Reviewing the relationship between thermal reservoir parameters and geothermal energy output

This meta-study draws upon contemporary literature to examine parameters of thermal reservoirs and their relationships to geothermal power station output metrics. The objectives of the meta-study are to identify trends and quantify the influence of each parameter on the system as a whole. This study provides a framework for industry and researchers exploring new potential geothermal fields. Six reservoir parameters – well depth, temperature, enthalpy, mass flow rate, thermal gradient and crust thickness – were plotted against the net electrical output per production well (Enet/well) and exergy efficiency (ηB) of 64 geothermal facilities. The meta-study identified that reservoir temperature has the greatest proportionality to power output, with yields above 10MWe exhibited only for high enthalpy reservoirs exceeding 500K. Well depth has the greatest inverse proportionality to exergy efficiency, with upper limit values declining below 80% for wells deeper than 3000m. Well depth has a similar trend line, though lesser correlation, as reservoir temperature to power output. Crust thickness has an inverse correlation to exergy efficiency, with upper limit values dropping from 100% to 65% as thickness increased from 30 to 45km. There was significant clustering of data points in most trendless plots, suggesting a considerable degree of homogeneity between currently tapped reservoirs and turbine efficiencies. The low number of well-defined data trends implies a high degree of complexity arising from the relationships between reservoir parameters that make quantification problematic. Despite this difficulty, examination of the aforementioned parameters suggests that although hotter reservoirs are usually found at greater depths, the hottest and shallowest reservoirs should be prioritized for use in order to return maximal power outputs and reduce exergy losses that occur along large lengths of piping.


Introduction
Geothermal energy refers to heat available in the Earth's crust.This heat is produced in approximately equal proportions from high core temperatures caused by the initial formation of the planet and the radioactive decay of matter [1].This energy can be utilized by pumping geothermal fluids, heated gases or liquids found in deep thermal reservoirs, into geothermal systems that contain steam-powered turbines to produce electricity that is directly supplied to the grid.A generalized schematic of a geothermal system is available in Figure 1, displaying the extraction of geothermal fluid from a heated reservoir, conversion to electricity, supply to the generator and transformer and finally condensing or cooling of the fluid for reinjection to the reservoir.
Geothermal systems are an advantageous branch of renewable energy production compared to fossil fuels due to minimal greenhouse emissions, producing less than 5% the CO2 per kWh of common coal plants [3].The few solid mineral byproducts of geothermal systems are readily extractable to be sold for use in commercial and industrial applications [4].Liquid byproducts are often reinjected into the Earth in order to maintain the reservoir enthalpy (Hres), energy contained in a kilogram of geothermal fluid, and reservoir mass flow rate (Fres), kilograms of geothermal fluid movement per second past a defined point [5].
Thermal reservoirs fall into three enthalpy categories -low, medium and high -corresponding to geothermal fluid temperatures of 323-373K, 373-525K and above 525K [6].Thermal gradient (G) is defined as a function of Tres to Dwell in order to quantify temperature increase per meter of depth increase -however this is not likely to have a significant outcome on performance metrics as the theorized proportionality of these two parameters will likely return very small values.Crust thickness (C) is defined as the depth from ground surface level to the bottom of the Earth's crust layer, and higher C values are likely to result in higher G values as heat can more readily flow towards the surface.
Geothermal facilities exhibit a high degree of scalability due to their low physical footprint [7], making them ideal for use in urban areas where the pollutant byproducts of fossil fuels would be destructive.This scalability, and a >90% energy production uptime [8], or availability factor, heavily contributes to their potential for use as grid-stabilizers.As a widely connected grid is more prone to a cascading failure and power outage, geothermal facility dispersion across the world can provide an important energy supply backbone to reduce chances of these failures.The high initial outlay costs associated with establishing a geothermal plant warrant significant consideration in choosing new geothermal thermal fields for utilization [9].Economics aside, a major drawback to the global expansion of geothermal energy production is the power stations substantial location dependency.This problem arises because performance is based on the thermodynamic parameters of reservoirs such as reservoir temperature (Tres) and well depth (Dwell-), in addition to Hres and Fres.This barrier affects the widespread formation of new geothermal power stations as the parameters of reservoirs in a geothermal field must be understood to a high degree of accuracy for the system to be thermodynamically feasible for use.The four aforementioned parameters contribute almost entirely to the performance outputs of a geothermal system, and thus geological surveyors must understand the importance of each.
Binary Cycle and Flash Steam plants are the most common under-construction and in-operation types of systems, respectively [10].As shown in Figure 2a, Flash Steam plants rely on a moderately heated liquid passing through either one (Single Flash, SF) or multiple (Double Flash, DF) high-pressure separators that catalyze vaporization by rapidly dropping the pressure of the fluid in order to power a turbine and supply electricity to the grid.Exergy losses in Flash Steam plants often exceed 50%, with optimization occurring through a slight reduction in separator pressure [11].
Binary Cycle plants, as represented in Figure 2b, generally rely on lower enthalpy liquid passing through an intermediate tank in order to heat a secondary working fluid.This fluid has a lower specific heat capacity and boiling point that vaporizes the fluid, powering a turbine and supplying electricity to the grid.Binary Organic Rankine Cycle (BORC) plants are a type of Binary Cycle plant that utilizes a pure organic high molecular mass fluid as their working fluid.Binary Kalina (BK) plants differ from BORC plants, and contain a 2 fluid mixture for their working fluid, generally NH3 and H2O -though both operate on the same Binary Cycle principles.BORC systems present average exergy losses exceeding 50% from numerous sources, primarily condensers and vaporizers [12].BK systems exhibit lower exergy losses of approximately one third of total exergy in, attributed in near-equal parts to the Kalina turbine, geothermal vapor turbine and across the heat exchangers [13].Despite a current reliance of only 0.67% on geothermal renewables [16], researchers and industry-affiliated organizations have identified a worldwide total of 2x10 24 W potential useable geothermal energy -enough to meet the world's current energy demands for multiple millennia [17].With a massive potential for growth in this relatively unexploited renewable energy industry, it is imperative that geological surveyors can accurately and efficiently identify reservoirs and locations that would be economically and thermodynamically favorable for establishing new geothermal systems.Figure 3 illustrates how the highest risk for new geothermal project failure occurs in the first four stages before well-field development, dropping off significantly after this.Here we investigated six parameters of thermal reservoirs and their relation to power output metrics, net electrical output per well (Enet/well) and exergy efficiency (ηB), in order to identify trends and quantify the influence of each parameter on the system as a whole.With this, we are aiming to provide an approximate framework for industry and researchers exploring new locations.

Methodology
This meta-study draws on literature concerning reservoir thermodynamics and geothermal energy production.Sources were accessed via Google Scholar, Access Science, ProQuest Science & Technology, Science Direct, SCOPUS and the Web of Science Core Collection.Literature selection criteria and data acquisition involved cross-referencing between industry websites, government organizations, review papers and original research.The object was to obtain relevant insights into the industry trends and precise figures for specific geothermal systems.There was an emphasis on material produced since 2005, ensuring the relevance of collected data due to rapid advancements in turbine technology.
A gap in the literature was identified concerning the classification of the effects that thermal reservoir parameters have on the net output and exergy efficiency of geothermal power systems.The extensive body of knowledge currently available was utilized to investigate this gap and provide a framework for geological surveyors looking to accurately identify the thermal reservoirs that are most likely to be thermodynamically, and thus economically, viable.Six data metrics were extracted and tabulated (Appendix 1) from over 70 sources -reservoir temperature, depth, mass flow rate, enthalpy, crust thickness and installed electrical output capacity -for a total of 64 Binary Cycle and Flash systems, due to their standing as the most common types of GS under construction and in use, respectively.
The turbines utilized by different geothermal systems function in the same manner, despite differences between input methods, allowing for a generalized comparison of input to output metrics.From these metrics, the net electrical output per well (Enet/well) was calculated using Equation 1, where GWh is net energy produced yearly and W is number of wells, with transformation to Mwe by multiplication of 1000 MW per GW and division by 8760 hours per year.Exergy efficiency (ηB) was calculated using a simple derivation of the initial Equation 2, by dividing the net electrical output (Enet) of a power station by its theoretical electrical production capacity (Ecap).This efficiency equation is based on the principles of the Carnot Cycle (Appendix 2) that take into account the 2 nd Law of Thermodynamics -that is, the quality of energy, energy degradation, entropy generation and work opportunity losses [19].Equation 3 defines the relationship between the amount of heat transferred from a hot reservoir to a Carnot system, where QH is heat transferred to system, TH is temperature of matter from the reservoir and SA and SB are the initial and final entropy states of the system.
Eq. 2 Reservoir parameters were initially plotted against each other to identify if any coactive relationships exist between them and determine if normalization would be useful in data presentation, though no proportional trends were acknowledged.The only normalization of data was the presentation of net and installed capacity power output as a function of the number of wells (Enet/well and Ecap/well), whereas ηB values were calculated from the total Enet and Ecap values of a power station.Out of 64 geothermal facilities analyzed, 28 had no enthalpy data available or calculable and 8 were missing mass flow rate data, excluding them from their respective plots.No distinction is made between traditional and enhanced geothermal systems, though enhanced systems can generally be taken as those with tapped wells above 2500m depth [20].Crust thickness values were acquired via Figure 2, though an error margin of ±2.5km is noted due to the large tile sizes in the figure and 5km increments per tile classification.Linear trendlines were only fitted to plots where there is an easily identifiable trend to the naked eye, i.e. the trends identified as primary and secondary parameters.All reservoir parameters were plotted against each other and against Enet/well and ηB to identify trends and quantify and rank each parameter's influence on output for the industry and researchers consideration in the exploration of new underground potential production wells.

Results and Discussion
A search of 50 papers on the topic of geothermal power output returned only 3 papers involving an explicit focus on thermal reservoir conditions as they influence output metrics, with many papers examining optimal working fluids for binary plants and turbine thermal efficiencies.No papers were found that focused on all four main thermal reservoir parameters -well depth, temperature, enthalpy and mass flow rate.This meta-study attempts to fill this gap in the literature by identifying trends in these four thermal reservoir parameters as well as crust thickness and thermal gradient as they relate to each other, and to the output metrics of geothermal systems.The influence of the aforementioned parameters on output metrics renders their classification as being primary, secondary or tertiary in nature in order of descending relationship strength.T res (K) η B vs. T res medium enthalpy reservoirs.This trend was expected as steam turbines operate on the principles of the Carnot Cycle, as defined in Equation 3. The equation states that the total thermal energy transferred from a hot reservoir to a system is the product of the reservoir fluid temperature and the change in entropy of the system from its initial to final state.Due to this equation, and temperature having a higher magnitude than entropy due to the nature of their definitions and units, it is clear how Tres has the most distinct effect on the power output of a geothermal system compared to the other five investigated parameters.Figure 5b was expected to exhibit a similar trend to that of 5a, as an increase in input temperature or decrease in exhaust temperature of a system leads to efficiency increasing, as defined by the Carnot engine efficiency equation in Equation 2. Tres was found to have no correlation to ηB, with a random scattering of data points across the plot with no discernible proportionality of any kind.The discrepancy between the trends in the Figure 5 plots appears to be explained by the exergy trend shown in Figure 6b.These losses theoretically occur through the walls of the large lengths of piping required to reach the reservoirs that contain superheated geothermal fluids above 500K, and may offset the effects of the higher temperatures in the sample data.The trends in Figures 5 and 6 are interrelated, as ηB noticeably drops off for production wells above 3000m there is a corresponding positive increase in Figure 6a for Enet/well as a function of Dwell.This suggests that Tres values above 500K, the transition point from moderate to high enthalpy systems, are associated with well depths exceeding 3000m, and that despite the corresponding exergy losses of a deeper well, the power output caused by a higher Tres offsets these losses to produce the positive trend seen in Figure 5a.In simple terms, tapping a hot reservoir is more important than tapping a shallow one -though in practice this is highly limited by the economics of drilling, and thus temperature should prioritized until the point at which drilling deeper begins to offset the net power output gains.Following on from the relation of Tres to Dwell, the plots of G vs. Enet/well and ηB in Figure 7 represent a normalization of the parameters seen in Figures 5 and 6 as thermal gradient was calculated as a function of Tres and Dwell.Figure 7a exhibits an L shape trend, with a high clustering of data points close to the y and x axes suggesting that a majority of geothermal systems utilize production wells with low thermal gradients (approx.0.2 K/m) and produce outputs in region of 1-5MWe per well.
In addition to signifying homogeneity in production wells, the low Enet/well values of the >0.4K/m thermal gradients hint at one of the following conclusions.Geothermal systems are either not designed in a manner that takes advantage of thermal gradient, or thermal gradient has no correlation to Enet/well in our data.This, as theorized, is attributed to the fact that Tres and Dwell increase proportionally, and thus small gradient values are returned by the normalization calculation and no trend is exhibited.Figure 7b similarly has significant clustering of data in the same gradient region as 7a, simply indicating that most G values for geothermal systems are <0.4K/m and a full spectrum of ηB values are found in this range.Figure 8a displays Enet/well as a function of C, appearing to exhibit a rough bell-shape curve -with noticeably low outputs for 25 and 35km thicknesses.This may be due to specialised plate tectonics in the geographical regions, further highlighted by the fact that four out of five of the 25km facilities are located in Japan.This trend requires further investigation as the majority of data values were of facilities with 30km thickness, and thus may be skewing the data away from the actual influence of C on electrical output.Examining equal numbers of facilities from each thickness category would allow for a more measured comparison between them.There was however a slight negative trend for ηB vs. C, with a noticeable drop in the upper limit exergy values that dropped from 100% at 30km to 65% at 45km.
Referring to the table in Appendix 1, most of the 40km > C values corresponded to Dwell values exceeding 2500m.These deep reservoirs were found to correspond to higher exergy losses, and thus may account for this trend seen in 8b -further analysis is required to conclude whether crust thickness or depth is responsible for the trend line produced.Plots 9 and 10 examine the relation of Hres and Fres to Enet/well and ηB.Hres has a near identical trend in both of its plots to Figure 5 as the equation for enthalpy relies heavily on the influence of temperature, and thus they cannot be viewed separately.Fres has a near identical trend to that of Figure 7, and similarly may be suggesting that this parameter has a tertiary influence on output metrics for a geothermal system.Figure 11 represents the overall relation between the output and exergy efficiency of a geothermal system, exhibiting a proportional correlation.This graph essentially confirms the data utilized in the meta-study is correct for a steam turbine system, as power output is expected to increase as more energy makes it through the system.Appendix 1 contains plots of all combinations of reservoir parameters, undertaken as an attempt to determine whether normalization was possible.Thermal Gradient, taken from the plot of Appendix C, was the only normalization displayed in the results and thus the rest were excluded from the main body.The trends exhibited in these figures are all established in the literature and accounted for thoroughly by thermodynamic theory, or explained better by the plots above.The strength of the trends identified in Figure 5a (Tres) and Figure 6b (Dwell) lead to the classification of these reservoir parameters as being primary in nature, in that they have the most direct influence on Enet/well and ηB, respectively.Figures 6a (Dwell) and 8b (C) represent the secondary parameters that have a significantly lesser, though not insignificant, relation to Enet/well and ηB, respectively.The trends suggest that production wells in prospective geothermal fields should be considered primarily by their maximum geothermal fluid temperature, with an attempt made to choose reservoirs requiring the smallest length of piping to reduce exergy losses.

Conclusions
The strength of the trends identified in Figure 5a (Tres) and Figure 6b (Dwell) lead to the classification of these reservoir parameters as being primary in nature, in that they have the most direct influence on Enet/well and ηB, respectively.Figures 6a (Dwell) and 7b (C) represent the secondary parameters that have a significantly lesser, though not insignificant, relation to Enet/well and ηB, respectively.The clustering of output values in many plots suggests that there are well-defined barriers for output and exergy efficiency based on the current state of the technology utilized in geothermal systems across the world.These barriers represent a clear hurdle for industry and research organizations to overcome through advancement of turbine efficiency and proper identification of high-production capability thermal reservoirs.This meta-study concludes that the maximum geothermal fluid temperature of a thermal reservoir should be prioritized in prospective geothermal fields.A secondary consideration should be made to choose shallow reservoirs that require the smallest length of piping, in order to reduce exergy losses.

Figure 3 .
Figure 3. Risk of project failure vs. cumulative development costs with bankability rating identified by colouring [18].

Figure 5 .
Figure 5. (a) Enet/well as a function of Tres (b) ηB as a function of Tres .

Figure
Figure5a, a plot of Tres to Enet/well, exhibits the strongest trend of a thermal reservoir parameter to power output, with no facilities exceeding 10MWe per well for reservoirs below 490K, i.e. low and

Figure 6 .
Figure 6.(a) Enet/well as a function of Dwell (b) ηB as a function of Dwell.

Figure 7 .
Figure 7. (a) Enet/well as a function of G (b) ηB as a function of G.

Figure 8 .
Figure 8.(a) Enet/well as a function of C (b) ηB as a function of C.

Figure 9 .
Figure 9. (a) Enet/well as a function of Hres (b) ηB as a function of Hres.

Figure 10 .
Figure 10.(a) Enet/well as a function of Fres (b) ηB as a function of Fres.

Figure 11 .
Figure 11.Enet/well as a function of ηB.
kJ/kg) E net/well vs. H res