Energy/exergy conversion factors of low 1 enthalpy geothermal plants

5 A geothermal heat plant is a not only a source of heat, but, in general, also a sink for relevant amounts 6 of electricity, consumed mainly by the pump(s). This electricity demand is usually not given much 7 attention although being decisive for operation costs, but also offering chances for demand side 8 management as a variable consumer. From the perspective of an integrated energy system, 9 geothermal installations basically move energy from the electricity sector into the heat sector, similar 10 to compression heat pumps. The main heat pump performance indicator is the ratio between invested 11 energy and useful heat, the COP. This paper transfers the COP concept to geothermal sites, by defining 12 and determining the quantity for a selection of mostly German geothermal sites.


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The integration of renewable energies into our energy system poses various challenges, as fluctuating 16 demand and weather dependent production have to be matched. Possible solutions are storage, 17 adaptive production by conventional plants, demand-side load management and energy transport 18 over long distances. Another approach is to leave the electric sector and make use of other energies. 19 Power-to-X is the catchy name for the transformation of surplus electric energy a into another energy 20 form which can be stored better or consumed directly. Power-to-Heat is the most promising option 1 , 21 which can be implemented by basically dissipating the electric energy in an electric resistor. This is very 22 simple technology that scales well and converts nearly 100 % of the input at any voltage, DC or AC, to 23 a In Germany 2019 6.4 TWh (2.8 % of the electricity from renewables or 1.2 % of total) were throttled 39,40 useful heat at virtually any temperature, right where it is needed without residuals, byproducts or 1 exhaust fumes. 2 The valuable electric energy can, however, be used much more efficiently for heat provision by 3 deploying complex technologies, such as compression heat pumps extracting heat from ambient air, 4 sewage water, soil and/or ground water using closed borehole heat exchangers or open groundwater 5 circuits. Heat pumps are designed to provide a heat output power of multiples of 100 % of the input 6 power by adding heat from a low temperature heat source. Their key performance indicator is the 7 coefficient of performance (COP) defined as heat output ̇o ut per electrical input ̇i n . It is limited by 8 the theoretical maximum, which is defined by the reversed Carnot's law. Hence, for a given heat pump 9 technology, the COP increases with source temperature and decreases with falling output. 10 (1) Ambient air as a heat source (ASHP) has low requirements, but also the inherent disadvantage of a 11 low COP especially when air temperature is low and heat demand consequentially high. Manufacturers 12 promise COP = 3…5 2 , but, often installed in sub-optimal conditions, ASHP often cannot keep that 13 promise, reaching COP < 2. Therefore, the German environmental NGO BUND demands to limit grants 14 to more efficient heat pumps with a COP ≥ 5, which would effectively exclude ASHP 3 . This requirement 15 could be fulfilled better by ground source heat pumps (GSHP), which operate with a more stable heat 16 source, but require the installation of heat exchangers in the underground. However, they, too, often 17 fail to reach their theoretical COPs in practice with average values below 3.5 4 . 18 Ground temperature and hence the COP generally increase with depth, but so do the technical effort 19 and requirements. At a given depth the ground is warm enough to use the harvested heat directly 20 without enhancing it by a heat pump. This reduces the electrical input approximately to the power 21 consumption of circulation pumps. A closed-circuit heat exchanger relies on heat transport by 22 conduction 5 and therefore does not allow as much heat extraction as an open circuit, which is based 23 on convective heat transport. The closed circuit does, however, avoid the problems caused by reservoir 1 hydraulics and precipitation of solutes from the brine. 2 Generally speaking, increasing the technical effort for a technology, such as increasing the depth of a 3 geothermal well can increase the heat output, absolute and relative to the electrical input, but 4 obviously also the financial cost (see Fig. 2). pumps are commonly available only up to a few dozen kW 2 as usually installed in single-family houses. 12 A few large-scale heat pumps are in operation with thermal outputs up to a few MW. Beyond their 13 range of thermal power are, however, geothermal wells, having an output of up to hundreds of MW 14 at a relatively smaller electrical expense, as will be shown in herein. 15 A geothermal plant, sketched in Fig. 2 with open loop and hydrothermal reservoir, comprises one or 16 more production wells and usually one or more injection wells. Hot (geo)fluid is produced from the 17 underground by a production pump. At the surface, heat is extracted from the geofluid, which is then 18 reinjected via the injection well, driven by an injection pump, if required. 19 Heat extraction rate obviously depends on production rate and reinjection temperature. The latter is 3 thermodynamically limited by the temperature of the heat sink, usually the return temperature of the 4 secondary loop. The lower the temperature required by the heat use technology, the more heat can 5 be extracted. Fluid chemistry, however, adds another limitation. Temperature reduction may trigger 6 precipitation, which, at the high mass flow rates realized in geothermal sites, can produce a 7 considerable mass of solids, that at best ends up in filters and at worst clogs pipes, heat exchangers or 8 the pores of the reservoir rock 6-9 . 9 Production rate is subject to friction, in the porous rock matrix of the reservoir as well as in the pipes 10 of the wells and the surface installations. The complex hydraulic rock properties with respect to flow 11 into/from a well determine the productivity/injectivity. It is quantified by the productivity/injectivity 12 index (PI/II), defined as the ratio between flow rate and the pressure drop/increase in the well during 13 production/injection. 14 The pumps have to overcome not only said friction, but also the level difference between static water 15 table and surface plus the production well-head-pressure. Consequently, unless the production well is 16 geothermal reservoir injection well injection pump production well production pump h at l ctricity artesian b and the injection well is absorbing (creates no relevant back pressure), considerable energy 1 is required to circulate the fluid in the geothermal circuit. This is independent of the installed pump 2 technology, be it an ESP c , a LSP d or a piston pump. 3 Hence, the electrical consumption of the pumps is considerable, albeit controllable by ramping up 4 and down the production rate and with it the heat production. Technically, this is feasible at a given 5 maximum ramp-up speed within the boundaries of minimal partial load and maximum flow-rate. 6 Economically it may make sense to do so given the necessary capacities in storage and/or backup heat 7 production as well as the right economic boundary conditions which gratify electric grid stabilizing 8 operation strategies. This upgrades geothermal energy from being a renewable energy not causing 9 fluctuations to one rather compensating them, thus increasing its benefit as a component of an energy 10 system. Accordingly, Schlagermann predicts the shift in the operation of geothermal power plants from 11 baseload to market oriented or even operating reserve optimized 10 . Whether an individual geothermal 12 plant should be operated this way, is a complex question and out of the scope of this work, which is 13 intended rather to quantify the potential service geothermal plants can render to the grid. 14 The presented approach is applicable irrespective of useful heat application, pump technology, 15 whether there are one or several production/injection wells, the reservoir is petrothermal, or the 16 geothermal is closed. The geothermal plant is simply considered as a system receiving electric energy 17 and returning thermal energy. 18 This paper gives an overview about the ratio of these two quantities, i.e. the harvested heat ̇o ut 19 relative to the auxiliary power demand ̇i n for a selection of existing geothermal sites: 20 =̇o uṫ in (2) b Flowing artesian well: the reservoir fluid pressure is high enough to make the fluid rise to the well-head, resulting in flow without pumping. c Electrical submersible pump -centrifugal pump installed together with the motor in the production well. d Line shaft pump -centrifugal pump installed in the production well driven by a motor at the surface via a shaft.
This quantity is h r in r rr d to as th " n rgy onv rsion i i n y a tor". In ontrast to 1 common efficiencies, is not limited to ≤ 1 by energy conservation, but rather nominally exceeds 1. 2 If it is below 1, i.e. if more energy is invested than is harvested, there is no benefit over the much 3 simpler direct transformation to heat in an electric resistor/heater. 4 The analogy to the COP of heat pumps is obvious. Using a given amount of electrical/mechanical 5 energy to provide a larger amount of energy as heat is what compression heat pumps (CHP) are made 6 for. While their efficiency has the aforementioned theoretical maximum, the of a geothermal plant 7 however, is not subject to this limitation derived from the fundamental laws of thermodynamics. That 8 is due to the fact that a geothermal plant is an open system. Given an artesian well, i.e. ̇i n = 0 , 9 even goes to infinity. 10 This key value combines the thermal and the hydraulic reservoir properties, but also site-specific 11 boundary conditions and design and operating parameters, primarily reinjection temperature as well 12 as production rate. It can be used to assess the systemic potential of geothermal plants in general or 13 to compare the energetic performance of single sites, but also, with limitations, for comparison with 14 other heat provision technologies in a multimodal energy system. 15 A fair comparison of heat provision technologies, however, requires taking into account the 16 temperature of the delivered useful heat. One way to do it is to look at the exergies driving and leaving 17 the plant. In analogy to , the exergetic conversion efficiency is calculated as the ratio of thermal exergy 18 ̇ * out output to driving electric energy ̇i n , which is pure exergy. 19 ( The exergy contained in ̇o ut is calculated by applying the Carnot or quality factor e,11 . It depends on 20 the temperature of heat provision amb and of the environment out . 21 e Here, the Carnot factor describes the amount of work achievable by a Carnot cycle operating between the brine and the ambient temperature amb . While the energy conversion factor can be compared to COPs of ideal or real heat pumps, the 1 reference for this exergy ratio is a reversible process with = 1 (ideal heat pump). Everything below 2 1 indicates an irreversible loss of exergy, while < 1 marks a gain of exergy, possible here because 3 the definition (3) intentionally leaves out the inflow of heat in to the system, as it is not invested in the 4 sense that electric energy is. 5 Another obvious reference is the heat provision by an electric resistor. There, the electric energy is 6 converted completely to heat, i.e. ̇i n =̇o ut ., yet only a fraction of ̇o ut being exergy. This fraction, 7 depends on temperature and is directly given by the Carnot factor f . The resistor could be operated at 8 a higher temperature, thus destroying less exergy, but nothing is gained if the heat is used eventually 9 at a lower temperature anyway. The sink temperature out eventually determines the system exergy 10 loss, no matter if the loss happens by dissipation in the resistor or during transfer to the heat sink. 11 Even though eventually the economic profitability of a site usually is pivotal, the conversion factors 12 give a first evaluation from the energetic/exergetic perspective how reasonable the operation of a 13 geothermal plant can be with a systemic perspective. 14 State of the Art 15 Thoroughly characterizing geothermal sites is complex as several key parameters must be 16 considered 7 , primarily obviously thermal output power and production temperature. They result from 17 technical installations (well setup, pump configuration, etc.), design and operating decisions 18 (production rate, reinjection temperature), the hydrogeological conditions (rock permeability and 19 porosity) and, last not least, the geochemistry. 20 The aquifer geometry is often simplified to a homogenous horizontal layer of rock with a given 21 thickness. The hydraulic behavior aquifer is usually linearized and described with the coefficients 22 productivity and injectivity relating drawdown and production rate. The brine composition is 23 thermodynamically relevant as a high salinity affects density, heat capacity and viscosity. 24 f For example, electric heating to out = 100 °C at amb = 0 °C, has an exergetic efficiency of 0.27.
One way to reduce the multitude of parameters to a single value is to determine the heat generation 1 cost in terms of money 12-14 or CO2 emissions 14 . This requires a usually rather extensive profitability 2 calculation considering geological, technical and economical boundary conditions. This value can be 3 compared against alternative heat provision technologies. 4 Schlagermann 10 conducted a comprehensive exergo-economic analysis for the geothermal power 5 plant in Bruchsal, Germany, focusing on the electricity production costs. 6 While an economic calculation is certainly indispensable for the decision about the realization of a 7 project, it is often too complex and requires too much economic input for purely energetic 8 considerations. For this purpose, the ratio proposed here is more suitable, as it represents a relatively 9 inexpensive and universal evaluation method.
This in turn requires the knowledge/assumption of the hydraulic properties of the assumed 1 homogenous horizontal aquifer, namely the natural water table depth wt and the injectivity which 2 they estimate via a porosity-permeability correlation. Kastn r's approach yields rather low production 3 rates and consequentially high conversion factors. With large uncertainties mostly due to the porosity 4 data, they estimate the average COP, the ratio of electricity input and thermal output, to be 16.2 for 5 the more productive one of the aquifers (Middle Buntsandstein). 6 Bugai 19 assessed a geothermal heat supply system and defined an "annual x rgy i i n y a tor" 7 as the exergy of the useful heat divided by the exergy input by geothermal fluid, peak reheater and 8 pump power supply. Yet no values are given. 9

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In order to be able to include also geothermal power plants, they are considered herein as heat plants 11 with an attached separate power cycle, such that the energy conversion efficiency can be determined 12 in the same way as for heat plants. The additional consumers which are present in a geothermal power 13 plant such as cooling facility and feed pumps are not of interest here. 14 The energy input into a geothermal heat plant is mainly consumed by the electrical consumption of 15 the pumps el wh r th lion's shar is onsu d by th produ tion pu p. 16 Data of pump power consumption in geothermal sites is scarce and often considered company secret. 17 For some sites information about net and gross electricity generation is available. The difference 18 between the two values is a hint to the pump power consumption, but potentially also includes cooling 19 effort for the power cycle and other auxiliary consumers. If unavailable, the electrical consumption of the pumps can be estimated with equ. (6) from 1 production rate and differential pump pressure Δ pump and assumed efficiencies. 2 If unknown, Δ pump can be estimated from the hydraulic work, using the productivity/injectivity 3 index PI / II of the well, production rate ̇, the static water table < 0 and brine density : 4 For the injection well, this equation is limited to Δ pump > 0 to avoid falsely calculating electricity 5 gain in absorbing wells: 6 If data about the electrical consumption of the injection pump is not available, it is assumed to be 7 insignificant in relation to the production pump consumption. If the static water table is unknown, it is 8 assumed to be 0. 9 The harvested heat ̇o ut can be calculated as the diff r n o th luid's enthalpy at both wellheads. 10 Disregarding any heat losses possibly occurring in the well or between heat extraction and delivery 11 and assuming one-phase flow (no gas phase), ̇o ut can be approximated by the product of production 12 rate ̇, a constant specific heat capacity and the temperature difference between the well heads. 13 If the well head temperature is not available, it is assumed to equal the reservoir temperature: 14 The production rate ̇ is assumed to equal the injection rate, i.e. there is no relevant fluid loss 15 between production and injection, i.e. none of the produced geofluid is diverted without being 16 reinjected and, in the case of HDR h reservoirs, all of the injected fluid volume is produced again. 17 h Hot Dry Rock method, applied to petrothermal reservoirs The flow rate, given as a volume flow rate ̇, is converted to mass flow rate ̇ with the fluid density 1 at production temperature: 2 ̇=( prod , ) .
Both and of the geofluid depend on temperature and salinity . In this study, their values were 3 estimated using the brine property model BrineProp 20 considering the respective salinity . Unless 4 indicated otherwise, the mean specific heat capacity for each site was calculated from the specific 5 enthalpies at wellhead conditions as follows: 6 = ℎ( prod , prod , ) − ℎ( prod , inj , ) The energetic conversion factor of a geothermal plant is hence calculated by equ.
(2) as 7 Equ. (12) does not directly consider the production temperature prod , the quality of the heat ̇o ut 8 provided by the geothermal plant. Hence, in the next step, equ. (12). This is again divided by the 9 electrical consumption ̇i n , which is pure exergy, to obtain the exergy ratio between output and input: 10 The exergetic conversion factor is calculated by equ.
Assuming a perfect storage, exergy depends on the minimum of the periodically varying ambient 12 temperature 21 . The average minimum air temperature in Germany is about -0.4 °C 22 . This matches 13 closely the conventional choice of amb = 0 °C which is also assumed herein. 14 m is used as the upper temperature, as the brine flow is a sensible heat source. m is the logarithmic 15 mean temperature of the heat transfer from the brine: Another way of taking into account the temperature level is to set into relation to the theoretical 1 maximum COP of a heat pump, i.e. a reversible heat pump, working between these two temperatures. 2 This results in the same equation as equ. (13), with prod replacing m , as the useful heat is non-3 sensitive here. This is how heat pump performance is assessed independently of temperatures. The 4 quotient is called " x rg ti i i n y" 11,23 or "Güt grad" 4 in German. 5 The net exergy output is defined as the difference of exergy output ̇ * out and the electric input ̇i n . 6 Sites 7 Motivated by a project dealing with the German energy system, this study focuses on German deep 8 geothermal sites and European sites with comparable conditions. All German sites were included 9 where enough data could be acquired to calculate the efficiencies. All sites have in common that their 10 wells are deeper than 1000 m and that they have at least one production and one injection well. 11 The source data are very heterogeneous in quality and in what quantities are disclosed. It was 12 acquired from publications, the GeotIS database 24 , personal communication with operators, but also 13 from project and news websites. While numbers about the thermal power of geothermal sites are 14 easily found, pump consumption data is rarely disclosed by commercial operators. In general, 15 operational parameters are varying due to a multitude of reasons. Hence, picking a number requires 16 some kind of averaging or an educated guess.   Table 1 lists the key parameters of the included geothermal sites as well as the calculated energy and 1 exergy conversion factors. Where the input parameters were available as ranges or in several variants, 2 they are listed as a value range of the resulting conversion factors. 3

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For the Soultz site, the calculation of electricity consumption is based on the specific parameters and 4 the simple model defined by equations (5) till (14). This allows an exemplary study of the sensitivity of 5 the efficiency on the production rate (Fig. 9). The small number of sites does not allow conclusions with respect to different regions. 6 The geothermal sites considered here provide heat at temperatures between 38 and 170 °C. They 7 show a wide range of energy conversion factors between 12 and 112 (Fig. 6) the feasible operation range beyond which a further increase of production will cost more exergy in 23 the form of electricity than is gained from additional provided heat. The flat curve, however, indicates 24 a low sensitivity to a change of production rate around the maximum, which makes the choice less 25 critical. The same may apply for an economic optimum as both electricity demand and heat production can be converted into cost and revenue. This optimum may, however, be offset, as it depends on these 1 prices as economic boundary conditions. 2 Conclusion 3 Geothermal heat is available independently of weather conditions. It may be considered as free, but 4 its exploitation certainly requires investment, not only of money, but also of energy. From the system 5 perspective, geothermal plants are commonly only considered as heat sources. However, they require 6 pumps to produce and/or reinject the geofluid, unless they operate at very favorable reservoir 7 conditions (i.e. artesian production well, absorbing injection well). These pumps consume considerable 8 amounts of electricity, with their nominal powers often amounting to several of hundreds of kW. This 9 makes GT plants effectively Power-to-Heat converters. 10 The energetic and exergetic analysis of the gathered production data of a selection of geothermal 11 sites shows that extracting heat from the underground requires considerable amounts of valuable 12 electric energy. Compared to alternative methods of electrically powered heat provision such as 13 electric heating or CHPs, however, this is a very efficient one, as far more heat and exergy is provided 14 than invested as electrical input, even though this ratio output/input varies by one order of magnitude 15 among the sites considered in this study. 16 The exergetic conversion factor used here can be helpful as a key parameter to characterize 17 geothermal plants in strongly simplified energy system models. For this and other purposes it would 18 be beneficial to include the pump power consumption to overview tables and databases 7,24,37 , which 19 usually lack it t , compiling only other key figures such as thermal/electric power, production rate and 20 temperature. 21 Similarly to the efficiency of a geothermal power cycle, the conversion factors are not the quantities 22 to be maximized by varying mass flows, as this would lead to small thermal output. More reasonable 23 is maximizing the net exergy output. Its maximum may help to identify the "sw t spot" with respect 1 the production rate independent from economic parameters. 2 Outlook 3 Including more sites in this assessment would potentially allow to draw further conclusions, e.g. by 4 correlating the conversion factors to plant design or operational parameters or clustering them by 5 geologic setting. 6 Considering geothermal plants as sinks for surplus electricity raises the question of their part load 7 performance and their part load ability, i.e. how far and how quickly can their output be reduced or 8 increased. This should be quantified and be used as additional key parameters to describe geothermal 9 plants from the perspective of the energy system. 10 The assessment method presented here could be extended from existing geothermal plants to 11 existing boreholes or even to unexploited geothermal reservoirs, founding on existing data of 12 geothermal potential 17 . Following Kastner et al. 18 , the energetic/exergetic conversion efficiency could 13 be calculated based on the well productivity/injectivity, the water table and the reservoir temperature. 14 Discarding the limitation in eq. (8). Eq. (12) would then be adapted as follows: 15 = ( prod − inj ) (PI −1 + II −1 )̇.

(15)
As d s rib d in th "stat o th art", this approach would yield rather high efficiencies at a small 16 production rate. Another choice for the mass flow could be on the other end of the range: The 17 maximum production mass flow limited by the maximum drawdown, which is limited by the given 18 production pump installation depth (ignoring NPSHR u ), which in turn is limited by the reservoir depth: 19 ̇m ax = PI ( wt − res ) u Required net positive suction head -minimal water column above a pump inlet required for safe operation Consequentially, this approach returns rather high flowrates, low efficiencies, and, assuming PI = II, 1 cancels the productivity from the equation only leaving the depths and the temperatures. 2 The practical optimum for production rate is somewhere between these two values, determined by 3 a variety of boundary conditions, e.g. geologically motivated pressure limits, demand side 4 requirements, financial deliberation or optimal net power output 38 . With this information being 5 unknown for non-existent plants, an educated guess for the design operating point could be made 6 using the net exergy maximum as discussed before. 7 The presented conversion efficiencies can be calculated for any electrically driven heat provision 8 technology, including geothermal sites operated as thermal storages (ATES, BTES, MTES v ). Like the 9 storage efficiency, the conversion efficiency could serve as key figure to assess different storage 10 technologies or to compare storage to other heat/cold provision technologies. Eq. (12) should then be 11 changed to include the energy invested for storing the heat/cold.   The author is grateful to the plant operators that provided helpful information. 2