The Value of Kalina Cycle in Engineering

The Value of Kalina Cycle in Engineering

E. H. Betelmal, Mohamed A. Naas

Department of Mechanical Engineering Tripoli University, Faculty of engineering Tripoli-Libya

DOI: https://doi.org/10.51244/IJRSI.2024.1109084

Received: 03 September 2024; Accepted: 12 September 2024; Published: 15 October 2024

ABSTRACT

Environmental issues and lack of energy resources have led to the utilization of industrial waste heat in thermodynamic applications to improve the performance of thermodynamic cycles and keep pace with climate change. This work examines the modified thermodynamic Kalina cycle to compare different cycle efficiencies. We then evolve the exergy balance equation for it to apply to each cycle component. Furthermore, we discuss future technologies for the modified Kalina cycle using a new working fluid.

INTRODUCTION

The continued pursuit of higher thermal efficiencies has led to modifications to the basic thermodynamic cycle. An essential aspect of thermodynamic applications is the analysis of power generation cycles. Exergy analysis is a powerful method for optimizing thermodynamic processes. Steam is the most used working fluid in vapor power cycles due to its many advantages, including low cost, availability, and high enthalpy of vaporization. This study is devoted to discussing steam and gas power plants, exploring steam power plants with renewable energy applications and industrial waste heat utilization—both of which are current trends in the energy sector. Regardless of the sources used to supply heat to the steam, the steam undergoes the same basic cycle. Therefore, all cycle processes are analyzed in the same manner.

LITERATURE REVIEW

The Kalina cycle is a result of developments made to the Rankine cycle. Dr. Alexander Kalina made advancements to the Rankine cycle in the late 1970s and early 1980s. The Kalina cycle is an unconventional thermodynamic cycle used to convert thermal energy from relatively low-temperature heat sources into mechanical power. The Kalina cycle is a modified closed Rankine cycle that includes a separator, evaporator, absorber, and a reducing valve, as shown in Figure 1. The Kalina cycle uses two working fluids with different boiling points, unlike the Rankine cycle, which uses a single pure substance. Many studies have focused on optimizing and analyzing the parameters of the Kalina cycle system and its working fluid. This cycle differs from conventional Rankine steam cycles and has high heat recovery due to the close temperature match between the cycle’s heat absorption and the heat source, as well as a high recuperation level [1]. The components of a Kalina power plant consist of the same devices (turbine, pumps, valves, etc.) as a conventional steam power plant. The molecular weight of the ammonia–water working fluid mixture slightly differs from that of pure water. A significant difference between the two cycles is that, in the Rankine cycle, heat addition and rejection occur at uniform temperatures during phase changes, whereas in the Kalina cycle, heat addition and rejection occur at varying temperatures, even during phase changes, because the working fluid is a mixture. The Kalina cycle has a lower average heat rejection temperature and a higher average heat addition temperature, leading to higher thermal efficiency. The Kalina cycle has demonstrated greater efficiency compared to the conventional Rankine cycle and shows potential for generating additional power from medium and low-temperature sources, as well as waste heat recovery systems. The advancements in the Kalina cycle and its potential to address future global electricity needs, driven by the rising demand for electricity as the population rises, have been  explored [2]. Recent studies on the Kalina cycle have focused on improving its efficiency, particularly through innovations in system design and working fluid management.  The performance enhancement of the Kalina cycle System  by replacing the traditional throttle valve with a single-screw expander was explored. This modification significantly reduces energy losses associated with throttling in the ammonia-lean solution, resulting in improved overall system performance. Two redesigned Kalina cycle systems were proposed, where the single-screw expander was integrated at different points in the cycle, and both showed improved thermodynamic performance compared to the original design [3]. Another study examined the impact of turbine staging in the Kalina cycle, with a focus on optimizing critical parameters like ammonia concentration and turbine inlet pressure. These factors were shown to substantially improve efficiency, particularly in high-temperature applications​ [4]. The Kalina cycle is recognized as one of the most thermodynamically efficient power cycle technologies in the world.

The thermodynamic cycle consists of five steps:

1. Compression in the pump.
2. Heat addition in the heat exchanger (boiler).
3. Expansion in the turbine.
4. Recuperation in the recuperators.
5. Heat rejection in the condenser.

Figure 1 Kalina Cycle and T-s Diagram

Many modifications can be applied to the Kalina cycle, depending on the required application. Another version of the Kalina cycle is illustrated in Figure 2. The ammonia–water working fluid mixture enters the heat recovery component before entering the generator at high pressure and temperature as concentrated ammonia vapor. The concentrated vapor then enters the superheater to further increase its temperature. Subsequently, the vapor exits the superheater and passes through the turbine, where it expands, reducing pressure and temperature, thereby converting thermal energy into mechanical energy. After leaving the turbine, the vapor passes through the absorber, where the weak solution mixes with the strong solution at a low temperature. At this stage, the concentrated solution is formed at a low temperature, and then it is pumped once more into the generator via the heat recovery unit, where the cycle.

Figure 2. Basic Configuration of a Kalina Cycle

ENERGY ANALYSIS OF KALINA CYCLE

The thermodynamic analysis of the Kalina cycle components is straightforward since mass and energy are conserved. All the above components are assumed to be in steady-state flow; therefore, the energy equation is applicable with the assumption that the kinetic and potential energy changes are negligible [5].

The equations are reduced to:

\[
\sum m_{\text{in}} = \sum m_{\text{out}} \tag{1}
\]

\[
\sum Q + \sum ( \dot{m}_{\text{in}} h_{\text{in}} ) = \sum W + \sum ( \dot{m}_{\text{out}} h_{\text{out}} ) \tag{2}
\]

Steam Generator

\[
Q_{\text{SG}} = \dot{m}_{\text{SG,in}} ( h_{\text{SG,out}} – h_{\text{SG,in}} ) \tag{3}
\]

Separator

Mass balance of the ammonia in the separator is written as follows.
\[
\dot{m}_{\text{s,in}} x_{\text{s,in}} = \dot{m}_{\text{s,out1}} x_{\text{s,out1}} + \dot{m}_{\text{s,out2}} x_{\text{s,out2}} \tag{4}
\]

\[
\dot{m}_{\text{s,in}} = \dot{m}_{\text{s,out1}} + \dot{m}_{\text{s,out2}} \tag{5}
\]

\[
\dot{m}_{\text{s,in}} h_{\text{s,in}} = \dot{m}_{\text{s,out1}} h_{\text{s,out1}} + \dot{m}_{\text{s,out2}} h_{\text{s,out2}} \tag{6}
\]

Turbine

\[
\dot{W}_t = \dot{m}_{\text{t,in}} ( h_{\text{t,out}} – h_{\text{t,in}} ) \tag{7}
\]

Absorber

\[
Q_{\text{abs}} = m_{\text{abs,in}} ( h_{\text{abs,in}} – h_{\text{abs,out}} ) \tag{8}
\]

Recuperator

\[
\dot{m}_{\text{R1,in}} ( h_{\text{1,out}} – h_{\text{1,in}} )_{\text{R}} = \dot{m}_{\text{2,in}} ( h_{\text{2,out}} – h_{\text{2,in}} )_{\text{R}} \tag{9}
\]

Valve

\[
\dot{m}_{\text{V,in}} h_{\text{V,in}} = \dot{m}_{\text{V,out}} h_{\text{V,out}} \tag{10}
\]

Condenser

\[
Q_c = m_{\text{c,in}} ( h_{\text{c,in}} – h_{\text{c,out}} ) \tag{11}
\]

Pump

\[
W_p = v_{\text{p,in}} ( P_{\text{t,out}} – P_{\text{t,in}} ) \tag{12}
\]

\[
\eta = \frac{W_t – W_p}{Q_{\text{in}}} \tag{13}
\]

EXERGY ANALYSIS OF KALINA CYCLE

The exergy analysis of the Kalina cycle plays a critical role in evaluating and improving the efficiency of energy conversion systems. Unlike traditional energy analysis, which only considers the amount of energy in a system, exergy analysis focuses on the quality and usability of that energy, offering deeper insights into inefficiencies. The Kalina cycle, which uses a mixture of ammonia and water as the working fluid, is an innovative thermodynamic cycle recognized for its ability to convert low-temperature heat sources into mechanical power more efficiently than conventional cycles like the Rankine cycle. Exergy analysis is particularly valuable for understanding the Kalina cycle’s performance and identifying potential areas for optimization. Exergy analysis is applied to each process to calculate the maximum available work input to the cycle and to determine how much energy is lost. As a thermodynamic cycle, the Kalina cycle involves complex interactions between heat, work, and mass flow rate, making exergy analysis especially important.

\[
S_{\text{gen}} = \frac{dS}{dt} + \sum S_{\text{out}} – \sum S_{\text{in}} – \sum \frac{Q_i}{T_i} \geq 0 \tag{14}
\]

Where:
\[
S_{\text{gen}} \text{ represents the generated entropy in the control volume,} \\
\frac{dS}{dt} \text{ the accumulation of entropy inside the control volume,} \\
\sum S_{\text{out}} \text{ and } \sum S_{\text{in}} \text{ the flow of entropy in and out of the control volume respectively,} \\
\sum \frac{Q_i}{T_i} \text{ the entropy generation associated with heat transfer.}
\]

\[
I = T_0 S_{\text{gen}} \tag{15}
\]

Exergy is defined as the maximum reversible work achievable when a system is in equilibrium with the environment. The total exergy of a system, when it is at rest with the surroundings, is equal to the sum of physical exergy and chemical exergy; magnetic, electric, nuclear, and surface tension effects are not included [6].

\[
\phi = \phi_{\text{Ph}} + \phi_{\text{Ch}} \tag{16}
\]

The physical exergy component is calculated using the following relation:

\[
\phi_{\text{Ph}} = \dot{m} \left( (h – h_0) – T_0 (s – s_0) \right) \tag{17}
\]

Chemical exergy represents the maximum work obtainable when the system reacts with reference substances present in the environment. The chemical exergy of the flow is calculated using the following equation:

\[
\phi_{\text{Ch}} = \dot{m}_i \left( \frac{\overline{\phi}_{\text{Ch,NH}_3}^0}{M_{\text{NH}_3}} Y + \frac{\overline{\phi}_{\text{Ch,H}_2 O}^0}{M_{\text{H}_2 O}} (1 – Y) \right) \tag{18}
\]

Where:
\[
\overline{\phi}_{\text{Ch,NH}_3}^0 \text{ and } \overline{\phi}_{\text{Ch,H}_2 O}^0 \text{ are the standard molar specific chemical exergies of ammonia and water respectively,} \\
Y \text{ is the mass fraction of ammonia.}
\]

At a known temperature of \( T \), the \( \phi_Q \) can be calculated from:

\[
\phi_Q = \sum \left( 1 – \frac{T_0}{T} \right) Q \tag{19}
\]

The exergy balance equation is applied to each component of the Kalina cycle, including the turbine, pumps, separator, generator, absorber, and condenser. The following equations quantify the exergy entering, leaving, and being destroyed within each system component.

Exergy balance in the turbine:

\[
\Delta \phi_t = \sum_{\text{in}} \phi_i \dot{m}_{\text{in}} – \sum_{\text{exit}} \phi_e \dot{m}_{\text{out}} = W_{\text{act}} \tag{20}
\]

\[
I_{\text{Turbine}} = T_0 \dot{m}_{\text{in}} (s_{\text{in}} – s_{\text{out}}) \tag{21}
\]

Exergy balance in a pump:

\[
\Delta \phi_{\text{Pump}} = \sum_{\text{in}} \phi_{\text{in}} \dot{m}_{\text{in}} – \sum_{\text{out}} \phi_{\text{out}} \dot{m}_{\text{out}} – W_{\text{in}} \tag{22}
\]

\[
I_{\text{pump}} = T_0 \dot{m}_{\text{in}} (s_{\text{out}} – s_{\text{in}}) \tag{23}
\]

Exergy balance in Separator:

\[
\dot{m}_{\text{in}} = \dot{m}_{1,\text{out}} + \dot{m}_{2,\text{out}} \tag{24}
\]

\[
\Delta \phi_{\text{Sep}} = \phi_{\text{in}} \dot{m}_{\text{in}} – (\phi_{\text{out}} \dot{m}_{\text{out}})_1 – (\phi_{\text{out}} \dot{m}_{\text{out}})_2 \tag{25}
\]

\[
I_{\text{Sep}} = T_0 \left( (m_1 s_1 + m_2 s_2)_{\text{out}} – m_{\text{in}} s_{\text{in}} \right) \tag{26}
\]

Exergy balance in Steam Generator:

\[
\Delta \phi_{\text{SG}} = \sum_{\text{in}} \phi_{\text{in}} \dot{m}_{\text{in}} – \sum_{\text{out}} \phi_{\text{out}} \dot{m}_{\text{out}} \tag{27}
\]

\[
I_{\text{SG}} = T_0 \dot{m}_{\text{in}} (s_{\text{in}} – s_{\text{out}}) \tag{28}
\]

Exergy balance in Absorber:

\[
Q_{\text{abs}} = m_{\text{abs,in}} (\phi_{\text{abs,in}} – \phi_{\text{abs,out}}) \tag{29}
\]

\[
I_{\text{abs}} = T_0 \dot{m}_{\text{in}} (s_{\text{in}} – s_{\text{out}}) – m_{\text{wa}} c_p \ln \left( \frac{T_0}{T_{\text{s,abs}}} \right) \tag{30}
\]

Exergy balance in Condenser:

\[
\Delta \phi_{\text{Cond}} = \sum_{\text{in}} \phi_{\text{in}} \dot{m}_{\text{in}} – \sum_{\text{out}} \phi_{\text{out}} \dot{m}_{\text{out}} \tag{31}
\]

\[
I_{\text{Cond}} = T_0 \dot{m}_{\text{in}} (s_{\text{in}} – s_{\text{out}}) – m_{\text{wa}} c_p \ln \left( \frac{T_0}{T_{\text{s,Cond}}} \right) \tag{32}
\]

The overall exergy efficiency of the Kalina cycle is determined by comparing the useful work output to the total exergy input. This metric provides a clearer picture of the cycle’s performance compared to traditional energy efficiency measures. Exergy efficiency is usually lower than first-law efficiency because it accounts for the quality of energy, not just the quantity. The second-law efficiency can be defined as the ratio of exergy output to exergy input. The exergy output depends on the degree of irreversibility within the cycle. Therefore:

\[
\eta_{\text{II}} = \frac{\text{useful exergy out}}{\text{exergy input}} = 1 – \frac{\text{exergy destruction}}{\text{exergy input}} \tag{33}
\]

KALINA CYCLE WORKING FLUID

The Kalina cycle is a new cycle in heat recovery and power generation that uses an ammonia–water mixture as a working fluid. The unique feature of the Kalina cycle lies in its working fluid. The working fluid is composed of two different substances with different boiling points. Since a mixture of two fluids boils over a range of temperatures, the ratio of the fluids can be varied in other parts of the system. This overall effect increases the thermodynamic efficiency of the process. The Kalina cycle has been studied for various applications involving low-temperature heat sources. Furthermore, there are different Kalina cycle families, each known by its unique name. For example, the KCS5 cycle is applied to direct fuel-fired power plants, while the KCS6 type applies to gas turbines in combined cycles. Other Kalina cycle types, such as KCS11 and KCS34, are designed for utilizing low-temperature heat sources. Although the ammonia–water working pair has zero ozone depletion potential and low global warming potential, special safety procedures should be considered due to its toxicity [7]. Therefore, there is a need to explore other working pairs to replace the ammonia–water combination in the Kalina cycle. Alternative working fluids commonly used in refrigeration and air conditioning, such as refrigerant mixtures including CFCs (chlorofluorocarbons), HCFCs (hydrochlorofluorocarbons), HFCs (hydrofluorocarbons), and commercial products like R407C, CO2–hydrocarbon blends, CO2–dimethyl ether (DME), and R32–hydrocarbon blends, could be considered. These refrigerants are chosen for their favorable ecological characteristics, such as zero ozone depletion, low global warming potential, and non-toxicity. A mixture of hydrocarbon refrigerants with CO2 reduces flammability and allows better control of carbon dioxide levels, depending on the concentration of the mixture. R32 is a good alternative working fluid because it is energy-efficient due to its relatively high pressure and density, making R32 mixtures highly effective. Zeotropic mixtures of HFCs, such as R22–R134a and R32–R134a, could also be used in the Kalina cycle. The principle of forming zeotropic mixtures is to combine fluids with different boiling points so that the evaporation or condensation process occurs over a temperature range.

RENEWABLE ENERGY

Kalina Cycle with Heat Recovery Energy

Dr. Alexander Kalina proposed a new basic cycle in 1984 to be used as a bottoming cycle, utilizing the waste heat from the exhausts of gas turbines as a heat source [8], as shown in Figure 3. This cycle arrangement is called the Kalina cycle system 1 (KCS 1). The working fluid in this cycle is an ammonia–water mixture. The concentration of ammonia is not steady and varies throughout the process, and any modification of the cycle arrangement depends on the application. For example, KCS 2 can be used for low-temperature geothermal applications, and KCS 5 is suitable for direct fuel-fired plants.

Figure 3. Simple Schematic Diagram of The Combined Brayton-Kalina Cycle.

Kalina Cycle Waste Heat Recovery

Using the Kalina cycle to recover industrial waste heat has a high energy conversion efficiency because the ammonia–water mixture working fluid evaporates and condenses at varying temperatures, leading to a suitable temperature match with the heat source and cooling water in the vapor generator and condenser, which reduces irreversible heat loss in the heat exchangers. Figure 4 illustrates an example of the Kalina cycle recovering waste heat [9].

Figure 4. A Kalina Cycle Recovering Waste Heat Recovery

Geothermal Kalina Cycle

Geothermal energy is considered clean and renewable, and geothermal energy can power the Kalina cycle, as shown in figure 5. The closed Kalina cycle uses low-temperature steam, water, or brine from the geothermal source to heat the working fluid and uses cooling water or air to cool the working fluid down in closed heat exchangers. Because the Kalina cycle’s working fluid consists of binary fluids and has different boiling temperatures, the solution boils and condenses over a range of temperatures, giving more heat extracted from the geothermal fluid than with a pure working fluid. The working fluid’s boiling temperatures depend on the heat input temperature, which is adjusted by modifying the ratio between the working fluid components; as a result, the average temperature of the working fluid in the heating process is higher, and the cooling process’s average temperature is lower, thus giving the cycle a higher efficiency. Also to increase efficiency, a more complex design with additional separators and recuperators is needed.

Figure 5. Kalina Cycle Geothermal Power Plant

Solar Kalina Cycle

The solar Kalina cycle is promising, a feasible way to generate power from low- and medium-temperature solar heat. The solar Kalina cycle is driven by solar heat of approximately 100–500 °C. Figure 6 shows the schematic diagram of the solar-driven Kalina cycle. The system contains three subsystems: a solar collector with a variable aperture area, the oil–ammonia exchanger and the Kalina cycle. The heat collected by the heat transfer fluid is exchanged with the ammonia–water mixture in the oil–ammonia exchanger [10].

Figure 6 Solar Kalina Cycle

CONCLUSION

Kalina Cycle Advantages

1. Generates more power than conventional steam power plants by 10% to 50%.
2. Has lower initial capital costs since it has a smaller heat exchanger and no heat transfer oil loop (compared to ORC systems)
3. Requires less supervision and results in lower plant loads.
4. Uses standard, easily available, and to a large degree proven plant components.
5. Superior heat transfer which decreases demand for cooling water and infrastructure.
6. Has the least maintenance downtime.

RECOMMENDATION 

This work would allow a deeper understanding of how the Kalina cycle can be improved by integrating it with other thermodynamic cycles and how it can be applied in real power plants, particularly in waste heat recovery, geothermal energy, and other low-temperature power generation systems. Practical considerations, such as economic study and technical challenges, should be evaluated separately for implementation of this technology in both existing and future power plants.

Moreover, future studies could improve the Kalina cycle’s adaptability to various industrial applications, enhance the integration of renewable energy sources into the cycle, or further optimize its performance under different operational conditions

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