Geothermal Energy. The Effectiveness Evaluation of Kalina Cycle and Clausius-Rankine’a Cycle with Wet Working Fluid

Abstract

In the paper has been performed the comparative analysis of Kalina cycle and Clausius-Rankine cycle with wet working fluid. As a heat source for both cycles is used geothermal water and the analysis of both systems is based on the results of the heat-flow calculations. For Kalina cycle the calculations was performed for ammonia-water mixture contains 70, 82 and 90% ammonia concentration and for Clausius-Rankine cycle for five wet working fluids: acetone, R134a, R152s, ammonia, R142b. The calculations, which goal was to mainly the work unit, power, thermal efficiency and exergy efficiency of Clausius-Rankine and Kalina cycle, were performed for temperature of geothermal water in terms of 100-120˚C. Calculations results were the basis for the implementation of graphs and to formulate final conclusions. Calculations were made using EES program (Engineering Equation Solver).

1. Introduction

Increasing demand for energy and environmental protection requirements are forcing the use of renewable energy sources, which include geothermal energy. Geothermal resources are used to reduce energy demand through the use of direct heating of homes, factories, greenhouses or can be used in heat pumps or for electricity generation, which takes place in 24 countries for several years. Generation of electricity by the use of geothermal vapour is carried out in Europe on Iceland, in Italy, Turkey, Portugal. Increasing interest in systems, in which power generation uses geothermal water temperatures of 100-120°C [1]. These systems are power plants with Kalina cycle used in Iceland and Germany and with Organic Rankine cycle located in Alaska. Thus, considering the growing interest in these systems powered by geothermal water at a temperature of 100-120˚C, was performed thermodynamic cycles analysis of Kalina and ORC with the aim of obtaining and comparing the performance of their work as work unit, power, thermal and exergy efficiency.

2. ORC system description

For ORC operating with wet working fluid as a heat source is used a geothermal water at temperature in terms of 100-120˚C. In this solution of vapour power plant, geothermal water transfers heat to water network in geothermal heat exchanger and then is injected to the reservoir. At the outlet of the geothermal heat exchanger, the water network mass flow illustration not visible in this excerpt, in node A is split into two smaller streams. The first water mass flow illustration not visible in this excerpt is directed into overheater and the second water mass flow illustration not visible in this excerpt to the evaporator. After transferring heat to vaporization and overheating wet working fluid, both water mass flows are combined in node B, in main water mass flow, which is directed to preheater. After transferring heat to wet working fluid, water mass flow is directed to geothermal heat exchanger.

In ORC cycle with wet working fluid, vapour superheat of this fluid at the inlet to turbine is necessary in order to eliminate the risk of turbine blades erosion. Therefore, in the analysed vapour power plant has been used an additional heat exchanger - vapour overheater . In the considered model of ORC cycle, superheated vapour of wet working fluid flows from overheater to the vapour turbine driven generator and after isentropic expansion in the turbine to the condensing pressure, point 2s in Figure 1a, is condensed to a saturated state at the point T3. By using a circulation pump saturated liquid of working fluid is then directed into the preheater, hence to the evaporator and the resulting working fluid vapor back into the overheater. Thermodynamic transitions for wet working fluids are shown on temperature-specific entropy diagram T-s in Figure 1b and vapour power plant scheme is shown in Figure 1a.

a)

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b)

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Fig. 1 Scheme of vapour power plant with wet working fluid: a) scheme of power plant powered by geothermal energy, b) temperature-specific entropy diagram T-s of wet working fluid [2]

According to temperature-specific entropy T-s diagram of wet working fluid shown in Fig. 2a, in ORC are implemented the following thermodynamic transitions:

- 1-2s isentropic expansion of wet working fluid vapour in the turbine,
- 2s-3 isobaric heat removal in the condenser,
- 3-4s isentropic pumping of saturated liquid by pump
- 4s-1 isobaric heat supplying, including: 4s-5 isobaric fluid preheating, 5-6 evaporation of working fluid, 6-1 overheating of fluid saturated vapour

3. Kalina system description

The vapour power plant with Kalina cycle, which scheme is shown in Figure 2a is also powered by geothermal water at temperature in terms 100-120˚C. In geothermal heat exchanger network water mass flow is heated to temperature Tw1 and then is directed to evaporator of Kalina cycle and after transferring heat to working fluid ammonia-water mixture returns to geothermal heat exchanger. In Kalina cycle, working fluid after evaporation is directed to separator in order to separate the liquid phase from vapour of ammonia-water mixture. This process is necessary because ammonia has a lower boiling point and evaporates faster than water. Vapour at the inlet to turbine contains about 95% of ammonia [3]. From separator working fluid vapour flows to turbine and after isentropic expansion, in node A is combined with liquid phase of working mixture at temperature Tm5. From node A mixture vapour-liquid mass flow illustration not visible in this excerpt is directed to low-pressure recuperator in which transfers heat to mixture mass flow flowing in from condenser and circulation pump. From recuperator working fluid is directed to condenser. After heating in recuperator mixture is directed to high-pressure recuperator, in which receives heat from liquid phase of mixture flowing in from separator. Then, mixture flows again to evaporator. Thermodynamic transitions for ammonia-water mixture are shown on temperature-specific entropy diagram T-s in Figure 2b and scheme of vapour power plant with Kalina cycle is shown in Figure 2a.

a)

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b)

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Fig. 2 Scheme of vapour power plant with ammonia-water mixture: a) scheme of power plant powered by geothermal energy [3], b) temperature-specific entropy diagram T-s of ammonia-water mixture

In Kalina cycle are implemented the following thermodynamic transitions (Fig.3b):

- 3-4s isentropic expansion of ammonia-water mixture vapour in the turbine,
- 8-9 isobaric heat removal in the condenser,
- 9-10s isentropic pumping of saturated liquid by pump,
- 1-2 evaporation of ammonia-water mixture,
- 10s-11 and 11-1 regenerative heating of working fluid.

4. Thermodynamic analysis of ORC and Kalina cycle

Comparative analysis of Kalina with ammonia-water mixture and ORC with wet working fluid was made for geothermal water at a temperature in the range of 100-120˚C and it was assumed, that the temperature of the condensing working fluid is equal to the Tcon=30°C. For the calculation it is assumed that the evaporator in Kalina and in ORC is supplied with a constant mass flow of water equals illustration not visible in this excerpt= 20 kg/s. Also it was assumed, that there is no pressure drop in heat exchangers and pipes, heat loss to the environment in ORC and Kalina cycle components are neglected, the system reaches a steady state. For the analysis of ORC have been chosen five wet working fluids: acetone, R134a, ammonia and R142b, for which chosen thermodynamic properties are shown in Table 1. Analysis of Kalina cycle was done for three ammonia concentrations 70, 82, 90% in the mixture with water. Thermodynamic properties of three considered ammonia-water mixtures are also shown in Table 1. It should be emphasized, that ammonia-water mixture is also wet working fluid.

Table 1 Thermodynamic properties of wet working fluids and ammonia-water mixture

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- ORC system

In ORC specified amount of heat transferred to the evaporator has been calculated form the following relation:

illustration not visible in this excerpt (1)

The next step was to determine a value of working fluid mass flow in cycle, which was calculated from the equation:

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and the amount of heat transferred to the superheater was calculated by the formula:

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The equation (3) allows to determine a value of water mass flow needed to supply the superheater, it allowed the following equation:

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Then, the amount of heat supplied to the preheater was determined from the relation below:

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and a water mass flow feed preheater:

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Water specific enthalpy temperature at the outlet from node B was calculated from equation:

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And water specific enthalpy at the outlet from preheater was determined from the relation below:

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Water temperature Tw5 returning from the cycle to geothermal heat exchanger is determined for its specific enthalpy hw5 determined from equation (8).

Unit work of cycle:

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Cycle power:

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Circulation pump power:

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Thermal efficiency::

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in which illustration not visible in this excerpt is heat supplied to cycle and calculated from equation below:

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The exergy efficiency of ORC has been calculated in according equation in [4] as:

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where:

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- Kalina cycle

In Kalina cycle specified amount of heat transferred to the evaporator has been calculated form the following relation:

illustration not visible in this excerpt (15)

The next step was to determine a value of working fluid mass flow in cycle, which was calculated from the equation:

illustration not visible in this excerpt (16)

The vapour mass flow at the inlet to turbine was determine from equation below:

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and mixture liquid phase mass flow was calculated from formula:

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Unit work of cycle:

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Cycle power:

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Circulation pump power:

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Thermal efficiency:

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in which illustration not visible in this excerpt is heat supplied to cycle and calculated from equation below:

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The exergy efficiency of Kalina cycle has been calculated in according equation in [4] as:

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where:

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6. Results analysis

The comparative effectiveness analysis of Kalina and ORC system operating with wet working fluid allowed to obtain the basic parameters of their work, which is presented in the form of the following graphs. Figure 3 shows and compares the values of a unit work cycle for ORC and Kalina cycle. The highest values of unit work were obtained for ammonia and for ammonia-water mixture with 70% ammonia concentration. The values of unit work obtained for fluids, R134a and 142b are similar, but for fluid R134a the unit work is the lowest. It is easy to see, that work for acetone is much higher than unit work for R152a, R142b and R134a.

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Fig. 3 Work unit comparison of Kalina and ORC system

On Figure 4 have been compared the calculations results of power for ORC and Kalina cycle. The power of ORC is the highest at using R134a, R142b and ammonia and the lowest for acetone. Analyzing additionally the graph shown in Figure 5, it was found, that generated ORC power cycle is dependent on mass flow, evaporation and overheating enthalpy of working fluid (Figure 6, 7). It means that, the highest power cycle was obtained at using fluid R134a, which is characterized by the lowest value of vaporization and low value of preheating enthalpy (Fig. 6, 8) and overheating enthalpy and the largest mass flow. Summarizing, for the lowest vaporization enthalpy and large mass flow of working fluid achieved ORC power cycle is the highest. In Kalina system, power cycle obtained for three ammonia-water mixtures is comparable and lower than power for ORC system. Despite the fact, that for 70% ammonia concentration to get the largest value of vaporization enthalpy and mass flow, power cycle at using this mixture is close to power for 82 and 90% ammonia in the mixture. It is easy to see, that in comparison to wet working fluid of ORC system, vaporization enthalpy of ammonia-water mixture not decreases with increasing temperature evaporation (Fig. 6).

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Fig. 4 Power cycle comparison of Kalina and ORC system

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Fig. 5 Working fluid mass flow comparison of Kalina and ORC system

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Fig. 6 Vaporization enthalpy comparison of ammonia-water mixture and wet working fluids of ORC

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Fig. 7 Overheating enthalpy comparison of wet working fluids of ORC

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Fig. 8 Preheating enthalpy comparison of wet working fluids of ORC

In the case of ORC cycle thermal efficiency (Fig. 9), the largest values are obtained at using of ammonia and acetone, the lowest at using of R134a, R142b and R152a. It can be seen that Kalina cycle thermal efficiency is much lower in comparison with ORC system. The higher value of thermal efficiency (in considered temperature range of heat source) can be obtained for 82 and 90% ammonia concentration.

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Fig. 9 Thermal efficiency comparison of Kalina and ORC system

The exergy efficiency (Fig.10) of ORC system is the highest at using R142b and acetone and the lowest for ammonia. Exergy efficiency of Kalina cycle is comparable with results for ammonia. One should add, that for 82% ammonia concentration exergy efficiency of Kalina cycle is the highest.

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Fig. 10 Exergy efficiency comparison of Kalina and ORC system

7. Conclusions

The comparative effectiveness analysis of ORC and Kalina cycle revealed, that for geothermal water temperature in range 100-120˚C, higher value of work unit, power, thermal and exergy efficiency may be obtained for ORC system in comparison with Kalina cycle. Effectiveness analysis showed, that on power cycle influences vaporization, preheating, overheating enthalpy and working fluid mass flow and that thermal and exergy efficiency decreases with increasing power cycle. Among five examined wet working fluids power of ORC cycle is the largest at using R134a and this power is higher than for Kalina cycle.

Literature

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