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Effects of the bubbles in slag on slag flow and heat transfer in the membrane wall entrained-flow gasifier
Applied Thermal Engineering 112 (2017) 1178–1186
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Research Paper
Effects of the bubbles in slag on slag flow and heat transfer in the membrane wall entrained-flow gasifier Binbin Zhang a,b, Zhongjie Shen a,b, Dong Han a,b, Qinfeng Liang a,b,c, Jianliang Xu a,b, Haifeng Liu a,b,⇑ a Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, PR China b Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, PR China c State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, PR China
h i g h l i g h t s The slag flow and heat transfer model were modified with the bubbles in slag. The bubbles in slag reduced the slag thermal conductivity and viscosity. The bubbles in slag increased the liquid slag velocity. The bubbles in slag reduced the liquid and solid slag layer thickness. The bubbles in slag reduced the slag heat flux.
a r t i c l e
i n f o
Article history: Received 4 May 2016 Revised 23 September 2016 Accepted 22 October 2016 Available online 24 October 2016 Keywords: Gasification Slag Bubble Thermal conductivity Viscosity
a b s t r a c t The slag from the industrial gasifier has porous structure, which has a non-ignorable influence on the characteristics of slag layer. The slag flow and heat transfer model were modified based on the effective thermal conductivity and viscosity, to predict the slag characteristics for the effects of bubbles in slag. The results show that bubbles inside slag reduce the slag thermal conductivity and viscosity. The modified model predicts the liquid slag velocity, slag layer thickness and heat flux of slag layer. The liquid slag flow velocity increases with the increase of bubbles inside slag, while the thickness of slag layer decreases. In addition, the increasing gas volume fraction of bubbles inside slag decreases the heat flux of slag layer. Two models are applied to calculate the bubbly slag effective thermal conductivity. The MaxwellEucken thermal conductivity model is more accurate than geometric mean model from the result of slag layer heat flux. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The entrained-flow gasification is a high efficient and clean coal conversion technology, which is widely used in the chemical industry such as the Integrated Gasification Combined Cycle (IGCC) plant [1–3]. The membrane wall entrained-flow gasifier has a long lifetime compared to the refractory brick wall entrained-flow gasifier [4]. In an entrained gasifier, the ash particles and unreacted coal particles would deposit on the wall and form solid and liquid slag layer, which can protect the metal tube from the high temperature gas corrosion [5]. Therefore slag layer properties (e.g. rheol-
⇑ Corresponding author at: Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, PR China. E-mail address: [email protected] (H. Liu). http://dx.doi.org/10.1016/j.applthermaleng.2016.10.141 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
ogy, thickness and heat transfer) are very important for the stability and security of a gasifier operation. Experiment study for slag flow and heat transfer in an industrial gasifier is limited and difficult due to the high temperature and pressure environment. Hosseini and Gupta [6] used an electrically heated vertical drop-tube furnace to study the effect of operating conditions on ash deposition and slag formation. Wang et al. [7] used the syrup to simulate the liquid slag and studied the slag deposition and growth at the slag tap hole region under the cold model experiment. The heat transfer and slag deposition characteristics were studied in a pilot-scale pulverized coal entrained-flow gasifier with the pilot test and calculation method [8]. For comparison with the experiment studies, numerical simulation and modeling are the main methods to study the slag flow and heat transfer in the membrane wall entrained-flow gasifier. The model which proposed by Seggiani [9], was widely used in the slag
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Nomenclature cg ci cmix cs D g h mex min qflux qin qout Tcv Tf Tg Tmr Tmw To Tw Twater u u0 x xi
gas specific heat (J/kg K) specific heat of component i (J/kg K) specific heat of two-phase mixture (J/kg K) slag specific heat (J/kg K) gasifier diameter (m) gravitational constant (m/s2) convective heat transfer coefficient (W/m2 K) vertical outlet slag mass flow rate per unit (kg/s) mass flow of particle deposition per unit (kg/s) heat flux through the slag (W/m2) heat flux to the slag surface (W/m2) heat flux from the slag to the refractory layer (W/m2) temperature of critical viscosity (K) slag flow temperature (K) gas temperature at slag-gas interface (K) metal-refractory wall interface temperature (K) water-metal wall interface temperature (K) slag temperature at slag-gas interface (K) refractory-slag interface temperature (K) average temperature of water (K) slag velocity at distance x from slag-gas interface (m/s) slag velocity in slag-gas interface (m/s) the distance from the slag-gas interface mole fraction of component i
Greek letters a thermal diffusivity (m2/s) b gas volume fraction of bubbles
flow and heat transfer studies [10,11]. In all of these references, the temperature in the slag layer was linear distribution, which was based on the assumption that the slag thermal conductivity is a fixed value. Based on Seggiani’s [9] model, the influence of shear stress due to particle deposition was considered in Ref. [12]. The slag flow between the temperature of critical viscosity (Tcv) and flow temperature (Tf) was considered in a modified model [13]. The influence of critical viscosity and its temperature on the slag behavior was considered in a numerical model [14]. A comprehensive numerical model was proposed to predict the thickness, velocity and temperature of the slag layer in an entrained flow gasifier [15], and also compared with existing analytical models. The heat transfer of slag layer was calculated by the discretization of the velocity in a black liquor recovery boiler [16]. The behaviors of slag flow were investigated in an oxy-coal combustor which considered the effects of particle burning near the wall [17]. The mathematical model for a gasifier included slag flow and heat transfer model, particle capture model and 3-D model [18]. The particles deposit behavior was determined by the viscosities of slag and incoming particles [19]. The temperature distribution and particle deposition rate inside the gasifier were important data which obtained from 3-D gasifier models as referred in the literatures [20–23]. Literatures about the slag structure have been studied [24–27], researchers gave the facts that one of the main characteristic of coal slag was the porous structure. The cooled slag has a porous structure, which mean that slag layer at the high temperature contains bubbles. However, seldom literature is referred for the influence of bubbles on slag flow and heat transfer. The objective of this paper is to study the effects of bubbles on slag flow and heat transfer in the membrane wall entrained-flow gasifier. The effects of bubbles in slag on the thermal conductivity and viscosity are studied with different models. The slag model
dl dm dr ds
e ge gg gl h
j kc kd ke kg kl km kr ks
qg ql qmix qs r u uA uv
thickness of liquid slag layer (m) thickness of metal wall (m) thickness of refractory wall (m) thickness of solid slag layer (m) emissivity effective viscosity (Pa s) viscosity of gas in slag (Pa s) liquid slag viscosity (Pa s) slope of the wall (°) mass fraction of gas thermal conductivity of continuous phase (W/m K) thermal conductivity of discrete phase (W/m K) effective thermal conductivity (W/m K) thermal conductivity of gas in slag (W/m K) thermal conductivity of liquid slag (W/m K) thermal conductivity of metal wall (W/m K) thermal conductivity of refractory wall (W/m K) thermal conductivity of solid slag (W/m K) density of gas in slag (kg/m3) density of liquid slag (kg/m3) density of two-phase mixture (kg/m3) slag density (kg/m3) blackbody radiation coefficient (W/m2 K4) porosity area fraction of pores volume fraction of pores
referred from Seggiani’s [9] work is coupled with the effective thermal conductivity models and an effective viscosity model. The influence of gas volume fraction inside slag layer on the liquid slag velocity, slag thickness and heat transfer of slag layer are also studied.
2. Mathematical models 2.1. Slag flow and heat transfer model The slag flow and heat transfer model is established according to the method proposed by Seggiani [9]. The schematic diagram of slag layer for cell i along the membrane wall is shown in Fig. 1. In addition, the following assumptions are proposed in this study: (1) The bubbles in liquid slag layer and solid slag layer are uniformly distributed. (2) The bubbles will not breakup or coalescence for the high viscosity of slag, and the bubbly slag is considering as a pseudohomogenous phase. (3) The gas components of bubbles are mainly carbon monoxide and hydrogen for the reducing atmosphere in the gasifier. The slag flow and heat transfer model for cell i in the steadystate condition is based on the following equations: The mass conservation for cell i can be expressed as:
min;i þ mex;i1 mex;i ¼ 0
ð1Þ
The momentum conservation in linear coordinates for cell i can be expressed as:
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mex,i-1 qex,i-1 Metal wall
Refractory wall
T0
T cv
min T in Particles
qflux
δl
δs T water
qin
Tw
T mr
Solid layer
Gas
Liquid layer
mex,i qex,i
Fig. 1. Schematic diagram of slag layer for cell i along the membrane wall.
d du gl i ¼ ql g cos hi ; dxi dxi
xi ¼ 0;
i gl du ¼0 dxi
xi ¼ dl;i ;
ui ¼ 0
ð2Þ
The energy conservation for cell i can be expressed as:
1 1 min;i C s T g þ ðT o;i1 þ T cv Þmex;i1 C s ðT o;i þ T cv Þmex;i C s 2 2 qout;i þ qin;i ¼0
ð3Þ
qin;i ¼ hðT g;i T o;i Þ þ er T 4g;i T 4o;i
ð4Þ
2.2. Slag properties model 2.2.1. Viscosity model Based on the model assumptions, slag behaves as liquid phase above Tcv and solid phase below Tcv. The liquid slag with bubbles behaves as gas-liquid two phase flow. Several models have been proposed to predict the viscosity of two phase flow. One of the most widely used model was proposed by McAdams et al. [28], which was applied to calculate the viscosity of two phase flow depend on liquid viscosity, gas viscosity and mass fraction of gas:
1
ge qout;i ¼ qflux;i ¼
T o;i T cv T cv T w;i T w;i T mr;i ¼ ¼ dl;i =kl ds;i =ks dr =kr
T mr;i T mw;i dm =km
¼
ð5Þ
where r is blackbody radiation coefficient, e is the slag emissivity, h is the convective heat transfer coefficient and computed based on the local flow field conditions. The slag velocity can be derived after twice integral for Eq. (2). The liquid slag average velocity is the average value along the liquid slag thickness, as shown in Eq. (6). The slag velocity multiply by the thickness, height and circumference is equal to the slag mass flow rate. Therefore, the liquid slag layer thickness can be derived from the slag mass flow rate and Eq. (6), as shown in Eq. (7). Eqs. (8) and (9) are directly derived from Eq. (5). The liquid slag average velocity, liquid slag layer thickness, solid slag layer thickness and the heat flux of slag layer can be expressed as follows:
ui ¼
qg cosðhi Þd2l;i ai 1 2 2 2 3 e þ gð0Þi ai a2i a3i ai
dl;i ¼
ds;i ¼
mex;i gð0Þi a3i 2 pDi q g cosðhi Þðeai ða2i 2ai þ 2Þ 2Þ
ks ks dm ks dr ðT cv T water Þ qflux;i km kr
qflux;i ¼
T o;i T cv dl;i =kl
ð6Þ 13
ð7Þ
ð8Þ
ð9Þ
where ai ¼ ln gðdl Þi =gð0Þi , g(0)i is the slag viscosity at the gasslag interface and g(dl)i is the slag viscosity at the solid-liquid slag interface.
¼
j 1j þ gg gl
ð10Þ
where ge is the effective viscosity of two-phase mixture, gg is the gas viscosity, gl is the liquid viscosity, and j is the mass fraction of gas. The slag viscosity is measured after the re-melting process by a high-temperature rotational viscometer. The Sutherland’s [29] law considered the effect of temperature variation on the gas viscosity:
gg ¼ g0
1 þ C=273:15 1 þ C=T
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T 273:15
ð11Þ
where g0 is the viscosity when the temperature is 0 °C for a given gas, and C is a given constant for a given gas. According to the assumption that gas component of bubbles is carbon monoxide, the initial parameters in Eq. (11) were given as: C = 100 and g0 = 1.68 105 Pa s. The mass fraction of gas (j) and the volume fraction of gas (b) have the following relationship:
b¼
qmix j qg
ð12Þ
where qmix is the density of bubbly slag (two-phase mixture) and qg is the density of gas in bubbles. The density of bubbly slag is calculated by:
qmix ¼ ð1 bÞqs þ bqg
ð13Þ
where qs is the density of slag without bubbles. The heat capacity of bubbly slag is calculated by:
cmix ¼ jcg þ ð1 jÞcs
ð14Þ
where cmix is the specific heat of bubbly slag, cg is the gas specific heat and cs is the specific heat of slag without bubbles.
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2.2.2. Thermal conductivity model Bubbly slag can be regarded as multiphase heterogeneous materials. Several models [30–33] have been proposed to predict the effective thermal conductivity of heterogeneous materials, ke. The models are based on the thermal conductivity of continuous phase, kc, thermal conductivity of discrete phase, kd, and volume fraction of discrete phase, b (equal to the porosity e in solid-gas two phase materials). Researchers also have built and modified the effective thermal conductivity models, such as Series model, Parallel model, the weighted geometric mean model, and Maxwell-Eucken model. The series model and parallel model represent the minimum and maximum values of effective thermal conductivity of two phase system, respectively. The MaxwellEucken model is applicable to heterogeneous materials that noninteracting spheres randomly distribute in continuous medium. Series model
kc kd ke ¼ bkc þ ð1 bÞkd
ð15Þ
Parallel model
ke ¼ bkd þ ð1 bÞkc
ð16Þ
Geometric mean model
ke ¼ kbd k1b c
ð17Þ
Maxwell-Eucken model
ke ¼ kc
2kc þ kd þ 2bðkd kc Þ 2kc þ kd bðkd kc Þ
ð18Þ
The temperature in the slag layer is linear distribution, which is based on the assumption that the slag thermal conductivity will not change with temperature. Regardless of the bubbles effects, the thermal conductivity of slag can be calculated according to the Mills and Rhine’s [34] work:
ks ¼ aqs cs
ð19Þ
where the thermal diffusivity a = 4.5 107 m2/s, qs is the slag density and cs is the slag specific heat. The slag density and specific heat are the functions of composition. Mills and Rhine [34] proposed the simple equation to calculate the slag density as follow:
qs ¼ 2460 þ 18ðwt%FeO þ wt%Fe2 O3 þ wt%MnOÞ
ð20Þ
where the slag components are expressed in weight percentages. According to the Mills and Rhine [34] method, the specific heat of slag can be calculated as:
cs ¼ x1 c1 þ x2 c2 þ x3 c3
ð21Þ
where cs is the specific heat of slag, ci is the specific heat of component i, and xi is the mole fraction of component i. The heat transfer process of bubbly slag is considered as the heat transfer of porosity materials, where gas phase play a significant role in effective thermal conductivity. Based on the assumption that bubble components inside slag are mainly carbon monoxide and hydrogen, the gas thermal conductivity in high temperature is about 7.5 104 W/m K according to the properties of the mixed gas. 3. Parameter conditions 3.1. Gas volume fraction in slag The micrographs of the industrial slag cross-section from Sinopec-ECUST Gasifier and Shell Gasifier are detected by a SU-
1181
1510 scanning electron microscope (SEM, HITACHI, Japan) as shown in Fig. 2. It is clearly observed that pores with different sizes distribute on the cross-section surface of the cooled slag sample. The existence of pores indicates that the slag at the high temperature in a gasifier is not a pure liquid phase or solid phase, but a gas phase doping. The ImageJ software is used to analyze each micrograph and calculate the area of the pores. Delesse and Rosiwal principle [35,36] have stated that while a structure contained a secondary phase, p, then the area fraction (uA) of phase p on a random cross section was equal to the volume fraction (uv) of that phase in the structure, represented as the following relationship:
u ¼ uv ¼ uA
ð22Þ
where uA is the average value of the area fraction in practical situation. Eq. (22) shows that the slag porosity is equal to the pores area fraction. The slag cross section is selected randomly, and plenty of photomicrographs (200 photos) are analyzed in this study, therefore the experiment data meet the applicable conditions of the formula. Combining the results of planar graph and Delesse and Rosiwal principle (Eq. (20)), the porosity of two slags are 0.076 (slag from Sinopec-ECUST Gasifier) and 0.093 (slag from Shell Gasifier), respectively. Bubbles at high temperature and pressure in the gasifier turn into pores inside slag after the cooling process. With the consideration for the opposite effect of the temperature and pressure on gas volume, we assume that the gas volume remain constant after the cooling process. The porosity of cooling slag is corresponding to the gas volume fraction in the high temperature slag on the gasifier. The magnitude of the gas volume fraction is of non-ignorable influence to effective thermal conductivity and viscosity of the bubbly slag as shown in next section, which affect the heat transfer and slag flow in gasifier. Furthermore, it is obviously observed that the pores are neither series distribution nor parallel distribution. Therefore, the series and parallel effective thermal conductivity models are not appropriate for bubbly slag in view of the physical structure.
3.2. Simulation conditions and slag properties The simulation condition is under steady state conditions with parameter from the CFD simulation of Shell pulverized coal gasifier (2000 t/d coal consumption). The configuration of Shell Gasifier is shown in Fig. 3. The particle mass deposition rate per unit area and near-wall gas temperature distribution are the average results from the 3-D CFD simulation results of industrial gasifier with the help of Fluent software (under 50% load condition), as shown in Figs. 4 and 5, respectively. The viscosity of coal slag was measured by a high-temperature rotational viscometer for the RV DVIII system (Theta Industries, Port Wahington, NY) and the viscositytemperature curve is present in Fig. 6. From the viscositytemperature curve, we can found the temperature of critical viscosity (the temperature in the point of mutational viscosity). The compositions and properties of coal slag without bubbles are shown in Table 1, including the slag critical viscosity temperature (Tcv), density, specific heat, thermal conductivity and emissivity. The thermal conductivities of refractory wall (SiC coating) and metal wall were 8 and 43 W/m K, respectively [14]. With the stable operation of the gasifier, the average temperature of the water in the membrane wall keeps for about 250 °C. In this study, we assume that the metal temperature at the metal-water interface was approximately equal to the average temperature of the water due to the turbulent convection heat transfer.
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Fig. 2. SEM micrographs of the slag cross-section (where (a) and (b) are industrial slag from Sinopec-ECUST Gasifier, (c) and (d) are industrial slag from Shell Gasifier).
2960 2 3 4 5
4670
8 15mm
Particle deposition rate (kg/(m2⋅s))
Refractory wall
547
Metal wall
0.08
0.06
0.04
0.02
0.00
0
1
2
3
4
5
6
7
Axial distance (m)
Burner
38 39 40
144
Burner
29 30
335
Fig. 4. Particle mass deposition rate per unit area.
Fig. 3. Structure and dimensions of Shell Gasifier.
4. Results and discussions 4.1. Effects of bubbles on slag viscosity Fig. 7 shows the viscosity-temperature curve of effective viscosity of bubbly slag at the temperature above Tcv. The effective vis-
cosity of bubbly slag shows a decreasing tendency with the gas volume fraction of bubbles increasing. Furthermore, the viscosity of bubbly slag decrease obviously from 1650 K to 1800 K, while almost keep unchanged at temperature above 1800 K. According to the gas temperature distribution near the wall, the slag in upper part of the gasifier is greatly influenced by the bubbles. 4.2. Effects of bubbles on slag thermal conductivity The thermal conductivity of slag without bubbles is calculated by the components of slag, which will not change with temperature according to the assumption. The effective thermal conductivities of bubbly slag are calculated by different models (Eqs. (15)–(18)) as shown in Fig. 8. The effective thermal conductivity of slag would decrease for the effect of bubbles. The value of effective thermal conductivity has different results with different models. The values of effective thermal conductivity calculated by parallel model and Maxwell-Eucken model have slight decrease
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2100
3
Efficient viscosity (Pa⋅s)
Temperature (K)
2000
1900
1800
1700
0
1
2
3
4
5
6
2
1
0 1600
7
Axial distance (m)
β=0 β=0.02 β=0.04 β=0.06 β=0.08 β=0.1
1700
1800
1900
2000
2100
Temperature (K)
Fig. 5. Gas temperature distribution near the wall. Fig. 7. The effective viscosity of slag at various gas volume fractions and temperatures.
Viscosity (Pa⋅s)
50 40 30 20 10 0
1350
1400
1450
1500
1550
Temperature (°C) Fig. 6. Viscosity-temperature data of slag in Shell Gasifier.
Efficient thermal conductivity (W/m ⋅K)
60
1.5
1.2
0.9 0.6
0.3
0.0 0.00
Parallel model Maxwell-Eucken model Geometric mean model Series model
0.02
0.04
0.06
0.08
0.10
Gas volume fraction of bubbles Fig. 8. The effective thermal conductivity at various gas volume fractions.
Table 1 Chemical composition and properties of slag. Component
wt.%
SiO2 Al2O3 CaO Fe2O3 Na2O MgO TiO2 K2O
40.07 22.14 14.16 20.59 0.36 0.62 1.43 0.63
Slag properties (without bubbles)
Value
Temperature of critical viscosity Tcv (K) Density qs (kg/m3) Specific heat cs (J/kg k) Thermal conductivity ks (W/m K) Emissivity
1617 2830 1118 1.42 0.83
for the effects of bubbles, and the values calculated by geometric mean model and series model have significantly decrease. According to the assumption that the bubbles uniformly distribute in slag layer instead of series distribution or parallel distribution, we exclude the parallel and serial thermal conductivity models in view of the physical structure. Moreover, the series model and parallel model represent the minimum and maximum values of effective thermal conductivity of two phase system, respectively. The actual
situation must fall in between the minimum and maximum values. Therefore, the Maxwell-Eucken model and geometric mean model are adopted to calculate the thermal conductivity of bubbly slag in the next section. 4.3. Effects of bubbles on slag flow velocity Fig. 9 shows the average velocity distribution of liquid slag at various gas volume fractions. The liquid slag velocity increases along the slag flow direction at the distance less than 6.5 m when the gas volume fraction (b) is 0, and suddenly decreases at the distance above 6.5 m. The axial distance of 6.5–7 m is contraction section which form cone angle with vertical plane. The molten slag from the vertical plane impacts to the conical surface, which can cause instantaneous kinetic energy loss. Therefore, the liquid slag flows to the conical surface with moments of slowing down. As the slag viscosity decrease with the increase of the gas volume fraction, the liquid slag velocity in each unit increase for the effect of bubbles in the slag as shown in Fig. 9. In addition, the slag thermal conductivity has no impact in liquid slag velocity as shown in Eq. (6), therefore, the slag velocities from the results of two thermal conductivity models are consistent. According to the measured porosity of slag in this study, the gas volume fraction of bubbles is 0.093, which has a non-ignorable influence on liquid slag velocity
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Liquid slag average velocity (cm/s)
3
β =0 β =0.01 β =0.05 β =0.093 β =0.1
2
1
0 0
1
2
3
4
5
6
7
Axial distance (m) Fig. 9. Liquid slag average velocity along the gasifier.
as shown in Fig. 9. The average velocities of liquid slag are 1.11 and 1.35 cm/s when gas volume fraction of bubbles is 0 and 0.093, respectively. The growth rate of liquid slag velocity is about 22% for the effect of bubbles.
4.4. Effects of bubbles on slag layer thickness The thickness distribution of liquid slag and solid slag with various gas volume fractions of bubbles are shown in Figs. 10 and 11, respectively. When the gas volume fraction inside slag is 0, the thickness distribution of solid and liquid slag depend on the temperature distribution, deposition rate in gasifier, the position of the nozzle and the gasification chamber shape. The thickness of slag suddenly changes at the axial distance of 6.5 m as shown in Figs. 10 and 11. The reason is similar to the previous section. The molten slag from the vertical plane impacts to the conical surface and the liquid slag velocity quickly decreases. In the case of total mass flow rate of slag keeps constant, the liquid slag thickness increases because the slag velocity slows down, and solid slag thickness also appears the corresponding change at the conical surface. Fig. 10 shows that the liquid slag layer thickness becomes thinner with the increase of gas volume fraction of bubbles. The slag thermal conductivity has no impact on the liquid slag thickness from Eq. (7), hence, the liquid slag thickness from the results of two thermal conductivity models are consistent. Fig. 11a shows
Liquid slag thickness (mm)
4 β=0 β=0.01 β=0.05 β=0.093 β=0.1
3
2
1
0
0
1
2
3
4
5
Axial distance (m) Fig. 10. Liquid slag thickness along the gasifier.
6
7
that the solid slag layer thickness decreases with the increase of gas volume fraction for the Maxwell-Eucken thermal conductivity model, especially in gasifier upper part. Fig. 11b shows that the solid slag layer thickness increases with the increase of gas volume fraction for the geometric mean thermal conductivity model, especially in gasifier bottom half. From the results of two thermal conductivity models, the solid slag layer thickness depends on the combined effect of effective thermal conductivity and effective viscosity. Furthermore, the slag effective viscosities in upper part of the gasifier obviously decrease for effects of the bubbles and almost keep unchanged in gasifier bottom half. The average thicknesses of liquid slag layer are 2.02 and 1.83 mm when the gas volume fractions of bubbles are 0 and 0.093, respectively. The reduction rate of the liquid slag layer thicknesses is about 10% for the effect of bubbles. The average thickness of solid slag layer is 6.62 mm when the gas volume fraction of bubbles is 0. For the Maxwell-Eucken model, the average thickness of solid slag layer is 6.07 mm when the gas volume fraction is 0.093, where the reduction rate is about 8%. For the geometric mean model, the average thickness of solid slag layer is 7.16 mm when the gas volume fraction is 0.093, where the growth rate is about 8%. The results show that two kinds of thermal conductivity model have different effects on solid slag layer thickness. 4.5. Effects of bubbles on heat flux of the slag The heat flux of slag with various gas volume fractions is shown in Fig. 12. When the gas volume fraction of bubbles is 0, the distribution of heat flux mainly depend on the temperature distribution, the position of the nozzle and the gasification chamber shape. The heat flux of slag has a peak near the nozzles, and also has a rapid increase at the conical surface. Fig. 12a shows that the heat fluxes of slag have a slight decrease for the effect of bubbles with the Maxwell-Eucken thermal conductivity model. However, Fig. 12b shows that the heat flux of slag decrease significantly for the effect of bubbles with the geometric mean thermal conductivity model. Fig. 13 shows the average heat flux of slag at various gas volume fractions with two thermal conductivity models. The average heat flux of slag is 180 kW/m2 when the gas volume fraction of bubbles is 0. For the Maxwell-Eucken model, the average heat flux of slag is 173 kW/m2 when the gas volume fraction is 0.093, where the reduction rate is about 4%. Meanwhile, for the geometric mean model, the average heat flux of slag is 99 kW/m2 when the gas volume fraction is 0.093, where the reduction rate is about 45%. The heat flux obviously decreases for the effect of bubbles with the geometric mean model. From two kinds of model results and Eq. (9), the heat flux of slag depends on the combined effect of thermal conductivity and liquid slag thickness. The heat flux of slag increases with the decrease of the liquid slag thickness, but decreases with the decrease of the thermal conductivity. In addition, the thermal conductivity of slag obviously decreases with the increase of gas volume fraction for the geometric mean model from the above results. Combining the changes of thermal conductivity and liquid slag thickness, the heat flux of slag obviously decreases with the increase of gas volume fraction in slag for the geometric mean thermal conductivity model. In order to distinguish which thermal conductivity model is better, the simulated results from two models were compared with the results calculated by industrial data. Under 50% load condition, the steam output of Shell pulverized coal gasifier can reach 15– 18 t/h. Based on the quantity of steam output, import and export of cooling water temperature, and the steam enthalpy, the range of average heat flux of slag is 140 165 kW/m2, as shown in Fig. 13. Compared with the industrial values, the results of Maxwell-Eucken model are more accurate than geometric mean model from the heat flux of slag layer. As a result, the
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18
(a)
16
β =0 β =0.01 β =0.05 β =0.093 β =0.1
14 12 10 8
Soild slag thickness (mm)
Soild slag thickness (mm)
18
6 4 2 0
0
1
2
3
4
5
6
β =0 β =0.01 β =0.05 β =0.093 β =0.1
14 12 10 8 6 4 2 0
7
(b)
16
0
1
2
Axial distance (m)
3
4
5
6
7
Axial distance (m)
Fig. 11. Solid slag thickness along the gasifier: (a) Maxwell-Eucken model; (b) geometric mean model.
400
β=0 β=0.01 β=0.05 β=0.093 β=0.1
300
200
100
0
0
1
2
3
β=0 β=0.01 β=0.05 β=0.093 β=0.1
(a)
Heat flux (KW/m2)
Heat flux (KW/m2)
400
4
5
6
7
300
200
(b)
100
0
0
1
Axial distance (m)
2
3
4
5
6
7
Axial distance (m)
Fig. 12. Heat flux of slag along the gasifier: (a) Maxwell-Eucken model; (b) geometric mean model.
Average heat flux (KW/m 2 )
200 180 160 140 Range of industrial values 120 100 80 0.00
Maxwell-Eucken model Geometric mean model 0.02
0.04
0.06
0.08
0.10
Gas volume fraction of bubbles
decrease about 10% for the effect of bubbles inside slag. Two models are applied to calculate the bubbly slag effective thermal conductivity. For the Maxwell-Eucken effective thermal conductivity model, the bubbles inside slag decrease the solid slag thickness especially in gasifier upper part and slightly decrease the heat flux of slag layer. For the geometric mean effective thermal conductivity model, the bubbles inside slag increase the solid slag thickness especially in gasifier bottom half and obviously decrease the heat flux of slag. The Maxwell-Eucken model is more accurate than geometric mean model from the result of slag layer heat flux. The Maxwell-Eucken thermal conductivity model is appropriate to simulate the actual condition for a gasifier. Acknowledgements
Maxwell-Eucken thermal conductivity model is better to simulate the actual condition.
This study was supported by the Foundation of Shanghai Science and Technology Committee (14dz1200100), the National Natural Science Foundation of China (U1402272), the National Natural Science Foundation of China (21376082), and the Foundation of State Key Laboratory of Coal Conversion (Grant No. J16-17-301).
5. Conclusions
References
Fig. 13. The average heat flux of slag at at various gas volume fractions.
The effects of bubbles inside slag on the slag flow and heat transfer were studied with the combination of effective thermal conductivity model, effective viscosity model, slag flow and heat transfer model. The effective viscosity and thermal conductivity decrease as the gas volume fraction of bubbles increase. Simulation results indicate that the liquid slag layer velocity increase about 22% for the effect of bubbles inside slag. The liquid slag thickness
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Effects of the bubbles in slag on slag flow and heat transfer in the membrane wall entrained-flow gasifier Binbin Zhang a,b, Zhongjie Shen a,b, Dong Han a,b, Qinfeng Liang a,b,c, Jianliang Xu a,b, Haifeng Liu a,b,⇑ a Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, PR China b Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, PR China c State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, PR China
h i g h l i g h t s The slag flow and heat transfer model were modified with the bubbles in slag. The bubbles in slag reduced the slag thermal conductivity and viscosity. The bubbles in slag increased the liquid slag velocity. The bubbles in slag reduced the liquid and solid slag layer thickness. The bubbles in slag reduced the slag heat flux.
a r t i c l e
i n f o
Article history: Received 4 May 2016 Revised 23 September 2016 Accepted 22 October 2016 Available online 24 October 2016 Keywords: Gasification Slag Bubble Thermal conductivity Viscosity
a b s t r a c t The slag from the industrial gasifier has porous structure, which has a non-ignorable influence on the characteristics of slag layer. The slag flow and heat transfer model were modified based on the effective thermal conductivity and viscosity, to predict the slag characteristics for the effects of bubbles in slag. The results show that bubbles inside slag reduce the slag thermal conductivity and viscosity. The modified model predicts the liquid slag velocity, slag layer thickness and heat flux of slag layer. The liquid slag flow velocity increases with the increase of bubbles inside slag, while the thickness of slag layer decreases. In addition, the increasing gas volume fraction of bubbles inside slag decreases the heat flux of slag layer. Two models are applied to calculate the bubbly slag effective thermal conductivity. The MaxwellEucken thermal conductivity model is more accurate than geometric mean model from the result of slag layer heat flux. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The entrained-flow gasification is a high efficient and clean coal conversion technology, which is widely used in the chemical industry such as the Integrated Gasification Combined Cycle (IGCC) plant [1–3]. The membrane wall entrained-flow gasifier has a long lifetime compared to the refractory brick wall entrained-flow gasifier [4]. In an entrained gasifier, the ash particles and unreacted coal particles would deposit on the wall and form solid and liquid slag layer, which can protect the metal tube from the high temperature gas corrosion [5]. Therefore slag layer properties (e.g. rheol-
⇑ Corresponding author at: Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, PR China. E-mail address: [email protected] (H. Liu). http://dx.doi.org/10.1016/j.applthermaleng.2016.10.141 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
ogy, thickness and heat transfer) are very important for the stability and security of a gasifier operation. Experiment study for slag flow and heat transfer in an industrial gasifier is limited and difficult due to the high temperature and pressure environment. Hosseini and Gupta [6] used an electrically heated vertical drop-tube furnace to study the effect of operating conditions on ash deposition and slag formation. Wang et al. [7] used the syrup to simulate the liquid slag and studied the slag deposition and growth at the slag tap hole region under the cold model experiment. The heat transfer and slag deposition characteristics were studied in a pilot-scale pulverized coal entrained-flow gasifier with the pilot test and calculation method [8]. For comparison with the experiment studies, numerical simulation and modeling are the main methods to study the slag flow and heat transfer in the membrane wall entrained-flow gasifier. The model which proposed by Seggiani [9], was widely used in the slag
B. Zhang et al. / Applied Thermal Engineering 112 (2017) 1178–1186
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Nomenclature cg ci cmix cs D g h mex min qflux qin qout Tcv Tf Tg Tmr Tmw To Tw Twater u u0 x xi
gas specific heat (J/kg K) specific heat of component i (J/kg K) specific heat of two-phase mixture (J/kg K) slag specific heat (J/kg K) gasifier diameter (m) gravitational constant (m/s2) convective heat transfer coefficient (W/m2 K) vertical outlet slag mass flow rate per unit (kg/s) mass flow of particle deposition per unit (kg/s) heat flux through the slag (W/m2) heat flux to the slag surface (W/m2) heat flux from the slag to the refractory layer (W/m2) temperature of critical viscosity (K) slag flow temperature (K) gas temperature at slag-gas interface (K) metal-refractory wall interface temperature (K) water-metal wall interface temperature (K) slag temperature at slag-gas interface (K) refractory-slag interface temperature (K) average temperature of water (K) slag velocity at distance x from slag-gas interface (m/s) slag velocity in slag-gas interface (m/s) the distance from the slag-gas interface mole fraction of component i
Greek letters a thermal diffusivity (m2/s) b gas volume fraction of bubbles
flow and heat transfer studies [10,11]. In all of these references, the temperature in the slag layer was linear distribution, which was based on the assumption that the slag thermal conductivity is a fixed value. Based on Seggiani’s [9] model, the influence of shear stress due to particle deposition was considered in Ref. [12]. The slag flow between the temperature of critical viscosity (Tcv) and flow temperature (Tf) was considered in a modified model [13]. The influence of critical viscosity and its temperature on the slag behavior was considered in a numerical model [14]. A comprehensive numerical model was proposed to predict the thickness, velocity and temperature of the slag layer in an entrained flow gasifier [15], and also compared with existing analytical models. The heat transfer of slag layer was calculated by the discretization of the velocity in a black liquor recovery boiler [16]. The behaviors of slag flow were investigated in an oxy-coal combustor which considered the effects of particle burning near the wall [17]. The mathematical model for a gasifier included slag flow and heat transfer model, particle capture model and 3-D model [18]. The particles deposit behavior was determined by the viscosities of slag and incoming particles [19]. The temperature distribution and particle deposition rate inside the gasifier were important data which obtained from 3-D gasifier models as referred in the literatures [20–23]. Literatures about the slag structure have been studied [24–27], researchers gave the facts that one of the main characteristic of coal slag was the porous structure. The cooled slag has a porous structure, which mean that slag layer at the high temperature contains bubbles. However, seldom literature is referred for the influence of bubbles on slag flow and heat transfer. The objective of this paper is to study the effects of bubbles on slag flow and heat transfer in the membrane wall entrained-flow gasifier. The effects of bubbles in slag on the thermal conductivity and viscosity are studied with different models. The slag model
dl dm dr ds
e ge gg gl h
j kc kd ke kg kl km kr ks
qg ql qmix qs r u uA uv
thickness of liquid slag layer (m) thickness of metal wall (m) thickness of refractory wall (m) thickness of solid slag layer (m) emissivity effective viscosity (Pa s) viscosity of gas in slag (Pa s) liquid slag viscosity (Pa s) slope of the wall (°) mass fraction of gas thermal conductivity of continuous phase (W/m K) thermal conductivity of discrete phase (W/m K) effective thermal conductivity (W/m K) thermal conductivity of gas in slag (W/m K) thermal conductivity of liquid slag (W/m K) thermal conductivity of metal wall (W/m K) thermal conductivity of refractory wall (W/m K) thermal conductivity of solid slag (W/m K) density of gas in slag (kg/m3) density of liquid slag (kg/m3) density of two-phase mixture (kg/m3) slag density (kg/m3) blackbody radiation coefficient (W/m2 K4) porosity area fraction of pores volume fraction of pores
referred from Seggiani’s [9] work is coupled with the effective thermal conductivity models and an effective viscosity model. The influence of gas volume fraction inside slag layer on the liquid slag velocity, slag thickness and heat transfer of slag layer are also studied.
2. Mathematical models 2.1. Slag flow and heat transfer model The slag flow and heat transfer model is established according to the method proposed by Seggiani [9]. The schematic diagram of slag layer for cell i along the membrane wall is shown in Fig. 1. In addition, the following assumptions are proposed in this study: (1) The bubbles in liquid slag layer and solid slag layer are uniformly distributed. (2) The bubbles will not breakup or coalescence for the high viscosity of slag, and the bubbly slag is considering as a pseudohomogenous phase. (3) The gas components of bubbles are mainly carbon monoxide and hydrogen for the reducing atmosphere in the gasifier. The slag flow and heat transfer model for cell i in the steadystate condition is based on the following equations: The mass conservation for cell i can be expressed as:
min;i þ mex;i1 mex;i ¼ 0
ð1Þ
The momentum conservation in linear coordinates for cell i can be expressed as:
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mex,i-1 qex,i-1 Metal wall
Refractory wall
T0
T cv
min T in Particles
qflux
δl
δs T water
qin
Tw
T mr
Solid layer
Gas
Liquid layer
mex,i qex,i
Fig. 1. Schematic diagram of slag layer for cell i along the membrane wall.
d du gl i ¼ ql g cos hi ; dxi dxi
xi ¼ 0;
i gl du ¼0 dxi
xi ¼ dl;i ;
ui ¼ 0
ð2Þ
The energy conservation for cell i can be expressed as:
1 1 min;i C s T g þ ðT o;i1 þ T cv Þmex;i1 C s ðT o;i þ T cv Þmex;i C s 2 2 qout;i þ qin;i ¼0
ð3Þ
qin;i ¼ hðT g;i T o;i Þ þ er T 4g;i T 4o;i
ð4Þ
2.2. Slag properties model 2.2.1. Viscosity model Based on the model assumptions, slag behaves as liquid phase above Tcv and solid phase below Tcv. The liquid slag with bubbles behaves as gas-liquid two phase flow. Several models have been proposed to predict the viscosity of two phase flow. One of the most widely used model was proposed by McAdams et al. [28], which was applied to calculate the viscosity of two phase flow depend on liquid viscosity, gas viscosity and mass fraction of gas:
1
ge qout;i ¼ qflux;i ¼
T o;i T cv T cv T w;i T w;i T mr;i ¼ ¼ dl;i =kl ds;i =ks dr =kr
T mr;i T mw;i dm =km
¼
ð5Þ
where r is blackbody radiation coefficient, e is the slag emissivity, h is the convective heat transfer coefficient and computed based on the local flow field conditions. The slag velocity can be derived after twice integral for Eq. (2). The liquid slag average velocity is the average value along the liquid slag thickness, as shown in Eq. (6). The slag velocity multiply by the thickness, height and circumference is equal to the slag mass flow rate. Therefore, the liquid slag layer thickness can be derived from the slag mass flow rate and Eq. (6), as shown in Eq. (7). Eqs. (8) and (9) are directly derived from Eq. (5). The liquid slag average velocity, liquid slag layer thickness, solid slag layer thickness and the heat flux of slag layer can be expressed as follows:
ui ¼
qg cosðhi Þd2l;i ai 1 2 2 2 3 e þ gð0Þi ai a2i a3i ai
dl;i ¼
ds;i ¼
mex;i gð0Þi a3i 2 pDi q g cosðhi Þðeai ða2i 2ai þ 2Þ 2Þ
ks ks dm ks dr ðT cv T water Þ qflux;i km kr
qflux;i ¼
T o;i T cv dl;i =kl
ð6Þ 13
ð7Þ
ð8Þ
ð9Þ
where ai ¼ ln gðdl Þi =gð0Þi , g(0)i is the slag viscosity at the gasslag interface and g(dl)i is the slag viscosity at the solid-liquid slag interface.
¼
j 1j þ gg gl
ð10Þ
where ge is the effective viscosity of two-phase mixture, gg is the gas viscosity, gl is the liquid viscosity, and j is the mass fraction of gas. The slag viscosity is measured after the re-melting process by a high-temperature rotational viscometer. The Sutherland’s [29] law considered the effect of temperature variation on the gas viscosity:
gg ¼ g0
1 þ C=273:15 1 þ C=T
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T 273:15
ð11Þ
where g0 is the viscosity when the temperature is 0 °C for a given gas, and C is a given constant for a given gas. According to the assumption that gas component of bubbles is carbon monoxide, the initial parameters in Eq. (11) were given as: C = 100 and g0 = 1.68 105 Pa s. The mass fraction of gas (j) and the volume fraction of gas (b) have the following relationship:
b¼
qmix j qg
ð12Þ
where qmix is the density of bubbly slag (two-phase mixture) and qg is the density of gas in bubbles. The density of bubbly slag is calculated by:
qmix ¼ ð1 bÞqs þ bqg
ð13Þ
where qs is the density of slag without bubbles. The heat capacity of bubbly slag is calculated by:
cmix ¼ jcg þ ð1 jÞcs
ð14Þ
where cmix is the specific heat of bubbly slag, cg is the gas specific heat and cs is the specific heat of slag without bubbles.
B. Zhang et al. / Applied Thermal Engineering 112 (2017) 1178–1186
2.2.2. Thermal conductivity model Bubbly slag can be regarded as multiphase heterogeneous materials. Several models [30–33] have been proposed to predict the effective thermal conductivity of heterogeneous materials, ke. The models are based on the thermal conductivity of continuous phase, kc, thermal conductivity of discrete phase, kd, and volume fraction of discrete phase, b (equal to the porosity e in solid-gas two phase materials). Researchers also have built and modified the effective thermal conductivity models, such as Series model, Parallel model, the weighted geometric mean model, and Maxwell-Eucken model. The series model and parallel model represent the minimum and maximum values of effective thermal conductivity of two phase system, respectively. The MaxwellEucken model is applicable to heterogeneous materials that noninteracting spheres randomly distribute in continuous medium. Series model
kc kd ke ¼ bkc þ ð1 bÞkd
ð15Þ
Parallel model
ke ¼ bkd þ ð1 bÞkc
ð16Þ
Geometric mean model
ke ¼ kbd k1b c
ð17Þ
Maxwell-Eucken model
ke ¼ kc
2kc þ kd þ 2bðkd kc Þ 2kc þ kd bðkd kc Þ
ð18Þ
The temperature in the slag layer is linear distribution, which is based on the assumption that the slag thermal conductivity will not change with temperature. Regardless of the bubbles effects, the thermal conductivity of slag can be calculated according to the Mills and Rhine’s [34] work:
ks ¼ aqs cs
ð19Þ
where the thermal diffusivity a = 4.5 107 m2/s, qs is the slag density and cs is the slag specific heat. The slag density and specific heat are the functions of composition. Mills and Rhine [34] proposed the simple equation to calculate the slag density as follow:
qs ¼ 2460 þ 18ðwt%FeO þ wt%Fe2 O3 þ wt%MnOÞ
ð20Þ
where the slag components are expressed in weight percentages. According to the Mills and Rhine [34] method, the specific heat of slag can be calculated as:
cs ¼ x1 c1 þ x2 c2 þ x3 c3
ð21Þ
where cs is the specific heat of slag, ci is the specific heat of component i, and xi is the mole fraction of component i. The heat transfer process of bubbly slag is considered as the heat transfer of porosity materials, where gas phase play a significant role in effective thermal conductivity. Based on the assumption that bubble components inside slag are mainly carbon monoxide and hydrogen, the gas thermal conductivity in high temperature is about 7.5 104 W/m K according to the properties of the mixed gas. 3. Parameter conditions 3.1. Gas volume fraction in slag The micrographs of the industrial slag cross-section from Sinopec-ECUST Gasifier and Shell Gasifier are detected by a SU-
1181
1510 scanning electron microscope (SEM, HITACHI, Japan) as shown in Fig. 2. It is clearly observed that pores with different sizes distribute on the cross-section surface of the cooled slag sample. The existence of pores indicates that the slag at the high temperature in a gasifier is not a pure liquid phase or solid phase, but a gas phase doping. The ImageJ software is used to analyze each micrograph and calculate the area of the pores. Delesse and Rosiwal principle [35,36] have stated that while a structure contained a secondary phase, p, then the area fraction (uA) of phase p on a random cross section was equal to the volume fraction (uv) of that phase in the structure, represented as the following relationship:
u ¼ uv ¼ uA
ð22Þ
where uA is the average value of the area fraction in practical situation. Eq. (22) shows that the slag porosity is equal to the pores area fraction. The slag cross section is selected randomly, and plenty of photomicrographs (200 photos) are analyzed in this study, therefore the experiment data meet the applicable conditions of the formula. Combining the results of planar graph and Delesse and Rosiwal principle (Eq. (20)), the porosity of two slags are 0.076 (slag from Sinopec-ECUST Gasifier) and 0.093 (slag from Shell Gasifier), respectively. Bubbles at high temperature and pressure in the gasifier turn into pores inside slag after the cooling process. With the consideration for the opposite effect of the temperature and pressure on gas volume, we assume that the gas volume remain constant after the cooling process. The porosity of cooling slag is corresponding to the gas volume fraction in the high temperature slag on the gasifier. The magnitude of the gas volume fraction is of non-ignorable influence to effective thermal conductivity and viscosity of the bubbly slag as shown in next section, which affect the heat transfer and slag flow in gasifier. Furthermore, it is obviously observed that the pores are neither series distribution nor parallel distribution. Therefore, the series and parallel effective thermal conductivity models are not appropriate for bubbly slag in view of the physical structure.
3.2. Simulation conditions and slag properties The simulation condition is under steady state conditions with parameter from the CFD simulation of Shell pulverized coal gasifier (2000 t/d coal consumption). The configuration of Shell Gasifier is shown in Fig. 3. The particle mass deposition rate per unit area and near-wall gas temperature distribution are the average results from the 3-D CFD simulation results of industrial gasifier with the help of Fluent software (under 50% load condition), as shown in Figs. 4 and 5, respectively. The viscosity of coal slag was measured by a high-temperature rotational viscometer for the RV DVIII system (Theta Industries, Port Wahington, NY) and the viscositytemperature curve is present in Fig. 6. From the viscositytemperature curve, we can found the temperature of critical viscosity (the temperature in the point of mutational viscosity). The compositions and properties of coal slag without bubbles are shown in Table 1, including the slag critical viscosity temperature (Tcv), density, specific heat, thermal conductivity and emissivity. The thermal conductivities of refractory wall (SiC coating) and metal wall were 8 and 43 W/m K, respectively [14]. With the stable operation of the gasifier, the average temperature of the water in the membrane wall keeps for about 250 °C. In this study, we assume that the metal temperature at the metal-water interface was approximately equal to the average temperature of the water due to the turbulent convection heat transfer.
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B. Zhang et al. / Applied Thermal Engineering 112 (2017) 1178–1186
Fig. 2. SEM micrographs of the slag cross-section (where (a) and (b) are industrial slag from Sinopec-ECUST Gasifier, (c) and (d) are industrial slag from Shell Gasifier).
2960 2 3 4 5
4670
8 15mm
Particle deposition rate (kg/(m2⋅s))
Refractory wall
547
Metal wall
0.08
0.06
0.04
0.02
0.00
0
1
2
3
4
5
6
7
Axial distance (m)
Burner
38 39 40
144
Burner
29 30
335
Fig. 4. Particle mass deposition rate per unit area.
Fig. 3. Structure and dimensions of Shell Gasifier.
4. Results and discussions 4.1. Effects of bubbles on slag viscosity Fig. 7 shows the viscosity-temperature curve of effective viscosity of bubbly slag at the temperature above Tcv. The effective vis-
cosity of bubbly slag shows a decreasing tendency with the gas volume fraction of bubbles increasing. Furthermore, the viscosity of bubbly slag decrease obviously from 1650 K to 1800 K, while almost keep unchanged at temperature above 1800 K. According to the gas temperature distribution near the wall, the slag in upper part of the gasifier is greatly influenced by the bubbles. 4.2. Effects of bubbles on slag thermal conductivity The thermal conductivity of slag without bubbles is calculated by the components of slag, which will not change with temperature according to the assumption. The effective thermal conductivities of bubbly slag are calculated by different models (Eqs. (15)–(18)) as shown in Fig. 8. The effective thermal conductivity of slag would decrease for the effect of bubbles. The value of effective thermal conductivity has different results with different models. The values of effective thermal conductivity calculated by parallel model and Maxwell-Eucken model have slight decrease
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2100
3
Efficient viscosity (Pa⋅s)
Temperature (K)
2000
1900
1800
1700
0
1
2
3
4
5
6
2
1
0 1600
7
Axial distance (m)
β=0 β=0.02 β=0.04 β=0.06 β=0.08 β=0.1
1700
1800
1900
2000
2100
Temperature (K)
Fig. 5. Gas temperature distribution near the wall. Fig. 7. The effective viscosity of slag at various gas volume fractions and temperatures.
Viscosity (Pa⋅s)
50 40 30 20 10 0
1350
1400
1450
1500
1550
Temperature (°C) Fig. 6. Viscosity-temperature data of slag in Shell Gasifier.
Efficient thermal conductivity (W/m ⋅K)
60
1.5
1.2
0.9 0.6
0.3
0.0 0.00
Parallel model Maxwell-Eucken model Geometric mean model Series model
0.02
0.04
0.06
0.08
0.10
Gas volume fraction of bubbles Fig. 8. The effective thermal conductivity at various gas volume fractions.
Table 1 Chemical composition and properties of slag. Component
wt.%
SiO2 Al2O3 CaO Fe2O3 Na2O MgO TiO2 K2O
40.07 22.14 14.16 20.59 0.36 0.62 1.43 0.63
Slag properties (without bubbles)
Value
Temperature of critical viscosity Tcv (K) Density qs (kg/m3) Specific heat cs (J/kg k) Thermal conductivity ks (W/m K) Emissivity
1617 2830 1118 1.42 0.83
for the effects of bubbles, and the values calculated by geometric mean model and series model have significantly decrease. According to the assumption that the bubbles uniformly distribute in slag layer instead of series distribution or parallel distribution, we exclude the parallel and serial thermal conductivity models in view of the physical structure. Moreover, the series model and parallel model represent the minimum and maximum values of effective thermal conductivity of two phase system, respectively. The actual
situation must fall in between the minimum and maximum values. Therefore, the Maxwell-Eucken model and geometric mean model are adopted to calculate the thermal conductivity of bubbly slag in the next section. 4.3. Effects of bubbles on slag flow velocity Fig. 9 shows the average velocity distribution of liquid slag at various gas volume fractions. The liquid slag velocity increases along the slag flow direction at the distance less than 6.5 m when the gas volume fraction (b) is 0, and suddenly decreases at the distance above 6.5 m. The axial distance of 6.5–7 m is contraction section which form cone angle with vertical plane. The molten slag from the vertical plane impacts to the conical surface, which can cause instantaneous kinetic energy loss. Therefore, the liquid slag flows to the conical surface with moments of slowing down. As the slag viscosity decrease with the increase of the gas volume fraction, the liquid slag velocity in each unit increase for the effect of bubbles in the slag as shown in Fig. 9. In addition, the slag thermal conductivity has no impact in liquid slag velocity as shown in Eq. (6), therefore, the slag velocities from the results of two thermal conductivity models are consistent. According to the measured porosity of slag in this study, the gas volume fraction of bubbles is 0.093, which has a non-ignorable influence on liquid slag velocity
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Liquid slag average velocity (cm/s)
3
β =0 β =0.01 β =0.05 β =0.093 β =0.1
2
1
0 0
1
2
3
4
5
6
7
Axial distance (m) Fig. 9. Liquid slag average velocity along the gasifier.
as shown in Fig. 9. The average velocities of liquid slag are 1.11 and 1.35 cm/s when gas volume fraction of bubbles is 0 and 0.093, respectively. The growth rate of liquid slag velocity is about 22% for the effect of bubbles.
4.4. Effects of bubbles on slag layer thickness The thickness distribution of liquid slag and solid slag with various gas volume fractions of bubbles are shown in Figs. 10 and 11, respectively. When the gas volume fraction inside slag is 0, the thickness distribution of solid and liquid slag depend on the temperature distribution, deposition rate in gasifier, the position of the nozzle and the gasification chamber shape. The thickness of slag suddenly changes at the axial distance of 6.5 m as shown in Figs. 10 and 11. The reason is similar to the previous section. The molten slag from the vertical plane impacts to the conical surface and the liquid slag velocity quickly decreases. In the case of total mass flow rate of slag keeps constant, the liquid slag thickness increases because the slag velocity slows down, and solid slag thickness also appears the corresponding change at the conical surface. Fig. 10 shows that the liquid slag layer thickness becomes thinner with the increase of gas volume fraction of bubbles. The slag thermal conductivity has no impact on the liquid slag thickness from Eq. (7), hence, the liquid slag thickness from the results of two thermal conductivity models are consistent. Fig. 11a shows
Liquid slag thickness (mm)
4 β=0 β=0.01 β=0.05 β=0.093 β=0.1
3
2
1
0
0
1
2
3
4
5
Axial distance (m) Fig. 10. Liquid slag thickness along the gasifier.
6
7
that the solid slag layer thickness decreases with the increase of gas volume fraction for the Maxwell-Eucken thermal conductivity model, especially in gasifier upper part. Fig. 11b shows that the solid slag layer thickness increases with the increase of gas volume fraction for the geometric mean thermal conductivity model, especially in gasifier bottom half. From the results of two thermal conductivity models, the solid slag layer thickness depends on the combined effect of effective thermal conductivity and effective viscosity. Furthermore, the slag effective viscosities in upper part of the gasifier obviously decrease for effects of the bubbles and almost keep unchanged in gasifier bottom half. The average thicknesses of liquid slag layer are 2.02 and 1.83 mm when the gas volume fractions of bubbles are 0 and 0.093, respectively. The reduction rate of the liquid slag layer thicknesses is about 10% for the effect of bubbles. The average thickness of solid slag layer is 6.62 mm when the gas volume fraction of bubbles is 0. For the Maxwell-Eucken model, the average thickness of solid slag layer is 6.07 mm when the gas volume fraction is 0.093, where the reduction rate is about 8%. For the geometric mean model, the average thickness of solid slag layer is 7.16 mm when the gas volume fraction is 0.093, where the growth rate is about 8%. The results show that two kinds of thermal conductivity model have different effects on solid slag layer thickness. 4.5. Effects of bubbles on heat flux of the slag The heat flux of slag with various gas volume fractions is shown in Fig. 12. When the gas volume fraction of bubbles is 0, the distribution of heat flux mainly depend on the temperature distribution, the position of the nozzle and the gasification chamber shape. The heat flux of slag has a peak near the nozzles, and also has a rapid increase at the conical surface. Fig. 12a shows that the heat fluxes of slag have a slight decrease for the effect of bubbles with the Maxwell-Eucken thermal conductivity model. However, Fig. 12b shows that the heat flux of slag decrease significantly for the effect of bubbles with the geometric mean thermal conductivity model. Fig. 13 shows the average heat flux of slag at various gas volume fractions with two thermal conductivity models. The average heat flux of slag is 180 kW/m2 when the gas volume fraction of bubbles is 0. For the Maxwell-Eucken model, the average heat flux of slag is 173 kW/m2 when the gas volume fraction is 0.093, where the reduction rate is about 4%. Meanwhile, for the geometric mean model, the average heat flux of slag is 99 kW/m2 when the gas volume fraction is 0.093, where the reduction rate is about 45%. The heat flux obviously decreases for the effect of bubbles with the geometric mean model. From two kinds of model results and Eq. (9), the heat flux of slag depends on the combined effect of thermal conductivity and liquid slag thickness. The heat flux of slag increases with the decrease of the liquid slag thickness, but decreases with the decrease of the thermal conductivity. In addition, the thermal conductivity of slag obviously decreases with the increase of gas volume fraction for the geometric mean model from the above results. Combining the changes of thermal conductivity and liquid slag thickness, the heat flux of slag obviously decreases with the increase of gas volume fraction in slag for the geometric mean thermal conductivity model. In order to distinguish which thermal conductivity model is better, the simulated results from two models were compared with the results calculated by industrial data. Under 50% load condition, the steam output of Shell pulverized coal gasifier can reach 15– 18 t/h. Based on the quantity of steam output, import and export of cooling water temperature, and the steam enthalpy, the range of average heat flux of slag is 140 165 kW/m2, as shown in Fig. 13. Compared with the industrial values, the results of Maxwell-Eucken model are more accurate than geometric mean model from the heat flux of slag layer. As a result, the
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18
(a)
16
β =0 β =0.01 β =0.05 β =0.093 β =0.1
14 12 10 8
Soild slag thickness (mm)
Soild slag thickness (mm)
18
6 4 2 0
0
1
2
3
4
5
6
β =0 β =0.01 β =0.05 β =0.093 β =0.1
14 12 10 8 6 4 2 0
7
(b)
16
0
1
2
Axial distance (m)
3
4
5
6
7
Axial distance (m)
Fig. 11. Solid slag thickness along the gasifier: (a) Maxwell-Eucken model; (b) geometric mean model.
400
β=0 β=0.01 β=0.05 β=0.093 β=0.1
300
200
100
0
0
1
2
3
β=0 β=0.01 β=0.05 β=0.093 β=0.1
(a)
Heat flux (KW/m2)
Heat flux (KW/m2)
400
4
5
6
7
300
200
(b)
100
0
0
1
Axial distance (m)
2
3
4
5
6
7
Axial distance (m)
Fig. 12. Heat flux of slag along the gasifier: (a) Maxwell-Eucken model; (b) geometric mean model.
Average heat flux (KW/m 2 )
200 180 160 140 Range of industrial values 120 100 80 0.00
Maxwell-Eucken model Geometric mean model 0.02
0.04
0.06
0.08
0.10
Gas volume fraction of bubbles
decrease about 10% for the effect of bubbles inside slag. Two models are applied to calculate the bubbly slag effective thermal conductivity. For the Maxwell-Eucken effective thermal conductivity model, the bubbles inside slag decrease the solid slag thickness especially in gasifier upper part and slightly decrease the heat flux of slag layer. For the geometric mean effective thermal conductivity model, the bubbles inside slag increase the solid slag thickness especially in gasifier bottom half and obviously decrease the heat flux of slag. The Maxwell-Eucken model is more accurate than geometric mean model from the result of slag layer heat flux. The Maxwell-Eucken thermal conductivity model is appropriate to simulate the actual condition for a gasifier. Acknowledgements
Maxwell-Eucken thermal conductivity model is better to simulate the actual condition.
This study was supported by the Foundation of Shanghai Science and Technology Committee (14dz1200100), the National Natural Science Foundation of China (U1402272), the National Natural Science Foundation of China (21376082), and the Foundation of State Key Laboratory of Coal Conversion (Grant No. J16-17-301).
5. Conclusions
References
Fig. 13. The average heat flux of slag at at various gas volume fractions.
The effects of bubbles inside slag on the slag flow and heat transfer were studied with the combination of effective thermal conductivity model, effective viscosity model, slag flow and heat transfer model. The effective viscosity and thermal conductivity decrease as the gas volume fraction of bubbles increase. Simulation results indicate that the liquid slag layer velocity increase about 22% for the effect of bubbles inside slag. The liquid slag thickness
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