J. Cent. South Univ. (2016) 23: 3160-3170

DOI: 10.1007/s11771-016-3382-8

Efficiency analysis of trilateral-cycle power systems for waste heat recovery-to-power generation

Habeeb A. AJIMOTOKAN

Department of Mechanical Engineering, University of Ilorin, Ilorin, Nigeria

Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: Numerous innovative heat recovery-to-power technologies have been resourcefully and technologically exploited to bridge the growing gap between energy needs and its sustainable and affordable supply. Among them, the proposed trilateral-cycle (TLC) power system exhibits high thermodynamic efficiency during heat recovery-to-power from low-to-medium temperature heat sources. The TLCs are proposed and analysed using n-pentane as working fluid for waste heat recovery-to-power generation from low-grade heat source to evaluate the thermodynamic efficiency of the cycles. Four different single stage TLC configurations with distinct working principles are modelled thermodynamically using engineering equation solver. Based on the thermodynamic framework, thermodynamic performance simulation and efficiency analysis of the cycles as well as the exergy efficiencies of the heating and condensing processes are carried out and compared in their efficiency. The results show that the simple TLC, recuperated TLC, reheat TLC and regenerative TLC operating at subcritical conditions with cycle high temperature of 473 K can attain thermal efficiencies of 21.97%, 23.91%, 22.07% and 22.9%, respectively. The recuperated TLC attains the highest thermodynamic efficiency at the cycle high temperature because of its lowest exergy destruction rates in the heat exchanger and condenser. The efficiency analysis carried out would assist in guiding thermodynamic process development and thermal integration of the proposed cycles.

Key words: trilateral cycle; waste heat recovery-to-power generation; thermodynamic performance simulation; efficiency analysis; process development and integration

1 Introduction

At present, heat recovery-to-power technologies have been resourcefully exploited for sustainable power generation; bridging the growing gap between energy needs and its sustainable and affordable supply [1], improving system efficiency potential [1-2] and reducing the unit costs of energy [1, 3]. Consequently, they decrease fossil fuels burning, and relax greenhouse gases emission [4] and thermal pollution of the environment [5]. Conventionally, the steam Rankine- cycle power system has been broadly utilised for heat recovery-to-power generation from thermal energy of external heat sources, such as combustion products [6]. However, due to the low conversion efficiency [7-9] or cost of the exploiting available work [1, 10], low-grade (low-to-medium temperature) thermal energy of numerous renewable energies and waste heat of industrial processes are ordinarily under-exploited. The consequence of these, is the renewed significance for innovative heat recovery-to-power technologies [1, 7, 11], for heat recovery-to-power generation from low-grade heat sources. Among them, the trilateral-cycle (TLC) power system, an advanced Rankine cycle for waste heat recovery-to-power applications [1, 12], is one of the most promising heat recovery-to-power cycles, which presents a great potential for development. This is due to its compact system configuration and high performance at relatively low compression work and low-to-moderate expander inlet temperature, which makes it very attractive particularly for remote or offshore applications where power-to-weight ratio of the power system is of significance [1, 7].

In contrast to the Rankine cycles, which use the conventional working fluid: the vapour steam, the TLC uses unconventional working fluids: hydrocarbons, refrigerants or siloxanes [13]. Primarily, the TLC has the same components as the Rankine-cycle power systems but unlike them, it does not evaporate the working fluid during the heating phase; instead expands it, from the saturated liquid condition, as a two-phase mixture [1, 7, 14]. The cycle attained better thermal match during heat exchange between the heat source and the working fluid due to the bypass of the isothermal boiling phase [1, 8, 12, 15], minimising irriversibilities and enhancing performance. In any power cycle, the working fluid performs a vital role in the processes of the cycle [16],and a careful selection that meets the cycle requirements is crucial for an efficient and safe operation [17]. Its applicability range must be within its thermo-physical properties and the chemical stability in a desirable range of temperature [16]. The economics of the cycle depend on the thermo-physical properties of the working fluid and the consequence of a wrong choice would be a grossly inefficient and costly power system [13, 18]. Moreover, the operating conditions of the thermodynamic cycle, its system efficiency, economic feasibility and environmental impact are influenced by the fluid selection [19-21].

There are several integration techniques for efficient usage of thermal energy like the pinch technology [22-24], thermo-economic and cost benefit analysis [25-27], exergy analysis [28-30] and exergo-economic analysis [31-32] that have been employed to analyse, evaluate and compare different power cycles in the recent times. Thermodynamic analysis in general and exergy analysis, in particular, is universally acceptable for the efficiency analysis of energy conversion systems and other processes or systems. This is because it is a systematic technique, which allows the localisation and measure of the degree of inefficiency, showing the utmost inefficient components of a process or system [1]. For heat recovery-to-power generation systems, the exergy-based efficiency analysis permits the determination of the maximum potential for power generation depending on the input thermal flows into the system. This maximum is achievable only when the utilisation of the input thermal flow into the processes ultimately brings it to complete thermodynamic equilibrium with the environment, while generating power.

Few studies and developmental efforts from the proof-of-concept towards a market-ready technology of the TLC power system have been carried out to demonstrate its feasibility for waste heat recovery- to-power generation [1, 7, 14, 33-35] onto the grid or for off-grid electricity supply. Despite the significant achievements in the development of the TLC technology, which are essentially in the areas of its applications [14, 36], working fluid selection [1, 37-38], two-phase expansion devices modelling and design [4, 39-40], thermodynamic performance simulation and optimisation [1, 7, 33], development of the simple TLC [35], process development and integration [1, 7] and thermo-economic assessment [41]; there are still gaps, in the development of the TLC technologies. Therefore, the need for continued research and development in order to guide thermodynamic process development and integration of this cycle for waste heat recovery-to-power generation using unconventional working fluid. Thus, this paper presents the efficiency analysis of simple TLC and its integrated power systems for low-grade waste heat recovery-to-power generation.

2 Trilateral-cycle systems

The simple trilateral-cycle (TLC) power system is studied for waste heat recovery-to-power generation from low-grade heat source. In order to improve the heat exchange performance and system efficiency, the TLC is integrated with a recuperator (internal heat exchanger), reheating and feed fluid-heating (regenerator). Thus, four distinct system configurations of the TLC, which include the simple TLC, recuperated TLC (TLC with recuperator), reheat TLC (TLC with reheating) and regenerative TLC (TLC with feed fluid-heating) are thermodynamically analysed. Previously established and implemented steady-state steady-flow models of the cycles are used to thermodynamically assess the performance metrics of the cycles and their predictions. The simulation models are established based on the corresponding thermodynamic processes of the cycles. The thermodynamic properties for temperature, pressure, enthalpy and entropy as well as the performance of the cycles during process simulations are computed at the subcritical operating conditions of the cycles. Energy and exergy analyses of the cycles are carried out using an expander inlet pressure of 3 MPa and expander isentropic efficiency of 90% at the cycle high temperature of 473 K and average condensing temperature of 309 K. The thermal and exergy efficiencies of all the cycles as well as the exergy efficiencies of the condensing and heating processes are computed and compared at the cycle high temperature and average condensing temperature.

2.1 Description of trilateral cycle systems

The schematic cycle configurations of the simple TLC and its integrated power systems are shown in Fig. 1, illustrating the distinct operating features of the various system configurations. Figure 1(a) shows the schematic cycle configuration of the simple TLC, which comprises four key components: feed pump, heater, expander and condenser.Similar to the Rankine cycles, the saturated working fluid is pressurised (state 1-2) to a higher pressure, afterward heated just to its saturated temperature (state 2-3) at constant pressure and is then injected into the expander (state 3-4); where shaft work is produced, driving a generator to produce power. Subsequently, the resulting vapour–liquid content is condensed (state 4-1) to start the new cycle. Figure 1(b) shows the schematic cycle configuration of the recuperated TLC, which comprises five key components: feed pump, heater, expander, recuperator and condenser. The latent heat extracted by the recuperator at the expander outlet is used to preheat the sub-cooled liquid at the pump outlet (state 2-3). Afterward, the fluid is heated to its saturated temperature (state 3-4) at constant pressure and is then injected into the expander (state 4-5), where shaft work is produced. Subsequently, the latent heat of the resulting vapour–liquid content is then bled (state 5) and condensed (state 6-1) to start the new cycle.

Fig. 1 Trilateral cycles, showing schematic cycle configurations of simple TLC (a), recuperated TLC (b), reheat TLC (c) and regenerative TLC (d)

Figure 1(c) shows the schematic cycle configuration of the reheat TLC, which comprises five key components: feed pump, heater, high-pressure (HP) expander, low-pressure (LP) expander and condenser. Unlike the simple TLC, the high-pressure fluid is injected into the HP expander (state 3-4); where it is first expanded. Afterwards, the fluid is then returned to the heater where it is reheated to its saturated temperature (state 4-5) and is expanded in the low LP expander (state 5-6), with the resulting vapour–liquid content then condensed (state 6-1) to start the new cycle. Figure 1(d) shows the schematic cycle configuration of the regenerative TLC, which comprises six key components: condensate pump, feed fluid-heater, feed pump, heater, expander and condenser. The working fluid is pressurized by the condensate pump (state 1-2), afterwards preheated in the feed fluid-heater (state 2-3) and is then pressurized to a high pressure with the feed pump (state 3-4). The high pressure fluid is heated (state 4-5) and injected into the expander (state 5-6); where shaft work is derived, with the resulting vapour–liquid content then bled (state 5a) for preheating the sub-cooled liquid at the condensate pump outlet (process 5a-7) and condensed (state 6-1) to start the new cycle.

The cycles’ temperature–entropy (T–s) diagrams of their thermodynamic processes are shown in Fig. 2. The simple TLC comprises four internally reversible processes. These include processes 1-2 and 3-4, which show the isentropic compression and expansion processes of the working fluid respectively during which work is either performed on or produced from the cycle; and processes 2-3 and 4-1, which show the constant pressure high-temperature heat addition and low- temperature heat rejection processes of the working fluid (Fig. 2(a)). While states 3 and 5 in Fig. 2(b) show the integration of the recuperator in the simple TLC; the reheating process is showed by states 4 and 5 (Fig. 2(c)) and states 5a and 7 (Fig. 2(d)) showed the regeneration process.

2.2 n-pentane

The working fluid adopted for the study is n-pentane because of its good thermo-physical properties (e.g. relatively high critical temperature and pressure), low-cost, and a boiling point slightly above room temperature. It displays a strong positive slope of vapour saturation curve on the T–s diagram and its saturated liquid expansion tends to dry out at temperatures slightly exceeding 453 K. More so, n-pentane is a dry fluid [20], whose thermo-physical properties are suitable for waste heat recovery-to-power generation.

Fig. 2 T–s diagrams of trilateral cycles, showing thermodynamic process of simple TLC (a), recuperated TLC (b), reheat TLC (c) and regenerative TLC (d) (A-B indicates huge thermal length)

3 System modelling

The steady-state steady-flow process simulation models of the described systems, corresponding to their thermodynamic processes are thermodynamically established and implemented [1, 7] employing engineering equation solver (EES) [42]. The thermodynamic performance simulation of models with model input parameters at the subcritical operating conditions are carried out and results obtained. The results of the thermodynamic performance simulations of the n-pentane based simple TLC, recuperated TLC, reheat TLC and regenerative TLC are computed, using the inlet pressure of 3 MPa and expander isentropic efficiency 90% at the cycle high temperature of 473 K and average condensing temperature of 309 K.

4 Energy and exergy analysis of trilateral cycles

The energy and exergy analyses for all the cycles are evaluated at the cycle high temperature of 473 K and average condensing temperature of 309 K. Energy efficiency which is dependent on the first-law of thermodynamics, is typically utilised to assess and compare power cycles. The first-law (energy or thermal) efficiency ηth is basically expressed as the ratio of the useful energy output to the total energy input. Mathematically, it is expressible for simple TLC system as

                       (1)

While the thermal efficiency of the recuperated TLC is expressed as

           (2)

The thermal efficiency of the reheat TLC is expressed as

              (3)

And the thermal efficiency of the regenerative TLC is expressed as

  (4)

In any thermodynamic cycle, total exergy input comprises the work input by the feed pump and as well the working fluid’s exergy input by thermal exergy transferred from the heat source; while net power output is the exergy output of the cycle. Therefore, the exergy efficiency of a power cycle η_II,cyc can be expressed as [43]

                               (5)

where denotes the working fluid’s exergy acquired by the heat exchange with the heat source, which is

         (6)

4.1 Exergy efficiency of heat exchange

As the heat exchange, i.e. heat addition to or heat rejection from the cycle takes place from a high- temperature heat source (hot stream) to a low- temperature heat sink (cold stream) irreversibly, exergy is destroyed. However, the rate of thermodynamic irreversibilities (exergy destruction) per unit thermal exergy transferred is substantially low, if the hot and cold streams are substantively higher than the ambient temperature [44]. This suggests that maximising the thermal match during heat exchange in the condensing

process is advantageous than in heating.

For any heat exchange processes, i.e. the heating and condensing processes, the change of exergy flow of the heat source is

            (7)

And the exergy change of the heat sink is

            (8)

Therefore, the heat exchange exergy efficiency η_II,hex is expressed as [44]

          (9)

The exergy efficiency analysis of the cycles is conducted to investigate the performance of the heating (i.e. the heat addition to the cycle from the heat source) and condensing (i.e. the heat rejection by the cycle to the heat sink) processes of the n-pentane in the cycles. Figures 3(a)-(d) and Figs. 4(a)-(d) are the T–s diagrams of the thermodynamic processes of the cycles, illustrating their thermal match of the heating and condensing processes at the top left corners of the Figures. Thermodynamic performance simulations of the cycles heating processes are carried out using heat transferred to the working fluid at state 2 to 3 (Figs. 3(a), (b) and (d)) and at state 2 to 3 alongside state 4 to 5 (Fig. 3(c)) by a pressurised heat source of 610.4 kJ/kg (0.5 MPa). The mass flow rate of the working fluid for each cycle (in kg/s) is heated to cycle high temperature of 473 K, assuming a fixed mass flow rate of heat source and its temperature that is constantly sufficient for heating the working fluid to 473 K. While those of the condensing processes are carried out using heat dissipated to the cooling fluid by the working fluid from saturated vapour–liquid condition to saturated liquid.

Fig. 3 Heating processes of n-pentane and their thermal match with heat source for simple TLC (a), recuperated TLC (b), reheat TLC (c) and regenerative TLC (d)

Fig. 4 Condensing processes of n-pentane and their thermal match with cooling fluid for simple TLC (a), recuperated TLC (b), reheat TLC (c) and regenerative TLC (d)

The exergy flow from the heat source at the heat exchanger inlet (point a) to the outlet (point b) (Figs. 3(a), (b) and (d)) of the cycles are

  (10)

And the exergy flow rate to the working fluid from subcooled liquid (state 2) to saturated liquid temperature (state 3) (Figs. 3(a), (b) and (d)) is similarly expressed as

(11)

where and denote the changes in energy flow per unit mass from point a to point b and from state 2 to state 3 respectively, is the heat source mass flow rate, h_a and h_b are the heat source specific enthalpies at points a and b respectively and h₂ and h₃ are the working fluid specific enthalpies at states 2 and 3 respectively. Hence, the exergy efficiency of the heating process η_II,hp of the working fluid for the cycles are computed to be 86.15%, 92.33% and 88.74% for the simple TLC, recuperated TLC and regenerative TLC respectively using Eq. (12):

                  (12)

While the exergy flow from the heat source at the heat exchanger inlet (point a) to the outlet (point b) coupled with reheating at point c to d (Fig. 4(c)) of the reheat TLC is expressed as

          (13)

And the exergy flow rate from the subcooled liquid (state 2) to saturated liquid temperature (state 3) coupled with the flow from the reheated resulting vapour–liquid (state 4) to saturated liquid temperature (state 5)(Fig. 4(c)) is similarly expressed as

                (14)

Hence, the exergy efficiency of the heating process η_II,hp of the working fluid for the reheat TLC is computed to be 87.45% using Eq. (15):

        (15)

While the mass flow rate of the cooling fluid is expressed based on the energy balance of the condenser at steady-state steady-flow as

                (16)

Hence, the cooling fluid mass flow rate is computed to be 27.77 kg/s using Eq. (16). The exergy flow of the cycles to the cooling fluid (water) at the condenser inlet (point e) to the outlet (point f)(Figs. 4(a)-(d)) is equally expressed as

(17)

And the exergy flow rate of working fluid from the vapour–liquid (state 4 or 6) to the cooling liquid (Figs. 4(a)-(d)) for the cycles is similarly expressed as

 (18)

Hence, the exergy efficiency of the condensing processes η_II,cp of the working fluid are computed to be 75.46%, 75.51%, 75.46% and 75.51% for the simple TLC, recuperated TLC, reheat TLC and regenerative TLC respectively using Eq. (19):

                 (19)

4.2 Exergy efficiencies of cycles

The exergy efficiency η_II of any power cycle is the ratio of the actual thermal efficiency η_th to the maximum possible (reversible) thermal efficiency η_th,rev under same conditions:

                                (20)

where η_th,rev denotes the reversible thermal efficiency (Carnot equivalent), which can be determined as follows:

                            (21)

where T_c and T_h denote the temperatures of heat sink (or cold stream) and heat source (or hot streams) respectively. Hence, the thermal efficiency η_th of the cycles are computed to be 21.97%, 23.91%, 22.07% and 22.9% for the simple TLC, recuperated TLC, reheat TLC and regenerative TLC, respectively, using Eqs. (1)-(4). Their corresponding exergy efficiency η_II are computed to be 63.34%, 68.96%, 63.65% and 66.05%, respectively, using Eq. (20).

5 Results and discussion

The thermodynamic performance simulation and efficiency analysis of the trilateral cycle (TLC) and its integrated power systems with the n-pentane as working fluid are investigated thermodynamically, from the resource and technology viewpoints. The thermodynamic performance simulations and detailed thermodynamic efficiency analysis of the simple TLC, recuperated TLC, reheat TLC and regenerative TLC, and their ancillary components at the subcritical operating conditions are conducted and results obtained. The computed thermodynamic properties for temperature, pressure, enthalpy and entropy of the various cycles’ thermodynamic states at the cycle high temperature of 473 K are listed in Table 1. Tables 2 and 3 present the comparison of the exergy efficiencies of the heating and condensing processes of working fluid in the cycles. It is observed that the exergy efficiencies of the heating processes are computed to be 86.15%, 93.46%, 87.05% and 88.74% respectively for the simple TLC, recuperated TLC, reheat TLC and regenerative TLC respectively. Their corresponding exergy efficiencies of the condensing processes are 75.46%, 75.51%, 75.51% and 75.46%.

A comparison of the thermodynamic analysis of the cycles is given in Fig. 5. Figures 5(a) and (b) show the thermal efficiencies and exergy efficiencies of the various cycles at the cycle high temperature of 473 K and average condensing temperature of 309 K.Figure 5(a) shows that the simple TLC attained a thermal efficiency of 21.97%, which is the lowest among the cycles, while the recuperated TLC attained 23.91%, which is the highest. Compared with the simple TLC, the thermal efficiency of the recuperated TLC attained an improvement of about 8.9% over the simple TLC. The regenerative TLC attained a thermal efficiency of 22.9%, which is higher than that of the reheat TLC and about a 4.2% improvement over the simple TLC. The reheat TLC attained a thermal efficiency of 22.07%, which is a marginal 0.5% improvement over the simple TLC.

Figure 5(b) shows that the simple TLC attained an exergy efficiency of 63.34%, which is the lowest among the cycles, while the recuperated TLC attained 68.96%, which is the highest. Compared with the simple TLC, the exergy efficiency of the recuperated TLC attained an improvement of about 8.9% over the simple TLC due to lower irreversibility rates in the heat exchanger and the condenser. The regenerative TLC attained an exergy efficiency of 66.05%, which is higher than that of the reheat TLC and an improvement of about 4.3% over the simple TLC. This is because there is no heat rejection (i.e. lower irreversibility rates) from about 40% of the working fluid in the condenser. The reheat TLC attained an exergy efficiency of 63.65%, which is a marginal 0.5% improvement over the simple TLC.

Table 1 Cycle thermodynamic properties

Table 2 Exergy efficiency of heating process of working fluid

Table 3 Exergy efficiency of condensing process of working fluid

Fig. 5 Comparison of thermodynamic performances of trilateral cycles

6 Conclusions

This study presents the thermodynamic efficiency analysis of the trilateral-cycle (TLC) power system as a solution for improved system efficiency. The thermal and exergy analyses of the simple TLC, recuperated TLC, reheat TLC and regenerative TLC operating at the subcritical conditions with low-grade heat at the cycle high temperature of 473 K for heat recovery-to-power generation are conducted and compared. The exergy analysis of the heat addition to and heat rejection from the power cycles to the heat reservoirs is computed.

1) The thermal and exergy efficiencies of the simple TLC are computed to be 21.97% and 63.34%, compared with 23.91% and 68.96% for the recuperated TLC, 22.07% and 63.65% for the regenerative TLC, and 22.9% and 6605% for the reheat TLC respectively.

2) The exergy efficiencies of heating and condensing processes of the simple TLC are 96.55% and 75.46%, compared with 93.46% and 75.51% for the recuperated TLC, 88.74% and 75.51% for the regenerative TLC, and 87.05% and 75.46% for the reheat TLC respectively.

3) These suggest that the integration of the recuperator, reheating and fluid-feed heating in the TLC enhanced heat exchange performance and as well as the system efficiency.

This exergy-based efficiency analysis carried out would guide the thermodynamic process development and integration of the TLC powers system. Moreover, it provides a valuable technique to evaluate the cycles, strictly from a thermodynamic perspective and their potential significance to the future power generation markets, as energy efficiency is a key part of the energy future.

Acknowledgements

The University of Ilorin, Nigeria financially supported this research through scholarship grant from Tertiary Education Trust Fund. The author acknowledges this support.

Nomenclature

1, 2, 3, 4

States of working fluid

a, b, c, d

Points of heat sources and sinks

Exergy flow rate (J·kg^-1)

H

Specific enthalpy (J·kg^-1)

Mass flow rate (kg·s^-1)

Heat transfer rate (J·kg^-1)

S

Specific entropy (J·kg^-1·K^-1)

T

Temperature (K)

Specific work (J·kg^-1)

Greek letters

η

Efficiency (%)

Δ

Rate of change

Superscripts

in

In/Inlet

out

Out/Outlet

Subscripts

o

Ambient state

exp

Expander

con

Condenser

c

Heat sink/Cold stream

cp

Condensate pump/condensing process

cyc

Cycle

fhx

Feed-fluid heat exchanger

fp

Feed pump

h

Heat source/Hot stream

hp

High pressure/heating process

hx

Heat exchanger

is

Isentropic

lp

Low pressure

recup

Recuperator

rev

Reversible

rh

Reheating

th

Thermal

wf

Working fluid

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(Edited by YANG Bing)

Received date: 2015-09-17; Accepted date: 2016-02-20

Corresponding author: Habeeb A. AJIMOTOKAN, PhD; Tel: +234-803-374-7444; E-mail: hajims@unilorin.edu.ng