1100
I n d . E n g . C h e m . R e s . 1987, 26, 1100-1108
A Thermodynamic Approach to the Design and Synthesis of Plant Utility Systems Chih-Chung Chout and Yen-Shiang Shih* D e p a r t m e n t of Chemical Engineering & Technology, National Taiwan I n s t i t u t e of Technology, Taipei, Taiwan, Republic of China
A systematic, thermodynamically oriented method for design and synthesis of plant utility systems is proposed. Heat requirements are satisfied in preference to power requirements. Taking a combined gassteam cycle as the most complex plant utility system, several significant new findings are obtained: 1. T h e thermal efficiency of a gas turbine cycle can be a function of heat input ratio exclusively. 2. A reheating steam cycle may not improve the overall thermal efficiency. 3. T h e improvement of overall thermal efficiency due to regenerative heating of the feedwater will be effective only when the thermal efficiency of steam generator is greater than the overall thermal efficiency. Systems can be constructed by taking all constraints into account to get the best maximum overall thermal efficiency design reachable. A case study is illustrated to describe this method. The effectiveness of an energy conservation effort would eventually depend upon the design of a plant’s utility system. The final objective of energy utilization improvement is to reduce the purchase of outside energy sources. A good design of a plant utility system should be able to match the plant’s heat and power variations and keep its operation always a t the highest thermal efficiency. There is little discussion in the literature concerning how to systematically design a good plant utility system. A more fundamental study of the system’s intrinsic properties is therefore required. Mathematical optimization methods, such as linear programming (Petroulas and Reklaitis, 1984; Nishio and Johnson, 1977) and mixed-integer linear programming (Papoulias and Grossmann, 1983))have been proposed for utility system design. Although a suitable formulation of the mathematical representation of a system can easily solve the problem, the usefulness of these approaches is detracted by the heavy dependence on mathematical calculations. Moreover, they are not powerful enough to increase essential understanding of the characteristics of solution. In addition, an inappropriate objective function may hinder the desired real solution, and the final unique numerical optimal solution of LP and MILP methods is generally not convincing enough in engineering practice. Nishio et al. (1984) have modified the above method with a decision tree to determine system structure in the solution space; however, this modification is still seriously constrained by the number of variables. To overcome these drawbacks, a solution procedure based on the thermodynamic analysis will be taken up here. Nishio et al. (1980) have proposed a similar approach to this problem. Although a useful strategy for the system design was constructed on the basis of systematic use of heuristic rules derived to decrease the loss of available energy as much as possible, this method still limits its discussion to the steam cycles. No fundamental treatment between steam cycles and gas turbine cycles has been given. In this paper, the design and synthesis problems will be concerned with steam cycles and simple and regenerative gas turbine cycles, as well as combined gas-steam cycles. The major difference between simple and regenerative gas turbine cycles is addition of a recuperator for heat ex-
* T o whom
correspondence should be addressed. Fountain Process Consultants Center, Fountain Company, P.O. Box 180, Taipei, Taiwan, Republic of China.
0888-5885/87/2626-1100$01.50/0
Table 1. P / H Characteristics utility system
PIH ratio
steam cycles simple gas turbine cycles regenerative gas turbine cycles combined gas-steam cycles
0.2 0.65 0.85 1.1
change between the turbine outlet and compressor outlet in latter cases. Brown (1982) has indicated that each utility system may be characterized by the power-to-process heat ratio, PIH. This ratio depends weakly upon the fuel type used. For general industrial plants, the required PIH ratio is below 0.2. Table I shows the ratio corresponding to each utility system. These ratios indicate that the most complex plant utility system will be the combined gas-steam cycle. In this study, the design and synthesis problem is to find a system that satisfies the plant’s heat and power requirements, subject to minimum energy consumption and capital investment. The power-to-process heat ratio for the plant will be designed at a specified value; i.e., heat and power requirements are matched exactly. The energy consumption is defined by the net fuel heat input. Since the energy cost of a utility system is an overwhelming factor in each year’s cost contribution analysis, no exact value of capital costs will be evaluated but the major equipment is taken into account and kept to a minimum. This strategy has been applied successfully in heat-exchanger network design (Linnhoff and Turner, 1981). According to this strategy, the importance of a numerical optimal value should not be overestimated so that significant new insight can be uncovered.
Thermodynamic Analysis of a Generalized Utility System Heat and power are of different energy qualities. They can, however, be regarded as the same if discussion and consideration are constrained to the first law of thermodynamics. Irregardless of how the first law and the second law are applied, the primary concern in design is to minimize the external energy input. An overall thermodynamic efficiency concept is desired in the energy system design. The overall thermodynamic efficiency of a utility system can be defined by W+AH, 170 = (1)
Q,,
0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1101 17p
Wto,
+
Wbot
Qbot
+
Wtop
=
Applying the general definition of cycle efficiency to the bottoming and topping cycles, cycle
(9) Supplementa fuel
and
+Q-Lk-
C.W.
WbP
Steam Rankine cycle
7ltop
Qtop
Figure 1. Typical simplified combined gas-steam cycle.
where AHs is the process heat required, W is the work generated (work is equivalent to the word upowern used in the preceding section), and Qh is the net fuel heat input. In this paper, we consider the combined gas-steam cycle shown in Figure 1,as the most complex plant utility system. Supposing that a steam cycle (also termed the bottoming cycle in a combined system) is evolved first to satisfy the process heat required; then, based on the given initial steam pressure and temperature levels a t the specified steam flow rate, the net heat input to the steam cycle, Qbt, and the corresponding work produced, Wbot, are calculable. The deficient work then is made up by the gas turbine cycle (the topping cycle). By Figure 1, if the heat exhausted by the gas turbine is fully recovered by the steam generator and the stack loss is lumped with Qbt,the energy balance around the steam generator can be described as Qbot
=
(Qtop
-
Wtop)
+ &sup
(2)
where Qtop is the net fuel heat input to the gas turbine combustor, and Qsupis the net supplementary fuel heat input to the steam generator. The overall net fuel heat input to the system is given by =
Qin
Qtop
+ Qsup
=-
(3)
where qbot and qtop are the bottoming and topping cycle efficiencies, respectively. After some lengthy derivation, eq 8 becomes
Qsup
+
Qprs
r
This equation expresses qp in terms of qtop, qbot, and heat input ratio, (Qsup Qprs)/Qtop. There is no constraint involved for the design of the topping and bottoming cycles during the derivation of eq 11. Both qtop and qbot are the resulting lumped values corresponding to each cycle. Furthermore, the ratio Qsup/Qto can be approximated by a temperature difference ratio, fT5- T4)/ ( T3- T2),in the preliminary design (Chou and Shih, 1987), where T5, T4, T3,and T , are the flame temperature to the steam generator, the gas turbine’s outlet and inlet temperatures, and the compressor outlet temperature, respectively. Equation 11 can be rearranged to
+
W is the sum of work produced by the gas turbine cycle, W, and work produced by the steam cycle, Wbv If these equivalences are sustituted into eq 1and by the relation of eq 2, eq 1 becomes
This equation states that the value of qo is fixed if the bottoming cycle has been designed first. Note that here the bottoming cycle can be either a steam cycle or a typical steam boiler with Wbt being zero. Equation 4 is also valid when steam used within the utility system is generated partly by the process heat or waste heat in a processing system. Now Qbot
=
Qblr
Qprs
(5)
where Qblr
=
(Qtop
-
Wtop)
+ QSUp
(6)
and Qpr8 denotes the net heat supplied by the processing system. Note that Qblris the net heat input to the steam generator. The overall net heat input is then given by Qin
=
Qtop
+
Qsup
+
Qprs
(7)
Supposing that only the work generation in a combined gasateam cycle is concerned; the overall thermal efficiency is given by
If a steam cycle has already been designed, then qp and qbot will be known, and qtop becomes a function of the heat input ratio only. The value of qtop, which is a performance specification for the gas turbine cycle, can be decided from variation of the heat input ratio. Therefore, this equation provides a fundamental design relationship between the topping cycle and bottoming cycle in a generalized utility system. From the above discussion, the most complex plant utility system can be divided into the design of steam cycle and the gas turbine cycle. Before discussing design methodology for the whole system, an arrangement analysis of the steam turbine configuration, which is helpful in further discussion, is given.
Driver Arrangement Analysis Figure 2 shows that the general condensing and noncondensing turbine arrangements (Polimeros, 1981) in a steam cycle can be decomposed into the corresponding basic components: typical turbine units, splitters, mixers, and heat exchangers (or heaters). Such a decomposition will provide the basis for the combination study. If there is no condensate in the extraction stream, then both the right-hand side and the left-hand side units of Figure 2
1102 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Type
Practical desiqn
a ) Straight Condensing
4
Component analysis
A
q*
C’
4
B
C (a!
b)Single extraction condensing
c) Double ex t roc t io n condensing
-
I
S
d) Feedwater heating ext mct ion or bleeder condensing
( C !
t
t
t
t
Figure 3. Combination study of extraction stream with condensate.
by a small increase in steam inlet flow rate. e) Mixed-pressure condensing
f ) Extmtion induction
condensing
g ) Low pressure condensing
i
i)Topping or back-pressure non -condensing
t;
ti
Figure 2. Decomposition analysis of the practical turbine arrangements.
will be theoretically equivalent. This is true even if the right-hand units have different isentropic turbine efficiencies. Care should be taken when there is condensate in the extraction stream. Taking a single extraction condensing system as an example, Figure 3a can be inferred from Figure 3b. However, as shown in the T-S diagram, Figure 3c, the final outlet state from the single arrangement is at point C , while that of Figure 3b is at point C’. A higher thermal efficiency would be obtained from Figure 3b. This means that, when combining Figure 3b into Figure 3a, there may be lower work generation. This can be refined through a change in the turbine’s isentropic efficiency specification in practical design or compensated
Design Methodology (i) Design Philosophy. Contrary to general practice, this method proposes that the process heat requirement is satisfied first. This is particularly desirable to those industries that use a very large amount of thermal energy such as the pulp and paper, the petrochemical, the metals, and the food processing industries. The steam cycle should be designed first so that the steam required will be supplied from noncondensing turbines, Le., back-pressure steam turbines. Note that the process heat required is typically from saturated steam. The deficient work requirement is best fulfilled by a gas turbine cycle. The energy and availability analysis of a simple steam cycle (El-Masri and Magnusson, 1984) reveals that most of the energy losses are due to the condenser and the stack, while the availability losses are caused mainly by combustion and heat transfer. This result suggests that, to achieve the highest overall thermal efficiency, heat transfer to the condenser and superheating the steam in the steam generator should be kept to a minimum. The priority of turbines is considered in the synthesis stage. Back-pressure steam turbines are applied first with the exhaust steam for process use in a steam cycle. Condensing turbines are taken into account only if there is a lot of excess steam or excess steam is generated by processing systems. A reheat cycle may not have a higher overall thermal efficiency as compared to a typical Rankine cycle. In a reheat cycle, steam is first expanded to some intermediate pressure in the turbine and is then reheated in the boiler after which it expands in the turbine to the exhaust pressure. A reheat cycle can raise the overall thermal efficiency only if the thermal efficiency contributed by the reheat part is greater than that of the other remaining parts, as shown in Appendix A. The required large heat-exchange area and the increased complexity in system design detracts from the gain in efficiency due to reheating. This means that if the steam that goes to the condensing turbine is just a small fraction of the total amount, there is no need to design a reheat cycle. The reheat cycle, therefore, will be of interest to power plant design only when a lot of heat is exhausted to cooling water.
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1103 One important factor that can improve the overall thermal efficiency is the installation of feedwater heaters which use extracted steam. The installation of feedwater heaters does improve the overall thermal efficiency when the thermal efficiency of steam generator is higher than the overall thermal efficiency, as shown in Appendix B. However, this increase is very limited; the efficiency rises only for low feedwater regeneration degree (Cerri and Colag6,1985),because large excess steam decreases overall thermal efficiency. The regeneration degree is defined as the ratio between the feedwater enthalpy rise due to regeneration and the feedwater enthalpy difference between the boiler saturation and the condenser extraction pump outlet. The design of a gas turbine cycle is mainly characterized by the given specifications of cycle efficiency, qtop,specific work output, and turbine inlet temperature. Cohen et al. (1972) give background and a description of the design method for this type of cycle. (ii) Estimation of Initial Steam Conditions. One of the major problems in steam cycle design is the selection of initial steam conditions. This selection strongly affects the capital cost, the operating costs, and the work production capacity of a utility system. We propose a method to estimate the initial steam temperature at any specified initial steam pressure from the given process heat conditions and turbine design constraints. These initial steam conditions are then used for optimal selection for minimum energy consumption. To find the initial steam header list quickly, we assume that the superheated steam can be treated, approximately, as an ideal gas because of its high critical pressure. The deviation will become significant when the pressure is high, P, > 0.25, and temperature is low, T , < 0.75. In most of the utility plants we encountered, the compressibility of steam used is higher than 0.8. This deviation can be expressed by the following example. Suppose that the initial state of steam is at 4.137 MPa and 371.3 "C. If it is expanded to 1.379 MPa in adiabatic and reversible conditions, the estimated temperature by the ideal gas law is a t 227 "C, while the temperature from the steam table is 221.4 "C. An error of 1.1%results, which is generally within a tolerable range in preliminary estimation. The relationship between the steam turbine outlet state and its inlet state can be derived based on the ideal gas behavior and by taking the turbine isentropic efficiency as a parameter. For an isentropic expansion system, the temperature and pressure relation can be expressed by
where y is the ratio of specific heats. For steam, y can be taken to be 1.3 in the preliminary estimation. The isentropic efficiency of a steam turbine is defined by hl - h2 (14) 9s = If the specific heat of steam is taken as a constant for the superheated steam passing through the turbine without condensing, eq 14 can be expressed approximately further by
For a steam turbine, if P I , T,, and P2, are given, then
The errors of this relationship are caused by the assumptions of the ideal gas equation of state, constant specific heat, and constant ratio of specific heats. Since this relationship's validity is limited to the vapor phase, eq 16 cannot be applied when the turbine outlet state is in the two-phase region. If the predicted outlet temperature is lower than the saturated temperature, the outlet state is in the two-phase region. The error will be larger when the outlet state is near saturation. To estimate the initial steam temperature at the specified initial pressure, we use eq 16 to get the initial value. From the required process steam conditions, PZsand T2 are the desired process steam pressure and temperature and qs is an assumed constant. If the initial steam pressure, P,, is given, then the initial temperature, T,, is calculated by eq 16. For cycle mass and energy balance calculations, this temperature is adjusted by using the steam table in a manner of finite increment so that the outlet of each turbine with the same steam inlet meets the design requirements, e.g., the steam quality in the outlet isn't less than 0.90, and has the minimum superheated temperature. In this way we can calculate a corresponding initial steam temperature which yields minimum superheating for each specified initial steam pressure. (iii) Design Strategy. The proposed method for the design and synthesis of a plant utility system consists of the following five steps. 1. The possible utility systems is screened by the characteristic value of P / H ratio. 2. The number of drivers is specified, i.e., the number of turbine drivers and electric motors. Turbine driver denotes the turbine machine, which may be a single extraction condensing, a double extraction condensing,or any other type of turbine machine. No generalized rule can be applied for the selection of drivers. The selection depends on the operational philosophy as well as the process requirements on a case by case basis (Peterson and Mann, 1985). 3. The preliminary configuration is set up. The initial structure is evolved according to the design philosophy discussed in the preceding section. This includes the following: (1) back-pressure steam turbines are chosen first; straight condensing turbines are chosen last. Turbines are shown in typical units, and no combination is allowed. (2) A reheating design is deleted unless there is a great amount of heat rejected to cooling water or its equivalent. (3) Regenerative heating of the feedwater is deferred until the heat recovery design or thermal efficiency enhancement is considered. 4. The appropriate initial steam headers are found by the procedure described in the preceding section. The material and energy balances of the initial flow sheet for each initial steam header with different steam flow rate are solved. Selection of the most appropriate initial steam header is based on energy consumption and capital costs as well as design constraints. 5. The system's configuration is rearranged so that the requisite number of driver units is met and that the heat recovery design is fully exploited or that the thermal efficiency enhancement design is employed. The major calculations in step 4 are further illustrated in Figure 4. The bottoming cycle may be a steam cycle or a steam boiler only, depending on the PIH ratio. The topping cycle is mainly a gas turbine cycle. The three constraints, cycle efficiency, heat input ratio, and flame temperature, are detected in sequence. The topping cycle efficiency is calculated from eq 12. Since Qprsis a known value from the problem definition,
1104 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 I . Based on the given initial steam header, solve the material ond energy balances for the initial structure w i t h a specified steam flowmte
I
2,Calculate the work produced and the t h e r m a l efficiency of the bottoming c y c l e , ) j b o t ,
I
3 . is a topping cycle necessory?NLPrint the results.
Iyf i
L,lterate the topping cycle efficiency by varying the heat input ratio. I 1 1 . Efficiency
-constraint algorithm
I
1
.-
0. Set 'heal input ratio=maximum value.
5.1s the maximum c y c l e e f f r c i e w y
I
met
I
t
constraint
No
Yes 6. Is the maximum heat ,input ratio constmint met?
IN. 1".
7, Is the maximum flame temperature o f Tempemture steam generator met 7 I 2.con st ra i n t algorithm
Re-calculate the topping cycle e'ticiency.
-
0.
Go to step 4
1
J
9.Calculate the preliminary dtsign o f the gas turbine c y c l e .
1
Table 11. System Requirements and the Associated Assumptions shaft work (MW) required with each unit: 18.64, 11.19, 10.44, 5.97, and 3.73 process heat requirements: 158.76 X lo3 kg/h a t 2.10 MPa and 215.2 "C 90.72 X lo3 kg/h a t 0.377 MPa and 141.9 "C assumptions: 1. The ambient state is a t 27 "C, sea level. 2. An excess of 10% steam flow rate is required a t minimum, based on consideration of boiler water blowdown, process leaks, and variations of heat load. 3. Steam turbine efficiencies are specified a t 80%. 4. The isentropic efficiency of gas turbine is at 87% and the corresponding compressor a t 85%. 5. The straight condensing turbines will exhaust to 13.5 kPa (Le., 4-in. abs.). 6. Maximum flame temperature in the steam generator is set a t 2000 "C; the flue gas temperature is presumed a t 177 "C (350 "F). Maximum gas turbine cycle = 25%. Maximum heat input ratio = 2.4. 7. The gas turbine combustor is full combustion, and its outlet is set a t 927 "C (1200 K). Pressure and heat losses within the system are neglected. 8. A minimum steam quality of 90% will be specified in the turbine outlet.
Print the results.
Figure 4. General calculation procedure for step 4.
different values of qtop are obtainable from iterations of heat input ratio, (Qsup + Qprs)/Qtop. Finally, the flame temperature, T5,of the steam generator can be estimated by T4+ (T3- Tz)(Qsup/Qtop). This is used for calculating the steam generator efficiency as described below. In the final design, the exact flame temperature should be calculated from the energy balance of the steam generator. When the net heat input to the bottoming cycle, Qbot, is to be calculated, the thermal efficiency of the steam generator must be known in advance. The initial assumed value is then modified by "
1
receiver
f
i
1
1
1
J
L W
Condensate return ' 5 8 8 Condenrote returP
907
Figure 5. Proposed initial flow sheet. The numbers shown on the figure are the fluid flow rate in lo3 kg/h.
estimated from the change of Equation 17 is derived by the definition that heat is recovered from the combustion gases with respect to the theoretically recoverable overall heat from the combustion gases. It is assumed that the specific heat of the combustion gases is constant in the applied temperature range. The flue gas temperature, Tg, is specified according to the fuel fired. The maximum cycle efficiency constraint and the maximum flame temperature constraint algorithms are illustrated in Appendix C. The maximum heat input ratio, Qsup/Qtop,is defined as the ratio of net fuel heat released by the supplementary fuel to the net fuel heat released by the fuel burnt in the gas turbine combustor. This is discussed further by Chou and Shih (1987). The maximum gas turbine cycle efficiency constraint can be regarded as a lumped design parameter for feasible gas turbine cycle design. As seen from eq 8, the overall net fuel heat input to the system is not necessarily affected by this constraint. qp will be fixed if the bottoming cycle has been designed. This implies that the overall net fuel heat input to the system is fixed irregardless of which vtop is applied. However, the value of vtopwill change the heat input ratio, as can be observed by eq 12. This means that the overall energy cost will be affected if different fuel types with different cost per unit of fuel heating value are used for the toping and bottoming cycles. If the thermal efficiency of the steam generator is changed by gas turbine exhaust, the effect on overall net fuel heat input can be
e-----------Q--l i
I
Qbot.
Case Study Application of the proposed method to design and synthesis of plant utility systems is illustrated with a typical example. Table I1 shows the system's requirements and the associated assumptions. A little adaptation in assumptions from the original source (Bloch, 1982) is taken for simplification in explanation. The P / H ratio of 0.3654 for this case is much higher than the characteristic value of steam cycles, so a combined gas-steam cycle is used. Since five shaft units are required, the use of a combined gas-steam cycle would be much more appropriate than a simple or regenerative gas turbine cycle. According to the problem requirements, five units of different shaft work are to be matched for the work suppliers, turbines in this case. Since there is a compressor in the gas turbine cycle, the total number of shafts is six. If any two shafts can be in tandem, it is possible to pair these six shafts with three turbines under some conditions. That is to say, the target minimum number of turbine machines is three. I. Setup of the Preliminary Configuration. Figure 5 shows the proposed initial flow sheet as evolved from the design philosophy. A simple gas turbine cycle is applied which will be explained further in the discussion. The outlet status of the first two steam turbines is used for supplying the process heat requirements. All excess steam will go to the exhaust condensing turbine for work gen-
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1105 Table 111. Steam Headers Estimated Using turbine inlet pres, MPa temw "C outiet temp, oc of turbine 1 (2.10 MPa) outlet temp, "C of turbine 2 (377 kPa) outlet temp, "C of turbine 3 (13.5 kPa)
Equation 16 and the Corresponding Revised Value by Steam Table" 3.55 4.24 4.93 5.62 5.96 6.31 371 399 413 427 427 441 307 314 319 315 314 313 308 303 307 315 310 310 212.4 220.7 238.9 151.7 185.4 110.3 167 163 166 168 166 162 149 153 154 158 155 153 496.4 515.4 490.8 437.1 466.1 395.4 52* 52* 52* 52* 52* 52* 52 52 52 52 52 52 881.8 885.3 904.8 831.8 858.8 790.1 0.903 0.906 0.908 0.906 0.906 0.904
7.00 455 314 307 262.6 169 154 538.2 52* 52 926.9 0.907
"E = estimated value; R = revised value; AH = enthalpy change, kJ/kg; x = steam quality; * = in the two-phase region.
eration. The deficient work over the steam cycle will be made up by the gas turbine cycle. The design of the deaerator and condensate receiver are preliminarily treated as a lumped block. g 11. Estimation of the Appropriate; InitialO Steam Conditions. The initial steam headers are selected such that each turbine's outlet state is as close as possible t o the corresponding process heat's state. If, for example, an initial steam pressure of 3.55 MPa (500 psig) is selected, then to have the first turbine's outlet state at P,, = 2.10 MPa and T 2 = 215.2 "C, the estimated initial steam temperature, by eq 16, is 264.2 "C (507.6 O F ) . Similarly, the initial steam temperature is estimated to be 350.5 "C (662.3 OF) to satisfy the second turbine's outlet state, P2, = 0.377 MPa and T2= 141.9 "C. If we apply this temperature for the condensing turbine calculations with the use of steam table, the outlet steam quality will be less than 0.90, which is unsatisfactory for the turbine's specification. Hence, the temperature must be adjusted. Note that in the following, all the calculations use the steam table. After a few trials, the final approximate minimum initial steam temperature is 371 "C (700 OF). The corresponding first and second steam turbine outlet temperatures are 310 and 153 "C, respectively. If they are estimated by eq 16, their values will be 313 and 162 "C, which are very close to the values calculated above. This result shows that eq 16 can generally be used for quick estimation. The condensing turbine outlet is in the two-phase region and has a steam quality of 0.904, which is satisfiable for the turbine's specification. All of the above calculated values are shown in the first column of Table 111. Table I11 shows the chosen initial steam pressures and the corresponding estimated initial temperatures as well as other data. ,111. Summary of the Calculated Results. (i) Define the steam flow rate. Figure 6 shows that for any given initial steam header, the overall thermal efficiency decreases with an increase of SR. SR is the steam flow rate ratio of the applied steam flow rate to the minimum steam flow rate required. The minimum flow rate is the sum of the process heat requirements without boiler water blowdown, process leaks, etc. The material and energy balances can be solved by the equation-solving method described in Westerberg et al. (1979). The falloff of the higher steam headers curves as SR increases is due to the fact that the maximum flame temperature constraint in the steam generator is met, which causes a great decrease in the gas turbine cycle efficiency. Therefore, much of the heat from the gas turbine exhaust must be rejected to the surroundings, resulting in a decrease in the overall thermal efficiency. To get the highest thermal efficiency, the minimum allowable SR should be used. In this case, it should be specified a t 1.10 by problem requirements. (ii) Choose the appropriate candidate initial steam conditions. Figure 7 shows that there is a valley on the
'
O
1.0
1.05
1.10
1.15
1.20
1.25
SR
Figure 6.
qa vs.
SR.
4.0
5.0 Pressure
6.0
7.0
(MP,1
Figure 7. Energy consumption for different steam heads with SR a t 1.10.
energy consumption curve. The curve rises again after passing the minimum point. This phenomena is caused by the same reasons as described above. Based on the desire of minimum energy consumption, the initial header of 5.96 MPa and 427 "C should be chosen. IV. Rearrangement of the System's Configuration. (i) Redistribute the turbine shaft work. Figure 5 presents the material and energy balance data and the operating conditions for the initial steam header. The work produced from each turbine is very different from the required shaft work. This calls for a redistribution of the work production so that it can fulfill the shaft work requirement's distribution. A combination study of the turbine units, as described in the Driver Arrangement Analysis section, will be employed here. Pairing of the shaft work with the turbine generated work can generally be described as a general mathematic permutations and combinations problem. However, this
1106 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Combination set
Pairing problem to be studied
i
Gas
By r u l e 1
P re Ii m im r y configuration 1
\rule
2b
problem is easily solved by the use of system’s characteristics. The designer has the freedom to decompose the work generated by the straight condensing turbine into several parts and then merge them into a general backpressure noncondensing turbine at will. This will result in a change of turbine type, for example, from a backpressure noncondensing turbine to a single extraction condensing type. The final objective of the pairing study is to find a combination set such that the capital target is satisfied but the energy penality will be minimum. The following sequences are proposed as a simple guideline for the study of pairing. Rule 1: match the back-pressure noncondensing types. Rule 2a: match the single extraction condensing types. Rule 2b: match the double extraction condensing types. Figure 8 illustrates the application of these rules. As shown on Figure 5, the generated work values, 18.59, 8.77, 12.41, and 10.2 MW, are matched with the required shaft work. Any two shafts can be put in tandem which is driven by a single turbine machine. By rule 1, the pairing of 18.64 with 18.59 MW can be taken as a “tolerable” match, so they are fixed as a pair. No other choice for the remaining units can be applied by using rule 1. Applying rule 2a, the problem can be illustrated with the following algebraic expressions: a+x=A a=8.77
+y =B x +y = c
Single steam extmct ion condensing turbine
+m
Single steam extract ion Condensing turbine
+@
Prelimimry configuration 2
Figure 8. Application procedure of synthesis rules.
b
turbine
turbine
R e m i n i n g units t o be further explored By rule/
Tarqet
b = 12.41
I
L
I
10.44
I
11.19
Supplementary
L
/condensate receiver
b ’-
Figure 9. Preliminary system structure from the combination set 3.
’
10.05MW
(18)
YTI
c = 10.15
where x > 0 and y > 0 and where a and b represent the work generated corresponding to the two noncondensing back-pressure turbines; x and y are the work fractions of the condensing turbine, which are to be merged into a noncondensing back-pressure turbines; c is the work remaining in the condensing turbine after sharing its partial work to the gas turbine, that is, c = 10.2 - (18.64 - 18.59); A and B are the sum of any two of the following shaft works, 10.44, 5.97, 11.19, and 3.73 MW. Table IV shows that there are five possible combination sets. This gives the designer more choice. The resulting system structure from combination set 3 is shown in Figure 9. The small turbine unit (i.e., 0.05 MW) can be eliminated completely from the system. Finally, by rule 2b, there is only one possible structure, shown in Figure 10. Figures 9 and 10 show that there are four turbine machines if all the designs are kept at minimum net fuel heat input. (ii) Refine the preliminary structure. Figure 9 is refined to demonstrate a complete system structure. The small turbine unit is eliminated first, and resulting work deficient is compensated by adjusting the design of the gas turbine cycle, which causes a small increase in the net fuel heat input to the gas turbine combustor. The excess steam, which does not produce work, is directly used for another purpose, e.g., feedwater deaerating or heating. The resulting refined configuration of Figure 9 is shown in Figure 11. The temperature of the water leaving the condensate
I
I
I
condenmte condensate
’r
Figure 10. Preliminary structure with the double extraction turbine. Flue Fuel,74,57w
1
was
177’c
J l receiver
Figure 11. Final preliminary configuration. The numbers shown on the figure are the fluid flow rate in lo3 kg/h.
receiver is fixed in the recalculations. This assumption is arbitrary in this study because the block of the deaerator
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1107 Table IV. Combination of A and B A B 10.44 + 5.97 1 11.19 + 3.73 3.73 + 10.44 2 11.19 + 5.97 3 10.44 5.97 11.19 3.73 4 3.73 + 5.97 11.19 + 10.44 5 3.73 + 10.44 11.19 + 5.97
+
+
X
Y
6.15 8.39 7.64 0.93 5.40
4.00 1.76 2.51 9.22 4.75
and condensate receiver in the flow sheet is treated as a blackbox. The new balance data and fuel consumption are shown on Figure 11. The increase in fuel consumption for the gas turbine cycle is 0.2 MW. The overall net fuel heat input is decreased by 0.05 MW because of a resulting 0.25 MW decrease in supplementary net fuel heat input. This is because the thermal efficiency of the steam generator, 0.922, is higher than the overall thermal efficiency, 0.82, so that installation of a feedwater heater reduces the overall net fuel heat input. A small increase in steam flow rate for feedwater regeneration can be employed, but this is not implemented in this work. This minor modification implies that little saving in net fuel heat input can be made. The configuration employs three turbines for work generation and requires 227.7 MW of net fuel heat input (LHV). This shows much improvement in energy consumption and capital investment as compared to the original source, where there are four turbine machines that require 299.82 MW of fuel beat input (HHV). However, because many important data, such as turbine efficiencies and flue gas temperature, are not shown in the original source, a rigorous comparison of the final numerical data cannot be made.
Discussion Throughout this study, we assumed that the steam turbine efficiencies were all the same. This may not be true in practice. Variations in turbine efficiencies are expected and can be accommodated in the final revision. In this case study, the topping cycle structure was confined to a simple gas turbine cycle. However, a regenerative gas turbine cycle should be taken into account if the fuel cost ratio between the topping and bottoming cycles is high. This will increase the capital investment, but the decrease in fuel cost rapidly recovers this capital cost difference. Since the net fuel heat input to the gas turbine cycle is reduced, the supplementary net fuel heat input must be increased, i.e., the ratio of Qsup/Qtopis increased. The effect on the overall thermal efficiency due to the increase in the initial steam temperature was also examined. Figure 12 shows that the higher the temperature of a given initial steam header, the lower the overall thermal efficiency will be because more heat is rejected to the cooling water and more water for desuperheating is required for the turbine outlet, which causes work loss.
Conclusions
A systematic procedure for the design and synthesis of plant utility systems for getting the maximum allowable overall thermal efficiency is shown. The final system configuration can be easily adapted according to the plant’s requirements or equipment constraints. This method not only provides a better understanding to the problem’s characteristics, but it also simplifies the calculations.
P=5.96MPo
I
I
I 1,05
1.10
1.15
1.20
1.25
SR Figure 12. Effect of header temperature on the overall thermal efficiency for Figure 5.
Nomenclature C, = mean specific heat at constant pressure h = specific enthalpy of the working fluid HHV = higher heating value of a fuel LHV = lower (or net) heating value of a fuel mair= mass of air P = pressure
P / H = power-to-process heat ratio Q = net fuel heat input r = compression ratio SR = steam flow rate ratio T = temperature W = work Greek Symbols 7 = efficiency AH = process heat AT- = heat-transfer pinch temperature difference in a steam generator y = ratio of specific heats Subscripts 1 = general input or air inlet to the gas turbine compressor 2 = general output or the gas turbine compressor outlet 2s = isentropic output 3 = gas turbine combustor outlet 4 = gas turbine outlet 5 = flame temperature of the steam generator, eq 17 9 = temperature of the flue gas, eq 17 a = air blr = boiler or steam generator bot = bottoming cycle c = compressor g = combustion gases in = input o = overall p = work generation prs = process r = reduced property of steam or parts that are concerned with reheating only, eq A5 s = isentropic system or process steam requirement sf = steam for feedwater heating sr = steam that is related to the design of reheat sup = supplementary fuel t = gas turbine top = topping cycle Superscript ’ = other parts except those related to the reheating parts, eq A5
Appendix A For a reheat steam cycle, the overall thermal efficiency can be expressed by
1108 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
where
w = W’+ w, AHs = AH: + AH,,
(A21
Q = Q’+ Q,
(A4)
Here the variables with primes denote the original typical steam cycle, and the variables with subscripts, r, are related to the parts with reheating. Define W’+ AH’s q’ = (A51
Q’
7’ and q, are the thermal efficiencies of the original steam cycle and the parts which are concerned with reheat, respectively. Then the following relation can be easily derived
From the above equation, qo/q’ > 1 exists if qr > q‘ is satisfied. Note also that in eq A6, AHs, = 0 generally, and q’ can be in the range from 0.7 to 0.85 typically. The condition of q, > q’ is seldom met. The turbine efficiency and the thermal efficiency of steam generator are the two major factors which affect qr. Suppose that their efficiencies are 0.7 and 0.9, respectively. Their product value of 0.63 is still smaller than 0.7. However, this product value is much higher than the thermal efficiency of a general power plant, which has an efficiency around 0.40. One condition that will make the possibility become positive is that q’ is low, which can be referred to the case with a lot of thermal energy rejected to the cooling water.
Appendix B Suppose that there is an extra steam, AHsf,for regeneration of feedwater heating; the effect on overall thermal efficiency can be expressed by w t o p + Wbot + SS + msf 77”’ = (B1) Qbot
To have
qo’/qo
4-
(5)
> 1, it requires that
T2 -
(-43)
+
wt~p
Vb],
> qo.
Appendix C Computational Algorithm. For the preliminary design of a simple gas turbine cycle, the following equations can
Vtop
Cpg(T3 - T,) -
- Cpa(T2
Cpg(T3- T J
-
Tad (C5)
where ya/(ya - 1) = 3.5 for air, yg/(yg- 1) = 4.0 for combustion gases generally, Cpa = 1.0042 kJ/(kg “C), and Cpg = 1.1464 kJ/(kg OC). The maximum cycle efficiency constraint algorithm is used to solve the compression ratio, r, subject to the specified cycle efficiency. The calculation sequences are listed as follows: 1. Estimate r (e.g., r = 1.05) initially. 2. Calculate T2by eq C3. 3. Calculate T4 by eq C4. 4. Calculate cycle efficiency by eq C5. 5. If the efficiency difference with the maximum constraint is within the tolerance, then stop. 6. If the cycle efficiency calculated is less than the maximum value, then increase the value of r , and go to step 2; otherwise, decrease the increment. The maximum flame temperature constraint algorithm is devised to solve the compression ratio, r, subject to the specified flame temperature. The algorithm is described as follows: 1. Estimate r (e.g., r = 1.05) initially. 2. Calculate T2 by eq C3. 3. Calculate T, by eq C4. 4. Calculate cycle efficiency by eq C5. 5. Calculate Qsup/Qtop by eq 12. 6. Estimate flame temperature by T4 + (T3Tz)(Qsup/Qmp).7. If the temperature difference with the maximum constraint is within the tolerance, then stop. 8. If the temperature estimated is less than the maximum value, then increase the guess of r, and go to step 2; otherwise, decrease the increment.
Literature Cited Bloch, H. P. Compressors and Expanders: Selection and Application for the Process Industry; Marcel Dekker: New York, 1982. Brown, D. H. I E E E Trans. Power A p p . Syst. 1982, 10l(8), 2597. Cerri, G.; Colag6, A. J . Eng. Gas Turbines Power 1985, 107, 574. Chou, C. C.; Shih, Y. S. Int J . Energy Res. 1987, in press. Cohen, H.; Rogers, G. F. C.; Saravanamuttoo, H. I. H. Gas Turbine Theory, 2nd ed.; Wiley: New York, 1972; Chapter 2. El-Masri, M. A,; Magnusson, J. H. J . Eng. Gas Turbines Power 1984, 106, 743. Linnhoff, B.; Turner, J. A. Chem. Eng. 1981, 88(22), 56. Nishio, M.; Johnson, A. I. Chem. Eng. Prog. 1977, 73(1), 73. Nishio, M.; Itoh, J.; Shiroko, K.; Umeda, T. Ind. Eng. Chem. Process Des. Deu. 1980, 19, 306. Nishio, M.; Koshijima, I.; Shiroko, K.; Umeda, T. Ind. Eng. Chem. Process Des. Deu. 1984, 23, 450. Papoulias, S . A.; Grossmann, I. E. Comput. Chem. Eng. 1983, 7(6), 695. Peterson, J. F.; Mann, W. L. Chem. Eng. 1985, 92(21), 62. Petroulas, T.; Reklaitis, G. V. AIChE J . 1984, 30(1), 69. Polimeros, G. Energy Cogeneration Handbook; Industrial Press: New York, 1981. Westerberg, A. W.; Hutchison, H. P.; Motard, R. L.; Winter, P. Process Flowsheeting; Cambridge: London, 1979.
Received for review March 7 , 1986 Revised manuscript receiued September 18, 1986 Accepted March 4,1987
