This study investigates three options for utilising the additional capacity of borehole heat exchanger (BHE) fields through gains along horizontal connec- tion pipes, whose contribution is routinely ignored. The analysis considers thermal load profiles with different heating to cooling ratios and finds that the effect of horizontal pipes becomes more significant with unbalanced loads. The study explores the potential of extended operation, increased loads and an optimised operating strategy to exploit the idle capacity gain from the hor- izontal connection pipes. It is shown that for the scenarios investigated, the BHE field operational time can be extended by more than 25 years without violating the critical fluid temperatures in the design phase. Alternatively, the thermal load can be increased by up to 26 %. In addition, the study highlights the potential of an optimised operating strategy involving adjust- ments to the number of BHEs operated to reduce power consumption and therefore reducing operating costs in existing systems by utilising heat gains from the horizontal connection pipes. Keywords: borehole heat exchanger, horizontal connection pipe, header pipe, heat loss, heat gain, optimised operation 1. Introduction Apartment blocks, commercial buildings or entire neighborhoods are in- creasingly being supplied with geothermal energy for heating and cooling. Shallow borehole heat exchangers (BHEs) with a typical depth of around Preprint submitted to Elsevier November 22, 2023 100 m are widely used in this context. Several BHEs are arranged in a bore- hole field to meet the energy needs of these large consumers. In Sweden alone the number of registered installations with 10 000 m or more total borehole length has almost quadrupled from 21 in 2015, to 76 systems in 2019, while the number of installations with 10 boreholes or more has increased by al- most 40 % during the same period (Lund and Toth, 2021). To reduce the thermal interference in these borehole fields, a minimum distance between the individual boreholes should be maintained (VDI, 2019). Depending on the arrangement of the boreholes, significant distances of several dozen me- ters between the BHEs and manifolds, header pipes or the consumers must be bridged with horizontal connection pipes. While these pipes are typically buried at shallow depths without thermal insulation, their thermal interac- tion with the ground is usually not considered in the design (Kavanaugh and Rafferty, 2014; VDI, 2019). The effect of the heat exchange along the horizontal connection pipes in geothermal borehole fields has been studied only very briefly. Luo et al. (2013) investigate the heat loss along a single buried pipe at different depths for flowing and stagnant fluid, and report the highest losses for stagnant fluid for heating operation in winter. Tian et al. (2022) investigate the effect of burial depth, surface temperature, backfill material and flow rate on the heat loss of horizontal connection pipes attached to a BHE in a sandbox exper- iment. The whole system of heat pump, connection pipes and BHE under different climatic conditions is investigated by D¨ uber et al. (2023). In con- trast to the previous work, their study shows that the horizontal connection pipes have a positive effect in many applications, reducing the thermal load of the BHE and increasing the capacity of the whole system. They show that considering the connection pipes in the design can reduce the required depth of the vertical boreholes and therefore the cost. In this work, we investigate how the extra capacity of connection pipes, not considered at the design stage, can be used in plants already in operation. Three optimisation options are investigated: longer operation ,higher loads and an optimised operating strategy to reduce the electricity consumption of the heat and circulation pump. The study is based on a mixed-use university building in Germany, which is supplied with heating and cooling energy by 40 BHEs 100 m deep (Clauser et al., 2017). In section 2 we present a detailed description of the system of connec- tion pipes and boreholes as well as the load profiles studied. Our modelling approach is presented in section 3, where we first introduce the model for 2 the connection pipes and BHEs, followed by our approach for the optimised operation strategy investigations. Finally, section 4 presents the results and some discussions, followed by conclusions in section 5. 2. Scenario The study is based on the example of the EON.ERC building in Aachen, Germany. The building houses laboratories, conference rooms and offices. A field of 40 2U-type BHEs with a depth of 100 m supplies the building with heating and cooling energy. The BHEs are operated in parallel and are grouped into three manifolds A, B and C (Figure 1). The connection pipes between the BHEs and the manifolds are buried at depths between 0.94 m and 1.54 m and are between 1.3 m (BHE 32) and 58.1 m (BHE 13) in length. The total length of all (supply and return pair of) connection pipes is 899 m, giving an average length per BHE of 22.5 m. This means that if the distance between the BHE and the manifold is 30 m, the length of the connecting pipe is here counted as 30 m, even though the supply and return pipe are each 30 m long. The properties of the BHEs, pipes and ground are listed in Table 1. NA BC Figure 1: Plan view of the connection pipe network of the 40 BHEs arranged in the three manifolds A, B and C. Figure 2 shows the hourly ground thermal load of the BHE field over a one year period, derived from measured flow rates and fluid temperatures. The load is cooling dominant, with a cooling/heating ratio of 3 .14. To introduce some variation, we investigate 5 different load profiles with cooling/heating ratios between 0 .1 and 10. We also perform the analysis with hourly load 3 profiles as well as monthly averaged profiles, which are often used in engi- neering practice during the design phase. All load profiles are based on the profile shown in Figure 2. To generate profiles with cooling/heating ratios of 0.1,0.32,1.0,3.14 and 10, the measured profile is shifted towards heating or cooling until the desired ratio is reached. It is then scaled as described in D¨ uber et al. (2023) to meet the design criteria of the German technical guideline VDI 4640 (VDI, 2019), which states that for heating operation the BHE inlet temperature should not fall below 0 °C on a monthly average and should not fall below −5°C at any time. In cooling mode, it should not ex- ceed the undisturbed ground temperature by more than 15 °C on a monthly average and 20 °C at any time. The range of load ratios may represent dif- ferent building uses and plants. Here, the g-function of the BHE field is calculated using the pygfuntcion toolbox (Cimmino and Cook, 2022) with the equal inlet temperature boundary condition and single segment BHEs which corresponds to our model as will be shown later in section 3. The design period for the scaling of the load profiles is assumed to be 50 years. Figure 3 shows all load profiles. To ensure that the monthly profiles have the same cooling/heating ratio as the hourly profiles, the profile in Figure 2 was first averaged monthly and then shifted until the desired ratio was achieved. /uni00000013 /uni00000015 /uni00000017 /uni00000019 /uni0000001b /uni00000014/uni00000013 /uni00000014/uni00000015 /uni00000037/uni0000004c/uni00000050/uni00000048/uni00000003/uni0000003e/uni00000050/uni00000057/uni0000004b/uni00000040/uni00000014/uni00000013/uni00000013 /uni00000018/uni00000013 /uni00000013/uni00000018/uni00000013/uni00000014/uni00000013/uni00000013/uni00000014/uni00000018/uni00000013/uni0000002a/uni00000055/uni00000052/uni00000058/uni00000051/uni00000047/uni0000004f/uni00000052/uni00000044/uni00000047/uni00000003/uni0000003e/uni0000004e/uni0000003a/uni00000040/uni00000046/uni00000052/uni00000052/uni0000004f/uni0000004c/uni00000051/uni0000004a /uni0000004b/uni00000048/uni00000044/uni00000057/uni0000004c/uni00000051/uni0000004a Figure 2: Actual hourly ground load of the BHE field derived from measurements. When scaling the load profiles, the monthly average fluid temperature was the critical limit for all unbalanced load profiles. Only for the hourly profile with a cooling/heating ratio = 1.0 was the maximum fluid temperature during cooling the decisive limit. However, for the monthly averaged profile with the same ratio, it was again the monthly averaged fluid temperature, this time during heating operation. 4 Table 1: BHE and ground properties of the BHE field. Domain Parameter Value Units Fluid Thermal conductivity 0.43 W m−1K−1 Fluid Density 1045 kg m−3 Fluid Volumetric heat capacity 3 800 000 J m−3K−1 Fluid Dynamic Viscosity 0.0035 Pa s Fluid Flow rate per BHE 1.5 m3h−1 BHE Length 100 m BHE Diameter 0.152 m BHE Shank space 0.04 m BHE Outer diameter pipes 0.032 m BHE Pipe wall thickness 0.0029 m BHE Thermal conductivity grout 2.0 W m−1K−1 BHE Volumetric heat capacity grout 1 000 000 J m−3K−1 BHE Thermal conductivity pipe 0.3 W m−1K−1 BHE Borehole thermal resistance 0.089 m K W−1 h. pipe Length 1.3 - 58.1 m h. pipe Depth 0.94 - 1.54 m h. pipe Outer diameter 0.04 m h. pipe Wall thickness 0.0037 m h. pipe Thermal conductivity 0.38 W m−1K−1 h. pipe Pipe thermal resistance 0.0989-0.0999 m K W−1 Ground BHE Thermal conductivity 2.3 W m−1K−1 Ground BHE Volumetric heat capacity 2 300 000 J m−3K−1 Ground BHE Undisturbed temperature 11.0 °C Ground h. pipe Thermal conductivity 2.0 W m−1K−1 Ground h. pipe Volumetric heat capacity 2 000 000 J m−3K−1 Ground h. pipe Undisturbed temperature 0.5 - 23.9 °C 5 Figure 3: Hourly (left) and monthly (right) load profiles with cooling/heating ratios (c/h) ranging from 0 .1 to 10. 3. Model and methods We use the model recently introduced in D¨ uber et al. (2023) for the sys- tem of BHEs and connection pipes. It is based on thermal resistances for the pipes and BHEs and thermal response functions, also known as g-functions (Eskilson, 1987), for the ground around the BHEs and pipes. In the pre- vious work we used the horizontal finite line source presented by Lamarche (2019) to calculate the g-functions for the horizontal pipes. Here, we use a 3D-numerical model to calculate the pipe g-functions. This allows us to take into account the different paths of the pipes as well as the impact of the building embedding into the ground (Figure 1). For the sake of simplicity we make the following assumptions that differ from the actual conditions at the building: the ground surface is flat, the ground is homogeneous and the building is embedded 3 m into the ground over its entire footprint. To reduce the modelling effort, we neglect the thermal interference of horizon- tal pipes belonging to different manifolds. The minimum distance between 6 connection pipes of different manifolds is about 10 m (BHE 23 and 24, see Figure 1), while the maximum burial depth is 1.54 m. With this arrange- ment, the effects of mutual interference are dominated by the effects of the ground surface, even over long observation periods. This allows us to use individual models for each manifold, resulting in fewer elements and less computation for each model. Figure 4 shows the numerical model for mani- fold C. The boundaries of the model are set to have a first order temperature boundary condition equal to the initial temperature of the model. Only the faces where the building is embedded in the ground are considered to be thermally insulated. Considering supply and return pipe individually results in (12 ·2)2= 576 g-functions for manifold A, (12 ·2)2= 576 g-functions for manifold B and (16 ·2)2= 1024 g-functions for manifold C (Figure 5). Taking into account the 402= 1600 borehole g-functions adds up to a total number of 3776 g-functions considered in the model. The g-functions for the boreholes are calculated with the finite line source as presented by Claesson and Javed (2011). Building footprint Figure 4: Numerical model for calculation of g-functions for manifold C. While the undisturbed ground temperature at the BHEs is assumed to be constant as T0,b= 11◦C, the undisturbed ground temperatures at the horizontal pipes vary throughout the year and are calculated according to Phetteplace et al. (2013): Ts(z, t) =Tave+e−z√π αstpTampsinh2π tp(t−Φ)−zrπ αstpi (1) where Taveis the average annual ground surface temperature, Tampthe amplitude of the ground surface temperature, tpis the period of soil tem- perature cycle and tis the time. zis the depth at which the temperature 7 /uni00000014/uni00000013/uni00000014/uni00000014/uni00000013/uni00000017/uni00000014/uni00000013/uni0000001a/uni00000013/uni00000014/uni00000015/uni00000016/uni00000017/uni00000018/uni0000004a/uni00000003/uni0000003e/uni00000010/uni00000040/uni00000024 /uni00000014/uni00000013/uni00000014/uni00000014/uni00000013/uni00000017/uni00000014/uni00000013/uni0000001a /uni00000037/uni0000004c/uni00000050/uni00000048/uni00000003/uni0000003e/uni00000050/uni0000004c/uni00000051/uni00000040/uni00000025 /uni00000014/uni00000013/uni00000014/uni00000014/uni00000013/uni00000017/uni00000014/uni00000013/uni0000001a/uni00000026Figure 5: G-functions for the horizontal pipes for manifolds A, B and C. is evaluated and αsis the thermal diffusivity of the ground. The constants for Equation 1 were derived from data from a nearby weather station as Tave= 12.2◦C,Tamp= 15.8◦C and Φ = 106 d. The resulting temperatures at the horizontal pipes are shown in Figure 6. /uni00000013 /uni00000015 /uni00000017 /uni00000019 /uni0000001b /uni00000014/uni00000013 /uni00000014/uni00000015 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 /uni0000005d/uni00000003/uni00000020/uni00000003/uni00000014/uni00000011/uni00000018/uni00000017/uni00000003/uni00000050 Figure 6: Range of undisturbed ground temperatures at the horizontal connection pipes which are buried between 0.94 m and 1.54 m below the surface starting on the first of January. The electricity consumers in a geothermal system are the circulation pump and the ground source heat pump. In section 4.4 we assume active heating and cooling and try to reduce the total electricity demand with an 8 optimised operating strategy. The idea is to not operate all BHEs at all times and therefore reduce the electricity demand of the circulation pump. This idea has already been explored by various authors outside the context of the horizontal connection pipes, partly in a modified form (e.g. Hackel and Pertzborn (2011), Hecht-M´ endez et al. (2013), Zarrella et al. (2017), Stoffel et al. (2022)). While the investigations on longer operation time and higher loads (sections 4.2 and 4.3) use the ground loads presented in the previous section, the analysis of an optimised operation strategy requires building loads and models for the heat pump and the circulation pump. Here, the ground load Qgis calculated based on the building load Qb, the temperature of the fluid exiting the BHE field and entering the heat pump Tin,HPand the coefficient of performance (COP) of the heat pump. For cooling loads we get: Qg=QbCOP c(Tin,HP) + 1 COP c(Tin,HP)(2) and for heating loads, Qg=QbCOP h(Tin,HP)−1 COP h(Tin,HP). (3) The COP is calculated based on manufacturer data (using Envision NKW150 as example only) shown in the left part of Figure 7. For the inter- and extrap- olation of the only pointwise available data we use the scipy.interpolate.interp1d function with a quadratic spline interpolater (Virtanen et al., 2020). To cal- culate the electricity consumption of the circulation pump, we use the same interpolation method on manufacturer data (using Wilo ChronoLine-IL-E 65 as example only) which is shown in the right part of Figure 7. It is also assumed that all BHEs are hydraulically balanced and have a flow rate of 1.5 m3h−1regardless of the length of the individual connection pipe. It should be noted that the heat pump data shown in Figure 7 does not correspond to the heat pump in the actual 20 yr old building, but to a contemporary GSHP, an assumption used here for our theoretical analysis. For the optimised operating strategy, we divide the operating period of the BHE field into smaller periods of one month for which we want to determine the optimal number of BHEs in operation so that the electricity consumption is minimised. We have chosen an optimisation period of one month, or 12 control events per year, because the effort involved in switching the BHEs on 9 /uni00000013 /uni00000015/uni00000013 /uni00000017/uni00000013 /uni00000037/uni0000004c/uni00000051/uni0000000f/uni0000002b/uni00000033/uni0000003e/uni00000083/uni00000026/uni00000040/uni00000017/uni00000018/uni00000019/uni0000001a/uni00000026/uni00000032/uni00000033/uni00000003/uni0000003e/uni00000010/uni00000040 /uni0000004b/uni00000048/uni00000044/uni00000057/uni0000004c/uni00000051/uni0000004a /uni00000046/uni00000052/uni00000052/uni0000004f/uni0000004c/uni00000051/uni0000004a /uni00000013 /uni00000015/uni00000013 /uni00000017/uni00000013 /uni00000019/uni00000013 /uni00000039/uni0000003e/uni00000050/uni000000f1/uni00000012/uni0000004b/uni00000040 /uni00000014/uni00000015/uni00000016/uni00000033/uni00000048/uni0000004f/uni0000003e/uni0000004e/uni0000003a/uni00000040Figure 7: Heat pump data (left) and circulation pump data (right) used for the model. Dashed lines indicate extrapolation. and off seems justifiable, even if the the task is undertaken manually without an automated control system or programmable BMS (building management system). To calculate the optimal number of BHEs for each period, we set up two models, a simulation model and a prediction model . The simulation model is the model already described, which is used for all analyses in this work. The predictor model is another instance of the same model, but with a coarser time step to reduce the computational effort. The inputs for the predictor model are the average building load Qbof the period and the temperatures at the boreholes T0band the horizontal pipes T0p. The predictor model simulates the period for all cases from 1 to 40 BHEs in operation (i.e., using only 1, or only 2, or up to 40 BHEs at a time to satisfy the load in that period of time), using the described heat pump and circulation pump models. The optimal number of BHEs is selected based on the total electricity consumption Ptotand the critical fluid temperatures. This means that the number of BHEs is selected so that the critical fluid temperatures are maintained and the total power consumption is as low as possible. To ensure the most efficient selection of BHEs, the BHEs are first ordered according to their borehole wall temperatures. This depends on the average load of the period. If the load of the period is a building cooling load, the boreholes are sorted in ascending order starting with the coldest borehole, since it would have more capacity to reject heat to the ground than other BHEs. If it is a building heating load, the order is reversed and sorting starts with the warmest borehole. A flowchart of the described procedure is shown in Figure 8. 10 simulator model T, T, Q 0b 0p b n BHEpredictor model calc n BHEsort BHEs simulate 1-40 BHEs operating calc min P tot simulator model simulate periodnext periodFigure 8: Procedure to calculate the optimal number of BHEs operating for each period. Figure 9 shows the results of the predictor model for a period of heating operation. The bottom part shows the electricity consumption of the heat pump PHP, the circulation pump Pcircand the sum of both Ptotas a function of the number of BHEs in operation. /uni00000018 /uni00000014/uni00000013 /uni00000014/uni00000018 /uni00000015/uni00000013 /uni00000015/uni00000018 /uni00000016/uni00000013 /uni00000016/uni00000018 /uni00000017/uni00000013 /uni00000051/uni00000003/uni00000025/uni0000002b/uni00000028/uni00000015/uni00000017/uni00000019/uni00000033/uni00000052/uni0000005a/uni00000048/uni00000055/uni00000003/uni0000003e/uni0000004e/uni0000003a/uni00000040/uni00000033/uni00000057/uni00000052/uni00000057 /uni00000033/uni0000002b/uni00000033 /uni00000033/uni00000046/uni0000004c/uni00000055/uni00000046/uni00000013/uni00000018/uni00000037/uni00000049/uni0000000f/uni0000004c/uni00000051/uni00000003/uni0000003e/uni00000083/uni00000026/uni00000040 Figure 9: Exemplary results of the predictor model. The top part shows the corresponding inlet fluid temperature of the BHE field. As the number of BHEs increases, the power consumption of the cir- culation pump increases while the power consumption of the heat pump de- creases, resulting in an overall optimum of 5 kW with 8 BHEs in operation. As the load for the period shown is a heating load, the fluid temperature in- creases as the number of BHEs increases. However, from 28 BHEs onwards we can see that it decreases slightly. This is due to the order of the BHEs. In the period prior to the current period of simulation, heating was also needed, 11 and only 12 BHEs were in operation. By sorting the BHEs according to their borehole wall temperatures, these 12 BHEs are the least favourable for this period and are therefore only selected when 28 or more BHEs are required. Again, the optimum selection in terms of power consumption is 8 BHEs op- erating in this case. To ensure comparability with the previous investigations on longer op- eration and higher loads (without heat pump model and ground load as boundary condition), the building loads are calculated so that the exact same ground loads occurs when using the heat pump model and building loads as boundary condition. Therefore we simulate the BHE field with 40 BHEs, including the connection pipes, with the specified ground loads (Figure 3). Based on the fluid temperatures and the heat pump data (Figure 7, left) we calculate the corresponding building load for each ground load profile. 4. Results and discussions 4.1. Effect of horizontal pipes To give a first impression of the effect of the horizontal pipes, we simulate the BHE field at a constant cooling load of 120 kW for a period of 50 years. Figure 10 shows the results for a simulation with our simulation model where the thermal conductivity of the horizontal pipes is set to zero (no pipes) and a simulation with the pygfunction toolbox as reference (pygfunc). Simula- tions with our model considering the pipes were performed with a constant undisturbed ground temperature around the pipes (pipes, T 0= const .) and with varying ground temperatures (pipes, T 0= f(t)). The inclusion of the horizontal pipes leads to a difference in the fluid temperature entering the BHE field of more than 10 °C at the end of the pe- riod. The effect of the seasonal temperature variations around the horizontal pipes on the fluid temperature is rather small, resulting in a peak-to-peak amplitude of about 2 °C in this case. However, for the load profiles shown in Figure 3, the effect of the horizontal pipes is less dramatic (Table 2). To demonstrate this, we simulate all scenarios with and without consideration of the horizontal pipes. Figure 11 shows the results for the hourly load profile on the example of the c/h = 3.14 scenario where the temperature difference at peak loads is just 2 °C in the last year. For the sake of clarity, we restrict the plots for all other cases to the envelopes of the fluid temperatures entering the BHE field. Figure 12 shows 12 /uni00000013 /uni00000014/uni00000013 /uni00000015/uni00000013 /uni00000016/uni00000013 /uni00000017/uni00000013 /uni00000018/uni00000013 /uni00000037/uni0000004c/uni00000050/uni00000048/uni00000003/uni0000003e/uni00000044/uni00000040/uni00000015/uni00000013/uni00000016/uni00000013/uni00000017/uni00000013/uni00000018/uni00000013/uni00000037/uni00000049/uni0000000f/uni0000004c/uni00000051/uni0000003e/uni00000083/uni00000026/uni00000040 /uni00000051/uni00000052/uni00000003/uni00000053/uni0000004c/uni00000053/uni00000048/uni00000056 /uni00000053/uni0000005c/uni0000004a/uni00000049/uni00000058/uni00000051/uni00000046/uni00000053/uni0000004c/uni00000053/uni00000048/uni00000056/uni0000000f/uni00000037/uni00000013/uni00000020/uni00000046/uni00000052/uni00000051/uni00000056/uni00000057/uni00000011 /uni00000053/uni0000004c/uni00000053/uni00000048/uni00000056/uni0000000f/uni00000037/uni00000013/uni00000020/uni00000049/uni0000000b/uni00000057/uni0000000cFigure 10: Development of the fluid temperature entering the BHE field at a constant load of 120 kW with and without consideration of the horizontal connection pipes. /uni00000013 /uni00000014/uni00000013 /uni00000015/uni00000013 /uni00000016/uni00000013 /uni00000017/uni00000013 /uni00000018/uni00000013 /uni00000037/uni0000004c/uni00000050/uni00000048/uni00000003/uni0000003e/uni00000044/uni00000040/uni00000018/uni00000014/uni00000013/uni00000014/uni00000018/uni00000015/uni00000013/uni00000015/uni00000018/uni00000016/uni00000013/uni00000037/uni00000048/uni00000050/uni00000053/uni00000048/uni00000055/uni00000044/uni00000057/uni00000058/uni00000055/uni00000048/uni00000003/uni0000003e/uni00000083/uni00000026/uni00000040 /uni00000053/uni0000004c/uni00000053/uni00000048/uni00000056 /uni00000051/uni00000052/uni00000003/uni00000053/uni0000004c/uni00000053/uni00000048/uni00000056 Figure 11: Fluid temperatures entering the BHE field with and without consideration of the horizontal connection pipes for the c/h = 3.14 hourly load profile. the results for the hourly and monthly load profiles. The results show that the more unbalanced the load profile, the greater the effect of the horizontal connection pipes (see also Tables 2 and 3). This is independent of whether the load profile is heating or cooling dominant. For unbalanced cooling-dominant profiles, the heat accumulates in the ground leading to a steady increase in fluid temperatures until eventually a steady state is reached. If the horizontal pipes are considered in the simulation, the capacity of the whole system is greater, leading to a slower temperature rise and possibly earlier reached state state. The same applies to the heating 13 pipeshourly monthly no pipes Figure 12: Envelopes of the fluid temperatures entering the BHE field for all c/h ratios and monthly and hourly load profiles. loads, except that the ground is cooling instead of heating. Interestingly, in the case of balanced loads, the effect of the horizontal pipes is hardly noticeable. This is a special case that rarely occurs in practice. Table 2 shows the average fluid temperature entering the BHE field for the design period of 50 years with and without consideration of the horizontal pipes. The biggest difference with 1.7 °C occurs in the c/h = 0.1 scenario, both for hourly and monthly profiles, while the smallest effect can be observed for the balanced monthly profile (c/h = 1.0) with just 0.3 °C. Table 3 shows the relative share of the load covered by the BHEs, taking into account the horizontal pipes. The dominant BHE thermal loads are reduced between 6 % (monthly profile, c/h = 3.14) and 19.3 % (hourly profile, c/h = 0.1). Load increases for the BHEs result exclusively for the non- dominant loads. 14 Table 2: Average fluid inlet temperature [ ℃] of the BHE field for operational period of 50 years with and without consideration of the horizontal connection pipes. hourly profile monthly profile c/h ratio no pipes pipes no pipes pipes 0.1 4 .6 6 .3 4 .5 6 .2 0.32 5 .8 7 .2 5 .7 7 .2 1.0 11 .0 11 .5 11 .0 11 .3 3.14 17 .6 16 .7 17 .4 16 .3 10.0 19 .1 18 .0 18 .9 17 .4 Table 3: Load share [%] covered by the BHEs for the different load profiles separated for cooling and heating operation. hourly profile monthly profile c/h ratio heating cooling heating cooling 0.1 80 .7 172 .8 82 .1 182 .6 0.32 89 .2 132 .0 91 .2 137 .0 1.0 95 .5 98 .8 97 .2 99 .6 3.14 118 .9 93 .3 123 .6 94 .0 10.0 174 .1 89 .7 214 .7 92 .8 4.2. Longer operation All load profiles have been scaled to reach the critical fluid inlet tem- peratures within the design period of 50 years, without consideration of the horizontal pipes. Based on technical guidelines, the BHE field can theoret- ically not be operated at the design loads after the 50-year period because the fluid temperatures will be either too high or too low. However, as shown in the previous section, the consideration of horizontal pipes leads to slower heat accumulation or depletion in the case of unbalanced load profiles. In this section we investigate how much longer the BHE field can operate with the same load profile by taking into account the horizontal connection pipes. Figure 13 shows the results for the monthly profiles for an additional 25 years of operation or a total of 75 years of operation. Here, we plot the envelopes of the monthly averaged fluid temperatures entering the BHE field, as these were the decisive design criteria when scaling the loads (section 2). Without the consideration of the pipes, the fluid temperatures reach the critical limit 15 exactly after 50 years. Considering the pipes however, the fluid temperatures do not reach the critical limits even after 75 years for the same load profiles for all cases. In fact, the BHE field is almost in a steady state after this time, with negligible temperature accumulation. Figure 14 shows the results for the hourly load profiles. The results are almost identical, only the absolute temperatures are slightly shifted. Figure 13: Envelopes of the monthly averaged inlet temperature of the BHE field with and without consideration of the connection pipes for the monthly load profiles. Figure 14: Envelopes of the monthly averaged inlet temperature of the BHE field with and without consideration of the connection pipes for the hourly load profiles. 16 4.3. Increased load The increased capacity of the BHE field due to the consideration of the horizontal pipes will also allow higher loads within the same temperature lim- its. As our model only considers heat transfer through conduction, we can use the linear relation between temperature change and thermal load to cal- culate the the possible load increase directly. The results in Table 4 roughly coincide with the reduced BHE loads in Table 3, where the biggest reductions were observed for the unbalanced heating dominant profiles, followed by the unbalanced cooling dominant scenarios. Table 4: Factors by which the load profiles can be multiplied until the critical fluid tem- peratures are reached considering the horizontal pipes. c/h ratio hourly profile monthly profile 0.1 1 .26 1 .26 0.32 1 .22 1 .22 1.0 1 .04 1 .07 3.14 1 .12 1 .13 10.0 1 .15 1 .16 Figure 15 shows an example of the results for the monthly load profiles. By considering the horizontal pipes, the load profile can be increased accord- ing to the factors in Table 4 so that at the end of the design period the exact same monthly average fluid temperatures are achieved as without considering the pipes. 4.4. Optimised operation The previous sections have shown that neglecting the horizontal pipes in the design leads to an oversized system that allows for higher loads or longer operational times. In this section, we investigate whether the over- sized system can be used more efficiently by applying an optimised operating strategy. Figure 16 shows detailed results for the second year of operation for the c/h = 3.14 case and the monthly load profile. The top part shows the fluid temperature entering the BHE field for the case with all BHEs operating and the optimal number of BHEs operating. The middle part shows the corresponding COP while the bottom part shows the electricity consump- tion of the heat and circulation pump. By not running all BHEs, the fluid 17 Figure 15: Envelope of the monthly averaged fluid temperatures entering the BHE field for the monthly load profiles including the increased load profiles according to Table 4 temperatures decrease during heating (first two and last three months, see also Figure 3) and increase during cooling. This results in a reduced COP of the heat pump and therefore increased electricity consumption, which is however compensated by the reduced electricity consumption of the circula- tion pump. For the period shown here the total electricity consumption if all BHEs are on at all times is 78 755 kW h while for the optimised number of BHEs operating it is just 69 211 kW h which corresponds to a reduction of 12 %. For better clarity we limit the analysis for all cases and the full 50 year period to annual values as shown in Figure 17. The left column shows the monthly averaged temperatures entering the BHE field of the month with the highest respectively lowest fluid temperature. The no pipes curves cor- respond to the scenario where the horizontal pipes are neglected, while the pipes curves show the fluid temperatures with consideration of the horizontal pipes. The pipes, n on curves finally show the fluid temperatures with some BHEs operating. The operation with less BHEs exploits the temperature reserve induced by the horizontal pipes, while staying within the tempera- ture limits at all times. The right column of Figure 17 shows the average annual electricity demand. The potential electricity savings are summarised in Table 5. The proposed operating strategy works well with the monthly load pro- files. The average monthly load used as input to the predictive model corre- 18 Figure 16: Detailed results for the second year of the c/h = 3.14 case with monthly loads. Table 5: Electricity savings with optimised operation strategy and the monthly load pro- files. c/h ratio electricity reduction % 0.1 17 0.32 12 1.0 3 3.14 11 10.0 15 sponds exactly to the load used later in the simulator model. Therefore, the predictive model is able to predict the fluid temperatures sufficiently accu- rately with significantly fewer calculation steps. However, applying the same approach to the hourly load profiles will result in temperature overshoots and even increased electricity consumption in some cases. Using a monthly average of the hourly load profile for the predictor model underestimates the 19 Figure 17: Monthly averaged fluid inlet temperatures of the critical month (left) and total electricity consumption (right) for the monthly load profiles and the optimised operating strategy. BHE demand, especially when both heating and cooling loads are averaged. Figure 18 shows this on the example of the c/h = 3.14 scenario. The critical temperatures are particularly violated during the third month, where both heating and cooling loads occur (compare Figure 3). Table 6 a) summarises the results for all other c/h ratios. For the c/h = 1.0 scenario, the optimised operating strategy results even in an increased electricity con- sumption of 3 %, while the for the c/h = 10.0 scenario the critical fluid temperatures are violated during 14.1 % of the operational hours. In order to avoid underestimating the absolute loads by averaging heating and cool- ing loads within one month, we adjusted the input of the predictor model. Instead of using the average load of the whole month, we average heating 20 /uni00000013 /uni00000015 /uni00000017 /uni00000019 /uni0000001b /uni00000014/uni00000013 /uni00000014/uni00000015 /uni00000037/uni0000004c/uni00000050/uni00000048/uni0000003e/uni00000050/uni00000057/uni0000004b/uni00000040/uni00000013/uni00000015/uni00000013/uni00000017/uni00000013/uni00000037/uni0000004c/uni00000051/uni0000000f/uni00000049/uni0000004c/uni00000048/uni0000004f/uni00000047/uni0000003e/uni00000083/uni00000026/uni00000040 /uni00000014/uni00000013 /uni0000001b /uni00000018 /uni0000001b /uni00000015/uni00000016 /uni00000017/uni00000013 /uni00000017/uni00000013 /uni00000017/uni00000013 /uni00000014/uni0000001a /uni00000014/uni00000013 /uni00000014/uni00000014 /uni00000014/uni00000019/uni00000051/uni00000003/uni00000052/uni00000051/uni0000001d/uni00000051/uni00000003/uni00000052/uni00000051 /uni00000044/uni0000004f/uni0000004f/uni00000003/uni00000052/uni00000051Figure 18: Fluid inlet temperature of the BHE field for a one year period with all BHEs operating and the optimised operating strategy based on monthly averaged loads.Range of critical fluid temperatures highlighted in grey. and cooling loads within the month separately and use the dominant average as input for the predictor model. The results listed under b) in Table 6 show that the temperature constrain violations are greatly reduced and the elec- tricity reduction is increased in most cases. In a final approach to prevent any temperature violations, we implemented a function in the simulation model, that activates two additional BHEs if 90 % of the critical fluid temperature is reached. The results are listed under c) in Table 6. For the unbalanced load profiles, the temperature violations could be reduced by one order of magnitude with just 1-4 additional control events (switching on additional BHEs) per year, while for the balanced profile the number of control events almost doubled. Figure 19 finally shows the results for the hourly load profiles in the same way as in Figure 17, here for the prediction based on the monthly average of the dominant load type (Table 6 c)). 5. Conclusions We investigated three ways to utilise the additional capacity of BHE fields due to the gains along horizontal connection pipes. The analysis with load profiles with different heating to cooling ratios showed that the more unbalanced the load profile, the greater the effect of the horizontal pipes. In fact, the effect of the pipes in combination with the perfectly balanced profile was almost negligible. 21 Table 6: Electricity reduction [%], operating hours [%] in which the critical fluid temper- atures were exceeded and average number of control events per year. elect. reduction temp. violation control events c/h ratio a) b) c) a) b) c) a) b) c) 0.1 10 12 12 5 .0 0 .004 0 .0 12 12 13 0.32 8 9 9 2 .7 0 .05 0 .004 12 12 13 1.0−3 2 2 7 .2 0 .4 0 .009 12 12 23 3.14 9 9 13 2 .3 0 .15 0 .003 12 12 15 10.0 11 13 13 14 .1 0.1 0 .001 12 12 16 a)prediction based on monthly average b)prediction based on monthly average of dominant load type c)prediction based on monthly average of dominant load type + addi- tional control events The German technical guideline VDI 4640 VDI (2019) requires that bore- hole heat exchangers are designed to ensure that the temperature of the fluid does not exceed certain limits during the operating period, which is typically 50 years. The investigations on longer operation revealed that even after 75 years of operation the critical temperatures were not reached for all sce- narios, due to the additional gains along the connection pipes. Prolonging the (efficient) operation of existing BHE fields with a constant load profile is therefore a valid option to utilise the capacity gain from the connecting pipes. Instead of extended operation, the thermal load can be increased (or conversely, the number of BHEs can be decreased in a new built situation). For the case c/h = 0.1, the load profile could be increased by 26 %, while for the case c/h = 1.0 it was only 4 %. The question here is to what extent this is possible in practice. With monovalent design, the BHE field is designed for the given building load, which is rather constant for many types of use and cannot be increased. If a BHE field is used mainly for cooling, the building loads may increase steadily due to climate change. In this case, the additional reserves provided by the connection pipes could ensure efficient operation. In a bivalent system, the share of geothermal energy can be increased according to the capacity reserve. The investigations into the optimised operating strategy are based on the assumption that the number of BHEs operated and the flow rate of the circu- 22 Figure 19: Monthly averaged fluid inlet temperatures of the critical month (left) and total electricity consumption (right) for the hourly load profiles and the optimised operating strategy. lation pump can be adjusted as required and that the energy demand for the optimisation period can be predicted with sufficient accuracy. By adjusting the number of BHEs operated on a monthly basis, the power demand could be reduced by up to 13 %. However, it was found that the critical fluid tem- peratures for the hourly load profiles were exceeded, but this occurred in less than 1 % of the operating hours. If the above conditions for an optimised operating strategy are met, it is a valid possibility to use the heat gains along the connection pipes to reduce operating costs in existing systems. 23