. Results The model used for the fo

. Results
The model used for the following simulations was validated against a cylindrical source model, as well as by comparison with the models developed by Kujawa et al. [35] and Bu et al. [2]. A more specific breakdown of the model validation is detailed in Templeton et al. [34]. Additionally, the proposed model simplifies the velocity profile of the fluid within the heat exchanger to a uniform profile.This assumption was considered due to the laminar nature of the flow, the relatively low fluid velocity, and comparison with results obtained from implementing a parabolic velocity profile for the fluid in the inner pipe and outer annulus. By verifying the Reynolds number of mass flow rates considered in the investigated scenarios,it was concluded that the fluid flow remains in the laminar region.In order to satisfy the no-slip condition for the inner pipe as well as to have a maximum velocity equal to double the mean velocity,Equation (2) was introduced to form the correct velocity profile.where VInner.pipe is the velocity within the inner pipe of the heat exchanger,VInner is the average velocity within the inner pipe of the heat exchanger, and rInner.pipe is the inside radius of the inner pipe of the heat exchanger. Equation (3) was developed by integrating the average velocity flowing through the annulus over the cross sectional area of the annular region of the heat exchanger where VAnnulus is the velocity within the annulus of the heat exchanger,VAnnulus is the average velocity within the annulus of the heat exchanger, and r1 and r2 are the inner and outer radii of the annulus, respectively. Replacing the uniform velocity profile with Equations (2) and (3) in the inner pipe and annulus, respectively, it is possible to investigate the effect of assuming a uniform velocity profile within the heat exchanger (c.f. Fig. 3). As can be observed in Fig. 3, the uniform velocity is a reasonable assumption due to the minor temperature difference observed between itself and the parabolic velocity profile (less than 3% relative difference). The most significant difference is a 0.6 C difference in outlet temperature during the injection cycles.In order to ascertain the validity of this model for applications to geothermal energy storage, the model is compared with the results obtained from a TRNSYS model [29]. TRNSYS operates with an extensive library of components that can be modelled to evaluate temperature profile over a 20 year period than the Eslami-nejad et al. [29] model. The main differences between the two models that could lead to such a difference have been narrowed down to the nature of the heat exchanger that is simulated, the differences in physical configurations, and assumptions made within the model. Due to the higher cross sectional area used for fluid flow in the double pipe heat exchanger design compared to the double utube configuration as well as the insulated inner pipe on the double pipe configuration, the double pipe heat exchanger has a clear ef-ficiency advantage over the double u-tube heat exchanger in this scenario. The efficiency of the heat exchanger is not accountable for the entire difference in outlet fluid temperatures however, as the physical configuration of the system is also important. Eslami-nejad et al. [29] make use of a heat exchanger that is capable of storing and extracting thermal energy simultaneously, while it is impossible to accomplish such a feat with a double pipe heat exchanger.The TRNSYS DST model utilized by Eslami-nejad et al. [29] simplifies the heat transfer from the working fluid of the u-tube to the ground by way of a thermal resistance relation (i.e. analytical solution),and the heat transfer in the remainder of the model is calculated with a finite difference method. Additionally, the TRYNSYS DST model assumes that the heat flux through the boundaries surrounding the heat exchanger is zero. The finite element model proposed in this work assumes that the far boundaries surrounding the heat exchanger are at a constant temperature, and therefore provide a heat flux to resupply the exploited volume of earth with geothermal energy. The outlet temperature profile provided by Eslami-nejad et al. [29] highlights only one data point for every year's worth of data, which is a highly simplified summary of the realistic outlet temperature profile (c.f.Fig. 4). The profile for the proposed model (equivalent total energy/ energy rate) in Fig. 4 demonstrates the seasonal variability that such a system has, with the outlet temperature during the summer phase accentuated due to the thermal energy from solar/cooling being dumped during the five month period. Because a year's worth of solar energy is injected during the summer phase of the total energy scenario for the proposed model, it is as if the solar collector for the proposed model is larger (i.e. same amount of solar energy stored but increased solar thermal power) than that assumed by Eslami-nejad et al. [29]. Because the proposed model can only inject solar thermal energy during the summer phase, compared to year round injection by the double u-tube model,there will be more significant capital costs associated with a larger solar collector for such an equivalent total energy scenario for the proposed model. Furthermore, the solar thermal energy storage during the summer will decrease the effectiveness of the borehole to provide cooling. However, these scenarios are based on a cold climate where heating is prioritized over cooling.It is worthwhile to investigate the effect of the energy storage rate (i.e. identical solar collector size) on the proposed model (c.f.Fig. 4- Proposed model (equivalent energy rate)). The rate of solar energy injection was determined over the summer period, which can be combined with the thermal energy supplied from space cooling to provide a summer rate of thermal energy injection equivalent to Eslami-nejad et al. [29]. Comparing the equivalent total energy and energy rate scenarios, there is little change on the lowest outlet fluid temperature and quite a noticeable change in the peaks of the outlet fluid temperatures. The change in the peak temperatures can be attributed to the decrease in power of the thermal energy that is injected into the double pipe heat exchanger.In order to ascertain the effect that solar injection might have on the long term outlet temperature of a geothermal system, a constant energy extraction model was set up with varying magnitudes of thermal solar injection. The scenarios presented in Fig. 4 correspond to a constant mass flow rate (i.e. independent of energy injection/extraction rates). The average outlet temperatures in the following figures are calculated based only on the outlet temperatures during the extraction phases of the year, so as to isolate the effects of extraction from the effects of injection. Additionally, the linear correlation of COP with the outlet temperatures associated with geothermal extraction can be used to approximate the whole system. From Fig. 5, it is obvious that the injection of solar thermal energy over the summer period results in an overall positive effect on the outlet temperature of the double pipe heat exchanger during the winter period. Increasing the thermal solar injection rate has the effect of increasing the outlet temperature of the working fluid as well as increasing the sustainability of the geothermal system. It is of particular importance to note that for an 1800 W solar thermal injection rate, the average outlet temperature remains relatively stable over 13 years (c.f. Fig. 5). Comparing the 1800 W injection scenario with the no injection scenario, it is clear from the average outlet temperature that the lack of solar injection results in a less sustainable geothermal system. By injecting 1800 W of solar thermal energy during the 5 summer months of the year, the average outlet temperature can be improved by 5% over the 13 year period. Logically, it follows that increasing the rate of heat extraction from a geothermal resource will result in diminishing outlet temperatures over time (c.f. Fig. 6). This hypothesis is demonstrated in Fig. 6, where varying rates of heat extraction are investigated without the aid of solar thermal injection. The sustainability of the geothermal resource is substantially reduced as increasing heat loads are applied (c.f. Fig. 6). The continual decrease in the average outlet temperature illustrates the fact that solar thermal injection can be used to increase the sustainability of a geothermal resource.It is important to note that a steady state is attained quicker for smaller extraction rates. For example, the 2000 W extraction rate will reach a plateau significantly sooner than the 4000 W extraction rate. For each of the scenarios in Fig. 6 the average outlet temperature has reached a pseudo-steady state, meaning that there is a minimal decrease in the average outlet temperature of the working fluid. The magnitude of the extraction rate will be dependent on the specific needs necessary to the situation.To investigate the influence of the working fluid's mass flow rate on the thermal storage capacity of the geothermal resource,various mass flow rates were investigated during the injection cycle of the system (i.e. summer period) while the mass flow rate during the extraction cycle were left constant. A slower mass flow rate through the double pipe heat exchanger allows the fluid more time to transfer the solar thermal energy to the geothermal resource. The transfer of thermal energy is aided by the thermally depleted volume of earth immediately surrounding the borehole,creating a larger temperature gradient. There is significant advantage to decreasing the mass flow rate of the working fluid as evidenced in Fig. 7. The decreased mass flow rates during the injection cycles lead to a 3.7% increase in average outlet temperature,which means that there is more efficient transfer of

ผลลัพธ์ (คลิงออน) 1:

. ghot'e' validated ghantoH lo' tlha' simulations against cylindrical Hal ghantoH, ben law' by comparison with ghantoH Hach kujawa lalDan yej'an al. [35] Bu lalDan yej'an al. [2] je. detailed ralqu'nIStaH specific breakdown ghantoH validation neH templeton lalDan yej'an al. [34]. additionally, ghoQIjneS ghantoH simplifies Do qoghDu'DajDaq 'emvo' tuj exchanger qoghDu'DajDaq HIp fluid. qel assumption muHIvtaHbogh laminar tlhoQ flow, relatively 'eS Do fluid, 'ej comparison je ghot'e' Suq vo' parabolic Do qoghDu'DajDaq fluid implementing inner pipe 'ej outer annulus. pong reynolds So'meH MaQa' flow rates investigate scenarios neH qel yI'ol, 'e' ratlh fluid flow wo' 'e' neH laminar Sep concluded 'oH. in order to ghobe'-slip je yon inner pipe je toH pe'vIl Heghbogh vajpu''e' ghaH 'aqroS Do equal qej Do, Equation (2) chonaDmo', cha'logh vaj ghaj lugh Do profile.where vinner.pipe Dumerbe' lIH 'emvo' inner pipe tuj exchanger Do, vinner motlhbogh Do 'emvo' inner pipe tuj exchanger, vaj rinner.pipe qoD inner pipe tuj exchanger radius. Hach equation (3) pong motlhbogh Do flowing vegh annulus rIn Hub'eghtaHvIS sectional mIchHom annular Sep tuj exchanger nuqDaq vannulus 'emvo' tuj exchanger annulus Do, vannulus motlhbogh Do 'emvo' tuj exchanger annulus, vaj r1 'ej r2 inner 'ej outer radii annulus integrating , respectively. HIp Do qoghDu'DajDaq ngaSwI' yuvtlhe' wIngaQmoHta'DI' Equations (2) (3) je inner pipe annulus, 'ej respectively, qIt 'angbogh Da HIp Do qoghDu'DajDaq 'emvo' tuj exchanger (c.f. Fig. 3) assuming investigate. Hoch laH lop neH Fig. 3, Do HIp reasonable assumption minor Hat difference lop DuqIppu'chugh narghtaHvIS 'oH parabolic Do qoghDu'DajDaq muHIvtaHbogh (qup puS 3 vatlhvI' relative difference). during injection cycles difference 'ach tera'Daq veQ puS [taH 0.6 wIvmeH qaStaHvIS 'eS Daqvam Hat. in order to ghantoH geothermal HoS storage applications validity per, compared ghantoH ghot'e' vo' trnsys ghantoH [29] Suq. Qap trnsys je Hoch 'ay' be'nI''a'wI', Datu' 'ay' 'ej QuQ 'e' laH ghantoH Hat qoghDu'DajDaq chov rIn 20 DIS puj puS eslami-nejad lalDan yej'an al. [29] ghantoH. leSpal 'elbogh differences SabtaHbogh cha' ghantoH 'e' laH Dev lojchu'mo' wIvmeH tlhoQ tuj exchanger simulated 'e' physical configurations 'ej assumptions chenmoH 'emvo' ghantoH differences. muHIvtaHbogh veb Hub'eghtaHvIS sectional mIchHom lo' fluid flow neH chonaDmo', cha'logh vaj pipe tuj exchanger chut lulajpu'bogh taHtaHghach chonaDmo', cha'logh vaj utube configuration law' law' insulate inner pipe chonaDmo', cha'logh vaj pipe configuration, HuvchoH ef-ficiency 'utmo' Dujvam rIn chonaDmo', cha'logh vaj 'oH 'u'-tube tuj exchanger qaStaHvIS scenario ghaj chonaDmo', cha'logh vaj pipe tuj exchanger. tuj exchanger efficiency 'oHbe' accountable naQ difference qaStaHvIS 'eS Daqvam fluid Hat 'ach Hoch physical configuration pat potlh je. chenmoH eslami-nejad lalDan yej'an al. [29] tuj exchanger 'e' capable ngevwI' 'ej thermal HoS extracting simultaneously, 'oH DuHbe' HaQchorHey feat je chonaDmo', cha'logh vaj pipe tuj exchanger ta' yIlo'. tuj Qay vo' working fluid 'oH 'u'-tube by way of thermal resistance relation (i.e. analytical taS) yav simplifies trnsys dst ghantoH utilized pong eslami-nejad lalDan yej'an al. [29] 'ej SIm tuj Qay qaStaHvIS ratlhlI' ghu' vIDelbogh ghantoH je finite difference method. additionally, tuj flux vegh veH tuj exchanger Dech pagh assumes trynsys dst ghantoH. 'e' legh choHbe' mIw vIHechbogh Hat 'ej tuj flux exploit muq HattaHvIS geothermal HoS resupply DuHIvDI' Hop veH tuj exchanger Dech assumes SuvwI' finite element ghantoH ghoQIjneS qaStaHvIS Qap. 'eS Daqvam Hat qoghDu'DajDaq DuHIvDI' eslami-nejad lalDan yej'an al. [29] highlights neH wa' De' lang Hoch DIS worth De', baS highly simplify summary realistic 'eS Daqvam Hat qoghDu'DajDaq (c.f.fig. 4). ghoQIjneS ghantoH qoghDu'DajDaq (equivalent HoS total ghap HoS rate) reH Fig. 4 seasonal variability Daghajbogh HaQchorHey pat, ghaH 'eS Daqvam Hat during poH tuj bI'reS phase accentuated thermal HoS vo' solar ghap cooling dumped during vagh jar puj muHIvtaHbogh 'agh. SeH injected DIS worth solar HoS poH tuj bI'reS phase total HoS scenario ghoQIjneS ghantoH during, Men solar collector ghoQIjneS ghantoH weghbogh (i.e. rap amount solar HoS, 'ach ghur solar thermal HoS ngevwI') puS 'e' assumed pong eslami-nejad lalDan yej'an al. [29]. mo' solar HoS thermal laH neH inject ghoQIjneS ghantoH during phase poH tuj bI'reS, taHtaHghach round DIS injection pong chonaDmo', cha'logh vaj 'oH 'u'-tube ghantoH, tu'lu' vI'Iprup tera'Daq veQ mon costs je weghbogh solar collector vIq equivalent HoS total scenario ghoQIjneS ghantoH maqochpu'na' maHtaH. novpu' nejtaH cooling DuHIvDI' borehole effectiveness nup solar HoS thermal storage during poH tuj bI'reS. 'ach waw' scenarios bIr climate nuqDaq prioritized heating rIn cooling. worthwhile 'angbogh Da HoS storage rate (i.e. nIb collector solar size) investigate ghoQIjneS ghantoH (c.f.fig. 4-ghoQIjneS ghantoH (equivalent HoS rate)). qIlmeH pIj solar HoS injection rate rIn poH tuj bI'reS puj, baS laH QamchoHmo' jIblIj Hoch tlhegh thermal HoS supplied vo' logh cooling poH tuj bI'reS rate thermal HoS injection equivalent eslami-nejad lalDan yej'an al. [29] DuHIvDI'. equivalent HoS total HoS rate scenarios 'ej comparing, tu'lu' loQ choH lowest 'eS Daqvam fluid Hat 'ej ngoDqoq luHar noticeable choH neH 'eS Daqvam peaks fluid Hat. laH attributed choH qaStaHvIS Hat peak nup qaStaHvIS yapbe'mo' thermal HoS injected vaj chonaDmo', cha'logh vaj pipe tuj exchanger 'e'. in order to 'angbogh Da Daghajbogh chaq solar injection tIq wabmey 'eS Daqvam Hat pat geothermal per, cher choHbe' mIw vIHechbogh HoS extraction ghantoH Sar magnitudes thermal solar injection. correspond scenarios neH Fig. 4 Dan choHbe' mIw vIHechbogh flow MaQa' rate (i.e. tlhab HoS injection ghap extraction rates). SIm 'eS Daqvam motlhbogh Hat qaStaHvIS tlha' figures waw' neH 'eS Daqvam Hat during extraction phases DIS, so as to 'angbogh Da extraction vo' 'angbogh Da injection isolate. additionally, laH DanoHmeH linear correlation COP je 'eS Daqvam Hat je geothermal extraction maqochpu'na' maHtaH pat naQ approximate. vo' Fig. 5, obvious 'e' ghot'e' injection solar HoS thermal rIn poH tuj bI'reS puj neH overall be 'angbogh Da 'eS Daqvam Hat chonaDmo', cha'logh vaj pipe tuj exchanger during winter puj. thermal solar injection rate ghur ghaj 'angbogh Da 'eS Daqvam Hat working fluid ghur law' law' geothermal pat sustainability ghur. 'oH bIH importance yIjunmoH 'e' 1800 w solar thermal injection rate, relatively ngaD 'eS Daqvam motlhbogh Hat remains rIn 13 DIS (c.f. Fig. 5). 1800 w injection scenario je pagh injection scenario comparing, HuvchoH vo' 'eS Daqvam motlhbogh Hat 'e' ghot'e' bIr mIw wIje'laHbe'chugh vaj solar injection Hutlh qaStaHvIS qup sustainable pat geothermal. pong 1800 bIr mIw wIje'laHbe'chugh vaj w solar thermal HoS during 5 injecting poH tuj bI'reS jar DIS, laH Dub 'eS Daqvam motlhbogh Hat pong 5 vatlhvI' rIn 13 DIS puj. logically, vaj ghot'e' tuj extraction vo' jo geothermal rate ghur qaStaHvIS 'eS Daqvam Hat diminishing rIn poH (c.f. Fig. 6) tlha' 'oH. 'agh hypothesis neH Fig. 6, nuqDaq investigated Sar rates tuj extraction Hutlh boQ solar thermal injection. substantially reduced sustainability geothermal Sup law' ghur tuj loads apply (c.f. Fig. 6). ngoD illustrates, continual nup qaStaHvIS 'eS Daqvam motlhbogh Hat 'e' laH DanoHmeH solar thermal injection sustainability geothermal Sup ghur. potlh yIjunmoH 'e' yIchav 'ach steady Sep quicker smaller extraction rates. example plateau SIch 2000 w extraction rate significantly sooner paQDI'norgh luchenmoHmeH law' 4000 w extraction rate. Hoch pa' Fig. 6 scenarios pseudo-steady Sep, 'e' tu'lu' minimal nup neH 'eS Daqvam motlhbogh Hat working fluid qej SIch 'eS Daqvam motlhbogh Hat. extraction rate magnitude ghaH specific nIS 'ut ghu' dependent. moH working fluid MaQa' flow rate thermal storage capacity geothermal jo investigate, Sar MaQa' flow investigated rates during injection cycle pat (i.e. poH tuj bI'reS puj) poStaHvIS MaQa' flow rate during extraction cycle mej choHbe' mIw vIHechbogh. fluid latlh poH HoS solar thermal Qay jo geothermal chaw' slower MaQa' flow rate vegh chonaDmo', cha'logh vaj pipe tuj exchanger. boQ thermal HoS Qay pong thermally deplete muq SIbI' borehole, Dech tera' chenmoH weghbogh Hat gradient. tera'Daq veQ 'utmo' Dujvam MaQa' flow rate working fluid je neH Fig. 7 yab nup tu'lu'. 3.7 vatlhvI' ghur qaStaHvIS 'eS Daqvam motlhbogh, Hat 'e' vI'Iprup nom Qay tu'lu' qej Dev nup MaQa' flow rates during injection cycles