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Molten Slag Flow and Phase Transformation Behaviors in a Slagging Entrained-Flow Coal Gasifier Jianjun Ni, Zhijie Zhou, Guangsuo Yu,* Qinfeng Liang, and Fuchen Wang Key Laboratory of Coal Gasification of Ministry of Education, East China UniVersity of Science and Technology, Shanghai 200237, China
A slag flow submodel has been developed to simulate the slag flow and phase transformation behaviors in coal gasifiers. The volume of the fluid (VOF) model is used to capture the free surface of the slag flow, and the continuum surface force (CSF) model is employed to calculate the surface tension between the gas phase and the liquid slag phase. The slag is treated as a Newtonian fluid when the slag temperature is above the critical viscosity temperature (Tcv), and plastic fluid is treated when the slag temperature is between the flow temperature (Tf) and the Tcv. The ash particle deposition, viscosity-temperature dependence, and different thermal conductivity for different slag phase are all included in the present simulation. For membrane wall coal gasification, the liquid slag and solid slag layer increases along the flow and total slag thickness increases as the operating temperature decreases. The velocity profiles and viscosity profiles at different operating temperatures are performed. The liquid slag flow will produce fluctuations when the slag temperature decreases to the lowest at the bottom of the gasifier. In addition, the temperature difference (To - Tf) between 150 and 200 °C is suitable for a membrane wall coal entrained-flow gasifier. For refractory wall coal gasification, the thicker refractory bricks can effectively prevent the heat lost from the gasifier wall, so the slag flow is steady when the operating temperature is higher than the critical operating temperature. An expression of solid slag layer formation criterion has been deduced from heat-transfer balance. The critical operating temperature of the different slag mass flow rate is studied by heat-transfer balance. In addition, the solid slag layer will rapidly increase as the operating temperature decreases to critical operating temperature. 1. Introduction The slag layer has a different effect on coal-fired slagging combustors and gasifiers. There has been considerable research into the effects of slagging and fouling during pulverized fuel combustion in conventional boilers. The occurrence of a slag layer has a great impact on heat transfer and is an operational disadvantage in pulverized fuel combustion boilers, which also reduces the efficiency of the boiler. However, slagging in entrained-flow gasifiers is an environmentally sound and efficient means of disposing of the unused mineral matter in the coal. In the gasifier, it is preferred to minimize the quantity of fly ash and maximize the passage of ash to slag to assist in disposal. The slag layer in the gasifier results in a molten protective coating and reduces heat loss to the wall, generally increasing the cold gas efficiency of the gasifier.1 Moreover, unsteady slag flow may produce slag plugging at the bottom of the gasifier. Thus, study of the slag flow and phase transformation processes is necessary for further improvements of its reliability and availability. The molten slag flow and phase transformation in a gasifier is a multiphase-multilayer flow process with complex heat and mass transfer. A number of models have been proposed to describe the flow behavior of the molten slag layer in the entrained-flow gasifier. Seggiani2 presented a model for timevarying slag flow in the Prenflo gasifier being used at the integrated gasification combined cycle (IGCC) plant in Puertollano. Bockelie et al.3 simulated the slag flow in a one-stage and two-stage gasifier using a slagging wall model, and it was carried out by Benyon et al.4 Li et al.5 also used this model to analyze the slag flow in a black liquor recovery boiler and coal gasifier. That model is based upon an analytical expression for * To whom correspondence should be addressed. Tel.: +86-2164252974. Fax: +86 21 64251312. E-mail:
[email protected].
velocity distribution, and three important assumptions have been made. The relationship of viscosity-temperature is assumed obeying the Weymann model, the temperature profile across the liquid slag layer is assumed to be a linear relation, and the slag flow has not been considered when the slag temperature is between the flow temperature (Tf) and the critical viscosity temperature (Tcv).6 Kittel et al.7 studied the heat transfer into the cooling screen of the Siemens gasifier (GSP) using a simplified dynamic model. Liu and Hao8 carried out a simulation on the local slag flow in a GE (Texaco) gasifier; the slag surface tension was included in the slag flow calculations. The objective of this work is to develop a multiphasemultilayer flow and phase transformation model to study the slag flow in a slagging entrained-flow gasifier under reducing conditions. We aim to overcome the assumptions about the viscosity-temperature relationship and temperature linear distribution in the liquid slag layer. Furthermore, the slag flow under the temperature between the critical viscosity temperature and the flow temperature (Tf) also is considered in the present simulations. On the basis of the above considerations, we simulated the slag multiphase-multilayer flow in a water jacket cooled wall gasifier (membrane wall for dry pulverized coal gasification) and refractory brick wall gasifier (for coal water slurry gasification). 2. Model Description 2.1. Previous Slag Flow Models. 2.1.1. Benyon and Seggiani Model.2,4 The running slag layer reaches a dynamic balance at steady-state conditions and has a constant thickness and steady velocity profile across the thickness. Benyon and Seggiani derived a simple model based on a series of assumptions.2,4 They assumed that the temperature of the critical viscosity (Tcv) is considered as the phase transition temperature. The basic schemes of the slag flow on a refractory wall and
10.1021/ie1013844 2010 American Chemical Society Published on Web 10/20/2010
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Figure 1. Scheme of the slagging wall in the entrained-flow slagging gasifier (a, refractory wall; b, membrane wall).
membrane wall are shown in Figure 1a and 1b, respectively. In Figure 1, Tpt represents the slag phase transformation temperature. Neglecting all acceleration terms, the liquid slag flow layer at distance x from the slag-gas interface is described by
{
dus d µ[T(x)] dx dx
}
) -Fsg cos β
(1)
where µ[T(x)] is the viscosity, us is the slag velocity at distance x, β is the slope of the wall, and g is the gravity. The boundary conditions are τ ) µ[T(x)](duy)/(dx) ) 0 (slag-gas friction is negligible) when x ) 0, us ) 0 when x ) δl, where τ is the shear stress at the wall and δl is the thickness of the liquid slag. Bird et al.6 proposed that the slag viscosity depends on the distance x in the slag layer which can be approximated as µ(x) ) µ(0)e-R(x/δl) where R ) -ln
(2)
µ(δl) µ(0)
(3)
where µ(0) is the viscosity at the slag surface and µ(δl) is the viscosity at Tcv. After substituting eq 2, eq 1 is integrated to obtain a relationship for the slag velocity with distance x uy(x) )
[(
)
(
Fsgδ2l cos(β) R 1 1 x 1 - 2 - eRx/δl e - 2 µ(0) R Rδ R R l
)]
[(
) ]
(6)
where ms,i is the slag mass, min,i is the mass flow rate of slag deposition, mex,i-1 is the incoming slag mass flow rate, and mex,i is the discharging slag mass flow rate. The discharging mass flow rate is calculated due to the assumption that the slag can be considered as a Newtonian fluid. Then the gravity Fg equals the friction force Ff in the steady state Fg,i ) FsgπDih(δl,i - x)cos β Ff,i ) Aµ[T(x)]
duy duy ) πDihµ[T(x)] dx dx
(7)
(8)
where h is the height of the slag layer and A is the area Hence duy ) Fsg cos β(δl,i - x)dx/µ[T(x)]
(9)
The thickness of the liquid slag layer is estimated under the assumption of a linear temperature distribution as Tsl(x) ) (Tcv - Tsg)x/δl + Tsg
(10)
Thus, the discharging slag mass flow rate can be calculated as
(4)
Equation 4 can then be integrated across the liquid slag thickness to obtain the mass flow rate of the slag exiting the ith cell as follows mex,i )
dms,i ) min,i + mex,i-1 - mex,i dt
πDiFs2gδ3l,i cos(β) R 1 1 1 2 - 2 + 3 - 3 e µ(0) R R R R
(5)
where πDi is the average circumferential length of the cell. The running slag thickness δl can be calculated from eq 5. 2.1.2. Discretizing Approach Model.7 In order to describe the process of the slag layer building, assumptions of the slag building model by Reid and Cohen9 were used. The mass, energy, and momentum quantity conservation equations are written for each control volume of the ith cell. The mass balance equation for the slag can be written
mex,i )
∫
δl,i
0
πDiFsuy dx
(11)
2.2. Slag Layer Model Description. 2.2.1. Slag Flow Model. The following assumptions are made to simplify the description of the slag flow in the gasifier. (1) The phase transition temperature between the liquid and the solid is the ash flow temperature. (2) The slag is considered as Newtonian fluid above the Tcv. In addition, the plastic fluid layer is treated when the slag temperature is between Tcv and Tf.8,10 (3) Chemical reactions in the slag layer are neglected. (4) The density and specific heat of the slag are independent of temperature. The problem has been simplified to axisymmetric geometries to make the calculation practical. Then the mass, energy, and momentum quantity conservation equations can be written as follows. Mass conservation equation
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∂(Fsuy) Fsux ∂(Fsux) + ) min + ∂y ∂x x
(12)
where ux is the radial velocity. Momentum conservation equation11 ∂(Fsu) + ∇ · (Fsuu) ) -∇p + ∇ · [µ(∇u + ∇uT)] + Fsg + F ∂t (13) where p is the pressure, g is the acceleration of gravity, and F is the outside force. Energy conservation equation
Fs ) 2460 + 18(FeO + Fe2O3 + MnO)(kg m-3)
∂ (F E) + ∇ · [u(FsE + p)] ) ∇ · (keff∇T) + minHm ∂t s
(17) (14)
The properties of slag and syngas in the momentum conservation equation and energy conservation equation are determined by the fractions of slag and syngas in each volume. keff is the effective conductivity. Hm is the state enthalpy of the deposition slag particles. The volume of fluid (VOF) model is used to describe the free surface between the liquid slag layer and syngas. The volume fraction of liquid slag and syngas, Rs and Rg, are introduced. In each control volume, the sum of the two phase’s volume fractions is unity. The fields for all variables and properties are shared by the phases and represent volumeaveraged values, as long as the volume fraction of each of the phases is known at each location. In other words, the following three conditions are possible for two-phase flow (syngas and liquid slag): Rs ) 0, the cell is full of syngas; Rs ) 1, the cell is full of liquid slag; 0 < Rs < 1, the cell contains the interface between the slag and the syngas. The implicit scheme is used for time discretization, and the Modified HRIC scheme12 is used to obtain the face fluxes for all cells, including those near the interface. The modified HRIC scheme provides improved accuracy for VOF calculations when compared to QUICK and second-order schemes and is less computationally expensive than the Geo-Reconstruct scheme. 2.2.2. Heat-Transfer Model. The heat transfer from the hot, particle-loaded syngas to the slag layer is due to radiation and convection. For calculation of radiative heat transfer the coupled syngas and particle radiation has to be considered. The discrete ordinate method (DOM)13 is used for thermal radiation heat transfer in the present model. In addition, the absorption coefficient of syngas is calculated by the weighted sum of gray gases model (WSGGM).14 The radiative heat-transfer equation for an absorbing, emitting, and scattering medium at position r in the direction s is dI(r, s) + (a + σs)I(r, s) ) ds σs σT4 + an2 π 4π
∫
4π
0
∂T ∂n
|
p
where the slag components are expressed in weight percentages. Slag flow is controlled by the viscosity of the slag, which in turn depends on the slag temperature, slag chemical composition, oxygen potential of the local atmosphere, and slag thermal history.4 Viscosity is the ratio of shear stress to shear rate and increases with a decrease in temperature. Browning et al.17 relate the abrupt change to the solid volume fraction. When the solid volume fractions are less than 10% the bulk viscosity increases linearly with the volume fraction of solids. When the solid volume fractions are higher than 10% the bulk viscosity increases exponentially. Thus, in this work, we assumed that the Tf is the phase transformation temperature. The viscositytemperature relationship can be measured or predicted, and a series of models has been introduced by Vargas et al.18 In addition, high-temperature RHEOTRONIC II has been used for direct measurement of the slag viscosity change with temperature under reducing atmosphere. The slag surface tension is described with the continuum surface force (CSF) model proposed by Brackbill et al.19 The surface tension can be written in terms of the pressure difference across the surface. The force at the surface can be expressed as a volume force using the divergence theorem. Volume force is the source term which is added to the momentum equation. This volume force in this work can be written as Fvol ) σgs
Frg∇Rg (Fg + Fs)/2
(15)
+ hf(Tw - Tf) + Qr
(16)
(18)
where F is the volume-averaged density which can be calculated as F ) RsFs +(1 - Rs)Fg and r is the curvature defined as follows r ) ∇ · nˆ )
1 n · ∇ |n| - (∇ · n) |n| |n|
[(
)
]
(19)
At the wall, the surface normal n at the live cell next to the wall is n ) nw cos θ + tw sin θ
I(r, s′)φ(r, s′)dΩ′
where a and σs represent the absorption and scattering coefficient, respectively. R is a function of the local concentrations of syngas species, path length, and total pressure. With the DOM, the radiative transfer equation is solved in a set of different directions n. The heat flux from a fluid cell to the wall is computed as15 Q ) -λ
where the terms on the right-hand side of eq 16 represent the heat flux exchange between the wall and the gas phase, gasphase convection heat transfer, and the radiative heat flux. The fluid-side heat-transfer coefficient hf is computed based on the local flow-field conditions. 2.2.3. Slag Properties for Flow. Several studies have been undertaken on the flow properties of the gasifier slag. The studies concentrate on the effects of the slag chemical composition on the slag viscosity, melting, and solidification phenomena and slag density. Mills and Rhine16 assess several means of predicting slag density and give the simplest as
(20)
where nw and tw are the unit vectors normal and tangential to the wall, respectively, and θ is the contact angle between the interface and the wall. The constant 67° is used in this work, and it was measured by Abbott and Austin.20 2.2.4. Slag Properties for Heat Transfer. The heat transfer into and from the semitransparent slag layer will depend on three sections: (1) the conducted heat through the slag layer to the refractory and cooling circuit or ambient conditions, (2) the radiative properties of the slag and two-phase flow medium, (3) the convective heat transfer between slag surface to syngas flow.
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Table 1. Ash Chemistry and Fusion Temperature of the Two Coals Used in This Work
Figure 2. Scheme of the gasifier slag throat.
Mills and Rhine21 measured the thermal properties of coal slags from the British/Lurgi slagging fixed bed gasifier between 298 and 1800 K. A constant emissivity, ε, of 0.83 is obtained for temperatures between 1070 and 1800 K by Mills and Rhine,21 which is used in this work. The Kopp-Neumann rule is adopted to estimate the slag heat capacity Cps Cps ) x1Cp1 + x2Cp2 + x3Cp3 + · · ·
(21)
where xi is the mole fraction and Cp is the partial molar heat capacity (usually taken to be that of the pure component). A commonly used method2,21 is implemented to calculate the effective thermal conductivity λeff of liquid slag λeff ) aeffFsCps
(22)
where the thermal diffusivity aeff ) 4.5 × 10-7 (m2/s) and Fs and Cps are obtained from eqs 17 and 21, respectively. The effective thermal conductivity of the solid slag layer is lower than the liquid layer, and there is a lack of reliable experimental data on solid slag from gasifiers. Zbogar et al.22 reviewed the limited slag thermal property data available. In addition, the thermal conductivity can be estimated for solid slag to be 0.6 ( 0.2 W m-1 K-1 by analyzing the original experimental data. Other thermal properties for slag flow simulation were measured by experiment, for example, the ash flow temperature (Tf) was measured by an intellectual ash melting point test
component (wt %, oxide)
Baodian
Beisu
Fe2O3 SiO2 Al2O3 CaO MgO Na2O K2O TiO2 SO3 ash flow temperature Tf (°C) Tcv (°C) density (kg m-3) specific heat Cp (kJ kg-1 K-1) emissivity
4.43 44.02 35.12 9.27 1.36 1.07 0.17 2.06 1.96 1367 1372 2540 1040 0.83
15.44 38.35 22.88 10.75 1.30 0.37 0.59 0.63 9.70 1283 1296 2820 1073 0.83
instrument. However, the ash thermal properties also can be predicted by mathematic models.23 3. Calculation Cases and Boundary Conditions. The gasifier slag throat is the key section for maintaining the slagging entrained-flow coal gasifier normal operation. The configuration of the entrained-flow gasifier slag throat is represented in Figure 2. Quad mesh is used in the mesh generation. The specified grid is fine enough to give grid-dependent solution and be validated through the grid-dependent tests. The number of grids for the present simulations is 335 410. The governing equation for the conservation of momentum, energy, mass, and radiation was solved sequentially by the finite volume method (FVM). DOM is treated by a second-order upwind scheme, and the momentum and energy terms are treated by the QUICK scheme. The PRESTO! scheme is used for pressure discretization. The calculation codes were performed on the FLUENT program. The user-defined functions (UDF) self-written in VC++ language are used for simulation of the slag viscosity and thermal conductivity temperature dependent. The UDF mass source term (min ) 0.5 kg s-1 m-1) is also used to achieve the ash particles deposition, and it is added to the free surface of the slag. The ash viscosity changes with temperature for two coal samples shown in Figure 3. The calculated zone is separated into two regions: high temperature (>Tcv) and low temperature (>Tf and
