Prediction of Acid Dew Point in Flue Gas of Boilers Burning Fossil Fuels

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Prediction of Acid Dew Point in Flue Gas of Boilers Burning Fossil Fuels Baixiang Xiang, Man Zhang, Hairui Yang, and Junfu Lu* Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: The temperature of flue gas should be controlled to be higher than the acid dew point to avoid fouling and corrosion of heating surfaces in the second pass of boilers. Decreasing the temperature of flue gas in boilers is one of the most effective ways to improve thermal efficiency, enhance electrostatic precipitator efficiency, and decrease water consumption of the desulfurization tower. Accurate knowledge in predicting acid dew point is required. Thus, based on previous research achievements, a measuring device is designed based on the principle of conductive dew point meter, and the acid dew points under different flue gas conditions are measured in this work. An improved thermodynamic correlation formula between the acid dew point and its influencing factors is also derived based on previous research achievements. Then, a semiempirical prediction model that considers the functions of H2SO4 and H2O is proposed. The proposed prediction model is validated by field test data, experimental data, and prediction models reported in previous studies. To date, different models for predicting acid dew points of flue gas have been reported in previous studies, as shown in Table 1.5−11,18 β, generally 125, depends on the excess air ratio of boilers.6 a, dependent on the partial pressure of water vapor in the flue gas, is 184, 194, and 201 when the partial pressure of water vapor is 5066, 10 132, and 15 199 Pa, respectively.5 The values of B and n in the correlation formula, which contained experimental constants under different flue gas conditions, are listed in Table 2.5 These models can be divided into empirical and semiempirical models according to the data processing methods during model establishment. The empirical models are established by fitting the experimental results and the field test data with mathematical methods directly. For example, Verhoff et al.9 proposed an empirical model by fitting the acid dew points of flue gas by using the smallest sum of the squared errors. The experimental data in the Verhoff model are measured by a cooled electrical conductivity probe with sulfuric acid partial pressure above 0.1013 Pa.9 Halstead et al.18 proposed a curve for predicting the acid dew point in the flue gas of the oil-fired power plant with the partial pressure of sulfuric acid vapor and water vapor ranging from 0 to 2 Pa and from 0 to 14 185.5 Pa, respectively. Okkes et al.10 proposed a graph for estimating the acid dew point in flue gas based on the fuel composition and excess combustion air. Haase et al.11 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.11 proposed an empirical prediction model. In Haase’s model, the partial pressure of sulfuric acid vapor ranges from 0.1013 to 20.265 Pa, whereas the partial pressure of water vapor ranges from 7092.75 to 101 325 Pa.11 By fitting the field test data

1. INTRODUCTION Given the presence of sulfur, nitrogen, carbon, and other elements in fuel, flue gas typically contains acidic gases, such as SO2, SO3, NO, NO2, CO, and CO2. These acidic gases react with water vapor in the flue gas and then generate acid vapors under low-temperature conditions.1−4 When the outer wall of the heating surface in the second pass of boilers is cooled down to acid dew point, which is dependent on the corresponding saturation temperature of acid vapor partial pressure in flue gas, the acid vapors in flue gas will condense and form acidic droplets on the outer wall of heating surfaces. The condensed acidic droplets will cause serious acidic corrosion to metal heating surfaces.5,6 More importantly, the condensed acidic droplets will further react with the flaking rust and the fly ash in the second pass of boilers. Fouling will occur under such conditions. Once fouling occupies the flow channel, the burden of induced draft fan will increase significantly. Not only will the content of O2 in boilers be reduced, the preheated temperature of air will also not be enough. Thus, combustion in boilers will be seriously deteriorated. Moreover, the flow rate of flue gas is increased by the occupied fouling in the flow channel. Thus, the abrasion of the heating surfaces in the second pass of boilers will become severe. Therefore, considering the safety of the power generation unit, the temperature of flue gas must be controlled and maintained higher than the acid dew point of flue gas.6−22 However, thermal efficiency of boilers could be improved significantly by decreasing the temperature of flue gas.23−25 According to Li et al.,23 the electrostatic precipitator efficiency could be improved by decreasing the temperature of flue gas because the specific resistance of the fly ash is positively correlated with temperature under low-temperature conditions. Jiang et al.25 found that the consumption of water in desulfurization tower can be also decreased by decreasing the temperature of flue gas. Therefore, the determination of flue gas temperature requires more accurate prediction of the acid dew point to meet the increasing demands in energy saving and emission reduction. © XXXX American Chemical Society

Received: March 1, 2016

A

DOI: 10.1021/acs.energyfuels.6b00491 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels Table 1. Prediction Models for the Sulfuric Acid Dew Point in Flue Gas name

correlation

Müller graph7,8

remark

tadp = 116.5515 + 16.06329lgPSO3 + 1.05377(lgPSO3)2

Halstead graph18

tadp = 113.0219 + 15.0777lgPH2SO4 + 2.0975(lgPH2SO4)2

Okkes-A10

tadp = 10.8809 + 27.6lgPH2O + 10.83lgPSO3 + 1.06(lgPSO3 + 2.9943)2.19

Pa

Okkes-B10

tadp = 203.25 + 27.6lgPH2O + 10.83lgPSO3 + 1.06(lgPSO3 + 8)2.19

atm

1000 = 1.7842 + 0.0269lgPH2O − 0.1029lgPSO3 + 0.0329lgPH2O tadp + 273.15

atm

Verhoff -A

9

lgPSO3 Verhoff -B9

1000 = 2.9882 − 0.1376lgPH2O‐0.2674lgPSO3 + 0.03287lgPH2O lgPSO3 tadp + 273.15

Japan Institute of Electric Power Industry5 Correlation contained experimental constants Haase

Pa

tadp = 20lgPSO3 + a − 80 5

11

tadp = tdp + B(PH2SO4)n

Table 2

tadp = 255.0 + 18.7lgPH2O + 27.6lgPSO3

BapaHOBa

5

tadp = 186 + 20lgPH2O + 26lgPSO3

Soviet thermodynamic calculation method

6

tadp =

β3 S + tdp 1.05ah • A

Table 2. B, n of the Correlation Formula Contained Experimental Constants5 PH2O + PSO3

Pa

2000

4000

6000

8000

12000

16000

20000

28000

36000

A

B n B n

200.2 0.1224 289.9 0.0987

202.4 0.0907 289.3 0.1014

204.2 0.0732 288.7 0.1038

206.3 0.0659 288.7 0.1063

210.2 0.0622 286.9 0.1107

214.2 0.0636 285.6 0.1145

218.3 0.0661 284.4 0.1178

226.4 0.0720 281.9 0.1229

234.0 0.0780 − −

B

acid dew point in flue gas cannot be predicted accurately using the EOS + γ. Thus far, based on the equivalent of chemical potential in each phase of H2SO4, Müller et al.7 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%,8 Müller et al.7 proposed a semiempirical prediction model. 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.23−25 Therefore, considering the safety and economical operation of the power generation unit, a more accurate semiempirical prediction model of the acid dew point in flue gas is necessary. Thus, in this work, a measuring device is designed, and the acid dew points under different flue gas conditions are measured. An improved thermodynamic correlation formula between the acid dew point and its influencing factors is derived based on the previous research achievements. Then, a semiempirical prediction model that considers the functions of H2SO4 and H2O is proposed. 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.

directly, the following prediction models are established, namely, the Soviet Union thermodynamic calculation standard of boiler in 1973, the correlation formula contained experimental constants, and the prediction model proposed by the Japan Institute of Electric Power Industry.5,6 However, according to the operating experience of many power plants in China,23−25 not only is the applicability of these empirical models strictly limited but also the predicted acid dew points are generally too high or too low. Compared with the empirical model, data processing of the semiempirical 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. Based on the equivalent of the fugacity in each phase of a component, we used the following models, namely, the equation of state (EOS) and the equation of state and activity coefficient (EOS + γ) models. The models in which the fugacity of the components are in both liquid state and vapor state are calculated by an EOS. The models in which the fugacity of the components in vapor state and liquid state are calculated by an equation of state and activity coefficient model, respectively, belong to EOS + γ. However, 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. Similarly, considering the lack of binary interaction coefficients of H2SO4 and H2O in the activity coefficient models reported in previous studies,21,22 the

2. INFLUENCE FACTORS ON ACID DEW POINT For the acidic gases in the flue gas of boilers burning fossil fuels, as the boiling point of sulfuric acid is the highest under the same conditions, the sulfuric acid vapor will condense first with the decrease of flue gas temperature.3 In this sense, the acid dew point in flue gas is mainly dependent on the dew point of sulfuric B


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Figure 1. Acid dew point testing apparatus. 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; 12, electrode; 13, pump; 14, Bakelite tube; 15, gas tank; 16, thermocouple; 17, heated cloth and insulate cotton; 18, regenerator.

When the temperature of flue gas is cooled down to 773 K in the second pass of boilers, SO3 in the flue gas starts to combine with H2O and form sulfuric acid vapor, as follows:

acid vapor. In fact, the dew point of sulfuric acid vapor is dependent on its partial pressure in flue gas. Therefore, the acid dew point is dependent on the partial pressure of SO3 and water vapor in the flue gas.2−5,9−16 The partial pressure of water vapor is mainly determined by the types of fuel and the moisture carried by air. Thus, the partial pressure of water vapor in the flue gas can be obtained based on the ultimate analysis of the fuel, the operational parameters of boilers, and online field test. However, no effective methods and ready-made instruments that can measure the partial pressure of SO3 in the flue gas accurately are available because both the generation and the consumption reactions of SO3 in the second pass of boilers are an ongoing process. The generation reactions contain heterogeneous gas−solid reaction and homogeneous gas phase reaction,3 as follows:

cooling

SO3(g) + HO2 (g) ⎯⎯⎯⎯⎯⎯→ H 2SO4 (g) 1

Fleig et al. and Stuart et al. found that SO3 is almost completely converted to H2SO4 when the temperature of flue gas is cooled down to 473 K. Therefore, no SO3 is present but only H2SO4 when the temperature of flue gas is near the acid dew point. However, SO2 only starts to combine with the condensed water droplets when the temperature of the flue gas is cooled down to dew point of the water vapor. NO2 can combine with water vapor to form nitric acid vapor only when the mole fraction in flue gas is relatively high (e.g., 50 ppm).2,13 Therefore, for boilers burning fossil fuel, the acid dew point of the flue gas is dependent on the dew point of sulfuric acid vapor when the flue gas contains SO3 or H2SO4, whereas it is dependent on the dew point of carbonic acid when there is no SO3 or H2SO4 in the flue gas.

catalyst

SO2 + O2 ⎯⎯⎯⎯⎯⎯→ SO3

(1)

catalyst

SO2 + O2 ⎯⎯⎯⎯⎯⎯→ SO3 + O

(2)

3. EXPERIMENTAL SECTION

> 1400K

SO2 + O ←⎯⎯⎯⎯→ SO3 < 1150K

SO2 + OH ←⎯⎯⎯⎯→ HOSO2

(3)

3.1. Experimental Section. To date, the conductive dew point meter, proposed by AMETEK Land, Inc., is considered as one of the most reliable measuring methods based on previous research achievements.7−14,18 As shown in Figure 1, based on the principle of conductive dew point meter, an acid dew point measuring device is built to simulate the condensation process of acid vapor by cooling down hightemperature mixture gases, including N2, O2, CO2, water vapor, and sulfuric acid vapor. Dilute sulfuric acid solution with a mass fraction of 2.1% and pure deionized water are mixed with high-temperature mixture gases at the exit of a tubular furnace. The flows of N2, O2, and CO2 are controlled by a three-way mass flow meter (D07), whereas the dilute sulfuric acid and pure deionized water are controlled by a microsyringe pump (LSP01-1A) and peristaltic pump (BT100-2J), respectively. During the experiment, to make sure that the sulfuric acid and deionized water evaporate completely, the temperature of the mixture gases is heated to 973 K using a tubular furnace. Then, the flue gas flows through a heated tube, long enough to measure acid dew point. The shortest length of the tube is determined by measuring the acid dew point of the flue gas under the same conditions repeatedly. During the experiment, the flue gas passes through the outer surface of the Bakelite tube laterally. When the outer surface of the Bakelite tube is heated above the corresponding acid dew point by high-temperature flue gas, the inner surface of the Bakelite tube begins to cool down gradually by adjusting the flow rate and temperature of the flowing water. The insulated

(4)

< 1150K

HOSO2 + O2 ←⎯⎯⎯⎯→ HO2 + SO3

(6)

2

(5)

Given the needs of catalysts, such as V2O5, Fe2O3, and other solid particles, eqs 1 and 2 are heterogeneous reactions.1,26−30 Different from eqs 1 and 2, eqs 3, 4, and 5 are homogeneous reactions with reaction temperature above 1400 and below 1150 K, respectively.1 However, the generated SO3 can be absorbed by the MgO, CaO, Na2CO3, charcoal, and other solid particles formed in the combustion process at the same time.27 Therefore, a series of factors affects the partial pressure of SO3 in the flue gas, including SO2, O2, CO2, CO, NO, NO2, H2O, the flue gas temperature, and the residence time of flue gas in each temperature zone.28−31 Hence, the content of SO3 in flue gas is difficult to be measured accurately. According to Fleig et al.,1 the ratio of SO3/SOx in flue gas is generally between 0.1% and 1% in FBC combustion. However, it will be increased approximately fourfold in oxyfuel combustion. C


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Figure 2. Electrode on the wall of Bakelite tube. 1, Bakelite tube; 2, negative electrode; 3, anode; 4, thermocouple.

Table 3. Experimental Flue Gas Conditions with Constant Flow Rates of CO2 and O2 NO.

CO2 (mL·min−1)

N2 (mL·min−1)

O2 (mL·min−1)

H2O (Pa)

H2SO4 (Pa)

0 ppm of H2SO4

1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800

7400 7100 6900 6600 6300 6100 7400 7100 6900 6600 6300 6100 7400 7100 6900 6600 6300 6100 7400 7100 6900 6600 6300 6100 7400 7100 6900 6600 6300 6100

600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600

2026 5066 7093 10132 13172 15199 2026 5066 7093 10132 13172 15199 2026 5066 7093 10132 13172 15199 2026 5066 7093 10132 13172 15199 2026 5066 7093 10132 13172 15199

0 0 0 0 0 0 0.5066 0.5066 0.5066 0.5066 0.5066 0.5066 1.0133 1.0133 1.0133 1.0133 1.0133 1.0133 1.5199 1.5199 1.5199 1.5199 1.5199 1.5199 2.0265 2.0265 2.0265 2.0265 2.0265 2.0265

5 ppm of H2SO4

10 ppm of H2SO4

15 ppm of H2SO4

20 ppm of H2SO4

Figure 3. Measured acid dew points under experimental flue gas conditions. substrate of the electrodes arranged on the outer surface of the Bakelite tube uses a smooth polyimide film to ensure that acid vapors form film

condensation between electrodes. Furthermore, positive and negative electrodes, connected in parallel, are sprayed on the polyimide film in a D


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Energy & Fuels zigzag manner. The distance between the positive and negative electrodes is 0.4 mm, as shown in Figure 2. Then, the current between the electrodes is recorded using a high-precision ammeter (Agilent 34401A), which is connected in series with the electrodes and power. Meanwhile, the corresponding temperature of the Bakelite tube’s outer surface is recorded using a JLY-C28 temperature logger. Thus, the temperature of the Bakelite tube’s outer surface, when current is applied in the circuit, is determined as the corresponding acid dew point in flue gas. Maintaining the flow rate of flue gas, O2, and CO2 at 10, 0.6, and 1.8 L/min respectively, a series of different flue gas conditions is adjusted by keeping N2 as the balance component, as shown in Table 3. With the development of fluidized bed combustion and improvement of flue gas desulfurization in recent years,32 the partial pressure of sulfuric acid vapor in flue gas has been reduced significantly. Thus, to comply with the actual values of flue gas in previous models, the partial pressure of sulfuric acid vapor should range from 0.5066 to 2.0265 Pa and the partial pressure of water vapor should range from 2026 to 15 199 Pa in the present work. 3.2. Experimental Results. Figure 3 shows the measured acid dew points with experimental flue gas conditions listed in Table 3. The dew points of pure water vapor without acidic gases are calculated based on the table of Thermodynamic Properties of the Water and Saturated Steam.33 As shown in Figure 3, the dew points in flue gas with CO2 increased slightly compared with the dew points of pure water vapor. However, as sulfuric acid vapor emerges in the flue gas, even with a small mole fraction (e.g., 5 ppm), the dew points increased significantly compared with the above two cases. In Figure 3, the increasing slope of the acid dew point in flue gas becomes smaller with higher partial pressure of sulfuric acid vapor at higher sulfuric acid vapor partial pressure. Similarly, the increasing slope of the acid dew point in flue gas is also smaller with higher partial pressure of water vapor at higher sulfuric acid vapor partial pressure. Moreover, a similar trend is observed with higher partial pressure of water vapor at higher water vapor partial pressure.

The chemical potential of sulfuric acid in liquid state can be computed using the following formula μ′ = μ′o + RT ln a

where a is the activity of sulfuric acid in liquid state and μ′o is the chemical potential of sulfuric acid in liquid state with the reference state. Thus RT ln P = μ′o − μ″o + RT ln a + RT ln Po ⎡∂ μ ⎢ T ⎢ ∂T ⎣

( ) ⎤⎥

(11)

T

H = H298 +

∫298 CpdT

(12)

Based on eqs 11 and 12, the following formula can be derived o o ∑ H298 ∑ H298 ∑ μo = − − T T 298 o ∑ μ298 + 298

∑Ho298,

T

T

∫298 T12 ∫298 ∑ CpodT dT (13)

where ∑μ , and in eq 13 can be computed using the following formulas, respectively: o

Cop

o ′ o − H298 ″o = H298 ∑ H298

(14)

∑ μo = μ′ o − μ″ o

(15)

∑ Cpo = Cp′ o − Cp″ o

(16)

C′po

where is the specific heat of sulfuric acid in liquid state with the reference state, Cp″o is the specific heat of sulfuric acid vapor o with the reference state, H′298 is the enthalpy of sulfuric acid in o liquid state with the reference pressure and 298 K, and H″298 is the enthalpy of the sulfuric acid vapor with the reference pressure and 298 K. Moreover, for μ′, μ′o, and ln a, the correlation formula is as follows: μ′(T , P) = μ′o (T , P) + RT ln a

(17)

By partial derivative on T, the following formula can be derived: dln a 1 ′ + = − 2 [H298 dT RT

o

T

S′ ∫298 Cp′dT − μ′o ] − RT

(18)

Thus, ln a can be computed using the following formula:

where μ′ is the chemical potential of sulfuric acid in liquid state and μ″ is the chemical potential of sulfuric acid vapor. The sulfuric acid vapor can be considered as the ideal gas approximately under low-pressure conditions. Therefore, the chemical potential of sulfuric acid vapor can be computed using the following formula: μ″ = μ″ + RT ln(P /Po)

H ⎥ = − T2 ⎦p

Moreover, H can be computed using the following formula:

(7)

o

(10)

For T, H, and μ, the correlation formula is as follows:

4. CORRELATION FORMULA OF ACID DEW POINT 4.1. Thermodynamic Analysis of the Acid Dew Point Factors. Mü ller et al.7 established the thermodynamic correlation formula between the dew point and pressure of sulfuric acid vapor based on the equivalent of chemical potential in each phase of H2SO4. However, as mentioned, due to the limited understanding on the consumption and formation of SO3 in the flue gas and the vapor−liquid equilibrium, the thermodynamic derivation seems to be not rigorous enough. Thanks to the research progress in SO3 of flue gas and the vapor− liquid equilibrium, an improved thermodynamic correlation formula between the dew point and pressure of sulfuric acid vapor can be derived in the present work. As the chemical potential of H2SO4 distributed in each phase is equal in the vapor−liquid equilibrium. Thus, μ″ = μ′

(9)

R(ln a − ln a 298) =

′ H298 T

−

′ 1 H298 298 T 2

T

∫298 (Cp′ − Cp′o)dT ]dT

[

+

(8)

where μ″ is the chemical potential of sulfuric acid vapor with the reference state (101 325 Pa and real temperature), P is the pressure of the sulfuric acid vapor, and P0 is the reference pressure (101 325 Pa). o

′o μ298 298

−

μ′ o 298 + S′o ln T T

(19)

where a298 is the activity of sulfuric acid in liquid state with 298 K, H298 ′ is the enthalpy of sulfuric acid in liquid state with 298 K, S′o is the entropy of sulfuric acid in liquid state with the reference o state, C′p is the specific heat of sulfuric acid in liquid state, and μ′298 E


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Energy & Fuels Table 4. Values of Coefficients in Eq 25 item

2026.5 ≤ PH2O < 5066.25

5066.25 ≤ PH2O ≤ 7092.75

7092.75 < PH2O ≤ 10132.5

10132.5 < PH2O < 13172.25

13172.25 ≤ PH2O ≤ 15198.75

a11 a12 a13 a14 a21 a22 a23 a24 a31 a32 a33 a34 a41 a42 a43 a44

6.0 624 × 10−5 −6.7 830 × 10−1 3.0 825 × 103 −5.8 585 × 106 3.4 752 × 10−7 −3.8 927 × 10−3 1.7 571 × 101 −3.2 742 × 104 −4.9 800 × 10−10 5.5 809 × 10−6 −2.5 028 × 10−2 4.5 795 × 101 −2.0 326 × 10−6 2.2 761 × 10−2 −1.0 287 × 102 1.9 237 × 105

0 4.9 480 × 10−1 −7.2 061 × 103 2.4 040 × 107 0 2.7 440 × 10−3 −3.9 919 × 101 1.3 337 × 105 0 −3.8 000 × 10−6 5.5 258 × 10−2 −1.8 483 × 102 0 −1.6 157 × 10−2 2.3 509 × 102 −7.8 524 × 105

−5.2 369 × 10−4 1.3 033 × 101 −1.0 790 × 105 2.9 436 × 108 −2.8 617 × 10−6 7.1 217 × 10−2 −5.8 956 × 102 1.6 082 × 106 3.9 080 × 10−9 −9.7 252 × 10−5 8.0 500 × 10−1 −2.1 958 × 103 1.6 892 × 10−5 −4.2 040 × 10−1 3.4 801 × 103 −9.4 934 × 106

1.3 629 × 10−4 −5.3 422 × 10° 6.7 965 × 104 −2.8 766 × 108 7.4 465 × 10−7 −2.9 145 × 10−2 3.7 046 × 102 −1.5 669 × 106 −1.0 170 × 10−9 3.9 733 × 10−5 −5.0 460 × 10−1 2.1 330 × 103 −4.3 957 × 10−6 1.7 210 × 10−1 −2.1 877 × 103 9.2 540 × 106

0 −7.7 830 × 10−1 2.5 084 × 104 −2.0 319 × 108 0 −4.2 050 × 10−3 1.3 555 × 102 −1.0 979 × 106 0 5.6 800 × 10−6 −1.8 310 × 10−1 1.4 826 × 103 0 2.4 869 × 10−2 −8.0 166 × 102 6.4 932 × 106

Figure 4. Comparison between the values predicted using the prediction models and previous experimental data.34

is the chemical potential of sulfuric acid in liquid state with the reference pressure and 298 K. By substituting eqs 19 and 13 into eq 10, the thermodynamic correlation formula between the dew point and the pressure of sulfuric acid can be derived as follows o H″o 1 ⎧ H′ ln P = ⎨ 298 − 298 − R⎩ T T

∑

o S298

+

′ H298 T

−

′ H298 298

When the temperature is not too high, it equals the sum of the first two items approximately. Thus, by substituting eq 22 into eq 20, the following formula can be derived: ln P =

−

−

∫

∑ Cp298ln

T − 298

o ∑ S298 +

′ H298 T

−

′ H298 298

∑ Cp298 298

T ∑α ∑α − (T − 298) + ∑ Cp298 − 2982 2 2T μ ′o ∑α μ′o 298 ⎤ ⎥ + ln a 298 298 + 298 − + + S′o ln 2 298 T T ⎦

′o μ298 ⎤ μ′ o 1 ⎡ T C T T d d ∑ + − + S′o ⎥ ⎢ p 2 ⎦ 298 T ⎣ 298 T 298 298 ⎫ ⎬ + ln Po + ln a 298 ln T ⎭ (20) T

′o H″o 1 ⎡ H298 ⎢ − 298 − R⎣ T T

∫

+ ln Po

where ∑Cp is computed using the following formula:

(23)

Then, by simplifying eq 23, the following formula can be derived

∑ Cp = ∑ Cpo + Cp′

(21)

ln P = A1

Conducting ∑Cp a power series expansion at T0 (298 K), ∑Cp can be computed using the following formula: 2

∑ Cp = ∑ Cp298 + ∑ αT + ∑ R n(T )

1 + A 2 ln T + A3T + A4 T

(24)

where A1−A4 are the coefficients dependent on the sulfuric acid; P is the pressure of sulfuric acid vapor, Pa; and T is the temperature of the flue gas, K.

(22) F


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Energy & Fuels 4.2. Acid Dew Point Correlation Formula. Equation 24 formulated the thermodynamic correlation between the acid dew point in flue gas and its influencing factors, ignoring the function of water vapor. However, according to the analysis of the influencing factors on the acid dew point in flue gas, the function of water vapor should not be ignored. Fortunately, the impact of water vapor can be formulated by the coefficients of the thermodynamic correlation formula between acid dew point in flue gas and its influencing factors. Considering that the trends of the acid dew point varied with the increase of water vapor partial pressure and the limited experimental data, such impact can be considered as a third-order polynomial of water vapor partial pressure with the following formula: Aj = aj1PH2O3 + aj2PH2O2 + aj3PH2O + aj 4

When the partial pressures of the sulfuric acid vapor and water vapor are 1.8542, 1.986, and 3.8807 Pa and 12 159, 10 234, and 8 511 Pa, the corresponding acid dew points of field test are 361, 366, and 372 K, respectively. Detailed compositions of coal and flue gas are listed in Table 5. Moreover, the partial pressures of sulfuric acid vapor in the flue gas are calculated based on chemical analysis.35 Table 5. Composition of Coal and Flue Gas of the 150 MWe Boiler35 value (Pa)

j = 1, 2, 3, 4

item

Mad

Aad

Vad

FCad

coal

7.49%

9.65%

30.54%

52.32%

the first case (361 K)

(25)

the second case (366 K) the third case (372 K)

Based on the measured acid dew points of flue gas compositions listed in Table 3, the corresponding coefficients of eq 25 are listed in Table 4. Thus, a semiempirical prediction model for the acid dew point in flue gas, the partial pressure of water vapor, and sulfuric acid ranging from 2026 to 15199 Pa and 0.5066 to 2.0265 Pa is proposed.

S

H

0.74%

4.09%

O2 4954.7925 O2 4458.3

H2O 12159 H2O 10233.825

SO3 1.8542 SO3 1.986

SO2 (mg·Nm3−) 47.03 SO2 (mg·Nm3−) 52.39

O2 4559.625

H2O 8511.3

SO3 3.8807

SO2 (mg·Nm3−) 103.05

Figure 5 compares the field test data35 and the values predicted using the present model, the models in Table 1, and the Soviet

5. DISCUSSION 5.1. Comparative Analysis of Experimental Result. Figure 4 compares the previous experimental data34 and the values predicted using the models listed in Table 1, the present model 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 graph ranges from 0 to 2 Pa and from 0 Pa to 14 185.5 Pa, respectively.18 The partial pressure of sulfuric acid in Müller graph ranges from 0 Pa to 1013.25 Pa.7 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 and 0.1013 Pa to 20.265 Pa, respectively.11 The experimental data in ref 34 are also measured using a device built based on the principle of conductive dew point meter. However, different from the measuring device designed in the present work, the flue gas is cooled using compressed air and 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 4, the compared results show that the values predicted with the models in Table 1 are generally too high with partial pressure of water vapor and sulfuric acid ranging from 2026 Pa to 15 199 Pa and 0.5066 to 2.0265 Pa, respectively, except for those predicted with the Haase model. However, for the values predicted with the above one, they are slightly higher than the corresponding experimental results at lower sulfuric acid vapor partial pressure, whereas they become slightly lower at higher sulfuric acid vapor partial pressure. Therefore, the values predicted with the model proposed in present work show better agreement with the previous experimental data in ref 34 compared with those predicted with the models listed in Table 1. 5.2. Comparative Analysis of Field Test. To further validate the prediction model proposed in the present work, the acid dew points in flue gas of a 150 MWe coal-fired circulating fluidized bed boiler with limestone desulfurization are tested under different flue gas conditions. Maintaining the sulfur content of the coal at 0.74%, a series of different flue gas compositions was obtained by adjusting the excess air ratio.

Figure 5. Comparison between the values predicted using the prediction models and field test data.35

one under the same flue gas conditions. As shown in Figure 5, the values predicted with the models in Table 1 are generally too high, except for those predicted with the Haase model and the Soviet one. Considering the impact of fly ash on the condensation of the acid vapor between electrodes, the field test data should be slightly lower than the corresponding acid dew points of flue gas.35 However, the comparative results of Figure 5 show that the values predicted with the Soviet one are even lower than the corresponding field test data at higher sulfuric acid vapor partial pressure. This result means that the values predicted with the Haase model and present model are more reliable compared with those predicted with the Soviet one. Therefore, based on the comparative analyses of field test and experimental result, the values predicted with the prediction model proposed in the present work are more reliable than those predicted using the models listed in Table 1. G


Article

Energy & Fuels

H′298 = the enthalpy of sulfuric acid in liquid state with 298 K, kJ/mol S′o = the entropy of sulfuric acid in liquid state with the reference state, kJ/K C′p = the specific heat of sulfuric acid in liquid state, kJ/mol·K Cp′o = the specific heat of sulfuric acid in liquid state with the reference state, kJ/mol·K o H″298 = the enthalpy of the sulfuric acid vapor with the reference pressure and 298 K, kJ/mol A1−A4 = the coefficients of thermodynamic correlation formula between acid dew point in flue gas and its influencing factors

6. SUMMARY AND CONCLUSIONS In this work, a series of acid dew points is measured using a measuring device built based on the principle of conductive dew point meter. It is found that the increasing slope of the acid dew point in flue gas becomes smaller with higher partial pressure of the sulfuric acid vapors as well as the water vapor at higher sulfuric acid vapor partial pressure. A similar trend is observed with higher partial pressure of water vapor at higher water vapor partial pressure. A semiempirical model for the acid dew point in flue gas that considers the functions of H2SO4 and H2O is proposed based on an improved thermodynamic correlation formula. Moreover, the present model is validated by previous experimental data, field test data, and the previous models. The acid dew points predicted using the previous models are generally too high. However, those predicted using the Haase model and Soviet model are slightly lower at higher sulfuric acid vapor partial pressure. Therefore, compared with the previous models, not only does the present model seem to be more reliable, but also the ranges of the partial pressure of water vapor and sulfuric acid in the present model are more consistent with the actual contents in the flue gas. As the prediction model on acid dew point proposed in this work is based on the content of H2SO4 and H2O, future research will focus on the content of SO3 in the flue gas. Moreover, the acid dew point measured using the apparatus designed based on the principle of conductive dew point meter is lower, whereas 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 as well.

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Subscripts

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p = constant-pressure process 298 = the temperature is 298 K

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Tel.: +86-0162792647. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support for this work by the National Program on Key Basic Research Project (973 Program) of China (No. 2012CB214900) is gratefully acknowledged.

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SYMBOLS μ′ = the chemical potential of sulfuric acid in liquid state, kJ/ mol μ298 ′o = the chemical potential of sulfuric acid in liquid state with the reference pressure and 298 K, kJ/mol μ′o = the chemical potential of sulfuric acid in liquid state with the reference state, kJ/mol μ″ = the chemical potential of the sulfuric acid vapor, kJ/mol μ″o = the chemical potential of the sulfuric acid vapor with the reference state, kJ/mol P = the partial pressure of the sulfuric acid vapor, Pa P0 = the reference pressure (=101 325 Pa) a = the activity of sulfuric acid in liquid state a298 = the activity of sulfuric acid in liquid state with 298 K T = the temperature of the flue gas, K H298 ′o = the enthalpy of sulfuric acid in liquid state with the reference pressure and 298 K, kJ/mol H


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Prediction of Acid Dew Point in Flue Gas of Boilers Burning Fossil Fuels

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