- Email: [email protected]
Thermal systems and thermal efficiency index deficiency - A thermodynamic case study of regenerative and CSP plants
Case Studies in Thermal Engineering 14 (2019) 100425
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering journal homepage: www.elsevier.com/locate/csite
Thermal systems and thermal efficiency index deficiency - A thermodynamic case study of regenerative and CSP plants
T
Paul N. Nwosua,b,∗ a b
School of Mechanical Engineering Science, 301 Xuefu Road, Zhenjiang, Jiangsu Province, China Formerly of the Department of Mechanical Engineering Science, University of Johannesburg, Auckland Park, PO 2322, South Africa
A R T IC LE I N F O
ABS TRA CT
Keywords: CSP Regenerative Rankine Optimization PQR Thermal efficiency Thermodynamics
As the determination of the power generation returns for a thermal plant system in conditions of optimality is of profitable, economic concern to a plant operator (that is, the income generated by the plant in converting a kilojoule (KJ) of fuel into useful power), the current study investigates the influence of thermodynamic variables on thermal efficiency, power production and prediction in regenerative and concentrated solar power (CSP) plants with a novel optimization technique. The thermal efficiency index shows significant variances in profiling the optimal power production state; however, when the index is combined with the PQR, the optimal value of the objective variable is construedly obtained. Beyond the optimal value of the objective variable, the operating upstream pressure, the difference in power generation output is obvious with potential losses. As a consequence, optimizing the process operations can lead to significant economic savings using the procedure.
1. Introduction This study investigates the thermodynamic performance of regenerative and concentrated solar power (CSP) rankine plants. Recently, the sustainability and profitability of a power plant operations are confronted mainly by rising fuel costs and constraints on permissible carbon footprint on the subject of climate change; wherefore some thermal plants would be subject to periodically suboptimal operating conditions, which could result to increased operational expenses. There are a number of investigations and studies into power plant modelling and optimization. Ho et al. [1] studied the power plants based on the organic flash cycle (OFC) and other advanced vapor cycles for intermediate and high temperature waste heat reclamation and solar thermal applications and concluded that aromatic hydrocarbons are better suited as working fluids in organic rankine cycle (ORC) plants, due to their relatively high-power output and potentially less complex turbine designs. Badr et [2] conducted a simulation study on the performance of Rankine cycle power plants which employed steam as the working fluid and developed a BASIC program to facilitate the optimal design condition of the plants. Kumar and Kasana [3] conducted a study into a rankine plant, and concluded that the efficiency can be improved by using an intermediate reheat cycle. Chen et al. [4] reviewed the Rankine and supercritical Rankine cycles for the conversion of low-grade heat into electrical power and concluded that thermodynamic and physical properties, stability, environmental impacts, safety, compatibility, availability and cost are important considerations for selecting a working fluid. Geete and Khandwawala [5] obtained correction curves for power output on account of conflicts between the actual and predicted output for a 120 MW thermal power plant. Also, Jamal [6] conducted a comparative study into working fluids of ORCs. It was determined that the temperature profile of the evaporator and the condenser could affect the ∗
School of Mechanical Engineering Science, 301 Xuefu Road, Zhenjiang, Jiangsu Province, China. E-mail address: [email protected].
https://doi.org/10.1016/j.csite.2019.100425 Received 3 July 2018; Received in revised form 26 February 2019; Accepted 4 March 2019 Available online 28 March 2019 2214-157X/ © 2019 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Nomenclature Q h Pt W E s P T υ E Sgen m m˙ ΔEsystem Δkes
cond dest p t out source sink e in i reg sup.
Heat (KJ/kg) Enthalpy (KJ/kg) Turbine (Generated) Power (W) Work (KJ/kg) Power (W) Entropy (KJ/kg) Pressure (Pa) Temperature (W) Specific volume (m3/kg) Power (W) Entropy generation (KJ/kgK) Mass fraction Mass flow rate (Kg/s) Energy difference (KJ/kg) Potential Energy difference (KJ/Kg)
Symbols 0 η b,in b,out
Subscripts boil
condenser destroyed pump turbine outlet pump pump Temperature (W) in Intermediate regenerator superheater
destroyed Efficiency system boundary, in system boundary, out
boiler
exergy losses and the best energy utilization. Wang et al. [7] studied an ORC system using low grade heat source and suggested a ratio of net power output to total heat transfer area as the performance evaluation criterion. Roy and Misra [8] performed a parametric optimization and performance analysis of a regenerative ORC using R-123 for waste heat recovery; and developed a computer program to optimize and compare the system under different heat source conditions. Geete and Khandwawala [9] examined a power plant system thermodynamically with the combined effect of constant inlet pressure (127.06 Bar) and condenser back pressures. The correction curves for the combined effect of constant inlet pressure and different condenser back pressures were obtained. Geete and Khandwawala [10] analyzed the effect pressure drop on the performance of a coal-fired thermal plant. The study showed that if the line pressure drop varies, the power output and the heat rate vary also. Other studies on power plant systems in line with the prospect and performance are given in Refs. [11–13]. In this analysis, the margin of potentially accruable returns in the operation of a power plant is determined with respect to the optimal power production and prediction based on the power-quantity ratio (PQR). The power-quantity ratio (PQR) is defined and compared with the thermal efficiency index. The optimization procedure also investigates the optimal thermodynamic performance
Fig. 1a. Schematic and process diagram of a regenerative plant. 2
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
of the plants with respect to an objective variable, indicating the profile of heat and work interaction, as well as the point of optimal power production. 2. Description The main components of a regenerative plant include the following: boiler/vaporizer, superheater, turbine, condenser, and regenerator. While a CSP plant comprises all of the above, in addition to feed-water heaters, purpose-built regenerators, solar field and a thermal storage facility. The regenerative Rankine plant can be organic or inorganic [14]. But, a CSP plant works with a renewable (solar) auxiliary heat source. The CSP plant studied is based on Siemens technology with a power output of approximately 7 MW and turbine inlet parameters of 130 bar and 530C; many of such plants are used around the world, [15]. The schematic diagrams of the regenerative and the CSP Rankine plants are shown in Fig. 1a and b, respectively. 3. Regenerative rankine plant - theory The thermodynamic models for the regenerative plant are derived from energy relation and mass balances [11]: . Q ≅ W ≅ Δke ≅ Δpe
. . . Ein − Eout = ΔEsystem
(1) (2)
.
⇒
∑ min hin= ∑ mout hout
(3)
In terms of work flow quantities, the total work done by the turbine(s) ∑ Wt is given by
∑ Wt = ∑ min hin
(4)
where min is the steam mass flow rate and hin is the enthalpy. Consequently, the amount of work done by the turbine can be expressed by
Wt = (h5 − h6) = v (P5 − P6)
(5)
Thermal energy (heat input) into the recuperator, vaporizer and superheater with heat rejection in the condenser can be
Fig. 1b. Schematic and process diagram of a typical CSP plant with multi-stage operation. 3
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
determined from:
Q˙ recup = h7 − h6
(6)
Q˙ vap = h4 − h3
(7)
Q˙ sup = h5 − h4
(8)
Q˙ cond = h7 − h1
(9)
Thus for the thermal efficiency, the following is defined:
ηth =
Wt − Wp1 Wnet = Q˙ boil + Q˙ sup ∑ Q˙ i
(10)
The power generated can be calculated from
Pgen = m˙ (h7 − h6)
(11)
4. CSP plant - theory Recalling the energy balance relation (eqn. (1)) for the CSP plant the relation is rendered differently:
∑ Wt = ∑ mi hi
(12)
Considering the plant components, the following is obtained
∑ Wt = (h7 − h8) + (h9 − h10) + (1 − m1)(h10 − h11) + (1 − m1 − m2)(h11−h12)
(13)
Based on the principle of conservation of energy and mass, the open-feed-water heaters (OFWHs), closed-feed-water heaters (CFHWs) and the thermal points between the condenser and pump1 are taken to be points where thermal equilibrium exits, such that for the OFWHs, the following is obtained
(1 − m1) h3 + m1 h10 = h4
(14)
And for the CFWHs,
(1 − m1) h2 + m2 h11 = (1 − m1) h3
(15)
The energy balance relation for the nodal junction between the condenser and pump1 can be written as
(1 − m1 − m2) h14 + m2 h13 = (1 − m1) h1
(16)
The mathematical models for the mass fractions m1 and m2 can be evaluated by solving the above equations. Work done by pumps 1 and 2, respectively, is obtained from
Wp1 = (1 − m1)(h1 − h2) = (1 − m1) υ (P1 − P2)
(17)
Wp2 (h5 − h4 ) = υ (P5 − P4 )
(18)
and
The heat transfer relations for the following components (the boiler/vaporizer, the superheater and the reheater) are
Q˙ boil = (h6 − h5)
(19)
Q˙ sup = (h7 − h6)
(20)
Q˙ reh = (h9 − h8)
(21)
also, the irreversible energy losses in the condenser could be determined from
Q˙ cond = (1 − m1 − m2)(h12 − h14 ) (22) . . . . where Qboil., Qsup , Qreh. and Qcond.. denote the heat transfer rate of the boiler/vaporizer, superheater, regenerator and condenser. The thermal efficiency of the plant can be determined from: ηth =
∑ Wt − (Wp1 − Wp2) Wnet = Q˙ boil + Q˙ vap + Q˙ reh ∑ Q˙ i
(23)
Given adiabatic conditions in the components thereof save the condenser and the boiler, the power generation potential is calculated from
Pgen = m˙ t [(h7 − h8) + (h9 − h10) + (1 − m1)(h10 − h11) + (1 − m1 − m2)(h11 −h12)] 4
(24)
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Where m1, m2 and (1 − m1 − m2) are the steam fractions of the high-pressure (HP) and low-pressure (LP) turbine flow channels and m⋅ in is the flow rate of the working fluid. In comparison with equation (11), equation (24) contains the mass fractions with the enthalpy variables for the complex multi-stage plant. 5. Optimization The overriding objective of the optimization procedure, concisely, is to operate the plant at the maximum thermodynamic and techno-economic potential. Writing the following variables:
Qs, cyc =
∑ Qi ∑H
(25)
Ws, cyc =
∑ Wi ∑H
(26)
in which
∑ Hi = ∑ Qi + ∑ Wi
(27)
The heat input and the thermodynamic quantity ratio (TQR) index are respectively determined from:
Qs, cyc =
∑ Qi, s ∑H
(28)
TQR cyc = Qs, cyc + Ws, cyc
(29)
and
TQR = Qs + Ws, cyc
(30)
where ∑ Qi, s is the total heat input into the plant (excluding the heat rejection in the condenser), ∑ Qi is the total (cycle) heat input and output, ∑ Wi is the total (cycle) work input and output, Ws, cyc is the proportion of the total (cycle) work input and output, Qs, cyc is the proportion of the total (cycle) heat input and output, and Qs is the proportion of heat input into the plant. The power-energy quantity ratio (PQR) gives an indication of the optimal power production potential
Pgen . Ws ⎤ PQR = ⎡ ⎢ ⎣ Qs ⎥ ⎦
(32)
Relatively, a judicious decision to adjust the operation of a plant is typically based on the nominal load. This consideration is implicitly related to the amount of energy converted to useful power. A simple relation, which can lessen decision times can be of considerable economic, technical, operational benefit in real-time conditions. Wherefore, the determination of the power generation returns for a thermal plant system in conditions of optimality, i.e., the income generated by the plant in converting a kilojoule (KJ) of fuel into power, is of profitable concern if the plant is to operate costeffectively. Defining the power generation returns on investment (PGR) as
⎛ Pgeni ⎤ ⎡ Pgen opt ⎤ ⎞ / PQR = ε ⎜ ⎡ ⎥⎟ ⎢ Q ⎥ ⎢Q ⎝ ⎣ s ⎦ ⎣ s, opt ⎦ ⎠
(33)
where ε is the returns or income of operating the plant on optimal conditions on daily basis, i.e., the income generated by the plant by converting a KJ of fuel to KW power in a day, ($/KW/KJ/day). The margin and deviation from the optimal thermodynamic and economic state can be predicted in principle. Identifying the economic loss potential by comparing the actual operating condition with the optimal will lead to operational modifications taking into account improved energy efficiency. Denoting the daily suboptimal income loss (SIC) as
Pgeni ⎤ ⎡ Pgen opt ⎤ ⎤ ⎡ / SIC losses = ε ⎢1 − ⎡ ⎢ ⎥⎥ ⎢ ⎣ Qs ⎥ ⎦ ⎣ Qs, opt ⎦ ⎦ ⎣
(34)
Consequently, on annual basis
Annual SIC losses = 365 days. SIC losses
(35)
The above can be used to assess the deviation (losses) in sub-optimal operating stages. The determination of the relative margin and the loss profile due to suboptimal power generation conditions with respect to an objective variable, enabling rapid assessment and real-time decision is potentially useful; this is expressed by the suboptimal power generation (SPG) relation, defined by
Pgeni ⎤ ⎡ Pgen opt ⎤ SPG losses = 1 − ⎡ / ⎢ ⎥ ⎢ ⎣ Qs ⎥ ⎦ ⎣ Qs, opt ⎦
(36) 5
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Plausibly, the above relations when used to assess the margin of sub-optimal operation as it relates to the optimal, could give an indication of the margin of potentially accruable returns; which could lead to technical enhancement for improved energy performance. 6. Results and discussion 6.1. Regenerative rankine plant In Fig. 2a, Pgen and PQR are plotted with Pvap . The thermal efficiency ηth is seen to increase with vaporizer pressure. The thermal efficiency values vary with Pvap values. Supposing the plant were operated at the peak thermal efficiency, beyond the optimum Pvap value, the plant would incur losses at the expense of power generation, entailing high operating costs. Therefore, in power plants operated at the peak thermal efficiency despite the power output, the cost expenses in generating a kilowatt of power per KJ of fuel could be relatively high compared to that at the optimal condition. Therefore, operating a power plant suboptimally will impact the economics of power generation. In Fig. 2b, the margin of the suboptimal income (SIC) losses, the fraction of the power generation income that would otherwise accrue to the plant operator had the plant been operated optimally is plotted with the projected power generation returns at varying pressure. It is seen that the SIC losses vary with pressure, considerably reducing the returns that the plant operator would otherwise earn had the plant been operated at the optimal pressure; however, at the point of optimal power generation, the losses are visibly low (zero); indicating that generating power at high sub-optimal pressures does not entail a cost-effective operation. In Fig. 3, the power generation returns increases markedly at the optimal pressure, around 10 MPa; parameter ε is assumed to be $2300 per KW/KJ/day. Beyond the optimal pressure, the power generation returns decrease with pressure; the annual suboptimal cost losses (Annual SCL) are maximum at the maximum pressure value, then zero at the optimal pressure level - that is at the optimal fuel-to-power ratio. Theoretically, that is the exact amount of pressure needed to extract the maximum amount of power possible from a unit volume of fuel. Thereby reducing the operational cost of the thermal plant and its sustainable production of power with potentially environmental impact. 6.2. CSP rankine plant The plots of Qs , Ws, cyc , Pgen and PQR in conjunction with Pvap. are shown in Fig. 4. Qs is given by Qs = Qsup + Qboil and Ws = Wp1 + Wt1. Notably, Qcond. is the dissipated heat, not an energy expense/heat input quantity, hence not included in the Qs expression in the foregoing. At the maximum value of the PQR, the generated power is at its maximum value also. Beyond the optimal value of the objective variable Pvap , the difference in power generation output is obvious with potential losses. As a consequence, optimizing the process operations can lead to significant economic savings using the procedure. The validation of the effects of pressure on thermal performance of power plants can be further investigated besides those in the literature [16].
Fig. 2a. Plot of Pgen and PQR with varying vaporizer pressure for the regenerative plant. 6
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Fig. 2b. Plot of Pgen and ηth with varying vaporizer pressure for the regenerative plant.
Fig. 3. Plot of PGR and Annual SIC losses with varying vaporizer pressure.
In Fig. 5, it is seen that the value of the power generation returns relation is maximum at the optimal pressure, around 10 MPa. But beyond the optimal pressure, the power generation returns decrease with pressure, while the annual suboptimal income losses (Annual SIC) are maximum at the maximum pressure value and zero at the optimal pressure - that is the point of optimal fuel-topower ratio.
7
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Fig. 4. Plot of Qs , Ws, cyc , Pgen and PQR with varying vaporizer pressure.
7. Conclusion The hybrid optimization tools, namely, the thermal efficiency index and the PQR are used in addition to the other indices of efficient operation, in determining the optimal value of the objective variable of power plants. The thermal efficiency index shows significant variances in profiling the optimal power production state; however, when the index is combined with the PQR, the optimal value of the objective variable is construedly obtained. As a consequence, the hybrid adaptive approach is technically superior to the use of the classical thermal efficiency index only in thermodynamic optimization of power plants. Beyond the optimal value of the objective variable (the operating upstream pressure), the difference in power generation output is obvious with potential losses. As a consequence, optimizing the process operations can lead to significant economic savings using the procedure. The validation of the effects of pressure on thermal performance of power plants can be further investigated.
Acknowledgement This is to gratefully acknowledge the assignment of the study on the CSP plant section by Prof. Alan Nurick (Late) of the Department of Mechanical Engineering Science, University of Johannesburg.
8
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Fig. 5. Plot of PGR and Annual SIC losses with varying vaporizer pressure values.
Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.csite.2019.100425. References [1] H. Tony, S.M. Samuel, G. Ralph, Comparison of the Organic Flash Cycle (OFC) to other advanced vapor cycles for intermediate and high temperature waste heat reclamation and Solar Energy, Energy 42 (1) (2012) 213–223. [2] O. Badr, S.D. Probert, P.W. O'Callaghan, Selecting a working fluid for a Rankine-cycle engine, Appl. Energy 21 (1985) 1–42. [3] R.K. Kumar Kapooria, S. Kumar, K.S. Kasana, An analysis of a thermal power plant working on a Rankine cycle: a theoretical investigation, J. Energy South. Afr. 19 (1) (February 2008). [4] C.D. Huijuan, G. Yogi, E.K. Stefanakos, A review of thermodynamic cycles and working fluids for the conversion of low-grade heat, Renew. Sustain. Energy Rev. 14 (2010) 3059–6. [5] G. Ankur, A.I. Khandwawala, Thermodynamic analysis of 120 MW thermal power plant with combined effect of constant inlet pressure (124.61 bar) and different inlet temperatures, Case Studies in Thermal Engineering 1 (1) (2013) 17–25. [6] J. Nouman, Comparative Studies and Analyses of Working Fluids for Organic Rankine Cycles - ORC Master of Science Thesis, KTH School of Industrial Engineering and Management Energy Technology, Sweden, 2012. [7] J. Wanga, Z. Yana, M. Wanga, S. Maa, Y. Daia, Thermodynamic analysis and optimization of an (organic Rankine cycle) ORC using low grade heat source, Energy Volume 49 (1 January 2013) 356–365. [8] J.P. Roy, A. Misra, Parametric optimization and performance analysis of a regenerative Organic Rankine Cycle using R-123 for waste heat recovery, Energy 39 (1) (March 2012) 227–235. [9] A. Geete, A.I. Khandwawala, Thermodynamic analysis of 120 MW thermal power plant with combined effect of constant inlet pressure (127.06 bar) and different condenser back pressures, IUP J. Mech. Eng. 07 (01) (2014) 25–46. [10] A. Geete, A.I. Khandwawala, To analyse the combined effect of different extraction line pressure drops on the performance of coal fired thermal power plant, Int. J. Ambient Energy 38 (04) (2017) 389–394, https://doi.org/10.1080/01430750.2015.1121919. [11] A. Geete, Exergy, exergy destruction rate and exergy efficiency analysis of thermal power plants by computer software at various operating conditions, imanager’s J. Future Eng. Technol. 11 (01) (2015) 07–22. [12] A. Geete, A. Bhargava, Combined effect of various operating loads, number of feed water heaters and makeup water quantities on the performance of coal fired thermal power plant: a case study, Cogent Engineering 03 (2016) 1–7 https://doi.org/10.1080/23311916.2016.1218115. [13] A. Geete, A.I. Khandwawala, Thermodynamic analysis of thermal power plant with combined effect of constant inlet temperature (507.78°C) and different inlet pressures, IUP J. Mech. Eng. 08 (03) (2015) 38–49. [14] Power generation, Siemens organic rankine cycle waste heat recovery with ORC, https://www.energy.siemens.com/hq/pool/hq/power-generation/steamturbines/orc-technology/presentation-siemens-organic-rankine-cycle.pdf. [15] Steam turbines for CSP plants Industrial steam, turbines https://www.energy.siemens.com/hq/pool/hq/power-generation/steam-turbines/downloads/steamturbine-for-csp-plants-siemens.pdf. [16] A.C. Yunus, A.B. Michael, Thermodynamics, an Engineering Approach, fifth ed., McGraw-Hill, 2006.
9
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering journal homepage: www.elsevier.com/locate/csite
Thermal systems and thermal efficiency index deficiency - A thermodynamic case study of regenerative and CSP plants
T
Paul N. Nwosua,b,∗ a b
School of Mechanical Engineering Science, 301 Xuefu Road, Zhenjiang, Jiangsu Province, China Formerly of the Department of Mechanical Engineering Science, University of Johannesburg, Auckland Park, PO 2322, South Africa
A R T IC LE I N F O
ABS TRA CT
Keywords: CSP Regenerative Rankine Optimization PQR Thermal efficiency Thermodynamics
As the determination of the power generation returns for a thermal plant system in conditions of optimality is of profitable, economic concern to a plant operator (that is, the income generated by the plant in converting a kilojoule (KJ) of fuel into useful power), the current study investigates the influence of thermodynamic variables on thermal efficiency, power production and prediction in regenerative and concentrated solar power (CSP) plants with a novel optimization technique. The thermal efficiency index shows significant variances in profiling the optimal power production state; however, when the index is combined with the PQR, the optimal value of the objective variable is construedly obtained. Beyond the optimal value of the objective variable, the operating upstream pressure, the difference in power generation output is obvious with potential losses. As a consequence, optimizing the process operations can lead to significant economic savings using the procedure.
1. Introduction This study investigates the thermodynamic performance of regenerative and concentrated solar power (CSP) rankine plants. Recently, the sustainability and profitability of a power plant operations are confronted mainly by rising fuel costs and constraints on permissible carbon footprint on the subject of climate change; wherefore some thermal plants would be subject to periodically suboptimal operating conditions, which could result to increased operational expenses. There are a number of investigations and studies into power plant modelling and optimization. Ho et al. [1] studied the power plants based on the organic flash cycle (OFC) and other advanced vapor cycles for intermediate and high temperature waste heat reclamation and solar thermal applications and concluded that aromatic hydrocarbons are better suited as working fluids in organic rankine cycle (ORC) plants, due to their relatively high-power output and potentially less complex turbine designs. Badr et [2] conducted a simulation study on the performance of Rankine cycle power plants which employed steam as the working fluid and developed a BASIC program to facilitate the optimal design condition of the plants. Kumar and Kasana [3] conducted a study into a rankine plant, and concluded that the efficiency can be improved by using an intermediate reheat cycle. Chen et al. [4] reviewed the Rankine and supercritical Rankine cycles for the conversion of low-grade heat into electrical power and concluded that thermodynamic and physical properties, stability, environmental impacts, safety, compatibility, availability and cost are important considerations for selecting a working fluid. Geete and Khandwawala [5] obtained correction curves for power output on account of conflicts between the actual and predicted output for a 120 MW thermal power plant. Also, Jamal [6] conducted a comparative study into working fluids of ORCs. It was determined that the temperature profile of the evaporator and the condenser could affect the ∗
School of Mechanical Engineering Science, 301 Xuefu Road, Zhenjiang, Jiangsu Province, China. E-mail address: [email protected].
https://doi.org/10.1016/j.csite.2019.100425 Received 3 July 2018; Received in revised form 26 February 2019; Accepted 4 March 2019 Available online 28 March 2019 2214-157X/ © 2019 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Nomenclature Q h Pt W E s P T υ E Sgen m m˙ ΔEsystem Δkes
cond dest p t out source sink e in i reg sup.
Heat (KJ/kg) Enthalpy (KJ/kg) Turbine (Generated) Power (W) Work (KJ/kg) Power (W) Entropy (KJ/kg) Pressure (Pa) Temperature (W) Specific volume (m3/kg) Power (W) Entropy generation (KJ/kgK) Mass fraction Mass flow rate (Kg/s) Energy difference (KJ/kg) Potential Energy difference (KJ/Kg)
Symbols 0 η b,in b,out
Subscripts boil
condenser destroyed pump turbine outlet pump pump Temperature (W) in Intermediate regenerator superheater
destroyed Efficiency system boundary, in system boundary, out
boiler
exergy losses and the best energy utilization. Wang et al. [7] studied an ORC system using low grade heat source and suggested a ratio of net power output to total heat transfer area as the performance evaluation criterion. Roy and Misra [8] performed a parametric optimization and performance analysis of a regenerative ORC using R-123 for waste heat recovery; and developed a computer program to optimize and compare the system under different heat source conditions. Geete and Khandwawala [9] examined a power plant system thermodynamically with the combined effect of constant inlet pressure (127.06 Bar) and condenser back pressures. The correction curves for the combined effect of constant inlet pressure and different condenser back pressures were obtained. Geete and Khandwawala [10] analyzed the effect pressure drop on the performance of a coal-fired thermal plant. The study showed that if the line pressure drop varies, the power output and the heat rate vary also. Other studies on power plant systems in line with the prospect and performance are given in Refs. [11–13]. In this analysis, the margin of potentially accruable returns in the operation of a power plant is determined with respect to the optimal power production and prediction based on the power-quantity ratio (PQR). The power-quantity ratio (PQR) is defined and compared with the thermal efficiency index. The optimization procedure also investigates the optimal thermodynamic performance
Fig. 1a. Schematic and process diagram of a regenerative plant. 2
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
of the plants with respect to an objective variable, indicating the profile of heat and work interaction, as well as the point of optimal power production. 2. Description The main components of a regenerative plant include the following: boiler/vaporizer, superheater, turbine, condenser, and regenerator. While a CSP plant comprises all of the above, in addition to feed-water heaters, purpose-built regenerators, solar field and a thermal storage facility. The regenerative Rankine plant can be organic or inorganic [14]. But, a CSP plant works with a renewable (solar) auxiliary heat source. The CSP plant studied is based on Siemens technology with a power output of approximately 7 MW and turbine inlet parameters of 130 bar and 530C; many of such plants are used around the world, [15]. The schematic diagrams of the regenerative and the CSP Rankine plants are shown in Fig. 1a and b, respectively. 3. Regenerative rankine plant - theory The thermodynamic models for the regenerative plant are derived from energy relation and mass balances [11]: . Q ≅ W ≅ Δke ≅ Δpe
. . . Ein − Eout = ΔEsystem
(1) (2)
.
⇒
∑ min hin= ∑ mout hout
(3)
In terms of work flow quantities, the total work done by the turbine(s) ∑ Wt is given by
∑ Wt = ∑ min hin
(4)
where min is the steam mass flow rate and hin is the enthalpy. Consequently, the amount of work done by the turbine can be expressed by
Wt = (h5 − h6) = v (P5 − P6)
(5)
Thermal energy (heat input) into the recuperator, vaporizer and superheater with heat rejection in the condenser can be
Fig. 1b. Schematic and process diagram of a typical CSP plant with multi-stage operation. 3
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
determined from:
Q˙ recup = h7 − h6
(6)
Q˙ vap = h4 − h3
(7)
Q˙ sup = h5 − h4
(8)
Q˙ cond = h7 − h1
(9)
Thus for the thermal efficiency, the following is defined:
ηth =
Wt − Wp1 Wnet = Q˙ boil + Q˙ sup ∑ Q˙ i
(10)
The power generated can be calculated from
Pgen = m˙ (h7 − h6)
(11)
4. CSP plant - theory Recalling the energy balance relation (eqn. (1)) for the CSP plant the relation is rendered differently:
∑ Wt = ∑ mi hi
(12)
Considering the plant components, the following is obtained
∑ Wt = (h7 − h8) + (h9 − h10) + (1 − m1)(h10 − h11) + (1 − m1 − m2)(h11−h12)
(13)
Based on the principle of conservation of energy and mass, the open-feed-water heaters (OFWHs), closed-feed-water heaters (CFHWs) and the thermal points between the condenser and pump1 are taken to be points where thermal equilibrium exits, such that for the OFWHs, the following is obtained
(1 − m1) h3 + m1 h10 = h4
(14)
And for the CFWHs,
(1 − m1) h2 + m2 h11 = (1 − m1) h3
(15)
The energy balance relation for the nodal junction between the condenser and pump1 can be written as
(1 − m1 − m2) h14 + m2 h13 = (1 − m1) h1
(16)
The mathematical models for the mass fractions m1 and m2 can be evaluated by solving the above equations. Work done by pumps 1 and 2, respectively, is obtained from
Wp1 = (1 − m1)(h1 − h2) = (1 − m1) υ (P1 − P2)
(17)
Wp2 (h5 − h4 ) = υ (P5 − P4 )
(18)
and
The heat transfer relations for the following components (the boiler/vaporizer, the superheater and the reheater) are
Q˙ boil = (h6 − h5)
(19)
Q˙ sup = (h7 − h6)
(20)
Q˙ reh = (h9 − h8)
(21)
also, the irreversible energy losses in the condenser could be determined from
Q˙ cond = (1 − m1 − m2)(h12 − h14 ) (22) . . . . where Qboil., Qsup , Qreh. and Qcond.. denote the heat transfer rate of the boiler/vaporizer, superheater, regenerator and condenser. The thermal efficiency of the plant can be determined from: ηth =
∑ Wt − (Wp1 − Wp2) Wnet = Q˙ boil + Q˙ vap + Q˙ reh ∑ Q˙ i
(23)
Given adiabatic conditions in the components thereof save the condenser and the boiler, the power generation potential is calculated from
Pgen = m˙ t [(h7 − h8) + (h9 − h10) + (1 − m1)(h10 − h11) + (1 − m1 − m2)(h11 −h12)] 4
(24)
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Where m1, m2 and (1 − m1 − m2) are the steam fractions of the high-pressure (HP) and low-pressure (LP) turbine flow channels and m⋅ in is the flow rate of the working fluid. In comparison with equation (11), equation (24) contains the mass fractions with the enthalpy variables for the complex multi-stage plant. 5. Optimization The overriding objective of the optimization procedure, concisely, is to operate the plant at the maximum thermodynamic and techno-economic potential. Writing the following variables:
Qs, cyc =
∑ Qi ∑H
(25)
Ws, cyc =
∑ Wi ∑H
(26)
in which
∑ Hi = ∑ Qi + ∑ Wi
(27)
The heat input and the thermodynamic quantity ratio (TQR) index are respectively determined from:
Qs, cyc =
∑ Qi, s ∑H
(28)
TQR cyc = Qs, cyc + Ws, cyc
(29)
and
TQR = Qs + Ws, cyc
(30)
where ∑ Qi, s is the total heat input into the plant (excluding the heat rejection in the condenser), ∑ Qi is the total (cycle) heat input and output, ∑ Wi is the total (cycle) work input and output, Ws, cyc is the proportion of the total (cycle) work input and output, Qs, cyc is the proportion of the total (cycle) heat input and output, and Qs is the proportion of heat input into the plant. The power-energy quantity ratio (PQR) gives an indication of the optimal power production potential
Pgen . Ws ⎤ PQR = ⎡ ⎢ ⎣ Qs ⎥ ⎦
(32)
Relatively, a judicious decision to adjust the operation of a plant is typically based on the nominal load. This consideration is implicitly related to the amount of energy converted to useful power. A simple relation, which can lessen decision times can be of considerable economic, technical, operational benefit in real-time conditions. Wherefore, the determination of the power generation returns for a thermal plant system in conditions of optimality, i.e., the income generated by the plant in converting a kilojoule (KJ) of fuel into power, is of profitable concern if the plant is to operate costeffectively. Defining the power generation returns on investment (PGR) as
⎛ Pgeni ⎤ ⎡ Pgen opt ⎤ ⎞ / PQR = ε ⎜ ⎡ ⎥⎟ ⎢ Q ⎥ ⎢Q ⎝ ⎣ s ⎦ ⎣ s, opt ⎦ ⎠
(33)
where ε is the returns or income of operating the plant on optimal conditions on daily basis, i.e., the income generated by the plant by converting a KJ of fuel to KW power in a day, ($/KW/KJ/day). The margin and deviation from the optimal thermodynamic and economic state can be predicted in principle. Identifying the economic loss potential by comparing the actual operating condition with the optimal will lead to operational modifications taking into account improved energy efficiency. Denoting the daily suboptimal income loss (SIC) as
Pgeni ⎤ ⎡ Pgen opt ⎤ ⎤ ⎡ / SIC losses = ε ⎢1 − ⎡ ⎢ ⎥⎥ ⎢ ⎣ Qs ⎥ ⎦ ⎣ Qs, opt ⎦ ⎦ ⎣
(34)
Consequently, on annual basis
Annual SIC losses = 365 days. SIC losses
(35)
The above can be used to assess the deviation (losses) in sub-optimal operating stages. The determination of the relative margin and the loss profile due to suboptimal power generation conditions with respect to an objective variable, enabling rapid assessment and real-time decision is potentially useful; this is expressed by the suboptimal power generation (SPG) relation, defined by
Pgeni ⎤ ⎡ Pgen opt ⎤ SPG losses = 1 − ⎡ / ⎢ ⎥ ⎢ ⎣ Qs ⎥ ⎦ ⎣ Qs, opt ⎦
(36) 5
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Plausibly, the above relations when used to assess the margin of sub-optimal operation as it relates to the optimal, could give an indication of the margin of potentially accruable returns; which could lead to technical enhancement for improved energy performance. 6. Results and discussion 6.1. Regenerative rankine plant In Fig. 2a, Pgen and PQR are plotted with Pvap . The thermal efficiency ηth is seen to increase with vaporizer pressure. The thermal efficiency values vary with Pvap values. Supposing the plant were operated at the peak thermal efficiency, beyond the optimum Pvap value, the plant would incur losses at the expense of power generation, entailing high operating costs. Therefore, in power plants operated at the peak thermal efficiency despite the power output, the cost expenses in generating a kilowatt of power per KJ of fuel could be relatively high compared to that at the optimal condition. Therefore, operating a power plant suboptimally will impact the economics of power generation. In Fig. 2b, the margin of the suboptimal income (SIC) losses, the fraction of the power generation income that would otherwise accrue to the plant operator had the plant been operated optimally is plotted with the projected power generation returns at varying pressure. It is seen that the SIC losses vary with pressure, considerably reducing the returns that the plant operator would otherwise earn had the plant been operated at the optimal pressure; however, at the point of optimal power generation, the losses are visibly low (zero); indicating that generating power at high sub-optimal pressures does not entail a cost-effective operation. In Fig. 3, the power generation returns increases markedly at the optimal pressure, around 10 MPa; parameter ε is assumed to be $2300 per KW/KJ/day. Beyond the optimal pressure, the power generation returns decrease with pressure; the annual suboptimal cost losses (Annual SCL) are maximum at the maximum pressure value, then zero at the optimal pressure level - that is at the optimal fuel-to-power ratio. Theoretically, that is the exact amount of pressure needed to extract the maximum amount of power possible from a unit volume of fuel. Thereby reducing the operational cost of the thermal plant and its sustainable production of power with potentially environmental impact. 6.2. CSP rankine plant The plots of Qs , Ws, cyc , Pgen and PQR in conjunction with Pvap. are shown in Fig. 4. Qs is given by Qs = Qsup + Qboil and Ws = Wp1 + Wt1. Notably, Qcond. is the dissipated heat, not an energy expense/heat input quantity, hence not included in the Qs expression in the foregoing. At the maximum value of the PQR, the generated power is at its maximum value also. Beyond the optimal value of the objective variable Pvap , the difference in power generation output is obvious with potential losses. As a consequence, optimizing the process operations can lead to significant economic savings using the procedure. The validation of the effects of pressure on thermal performance of power plants can be further investigated besides those in the literature [16].
Fig. 2a. Plot of Pgen and PQR with varying vaporizer pressure for the regenerative plant. 6
Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Fig. 2b. Plot of Pgen and ηth with varying vaporizer pressure for the regenerative plant.
Fig. 3. Plot of PGR and Annual SIC losses with varying vaporizer pressure.
In Fig. 5, it is seen that the value of the power generation returns relation is maximum at the optimal pressure, around 10 MPa. But beyond the optimal pressure, the power generation returns decrease with pressure, while the annual suboptimal income losses (Annual SIC) are maximum at the maximum pressure value and zero at the optimal pressure - that is the point of optimal fuel-topower ratio.
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Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Fig. 4. Plot of Qs , Ws, cyc , Pgen and PQR with varying vaporizer pressure.
7. Conclusion The hybrid optimization tools, namely, the thermal efficiency index and the PQR are used in addition to the other indices of efficient operation, in determining the optimal value of the objective variable of power plants. The thermal efficiency index shows significant variances in profiling the optimal power production state; however, when the index is combined with the PQR, the optimal value of the objective variable is construedly obtained. As a consequence, the hybrid adaptive approach is technically superior to the use of the classical thermal efficiency index only in thermodynamic optimization of power plants. Beyond the optimal value of the objective variable (the operating upstream pressure), the difference in power generation output is obvious with potential losses. As a consequence, optimizing the process operations can lead to significant economic savings using the procedure. The validation of the effects of pressure on thermal performance of power plants can be further investigated.
Acknowledgement This is to gratefully acknowledge the assignment of the study on the CSP plant section by Prof. Alan Nurick (Late) of the Department of Mechanical Engineering Science, University of Johannesburg.
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Case Studies in Thermal Engineering 14 (2019) 100425
P.N. Nwosu
Fig. 5. Plot of PGR and Annual SIC losses with varying vaporizer pressure values.
Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.csite.2019.100425. References [1] H. Tony, S.M. Samuel, G. Ralph, Comparison of the Organic Flash Cycle (OFC) to other advanced vapor cycles for intermediate and high temperature waste heat reclamation and Solar Energy, Energy 42 (1) (2012) 213–223. [2] O. Badr, S.D. Probert, P.W. O'Callaghan, Selecting a working fluid for a Rankine-cycle engine, Appl. Energy 21 (1985) 1–42. [3] R.K. Kumar Kapooria, S. Kumar, K.S. Kasana, An analysis of a thermal power plant working on a Rankine cycle: a theoretical investigation, J. Energy South. Afr. 19 (1) (February 2008). [4] C.D. Huijuan, G. Yogi, E.K. Stefanakos, A review of thermodynamic cycles and working fluids for the conversion of low-grade heat, Renew. Sustain. Energy Rev. 14 (2010) 3059–6. [5] G. Ankur, A.I. Khandwawala, Thermodynamic analysis of 120 MW thermal power plant with combined effect of constant inlet pressure (124.61 bar) and different inlet temperatures, Case Studies in Thermal Engineering 1 (1) (2013) 17–25. [6] J. Nouman, Comparative Studies and Analyses of Working Fluids for Organic Rankine Cycles - ORC Master of Science Thesis, KTH School of Industrial Engineering and Management Energy Technology, Sweden, 2012. [7] J. Wanga, Z. Yana, M. Wanga, S. Maa, Y. Daia, Thermodynamic analysis and optimization of an (organic Rankine cycle) ORC using low grade heat source, Energy Volume 49 (1 January 2013) 356–365. [8] J.P. Roy, A. Misra, Parametric optimization and performance analysis of a regenerative Organic Rankine Cycle using R-123 for waste heat recovery, Energy 39 (1) (March 2012) 227–235. [9] A. Geete, A.I. Khandwawala, Thermodynamic analysis of 120 MW thermal power plant with combined effect of constant inlet pressure (127.06 bar) and different condenser back pressures, IUP J. Mech. Eng. 07 (01) (2014) 25–46. [10] A. Geete, A.I. Khandwawala, To analyse the combined effect of different extraction line pressure drops on the performance of coal fired thermal power plant, Int. J. Ambient Energy 38 (04) (2017) 389–394, https://doi.org/10.1080/01430750.2015.1121919. [11] A. Geete, Exergy, exergy destruction rate and exergy efficiency analysis of thermal power plants by computer software at various operating conditions, imanager’s J. Future Eng. Technol. 11 (01) (2015) 07–22. [12] A. Geete, A. Bhargava, Combined effect of various operating loads, number of feed water heaters and makeup water quantities on the performance of coal fired thermal power plant: a case study, Cogent Engineering 03 (2016) 1–7 https://doi.org/10.1080/23311916.2016.1218115. [13] A. Geete, A.I. Khandwawala, Thermodynamic analysis of thermal power plant with combined effect of constant inlet temperature (507.78°C) and different inlet pressures, IUP J. Mech. Eng. 08 (03) (2015) 38–49. [14] Power generation, Siemens organic rankine cycle waste heat recovery with ORC, https://www.energy.siemens.com/hq/pool/hq/power-generation/steamturbines/orc-technology/presentation-siemens-organic-rankine-cycle.pdf. [15] Steam turbines for CSP plants Industrial steam, turbines https://www.energy.siemens.com/hq/pool/hq/power-generation/steam-turbines/downloads/steamturbine-for-csp-plants-siemens.pdf. [16] A.C. Yunus, A.B. Michael, Thermodynamics, an Engineering Approach, fifth ed., McGraw-Hill, 2006.
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