1492
Energy & Fuels 2003, 17, 1492-1500
Conceptional Design Modeling of Combined Power Generation Cycle for Optimum Performance Hany Ahmed Mohamed* Mechanical Engineering Department, Faculty of Engineering, Assiut University, Assiut, Egypt Received November 19, 2002. Revised Manuscript Received August 19, 2003
The present paper studies the general characteristics and evaluates the optimum performance of a simple two-stage compression partial oxidation gas turbine (POGT) cycle that has been combined with a Rankine cycle. The controlling parameters of the combined cycle that give optimum performance are determined and fitted into functional correlation equations. The values of the first-law efficiency and the second-law efficiency (ηI and ηII, respectively) for the combined cycle are compared with those obtained for single POGT cycles. The effects of irreversibilities of the different units of the cycles are considered in the study. The combination of a POGT cycle with the Rankine cycle has achieved a maximum enhancement in net work output of ∼28.76% and optimum values of ηI ≈ 58% and ηII ≈ 80%. The present findings can form a very important basis for a complete phenomenological design of a combined POGT/Rankine cycle to achieve optimum performance.
1. Introduction Turbine efficiencies, along with cost and reliability, are among the most important criteria when power producers place orders for new plants. Therefore, the gas turbine gains in efficiency, which is the result of technological development, have been crucial for their success. Turbine research and development studies always try to implement new technologies to enhance their efficiencies in all possible ways. Phenomenological designs of turbine cycles have expanded very extensively in the past few years, to expose all possible contributions of the different units of the cycle for improving overall cycle efficiency. One of these designs is the partial oxidation gas turbine (POGT), which is based on the partial burning of a rich fuel/air mixture (into a mixture of CO and H2) in a first-stage combustion chamber at pressures of ∼60 bar and temperatures of ∼1300 °C, which is determined by the equivalence ratio.1 Characteristics of ideal and actual partial oxidation cycles were studied for optimum performance conditions.2 Development trends have concentrated on increased efficiency and power output from gas turbines, which has resulted in an increased interest for combined cycle plants. The basic components of the combined cycle are the gas turbine, heat recovery steam generator (HRSG), and steam turbine. A fuel (usually natural gas) is used to heat compressed air to a high temperature, which then drives the gas generator and power turbine. The turbine drives the first electrical generator. The flue gas from the gas turbine passes through the heat recovery for steam production, which is fed to a steam turbine, which then drives a second electrical generator. A brief * Author to whom correspondence should be addressed. E-mail:
[email protected]. (1) Hsu, S. M.; Smith, K. D. Repairs of Advanced Land-Based Gas Turbines. Diesel Gas Turbine Worldwide 2000, April. (2) McNeely, M. GE’s 7FB Gas Turbines Aimed at U.S. CombinedCycle Market. Diesel Gas Turbine Worldwide 2000, Jan.-Feb.
history of different combined cycles is surveyed in the work by Mullins.3 A doubling of the efficiency has occurred for simple cycles, with the introduction of combined cycles causing a tripling in efficiency.4 Sunao Aoki5 reported that the combined-cycle efficiency for a firing temperature of ∼1500 °C and a pressure ratio of 14 achieves a combined cycle efficiency of 58% (lower heating value, LHV) and it is expected to achieve an efficiency of 60% or more for another class of gas turbines. In a combined-cycle investigation by Westinghouse Electric Corporation, the Institute of Gas Technology and United States Department of Energy (USDOE)6 have claimed LHV efficiencies up to 68%. Another phenomenological design, which was based on thermochemical recuperation, recycling of exhaust gases, partial oxidation, and intercooling, was studied by Kumar and Coyle7 and reached a LHV efficiency of 65.4%. Optimization studies of simple gas turbines and those augmented with bottoming-air cycles have been conducted.8 Analysis and concepts of different combined cycles are presented in the work by Sunao Aoki.9 All the aforementioned works illustrate that an enhancement in the overall efficiency is achieved be(3) Mullins, P. First Cyclone to Start Commercial Service. Diesel Gas Turbine Worldwide 2000, Jan.-Feb. (4) Tindall, R. M.; Crews, M. A. Alternative Technologies to SteamMethane Reforming. Hydrocarbon Process. 1995, November. (5) Christianovich, S. A.; Maslennikov, V. M.; Shterenberg, V. Ya. Steam-Gas Power Stations with Multi-stage Residual-Oil Combustion. Appl. Energy 1976, 2, 175-187. (6) Mohamed, H. A. Optimum Performance Characteristics of Ideal and Actual Partial Oxidation Cycles and Reheat CyclesA Comparative Study. Bull. Fac. Eng., Minia Univ. 2001, 20, (1), 84-92. (7) Kumar, S.; Coyle, T. Combined Cycle Power Plants Offer Efficient Alternative Energy. AFE Facilities Eng. 2000, November/ December, 10-19. (8) Unger, D.; Herzog, H. Comparative Study on Energy R&D Performance: Gas Turbine Case Study, Massachusetts Institute of Technology Energy Laboratory Final Report, Massachusetts Institute of Technology, Cambridge, MA, August 1998.
10.1021/ef0202743 CCC: $25.00 © 2003 American Chemical Society Published on Web 10/16/2003
Modeling of Combined Power Generation Cycle
Energy & Fuels, Vol. 17, No. 6, 2003 1493
Figure 1. Schematic (left) and T-s diagrams (right) of a simple POGT cycle combined with a Rankine cycle.
cause of the POGT or combined cycle. However, the enhancement in the overall efficiency using the POGT in a combined cycle has not yet been studied. Turbine research and development studies always attempt to implement new technologies to enhance their performance in all possible ways. For example, the General Electric (GE) model 7H combined-cycle turbine has an efficiency that reaches 60% by incorporating advanced bucket and airfoil materials with multilayer protective coatings, forced-air or steam cooling technology, and advanced manufacturing techniques such as directionsolidification and single-crystal super alloys.1 Other GE models (e.g., model 7FB) are reported to operate at pressure ratios reaching 18.5:1 and firing temperatures of 2500 °F (1371 °C).2 Another cycle technology, which is based on the cyclone effect and a multistage compressor with transonic flow conditions, is reported to have overall plant efficiencies of 80% and higher.3 As a dominant means of power production, the USDOE has estimated that, over the next 10 to 15 years, natural gas turbines will comprise more than 80% of the powergenerating capacity in the United States and possibly around the world.4 Because of these and similar advantages, phenomenological designs of turbine cycles have expanded very extensively in the past few years to expose all possible contributions of the different units of the cycle for improving overall cycle performance. One of these designs is the partial oxidation gas turbine (POGT), which is based on the partial burning of a rich fuel/air mixture (into a mixture of CO and H2) in a first-stage combustion chamber at pressures of ∼60 bar and temperatures of ∼1300 °C, which is determined by the equivalence ratio.5 One practical application of this design is to reform oil residues into fuel gas, remove sulfur components (in the form of H2S), and utilize the remaining gas in a turbine. The same group of researchers5 found that the so-called incremental POGT efficiency (incremental power/incremental fuel consumption) could reach 80%. Characteristics of ideal and actual partial oxidation cycles were studied for optimum performance conditions.6 In a combined-cycle investigation by Westinghouse Electric Corporation, the Institute of Gas Technology and the USDOE7 have claimed LHV efficiencies up to 68%. Another phenomenological design, which is based on thermochemical recuperation, recycling of exhaust gases, partial oxidation, and intercooling, was studied
in the work of Unger and Herzog8 and reached a LHV efficiency of 65.4%, which represented an ∼1.4% gain in cycle efficiency. A third technology in the Chemical Gas Turbine9-12 with fuel-rich combustion in the first stage has used carbon-fiber-reinforced composites as a material for the turbine blades, to withstand the high temperatures (of ∼1800 °C). These blades suffer rapid degradation when exposed to a small amount of oxygen. Optimization studies of simple gas turbines and those augmented with bottoming-air cycles13 have been performed. The main objective of the present research is to study the general characteristics and to evaluate optimum performance of a simple two-stage compression POGT cycle combined with a Rankine cycle (shown in Figure 1). The values of the controlling parameters of the combined cycle that give optimum performance (e.g., first-law and second-law efficiencies (ηI and ηII, respectively) and a net work output, wnet) are determined and fitted into functional correlation equations. The values of ηI and ηII for the combined cycle are compared with those obtained for the simple POGT cycle and the advanced POGT cycle, shown in Figure 2. The performance characteristics of the POGT cycle are presented in another work.6 The effects of the irreversibility of the different units of the cycles are considered in the study. (9) Sunao, A. Trend and Key Technologies for Gas Turbine Combined Cycle Power Generation in a Globally Competitive Market and Environmental Regulations. Proceedings of 2000 International Joint Power Generation Conference, Miami Beach, FL, July 23-26, 2000, pp 1-6. (10) Maslennikov, V. M.; Batenin, V. M.; Shterenberg, V. Ya.; Vyskubenko, Yu. A.; Tsalko, E. A. Advanced Gas Turbine System Utilizing Partial Oxidation Technology for Power Generation, ASME Paper No. 97-GT-378, 1997. (11) Rabovitser, J. K.; Khinkis, M. K.; Bannister, R. L.; Miao, F. Q. Evaluation of Thermochemical Recuperation and Partial Oxidation Concepts for Natural Gas-Fired Advanced Turbine Systems, ASME Paper No. 96-GT-290, 1996. (12) Mohamed, H. A.; Abdel-Rahim, Y. M. Optimum Combined Gas Turbine-Bottoming Air Cycle Characteristics. Bull. Fac. Eng., Assiut Univ. 2001, 29, (2), 129-137. (13) Hodrien, R. C.; Fairbairn, G. W. Power into the 21st Century. Gas Eng. Manage. 1994, March. (14) Harvey, S. P.; Knoche, K. F.; Richter, H. J. Reduction of Combustion Irreversibility in a Gas Turbine Power Plant through OffGas Recycling. J. Eng. Gas Turbines Power 1995, 117, 24-30. (15) Arai, N.; Kobayashi, N. Challenges for Development of Highly Efficient Gas Turbine Systems: Chemical Gas Turbine System. Presented at the ASME International Joint Power Generation Conference, Denver, CO, Nov. 3-5, 1997. (16) Korobitsyn, M. A. New and Advanced Energy Conversion Technologies. Analysis of Cogeneration, Combined and Integrated Cycles. Ph.D. Thesis, Thermal Engineering Laboratory, Twente University, Amsterdam, The Netherlands, 1998.
1494 Energy & Fuels, Vol. 17, No. 6, 2003
Mohamed
Figure 2. Schematic (left) and T-s diagrams (right) of the simple and advanced POGT cycles studied in the previous work.6
The present findings can form a very important basis for a complete phenomenological design of a combined POGT/Rankine cycle to achieve optimum performance. 2. Analysis 2.1. Cycles Description. Figure 1 shows a combined cycle composed of a simple partial oxidation cycle (POGT) and a superheated steam Rankine cycle. For a 100% value of the air fraction introduced into the primary combustion chamber (i.e., mass fraction of m ) 1.0), the POGT cycle approaches the RHGT Reheat cycle. This means that the POGT cycle is a reasonable generalization to the RHGT Reheat cycle. In the topping POGT cycle, a portion of the compressed air delivered from a low-pressure compressor (LPC) (hereafter represented by m) is fed to the economizer for cooling, where an amount of heat is transferred to the working fluid (water) in the Rankine cycle. The compressed air delivered from the high-pressure compressor (HPC) is fed to the partial oxidation combustion chamber (cc1) to burn the fuel partially as a very rich mixture. After expansion in the high-pressure turbine (HPT), the combustion gases are mixed with the remaining portion of the compressed air (1 - m) and fed to the second combustion chamber (cc2) to complete the combustion of the fuel and then expanded in the low-pressure turbine (LPT). The exhaust gases leaving that turbine are used to heat the working fluid in the Rankine cycle through the heat recovery steam generator (HRSG). In the advanced POGT cycle shown in Figure 2, the exhaust gases are used to heat some of the compressed air in the heat exchanger (HE) unit. In the present analysis, the operating conditions of the Rankine cycle are selected by assuming the high pressure, the low pressure, the high temperature (T6), and the efficiencies of the steam turbine and the pump: 8 MPa, 10 kPa, 500 °C, 0.85 and 0.85, respectively. A unit mass of air (entering under atmospheric conditions) is used as the basis for the calculations. The actual operations of the combined cycle units (e.g., compressors, turbines, economizer, combustion chambers, and HRSG) are resembled by assumed efficiencies, effectiveness, and pressure drop
values to account for the irreversibilities of each unit. The properties of the working medium of the POGT cycles in each respective path are calculated from their specific heats and isentropic exponent values. In the present analysis, the efficiencies, the isentropic temperature ratio, and the effectiveness values, as well as the values of the operating parameters (fuel/air ratio, maximum-to-minimum cycle temperature ratio, and the fraction of air entering the primary combustion chamber) are varied over some ranges that slightly exceed their practically acceptable bounds, to investigate their effects on cycle characteristics comprehensively. 2.2. Controlling Parameters. The controlling parameters for the combined cycle are the compressor and turbine efficiencies (ηc, ηt, respectively), the isentropic temperature ratio (x), the maximum-to-minimum cycle temperature ratio (θ), the fuel/air ratio (f), the HRSG and economizer effectiveness (ηG and ηEe, respectively), the mass fraction of air in the first combustor (m), and the ratios of the pressure decrease to initial (entering) pressure (pressure decrease/P1) in the first combustor (denoted as ∆Pcc1), the second combustor (denoted as ∆Pcc2), the economizer (denoted as ∆Pe), and the HRSG (denoted as ∆PG). The performance characteristics of the cycles are the dimensionless heat supplied to the cycle (q ) (heat supplied)/(CpT1)), the dimensionless output work from the cycle (wnet ) (output work)/(CpT1)), the first-law efficiency ηI, and the second-law efficiency ηII. In calculating ηII, the available energy associated with the heat input into the combustion chambers (instead of its chemical value that was based on the composition and the amount of fuel introduced into the cycle) has been utilized as an approximation to the exact value of available energy input to cycle. 2.3. Combined Cycle Characteristics. The irreversibilities in the compressors, turbines, economizer, HRSG, pump, and steam turbine are taken into consideration by the thermal efficiency or effectiveness of each unit beside the pressure-decrease ratio through some units. The assumptions for the combined cycle shown in Figure 1 are as follows:
Modeling of Combined Power Generation Cycle
Energy & Fuels, Vol. 17, No. 6, 2003 1495
(1) In the Rankine cycle, half the mass of the water passes through the economizer. (2) The specific heat at constant pressure for the products (CP,gas) can vary significantly (especially that for CO2) and equals the average value for gaseous products at atmospheric pressure. (3) The specific heat ratio for air is constant and is equal to 1.4. (4) The efficiency of the LPC is equal to that of the HPC (which is ηc). (5) The efficiency of the LPT is equal to that of the HPT (which is ηt).
q)
fCP,gas(T3 - T1) + mCp(T3 - T2) + CPT1 CP,gas(f + m)(Tb - Ta) + (1 - m)CP(Tb - Tc) CPT1
)
}
(1 - ∆Pcc1)](1-γ)/γ +
T2s T1
θ)
T3 T1
n)
(
)
() ()
By substituting the values of enthalpy in the aforementioned equations, the net work obtained from the Rankine cycle in a dimensionless form, wnet(Rankine), becomes
P1 1 - ∆PG
wnet(Rankine) )
∆Ptotal ) ∆Pcc1 + ∆Pe + ∆Pcc2 + ∆PG Applications of the conventional thermodynamic laws and relationships to the different parts of the cycle, and with some manipulations formulated for the performance characteristics of the combined cycle in the equations (eqs 1a-1i), are given below.
(γ-1)/γ
ms(h6 - h7) - ms(h9 - h8) CPT1
) 0.315
()
ηe [x(1 - ∆Pc)(γ-1)/γ - 0.9] + ηc
0.315(1 + f)ηG[θ(1 - ηt) - 1] + 0.315(1 +
()
f)ηeηG
mCp(T2 - T1) + Cp(Tc - T1) CpT1
m(x - 1) x(1 - ∆Pe) ) + ηc ηc
ηe × ηc
θ × x [(1 - ∆Pe)(1 - ∆PG)(1 - ∆Pcc2)] (1e)
Pb ) Pa(1 - ∆Pcc2)
θ [(1 - ∆Pe)(1 - ∆PG)(1 - ∆Pcc2)] (1f) x
Then,
-1
(1a)
wnet ) wnet(Rankine) + wnet(POGT)
(f + m)CP,gas(T3 - Ta) + (f + 1)CP,gas(Tb - T4) CPT1 (f + m)ηtθ {x - [(1 - ∆Pe)(1 - ∆Pcc1)](1-γ)/γ} + nx (f + 1)ηtθ {x - [(1 - ∆Pe)(1 - ∆Pcc2) × nx (1b) (1 - ∆PG)](1-γ)/γ}
wnet(POGT) ) wt - wc
(
[x(1 - ∆Pc)(γ-1)/γ - 1] + (1 + f)ηeηG
Pd ) Pc(1 - ∆Pe)
)
)
) (1 + f)ηG[θ(1 - ηt) - 0.9] +
P3 ) P2(1 - ∆Pcc1)
wt )
]
x-1 (1d) ηc
ms(h6 - h9) T4 T5 Tc T d ) (1 + f)ηG + mηe CPT1 T1 T1 T1 T1
CP,air CP,gas
Pc ) Pa ) xP1P2
wc )
[
The mass flow rate of the water flowing through the Rankine cycle, relative to the mass of air flowing through the POGT cycle, is obtained from the following equation:
T3 ) Tb
P4 )
1-m [1 - ηc + ηcθ ηc
x(1 - ∆Pe)(γ-1)/γ] + m (θ - 1) -
T1 ) Td ) 0.9T5 x)
{
ηt f(θ - 1) θ(f + m) ηt - [(1 - ∆Pe) × + n n x
(1c)
(1g)
ηI )
wnet q
(1h)
ηII )
wnet a
(1i)
and
where
1496 Energy & Fuels, Vol. 17, No. 6, 2003
a)q-
Mohamed
() ( ) ()
T3 Tb f ln θ f+m ln - m ln n T2 n Ta
Table 1. Ranges of the Controlling Parameters
()
(1 - m) ln )q-
(
)
ηc θ f ln θ - m ln + n (x - 1) + ηc
[
(1 - m) ln
Tb Ta
]
(ηc - 1) + x(1 - ∆Pe)(γ-1)/γ + ηc θ
( ){
ηt f+m ln (1 - ηt) + [(1 - ∆Pe) × n x (1 - ∆Pcc1)](1-γ)/γ
}
2.4. Optimization of the Combined Cycle. The aforementioned relations (eqs 1a-1i) show all the performance characteristics of the combined cycle as functions of the controlling parameters. A systematic optimization procedure (based on partial differentiation and equating to zero, or other conventional optimization gradient methods) for fruitful results is very difficult and cannot lend itself to optimize the performance characteristics without mathematical complications. This is due to the interlaced effects of cycle parameters on its characteristic high nonlinearity in the resulting equations containing the partial derivatives, and their solution leads to a multivalued solution that needs sophisticated subroutines to achieve convergence and avoid rounding and truncation errors. To overcome this difficulty and to meet the goal of locating an objective optimum performance, an alternative optimization method is adopted in the present work and has been programmed based on two statistical tools: a random number generator and Monto Carlo random search. In this method, the widest acceptable ranges for all controlling parameters (given in Table 1) are used in a random number generator. The method is as follows: (1) Pick a random set of values, from which the performance characteristics ηI, ηII, and wnet) for the combined system are calculated. (2) Reject the results if the maximum calculated ηI value is 0.56) from which 139 data points have ηI ) 0.56-0.58. The correlation equations that relate the optimum ηI, ηII, and wnet values of the combined cycle to controlling parameters of the combined cycle are given below. These equations are the result of numerous
trial equations related to these variables, with each trial equation tested and accepted by the statistical standard tests. The total number of data points used in obtaining these equations is 139. All of them have ηI ) 0.56-0.58, with ηII values varying in the range of 0.77-0.8. Table 3 is a reduced version of the statistical results for these equations. The practical benefit of these equations lies in their inclusion in more-detailed and rational design procedures that integrate both the present theoretical analysis and more experimental set points for developing specific combined cycles.
wnet ) 4.044365 -
1.35211 - 0.27272(∆Pcc1 + ∆Pe + ηtηc
∆Pcc2 + ∆PG) + 1.700811(fηG)0.5 + 1.408008m 0.82732ηc (2a)
(
)
1.0 η0.5 t 2.0082 2.700593 + (2b) ηtηc η0.5 c
q ) 0.378702 + 2.336242 m + f0.8 +
Based on statistical measures, the functions of the controlling parameters that greatly affect optimum performance characteristics for the combined cycle are 0.5 (i) m + f0.8 + 1.0/(η0.5 t ), 1.0/(ηtηc), and (fηG) , whereas the other functions of the controlling parameters used in the aforementioned eqs 2a and 2b have a small effect on the optimum performance parameters of the combined cycle. This means the values of the mass fraction of air in the POGT cycle (m), the fuel/air ratio (f), and the efficiencies of the HRSG, compressors, and gas turbines have a dominant effect on the combined cycle performance. The mass fraction of air in the POGT cycle has a dramatic effect on the optimum performance parameters of the combined cycle. Equations 2a and 2b show that the controlling parameter m has a linear effect on the optimum performance parameters, whereas the other controlling parameters have an almost parabolic effect. 4. Conclusions The present paper reveals that the combined-cycle performance characteristics (the first-law efficiency (ηI), the second-law efficiency (ηII), and the net work output of the cycle (wnet)) are dependent on the controlling parameters of the cycle. Under the operating conditions at certain values of the controlling parameters through the present chosen ranges, the following conclusions can be drawn: (1) The values of ηI, ηII, and wnet for the combined cycle reach their peak values and decline with increasing x values. The value of x ) 1.8 corresponds to these peak values for the combined cycle. This means that the
Table 3. Statistical Analyses for the Aforementioned Equations
a
equation number
regression factor, R2
standard error
t-test for equation coefficients, in respective ordera
2a 2b
0.983 0.976
0.012 0.024
19.123, -18.109, -8.077, 32.878, 75.221, -7.474 1.974, 69.026, -35.875, 12.958
Values of the t-test show significant confidence (98% confidence level) in all the calculated coefficients of the equations.
1500 Energy & Fuels, Vol. 17, No. 6, 2003
optimum performance for the combined cycle can be achieved at a value of x related to a pressure compression ratio of 7.8. Consequently, the combined cycle of the Rankine cycle with partial oxidation gas turbine (POGT) cycle can be recommended for use in practical power-generation plants. (2) Correlation equations that have been determined in the paper should provide a good basis for the design process of actual combined-cycle units with the following values: ηI ) 0.56-0.58 and ηII ) 0.77-0.8. (3) The combination of the Rankine bottoming cycle with a simple POGT cycle has achieved a maximum enhancement in wnet of ∼28.76%. (4) Based on statistical measures, the controlling parameters that greatly affect optimum performance for the combined cycle are m, m + f0.8 + 1.0/(η0.5 t ), 1.0/ (ηtηc), and (fηG)0.5. This means the values of the mass fraction of air in the POGT cycle (m), the fuel/air ratio (f), and the efficiencies of the HRSG, compressors, and gas turbines have a dominant effect on the combined cycle performance. (5) The controlling parameter m exhibits a linear effect on the optimum performance parameters, whereas the other controlling parameters have an almost parabolic effect. (6) Finally, note that, without the augmentation of some statistical tools, the present findings could not be obtained. Nomenclature Alphabetic Symbols a CP CP,gas f m ms
available energy input to cycle (dimensionless) specific heat of air at constant pressure specific heat of gas at constant pressure fuel/air mass ratio mass fraction of the air steam-to-air mass ratio
Mohamed n P Pr q T w x
CP/CP,gas pressure pressure ratio for each compressor heat supplied (dimensionless) temperature work (dimensionless) isentropic temperature ratio, T2s/T1 Greek Symbols
η θ
work ratio ratio of specific heats ratio of pressure decrease to entering pressure to cycle unit efficiency maximum-to-minimum cycle temperature ratio
c cc1 cc2 e G gas net s t x o (1,2,..,4) I II
compressor first combustion chamber second combustion chamber economizer heat recovery steam generator gas (combustion) products net work isentropic state turbine exchanger ambient (entry) condition cycle state points (see Figures 1 and 2) first law second law
HE HPC HPT HRSG LHV LPC LPT POGT
heat exchanger high-pressure compressor high-pressure turbine heat recovery steam generator lower heating value low-pressure compressor low-pressure turbine partial oxidation gas turbine
γ ∆
Subscripts
Abbreviations
EF0202743
