Submodel for Predicting Slag Deposition Formation in Slagging

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Submodel for Predicting Slag Deposition Formation in Slagging Gasification Systems Jianjun Ni, Guangsuo Yu,* Qinghua Guo, Zhijie Zhou, and Fuchen Wang Key Laboratory of Coal Gasification of Ministry of Education, East China University of Science and Technology, Shanghai 200237, People’s Republic of China ABSTRACT: In a slagging combustion system, some of ash/slag generated through the combustion of solid fuels is molten and adheres to tube surfaces or the refractory wall during operation. A submodel for predicting molten slag droplet deposition in the slagging combustion systems has been developed. The maximum spread diameter and excess rebound energy have been defined and applied to establish the rebound criterion. The slag solidification is also considered when the molten slag droplet impacts a lowtemperature surface, such as the membrane wall surface. The effect of slag viscosity, slag surface tension, particle impact angle, and impact velocity are investigated at typical conditions. The results indicated that the maximum spread diameter of the slag droplet is the key parameter for the impact process. The maximum spread can be presented as a function of the Reynolds number, Weber number, and contact angle. For molten slag particles, the results show that, the larger the particle, the higher the deposition probability. The deposition probability increases with an increasing droplet temperature. The effect of the impact velocity can be divided into two parts as low- and high-impact velocities. The deposition probability increases with the particle size and impact velocity. However, the effect of the contact angle is less significant.

1. INTRODUCTION Slagging combustion technology has been applied to coal combustion and integrated gasification combined cycle (IGCC) to enhance the net thermal efficiency. Under those high-temperature conditions, some of ash/slag generated through the combustion of solid fuels, such as pulverized coal and coal water slurry, is molten and adheres to tube surfaces or the refractory wall during operation. Hence, the molten slag droplet causes slagging and fouling problems in the coal combustors. For the coal gasifiers, the increasing slag layer can bring about gasifier plugging and the deposition on the membrane wall reduces the overall heat-transfer coefficient.1 To date, various studies have been conducted for solving a number of practical problems. These include analyzing the chemistry components of the ash and evaluating the deposition mechanism in coal-fired combustors and the syngas cooler of the gasifier.2-4 The slag deposition processes and results can also be given by the ash deposition experiment,5-8 and the computercontrolled scanning electron microscope (CCSEM) usually is applied to analyze the coal ash deposition. However, the ash deposition mechanism is complex and changes with the fuel type. Therefore, we must develop a new method to use the limited data from the experiment to predict the deposition process under high-temperature and high-pressure conditions. Computational fluid dynamics (CFD) has been used to quantitatively predict the molten ash deposition behaviors, such as the molten alkali-rich fly ash deposition behavior, by combining the experiment and CFD-based ash deposition model.9,10 Slag viscosity is also commonly used as particle-sticking criteria for the prediction of the results of the particle impact process,11,12 and the modified Urbain method is used to approximate slag droplet viscosity in the original study. Li et al.13 combined the experiment and CFD simulation to study the ash deposition behavior in the gasifier. However, in a slagging combustor or gasifier, the slag droplet r 2011 American Chemical Society

impact velocity, impact angle, slag contact angle, and wall temperature will change with operating conditions. Those parameters have important effects on impact results and have been ignored in previous deposition predictions. Therefore, the previous ash deposition prediction models are not enough to describe the real particle deposition process in the slagging combustors. In this paper, we focus on developing a slag droplet rebound model to predict the impact process on the wall. This mechanism model can be applied to predict the slag/ash deposition processes and the results in the slagging gasification or combustion system. The maximum spread diameter and rebound criterion have been presented, and the effects of slag viscosity, impact velocity, impact angle, molten slag surface tension, molten slag contact angle, and particle size are all considered.

2. THEORETICAL ANALYSIS 2.1. Description of the Impact Process. The slag droplet impact-rebound process can be divided into five distinct stages, and it has been shown in Figure 1. Stage 1, before impact: The slag droplet impact energy consists of surface energy, kinetic energy, and potential energy. Stage 2, maximum spread: This is the point at which the molten liquid flow changes direction from spreading outward to recoiling inward. The surface energy of the droplet will reach its maximum value, while the kinetic energy is zero. Received: December 14, 2010 Revised: January 28, 2011 Published: February 23, 2011 1004

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The growth in thickness of the solidified layer was calculated using an approximate analytical solution developed by Poirier and Poirier.17 The thermal contact resistance at the droplet-wall interface is ignored. The dimensionless solidification thickness was expressed as a function of the Stefan number (Ste), Peclet number (Pe), and φ sffiffiffiffiffiffiffiffiffiffi s 2 t φw ¼ pffiffiffi Ste ð8Þ Peφd D0 π Figure 1. Configuration states during molten slag droplet impact. Stages 3 and 4, recoil/rebound:

At this moment, the droplet rebounds from the combustor wall and entrained by syngas flow. Stage 5, sticking: The droplet deposits on the combustor wall and never is entrained by syngas flow. The potential energy in both stages 1 and 2 is negligible compared to other forms of energy.14 Before estimation of whether the process (deposition or rebound) will take place, we must obtain the maximum spread diameter of stage 2 first. 2.2. Models of Molten Slag Droplet Spread. A simple model to predict the maximum spread diameter of an impacting droplet has been developed by Pasandideh-Fard et al.15 They calculated the energy before and after impact, considered the energy dissipation during the impact process. The initial kinetic energy (Ek1) and surface energy (Es1) of a liquid droplet before impact are

 1 1 1 Fu0 2 πD0 3 ð1Þ Ek1 ¼ mu0 2 ¼ 2 2 6 Es1 ¼ Aγ ¼ πD0 2 γ ð2Þ At the impact state (stage 2), the droplet is at its maximum extension, the kinetic energy is zero (Ek2 = 0), and the surface energy (Es2) can be presented as π ð3Þ Es2 ¼ Dmax 2 γð1 - cos RÞ 4 where R is the liquid-solid contact angle. The work (W) in deforming the droplet against viscosity is16 π 1 Fu0 2 D0 Dmax 2 pffiffiffiffiffi ð4Þ 3 Re The molten slag will solidify when the droplet impacts the cooling tube surface. The effect of solidification in restricting droplet spread is modeled by assuming that all of the kinetic energy stored in the solidified layer is lost. If the solid layer has an average thickness () and diameter () when the droplet is at its maximum extension, then the loss of kinetic energy (ΔEk) is approximated by 

π 2 1 ð5Þ d s Fu0 2 ΔEk ¼ 4 2 W ¼

The diameter varies from 0 to Dmax during droplet spread. A reasonable estimate of its mean value is Dmax/2. According to the energy balance law Ek1 þ Es1 ¼ Ek2 þ Es2 þ W þ ΔEk

ð6Þ

Substituting eqs 1-5 into eq 6 yields an expression for the maximum spread factor vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Dmax We þ 12 u ð7Þ ¼ u 3s ξmax ¼ 4We t D0 We þ 3ð1 - cos RÞ þ pffiffiffiffiffi 8D0 Re where We is the Weber number (We = FV02D0/σ) and dimensionless solid layer thickness ( = s/D0).

is the

where Ste = C(Tm - Tw,i)/Hf, Pe = u0D0/ω, and φ = kFC. Substituting eq 8 into eq 7 gives the maximum spread of the slag droplet that is solidifying during impact vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u We þ 12 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ξmax ¼ u ð9Þ u 3φw 4We t þ 3ð1 - cos RÞ þ pffiffiffiffiffi WeSte 2πPeφd Re When the slag solidification process does not exist, eq 9 can be modified as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u We þ 12 u ð10Þ ξmax ¼ u 4We t 3ð1 - cos RÞ þ pffiffiffiffiffi Re

2.3. Rebound Criterion. Mao et al.14 proposed that the droplet impact process can be divided into four stages and suggested that the rebound criterion can be determined by impact energy. This criterion has been applied to predict the carryover deposition in boilers.18 After the droplet reaches the maximum spread diameter, the droplet changes its direction of motion from down to up and under the effect of gravity. Hence, if the energy possessed by a droplet after reaching the maximum spread diameter is great enough, the droplet will further pop up and be swept away by the strong shear force of the syngas in the near wall regions. Therefore, a rebound criterion is formulated14 

Ee ¼ 0:25ðξmax Þ2 ð1 - cos RÞ - 0:12ðξmax Þ2:3 ð1 - cos RÞ0:63 þ 2=3ðξmax Þ - 1

ð11Þ

whereE*isdefinedastheexcessreboundenergyanddescribesthe e tendency of a droplet to rebound upon impact. A droplet remains on the surfacewhenEe*e0,whichistheparticledepositionformation.

3. MODEL APPLICATION 3.1. Case Description. Two types of coal samples have been studied through applying the above slag deposition model. The chemical compositions of the two coal ash samples are shown in Table 1. The ash/slag particles in the boiler are all assumed as molten droplet, and solidification only appears when the particle impacts the wall. The different wall temperatures will be discussed in the following content. Before the particle impact process is predicted, it is necessary to establish the parameters of slag viscosity, impact velocity, impact angle, molten slag surface tension, and molten slag contact angle. 3.2. Effect of the Surface Tension and Viscosity. Surface tension and viscosity are only two physical properties that are relevant to slag layer interactions (wetting). Various coal samples were investigated by series methods. Melchior et al.19 measured slag surface tension under reducing conditions. They found that the surface tension value is between 400 and 700 mN/m for different coal ash samples. In published literature, surface tension data of coal ash slag are limited. However, the slag surface tension can be evaluated by the following formula:20 1005

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γ ¼ x1 γ1 þ x2 γ2 þ x3 γ3 þ :::

ð12Þ

where γ hi is the surface tension corresponding to each oxide i and xi is its molar percentage. Table 2 gives the tension coefficient of some oxides present in ash deposition. Table 2 shows the surface tension value of main slag compositions. The researchers have found that the surface tension of coal slag oxide is weakly dependent upon both compositions and temperature.21 It is possible to approximate the surface tension versus temperature variation by subtracting or adding 0.004 N/m when the temperature decreases or increases by 100 °C, respectively. The molten slag viscosity can be predicted from ash composition and temperature. A number of empirical models have been developed for the prediction of slag viscosity. At first, the Urbain model and “modified Urbain model” developed by Kalmanovitch22 have been applied to predict the slag viscosity, but the predicted results are higher than measured data. Therefore, in the present work, an empirical method developed by Browing et al.23 was applied to predict the relationship of viscosity and temperature. The expression for the standard viscosity curve can be written as
 η 14788 - 10:931 ð13Þ log ¼ T - Ts T - Ts

Table 1. Ash Chemistry and Fusion Temperature of the Two Coals Used in This Work component (wt %, oxide)

Shenfu

Fe2O3

4.43

14.17

SiO2 Al2O3

44.02 35.12

36.78 17.43

CaO

9.27

25.74

MgO

1.36

1.29

Na2O

1.07

1.13

K2O

0.17

1.36

TiO2

2.06

0.57

SO3

1.96

0.29

MnO ash flow temperature, Tf (°C)

0.05 1367

0.32 1128 1235

temperature of critical viscosity, Tcv (°C)

1378

density (kg/m3)

2540

2715

specific heat, Cp (kJ kg-1 K-1)

1040

990

Table 2. Surface Tension at 1300 °C for Different Slag Constituents20,21 oxide

K2O TiO2 SiO2 Na2O CaO MgO Al2O3 BaO FeO MnO

hγi (mN/m) 10

The temperature shift is a function of a weighted molar ratio Ts ¼ 306:63 lnðAÞ - 574:31

Baodian

250 290

295

510

520

580

553 638 638

ð14Þ

Here, the molar ratio, A, is given by the following expression: A ¼ ð3:19Si4þ þ 0:855Al3þ þ 1:6K þ Þ= ð0:93Ca2þ þ 1:50Fenþ þ 1:21Mg2þ þ 0:69Na þ þ 1:35Mnnþ þ 1:47Ti4þ þ 1:91S2- Þ ð15Þ The quantities of each component are in terms of the mole fraction Si4þ þ Al3þ þ K þ þ Ca2þ þ Fenþ þ Mg2þ þ Naþ þ Mnnþ þ Ti4þ þ S2- ¼ 1

ð16Þ

Substituting eqs 14-16 into eq 13 yields an expression for calculating the slag viscosity changing with the temperature. The oxide component X-ray fluorescence (XRF) spectrometer analysis data of two coal ash samples are listed in Table 1. Predicted and experimental viscosity for two coal ash samples is shown in Figure 2. The calculated data agree well with the value measured by high-temperature rheotronic II. The temperature where the viscosity sharply increases is called the critical viscosity temperature, denoted by Tcv. It is because of the formation of crystals in the liquid. The temperature at which this occurs is the highest temperature at which solid and liquid slag can coexist in equilibrium. Therefore, the temperature of critical viscosity can be used to determine whether the solid phase has formed. We found that the temperatures of critical viscosity for two coal ash samples are 1235 and 1378 °C, respectively. Slag surface tension and viscosity are the function of the particle temperature. Hence, the effect of surface tension and viscosity can be considered through changing the particle temperature. Figure 3 shows the excess rebound energy varying with the particle size at different slag temperatures. It can be found that the excess rebound energy increases with the particle size and decreases with the particle temperature. It means that,

Figure 2. Comparison of the predicted values of molten slag and measurement values.

Figure 3. Variation of excess rebound energy with the slag temperature (β, 90°; u0, 3 m/s; and Tw, 400 °C). 1006

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Table 3. Boltzmann Fitting Parameter Values for Three U.S. Coals ash sample

a

b

c

d

R2

Keystone coal

54.795

159.165

347.525

117.930

0.980

Tunnelton coal Montour coal

69.439 71.309

145.217 138.229

275.683 260.286

15.531 24.980

0.990 0.953

Figure 4. Apparent contact angle changed with the substrate temperature.

the larger the particle, the higher the deposition probability. The surface tension increases with the particle temperature, and the maximum spread diameter increases with the surface tension and particle size. The excess rebound energy decreases with the maximum spread diameter. That is to say that, the higher the particle temperature, the less the tendency for it to rebound. The particle size also has the same effect on the result of the particle impact. These predictions are in agreement with the experimental observations.18,24 Moreover, the particle will not rebound for all particle sizes when the particle temperature is 1750 °C. 3.3. Effect of the Contact Angle. The Moza-Austin sticking test has been used to investigate the sticking behaviors of slag drops from low-temperature ash, and three eastern U.S. coals with similar ash components were studied.25 Rawers et al.26 also studied the molten slag droplet spreading on the refractory, and the contact angle was measured by the experiment. The contact angle changes from 50 to 120° with the ash temperature. Most researchers found that the contact angle changed with the substrate temperature, substrate materials, slag particle temperature, and coal ash types. Hence, the contact angle should be measured and fit by the following Boltzmann fitting equation for model application: R ¼ a þ ðb - aÞ=f1 þ exp½ðTs - cÞ=dg

ð17Þ

where Ts is the substrate temperature and a, b, c, and d are constant. The fitting results and parameter value for three U.S. coals are shown in Figure 4 and Table 3. The fitting values are in good agreement with the measured data. It can be used to convert the discrete real contact angle value to a function of the substrate temperature for model calculation. However, the contact angle tends to be steady (about 70°) for Tunnelton and Montour coals when the substrate temperature is higher than 500 °C. The contact angle can be presented as a function of the wall temperature. Hence, the effect of the contact angle can be considered as the effect of the wall temperature. For example, the molten slag contact angle of Keystone coal can be written as: R = 54.795 þ 104.37/{1 þ exp[(Ts - 347.525)/117.93]}. Hence, when the impact angle, impact velocity, and particle temperature are fixed, the variation of excess rebound energy with the wall temperature is shown in Figure 5. The results indicate that the wall temperature has a great effect on the impact process when the wall temperature is low. The deposition particle size decreases from 27.3 to 18.6 mm with the wall

Figure 5. Variation of excess rebound energy with the wall temperature (β, 90°; u0, 3 m/s; and Tp, 1300 °C).

Figure 6. Variation of excess rebound energy with the impact angle (u0, 3 m/s; Tp, 1300 °C; and Tw, 400 °C).

temperature increasing from 300 to 500 °C. However, the higher the wall temperature, the lower its effect. Therefore, it can be concluded that the contact angle has less effect on the refractory combustor than the membrane wall combustor, because the temperature of the refractory wall is higher than the membrane wall in the slagging combustor. 3.4. Effect of the Impact Angle. In all of the simulations above, the slag droplet impacts the substrate at a 90° angle that is perpendicular to the substrate surface. In the combustor, the slag droplet flow direction and impact angle will change under the effect of the gas flow entrained force. The effect of the impact angle on the impact process can be considered through modifying the maximum spread value. The modified ξmax = Dmax/D0 can be calculated by incorporating the impact angle, β, into the Re and We numbers in the maximum spread model developed for normal impact We ¼ ðFu0 2 D=γÞsin2 β 1007

ð18Þ

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Figure 7. Variation of excess rebound energy with the impact velocity (β, 90°; Tp, 1300 °C; and Tw, 400 °C).

Re ¼ ðFu0 D=ηÞsin β

ð19Þ

The variation of excess rebound energy with the impact angle is shown in Figure 6. When the impact angle is larger than 30°, the smaller the impact angle, the higher the excess rebound energy. That is, for a given condition, the deposition probability will reach the maximum when the impact angle is 90°. This prediction agrees well with experimental observations.18 However, closer inspection of Figure 6 shows that the small particles will deposit on the substrate when the impact angle is 10°. A further calculation concludes that the small particle (size of about 0.01 mm) will deposit on the substrate until the impact angle increases to 30° for present conditions. 3.5. Effect of the Impact Velocity. The effect of the impact velocity is shown in Figure 7. In this case, the impact angle was assumed to be 90°, the slag droplet temperature was assumed to be 1300 °C, and the wall temperature was assumed to be 400 °C. The effect of low-impact velocities is shown in Figure 7a, from 0.1 to 1 m/s. The results show that all molten droplets stick to the surface when the impact velocity is 0.1 m/s. The excess rebound energy increases with an increasing impact velocity when the droplet diameter is smaller than about 10 mm. This means that the excess rebound energy has a peak value when the impact velocity is low and then decreases with the droplet diameter. The effect of high-impact velocities is shown in Figure 7b, from 3 to 20 m/s. The results show that the excess rebound energy decreases with an increasing droplet diameter and impact velocity. At 5 m/s, only droplets larger than 13.1 mm can deposit, the critical diameter, below which the molten droplet will rebound. It decreases with the impact velocity. This means that large droplets with high-impact velocities are more likely to deposit on the wall surface than small droplets with low-impact velocities. When the low-impact velocity (3.0 m/s), it can be found that different laws about impact result in changes to the droplet diameter.

4. CONCLUSIONS This work suggests that it is possible to estimate the maximum spread of a molten ash particle and to predict the tendency of such a slag droplet to deposit on a combustor wall surface, if the slag droplet size, impact velocity, impact angle, particle temperature, and other physical and thermal properties are known. Moreover, the particle impact velocity, impact angle, and particle temperature can be established through CFD simulation. A

mechanism model has been developed for simulating the dynamic process of molten slag droplets impacting the tube surface. The results indicated that the slag droplet maximum spread diameter is the key parameter for the impact process. The maximum spread can be presented as a function of the Reynolds number, Weber number, and contact angle. For the molten slag particle, the results indicted that, the larger the particle, the higher the deposition probability. The deposition probability increases with an increasing droplet temperature. The effect of the impact velocity can be divided into two parts as low- and high-impact velocities. However, the effect of the contact angle is less significant. These results agree well with the literature data through qualitative comparison. Further studies are needed to develop improved models for predicting droplet deposition. These include deposition of molten slag droplets on molten and slagging deposit surfaces, deposition of partially molten droplets on partially molten deposit surfaces, and the effect of deposit surface roughness on deposition.

’ AUTHOR INFORMATION Corresponding Author

*Telephone: þ86-21-64252974. Fax: þ86-21-64251312. E-mail: [email protected].

’ ACKNOWLEDGMENT This work is financially supported by the National Nature Science Foundation of China (20876048) and the National Key State Basic Research Development Program of China (973 Program, 2010CB227006). ’ NOMENCLATURE A = droplet surface area (m2) Cp = specific heat (J kg-1 K-1) D0 = droplet diameter (m) Dmax = droplet maximum spread diameter (m) = diameter when the droplet is at its maximum extension (m) Ee* = excess rebound energy Ek = initial kinetic energy (J) Es = surface energy (J) ΔEk = loss of kinetic energy (J) Hf = latent heat of fusion (J/kg) k = slag conductivity (J m-1 K-1) m = droplet mass (kg) 1008

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Energy & Fuels Pe = Peclet number u0 = impact velocity (ms-1) W = work performed in deforming the droplet against viscosity (J) We = Weber number Re = Reynolds number Ste = Stefan number = solid layer average thickness (m) Tf = ash flow temperature (°C) Tm = slag melting temperature (°C) Tw = wall temperature (°C) Ts = slag droplet temperature (°C) t* = dimensionless time xi = molar percentage of slag components R = contact angle (deg) β = impact velocity (deg) γ = molten slag surface tension (mN/m) γhi = surface tension of slag component i (mN/m) η = slag viscosity (Pa s) ξmax = dimensionless maximum spread diameter F = droplet density (kg/m3)

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