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Predicting acid dew point with a semi-empirical model
Accepted Manuscript Predicting Acid Dew Point with A Semi-empirical Model Baixiang Xiang, Bin Tang, Yuxin Wu, Hairui Yang, Man Zhang, Junfu Lu PII: DOI: Reference:
S1359-4311(16)30946-2 http://dx.doi.org/10.1016/j.applthermaleng.2016.06.040 ATE 8451
To appear in:
Applied Thermal Engineering
Received Date: Accepted Date:
20 April 2016 6 June 2016
Please cite this article as: B. Xiang, B. Tang, Y. Wu, H. Yang, M. Zhang, J. Lu, Predicting Acid Dew Point with A Semi-empirical Model, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng. 2016.06.040
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Predicting Acid Dew Point with A Semi-empirical Model Baixiang Xiang, Bin Tang, Yuxin Wu, Hairui Yang, Man Zhang, Junfu Lu* Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China
ABSTRACT Decreasing the temperature of exhaust flue gas in boilers is one of the most effective ways to further improve the thermal efficiency, electrostatic precipitator efficiency and to decrease the water consumption of desulfurization tower, while, when this temperature is below the acid dew point, the fouling and corrosion will occur on the heating surfaces in the second pass of boilers. So, the knowledge on accurately predicting the acid dew point is essential. By investigating the previous models on acid dew point prediction, an improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived first. And then, a semi-empirical prediction model is proposed, which is validated with the data both in field test and experiment, and comparing with the previous models. Keywords: Flue gas; Acid dew point; Aspen plus; Semi-empirical model
1. INTRODUCTION Given the presence of sulfur, nitrogen, carbon and other elements in the fuel, the flue gas in boilers typically contains some acidic gases such as SO2, SO3, NO, NO2 and CO2, etc. These acidic gases will further react with the water vapor in the flue gas to generate acid vapors under low temperature conditions [1-4]. When the temperature of outer wall of convection heating surface in the second pass of boilers is below the acid dew point, the acid vapors in flue gas will condense and form acidic droplets on the heating surfaces. Actually, the acid dew point depends on the content of sulfur trioxide and the partial pressure of water vapor in flue gas [2-15]. The condensed acidic droplets not only cause serious acidic corrosion to the metal heating surfaces [5-6], but also further react with the flaking rust and the fly ash in the second pass of boilers. The fouling will occur under such condition. Once the fouling occupies in the flow channel, the burden
of induced draft fan will be significantly increased. The increasing burden of induced draft fan will cause the content of O2 in boilers decreased. More importantly, the combustion in boilers will be seriously deteriorated under such a condition. Besides, the velocity of flue gas is increased by a great extent due to the occupied fouling in the flow channel. The wear of the metal heating surfaces in the second pass of boilers will be severe. Considering the safety of the power generation unit, the temperature of exhaust flue gas must be strictly controlled over the acid dew point [14-19]. However, in order to cope with the increasing demand of the energy-saving and emission-reduction, decreasing the temperature of exhaust flue gas in boilers is one of the most effective ways to further improve the thermal efficiency, electrostatic precipitator efficiency and to decrease the water consumption of desulfurization tower [20-30]. Therefore, how to accurately predict the acid dew point become the key point. So far, different models for predicting acid dew points of flue gas have been reported in previous studies, as listed in Table 1 [5-6, 14-18, 25]. Theβ, generally 125, depends on the excess-air ratio in the boiler [6]. The a, dependent on the partial pressure of water vapor in the flue gas, is 184, 194 and 201 when the water vapor partial pressure is 5066 Pa, 10132 Pa and 15199 Pa, respectively [5]. And the values of B and n in the correlation formula contained experimental constants under different flue gas conditions are listed in Table 2 [5]. Moreover, with the research progress in computer technology and multiple phase equilibrium in recent years [31-39], the acid dew point of flue gas can be also predicted using a software, namely, Aspen plus. In general, these models can be divided into empirical and semi-empirical according to the data processing methods. The empirical models are usually established by fitting the experimental results and the field test data with mathematical methods directly. For example, Verhoff, et al. [18] proposed an empirical model by fitting the acid dew points of flue gas using the least square method, which measured with a cooled electrical conductivity probe. Halstead, et al. [25] derived a graph between the acid dew point and its influencing factors based on the vapor pressure data determined by using the gas saturation technique, which used to predict the acid dew point in the flue gas of oil-fired power plant. Okkes, et al. [14] proposed a graph for estimating the sulfuric acid dew point in flue gas based on the fuel compositions and excess-air ratio. Haase et al. [15] measured the acid dew points and the resistance of flue gas with a circulation system designed
according to the boiling point measurement principle of Cottrell. The compositions of the flue gas are determined according to the corresponding measured resistance. Based on the measured acid dew points and compositions of flue gas, Haase et al. [15] proposed an empirical prediction model. In addition, there have been other empirical models, which built by fitting the field test data directly, such as the Soviet Union thermodynamic calculation standard of boiler in 1973, the correlation formula contained experimental constants and the prediction model proposed by Japan institute of electric power industry [5-6]. However, according to the long operating experience of many power plants in China [28-30], not only is the applicability of the above empirical prediction models strictly limited, but the predicted values are generally not so good. Different to the empirical prediction models, data processing of the semi-empirical model is correlated to the thermodynamic correlation formula between the acid dew point and its influencing factors. Thus, not only the accuracy of the predicted acid dew points in flue gas can be improved, but also the applicability of the prediction model. In fact, the thermodynamic correlation formula can be derived according to the equivalent of the chemical potential and fugacity in each phase of a component in the vapor–liquid equilibrium. The fugacity in each phase of a component can be used the following models, namely, the equation of state (EOS) and the equation of state and activity coefficient (EOS + γ) models. Given the lack of an equation of state that can formulate the sulfuric acid in both vapor state and liquid state, the acid dew point in flue gas cannot be predicted accurately using EOS. To date, Aspen plus established the thermodynamic correlation formula based on EOS + γ. However, given the lack of binary interaction coefficients of H2SO4 and H2O in the activity coefficient models reported in previous studies [31-32], the acid dew point in flue gas seems difficult to be predicted accurately using Aspen plus. Thus far, based on the equivalent of chemical potential in each phase of H 2SO4, Müller et al. [16] derived the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid. Then, according to the dew points of sulfuric acid with a concentration ranging from 5% to 85% [17], Müller et al. [16] proposed a semi-empirical prediction model, as shown in Figure 1. However, given the limited understanding on the influencing factors of acid dew point and not enough rigorous derivation of the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid, the predicted values seem to be too high [28-30]. Thus, in this work, the
semi-empirical prediction models reported in previous studies are investigated, and an improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived. Then, a semi-empirical prediction model for the acid dew point in flue gas that considers the function of sulfuric acid and water is proposed based on previous experimental data. Moreover, the prediction model proposed in this work is validated by the field test data, the experimental data, and prediction models reported in previous studies.
2. PREVIOUS SEMI-EMPIRICAL PREDICTION MODELS 2.1 Prediction Model of Aspen plus The optimal physical method is ELECNRTL when the acid dew point in flue gas is predicted using Aspen plus [33-35]. Actually, the ELECNRTL is derived based on the vapor–liquid equilibrium in the multi-compound poly-phase system [31-39]. As the fugacity of one component distributed in different phases are equal in the vapor–liquid equilibrium, the following equation can be derived: fˆi v fˆi l
(1)
For the ELECNRTL, the activity coefficient of components in liquid state is calculated with the Electrolyte NRTL, while the fugacity coefficient of components in vapor state is calculated with the state equation of Redlich-Kwong. In the Electrolyte NRTL, due to the small mole fraction of sulfuric acid in flue gas (e. g. several ppm), the activity coefficient of component i in liquid state ( fˆi l ) can be calculated with the unsymmetrical convention [32, 36]. So, there is fˆi l H i,
Solvent
* xi
(2)
i
where H i, Solvent is the Henry constant of solute i in the solvent, xi is the mole fraction of component i in the liquid mixtures and i* , the activity coefficient of component i with the unsymmetrical convention, is the ratio of the fugacity of component i in the real solution to that in the ideal dilute solution under the same temperature, pressure and compositions. For the fugacity of component i in vapor state ( fˆi v ), it can be calculated as the following equation approximately under low pressure conditions [38],
(3)
fˆi v Pg yiˆi
where Pg is the total pressure of flue gas, yi is the volume fraction of component i in the vapor mixtures and ˆi is the fugacity coefficient of component i in vapor state. Based on the previous studies on the Electrolyte NRTL [32, 36], the excess Gibbs free energy contains three contributions: the short-range interactions between species ( G*,SR ), the long-range electrostatic interactions ( G*,LR ) and the energy needed to transfer the ionic species from the infinitely dilute mixed-solvent medium to the infinitely diluted aqueous solution ( G*,Born ). So, there is G*,ex G*,SR G*,LR G*,Born
(4)
Moreover, for ln i* and G*,ex , the correlation formula is as follows:
ln i*
1 G*,ex RT Ni T , P , N ji
(5)
Submitting Eq. (4) to Eq. (5), the expression of the activity coefficient of component i in liquid state is derived: ln i* ln i*Born ln i*L R ln i*S R
(6)
where i*SR is the activity coefficient of component i in the short-range interactions, i*L R is the activity coefficient of component i in the long-range interactions, ln i*Born is the born term correction to logarithm of activity coefficient of component i. For the activity coefficient of component i in the short-range interactions ( i*SR ), Bollas et al. [32] and Chen et al. [36] introduced its derivation in some detail. To account for the long-range ion-ion interactions ( ln i*L R ), Pitzer et al. [37] proposed the Pitzer-Debye-Hückel theory. Thus, there is ln i*LR A [
2 zi2
ln(1 I x1/ 2 )
zi2 I x1/ 2 2 I x3/ 2 ] 1 I x1/ 2
(7)
where I x is the ionic strength, A is the Debye-Hückel parameter, is the closest approach parameter and zi is the charge number of segment-based species i. Besides, for the born term correction to logarithm of activity coefficient ( ln i*Born ), Bollas et al. [32] proposed its expression as the following formula:
ln i*Born
Qe2 1 1 z2 ( ) i 102 2kT s w ri
(8)
where k is the Boltzmann constant, 1.3806 1023 J/ K , ri is the Born radius of segment species i, s is the dielectric constant of the solvent, w is the dielectric constant of the water and Qe is the electron charge. Compared to the state equation of Benedict-Webb-Rubin (B-W-R), the state equation of Redlich-Kwong (R-K) is more attractive for the mixtures because the simple manner in which binary interaction constants can be introduced into it. Thus, Zudkevitch et al. [38] derived the fugacity coefficient of component i in vapor state ( ˆi ) based on R-K.
2.2 Prediction Model Proposed by Müller For the semi-empirical prediction model on acid dew point proposed by Müller and Abel [16-17], the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid is derived based on the equal of chemical potential in each phase of sulfuric acid in the vapor–liquid equilibrium. So, there is i" i'
(9)
where i' is the chemical potential of sulfuric acid in liquid state, while i" is the chemical potential of sulfuric acid in vapor state. Considered as the ideal gas approximately under low pressure conditions, the chemical potential of sulfuric acid in vapor state can be calculated as the following formula: i" i"o RT ln( Pi / Po )
(10)
where i"o is the chemical potential of sulfuric acid in vapor state with the reference state (101325 Pa and real temperature), Pi is the pressure of the sulfuric acid vapor and Po is the reference pressure (101325 Pa). However, as the sulfuric acid in liquid state cannot be considered as the ideal solution approximately, its chemical potential should be calculated as the following formula: i' i'o RT ln ai
(11)
where ai is the activity of sulfuric acid and i'o is the chemical potential of sulfuric acid in liquid state with the reference state. Submitting Eqs. (10) and (11) to Eq. (9), there is
RT ln Pi = i'o i"o + RT ln ai
(12)
Additionally, SO3 in the flue gas starts to combine with H2O and form sulfuric acid vapor when the temperature of flue gas is cooled down to 773 K: C o o l i n g S O3 ( g ) + H g ) 2 O(
2
H SO (g) 4
(13)
where the partial pressure of reactants in Eq. (13) can be essentially equal to the corresponding fugacity. Thus, for the equilibrium constant of Eq. (13), there is RT ln Kp = i"o w"o o"o
(14)
where K p is the equilibrium constant of Eq. (13), w"o is the chemical potential of water vapor with the reference state and o"o is the chemical potential of sulfur trioxide with the reference state. Submitting Eq. (12) to Eq. (14), the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid is derived: RT ln Pi i'o w"o o"o RT ln Kp RT ln ai
(15)
3. A SEMI-EMPIRICAL PREDICTION MODEL 3.1 An Improved Thermodynamic Model In the ELECNRTL, the acid dew pint of flue gas is calculated based on the vapor–liquid equilibrium in the multi-compound poly-phase system. However, Huijbrejts et al. [3] found that the sulfuric acid vapor will condense first with the decreasing of flue gas temperature, because the boiling point of sulfuric acid is highest in flue gas under the same conditions. Actually, as mentioned, the acid dew point depends mainly on the content of sulfur trioxide and the partial pressure of water vapor in flue gas [2-15]. Thus, the multi-compound poly-phase system in ELECNRTL can be simplified to the binary sulfuric acid-water system. Besides, in the Electrolyte NRTL, the activity coefficient of component i in liquid state ( fˆi l ) is calculated with the unsymmetrical convention. However, Fleig et al. [41] and Land et al. [42] found that the condensed sulfuric acid and water formed an azeotrope and the condensate sulfuric acid-water mixture typically contained more than 70 mole % sulfuric acid. More importantly, there is a lack of binary interaction coefficients of sulfuric acid and water in the thermodynamic models reported
in the previous studies [31-32]. Therefore, the activity coefficient calculated using the Electrolyte NRTL seems to be not accurate enough. For the semi-empirical prediction model for acid dew point proposed by Müller and Abel [16-17], not only is the influencing factor of water vapor not considered, but the reaction equilibrium constant of Eq. (13) ( K p ) seems no need to be calculated because Fleig et al. [1] and Stuart et al. [2] found that the sulfur trioxide is almost completely converted to sulfuric acid when the temperature of flue gas is cooled down to 473 K. Considering the above reasons, thus, an improved thermodynamic correlation formula between the acid dew point and its influencing factors is required. Similar to the property of fugacity, the chemical potential of component i distributed in two phases are equal in the vapor–liquid equilibrium. Thus, there is i" i'
(16)
where i' is the chemical potential of component i in liquid state and i" is the chemical potential of component i in vapor state. As the vapors in flue gas can be considered as the ideal gas approximately under low pressure conditions, the chemical potential of component i in vapor state is calculated as the following equation: i" i" RT ln yi
(17)
where i" is the chemical potential of pure component i in vapor state with the same pressure and temperature to the vapor mixtures, yi is the volume fraction of component i in the vapor mixtures. However, for the components in liquid state, due to the large difference between molecular structure, chemical formula and electrical property, they cannot be considered as the ideal solution approximately. Thus, the chemical potential of the component i in liquid state should be calculated as the following equation: i' i' RT ln ai
(18)
where ai is the activity of component i and i' is the chemical potential of pure component i in liquid state with the same pressure and temperature to the liquid mixtures. By submitting Eqs. (17) and (18) to Eq. (16), there is
i' RT ln ai i" RT ln yi
(19)
For T , H and , the correlation formula is as follows: T H 2 T T
(20)
where H can be computed using the following formula: T
H H 298 +
C
p
(21)
dT
298
Additionally, as discussed above, the multi-component system in the ELECNRTL can be simplified as a binary sulfuric acid-water system. Henceforth, the component of sulfuric acid is represented with the subscript 1, while the subscript 2 represents the component of water vapor in this work. Therefore, an improved thermodynamic correlation formula between the acid dew point in flue gas and its influencing factors is derived: ln P1 ln(
T T P2 1 1 ' ' ' ' ) ( 1,298 1,298 CP1' CP1' dT ) ( 2,298 2,298 CP2' CP2' dT ) sat RT RT P2 298 298
ln P
' " 1,298 1,298
R 298
' " H1,298 H1,298
RT
' " H1,298 H1,298
R 298
T
T
T C 1
2
298
' P1
(22)
CP1" dTdT
298
where P is the total partial pressure of water vapor and sulfuric acid in the flue gas, P2sat is the saturated vapor pressure of water in flue gas, i' 298 is the chemical potential of component i in liquid state at 298 K, i'298 is the chemical potential of pure component i in liquid state at 298 K, CPi' is the specific heat of pure component i in liquid state, H i' 298 is the enthalpy of component i
in liquid state at 298 K, H i"298 is the enthalpy of component i in vapor state at 298 K, specific heat of component i in vapor state, and
CPi'
Cpi'
Cpi"
is the
is the specific heat of component i in liquid state
is the partial specific heat of component i in liquid state. For the derivation of Eq. (22), it
is given in detail in Appendix. By simplifying Eq. (20), there is ln P1 AT 1
A2 P2 A3 ln T A4 ln P ln( sat ) T P2
(23)
where A1–A4 are the constants depended on the sulfuric acid and water. The units of P , P1 , P2 , P2sat and T are Pa, Pa, Pa, Pa and K, respectively.
3.2 A Semi-empirical Prediction Model Eq. (23) presented the thermodynamic correlation formula between the acid dew point in flue
gas and its influencing factors, however, it can’t be used to predict the acid dew point in flue gas because it seems impossible to calculate the constants of Eq. (23) directly based on the thermophysical parameters of sulfuric acid and water. Fortunately, the correlation formula between the constants of Eq. (23) and the partial pressure of water vapor and sulfuric acid can be fitted using mathematic methods based on the experimental data. In our previous work [43], the acid dew points in flue gas under different conditions were measured by a measuring apparatus designed based on the principle of conductive dew point meter, as shown in Figure 2. With the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa respectively, the measured results are shown in Figure 3 [43]. Considering the trends of the acid dew point with the partial pressure of water vapor and sulfuric acid and the first approximation theorems of Weierstrass [44], the correlation formula between the constants of Eq. (23) and the partial pressure of water vapor and sulfuric acid can be expressed by a polynomial. By fitting the experimental data in Figure 3 with the least square method, the correlation formula between the constants of Eq. (23) and the partial pressure of water vapor can be formulated as the following third-order polynomial with the partial pressure of sulfuric acid ranging from 0.5066 Pa to 2.0265 Pa, Aj a j1 PH2 O3 a j 2 PH2 O 2 a j 3 PH2 O a j 4
j 1, 2, 3, 4
(24)
The coefficients of Eq. (24) under different conditions are listed in Table 3, thus, the constants of Eq. (23) can be determined. Therefore, a semi-empirical prediction model for the acid dew point in flue gas, the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa, is proposed, as shown in Figure 4. It can be found that the increasing slope of the acid dew point becomes smaller both at higher sulfuric acid vapor partial pressure and higher water vapor partial pressure.
4. RESULTS AND DISCUSSION 4.1 Comparative Analysis of Experimental Data Figure 5 describes a comparison between the experimental data in a previous paper [45] and the values predicted using the model proposed in this work, Aspen plus and the models listed in
Table 1 under the same flue gas conditions. As mentioned, different from the application of the present model, the partial pressure of sulfuric acid and water vapor in Halstead model ranges from 0 Pa to 2 Pa and from 0 Pa to 14,185.5 Pa, respectively [25]. The partial pressure of sulfuric acid in the Müller model ranges from 0 Pa to 1,013.25 Pa [16]. Moreover, for the prediction model proposed by Haase, the partial pressure of water vapor and sulfuric acid ranges from 7,092 Pa to 101,325 Pa and 0.1013 Pa to 20.265 Pa, respectively [15]. The experimental data in reference [45] are measured using a device built based on the principle of conductive dew point meter, which is completely different from the measuring device designed in reference [43]. Not only is the flue gas cooled using compressed air, but the electrodes are arranged in a ring-shaped manner. Moreover, the distance between the positive and negative electrodes is increased to 3 mm. As shown in Figure 5, the values predicted with the previous models, except for the model suggested by Haase and Aspen plus, are generally too high under the same conditions mentioned above. The values predicted using the Haase model and Aspen plus are slightly higher than the corresponding experimental data for small mole fraction of sulfuric acid, while they become significantly lower for large mole fraction of sulfuric acid. Comparably, the values predicted using Aspen plus seems to be better consistent with the experimental data for small mole fraction of sulfuric acid, while, the values predicted using the Haase model seems to be better consistent for large mole fraction of sulfuric acid. Thus, compared to the above two models, the values predicted with the present model show better agreement with the experimental data.
4.2 Comparative Analysis of Field Test Data To further validate the prediction model proposed in this work, the acid dew points of a 150MWe coal-fired circulating fluidized bed boiler with limestone desulfurization are tested under different flue gas conditions [46]. In the field test, the sulfur content of the coal is maintained at 0.74%, and a series of different flue gas conditions were obtained by adjusting the excess-air ratio. When the partial pressure of the sulfuric acid vapor and water vapor are 1.8542 Pa, 1.986 Pa, 3.8807 Pa and 12159 Pa, 10234 Pa, 8511 Pa respectively, the tested acid dew point is 361K, 366K and 372K, respectively [46]. Figure 6 shows a comparison between the field test data and the values predicted using the present model, Aspen plus and the previous models listed in Table 1 under the same flue gas conditions mentioned above. Similar to the comparative results showed in
Figure 5, the values predicted with the previous models, except for the Haase model, Aspen plus and the Soviet one, are generally too high. In the field test, it found that the fly ash in flue gas could wrap the condensate sulfuric acid droplets and seemed to cause the measured acid dew points lower by the measuring apparatus [46]. In addition, the comparative results of Figure 6 show that the values predicted with Aspen plus and the Soviet one are even lower than the corresponding field test data for large mole fraction of sulfuric acid. Besides, the values predicted using the Soviet one slightly decreases with the increasing of mole fraction of sulfuric acid. Comparably, the values predicted with the model proposed in this work seems to be better consistent with the field test data. Therefore, based on the comparative results of field test and experimental data, the values predicted with the present model are more reliable than those predicted using the previous models.
5. CONCLUSIONS By investigating the previous models on acid dew point prediction, an improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived first. And then, a semi-empirical prediction model is proposed. In the condition of water vapor and sulfuric acid partial pressure ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa, the prediction model proposed in this work seems to be more reliable than the previous models. The fly ash in flue gas, the average size and the concentration, may have unclear effective on the acid dew point. In present work, the acid dew point measured by using the apparatus designed based on the principle of conductive dew point meter is lower, while, some researchers argued that the measured one seemed to be higher due to the function of the condensation nucleus formed by the submicron fly ash particles. Therefore, the influence of fly ash particles in the flue gas will be studied in future research.
AUTHOR INFORMATION Corresponding author
*E-mail address: [email protected] (J. Lu). Tel.: +86-01-62792647.
Notes The authors declare no competing financial interest.
ACKNOWLEDGEMENTS Financial support of this work by the National Program on Key Basic Research Project (973 Program) of China (No. 2012CB214900) is gratefully acknowledged.
NOMENCLATURE fˆi v =
the fugacity of component i in vapor state
fˆi l =
the fugacity of component i in liquid state
H i, Solvent = the Henry constant of solute i in the solvent
xi = the mole fraction of component i in the liquid mixtures yi = the mole fraction of component i in the vapor mixtures Pi = the partial pressure of component i, Pa Po = the reference pressure (=101 325 Pa)
ˆi = the fugacity coefficient of component i in vapor state I x = the ionic strength (segment mole fraction scale)
= the closest approach parameter A = the Debye-Hückel parameter
k = the Boltzmann constant, 1.3806 1023 , J/K K p = the reaction equilibrium constant of Eq. (13) "o w = the chemical potential of water vapor with the reference state
o"o = the chemical potential of sulfur trioxide with the reference state zi = the charge number of segment-based species i ri = the Born radius of segment species i
Qe = the electron charge
i' = the chemical potential of component i in liquid state, kJ/mol i" = the chemical potential of component i in vapor state, J/mol f i = the fugacity of pure component i with the same pressure and temperature to the liquid
mixtures ai = the activity of component i in liquid state T = the temperature of the flue gas, K P = the total partial pressure of water vapor and sulfuric acid in flue gas, Pa Pg = the total pressure of flue gas, Pa H i' 298 =
the enthalpy of component i in liquid state at 298 K, kJ/mol
H i"298 =
the enthalpy of component i in vapor state at 298 K, kJ/mol
Cpi" =
the specific heat of component i in vapor state, kJ/K
Cpi' =
the specific heat of component i in liquid state, kJ/mol·K
CPi'
= the partial specific heat of component i in liquid state, kJ/mol·K
A1–A4 = the constants depended on the sulfuric acid and water GREEK LETTERS = the activity coefficient
= the dielectric constant
SUPERSCRIPTS o=
the reference state (=101 325 Pa and real temperature)
= the pure substance of components
* = the property expressed in the unsymmetrical scale sat =
the saturation vapor pressure at the same temperature
SUBSCRIPTS SR = LR
the short-range interactions
= the long-range interactions
Born =
Born term correction to the unsymmetric Pitzer-Debye-Hückel formula
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gases by using an artificial neural network model. Energy Conv. Manag. 2011, 52 (2), 911-916. (13) Hrastel, I.; Gerbec, M.; Stergaršek, A. Technology optimization of wet flue gas desulfurization process. Chem. Eng. Technol. 2007, 30 (2), 220-233. (14) Okkes, A. G.; Badger, B. V. Get acid dew point of flue gas. Hydrocarb. Process. 1987, 66 (7), 53-55. (15) Haase, R.; Borgmann, H. W. Präzisionsmessungen zur ermittlung von sauertaupunkten. Korrosion. 1963, 15, 47-49. (16) Müller, P. Contribution to the problem of the action of sulfuric acid on the dew point temperature of flue gases. Chem. Eng. Technol. 1959, 31, 345-350. (17) Abel, E. The vapour-phase above the system sulphuric acid-water. J. Chem. Phys. 1946, 50 (3), 260-283. (18) Verhoff, F. H.; Banchero, J. T. Predicting dew pionts of fiue gas. Chem. Eng. Prog. 1974, 70 (8), 71-72. (19) Bahadori, A. Estimation of combustion flue gas acid dew point during heat recovery and efficiency gain. Appl. Therm. Eng. 2011, 31 (8), 1457-1462. (20) Weise, C.; Güsewell, M.; Heinze, G.; Tulling, R. Industrial investigations for the estimation of flue gas dew points. VGB Power Technology. 2000, 80 (8), 43-47. (21) ZareNezhad, B.; Aminian, A. A multi-layer feed forward neural network model for accurate prediction of flue gas sulfuric acid dew points in process industries. Appl. Therm. Eng. 2010, 30 (6), 692-696. (22) Weise, C.; Güsewell, M. Modeling of three-phase systems in flue gas. Chem. Eng. Technol. 2000, 23 (6), 489-493. (23) Liu, L.; Chen, Y.; Kang, Y. X.; et al. An industrial scale dehydration process for natural gas involving membranes. Chem. Eng. Technol. 2001, 24 (10), 1045-1048. (24) Blanco, J. M.; Pena, F. Increase in the boiler’s performance in terms of the acid dew point temperature: Environmental advantages of replacing fuels. Appl. Therm. Eng. 2008, 28 (7), 777-784. (25) Halstead, W. D.; Talbot, J. Sulphuric acid dew point in power station flue gases. J. Energy Inst. 1980, 53, 142-145. (26) Kamata, H.; Ohara, H.; Takahashi, K.; Yukimura, A.; Seo, Y. SO2 oxidation over the
V2O5/TiO2 SCR catalyst. Catal. Lett. 2001, 73 (1), 79-83. (27) Guo, Z. H.; Wang, Q. H.; Fang, M. X.; et al. Simulation of a lignite-based polygeneration system coproducing electricity and tar with carbon capture. Chem. Eng. Technol. 2015, 38 (3), 463-472. (28) Li, J.; Yan, W. P.; Gao, B. T.; Li, C. The calculation of the gas acid dew-point in utility boiler. Boiler Technology 2009, 40 (5), 14-17 (in Chinese). (29) Li, P. F.; Tong, H. L. Comparison and analysis on the calculation methods of acid dew point of flue gas. Boiler Technology 2009, 40 (6), 5-8 (in Chinese). (30) Jiang, A. Z.; Wang, G.; Shi, S. Y.; Zheng, S. H. Discussion on calculation formulate of boiler's acid dew-point temperature of gas. Boiler Technology 2009, 40 (5), 11-13 (in Chinese). (31) Wilson; G. M. Vapor–Liquid Equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc. 1964, 86 (2), 127-130. (32) Bollas, G. M.; Chen, C. C.; Barton, P. I. Refined electrolyte-NRTL model: Activity coefficient expressions for application to multi-electrolyte systems. AIChE Journal 2008, 54 (6), 1608-1624. (33) Chen, M. B.; Sun, K. Q.; Xu, H. T.; et al. Simulation of FGD by ammonia based on Aspen plus software. Pollution Control Technology 2009, 22 (1), 28-32 (in Chinese). (34) Chen, M. B.; Sun, K. Q. The application of Aspen plus software on the simulation of FGD by ammonia. Electric Power Environmental 2009, 25 (4), 30-32 (in Chinese). (35) Sun, Z. A.; Jin, B. S.; Li, Y.; Zhou, S. M. Simulation of wet FGD based on Aspen plus. Clean Coal Technology 2006, 12 (3), 82-85 (in Chinese). (36) Chen, C. C.; Song, Y. Generalized electrolyte-NRTL model for mixed-solvent electrolyte systems. AIChE Journal 2004, 50 (8), 1928-1941. (37) Pitzer, K. S. Electrolytes: From dilute solutions to fused salts. J. Am. Chem. Soc. 1980, 102 (9), 2902-2906. (38) Zudkevitch, D.; Joffe, J. Correlation and prediction of vapor–liquid equilibria with the Redlich-Kwong equation of state. AIChE Journal 1970, 16 (1), 112-119. (39) Chueh, P. L.; Prausnitz, J. M. Vapor–liquid equilibria at high pressures: Vapor–phase fugacity coefficients in nonpolar and quantum-gas mixtures. Ind. Eng. Chem. Fundamentals 1967, 6 (4), 492-498.
(40) Thomson, G. W. The Antoine equation for vapor–pressure data. Chemical reviews 1946, 38 (1), 1-39. (41) Fleig, D.; Vainio, E.; Andersson, K.; et al. Evaluation of SO3 measurement techniques in air and oxy-fuel combustion. Energy Fuels 2012, 26 (9), 5537-5549. (42) Land, T. The theory of acid deposition and its application to the dew-point meter. J. Inst. Fuel 1977, 50 (403), 68-75. (43) Xiang, B. X.; Zhang, M.; Zhang, H. R.; Lu, J. L.; et al. Prediction of the acid dew point in flue gas of boilers burning fossil fuels. Energy Fuels 2016, doi: 10.1021/acs.energyfuels.6b00491. (44) Weierstrass, V. K. Uber die analytische darstellbarkeit sogenannter willkürlicher funktionen einer reellen veränderlichen. Dtsch. Akad. Wiss. Berl. Kl. Math. Phys. Tech 1856, 9, 633-639. (45) Xiang, B. X.; Zhao, C. Z.; Ding, Y. J.; et al. Measuring and analyzing the prediction model on the acid dew point in flue gas. Journal of Tsinghua University (Science and Technology) 2015, 55 (10), 1117-1124 (in Chinese). (46) Xiang, B. X.; Xing, W. C.; Li, J. F.; et al. The measurement and correction of correlation formulas of flue gas acid dew point. Boiler Technology 2014, 45 (1), 1-4 (in Chinese).
APPENDIX Similar to the property of fugacity, the chemical potential of component i distributed in two phases are equal in the vapor–liquid equilibrium: i" i'
(A1)
As the vapors in flue gas can be considered as the ideal gas approximately under low pressure conditions, the chemical potential of component i in vapor state can be calculated as the following equation: i" i" RT ln yi
(A2)
^ v
For the ideal gas, f i is equal to the partial pressure of component i in vapor mixtures approximately: ^ v
f i Pi
(A3)
However, for the components in liquid state, due to the large difference between molecular
structure, chemical formula and electrical property, they can’t be considered as the ideal solution approximately. Then, the chemical potential of the component i in liquid state should be calculated as the following equation: i' i' RT ln ai
(A4)
For ai , it is equal to the ratio of the fugacity of component i in liquid state to that of the pure substance of component i under the same temperature and pressure conditions. So, there is ^ l
f ai i xi i fi
(A5)
where f i is the fugacity of pure component i with the same pressure and temperature to the liquid mixtures and xi is the volume fraction of component i in the liquid mixtures. And i , the activity coefficient of component i, is the ratio of the fugacity of component i in the real solution to that in the ideal solution under the same temperature, pressure and compositions. For f i , it can be considered as the saturation vapor pressure of component i at the same temperature approximately. By substituting Eqs. (1) and (A3) into Eq. (A5), the following formula can be derived: ai
Pi Pi sat
(A6)
By substituting Eqs. (A2) and (A4) into Eq. (A1), there is i' RT ln ai i" RT ln yi
(A7)
For T , H and , the correlation formula is as follows: T H 2 T T
(A8)
Moreover, H can be computed using the following formula: T
H H 298 +
C
p
dT
298
By substituting Eq. (A9) into Eq. (A8), there is
(A9)
T T 1 2 H 298 CP d T T T 298
(A10)
Thus, the following equations can be derived: i' T T
T 1 H ' C ' d T i 298 Pi 2 T 298
(A11)
i" T T
T 1 H " C " d T i 298 Pi T2 298
(A12)
By substituting Eqs. (A11) and (A12) into Eq. (A10), there is i' i" T T
T 1 H ' H " CPi' CPi" d T i 298 i 298 2 T 298
(A13)
By integration on T of Eq. (A13), the following equation can be derived: i' i" T
i'298 i"298
298
T T H i'298 H i"298 H ' Hi"298 1 i 298 2 CPi' CPi" dTdT T 298 298 T 298
(A14)
Moreover, as discussed above, the multi-component system in the ELECNRTL can be simplified as a binary sulfuric acid-water system. Henceforth, the component of sulfuric acid is represented with the subscript 1, while the subscript 2 represents the component of water vapor in this work. By submitting Eq. (A5) to Eq. (A6), there is ln a1 ln( x1 1 ) ln(
P P2 ) P1sat
(A15)
By submitting Eq. (A15) into Eq. (A6), there is P1sat
P P2 a2 sat P2 P2 a1
(A16)
where P2sat , depended on the temperature of water vapor, can be calculate as the following formula approximately [38], ln P2sat 9.3876
3826.36 T 45.47
(A17)
By simplifying Eq. (A4), there is ai exp(
i' i' RT
Thus, the following equation can be derived:
)
(A18)
a2 ' 2' 1' 1' exp( 2 ) a1 RT RT
(A19)
By substituting Eq. (A18) into Eq. (A16), there is P1sat
P P2 ' 2' 1' 1' exp( 2 ) P2sat P2 RT RT
(A20)
Additionally, i' and i' in Eq. (A20) can be calculated from the following equations respectively: i' i' 298
T
C
' Pi
dT
(A21)
' Pi
dT
(A22)
298
i' i'298
T
C
298
By substituting Eqs. (A16) and (A19) into Eq. (A15), there is ln a1 ln(
P2 1' 1' 2' 2' ) RT RT P2sat
(A23)
By submitting Eqs. (A20), (A21), (A22) and (A23) into (A15), an improved thermodynamic correlation formula between the acid dew point in flue gas and its influencing factors is derived: ln P1 ln(
T T P2 1 1 ' ' ' ' ' ' ' ' ) ( C C dT ) ( 1,298 1,298 2,298 2,298 298 P1 P1 298 CP2 CP2 dT ) RT RT P2sat
ln P
' " 1,298 1,298
R 298
' " H1,298 H1,298
RT
' " H1,298 H1,298
R 298
T
1 2 298 T
T
C
298
' P1
CP1" dTdT
(A24)
LIST OF TABLES 1.
Table 1. The prediction models on the acid dew point in previous studies [5-6, 14-18, 25]
2.
Table 2. B, n of the correlation formula contained experimental constants [5]
3.
Table 3. The coefficients in Eq. (24) with the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa
Table 1. The prediction models on the acid dew point in previous studies Name
Correlation
Müller[16, 17]
tadp = 116.5515 +16.06329lg PSO 3 +1.05377(lg PSO 3 )2
Halstead[25]
tadp = 113.0219 +15.0777lg PH 2SO 4 + 2.0975(lg PH 2SO 4 )2
Okkes-A[14]
tadp = 10.8809 + 27.6lg PH 2 O +10.83lg PSO 3 +1.06(lg PSO 3 + 2.9943) 2.19
Pa
Okkes-B[14]
tadp = 203.25 + 27.6lg PH 2 O +10.83lg PSO 3 +1.06(lg PSO 3 + 8)2.19
atm
Verhoff-A[18]
1000 = 1.7842 + 0.0269lg PH 2 O - 0.1029lg PSO 3 + 0.0329lg PH 2 O lg PSO 3 tadp + 273.15
atm
Verhoff-B[18]
1000 = 2.9882 0.1376lg PH 2 O - 0.2674lg PSO 3 + 0.03287lg PH 2 O lg PSO 3 tadp + 273.15
Pa
Japan Institute of Electric Power Industry[5]
tadp = 20lg PSO3 + a - 80
Correlation contained experimental constants[5]
tadp = tdp + B( PH 2SO 4 )n
Haase[15]
tadp = 255.0 +18.7lg PH 2 O + 27.6lg PSO3
Bаранова[5]
tadp = 186 + 20lg PH 2 O + 26lg PSO3
Soviet Union calculation standard[6]
tadp =
3 S 1.05ah
A
tdp
Remark
Table 2
Table 2. B, n of the correlation formula contained experimental constants [5] PH 2O PSO3 A B
Pa B n B n
2000 200.2 0.1224 289.9 0.0987
4000 202.4 0.0907 289.3 0.1014
6000 204.2 0.0732 288.7 0.1038
8000 206.3 0.0659 288.7 0.1063
12000 210.2 0.0622 286.9 0.1107
16000 214.2 0.0636 285.6 0.1145
20000 218.3 0.0661 284.4 0.1178
28000 226.4 0.0720 281.9 0.1229
36000 234.0 0.0780 -
Table 3. The coefficients in Eq. (24) with the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa item
a11 a12 a13 a14 a21 a22 a23 a24 a31 a32 a33 a34 a41 a42 a43 a44
2026.5 PH2O <5066.25 -10
-4.9 700×10 5.7 733×10-6 -2.4 998×10-2 4.5 769×101 6.0 543×10-5 -6.7 732×10-1 3.0 788×103 -5.8 617×106 3.4 706×10-7 -3.8 873×10-3 1.7 550×101 -3.2 727×104 -2.0 321×10-6 2.2 756×10-2 -1.0 286×102 1.9 244×105
5066.25 PH2O <8106 -9
4.3 130×10 -8.8 577×10-5 5.9 715×10-1 -1.3 152×103 -5.6 583×10-4 1.1 622×101 -7.8 363×104 1.7 251×108 -3.1 256×10-6 6.4 194×10-2 -4.3 280×102 9.5 300×105 1.8 417×10-5 -3.7 825×10-1 2.5 502×103 -5.6 152×106
8106 PH2O 10132.5
10132.5< PH2O 12159
12159< PH2O 15198.75
0 -8.4 598×10-6 1.4 831×10-1 -6.438×102 0 1.1 067×100 -1.9 400×104 8.4 116×107 0 6.1 212×10-3 -1.0 731×102 4.6 558×105 0 -3.6 058×10-2 6.3 213×102 -2.7 423×106
0 -3.5 724×10-6 7.7 289×10-2 -4.2 592×102 0 4.6 972×10-1 -1.0 156×104 5.5 851×107 0 2.5 913×10-3 -5.6 046×101 3.0 856×105 0 -1.5 272×10-2 3.3 028×102 -1.8 180×106
-3.3 980×10-9 1.4 328×10-4 -1.9 955×100 9.1 746×103 4.5 294×10-4 -1.9 094×101 2.6 588×105 -1.2 224×109 2.4 819×10-6 -1.0 464×10-1 1.4 572×103 -6.6 995×106 -1.4 644×10-5 6.1 736×10-1 -8.5 973×103 3.9 527×107
LIST OF FIGURES 1. Fig. 1 The predicted acid dew points using Müller model [16] 2. Fig. 2 The acid dew point testing apparatus [43] 3. Fig. 3 The measured acid dew points under the experimental flue gas conditions [43] 4. Fig. 4 The predicted acid dew points using present model 5. Fig. 5 Comparison between the values predicted using the models and experimental data in a previous paper [45] 6. Fig. 6 Comparison between the values predicted using the models and field test data [46]
Figure 1. The predicted acid dew points using Müller model [16]
Figure 2. The acid dew point testing apparatus [43] 1-syringe pump; 2-sulfuric acid; 3-quartz glass tube; 4-tubular furnace; 5-mass flow meter; 6-mass flow controller; 7-peristaltic pump; 8- temperature instrument; 9- ammeter; 10- DC power; 11- thermostatic water tank; 12electrode; 13- pump; 14- bakelite tube; 15- gas tank; 16- thermocouple; 17-heated cloth and insulate cotton; 18regenerator
Figure 3. The measured acid dew points under the experimental flue gas conditions [43]
Figure 4. The predicted acid dew points using present model
Figure 5. Comparison between the values predicted using the models and experimental data in a previous paper [45]
Figure 6. Comparison between the values predicted using the models and field test data [46]
Highlights
The previous semi-empirical models are systematically studied
An improved thermodynamic correlation is derived
A semi-empirical prediction model is proposed
The proposed semi-empirical model is validated
S1359-4311(16)30946-2 http://dx.doi.org/10.1016/j.applthermaleng.2016.06.040 ATE 8451
To appear in:
Applied Thermal Engineering
Received Date: Accepted Date:
20 April 2016 6 June 2016
Please cite this article as: B. Xiang, B. Tang, Y. Wu, H. Yang, M. Zhang, J. Lu, Predicting Acid Dew Point with A Semi-empirical Model, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng. 2016.06.040
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Predicting Acid Dew Point with A Semi-empirical Model Baixiang Xiang, Bin Tang, Yuxin Wu, Hairui Yang, Man Zhang, Junfu Lu* Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China
ABSTRACT Decreasing the temperature of exhaust flue gas in boilers is one of the most effective ways to further improve the thermal efficiency, electrostatic precipitator efficiency and to decrease the water consumption of desulfurization tower, while, when this temperature is below the acid dew point, the fouling and corrosion will occur on the heating surfaces in the second pass of boilers. So, the knowledge on accurately predicting the acid dew point is essential. By investigating the previous models on acid dew point prediction, an improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived first. And then, a semi-empirical prediction model is proposed, which is validated with the data both in field test and experiment, and comparing with the previous models. Keywords: Flue gas; Acid dew point; Aspen plus; Semi-empirical model
1. INTRODUCTION Given the presence of sulfur, nitrogen, carbon and other elements in the fuel, the flue gas in boilers typically contains some acidic gases such as SO2, SO3, NO, NO2 and CO2, etc. These acidic gases will further react with the water vapor in the flue gas to generate acid vapors under low temperature conditions [1-4]. When the temperature of outer wall of convection heating surface in the second pass of boilers is below the acid dew point, the acid vapors in flue gas will condense and form acidic droplets on the heating surfaces. Actually, the acid dew point depends on the content of sulfur trioxide and the partial pressure of water vapor in flue gas [2-15]. The condensed acidic droplets not only cause serious acidic corrosion to the metal heating surfaces [5-6], but also further react with the flaking rust and the fly ash in the second pass of boilers. The fouling will occur under such condition. Once the fouling occupies in the flow channel, the burden
of induced draft fan will be significantly increased. The increasing burden of induced draft fan will cause the content of O2 in boilers decreased. More importantly, the combustion in boilers will be seriously deteriorated under such a condition. Besides, the velocity of flue gas is increased by a great extent due to the occupied fouling in the flow channel. The wear of the metal heating surfaces in the second pass of boilers will be severe. Considering the safety of the power generation unit, the temperature of exhaust flue gas must be strictly controlled over the acid dew point [14-19]. However, in order to cope with the increasing demand of the energy-saving and emission-reduction, decreasing the temperature of exhaust flue gas in boilers is one of the most effective ways to further improve the thermal efficiency, electrostatic precipitator efficiency and to decrease the water consumption of desulfurization tower [20-30]. Therefore, how to accurately predict the acid dew point become the key point. So far, different models for predicting acid dew points of flue gas have been reported in previous studies, as listed in Table 1 [5-6, 14-18, 25]. Theβ, generally 125, depends on the excess-air ratio in the boiler [6]. The a, dependent on the partial pressure of water vapor in the flue gas, is 184, 194 and 201 when the water vapor partial pressure is 5066 Pa, 10132 Pa and 15199 Pa, respectively [5]. And the values of B and n in the correlation formula contained experimental constants under different flue gas conditions are listed in Table 2 [5]. Moreover, with the research progress in computer technology and multiple phase equilibrium in recent years [31-39], the acid dew point of flue gas can be also predicted using a software, namely, Aspen plus. In general, these models can be divided into empirical and semi-empirical according to the data processing methods. The empirical models are usually established by fitting the experimental results and the field test data with mathematical methods directly. For example, Verhoff, et al. [18] proposed an empirical model by fitting the acid dew points of flue gas using the least square method, which measured with a cooled electrical conductivity probe. Halstead, et al. [25] derived a graph between the acid dew point and its influencing factors based on the vapor pressure data determined by using the gas saturation technique, which used to predict the acid dew point in the flue gas of oil-fired power plant. Okkes, et al. [14] proposed a graph for estimating the sulfuric acid dew point in flue gas based on the fuel compositions and excess-air ratio. Haase et al. [15] measured the acid dew points and the resistance of flue gas with a circulation system designed
according to the boiling point measurement principle of Cottrell. The compositions of the flue gas are determined according to the corresponding measured resistance. Based on the measured acid dew points and compositions of flue gas, Haase et al. [15] proposed an empirical prediction model. In addition, there have been other empirical models, which built by fitting the field test data directly, such as the Soviet Union thermodynamic calculation standard of boiler in 1973, the correlation formula contained experimental constants and the prediction model proposed by Japan institute of electric power industry [5-6]. However, according to the long operating experience of many power plants in China [28-30], not only is the applicability of the above empirical prediction models strictly limited, but the predicted values are generally not so good. Different to the empirical prediction models, data processing of the semi-empirical model is correlated to the thermodynamic correlation formula between the acid dew point and its influencing factors. Thus, not only the accuracy of the predicted acid dew points in flue gas can be improved, but also the applicability of the prediction model. In fact, the thermodynamic correlation formula can be derived according to the equivalent of the chemical potential and fugacity in each phase of a component in the vapor–liquid equilibrium. The fugacity in each phase of a component can be used the following models, namely, the equation of state (EOS) and the equation of state and activity coefficient (EOS + γ) models. Given the lack of an equation of state that can formulate the sulfuric acid in both vapor state and liquid state, the acid dew point in flue gas cannot be predicted accurately using EOS. To date, Aspen plus established the thermodynamic correlation formula based on EOS + γ. However, given the lack of binary interaction coefficients of H2SO4 and H2O in the activity coefficient models reported in previous studies [31-32], the acid dew point in flue gas seems difficult to be predicted accurately using Aspen plus. Thus far, based on the equivalent of chemical potential in each phase of H 2SO4, Müller et al. [16] derived the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid. Then, according to the dew points of sulfuric acid with a concentration ranging from 5% to 85% [17], Müller et al. [16] proposed a semi-empirical prediction model, as shown in Figure 1. However, given the limited understanding on the influencing factors of acid dew point and not enough rigorous derivation of the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid, the predicted values seem to be too high [28-30]. Thus, in this work, the
semi-empirical prediction models reported in previous studies are investigated, and an improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived. Then, a semi-empirical prediction model for the acid dew point in flue gas that considers the function of sulfuric acid and water is proposed based on previous experimental data. Moreover, the prediction model proposed in this work is validated by the field test data, the experimental data, and prediction models reported in previous studies.
2. PREVIOUS SEMI-EMPIRICAL PREDICTION MODELS 2.1 Prediction Model of Aspen plus The optimal physical method is ELECNRTL when the acid dew point in flue gas is predicted using Aspen plus [33-35]. Actually, the ELECNRTL is derived based on the vapor–liquid equilibrium in the multi-compound poly-phase system [31-39]. As the fugacity of one component distributed in different phases are equal in the vapor–liquid equilibrium, the following equation can be derived: fˆi v fˆi l
(1)
For the ELECNRTL, the activity coefficient of components in liquid state is calculated with the Electrolyte NRTL, while the fugacity coefficient of components in vapor state is calculated with the state equation of Redlich-Kwong. In the Electrolyte NRTL, due to the small mole fraction of sulfuric acid in flue gas (e. g. several ppm), the activity coefficient of component i in liquid state ( fˆi l ) can be calculated with the unsymmetrical convention [32, 36]. So, there is fˆi l H i,
Solvent
* xi
(2)
i
where H i, Solvent is the Henry constant of solute i in the solvent, xi is the mole fraction of component i in the liquid mixtures and i* , the activity coefficient of component i with the unsymmetrical convention, is the ratio of the fugacity of component i in the real solution to that in the ideal dilute solution under the same temperature, pressure and compositions. For the fugacity of component i in vapor state ( fˆi v ), it can be calculated as the following equation approximately under low pressure conditions [38],
(3)
fˆi v Pg yiˆi
where Pg is the total pressure of flue gas, yi is the volume fraction of component i in the vapor mixtures and ˆi is the fugacity coefficient of component i in vapor state. Based on the previous studies on the Electrolyte NRTL [32, 36], the excess Gibbs free energy contains three contributions: the short-range interactions between species ( G*,SR ), the long-range electrostatic interactions ( G*,LR ) and the energy needed to transfer the ionic species from the infinitely dilute mixed-solvent medium to the infinitely diluted aqueous solution ( G*,Born ). So, there is G*,ex G*,SR G*,LR G*,Born
(4)
Moreover, for ln i* and G*,ex , the correlation formula is as follows:
ln i*
1 G*,ex RT Ni T , P , N ji
(5)
Submitting Eq. (4) to Eq. (5), the expression of the activity coefficient of component i in liquid state is derived: ln i* ln i*Born ln i*L R ln i*S R
(6)
where i*SR is the activity coefficient of component i in the short-range interactions, i*L R is the activity coefficient of component i in the long-range interactions, ln i*Born is the born term correction to logarithm of activity coefficient of component i. For the activity coefficient of component i in the short-range interactions ( i*SR ), Bollas et al. [32] and Chen et al. [36] introduced its derivation in some detail. To account for the long-range ion-ion interactions ( ln i*L R ), Pitzer et al. [37] proposed the Pitzer-Debye-Hückel theory. Thus, there is ln i*LR A [
2 zi2
ln(1 I x1/ 2 )
zi2 I x1/ 2 2 I x3/ 2 ] 1 I x1/ 2
(7)
where I x is the ionic strength, A is the Debye-Hückel parameter, is the closest approach parameter and zi is the charge number of segment-based species i. Besides, for the born term correction to logarithm of activity coefficient ( ln i*Born ), Bollas et al. [32] proposed its expression as the following formula:
ln i*Born
Qe2 1 1 z2 ( ) i 102 2kT s w ri
(8)
where k is the Boltzmann constant, 1.3806 1023 J/ K , ri is the Born radius of segment species i, s is the dielectric constant of the solvent, w is the dielectric constant of the water and Qe is the electron charge. Compared to the state equation of Benedict-Webb-Rubin (B-W-R), the state equation of Redlich-Kwong (R-K) is more attractive for the mixtures because the simple manner in which binary interaction constants can be introduced into it. Thus, Zudkevitch et al. [38] derived the fugacity coefficient of component i in vapor state ( ˆi ) based on R-K.
2.2 Prediction Model Proposed by Müller For the semi-empirical prediction model on acid dew point proposed by Müller and Abel [16-17], the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid is derived based on the equal of chemical potential in each phase of sulfuric acid in the vapor–liquid equilibrium. So, there is i" i'
(9)
where i' is the chemical potential of sulfuric acid in liquid state, while i" is the chemical potential of sulfuric acid in vapor state. Considered as the ideal gas approximately under low pressure conditions, the chemical potential of sulfuric acid in vapor state can be calculated as the following formula: i" i"o RT ln( Pi / Po )
(10)
where i"o is the chemical potential of sulfuric acid in vapor state with the reference state (101325 Pa and real temperature), Pi is the pressure of the sulfuric acid vapor and Po is the reference pressure (101325 Pa). However, as the sulfuric acid in liquid state cannot be considered as the ideal solution approximately, its chemical potential should be calculated as the following formula: i' i'o RT ln ai
(11)
where ai is the activity of sulfuric acid and i'o is the chemical potential of sulfuric acid in liquid state with the reference state. Submitting Eqs. (10) and (11) to Eq. (9), there is
RT ln Pi = i'o i"o + RT ln ai
(12)
Additionally, SO3 in the flue gas starts to combine with H2O and form sulfuric acid vapor when the temperature of flue gas is cooled down to 773 K: C o o l i n g S O3 ( g ) + H g ) 2 O(
2
H SO (g) 4
(13)
where the partial pressure of reactants in Eq. (13) can be essentially equal to the corresponding fugacity. Thus, for the equilibrium constant of Eq. (13), there is RT ln Kp = i"o w"o o"o
(14)
where K p is the equilibrium constant of Eq. (13), w"o is the chemical potential of water vapor with the reference state and o"o is the chemical potential of sulfur trioxide with the reference state. Submitting Eq. (12) to Eq. (14), the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid is derived: RT ln Pi i'o w"o o"o RT ln Kp RT ln ai
(15)
3. A SEMI-EMPIRICAL PREDICTION MODEL 3.1 An Improved Thermodynamic Model In the ELECNRTL, the acid dew pint of flue gas is calculated based on the vapor–liquid equilibrium in the multi-compound poly-phase system. However, Huijbrejts et al. [3] found that the sulfuric acid vapor will condense first with the decreasing of flue gas temperature, because the boiling point of sulfuric acid is highest in flue gas under the same conditions. Actually, as mentioned, the acid dew point depends mainly on the content of sulfur trioxide and the partial pressure of water vapor in flue gas [2-15]. Thus, the multi-compound poly-phase system in ELECNRTL can be simplified to the binary sulfuric acid-water system. Besides, in the Electrolyte NRTL, the activity coefficient of component i in liquid state ( fˆi l ) is calculated with the unsymmetrical convention. However, Fleig et al. [41] and Land et al. [42] found that the condensed sulfuric acid and water formed an azeotrope and the condensate sulfuric acid-water mixture typically contained more than 70 mole % sulfuric acid. More importantly, there is a lack of binary interaction coefficients of sulfuric acid and water in the thermodynamic models reported
in the previous studies [31-32]. Therefore, the activity coefficient calculated using the Electrolyte NRTL seems to be not accurate enough. For the semi-empirical prediction model for acid dew point proposed by Müller and Abel [16-17], not only is the influencing factor of water vapor not considered, but the reaction equilibrium constant of Eq. (13) ( K p ) seems no need to be calculated because Fleig et al. [1] and Stuart et al. [2] found that the sulfur trioxide is almost completely converted to sulfuric acid when the temperature of flue gas is cooled down to 473 K. Considering the above reasons, thus, an improved thermodynamic correlation formula between the acid dew point and its influencing factors is required. Similar to the property of fugacity, the chemical potential of component i distributed in two phases are equal in the vapor–liquid equilibrium. Thus, there is i" i'
(16)
where i' is the chemical potential of component i in liquid state and i" is the chemical potential of component i in vapor state. As the vapors in flue gas can be considered as the ideal gas approximately under low pressure conditions, the chemical potential of component i in vapor state is calculated as the following equation: i" i" RT ln yi
(17)
where i" is the chemical potential of pure component i in vapor state with the same pressure and temperature to the vapor mixtures, yi is the volume fraction of component i in the vapor mixtures. However, for the components in liquid state, due to the large difference between molecular structure, chemical formula and electrical property, they cannot be considered as the ideal solution approximately. Thus, the chemical potential of the component i in liquid state should be calculated as the following equation: i' i' RT ln ai
(18)
where ai is the activity of component i and i' is the chemical potential of pure component i in liquid state with the same pressure and temperature to the liquid mixtures. By submitting Eqs. (17) and (18) to Eq. (16), there is
i' RT ln ai i" RT ln yi
(19)
For T , H and , the correlation formula is as follows: T H 2 T T
(20)
where H can be computed using the following formula: T
H H 298 +
C
p
(21)
dT
298
Additionally, as discussed above, the multi-component system in the ELECNRTL can be simplified as a binary sulfuric acid-water system. Henceforth, the component of sulfuric acid is represented with the subscript 1, while the subscript 2 represents the component of water vapor in this work. Therefore, an improved thermodynamic correlation formula between the acid dew point in flue gas and its influencing factors is derived: ln P1 ln(
T T P2 1 1 ' ' ' ' ) ( 1,298 1,298 CP1' CP1' dT ) ( 2,298 2,298 CP2' CP2' dT ) sat RT RT P2 298 298
ln P
' " 1,298 1,298
R 298
' " H1,298 H1,298
RT
' " H1,298 H1,298
R 298
T
T
T C 1
2
298
' P1
(22)
CP1" dTdT
298
where P is the total partial pressure of water vapor and sulfuric acid in the flue gas, P2sat is the saturated vapor pressure of water in flue gas, i' 298 is the chemical potential of component i in liquid state at 298 K, i'298 is the chemical potential of pure component i in liquid state at 298 K, CPi' is the specific heat of pure component i in liquid state, H i' 298 is the enthalpy of component i
in liquid state at 298 K, H i"298 is the enthalpy of component i in vapor state at 298 K, specific heat of component i in vapor state, and
CPi'
Cpi'
Cpi"
is the
is the specific heat of component i in liquid state
is the partial specific heat of component i in liquid state. For the derivation of Eq. (22), it
is given in detail in Appendix. By simplifying Eq. (20), there is ln P1 AT 1
A2 P2 A3 ln T A4 ln P ln( sat ) T P2
(23)
where A1–A4 are the constants depended on the sulfuric acid and water. The units of P , P1 , P2 , P2sat and T are Pa, Pa, Pa, Pa and K, respectively.
3.2 A Semi-empirical Prediction Model Eq. (23) presented the thermodynamic correlation formula between the acid dew point in flue
gas and its influencing factors, however, it can’t be used to predict the acid dew point in flue gas because it seems impossible to calculate the constants of Eq. (23) directly based on the thermophysical parameters of sulfuric acid and water. Fortunately, the correlation formula between the constants of Eq. (23) and the partial pressure of water vapor and sulfuric acid can be fitted using mathematic methods based on the experimental data. In our previous work [43], the acid dew points in flue gas under different conditions were measured by a measuring apparatus designed based on the principle of conductive dew point meter, as shown in Figure 2. With the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa respectively, the measured results are shown in Figure 3 [43]. Considering the trends of the acid dew point with the partial pressure of water vapor and sulfuric acid and the first approximation theorems of Weierstrass [44], the correlation formula between the constants of Eq. (23) and the partial pressure of water vapor and sulfuric acid can be expressed by a polynomial. By fitting the experimental data in Figure 3 with the least square method, the correlation formula between the constants of Eq. (23) and the partial pressure of water vapor can be formulated as the following third-order polynomial with the partial pressure of sulfuric acid ranging from 0.5066 Pa to 2.0265 Pa, Aj a j1 PH2 O3 a j 2 PH2 O 2 a j 3 PH2 O a j 4
j 1, 2, 3, 4
(24)
The coefficients of Eq. (24) under different conditions are listed in Table 3, thus, the constants of Eq. (23) can be determined. Therefore, a semi-empirical prediction model for the acid dew point in flue gas, the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa, is proposed, as shown in Figure 4. It can be found that the increasing slope of the acid dew point becomes smaller both at higher sulfuric acid vapor partial pressure and higher water vapor partial pressure.
4. RESULTS AND DISCUSSION 4.1 Comparative Analysis of Experimental Data Figure 5 describes a comparison between the experimental data in a previous paper [45] and the values predicted using the model proposed in this work, Aspen plus and the models listed in
Table 1 under the same flue gas conditions. As mentioned, different from the application of the present model, the partial pressure of sulfuric acid and water vapor in Halstead model ranges from 0 Pa to 2 Pa and from 0 Pa to 14,185.5 Pa, respectively [25]. The partial pressure of sulfuric acid in the Müller model ranges from 0 Pa to 1,013.25 Pa [16]. Moreover, for the prediction model proposed by Haase, the partial pressure of water vapor and sulfuric acid ranges from 7,092 Pa to 101,325 Pa and 0.1013 Pa to 20.265 Pa, respectively [15]. The experimental data in reference [45] are measured using a device built based on the principle of conductive dew point meter, which is completely different from the measuring device designed in reference [43]. Not only is the flue gas cooled using compressed air, but the electrodes are arranged in a ring-shaped manner. Moreover, the distance between the positive and negative electrodes is increased to 3 mm. As shown in Figure 5, the values predicted with the previous models, except for the model suggested by Haase and Aspen plus, are generally too high under the same conditions mentioned above. The values predicted using the Haase model and Aspen plus are slightly higher than the corresponding experimental data for small mole fraction of sulfuric acid, while they become significantly lower for large mole fraction of sulfuric acid. Comparably, the values predicted using Aspen plus seems to be better consistent with the experimental data for small mole fraction of sulfuric acid, while, the values predicted using the Haase model seems to be better consistent for large mole fraction of sulfuric acid. Thus, compared to the above two models, the values predicted with the present model show better agreement with the experimental data.
4.2 Comparative Analysis of Field Test Data To further validate the prediction model proposed in this work, the acid dew points of a 150MWe coal-fired circulating fluidized bed boiler with limestone desulfurization are tested under different flue gas conditions [46]. In the field test, the sulfur content of the coal is maintained at 0.74%, and a series of different flue gas conditions were obtained by adjusting the excess-air ratio. When the partial pressure of the sulfuric acid vapor and water vapor are 1.8542 Pa, 1.986 Pa, 3.8807 Pa and 12159 Pa, 10234 Pa, 8511 Pa respectively, the tested acid dew point is 361K, 366K and 372K, respectively [46]. Figure 6 shows a comparison between the field test data and the values predicted using the present model, Aspen plus and the previous models listed in Table 1 under the same flue gas conditions mentioned above. Similar to the comparative results showed in
Figure 5, the values predicted with the previous models, except for the Haase model, Aspen plus and the Soviet one, are generally too high. In the field test, it found that the fly ash in flue gas could wrap the condensate sulfuric acid droplets and seemed to cause the measured acid dew points lower by the measuring apparatus [46]. In addition, the comparative results of Figure 6 show that the values predicted with Aspen plus and the Soviet one are even lower than the corresponding field test data for large mole fraction of sulfuric acid. Besides, the values predicted using the Soviet one slightly decreases with the increasing of mole fraction of sulfuric acid. Comparably, the values predicted with the model proposed in this work seems to be better consistent with the field test data. Therefore, based on the comparative results of field test and experimental data, the values predicted with the present model are more reliable than those predicted using the previous models.
5. CONCLUSIONS By investigating the previous models on acid dew point prediction, an improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived first. And then, a semi-empirical prediction model is proposed. In the condition of water vapor and sulfuric acid partial pressure ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa, the prediction model proposed in this work seems to be more reliable than the previous models. The fly ash in flue gas, the average size and the concentration, may have unclear effective on the acid dew point. In present work, the acid dew point measured by using the apparatus designed based on the principle of conductive dew point meter is lower, while, some researchers argued that the measured one seemed to be higher due to the function of the condensation nucleus formed by the submicron fly ash particles. Therefore, the influence of fly ash particles in the flue gas will be studied in future research.
AUTHOR INFORMATION Corresponding author
*E-mail address: [email protected] (J. Lu). Tel.: +86-01-62792647.
Notes The authors declare no competing financial interest.
ACKNOWLEDGEMENTS Financial support of this work by the National Program on Key Basic Research Project (973 Program) of China (No. 2012CB214900) is gratefully acknowledged.
NOMENCLATURE fˆi v =
the fugacity of component i in vapor state
fˆi l =
the fugacity of component i in liquid state
H i, Solvent = the Henry constant of solute i in the solvent
xi = the mole fraction of component i in the liquid mixtures yi = the mole fraction of component i in the vapor mixtures Pi = the partial pressure of component i, Pa Po = the reference pressure (=101 325 Pa)
ˆi = the fugacity coefficient of component i in vapor state I x = the ionic strength (segment mole fraction scale)
= the closest approach parameter A = the Debye-Hückel parameter
k = the Boltzmann constant, 1.3806 1023 , J/K K p = the reaction equilibrium constant of Eq. (13) "o w = the chemical potential of water vapor with the reference state
o"o = the chemical potential of sulfur trioxide with the reference state zi = the charge number of segment-based species i ri = the Born radius of segment species i
Qe = the electron charge
i' = the chemical potential of component i in liquid state, kJ/mol i" = the chemical potential of component i in vapor state, J/mol f i = the fugacity of pure component i with the same pressure and temperature to the liquid
mixtures ai = the activity of component i in liquid state T = the temperature of the flue gas, K P = the total partial pressure of water vapor and sulfuric acid in flue gas, Pa Pg = the total pressure of flue gas, Pa H i' 298 =
the enthalpy of component i in liquid state at 298 K, kJ/mol
H i"298 =
the enthalpy of component i in vapor state at 298 K, kJ/mol
Cpi" =
the specific heat of component i in vapor state, kJ/K
Cpi' =
the specific heat of component i in liquid state, kJ/mol·K
CPi'
= the partial specific heat of component i in liquid state, kJ/mol·K
A1–A4 = the constants depended on the sulfuric acid and water GREEK LETTERS = the activity coefficient
= the dielectric constant
SUPERSCRIPTS o=
the reference state (=101 325 Pa and real temperature)
= the pure substance of components
* = the property expressed in the unsymmetrical scale sat =
the saturation vapor pressure at the same temperature
SUBSCRIPTS SR = LR
the short-range interactions
= the long-range interactions
Born =
Born term correction to the unsymmetric Pitzer-Debye-Hückel formula
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APPENDIX Similar to the property of fugacity, the chemical potential of component i distributed in two phases are equal in the vapor–liquid equilibrium: i" i'
(A1)
As the vapors in flue gas can be considered as the ideal gas approximately under low pressure conditions, the chemical potential of component i in vapor state can be calculated as the following equation: i" i" RT ln yi
(A2)
^ v
For the ideal gas, f i is equal to the partial pressure of component i in vapor mixtures approximately: ^ v
f i Pi
(A3)
However, for the components in liquid state, due to the large difference between molecular
structure, chemical formula and electrical property, they can’t be considered as the ideal solution approximately. Then, the chemical potential of the component i in liquid state should be calculated as the following equation: i' i' RT ln ai
(A4)
For ai , it is equal to the ratio of the fugacity of component i in liquid state to that of the pure substance of component i under the same temperature and pressure conditions. So, there is ^ l
f ai i xi i fi
(A5)
where f i is the fugacity of pure component i with the same pressure and temperature to the liquid mixtures and xi is the volume fraction of component i in the liquid mixtures. And i , the activity coefficient of component i, is the ratio of the fugacity of component i in the real solution to that in the ideal solution under the same temperature, pressure and compositions. For f i , it can be considered as the saturation vapor pressure of component i at the same temperature approximately. By substituting Eqs. (1) and (A3) into Eq. (A5), the following formula can be derived: ai
Pi Pi sat
(A6)
By substituting Eqs. (A2) and (A4) into Eq. (A1), there is i' RT ln ai i" RT ln yi
(A7)
For T , H and , the correlation formula is as follows: T H 2 T T
(A8)
Moreover, H can be computed using the following formula: T
H H 298 +
C
p
dT
298
By substituting Eq. (A9) into Eq. (A8), there is
(A9)
T T 1 2 H 298 CP d T T T 298
(A10)
Thus, the following equations can be derived: i' T T
T 1 H ' C ' d T i 298 Pi 2 T 298
(A11)
i" T T
T 1 H " C " d T i 298 Pi T2 298
(A12)
By substituting Eqs. (A11) and (A12) into Eq. (A10), there is i' i" T T
T 1 H ' H " CPi' CPi" d T i 298 i 298 2 T 298
(A13)
By integration on T of Eq. (A13), the following equation can be derived: i' i" T
i'298 i"298
298
T T H i'298 H i"298 H ' Hi"298 1 i 298 2 CPi' CPi" dTdT T 298 298 T 298
(A14)
Moreover, as discussed above, the multi-component system in the ELECNRTL can be simplified as a binary sulfuric acid-water system. Henceforth, the component of sulfuric acid is represented with the subscript 1, while the subscript 2 represents the component of water vapor in this work. By submitting Eq. (A5) to Eq. (A6), there is ln a1 ln( x1 1 ) ln(
P P2 ) P1sat
(A15)
By submitting Eq. (A15) into Eq. (A6), there is P1sat
P P2 a2 sat P2 P2 a1
(A16)
where P2sat , depended on the temperature of water vapor, can be calculate as the following formula approximately [38], ln P2sat 9.3876
3826.36 T 45.47
(A17)
By simplifying Eq. (A4), there is ai exp(
i' i' RT
Thus, the following equation can be derived:
)
(A18)
a2 ' 2' 1' 1' exp( 2 ) a1 RT RT
(A19)
By substituting Eq. (A18) into Eq. (A16), there is P1sat
P P2 ' 2' 1' 1' exp( 2 ) P2sat P2 RT RT
(A20)
Additionally, i' and i' in Eq. (A20) can be calculated from the following equations respectively: i' i' 298
T
C
' Pi
dT
(A21)
' Pi
dT
(A22)
298
i' i'298
T
C
298
By substituting Eqs. (A16) and (A19) into Eq. (A15), there is ln a1 ln(
P2 1' 1' 2' 2' ) RT RT P2sat
(A23)
By submitting Eqs. (A20), (A21), (A22) and (A23) into (A15), an improved thermodynamic correlation formula between the acid dew point in flue gas and its influencing factors is derived: ln P1 ln(
T T P2 1 1 ' ' ' ' ' ' ' ' ) ( C C dT ) ( 1,298 1,298 2,298 2,298 298 P1 P1 298 CP2 CP2 dT ) RT RT P2sat
ln P
' " 1,298 1,298
R 298
' " H1,298 H1,298
RT
' " H1,298 H1,298
R 298
T
1 2 298 T
T
C
298
' P1
CP1" dTdT
(A24)
LIST OF TABLES 1.
Table 1. The prediction models on the acid dew point in previous studies [5-6, 14-18, 25]
2.
Table 2. B, n of the correlation formula contained experimental constants [5]
3.
Table 3. The coefficients in Eq. (24) with the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa
Table 1. The prediction models on the acid dew point in previous studies Name
Correlation
Müller[16, 17]
tadp = 116.5515 +16.06329lg PSO 3 +1.05377(lg PSO 3 )2
Halstead[25]
tadp = 113.0219 +15.0777lg PH 2SO 4 + 2.0975(lg PH 2SO 4 )2
Okkes-A[14]
tadp = 10.8809 + 27.6lg PH 2 O +10.83lg PSO 3 +1.06(lg PSO 3 + 2.9943) 2.19
Pa
Okkes-B[14]
tadp = 203.25 + 27.6lg PH 2 O +10.83lg PSO 3 +1.06(lg PSO 3 + 8)2.19
atm
Verhoff-A[18]
1000 = 1.7842 + 0.0269lg PH 2 O - 0.1029lg PSO 3 + 0.0329lg PH 2 O lg PSO 3 tadp + 273.15
atm
Verhoff-B[18]
1000 = 2.9882 0.1376lg PH 2 O - 0.2674lg PSO 3 + 0.03287lg PH 2 O lg PSO 3 tadp + 273.15
Pa
Japan Institute of Electric Power Industry[5]
tadp = 20lg PSO3 + a - 80
Correlation contained experimental constants[5]
tadp = tdp + B( PH 2SO 4 )n
Haase[15]
tadp = 255.0 +18.7lg PH 2 O + 27.6lg PSO3
Bаранова[5]
tadp = 186 + 20lg PH 2 O + 26lg PSO3
Soviet Union calculation standard[6]
tadp =
3 S 1.05ah
A
tdp
Remark
Table 2
Table 2. B, n of the correlation formula contained experimental constants [5] PH 2O PSO3 A B
Pa B n B n
2000 200.2 0.1224 289.9 0.0987
4000 202.4 0.0907 289.3 0.1014
6000 204.2 0.0732 288.7 0.1038
8000 206.3 0.0659 288.7 0.1063
12000 210.2 0.0622 286.9 0.1107
16000 214.2 0.0636 285.6 0.1145
20000 218.3 0.0661 284.4 0.1178
28000 226.4 0.0720 281.9 0.1229
36000 234.0 0.0780 -
Table 3. The coefficients in Eq. (24) with the partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15199 Pa and 0.5066 Pa to 2.0265 Pa item
a11 a12 a13 a14 a21 a22 a23 a24 a31 a32 a33 a34 a41 a42 a43 a44
2026.5 PH2O <5066.25 -10
-4.9 700×10 5.7 733×10-6 -2.4 998×10-2 4.5 769×101 6.0 543×10-5 -6.7 732×10-1 3.0 788×103 -5.8 617×106 3.4 706×10-7 -3.8 873×10-3 1.7 550×101 -3.2 727×104 -2.0 321×10-6 2.2 756×10-2 -1.0 286×102 1.9 244×105
5066.25 PH2O <8106 -9
4.3 130×10 -8.8 577×10-5 5.9 715×10-1 -1.3 152×103 -5.6 583×10-4 1.1 622×101 -7.8 363×104 1.7 251×108 -3.1 256×10-6 6.4 194×10-2 -4.3 280×102 9.5 300×105 1.8 417×10-5 -3.7 825×10-1 2.5 502×103 -5.6 152×106
8106 PH2O 10132.5
10132.5< PH2O 12159
12159< PH2O 15198.75
0 -8.4 598×10-6 1.4 831×10-1 -6.438×102 0 1.1 067×100 -1.9 400×104 8.4 116×107 0 6.1 212×10-3 -1.0 731×102 4.6 558×105 0 -3.6 058×10-2 6.3 213×102 -2.7 423×106
0 -3.5 724×10-6 7.7 289×10-2 -4.2 592×102 0 4.6 972×10-1 -1.0 156×104 5.5 851×107 0 2.5 913×10-3 -5.6 046×101 3.0 856×105 0 -1.5 272×10-2 3.3 028×102 -1.8 180×106
-3.3 980×10-9 1.4 328×10-4 -1.9 955×100 9.1 746×103 4.5 294×10-4 -1.9 094×101 2.6 588×105 -1.2 224×109 2.4 819×10-6 -1.0 464×10-1 1.4 572×103 -6.6 995×106 -1.4 644×10-5 6.1 736×10-1 -8.5 973×103 3.9 527×107
LIST OF FIGURES 1. Fig. 1 The predicted acid dew points using Müller model [16] 2. Fig. 2 The acid dew point testing apparatus [43] 3. Fig. 3 The measured acid dew points under the experimental flue gas conditions [43] 4. Fig. 4 The predicted acid dew points using present model 5. Fig. 5 Comparison between the values predicted using the models and experimental data in a previous paper [45] 6. Fig. 6 Comparison between the values predicted using the models and field test data [46]
Figure 1. The predicted acid dew points using Müller model [16]
Figure 2. The acid dew point testing apparatus [43] 1-syringe pump; 2-sulfuric acid; 3-quartz glass tube; 4-tubular furnace; 5-mass flow meter; 6-mass flow controller; 7-peristaltic pump; 8- temperature instrument; 9- ammeter; 10- DC power; 11- thermostatic water tank; 12electrode; 13- pump; 14- bakelite tube; 15- gas tank; 16- thermocouple; 17-heated cloth and insulate cotton; 18regenerator
Figure 3. The measured acid dew points under the experimental flue gas conditions [43]
Figure 4. The predicted acid dew points using present model
Figure 5. Comparison between the values predicted using the models and experimental data in a previous paper [45]
Figure 6. Comparison between the values predicted using the models and field test data [46]
Highlights
The previous semi-empirical models are systematically studied
An improved thermodynamic correlation is derived
A semi-empirical prediction model is proposed
The proposed semi-empirical model is validated