponds,International Journal of Mining, Reclamation and Environment, 27:4, 257-274, DOI:10.1080/17480930.2012.697785

To link to this article: https://doi.org/10.1080/17480930.2012.697785

Published online: 18 Jul 2012.

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A study into extraction of geothermal energy from tailings ponds

S.A. Ghoreishi-Madiseha*, F.P. Hassanib, A. Mohammadianc andP.H. Radziszewskia

aMechanical Engineering Department, McGill University, Montreal, Canada; bMining andMaterials Engineering Department, McGill University, Montreal, Canada; cDepartment of Civil

Engineering, University of Ottawa, Ottawa, Canada

(Received 26 April 2012; final version received 22 May 2012)

Assessing the performance of ground-coupled heat exchangers (GCHE) of closed-loop geothermal systems installed in tailings ponds is studied. A heat transfermodel is constructed, taking into account heat conduction as well as groundwateradvection. A three-dimensional finite volume discretisation method over astructured mesh with variable grid size is used to solve the governing equations.The performance of a GCHE system installed in tailings ponds is assessed basedon the rate of energy extraction and the outlet fluid temperature. The geothermalcapacity of mine tailings ponds and its sustainable rate of heat extraction areestimated. Effects of tube network configuration and horizontal and verticalunderground advection on the performance of the system are investigated. It isfound that two-dimensional heat transfer models may lead to over-designedsystems and the effect of advection cannot be neglected in highly pervious tailings.

Keywords: geothermal; tailings; closed loop; renewability; sustainability

1. Introduction

The increasing cost of fossil fuels, their scarcity and the green house gas by-productsof their combustion have motivated researchers to search for renewable and cleansources of energy. Geothermal energy is one of the most promising sources ofrenewable energy with small carbon footprint and relatively affordable productioncost, especially for the purposes of heating and cooling. As a result, the applicationof geothermal heating/cooling systems in residential and commercial facilities isgrowing significantly around the world.

There are two techniques widely used for geothermal heat extraction. The firsttechnique is the open-loop case where a heat pump is used to extract energy fromwater from underground aquifers being delivered to the surface. The water is usuallycycled back to a shallow depth underground, permitting it to re-gain energy while itreturns to the aquifer. The second method is the closed-loop system where heat isextracted from the ground and conveyed to the surface by a fluid circulating inside anetwork of tubes embedded in the ground. The fluid passes through a heat pump,which extracts heat from the fluid before it is re-circulated through the tube network.

*Corresponding author. Email: seyed.ghoreishimadiseh@mail.mcgill.ca

� 201 Taylor & Francis

http://dx.doi.org/10.1080/17480930.2012.697785Vol. 27, No. 4, 257–274,International Journal of Mining, Reclamation and Environment, 2013

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Although both methods are quite popular, the application of open-loop systems isconstrained to the existence of groundwater aquifers. There are also environmentalissues related to the delivery of the groundwater to the surface and its exposure toair, which limits application of open-loop cycles [1]. As a result, the closed-loopgeothermal system is a popular alternative and has been integrated into the heatingsystems of buildings over the last three decades.

One of the most important components of a closed-loop geothermal cycle is theground-coupled heat exchanger (GCHE). Every closed-loop system has a speciallydesigned GCHE which consists of a network of tubes installed in the ground.However, the drilling and excavation cost associated with the installation of GCHEsis often a financial barrier to the application of such systems. Mining operationsprovide a novel solution to this problem by the implementation of a closed-loopgeothermal system in tailings ponds of these operations, thereby saving the costassociated with excavation. In some mining operations, millions of tonnes of tailingsmass (which is the pulp leftover from the mineral processing plant) is stored inspecially prepared sites called tailings pond. The new idea is to install the tubenetwork of the GCHE in the prepared tailings pond sites prior to tailings placement.After tailings placement, the mass will surround the tube network of the GCHE forthe possible heat exchange with the fluid that is circulated through the tubes. Inaddition to the elimination of drilling and excavation costs, another economicadvantage of installing GCHEs in tailings ponds is that this method does not requiregrouting, unlike the conventional technique for installing GCHEs, where groutmaterial is poured into the drilled borehole to guarantee a proper heat transferbetween the heat exchange U-tubes and the ground. The implementation of GCHEsin tailings ponds is deemed to be considerably more economic and moretechnologically advantageous compared to conventional closed-loop geothermalsystems because there are no incurred costs for drilling, excavation and grouting.Using this technique, tailings ponds could be converted to reliable and sustainablesources of geothermal energy. Therefore, tailing ponds of mining operations can beconverted from an economic liability to truly sustainable energy resources.Eventually, mining communities can benefit from this renewable, inexpensive andclean source of energy during ore extraction and even after the minerals are depleted.

In order to achieve a thorough understanding of the performance of GCHEsinstalled in tailings ponds, this work seeks a numerical simulation of the heat transferphenomenon inside the GCHE. Although a preliminary study of extracting heatfrom mine tailings ponds was carried out by Raymond et al. [2], there are very fewstudies exclusively dedicated to the application of closed-loop geothermal systems inmine tailings. Though there are similarities between the GCHEs installed in tailingsponds and the conventional types of residential or commercial GCHEs, there aresome engineering issues which should be addressed to ensure the technical andeconomic feasibility of the proposed idea. The first issue is the suitability of tailingsmaterial for conveying the geothermal heat to the tube network of the GCHE. Forexample, a low thermal conductivity of the tailings mass leads to a poor performingGCHE shortly after its operation begins [1]. This article addresses this issue bydeveloping a numerical simulation model for assessing the performance of GCHEsinstalled in mine tailings ponds. The second issue arises from the arrangement of thetube network; in conventional GCHEs, a U-tube is installed inside each borehole.However, in this study, the tube network of the GCHE is installed prior to theplacement of tailings without the need of U-tube boreholes. Therefore, the tubes can

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be placed farther apart from each other and a tube network comprised of ‘single-tube’ elements can be designed. Single-tubes could then be connected in series inorder to improve the temperature of the outlet fluid. The application of single-tubesin GCHEs introduces a new approach to the design of GCHEs which will be furtherdiscussed in this article. For example, most of the existing literature studies haveassumed a constant heating/cooling load along the borehole length [3,4]. However,this assumption is not valid for the case of single-tubes since the heat flux transferredto the fluid circulating in a single-tube is dependent on the bulk fluid temperature,which varies along the tube length as it approaches the ground temperature. To solvethis problem, the authors propose a constant inlet temperature assumption that isbased on the calculation of the local value of heat flux directly from the rate of heatexchanged between single-tube and fluid at each point.

So far, most studies have assessed heat transfer in GCHEs using a conductiveheat transfer approach [1,5,6]. This assumption is valid for GCHEs with little or nogroundwater movement where the advection mechanism is negligible compared toconduction. Diao et al. [7] and Fan et al. [8] suggested a two-dimensional (2D)advection–diffusion model and showed that groundwater flow affects the heattransfer of a GCHE. However, this 2D assumption rules out gravitationalunderground flow which is very likely to happen in closed-loop systems sincegravitational force is always present and groundwater flow is probable if the heattransfer medium is hydraulically conductive. Another drawback of the 2D model isthat the conductive heat flux along the tube length is assumed to be negligible. But,as the bulk temperature of the fluid circulating inside a single-tube varies along thetube length, a temperature gradient is created along the tube length which maydisprove the validity of the 2D model assumption. Considering these potentialdownsides of the 2D models, a three-dimensional (3D) conductive-advection modelfor assessing the heat transfer in GCHEs installed in tailings ponds is proposed inthis article.

The main objective of this article is to develop a numerical model capable ofassessing the heat transfer in GCHEs installed in tailings ponds. The developednumerical model is also used to investigate the possibility of improving theperformance of such GCHEs by studying the effect of groundwater flow and varioustube network arrangements. To the authors’ best knowledge, this is the first studydedicated to a comprehensive investigation of the implementation of GCHEs intailings ponds.

The mathematical model is explained in Section 2 of this article with theintroduction of the associated GCHE geometry, the related physical domain and theboundary conditions. In addition, the governing equations and their physicalmeaning are discussed in this section. Then, the numerical procedure anddiscretisation methods are described in Section 3, followed by discussion of theresults in Section 4. The conclusions of the study are summarised in Section 5.

2. Heat transfer model

Figure 1 shows a cubic control volume of tailings that was used as the maingeometric cell of this study. In order to focus on the canonical cases, GHCE tubesare supposed to be vertically buried in tailings at a depth of HD. It is considered thatthe tubes are placed in an organised matrix formation. Also, the walls of the tailingspond surrounding the tube matrix are assumed to be sufficiently far from the tubes

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such that extending these boundary walls any further does not affect the interiortemperature field. The single-tubes can be connected in series. For instance, Figure 1shows a tube network consisting of 12 single-tubes in which every four sequentialsingle-tubes are connected in series. Water is assumed to be the fluid which iscirculated in the single-tubes. Considering the fact that the total length of thehorizontal tubes (connecting the vertical tubes to each other) is much shorter thanthe total length of the vertical tubes, heat transfer in horizontal tube links isconservatively not considered for the purpose of the simplicity of the simulations.

Considering the porous structure of tailings and the effect of groundwatermoving through its pores, the governing equation of heat transfer in the GCHE is aconvective heat transfer in porous medium, including a heat source/sink functionwhich represents the heat conveyed from tailings mass to water tubes [9]. It isassumed that the effect of natural convection due to the ground temperaturegradient in the z-direction is negligible. According to Love et al. [10], this assumptionis valid since the z-dimension is not sufficiently long to create a significantbuoyancy driven flow regime. Therefore, the governing heat transfer equation isexpressed by

rm Cm@T

@tþ rf Cf u

@T

@xþ v

@T

@yþ w

@T

@z

� �

¼ @

@xkm

@T

@x

� �þ @

@ykm

@T

@y

� �þ @

@zkm@T

@z

� �þ q

:ð1Þ

Figure 1. Geometry of a GCHE installed in a tailings pond.

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where rm, Cm, km, rf, Cf and q are, respectively, density of tailings, specific heatcapacity of tailings, thermal conductivity of tailings, density of water, specific heatcapacity of water and rate of heat generation (or extraction) per unit volume. Also, uv and w are the respective x, y and z components of volume averaged velocity ofwater in porous tailings.

It is assumed that the tailings mass has an initial temperature equal to theboundary temperature. Thus, the boundary and initial conditions are as follows:

Tjx¼0 ¼ Tjx¼L2¼ Tjy¼0 ¼ Tjy¼W2

¼ Tjz¼0 ¼ Tjz¼H2¼ Tb ð2Þ

and

Tjt¼0 ¼ Tb ð3Þ

where Tb is the boundary temperature. The source term q:in Equation (1) represents

the heat conveyed to water through the tube wall per volume of the tailings. Figure 2shows a tube cell and its surrounding control volume. Obviously, q

:is non-zero only

at locations where single-tubes rest and is zero elsewhere. So far, existing modelshave considered the cooling (or heating) effect of the tube network as a uniform heatsource function along the length of the U-tubes. However, since the bulktemperature of the fluid approaches the ground temperature as it travels throughthe tube length, the validity of this assumption may be rejected. Thus, a morerealistic approach of deriving q

:is sought in this work where the calculation of q

:is

based on the local rate of heat exchanged between the tailings mass and the single-

Figure 2. Tube cell and its surrounding control volume.

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tube(s). Assuming an arbitrary tube cell, shown in Figure 2, and considering the factthat the energy extracted from the tailings mass is stored in water in the form ofenthalpy change, q

:will be expressed by [11]

q:¼ �m

:CfðTf þ DTf � TfÞ �

1

DV¼ �

m:CfDTf

DVð4Þ

where Tf, m:and DV are the bulk temperature of water flowing through the tube cell,

mass flow of water through the tube cell and volume of the finite volume cellsurrounding the tube cell, respectively. On the other hand, the energy balance impliesthat the rate of energy stored in water must be equal to the rate of energy extractedfrom the tube wall. In other words, the energy balance is written as

m:Cf DTf ¼ UO ðpD Þ ðTwall � TfÞDL ð5Þ

where Twall, UO, DL and D are the wall temperature, overall heat transfer coefficient,length of the tube cell and inner diameter of the tube cell, respectively. Integratingthe differential form of Equation (5) over the length of a tube cell will lead to

m:Cf

ZTfþDTf

Tf

dTf

Twall � Tf¼ pDUO

ZDL

0

dL: ð6Þ

Therefore,

DTf ¼ ðTwall � TfÞð1� e�bÞ ð7Þ

where,

b ¼ pD UO DLm:Cf

: ð8Þ

Equation (7) formulates the change in the bulk temperature of water flowingthrough the tube cell shown in the Figure 2. It is noteworthy that in Equation (7),Twall is considered as the temperature of tailings mass confined inside the controlvolume in which the tube cell resides. Thus, Equation (7) couples the temperature ofthe fluid inside the tube with the temperature of the tailings surrounding the tubewall. This is physically meaningful since the temperature of tailings mass and thetemperature of the water in the tube network are dependent on each other.

The overall heat transfer coefficient is formulated as [11]

1

UO¼ r2

r1� 1

hþ r2 lnðr2=r1Þ

ktubeð9Þ

where, h, r1 and ktube are the convection coefficient of water inside the tube, innerradius of the tube and thermal conductivity of the tube, respectively. Equation (9)

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expresses the overall heat transfer coefficient on the outer surface of the tube wall.The first term on the right-hand side of Equation (9) corresponds to the convectivethermal resistance between fluid and the inner tube wall, while the second term onthe right-hand side refers to the thermal resistivity of tube thickness. Unlike theconventional GCHEs where grouting the borehole is necessary, there is no need totake into account the thermal resistivity of grout material since there is no need forgrouting. Equation (9) states that the conductive resistivity of the tube material is asimportant as the convective resistivity of the flow of water inside the tube. Forexample, a negligible tube thickness (r2 � r1 or ktube � 1) means that there is noresistivity due to tube thickness and the overall heat transfer coefficient is equal tothe convective heat transfer (UO ¼ h). On the other hand, a large value of convectioncoefficient h � 1 will lead to an overall heat transfer coefficient equal to the thermalconductance of the tube. The convection coefficient, h, is obtained using thefollowing relation developed by Dittus and Boelter [12].

NuD ¼ hD=kf ¼ 0:023Re0:8D Pr0:3 ð10Þ

where, NuD, ReD, Pr and kf are, respectively, the Nusselt number, Reynolds number,Prandtl number and thermal conductivity of water. The physical interpretation ofEquations (7)–(10) is better understood by examining its two possible extremes. Forinstance, Uo � 1 or m � 1 (associated to b � 1) leads to DTf � 0; which meansthat if, in a tube cell, the overall heat transfer coefficient is low or the fluid flow rate ishigh, then the fluid temperature at the outlet of the tube cell will be the same as itsinlet temperature. However, Uo � 1 or m � 1 (associated to b � 1) leads to DTf

Twall 7 Tf; which conveys that if the overall heat transfer coefficient is high or thefluid flow rate is low, then the temperature of the fluid at the outlet of the tube cellwill approach the temperature of the tailings mass surrounding the tube cell. Thisnew approach in the modelling of the heat exchange between the single-tubeelements of the embedded tube network and the tailings mass provides theopportunity to capture the vertical temperature gradient created along the length ofthe single-tube(s).

3. Numerical method

In order to discretise the governing Equations (1) and (7), the finite volume method,developed by Patankar [13], is employed. In this method, the temperature of eachpoint is expressed in terms of its neighbours. A schematic view of the points involvedin such a formulation is shown in Figure 3, where the upper case characters representthe grid points while the lower case symbols stand for boundary surfaces.Accordingly, the discretised equation would be written as follows:

aP TP ¼Xnb

anbTnb þ b ð11Þ

where, aP, anb, TP, Tnb and b are the coefficients associated to the point of interest,the coefficients associated to the neighbour points, the temperature of the point ofinterest, the temperature of the neighbour points and the source term associated to

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the control volume, respectively. Assuming a fully explicit discretisation, anexpanded form of Equation (11) is given by

anP TnP ¼ aP TP þ aW TW þ aE TE þ aS TS þ aN TN þ aB TB þ aT TT þ b ð12Þ

where anP and TnP are the coefficient and the temperature of point P in the next time

step, respectively. Similarly, aP, aW, aE, aS, aN, aB and aT are the coefficientsassociated to the points P, W, E, S, N, B and T in current time step, respectively.Also, TP, TW, TE, TS, TN, TB and TT are the temperatures associated to the points P,W, E, S, N, B and T in current time step, respectively. In order to calculate thecoefficients, the spatial integral over finite volume should be performed on Equation(1), which leads to the following equation:

rm CmTnP � TP

DtDxDyDz þ rf Cf fðue Te � uw TwÞDyDzþ ðvn Tn � vs TsÞDxDz

þ ðwt Tt � wb TbÞDxDyg ¼ kme

TE � TP

dxe� kmw

TP � TW

dxw

� �DyDz

þ kmn

TN � TP

dyn� kms

TP � TS

dys

� �DxDzþ kmt

TT � TP

dzt� kmb

TP � TB

dzb

� �DxDy

þ q:DxDyDz ð13Þ

where ue, uw, vn, vs, wt and wb are normal velocities on boundary surfaces e, w, n, s, tand b, respectively. Similarly, Te, Tw, Tn, Ts, Tt and Tb are the values of temperatureon these boundary surfaces which were calculated using the Kappa scheme [14]. Inorder to calculate _q using Equation (13) for each time step of the numericalprocedure, Equation (7) was used to calculate DTf which was substituted into

Figure 3. Schematics of grid points used in finite volume discretisation method.

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Equation (4). The temperature of water at the inlet of the tubes was assumed to beTin. However, if two or more single-tubes were connected in series, the outlet watertemperature of a preceding tube was set as the inlet water temperature of the single-tube that sequentially followed it.

A slope limiter function was employed to prevent instabilities close to the tubewalls [15]. Assuming a control volume shown in Figure 4, the value of Te wasexpressed by

Te ¼ TP þS

4ðð1� kSÞD� þ ð1þ kSÞDþÞ ð14Þ

with

D ¼ ðdxw2 � dxedxwÞðTE � TPÞ þ 2dxe2ðTP � TWÞ

dxw2 þ dxe dxwDþ ¼ TE � TP

S ¼ 2D� Dþ þ e

D2� þ D2

þ þ e

ð15Þ

where S is the slope limiter function, e is a very small number (chosen to be 1078

here) and k is the scheme selection parameter chosen to be 1/6 which leads to a third-order upwind scheme [16]. A structured Cartesian mesh with variable grid size wasused with finer grid sizes in closest to the tubes and transitioning into coarser sizesfarther away from the tubes.

4. Results and discussion

4.1. Physical and geometrical properties

In order to concentrate on the canonical cases, a representative GCHE withL1 ¼ W1 ¼ H1 ¼ 20 m buried in the depth of 10 m of a tailings pond, HD ¼ 10 m,

Figure 4. A control volume located at point P with its neighbour grid points (W and E).

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with the sizes of L2 ¼ W2 ¼ H2 ¼ 40 m is assumed. The sizes of the physical domain(L2, W2 and H2) are chosen such that extending them does not have any furthereffect (i.e. less than 1076 relative difference) on the results of the temperature field. Atotal water mass flow rate of 64 l/min is assumed to flow through a tube networkcomprising 36 equally distanced single-tubes. Independence of mesh size on theresults is examined by considering a criterion of 1076 (or less) relative differencebetween the results of the temperature field for different mesh sizes or number of gridnodes. In other words, the mesh size was made finer as long as the relative differencebetween the results associated with two consecutive mesh sizes is bigger than 1076. Itwas eventually found that Nx ¼ Ny ¼ 145 and Nz ¼ 40 is the number of grid nodeswhich meets this criterion. Energy balance of the results is checked in each time stepand a relative difference criterion of less than 1074 is set for it; i.e. the amount ofinflux heat transferred through the boundary surfaces into the tailings pondsubtracted by the rate of change in the sensible heat of the tailings mass shouldmatch the heat power extracted by the tube network from the medium. The initialtemperature of tailings is chosen to be 108C. Based on stability considerations, thetime step is set to be Dt ¼ 600 s. In each time step, the temperature at the grid points,inlet and outlet temperature of the tube cells as well as the overall heat power andenergy gained by GCHE are calculated. It is important to note that the thermalconductivity of tailings mass depends on various parameters, such as the thermalconductivity of its solid particles, the porosity of the tailings and its moisturecontent. So, it is required to work out the thermal conductivity of the tailings massby measuring the thermal conductivities of prepared samples. Tailings from aCanadian mine site located in the province of Ontario were selected for this work.The values of thermal properties measured for the tailings, water and tube are givenin Table 1. The resulting temperature field at the mid plane (y ¼ W2/2) of the tailingsis shown in Figure 5 while Figure 6 shows the curves for heat power and the totalenergy gained. A non-dimensional temperature is described as:

y ¼ ðT� TinÞ=ðTb � TinÞ ð16Þ

where Tin is the temperature of water at the inlet of the tube network. Initially, thetailings mass has a temperature of Tb and y equals 1. However, with the gradualprogress of heat extraction from the tailings, y decreases (with a minimum value of0). According to Figure 5, although the geometry of the GCHE is symmetric, theresulting temperature field is not symmetric. This is due to the fact that a number ofsingle-tubes are connected in series which means that the temperature of water at theinlet of the tubes is not the same for all the single-tubes. The non-symmetrical resultfor the temperature field eliminates the option of reducing the numerical domain to aquarter or half of the physical domain. Figure 6(a) illustrates that the heat power

Table 1. Thermal properties of tailings, tube and water.

Tailings Water Tube

Density (kg/m3) 2500 998 1400Heat capacity (J/kg8C) 1100 4180 1047Thermal diffusivity (m2/s) 2.91 6 1077 1.39 6 1077 1.02 6 1076

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gained by water drastically drops in the first five days of operation showing the factthat there is a substantial decrease in the outlet water temperature of the GCHE inits early period of operation. Afterwards, a gradual decrease is observed in the heat

Figure 5. Non-dimensional temperature field at the mid plane (y ¼ 0.5W2) after: (a) 15 days,(b) 1 month, (c) 1 year and (d) 8 years.

Figure 6. (a) Heat power vs. time and (b) energy gain vs. time.

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power until it reaches the value of 4.45 kW in day 100. The total heat energy, shownin Figure 6(b), seems to have an almost linear character starting initially from 0 andreaching the value of 12.2 MW.h after 100 days.

4.2. Model evaluation

The unique characteristics of the proposed model, which include 3D heat transfertreatment and single-tube components, do not permit a good comparison withexisting models. This is due to the fact that the existing GCHE models are mostlycomposed of U-tube boreholes and are based on a 2D analysis of heat transfer.Thus, in order to evaluate the results of the proposed 3D model and to betterunderstand its significance, the results of the model are compared with a canonicaltest case. In this test case, shown in Figure 7(a), it is assumed that non-steady heattransfer occurs in a homogenous cylinder of tailings with a tube located in its centre.The water flowing through the central tube extracts heat from the tailings mass. Inthe Cartesian coordinate system, this test case is a 2D heat transfer problem.However, if coordinated in a radial coordinate system, the problem would beconverted to a single-axis radial problem (i.e. one-dimensional problem). Assumingthe thermal resistance of tube thickness to be negligible and conduction to be thedominant heat transfer mechanism, the governing equation for heat transfer intailings is expressed by

rmCm@T

@t¼ 1

r

@

@rrkm

@T

@r

� �ð17Þ

Figure 7. (a) Geometry of the 1D axisymmetric model and (b) outlet water temperature ofthe 1D axisymmetric models and the 3D model.

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where r is radial distance? The boundary conditions of this case are:

r ¼ Din=2! km@T

@r¼ hðT� TfÞ

r ¼ Dout=2! T ¼ Tb

ð18Þ

where Din, Dout, Tf and h are the inner diameter, the outer diameter, bulk tem-perature of water and the coefficient of convection inside the tube, respectively.Table 2 presents the properties assumed for the 3D model and its radial counterpart.By averaging the temperature field of the 3D model in the z-direction, the results ofthe two models are compared in Figure 7(b). According to Figure 7(b), the radialmodel results in higher temperature values on day 1 and day 30. This means that theradial model predicts a lower heat power extracted from the tailings mass incomparison to its 3D counterpart. This difference is created by the absence of thevertical conduction heat flux in the radial model. As a result, shortly after the start ofheat transfer, the cold water flowing through the tube cools the area surrounding theentrance zone of tube wall more effectively than the rest of the tube length resultingin considerable conduction flux in a vertical direction. This fact proves that the z-component of heat conduction flux plays an important role in heat transfer in thetailings. However, there is not much difference in the results on day 365, whichimplies that after a relatively long period of time, a steady-state temperature field isreached and the effect of vertical conduction is diminished. An illustration of thearea affected by circulating water is shown in Figure 8. The contribution of verticalconduction to heat transfer in tailings can be better expressed through the followingscale analysis:

km@2T

@z2

����t�0ffi km

Tb � Tin

Dz21>> km

@2T

@z2

����t� 0

ffi kmTb � Tin

Dz22ð19Þ

where Dz1 and Dz2 are the areas affected by heat extraction in the z-direction aftershort and long periods of time, respectively. The results of this test case imply thatvertical conduction cannot be neglected in assessing the performance of GCHEs andthat 3D modelling is essential for precise assessment of the performance of closed-loop geothermal systems. In the following sections, the developed 3D numericalmethod is used to investigate the performance of GCHEs installed in tailings ponds.

Another characteristic shared among Figures 5 and 6 is that after a relativelyshort period of continuous operation of the GCHE (i.e. after a few months), arelatively cold temperature zone is formed around the tube network (of Figure 5).This cold temperature zone lowers the heat transfer rate and leads to a drastic fall inheat power, P and the outlet water temperature, y (Figure 6). On the other hand,improving P while enhancing y, will boost the coefficient of performance (COP) of

Table 2. Properties of the radial model and its 3D counterpart model.

rm ¼ 2300 (kg/m3) Din ¼ 0.013 (m)Cm ¼ 939 (J/kg8C) Dout ¼ 20 (m)Tb ¼ 12 (8C) Tube length ¼ 50 (m)Tin ¼ 3 (8C) Tube flow rate ¼ 1.33 (l/s)

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the geothermal heat pump system leading to less electricity consumption. Thus, anyplausible improvement in P and y will raise the economic feasibility of the wholesystem. In the following sections, the developed numerical simulation tool will beused to investigate the effects of tube network arrangement and groundwater flow onthe performance of GCHEs installed in tailings ponds. In other words, thediscussions that will follow are some engineering guidelines proposed for improvingthe performance of GCHEs installed in tailings ponds.

4.3. Effect of tube network arrangement

Changing the spacing between tubes and the order of their interconnectivity couldaffect both the extracted heat power, P and the dimensionless outlet watertemperature, y. In order to investigate some of these effects, various tubes withmaterial properties shown in Tables 1 and 3 were assumed to be installed in a GCHE

Table 3. Properties of the GCHE.

Tb ¼ 10 (8C), Tin ¼ 3 (8C) Tube length ¼ 20 (m)Dtube ¼ 0.0274 (m) Tube flow ¼ 0.089 (l/s)L1 ¼ H1 ¼ W1 ¼ 40 (m) Number of tube ¼ 36L2 ¼ H2 ¼ W2 ¼ 20 (m) Number of tubes serried ¼ 3

Figure 8. Extent of area affected by cold water after (a) short period of time and (b) longperiod of time.

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at fixed fluid flow rates through each tube. Figure 9(a) shows that the extracted heatpower increases with increasing the total number of tubes, Ntube for a constant set ofserried tubes Ns. This is caused by the fact that installing more tubes in a tailingsmass means having a larger surface for the exchange of heat between the tubenetwork and the tailings mass. However, at the same time, Figure 9(b) indicates thatthe dimensionless temperature of the outlet water y decreases for the sameconditions. Since the COP of a geothermal heat pump is significantly dependenton y, a higher y means a better performing GCHE. According to Figure 9(b),increasing the number of serried tubes, Ns improves y. For instance, on day 100, for(Ntube, Ns) ¼ (16, 1), the resulting y is 0.0527, while for (Ntube, Ns) ¼ (16, 4), y israised to 0.1935. To better understand the effect of Ntube and Ns on P and y, the heatenergy is plotted against dimensionless temperature as shown in Figure 10. Thisfigure reveals that increasing the number of serried tubes led to a linear decrease ingained energy. However, the optimum configuration for GCHE should be selected inaccordance to the heat load demands as elaborated in the following examplesobtained from Figure 10:

(1) When y exceeds 0.3, the only possible choice will be (Ntube, Ns) ¼ (64, 8).(2) When a minimum y of 0.24 is required, both (Ntube, Ns) ¼ (64, 8) and (Ntube,

Ns) ¼ (36, 6) configurations would be possible choices even though the (64,8) provides 65.7% more energy than the (36, 6) configuration.

(3) When y does not exceed 0.12, the highest energy gained is obtained with the(Ntube, Ns) ¼ (64, 2) configuration.

4.4. Effect of groundwater flow

Figure 11 shows the effect of vertical underground flow on heat power extractedfrom the GCHE of Table 3. As can be seen, in day 100, increasing the verticalgroundwater flow from 0 to 100 m/year raises the power from 4.45 to 4.96 kW. It isalso seen that the advection becomes more significant with time.

Figure 9. Effect of tube arrangement on (a) extracted heat power and (b) non-dimensionaloutlet temperature of water.

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Figure 10. Total heat energy gained vs. dimensionless temperature for various tubearrangements after 50 and 100 days.

Figure 11. Effect of vertical groundwater flow on extracted heat power.

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Figure 12 compares the effect of horizontal underground flow on the heat powerextracted from the GCHE of Table 3 with the effect of an identical verticalunderground flow. In Figure 12, ~ujj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 þ v2 þ w2p

and a ¼ tan(u/v) represent themagnitude of the groundwater velocity vector and direction of the horizontalgroundwater velocity, respectively. The fact that a has an effect on P reveals that forconstant groundwater flow, there is an angle for which horizontal groundwater flowprovides optimum positive influence depending on the dimensions of the GCHE.The optimum angle is 308 for the GCHE that was used to develop Figure 12. Also,the extracted heat power is higher for a horizontal groundwater water velocity of 40m/year compared to a vertical groundwater velocity of 40 m/year, which shows thathorizontal advection is more effective than its vertical counterpart.

5. Summary and conclusion

The results of this study show that implementation of closed-loop geothermalsystems in tailings ponds has the potential of converting them to reliable geothermalresources, which can sustainably produce geothermal energy during and after miningactivities.

It is found that vertical temperature gradient plays an important role in creatingthe temperature field inside the GCHEs installed in tailing ponds. Thus, a 3D

Figure 12. Effect of horizontal and vertical advection on extracted heat power.

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modelling is essential in numerical simulation of heat transfer in GCHE. Since thebulk temperature of water approaches that of the tailings mass as water flowsthrough the single-tube(s), the rate of heat exchange between the tailings and thewater is not constant and therefore, the assumption of constant heat flux is notapplicable. Accordingly, it is necessary to calculate the local rate of heat exchangedbetween the tailings mass and the fluid. This approach is capable of capturing thevertical temperature gradient across the tailings pond.

Increasing the number of tubes connected in series in a tube network improvesthe temperature of water at the outlet of the tube network. However, there is anassociated linear decrease in the gained energy. Groundwater movement has apositive influence on the efficiency of GCHE; horizontal advection improves theperformance better than vertical advection. It is more efficient to position the single-tube(s) facing the direction of groundwater flow, rather than along the flow.

Acknowledgement

This publication was made possible by NPRP 09-1043-2-404 from the Qatar NationalResearch Fund (a member of Qatar Foundation).

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