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Adaptive simulation of boiler unit performance
PII:
Energy Convers. Mgmt Vol. 39, No. 13, pp. 1383±1394, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0196-8904(98)00021-1 0196-8904/98 $19.00 + 0.00
ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE ZHONGSHENG NIU and KAU-FUI V. WONG Mechanical Engineering Department, University of Miami, Coral Gables, FL 33124, USA (Received 9 May 1997) AbstractÐIndustrial boilers of a particular type will behave dierently due to manufacturing or assembly tolerances. In addition, the performance of a boiler will vary at dierent times of its service life. The objective of the present study is to simulate a boiler unit. In the boiler model, heat transfer in the combustion chamber is simulated by the zone method; heat transfer in the secondary superheater, the reheater, the primary superheater, and the economizer is simulated by lump parameter analysis. One feature of the method used is that the models of the major components have been coupled sequentially according to the boiler con®guration. Thus, it is assumed that this method may be applied to dierent boiler systems with dierent con®gurations. The uncertainty factors, such as water tube deposits, component deterioration and so on, are considered by modi®cation factors which are determined from on-line measurements. Another feature of the boiler system simulation is that the major parts of the boiler system are simulated and coupled together to analyze some important operational parameters which impose a signi®cant eect on boiler eciency, such as main stream temperature, reheat temperature and reheat pressure drop. The boiler model has been tested and compared to online measurements data. The results are within a reasonable error range. # 1998 Elsevier Science Ltd. All rights reserved Performance modelling
Boiler
NOMENCLATURE A=Area C(i)=Constant at point i D(i)=Constant at point i Dj,o=Tube inside/outside diameter E=Energy EAFA=Experimental constant EAFG=Experimental constant =Fuel ¯ow rate G=Generation or heat source H=Steam enthalpy h=Convection heat transfer coecient HP=High pressure IP=Intermediate pressure M=Mass ¯ow MF(j)=Modi®cation factor at zone j P = Pressure Pr=Prandtl number Q=Heat r=Distance between two zones R=Gas constant, thermal resistance Re=Reynolds number S=Entropy T=Temperature U=Conductance SS=Surface±surface exchange factor SG=Surface±volume exchange factor GG=Volume±volume exchange factor Greek symbols E=Surface emissivity s=Stefan±Boltzmann constant Z=Eciency 1383
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Subscripts a=Air c=Convection g=Flue gas i=Inlet state m=Metal o=Reference state r=Radiation s=Surface or steam cr=Cold return hr=Hot return mst=Main steam
INTRODUCTION
In an eort to run existing steam power plants as eciently as possible, many computer programs have been developed. Among these, some programs deal only with theoretical cycles (such as [6, 27, 32]), and some programs are mainly used to calculate/analyze the power system based on on-line measurements, such as GATE/CYCLE and PEPSE software. There are some limitations for these programs. The programs cannot be coupled with the existing control systems in a power plant. There is a need to improve the predictive quality of these models. The main purpose of the present work is to develop a boiler model whereby, based on the program, the system details can be either predicted without on-line measurements or calculated from the test data. Speci®cally, the following is intended to be predicted/calculated: 1. The cycle details at dierent operational conditions, such as heat ¯ux distribution along the boiler, steam pressure and temperature changes across each stage. 2. The performance parameters at dierent operational conditions. 3. An optimal operational condition for given output. 4. Second law eciency analysis of the whole system and individual components. Because of its complexity, we can only deal with steady performance models for each major component with necessary simpli®cations. The three features emphasized throughout the programming work are integrity, ¯exibility and practicability. For integrity, all the components in the system are together regarded as one integral unit, with interactions between these components assumed close to ideal. For ¯exibility, all the information needed is obtained through a ``REQUEST±ANSWER'' format, which enables the program to be used for dierent con®gurations and variations in a component's dimensions. For practicability, the program must be able to self-adjust so that it can correctly predict a component's performance despite the component's deterioration. LITERATURE REVIEW
The key process in¯uencing performance of boiler furnaces is the heat transfer process. Therefore, the main eorts in the boiler modeling have been directed towards development of more reliable methods for boiler heat transfer predictions. Depending on the number of fundamental physical laws considered and the degree of simpli®cation, a wide range of mathematical boiler modeling has been developed. Three groups of the models can be roughly classi®ed as semi-empirical models, zone models and ®nite dierence models. Semi-empirical modeling Huang [18] described a nonlinear steady state thermal performance model of a ®re-tube boiler. The model consists of two semi-empirical equations for the radiative heat ¯ux from the combustion gas to the boiling water and the heat loss ¯ux from the body surface to the ambient. The boiler performance under nominal operating conditions can be simulated by this model. There are six unknown parameters in the model, which are assumed to be ®xed for a given boiler and determined by the experimental data. GuÈruÈz [12] presents a well-stirred furnace model including soot radiation, which can be used to predict the overall performance of fuel-oil-®red boilers as a ®rst approximation. Claus [4] described a computer simulation model to calculate
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the thermal state of a boiler by using the method of indirect determination of the boiler eciency. The basic application of this semi-analytic model is to investigate the eects of dierent parameters on the behavior of the boiler and energy consumption. Hottel [16] described a onegas-zone model of industrial furnace performance with allowance for wall losses, sink temperature variation and departure from perfect stirring. Maimstrom [23] described a simple boiler model with no iterative processes. Zone-method modeling According to the way of handling radiative heat transfer, zone methods can be loosely grouped into ``classical'' methods and so-called Monte Carlo calculation techniques. The classical methods, which were ®rst published by Hottel [17], use precalculated radiative heat exchange coecients for total energy balances. The zone method of analysis requires input data, such as the speci®cation of the ¯ow ®eld, the combustion patterns throughout the enclosure, convective heat transfer coecients between the combustion products and the furnace walls, radiative properties of the enclosed medium and its surrounding surfaces and the total radiative interchange factors in the system. Monte Carlo methods allow direct evaluation of the radiative interchange and direct coupling with the furnace total energy balance. It is a probabilistic formulation of the radiative interchange which uses energy bundles to simulate the actual physical process. Steward [33] described a mathematical simulation of the heat transfer in a large modern boiler by using the zone method of analysis. It was shown that the simulation of the heat transfer can be performed using the data normally available in an operating plant, and that the method is a useful mathematical description technique for evaluating the radiative heat transfer in a furnace enclosure. Lowe [22] investigated a zoned heat transfer model for a large tangentially ®red pulverized coal boiler of 900 MW thermal input, in which a zoned method of computation predicts the temperature distribution within the chamber and the heat absorbed by the water tube walls. Bueters [3] presented a simple model for the performance prediction of tangentially ®red utility furnaces. The model views the furnaces as an equivalent rectangular parallellipiped divided, usually, into 20 to 30 horizontal slices. Richter and Payne [30] presented a paper which demonstrated that advanced computer models can provide the combustion engineer with valuable information for furnace design and performance analysis. The 3-D furnace developed by Richter and Payne [30] allows predictions of local and overall heat transfer, temperature pro®les and burnout of solid fuel particles in boiler combustion chambers and industrial furnaces dependent on actual furnace geometry and operating conditions, fuel characteristics and characteristics of wall deposits. Finite dierence modeling Finite dierence models allow a ®ner resolution of ¯ame temperatures and other furnace variables. They also need a much smaller amount of input data than zone methods, since the velocity distribution in the furnace is calculated simultaneously with the heat transfer. However, because of the small size of control volume, sophisticated turbulence models are necessary [29]. Finite dierence furnace models are usually based on computation techniques for turbulence ¯ows developed by Spalding and co-workers (for instance, [25]), and have been improved in many details [2, 21]. Fiveland [8] presented a model to simulate steady state, three dimensional pulverized-fuel combustion in practical furnace geometries. This model is based on a fundamental description of various interacting processes which occur during combustion: turbulent ¯ow, heterogeneous and homogeneous chemical reactions and heat transfer. The detailed analysis achieved by the method is useful for evaluating furnace performance and in the interpretation of laboratory and utility test data. Semi-empirical models can only be used as a ®rst approximation for boiler performance analysis in most cases. As for ®nite dierence models, on one hand, the air-fuel mixing model, combustion model, and turbulence ¯ow model for an industrial boiler have not been studied suciently; on the other hand, the computation time, the complexity of boiler geometry and boundary conditions also retard the application of the ®nite dierence model in industrial boilers. Examples in the published literature have demonstrated that advanced zone methods are
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well suited as engineering tools for simulation and performance analysis of newly designed or existing boiler combustion chambers. Therefore, a zone method model is used in the present work. For practical use, an ecient zone model is very important with respect to input data and running time. BOILER UNIT RATING
The model developed is based on the Florida Power & Light's Martin Unit No. 1. The boiler unit is a Foster±Wheeler natural circulation, radiant, single reheat, balanced draft unit. It is designed to ®re gas and soil through four elevations of eight nozzles located on the front wall of the furnace. The design maximum continuous rating (MCR) for superheat steam ¯ow and reheat steam ¯ow is 2,614,091 kg/h (5,751,000 lb/h) and 2,480,455 kg/h (5,457,000 lb/h), respectively [26]. Predicted superheat and reheat steam conditions at this rating are 5418C/377 kpag (10058F/2590 psig) and 5418C/87.3 kpag (10058F/600 psig), respectively. The superheat control range is from 1,307,273 kg/h (2,876,000 lb/h) to 2,614,091 kg/h (5,751,000 lb/h) steam ¯ow, with temperature controlled by two pairs of superheat desuperheaters, gas recirculation and damper grids in the superheat convection passageway. The reheat control range is from 1,222,273 kg/h (2,689,000 lb/h) to 2,480,455 kg/h (5,457,000 lb/h) steam ¯ow, with temperatures controlled by a reheat desuperheater. COMBUSTION CHAMBER MODELING
Generally speaking, there are three physical processes that have to be adequately represented in the combustion chamber model. These are ¯uid dynamics, combustion, and heat transfer. In terms of ¯uid dynamics, we just simplify the ¯ow as plug ¯ow, instead of calculating the ¯ow from the Navier-Stokes equations, because of its complexity, insucient study for an industrial boiler unit and our intent to set up a performance model. In view of the importance of recirculating ¯ows, a modi®cation factor is introduced in the present work instead of assuming a proportion of the mass of combustion products to ``back-mix'' with the ¯ow in the circulating region of the boiler. As for combustion modeling, it involves complex chemistry and chemicalkinetic reaction in turbulent ¯ows. Up to now, there is no well developed combustion model for an industrial boiler. In the present work, we assume that combustion takes place completely in the zone where the burners are placed. The simpli®cation is justi®ed based on the facts that: (1) the volume zones are selected as a whole section of the boiler along the boiler chamber height and (2) we are only interested in the heat release not in the heat release rate or pattern. As for heat transfer, it includes convective terms which couple to the ¯ow ®eld, an energy production term and terms that derive from radiative transfer. The following are the major assumptions for the combustion chamber modeling: 1. 2. 3. 4. 5. 6. 7.
plug ¯ow inside the chamber; ¯ue gas and air considered as perfect gases; no matter storage; combustion takes place completely in the volume zone where the burner was placed; saturated liquid water inside the water wall; uniform deposit thickness on the water wall; burner angles do not change for dierent loads.
Radiation is a key process in the boiler. First, we need to calculate the radiative transfer coecients, that is, exchange factors of surface±surface, surface±gas, and gas±gas so that we can calculate the heat ¯ux distribution. A procedure in the present program has been used to calculate the exchange factors numerically. The combustion chamber is divided into 14 volume zones and 14 surface zones. A sensitivity study was done, and the use of 14 zones provided an acceptable tradeo between accuracy and computation time. The boiler is sliced into 14 sections along its height. Each slice is a volume zone, and its surrounding surface is one surface zone. From energy conservation and mass balance, the following equations can be obtained:
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Fig. 1. Schematic arrangement of boiler heaters.
For volume i: n X j1
Sj Gi Es sAsj Tsj4 Gj Gi Eg sAgj Tgj4 MF j
hAsi Tsi ÿ Tgi Gi cp ff Tgiÿ1 ÿ Tgi1 Eg Ag sTgi4 :
1
For surface zone i: n X j1
Sj Si Es sTsj4 Asj
n X j1
Gj Si Eg sAgj Tgj4 MF j
Tsi ÿ Tw Asi Ei sTsi4 : h Tgi ÿ Tsi Asi Asi R
2
For each surface zone and volume zone, the corresponding energy equation can be derived from the above equations. The MF(j) in the two equations are called modi®cation factors and are set to 1 when the program is run the ®rst time for a speci®c boiler (refer to modi®cation factor section for details). The ¯ue gas emissivity, Eg, is obtained by a regression method based on Figs 17-11 and 17-13 of Siegel [31]. The combustion products properties, such as density, speci®c heat and so on, are calculated based on the procedure in [11]. A procedure in the program was developed to calculate the combustion products and their properties for both natural gas and oil. MODELING OF BOILER HEATERS
The boiler heaters model includes modeling of the primary superheater, secondary superheater, reheater, economizer, and air preheater. The schematic diagram of the heaters arrangement is given in Fig. 1. There is hardly any modeling available for these heaters. Only Lausterer et al. [20] presented a nonlinear model for the boiler heater. Our present work is mainly based on the book by Babcock & Wilcox Co. [1]. The following are the major assumptions for the modeling of the heaters: 1. lumped parameter analysis; 2. steady state for ¯owrate and temperature;
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
3. counter-¯ow heat transfer except air preheater; 4. metal thermal resistance can be neglected.
Tubular heater performance simulation Based on the above assumptions, the energy equations for the secondary superheater are: Ws Cs Tso ÿ Tsi Mg Cg Tgi ÿ Tgo
3
Q US 0 DTm
4
where M represents ¯owrate, C speci®c heat of steam or ¯ue gas, S' the surface area and U the conductance de®ned as: U
Ur Uc Us : Ur Uc Us
5
The equations for radiation conductance, Ur, and convection conductance, Uc, are obtained based on Figs 11-23 to 11-30 [1] by using curve ®tting (variables in the equations are in SI units). Uc Fa ÿ0:90283E ÿ 2 0:732E ÿ 2wg 0:37967E ÿ 3w2g 0:30765E ÿ 4Tf ÿ 0:50751E ÿ 8Tf2 Ur K SbÿSp=Sb ÿ0:045846 0:42611E ÿ 4DTm 0:38922E ÿ 8DTm 0:74967E ÿ 4Ts 0:1324E ÿ 7Ts2 :
6
An empirical equation for establishing Us, the steam ®lm conductance, can be expressed as: 1:5096E ÿ 4 Ws :8 d Cs m:2 : Us :2 D A d=12 s
7
The calculation of the secondary superheater system is quite straightforward and simple, and usually 15 iterations are required. For the primary superheater, reheater, and economizer, similar equations and calculation procedures as with the secondary superheater are applied to analyze their performances [24]. Therefore, the description of the primary superheater, reheater, and economizer system modeling is omitted here. For the economizer, both the Us and the Ur terms are neglected. Air preheater performance simulation There are generally two types of air preheaters, ``tubular'' and rotary [37]. In the program, the same equations are used if the air preheater is of tubular type with Us replaced by Uca (Uca convection conductance of air ®lm). The Uca is determined by the following equation [15]: Uca 0:023
K Re0:8 Pr0:4 DH
8
where DH is the passageway hydraulic diameter. Another type of air heater is the rotary air heater. The most common rotary air heaters are made of a metal cylinder, divided into thin steel plates and rotating around its axis. Flue gases cross longitudinally one half of the cylinder, thus heating the steel plates, which then release the stored heat to the air stream, crossing in counter¯ow on the other half of the cylinder [5]. Two major assumptions are made about the rotary air heater model: 1. no heat losses to the environment; 2. speci®c heats of air, metal, and ¯ue gas are constant throughout the temperature range. Suppose the angular speed of the air heater is X per second, air-sector angular Xa, and gas sector angular Xg. To simulate the air-heater performance, the heat transfer of a plate at the gas sector
NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
is written as:
Z Mm
Tmh Tml
Z Cm dT Am EAFG
0
xg xu
Tgi Tgo ÿ T dt: h 2
The heat transfer of a plate at the air sector is written as: Z x uxg Z T ml Tai Tao Cm dT Am EAFA ha T ÿ dt: Mm 2 T mh 0
1389
9
10
where EAFG is the experimental air heater factor of the gas sector. The energy balance equations for the air preheater can be written as: Qm Mm Cm Tmh ÿ Tml X g Qf Qa :
11
The above equations can be solved numerically. A procedure was programmed, based on the above equations, to analyze the air preheater performance and predict the outlet air temperature, exit ¯ue gas temperature and heater eectiveness. As a summary of the simulations of the boiler heaters, the variables used for describing the temperature changes for ¯ue/steam/water/air across these heaters and the ¯ow pattern of each heater are given in Fig. 2. MODIFICATION FACTORS CALCULATION
The ¯ue gas temperature near the water wall is much less than the ¯ue gas temperature in the center of the boiler chamber. The low temperature ¯ue has a great eect on the radiation transfer to the water wall. Dierent boiler geometries and dierent arrangements in burners will aect the ¯ow pattern and heat transfer in the boiler. On the other hand, the temperature distribution inside the boiler will be dierent for dierent loads. It is obvious that these factors signi®cantly aect the boiler heat transfer processes. In order to develop a simple but versatile program for dierent boilers at dierent service times, modi®cation factors are introduced in the present work to consider these eects. The deposit on both sides of a water tube also play an important role in heat transfer. At dierent service times, the quantity of deposits will be dierent. In order to ®nd these factors for dierent boilers at dierent service times, experimental data are used. Based on the test data and energy conservation equations derived, these modi®cation factors are obtained through two procedures in the program. In order to simplify the boiler wall deposits calculation, a uniform deposit on the water wall is assumed. In the following, the calculation of the modi®cation factors MF(j) is discussed. Based on energy conservation, the average thermal resistance on both sides of a water tube can be calculated by: Q
n X i1
Ts;i ÿ Tw Ai : Rdep: Rmetal Rconv:
12
As discussed above, the modi®cation factors are actually a set of functions. In the present work, the function is chosen as: MF i C i D i load:
13
This is the next level of complexity above the level where the MF(i)s are mere constants. Preliminary studies showed that this level of complexity was adequate for the present study. For dierent loads, the value of MF(i) is expected to be between 0.9 and 1.1. Otherwise, the factors would not be mere modi®cation factors, and one would have to go back to fundamentals to investigate if the fundamental modelling was adequate. In other words, the modi®cation factors are not expected to change the results of the model radically if the basic model is adequate. Based on the energy balance and on site measurements (i.e., ¯ue gas exit temperature, steam ¯ow rate, and water circulation), the following equations have been derived for determining the
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
modi®cation factors (i.e., C(i) and D(i)): a1 j b1 j MF j j 0 a2 j b2
14
a1 j Gj Gi Eg sAgj Tgj4 a2 j
n X i1
b1
n X j1
15
Gj Si Eg sAgj Tgj4
16
Sj Gi Es sAsj Tsj4 hAsi Tsi ÿ Tg cp ff Tgiÿ1 ÿ Tgi1 ÿ Eg Ag sTg4 :
b2
" n n X X i1
j1
17
# Sj Si Es sTsj4 Asj
h Tgi ÿ Tsi Asi ÿ
Fig. 2. Variables of the boiler heaters.
Asi Ei sTsi4
ÿQ
18
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1391
where Tg, the ¯ue exit temperature, is measured on site; Q, the actual heat absorption in the chamber, is calculated based on the on site measurements of steam ¯ow rate and steam pressure. When the program is ®rst used for an existing boiler, the MF(j) are set to unity. After it is run by 14 times, the procedure MODIFICATION will be expected to solve the above linear equations by the LU decomposition method [28], so that the modi®cation factors are determined. The approximate MF(i) are used instead of unity in the program, and the above procedures are repeated until two successive MF(i) are quite close at ten given loads. The modi®cation factor thus obtained can only be used for this particular boiler. The model with the modi®cation factors can accurately predict the boiler performance because the boiler peculiarities are included in the model through the factors. Similarly, in order to consider the particularities and the working conditions of the superheater, reheater, economizer, and air heater, modi®cation factors are also introduced such as EAFA and EAFG in the air heater (EAFA and EAFG: experimental air heater factor of air sector and experimental air heater factor of gas sector, respectively). SECOND LAW ANALYSES
Second law analysis is valuable in pinpointing the ``true'' losses [9]. Publications concerning the analysis of energy systems by using the second law include [7, 10, 19, 34, 35]. According to the report on boiler analysis by Wong [36], based on the traditional ®rst law equation and the second law eciency equation, the eciency of the second law, F2b, is consistent with the eciency of the ®rst law, F1b. On the other hand, although the ®rst law analysis on the power cycle can provide correct results, it fails to locate the sources of the thermodynamic losses [14]. Second law analysis in terms of irreversibility helps to identify and quantify these sources. The second law analysis is included in the program. In order to calculate the irreversibility inside the boiler and turbines, the energy balance is utilized. The exergies of compressed water, exist ¯ue gas, steam at dierent pressures and temperatures and preheated air are calculated. A procedure in the program was written to calculate the steam properties based on T&P, P&S, or T&S. This procedure, based on the steam tables by Haar [13] are mainly developed for large modern power plant second law analysis. According to the pressure range of the HP turbine, IP turbine, and LP turbine, three sets of steam data (100 for each set) are used to ®nd the necessary regression formulae which are needed in the STEAMP procedure. The equation for the boiler second law eciency in the program is expressed as: Z Exmst ÿ Excr Exhr = Exfuel Exwater :
19
As for the second law eciency of the boiler heaters, we de®ne the second law eciency of heaters as: Z steam exergy increase=flue exergy decrease:
20
Steam exergy can be calculated from the procedure STEAMP. The ¯ue gas energy is calculated under the assumption that the ¯ue gas is an ideal gas. The analyses include the ®rst law eciency and second law eciency of the combustion chamber, exergy destroyed in the chamber through the heaters and second law eciency of the superheater, reheater, economizer and air preheater. NUMERICAL CALCULATION AND RESULTS
The boiler model developed here is to be part of a power plant performance simulation package. The steam cold return temperature and ¯owrate in the boiler model should be calculated from the steam turbine model, and the water temperature entering the economizer should be calculated from the feedwater heater model. Because the steam turbine model and the feedwater heater model are not discussed here, these parameters in the boiler model are taken from the test data. The boiler unit model is written for steady state operation. The numerical calculation of the modeling is performed by iterations. In Fig. 3, a simpli®ed ¯ow chart for the numerical calculation of the boiler unit model is presented.
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
Fig. 3. Flow chart of boiler modeling computation.
The program has been veri®ed using experimental data. In Table 1, some simulation results of the boiler performance and their corresponding test data are presented. Some comparisons between the experimental results and the simulation results cannot be performed for the lack of test data, such as the heat ¯ux distribution and temperatures. In Fig. 4, the average gas temperature distributions at dierent loads are given. In Fig. 5, the heat ¯ux at dierent loads along the boiler chamber height are presented. The boiler unit ®rst law eciencies at 837 MW, 572 MW and 417 MW are predicted as 86.2%, 88.6% and 91.5%, respectively. The boiler unit second law eciencies at these loads are predicted as 35.2%, 38.5% and 43.3%, respectively. The second law eciencies vary with the ®rst law eciencies, except that the former are smaller in magnitude. This is to be expected since the second law eciency is de®ned with the water exergy in the denominator, whereas it is conventional not to include this term for ®rst law eciency.
Table 1. Model results and test data Items
Load = 400 MW By test Predicted
Load = 800 MW By test Predicted
Boiler eciency (%) Primary superheat Dt (K) Superheat spray (kg/s) Reheat spray (kg/s) Economizer water Dt (K) Preheater air D t (K) Exit ¯ue temperature (K)
90.3 46.6 28.2 0 52.2 193.1 420.0
88.6 45.0 35.3 13.2 51.6 242.2 417.4
92.2 49.0 18.1 ÿ2.5 41.4 185.6 443.1
89.7 48.8 19.6 6.2 79.2 224 452
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Fig. 4. Gas temperature distribution along the boiler height.
CONCLUSIONS
A method is presented in the paper to simulate the boiler unit performance, which does not need as input data the details of the boiler unit con®guration. By introducing the modi®cation factors, the speci®c characteristics of the boiler unit and the eects of dierent service-life (such as the deposits on tubes) can be taken into consideration in the program. The program, thus developed, may be conveniently applied to dierent utility boilers of the same con®guration. It is suspected that the method may be applied to dierent boiler systems with dierent con®gurations. Results on the boiler unit performance are presented. A comparison has been made between the model results and test data. The results are within a reasonable error range. The predicted ®rst law eciencies were higher than the actual, probably because some losses were not taken
Fig. 5. Heat ¯ux along the boiler height.
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
into account in the model. Consistent with the higher predicted eciencies, the primary superheat temperature dierences were predicted to be higher. In addition, the lower predicted superheat spray rate and predicted reheat spray rate lead to higher predicted eciencies. The preheater air temperature dierence and the exit ¯ue gas temperature will not aect the ®rst law eciency of the boiler predicted here. In general, a higher economizer water temperature dierence will lead to a higher eciency, all other parameters remaining the same. However, for the case of the load at 400 MW, the eect of the lower predicted economizer water temperature dierence may have been overshadowed by the other parameters. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.
Babcock, and Wilcox, Co. , in SteamÐIts Generation and Use, 37th edn, 1955. Bhashyam, A. T. et al., Combustion Sci. and Tech., 1986, 46, 223. Bueters, K. A., Cogoli, J. G. and Habelt, W. W., The Combustion Institute, 1975, 1245±1260. Claus, G., ASHRAE, 1985, CH-85-02-1, 47. Corno, D. et al., in Proc. of the IFAC Workshop, Como, Italy, 1983, p. 11. El-Masri, M. A., J. of Engineering for Gas turbines and Power, 1988, 201. Fehring, T. H. and Gaggioli, R. A., ASME, J. of Engineering for Power, 1977, 482. Fiveland, W. A. and Wessel, R. A., J. of Engineering for Gas Turbines and Power, 1988, 110, 117. Gaggioli, R. A. et al., in Proceedings of the American Power Conference, Vol. 37, 1975, p. 656. Gaggioli, R. A. et al., ASME, Energy Resource Tech., 1988, 110, 114. Gunn, D., in Boiler. Wiley, New York, 1989, p. 262. GuÈruÈz, K., Combustion Science and Technology, 1977, 17, 163. Haar, L. et al., in Steam Tables. Hemisphere Publishing Corp., 1984. Habib, M. A. and Zubair, S. M., ASME, 1990, 19, 29. Hadvig, S., Int. Inst. Fuel, 1970, 35, 129. Hottel, H. C., Scripta Book Co., 1974, 5. Hottel, H. C. et al., J. Am. Inst. Chem. Eng., 1958, 1, 3. Huang, B. J. et al., ASME, J. of Engineering For Gas Turbines and Power, 1988, 110, 173. Kenney, W. F., ACS Symp. Series, 1983, 235, 51. Lausterer, G. K. et al., Modular Modelling Applied to a Benson Boiler, Modeling and Control of Electric Power Plants, in Proc. of the IFAC Workshop, Como, Italy, 1983, p. 11. Lockwood, F. C. et al., Combustion Flame, 1983, 54, 23. Lowe, A., Wall, T. W. and Stewart, I. McC, A Zoned Heat Transfer Model of a Large Tangentially Fired Pulverized Coal Boiler, 15th Symp. (Int.) on Combustion, The Combustion Institute, 1975, p. 1261. Maimstrom, T. G., Mundt, B. and Bring, A. G., ASRAE, 1985, CH-85-02, 3. Niu, Z., Simulation and Performance Analysis of a Power System. Ph.D. Dissertation, Mech. Engr. Dept., Univ. of Miami, Coral Gables, FL, U.S.A., 1992. Patankar, S. V. and Spalding, D. B., Simultaneous Predictions of Flow Pattern and Radiation for ThreeDimensional Flames, Heat Transfer in Flames, Scripta, 1974. Performance Testing Services, Cyclic and Steady State Boiler Performance Evaluation at FPL Martin Unit 1, Combustion Engineering, Report no. 89-6, 1989. Perz, E., J. of Engineering for Gas Turbines and Power, 1991, 113, 185. Press, W. H. et al., Numerical Recipes in Pascal, Cambridge Univ. Press, 1989, p. 39. Richter, W., Scale-up and Advanced Performance Analysis of Boiler Combustion Chambers, ASME Paper No. 85WA/HI-80, 1985. Richter, W. and Payne, R., in Proc. of 1st Annual Pittsburgh Coal Technology Conference and Exhibition, 1984, pp. 592±611. Siegel, R. and Howell, J. R., in Thermal Radiation Heat Transfer, 2nd edn. McGraw-Hill Book Co., 1981, p. 621 & 622. Somerton, C. W. et al., J. of Engineering for Gas Turbines and Power, 1987, 109/222. Steward, F. R. et al., in Heat Transfer in Flames, ed. N. H. Afgan. Scripta Book Co., 1974, p. 47. Tsatsaronis, G. and Winhold, M., Energy, 1985, 10(1), 69. Wong, K. V. in Boiler First and Second Law Eciencies. Research Report. Mech. Eng. Dept., University of Miami, 1990. Wong, K. V., in Turbine Heat Rate, Research Report edn. Mech. Eng. Dept., University of Miami, 1989. Woodru, E. B. et al., in Steam Plant Operation, 5th ed. edn. McGraw-Hill Book Co., 1984, p. 27.
Energy Convers. Mgmt Vol. 39, No. 13, pp. 1383±1394, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0196-8904(98)00021-1 0196-8904/98 $19.00 + 0.00
ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE ZHONGSHENG NIU and KAU-FUI V. WONG Mechanical Engineering Department, University of Miami, Coral Gables, FL 33124, USA (Received 9 May 1997) AbstractÐIndustrial boilers of a particular type will behave dierently due to manufacturing or assembly tolerances. In addition, the performance of a boiler will vary at dierent times of its service life. The objective of the present study is to simulate a boiler unit. In the boiler model, heat transfer in the combustion chamber is simulated by the zone method; heat transfer in the secondary superheater, the reheater, the primary superheater, and the economizer is simulated by lump parameter analysis. One feature of the method used is that the models of the major components have been coupled sequentially according to the boiler con®guration. Thus, it is assumed that this method may be applied to dierent boiler systems with dierent con®gurations. The uncertainty factors, such as water tube deposits, component deterioration and so on, are considered by modi®cation factors which are determined from on-line measurements. Another feature of the boiler system simulation is that the major parts of the boiler system are simulated and coupled together to analyze some important operational parameters which impose a signi®cant eect on boiler eciency, such as main stream temperature, reheat temperature and reheat pressure drop. The boiler model has been tested and compared to online measurements data. The results are within a reasonable error range. # 1998 Elsevier Science Ltd. All rights reserved Performance modelling
Boiler
NOMENCLATURE A=Area C(i)=Constant at point i D(i)=Constant at point i Dj,o=Tube inside/outside diameter E=Energy EAFA=Experimental constant EAFG=Experimental constant =Fuel ¯ow rate G=Generation or heat source H=Steam enthalpy h=Convection heat transfer coecient HP=High pressure IP=Intermediate pressure M=Mass ¯ow MF(j)=Modi®cation factor at zone j P = Pressure Pr=Prandtl number Q=Heat r=Distance between two zones R=Gas constant, thermal resistance Re=Reynolds number S=Entropy T=Temperature U=Conductance SS=Surface±surface exchange factor SG=Surface±volume exchange factor GG=Volume±volume exchange factor Greek symbols E=Surface emissivity s=Stefan±Boltzmann constant Z=Eciency 1383
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Subscripts a=Air c=Convection g=Flue gas i=Inlet state m=Metal o=Reference state r=Radiation s=Surface or steam cr=Cold return hr=Hot return mst=Main steam
INTRODUCTION
In an eort to run existing steam power plants as eciently as possible, many computer programs have been developed. Among these, some programs deal only with theoretical cycles (such as [6, 27, 32]), and some programs are mainly used to calculate/analyze the power system based on on-line measurements, such as GATE/CYCLE and PEPSE software. There are some limitations for these programs. The programs cannot be coupled with the existing control systems in a power plant. There is a need to improve the predictive quality of these models. The main purpose of the present work is to develop a boiler model whereby, based on the program, the system details can be either predicted without on-line measurements or calculated from the test data. Speci®cally, the following is intended to be predicted/calculated: 1. The cycle details at dierent operational conditions, such as heat ¯ux distribution along the boiler, steam pressure and temperature changes across each stage. 2. The performance parameters at dierent operational conditions. 3. An optimal operational condition for given output. 4. Second law eciency analysis of the whole system and individual components. Because of its complexity, we can only deal with steady performance models for each major component with necessary simpli®cations. The three features emphasized throughout the programming work are integrity, ¯exibility and practicability. For integrity, all the components in the system are together regarded as one integral unit, with interactions between these components assumed close to ideal. For ¯exibility, all the information needed is obtained through a ``REQUEST±ANSWER'' format, which enables the program to be used for dierent con®gurations and variations in a component's dimensions. For practicability, the program must be able to self-adjust so that it can correctly predict a component's performance despite the component's deterioration. LITERATURE REVIEW
The key process in¯uencing performance of boiler furnaces is the heat transfer process. Therefore, the main eorts in the boiler modeling have been directed towards development of more reliable methods for boiler heat transfer predictions. Depending on the number of fundamental physical laws considered and the degree of simpli®cation, a wide range of mathematical boiler modeling has been developed. Three groups of the models can be roughly classi®ed as semi-empirical models, zone models and ®nite dierence models. Semi-empirical modeling Huang [18] described a nonlinear steady state thermal performance model of a ®re-tube boiler. The model consists of two semi-empirical equations for the radiative heat ¯ux from the combustion gas to the boiling water and the heat loss ¯ux from the body surface to the ambient. The boiler performance under nominal operating conditions can be simulated by this model. There are six unknown parameters in the model, which are assumed to be ®xed for a given boiler and determined by the experimental data. GuÈruÈz [12] presents a well-stirred furnace model including soot radiation, which can be used to predict the overall performance of fuel-oil-®red boilers as a ®rst approximation. Claus [4] described a computer simulation model to calculate
NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
1385
the thermal state of a boiler by using the method of indirect determination of the boiler eciency. The basic application of this semi-analytic model is to investigate the eects of dierent parameters on the behavior of the boiler and energy consumption. Hottel [16] described a onegas-zone model of industrial furnace performance with allowance for wall losses, sink temperature variation and departure from perfect stirring. Maimstrom [23] described a simple boiler model with no iterative processes. Zone-method modeling According to the way of handling radiative heat transfer, zone methods can be loosely grouped into ``classical'' methods and so-called Monte Carlo calculation techniques. The classical methods, which were ®rst published by Hottel [17], use precalculated radiative heat exchange coecients for total energy balances. The zone method of analysis requires input data, such as the speci®cation of the ¯ow ®eld, the combustion patterns throughout the enclosure, convective heat transfer coecients between the combustion products and the furnace walls, radiative properties of the enclosed medium and its surrounding surfaces and the total radiative interchange factors in the system. Monte Carlo methods allow direct evaluation of the radiative interchange and direct coupling with the furnace total energy balance. It is a probabilistic formulation of the radiative interchange which uses energy bundles to simulate the actual physical process. Steward [33] described a mathematical simulation of the heat transfer in a large modern boiler by using the zone method of analysis. It was shown that the simulation of the heat transfer can be performed using the data normally available in an operating plant, and that the method is a useful mathematical description technique for evaluating the radiative heat transfer in a furnace enclosure. Lowe [22] investigated a zoned heat transfer model for a large tangentially ®red pulverized coal boiler of 900 MW thermal input, in which a zoned method of computation predicts the temperature distribution within the chamber and the heat absorbed by the water tube walls. Bueters [3] presented a simple model for the performance prediction of tangentially ®red utility furnaces. The model views the furnaces as an equivalent rectangular parallellipiped divided, usually, into 20 to 30 horizontal slices. Richter and Payne [30] presented a paper which demonstrated that advanced computer models can provide the combustion engineer with valuable information for furnace design and performance analysis. The 3-D furnace developed by Richter and Payne [30] allows predictions of local and overall heat transfer, temperature pro®les and burnout of solid fuel particles in boiler combustion chambers and industrial furnaces dependent on actual furnace geometry and operating conditions, fuel characteristics and characteristics of wall deposits. Finite dierence modeling Finite dierence models allow a ®ner resolution of ¯ame temperatures and other furnace variables. They also need a much smaller amount of input data than zone methods, since the velocity distribution in the furnace is calculated simultaneously with the heat transfer. However, because of the small size of control volume, sophisticated turbulence models are necessary [29]. Finite dierence furnace models are usually based on computation techniques for turbulence ¯ows developed by Spalding and co-workers (for instance, [25]), and have been improved in many details [2, 21]. Fiveland [8] presented a model to simulate steady state, three dimensional pulverized-fuel combustion in practical furnace geometries. This model is based on a fundamental description of various interacting processes which occur during combustion: turbulent ¯ow, heterogeneous and homogeneous chemical reactions and heat transfer. The detailed analysis achieved by the method is useful for evaluating furnace performance and in the interpretation of laboratory and utility test data. Semi-empirical models can only be used as a ®rst approximation for boiler performance analysis in most cases. As for ®nite dierence models, on one hand, the air-fuel mixing model, combustion model, and turbulence ¯ow model for an industrial boiler have not been studied suciently; on the other hand, the computation time, the complexity of boiler geometry and boundary conditions also retard the application of the ®nite dierence model in industrial boilers. Examples in the published literature have demonstrated that advanced zone methods are
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
well suited as engineering tools for simulation and performance analysis of newly designed or existing boiler combustion chambers. Therefore, a zone method model is used in the present work. For practical use, an ecient zone model is very important with respect to input data and running time. BOILER UNIT RATING
The model developed is based on the Florida Power & Light's Martin Unit No. 1. The boiler unit is a Foster±Wheeler natural circulation, radiant, single reheat, balanced draft unit. It is designed to ®re gas and soil through four elevations of eight nozzles located on the front wall of the furnace. The design maximum continuous rating (MCR) for superheat steam ¯ow and reheat steam ¯ow is 2,614,091 kg/h (5,751,000 lb/h) and 2,480,455 kg/h (5,457,000 lb/h), respectively [26]. Predicted superheat and reheat steam conditions at this rating are 5418C/377 kpag (10058F/2590 psig) and 5418C/87.3 kpag (10058F/600 psig), respectively. The superheat control range is from 1,307,273 kg/h (2,876,000 lb/h) to 2,614,091 kg/h (5,751,000 lb/h) steam ¯ow, with temperature controlled by two pairs of superheat desuperheaters, gas recirculation and damper grids in the superheat convection passageway. The reheat control range is from 1,222,273 kg/h (2,689,000 lb/h) to 2,480,455 kg/h (5,457,000 lb/h) steam ¯ow, with temperatures controlled by a reheat desuperheater. COMBUSTION CHAMBER MODELING
Generally speaking, there are three physical processes that have to be adequately represented in the combustion chamber model. These are ¯uid dynamics, combustion, and heat transfer. In terms of ¯uid dynamics, we just simplify the ¯ow as plug ¯ow, instead of calculating the ¯ow from the Navier-Stokes equations, because of its complexity, insucient study for an industrial boiler unit and our intent to set up a performance model. In view of the importance of recirculating ¯ows, a modi®cation factor is introduced in the present work instead of assuming a proportion of the mass of combustion products to ``back-mix'' with the ¯ow in the circulating region of the boiler. As for combustion modeling, it involves complex chemistry and chemicalkinetic reaction in turbulent ¯ows. Up to now, there is no well developed combustion model for an industrial boiler. In the present work, we assume that combustion takes place completely in the zone where the burners are placed. The simpli®cation is justi®ed based on the facts that: (1) the volume zones are selected as a whole section of the boiler along the boiler chamber height and (2) we are only interested in the heat release not in the heat release rate or pattern. As for heat transfer, it includes convective terms which couple to the ¯ow ®eld, an energy production term and terms that derive from radiative transfer. The following are the major assumptions for the combustion chamber modeling: 1. 2. 3. 4. 5. 6. 7.
plug ¯ow inside the chamber; ¯ue gas and air considered as perfect gases; no matter storage; combustion takes place completely in the volume zone where the burner was placed; saturated liquid water inside the water wall; uniform deposit thickness on the water wall; burner angles do not change for dierent loads.
Radiation is a key process in the boiler. First, we need to calculate the radiative transfer coecients, that is, exchange factors of surface±surface, surface±gas, and gas±gas so that we can calculate the heat ¯ux distribution. A procedure in the present program has been used to calculate the exchange factors numerically. The combustion chamber is divided into 14 volume zones and 14 surface zones. A sensitivity study was done, and the use of 14 zones provided an acceptable tradeo between accuracy and computation time. The boiler is sliced into 14 sections along its height. Each slice is a volume zone, and its surrounding surface is one surface zone. From energy conservation and mass balance, the following equations can be obtained:
NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
1387
Fig. 1. Schematic arrangement of boiler heaters.
For volume i: n X j1
Sj Gi Es sAsj Tsj4 Gj Gi Eg sAgj Tgj4 MF j
hAsi Tsi ÿ Tgi Gi cp ff Tgiÿ1 ÿ Tgi1 Eg Ag sTgi4 :
1
For surface zone i: n X j1
Sj Si Es sTsj4 Asj
n X j1
Gj Si Eg sAgj Tgj4 MF j
Tsi ÿ Tw Asi Ei sTsi4 : h Tgi ÿ Tsi Asi Asi R
2
For each surface zone and volume zone, the corresponding energy equation can be derived from the above equations. The MF(j) in the two equations are called modi®cation factors and are set to 1 when the program is run the ®rst time for a speci®c boiler (refer to modi®cation factor section for details). The ¯ue gas emissivity, Eg, is obtained by a regression method based on Figs 17-11 and 17-13 of Siegel [31]. The combustion products properties, such as density, speci®c heat and so on, are calculated based on the procedure in [11]. A procedure in the program was developed to calculate the combustion products and their properties for both natural gas and oil. MODELING OF BOILER HEATERS
The boiler heaters model includes modeling of the primary superheater, secondary superheater, reheater, economizer, and air preheater. The schematic diagram of the heaters arrangement is given in Fig. 1. There is hardly any modeling available for these heaters. Only Lausterer et al. [20] presented a nonlinear model for the boiler heater. Our present work is mainly based on the book by Babcock & Wilcox Co. [1]. The following are the major assumptions for the modeling of the heaters: 1. lumped parameter analysis; 2. steady state for ¯owrate and temperature;
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
3. counter-¯ow heat transfer except air preheater; 4. metal thermal resistance can be neglected.
Tubular heater performance simulation Based on the above assumptions, the energy equations for the secondary superheater are: Ws Cs Tso ÿ Tsi Mg Cg Tgi ÿ Tgo
3
Q US 0 DTm
4
where M represents ¯owrate, C speci®c heat of steam or ¯ue gas, S' the surface area and U the conductance de®ned as: U
Ur Uc Us : Ur Uc Us
5
The equations for radiation conductance, Ur, and convection conductance, Uc, are obtained based on Figs 11-23 to 11-30 [1] by using curve ®tting (variables in the equations are in SI units). Uc Fa ÿ0:90283E ÿ 2 0:732E ÿ 2wg 0:37967E ÿ 3w2g 0:30765E ÿ 4Tf ÿ 0:50751E ÿ 8Tf2 Ur K SbÿSp=Sb ÿ0:045846 0:42611E ÿ 4DTm 0:38922E ÿ 8DTm 0:74967E ÿ 4Ts 0:1324E ÿ 7Ts2 :
6
An empirical equation for establishing Us, the steam ®lm conductance, can be expressed as: 1:5096E ÿ 4 Ws :8 d Cs m:2 : Us :2 D A d=12 s
7
The calculation of the secondary superheater system is quite straightforward and simple, and usually 15 iterations are required. For the primary superheater, reheater, and economizer, similar equations and calculation procedures as with the secondary superheater are applied to analyze their performances [24]. Therefore, the description of the primary superheater, reheater, and economizer system modeling is omitted here. For the economizer, both the Us and the Ur terms are neglected. Air preheater performance simulation There are generally two types of air preheaters, ``tubular'' and rotary [37]. In the program, the same equations are used if the air preheater is of tubular type with Us replaced by Uca (Uca convection conductance of air ®lm). The Uca is determined by the following equation [15]: Uca 0:023
K Re0:8 Pr0:4 DH
8
where DH is the passageway hydraulic diameter. Another type of air heater is the rotary air heater. The most common rotary air heaters are made of a metal cylinder, divided into thin steel plates and rotating around its axis. Flue gases cross longitudinally one half of the cylinder, thus heating the steel plates, which then release the stored heat to the air stream, crossing in counter¯ow on the other half of the cylinder [5]. Two major assumptions are made about the rotary air heater model: 1. no heat losses to the environment; 2. speci®c heats of air, metal, and ¯ue gas are constant throughout the temperature range. Suppose the angular speed of the air heater is X per second, air-sector angular Xa, and gas sector angular Xg. To simulate the air-heater performance, the heat transfer of a plate at the gas sector
NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
is written as:
Z Mm
Tmh Tml
Z Cm dT Am EAFG
0
xg xu
Tgi Tgo ÿ T dt: h 2
The heat transfer of a plate at the air sector is written as: Z x uxg Z T ml Tai Tao Cm dT Am EAFA ha T ÿ dt: Mm 2 T mh 0
1389
9
10
where EAFG is the experimental air heater factor of the gas sector. The energy balance equations for the air preheater can be written as: Qm Mm Cm Tmh ÿ Tml X g Qf Qa :
11
The above equations can be solved numerically. A procedure was programmed, based on the above equations, to analyze the air preheater performance and predict the outlet air temperature, exit ¯ue gas temperature and heater eectiveness. As a summary of the simulations of the boiler heaters, the variables used for describing the temperature changes for ¯ue/steam/water/air across these heaters and the ¯ow pattern of each heater are given in Fig. 2. MODIFICATION FACTORS CALCULATION
The ¯ue gas temperature near the water wall is much less than the ¯ue gas temperature in the center of the boiler chamber. The low temperature ¯ue has a great eect on the radiation transfer to the water wall. Dierent boiler geometries and dierent arrangements in burners will aect the ¯ow pattern and heat transfer in the boiler. On the other hand, the temperature distribution inside the boiler will be dierent for dierent loads. It is obvious that these factors signi®cantly aect the boiler heat transfer processes. In order to develop a simple but versatile program for dierent boilers at dierent service times, modi®cation factors are introduced in the present work to consider these eects. The deposit on both sides of a water tube also play an important role in heat transfer. At dierent service times, the quantity of deposits will be dierent. In order to ®nd these factors for dierent boilers at dierent service times, experimental data are used. Based on the test data and energy conservation equations derived, these modi®cation factors are obtained through two procedures in the program. In order to simplify the boiler wall deposits calculation, a uniform deposit on the water wall is assumed. In the following, the calculation of the modi®cation factors MF(j) is discussed. Based on energy conservation, the average thermal resistance on both sides of a water tube can be calculated by: Q
n X i1
Ts;i ÿ Tw Ai : Rdep: Rmetal Rconv:
12
As discussed above, the modi®cation factors are actually a set of functions. In the present work, the function is chosen as: MF i C i D i load:
13
This is the next level of complexity above the level where the MF(i)s are mere constants. Preliminary studies showed that this level of complexity was adequate for the present study. For dierent loads, the value of MF(i) is expected to be between 0.9 and 1.1. Otherwise, the factors would not be mere modi®cation factors, and one would have to go back to fundamentals to investigate if the fundamental modelling was adequate. In other words, the modi®cation factors are not expected to change the results of the model radically if the basic model is adequate. Based on the energy balance and on site measurements (i.e., ¯ue gas exit temperature, steam ¯ow rate, and water circulation), the following equations have been derived for determining the
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
modi®cation factors (i.e., C(i) and D(i)): a1 j b1 j MF j j 0 a2 j b2
14
a1 j Gj Gi Eg sAgj Tgj4 a2 j
n X i1
b1
n X j1
15
Gj Si Eg sAgj Tgj4
16
Sj Gi Es sAsj Tsj4 hAsi Tsi ÿ Tg cp ff Tgiÿ1 ÿ Tgi1 ÿ Eg Ag sTg4 :
b2
" n n X X i1
j1
17
# Sj Si Es sTsj4 Asj
h Tgi ÿ Tsi Asi ÿ
Fig. 2. Variables of the boiler heaters.
Asi Ei sTsi4
ÿQ
18
NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
1391
where Tg, the ¯ue exit temperature, is measured on site; Q, the actual heat absorption in the chamber, is calculated based on the on site measurements of steam ¯ow rate and steam pressure. When the program is ®rst used for an existing boiler, the MF(j) are set to unity. After it is run by 14 times, the procedure MODIFICATION will be expected to solve the above linear equations by the LU decomposition method [28], so that the modi®cation factors are determined. The approximate MF(i) are used instead of unity in the program, and the above procedures are repeated until two successive MF(i) are quite close at ten given loads. The modi®cation factor thus obtained can only be used for this particular boiler. The model with the modi®cation factors can accurately predict the boiler performance because the boiler peculiarities are included in the model through the factors. Similarly, in order to consider the particularities and the working conditions of the superheater, reheater, economizer, and air heater, modi®cation factors are also introduced such as EAFA and EAFG in the air heater (EAFA and EAFG: experimental air heater factor of air sector and experimental air heater factor of gas sector, respectively). SECOND LAW ANALYSES
Second law analysis is valuable in pinpointing the ``true'' losses [9]. Publications concerning the analysis of energy systems by using the second law include [7, 10, 19, 34, 35]. According to the report on boiler analysis by Wong [36], based on the traditional ®rst law equation and the second law eciency equation, the eciency of the second law, F2b, is consistent with the eciency of the ®rst law, F1b. On the other hand, although the ®rst law analysis on the power cycle can provide correct results, it fails to locate the sources of the thermodynamic losses [14]. Second law analysis in terms of irreversibility helps to identify and quantify these sources. The second law analysis is included in the program. In order to calculate the irreversibility inside the boiler and turbines, the energy balance is utilized. The exergies of compressed water, exist ¯ue gas, steam at dierent pressures and temperatures and preheated air are calculated. A procedure in the program was written to calculate the steam properties based on T&P, P&S, or T&S. This procedure, based on the steam tables by Haar [13] are mainly developed for large modern power plant second law analysis. According to the pressure range of the HP turbine, IP turbine, and LP turbine, three sets of steam data (100 for each set) are used to ®nd the necessary regression formulae which are needed in the STEAMP procedure. The equation for the boiler second law eciency in the program is expressed as: Z Exmst ÿ Excr Exhr = Exfuel Exwater :
19
As for the second law eciency of the boiler heaters, we de®ne the second law eciency of heaters as: Z steam exergy increase=flue exergy decrease:
20
Steam exergy can be calculated from the procedure STEAMP. The ¯ue gas energy is calculated under the assumption that the ¯ue gas is an ideal gas. The analyses include the ®rst law eciency and second law eciency of the combustion chamber, exergy destroyed in the chamber through the heaters and second law eciency of the superheater, reheater, economizer and air preheater. NUMERICAL CALCULATION AND RESULTS
The boiler model developed here is to be part of a power plant performance simulation package. The steam cold return temperature and ¯owrate in the boiler model should be calculated from the steam turbine model, and the water temperature entering the economizer should be calculated from the feedwater heater model. Because the steam turbine model and the feedwater heater model are not discussed here, these parameters in the boiler model are taken from the test data. The boiler unit model is written for steady state operation. The numerical calculation of the modeling is performed by iterations. In Fig. 3, a simpli®ed ¯ow chart for the numerical calculation of the boiler unit model is presented.
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
Fig. 3. Flow chart of boiler modeling computation.
The program has been veri®ed using experimental data. In Table 1, some simulation results of the boiler performance and their corresponding test data are presented. Some comparisons between the experimental results and the simulation results cannot be performed for the lack of test data, such as the heat ¯ux distribution and temperatures. In Fig. 4, the average gas temperature distributions at dierent loads are given. In Fig. 5, the heat ¯ux at dierent loads along the boiler chamber height are presented. The boiler unit ®rst law eciencies at 837 MW, 572 MW and 417 MW are predicted as 86.2%, 88.6% and 91.5%, respectively. The boiler unit second law eciencies at these loads are predicted as 35.2%, 38.5% and 43.3%, respectively. The second law eciencies vary with the ®rst law eciencies, except that the former are smaller in magnitude. This is to be expected since the second law eciency is de®ned with the water exergy in the denominator, whereas it is conventional not to include this term for ®rst law eciency.
Table 1. Model results and test data Items
Load = 400 MW By test Predicted
Load = 800 MW By test Predicted
Boiler eciency (%) Primary superheat Dt (K) Superheat spray (kg/s) Reheat spray (kg/s) Economizer water Dt (K) Preheater air D t (K) Exit ¯ue temperature (K)
90.3 46.6 28.2 0 52.2 193.1 420.0
88.6 45.0 35.3 13.2 51.6 242.2 417.4
92.2 49.0 18.1 ÿ2.5 41.4 185.6 443.1
89.7 48.8 19.6 6.2 79.2 224 452
NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
1393
Fig. 4. Gas temperature distribution along the boiler height.
CONCLUSIONS
A method is presented in the paper to simulate the boiler unit performance, which does not need as input data the details of the boiler unit con®guration. By introducing the modi®cation factors, the speci®c characteristics of the boiler unit and the eects of dierent service-life (such as the deposits on tubes) can be taken into consideration in the program. The program, thus developed, may be conveniently applied to dierent utility boilers of the same con®guration. It is suspected that the method may be applied to dierent boiler systems with dierent con®gurations. Results on the boiler unit performance are presented. A comparison has been made between the model results and test data. The results are within a reasonable error range. The predicted ®rst law eciencies were higher than the actual, probably because some losses were not taken
Fig. 5. Heat ¯ux along the boiler height.
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NIU and WONG: ADAPTIVE SIMULATION OF BOILER UNIT PERFORMANCE
into account in the model. Consistent with the higher predicted eciencies, the primary superheat temperature dierences were predicted to be higher. In addition, the lower predicted superheat spray rate and predicted reheat spray rate lead to higher predicted eciencies. The preheater air temperature dierence and the exit ¯ue gas temperature will not aect the ®rst law eciency of the boiler predicted here. In general, a higher economizer water temperature dierence will lead to a higher eciency, all other parameters remaining the same. However, for the case of the load at 400 MW, the eect of the lower predicted economizer water temperature dierence may have been overshadowed by the other parameters. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.
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