Assessment of Possibilities of Electricity Production in Flash Geothermal System in Poland

An analytical method is described that expresses the specifi c power of a fl ash geothermal power plant with fl ash temperature regarded as a variable. The analysis was carried out for a condensation temperature for fl uid exiting a theoretical turbine and for a given geothermal reservoir temperature. The method is a linear approximation of the established method for optimizing separator pressure. This linear approximation makes it possible to obtain an analytical expression for the optimum fl ash temperature (fi xing the separation pressure) at which the maximal specifi c power is obtained. A discussion arose in Poland during extensive research related to the application of binary systems, HDR (Hot Dry Rock), and EGS (Enhanced Geothermal System) technologies for the production of electricity. This concerned the hypothetical possibility of using geothermal fl ash systems for this purpose. Therefore, the above procedure was applied to Polish geothermal conditions to assess the theoretical possibilities of operating such systems at the reservoir temperatures anticipated in Poland. In the lower Triassic formations in central Poland, there are geothermal resources with temperatures hovering above 130°C. However, low net power values were estimated following the application of the procedure; when combined with the large investment costs involved (the high-temperature resources lie at a depth more than 4000 m), this is not condusive for the effi cient application of such systems. On the other hand, the possible application of binary systems to electricity production in that area is realistic and justifi ed.


Introduction
The variety of reservoir conditions in Poland demonstrates the variety of possible contexts in which geothermal energy can be used (adjusted to local conditions and needs).
Growing interest has been observed here, especially in the geothermal bathing sector (which has att racted private investors).Systems based on deep hydrothermal resources as well as on shallow groundwater and rock formations (heat pumps) have successfully been exploited [2,3,5,16,19].
It is also worth noticing that the interest in recreation and balneotherapy is growing.Eight new centers have been opened in Poland in recent years [12].In some cases, geothermal waters have been proposed not only as an exclusive energy source but also as a source of fresh water after desalination [17,18].
However, compared to the well-known Italian (Larderello), Icelandic (Nesjavellir), Turkish (Germencik), New Zealand (Wairakei), American (Geysers), and Japanese (Otake) geothermal resources, Polish geothermal resources look much more modest in terms of energy.Of course, Poland is not on a tectonic plate boundary, and only the central part of Poland has conditions for the production of electricity.These geothermal resources can be classifi ed as intermediate resources [2,4].
Recently, large-scale research has been carried out in Poland on the possibilities for using geothermal energy in the production of electricity in HDR (Hot Dry Rock) and EGS (Enhanced Geothermal System) systems.Future deep drilling is planned in Poland, and HDR technology gives us the opportunity to fi nd geothermal resources at depths of 4000-5000 m, with temperatures signifi cantly exceeding 100°C.Such opportunities occur in central Poland in the lower Triassic formations [10] as well as the granite structures of the Karkonosze mountains (region of Sudetes) [7].
The potential possibility of fi nding reservoirs with temperatures above 130°C in these structures prompted speculation about the theoretical possibility of applying single fl ash systems for the production of electricity.The use of geothermal resources with such temperatures in fl ash systems has been discussed in numerous papers (e.g., [9,15]).
In Poland, however, there is no reliable borehole data relating to the thermodynamic parameters in such zones nor giving well productivity curves providing information on the relationship between the mass fl ow rate and wellhead pressure.Because these parameters were arbitrarily established, the estimates presented in this paper are more of an indication and guide than hard data for practical use for a specifi c project.
The analyses were intended to estimate the optimal parameters required for a hypothetical fl ashing process to achieve the maximum power for a geothermal power plant.The problem of maximizing the power output of a single fl ash plant is a well-known issue and involves identifying the optimal fl ash temperature at which the maximum of the product of the steam mass fl ow rate and expansion enthalpy are obtained (for any given wellhead and condensation temperatures).An important element of the analysis is the fact that, with reducing fl ash temperatures, the steam mass fl ow rate increases; however, the expansion enthalpy decreases.The standard estimation of the optimal value of fl ash temperature applies the formula of defi ning the square root of the product of the absolute wellhead and absolute condensation temperatures.The article presents an alternative formula and compares the obtained results based on the procedure presented, the square root formula, and thermodynamic diagrams.

Power Estimation of Flash Cycle in Geothermal Plant
A schematic diagram for a simple fl ash geothermal plant is presented in Figure 1.Flash steam plants are used to generate power from liquid-dominated resources that are hot enough to fl ash the water to steam in surface equipment (e.g., via a fl ash valve).The steam fl ows through the turbine to produce power, while the brine can serve as the input heat for space heating and/or a binary cycle plant before being re-injected back into the well.Steam exiting the turbine is condensed in the condenser and also re-injected into the same well.A method for expressing the effi ciency and specifi c power of a fl ash geothermal plant as a function of fl ash temperature was examined by Ryley [14].
Issues referring to geothermal fl ash plants were presented in papers by DiPippo [8] and Kanoglu, Dincer and Rosen [11], among others.
In the analysis presented, the following are assumed: saturated thermal water (mostly two-phase fl uids) at the wellhead (t 0 , p 0 ), an isenthalpic fl ash process, a minimum fl ash temperature (t 1 ) of 100°C (with a minimum fl ash pressure p 1 of 1 bar), and a maximum thermal water temperature t 0 up to 250°C (p 0 up to 40 bar).
In a conventional steam turbine, the geothermal power (W) is the change in the isentropic enthalpy that takes the turbine effi ciency and mass fl ow rate into account: where: h 2 -specifi c enthalpy of steam entering the turbine, h 3 -specifi c enthalpy of fl uid exiting the turbine (assuming an isentropic turbine), η -turbine effi ciency (usually 0.75-0.85),m  -total mass fl ow rate from the well (also depending on the fl ash temperature in most cases).
In a fl ash system, the mass fl ow rate entering the turbine (Fig. 1) equals x m   ; thus, according to (1), the specifi c power of the turbine is: where: h 2 -specifi c enthalpy of saturated steam (Point 2, Fig. 2) at fl ash temperature t 1 , h 3 -specifi c enthalpy of fl uid exiting the turbine at condensation temperature t 2 (Point 3, Fig. 2) x -steam fraction (Point 1, Fig. 2a).
It is a known fact that, if x increases during the fl ash process, the diff erence of enthalpy drops (h 2 -h 3 ); thus, gett ing more steam does not always mean increasing the power value.The change in x is produced by the isenthalpic decrease of fl ash temperature and pressure (Figs. 1, 2).This relationship is seen in Diagram (t -h) (Fig. 2b) and can be writt en as: where: R 1 -latent heat for fl ash temperature t 1 and pressure p 1 , R 0 -latent heat for thermal water temperature t 0 and pressure p 0 .
It was assumed that, in the range of changes t 1 = (100-250°C), the value of factor δh is negligible (small changes of h 2 ); thus, equation ( 3) can be writt en in the following form: where: h 0 -specifi c enthalpy of saturated thermal water at point 0 (Fig. 2), h 1 -specifi c enthalpy of saturated water at fl ash temperature t 1 .Taking into account that x and h 1 = f(t 1 ): Thus, an approximation of parameter x(t 1 ) is expressed by fl ash temperature t 1 .
Relationship (h 2 -h 3 ) depending on parameter t 1 is more complicated.It is presented in the fragment of Diagram (t -h) (Fig. 3). Figure 3a shows the processing of the "transfer" working fl uid by a hypothetical turbine alongside the line of constant entropy, which is connected to the fall of its temperature Δt to condensation value t 2 .
If the lines of constant entropy on Diagram (t -h) in the two-phase area were straight parallel lines, the determination of the relationship between (h 2 -h 3 ) and t 1 at established t 2 would be simple; namely, according to Figure 3a: and: where a -isentropic expansion of heat capacity (the value determined from the lines of constant entropy) [kJ/(kg•K)].
However, the lines of constant entropy in Diagram (t -h) (Fig. 3a) do not fulfi ll the condition of linearity or parallelism, because a = f(t 1 ) (in reality, alongside the line of constant entropy, the value of parameter a also depends on t 2 ): According to the data from the diagram in Figure 3a, relationship a = f(t 1 ) was established and presented in Figure 3b.The values of parameter a depend almost linearly on fl ash temperature t 1 in the range of temperatures analyzed by the following function: From the graph in Figure 3a, we can see that, the smaller t 1 is, the higher h 3 and smaller h 2 − h 3 are -but from Formula (5) -then, the higher x is.Thus, the maximal value of specifi c power in Expression (2) can only occur at a strictly defi ned parameter of t 1 .
Putt ing (5), (8), and ( 9) to (2), we obtain: Expression (10) presents an alternative, semi-analytical formula for the estimation of the specifi c power of a single fl ash geothermal plant as a function of fl ash temperature t 1 , where the established parameters are η, t 0 , and t 2 .Examples of the calculations of specifi c power and t 1 opt for the assumed parameters of the thermal fl uid (t 0 , p 0 ) and assumed condensation temperature t 2 , are shown in Figure 4. Flash temperature t 1 can theoretically decrease to value t 2 where, according to Formula (10), the power becomes zero.
Function w(t 1 ) is almost a symmetrical "parabola"; thus, maximum power occurs for the value of t 1 close to the arithmetic average of t 0 and t 2 : The known and simple formula of the maximization of the power output of a fl ash plant is the one that correlates t 1 opt according to the square root of the product of t 0 and t 2 (using the Kelvin scale): or: Examples of the calculations of specifi c power and t 1 opt for the assumed parameters of the thermal fl uid (t 0 , p 0 ) and assumed condensation temperature t 2 are shown in Figure 4.The results were compared to the values obtained from the REFPROP and CoolPack databases.
Flash temperature t 1 can theoretically decrease to value t 2 where, according to Formula (10), the power becomes zero.The results were compared to the values obtained on the basis of the REFPROP and CoolPack databases and also from the square root formula.
The values of t 1 opt and the maximum specifi c power taken from the REFPROP and CoolPack databases (regarded as accurate) indicate a small deviation from those estimated using Formulas (10) and (11).The estimation error mainly results from the estimation error of parameter x (assumption of δh ≈ 0 in [3]).
Despite the fact that the estimation gives some errors, it allows for a quick and simple assessment of the maximal power of a fl ash geothermal plant for defi ned parameters t 0 and t 2 through the substitution of value t 1 opt from ( 11) or ( 13) into Expression (10).

Implications for Geothermal Conditions of Poland
As mentioned above, Polish geothermal resources look much more modest in energy terms when compared to well-known global geothermal resources.Only in the central area of Poland are there realistic local conditions for the production of electricity from geothermal fl uids (e.g., the Konin region, [1]); even so, the temperatures of thermal waters occurring in these places do not exceed 130-140°C.Thus, the possibility of the application of single fl ash systems is only hypothetical.The values of specifi c power (w) presented in Figure 4b signifi cantly depend on the accepted value of temperature t 2 ; however, even for the optimal conditions assumed in Poland, they do not exceed a value of 9 kW/(kg/s).As shown in Figure 4b, the highest specifi c power for a given t 0 is theoretically obtained from the maximal cooling of liquids exiting the turbine.However, the effi ciency of the turbine depends on the relationships between p 1 and p 2 (= t 1 and t 2 ); additionally, the mass fl ow rate depends on the value of fl ash temperature t.In Poland, the pressure at the wellhead is also a problem.Although there is the potential possibility of producing the required pressure by installing suffi cient deep pumps in the boreholes in the subartesian conditions that often occur in central Poland, the energy consumed by the pumps might drastically lower the value of net power.The total power produced by the well in a fl ash system may be calculated from the specifi c power (w) and mass fl ow rate (m  ): For the geothermal conditions in the Lower Triassic reservoirs in central Poland [9], maximal values m  are about 30 kg/s (~100 m 3 /h); according to Formulae ( 10) and ( 11), the maximal value of specifi c power (w) that could be obtained is 8 kW/(kg/s) for the established conditions of the saturated water: t 0 = 130°C, p 0 = 2.7 bar, and t 2 = 70°C (Fig. 4b).Thus, the maximal power of a hypothetical fl ash system is ~0.8 MW.However, even if all of the established conditions were to be fulfi lled, the real net power could be about 25% lower [9] and might not exceed 0.6 MW.

Conclusions
Based on the analytical estimations carried out, it can be stated that the single fl ash cycle process is not relevant for Poland.The estimations presented indicate that, even optimistically assuming a mass fl ow rate of about 100 m 3 /h, the proper pressure and thermal conditions (p 0 ~3 bar gauge, t 0 = 130°C), and the signifi cant cooling of fl uids exiting the turbine (t 2 ~ 70°C), the value of net power would probably be below 0.6 MW (Fig. 4b).Taking into account the investment costs (depth of resources at about 4-5 km), the implementation of single fl ash systems would also not be justifi ed due to economic reasons.On the other hand, the hydrogeothermal conditions of central Poland presented indicate real possibilities for using resources in binary systems [6,13].
The examples of world geothermal plants indicate that a combination of the technology of fl ash and binary systems can signifi cantly increase the power obtained and (in this manner) improve the effi ciency of power plants.However, the temperatures of Polish resources are too low to make such a combination of processes viable (single fl ash systems need a reservoir temperature in the region of 170-200°C to be superior to binary).
The above conclusions are the result of applying simple analytical formulae for the single fl ash cycle and providing an alternative method for estimating the maximal specifi c power.The analysis carried out formulated the relationship between specifi c power in the single-fl ash cycle and the value for fl ash temperature t 1 representing the decrease of temperature in the geothermal fl uid t 0 during the fl ash process.The formula defi nes at which value of fl ash temperature t 1 the maximal value of specifi c power at the established temperatures of geothermal fl uid and the established condensing temperature of fl uid exiting the turbine is obtained.This is a well-known problem; however, from a scientifi c point of view, it would be interesting to present the analytical solution and compare the results with those obtained from thermodynamic diagrams and the square root formula.The estimated errors of the procedure applied are within a range of 2-5% of the values defi ned on the basis REFPROP and CoolPack data.
In the estimation, the values of some parameters are assumed, whereas these assumptions are not really appropriate for the actual processes occurring during the generation of electricity in a power plant.For instance, the calculations are based on ideal thermodynamic processes, and some values (such as isentropic turbine effi ciency) were accepted in an arbitrary manner, while parameter (x) is a crude estimate.

Fig. 1 .
Fig. 1.Scheme of single fl ash geothermal power plant (characteristic points and symbols as in Figure 2): t -temperature, p -pressure, h -specifi c enthalpy, -mass fl ow rate, x -dryness (steam) fraction

Fig. 3 .
Fig. 3. Values of parameter (a) shown on (t -h) diagram along constant entropy lines of two-phase area (a).Linear extrapolation of a (t 1 ) function (b)

Fig. 4 .
Fig. 4. Plots of specifi c power for single fl ash geothermal cycles (w) as a function of fl ash temperature t 1 : a) for identical temperatures of thermal fl uids t 0 and diff erent condensation temperatures t 2 ; b) for identical temperatures of thermal fl uids t 0 and diff erent condensation temperatures t 2