BINGZHI LI, ANDERS BRINK, AND MIKKO HUPA
Process Chemistry Centre, Åbo Akademi University
Piispankatu 8, FI-20500 Turku, Finland
Email: firstname.lastname@abo.fi
ABSTRACT
Extensive slagging can influence the heat transfer in the uptake shaft in the copper and nickel flash smelting process. In this work a slag model, developed for determining local heat flux boundary conditions for slagging wall, is tested using viscosity-temperature relations typical for slag in the nickel flash smelting process. The model consists of two modules: one for calculating the thickness of the slag and one for calculating the surface temperature of the slag layer. From these the heat flux through the slagging wall can be obtained. The model can be implemented as a subroutine and be used in CFD analysis of an uptake shaft. It can also be used in other combustion applications.
KEYWORDS: flash smelting process; slagging wall; slag model

1. INTRODUCTION
In the flash smelting process, a significant amount of dust particles are generated. The dust particles are carried by the off-gas to the uptake shaft and the heat recovery boiler, where they can form deposits on the walls. The deposits can have a great impact on the efficiency of the heat recovery boiler (Yang, 1996; Yang et al, 1999). Here the conditions the dust particles undergo in the uptake shaft can influence their deposition behavior in the heat recovery boiler. In the uptake shaft, some of the deposits are molten and flow down the wall, which leads to slagging walls. These slagging walls can affect the dust-laden gas phase.
CFD (computational fluid dynamics) can provide detailed insights into the process. For the uptake shaft, CFD can be utilized to investigate the interactions between the slagging walls and the gas phase, and those between the dust particles and the gas phase. In this work a slag model, developed for determining local heat flux boundary conditions for slagging wall, is tested using viscosity-temperature relations typical for slag in the nickel flash smelting process. The model consists of two modules: one for calculating the thickness of the slag and one for calculating the surface temperature of the slag layer. From these the heat flux through the slagging wall can be obtained.
Many nickel matte smelting slags contain magnesia introduced from the concentrate.
Magnesia increases the liquidus temperature of slags, and beyond a certain level it raises the viscosity of slags. Usually, lime is added to prevent accretion build-up and tapping difficulties. Ducret (1995) measured viscosities of artificial slags similar to nickel matte smelting slags, with different MgO and CaO content. In addition, he also made measurements of one industrial slag from a nickel smelter. These viscosity-temperature relations are used to investigate the behavior of different slags on the uptake shaft walls.
2. MODEL DESCRIPTION
2.1 Slag flow model
At steady state conditions, the running slag layer reaches a constant thickness and a steady velocity profile across the thickness. The balance between the gravitational force and the shear stress shall be fulfilled at any point in the layer. This force balance can be written: d dx
( ( x ) dv dx
) g cos (1), where (x) is the viscosity, dv/dx is the velocity gradient, and is the slope of the wall. At the surface of the running slag layer a zero-gradient boundary condition is used for the velocity. At the interface of liquid running layer and solid layer a non-slip boundary condition is used.
Bird et al. (1960) presented a solution for a steady flow of a nonisothermal film. The solution relies on that the temperature dependence of viscosity can be expressed using the following equation:

Ae
B / T
(2), where A and B are empirical constants. Assuming a linear temperature profile across the liquid slag layer, the relation between the viscosity and the position can be written as
( x ) ( f
) exp( f x
) (3), with
(3) give: ln( ( 0 ) / ( f
)) and f
is the thickness of running slag layer. Equation (1) and v ( x ) g cos(
( f
)
) f
2 e (
1 1
2
) x e f ( x f
1
2
) (4).
In a model of slag flow in coal gasifier, Seggiani (1998) integrated the product between the velocity and the density to obtain an expression for the mass flow rate per unit length of a running slag: m '
2 g cos(
( f
)
) f
3 e (
1 2
2
2
3
)
2
3
(5).
The equation can be used to calculate the thickness of running slag layer.
2.2 Heat flux calculation
The heat balance on slag at steady state is described as following equation: q flowin q radiation q deposition q conduction q flowout
(6), where q flowin
and q flowout
are heat flux in the slag flowing in and out of the control volume, q deposition
is the heat flux in the impacting ash particles adding to the control volume, q radiation
is the heat flux from gas phase by radiation, and refractory wall. Here, q conduction
is the heat flux to the q flow m flow c p
T flow
(7),

q deposition m deposition c p
T g
(8), q radiation
( T g
4
T outer
4
) A (9), q conduction
T outer f
T inner
/ k f
A (10), m flowin m deposition m flowout
(11) and c p
is the specific heat of the running slag, (5.67e-8 W/m
2
-K
4
) is the Stefan-Boltzmann constant, is the emissivity of the running slag, k f
is the thermal conductivity of the running slag, and T g
is the gas phase temperature, T outer
is the temperature at the slag surface, T inner is the temperature at the interface of solid and liquid slag layers. If the mass flow rate of the impacting ash particles m deposition
is so small comparing with the slag flow on the wall m flow
, the term q deposition
in Equation (6) can be neglected. Also, when the temperature of the running slag is only slightly changed through the control volume, q flowin q flowout
can be approximated to be zero. So a simplified heat balance comprises only the radiation part and conduction part of Equation (6): q radiation q conduction
(12).
Additionally, once the thickness of the running slag layer is solved, the heat flux through the running layer can be determined according to Equation (10). The thickness of the solid layer can be calculated according to the following equation: s
T inner
T wall , outer
A q conduction
/ k s
(13), where s
is the thickness of the solid slag layer and k s
is the thermal conductivity of solid slag.
T wall.outer
is the temperature at the interface of solid slag and refractory wall.
3. MODEL PARAMETERS
In this work, viscosity-temperature relations for the slags are taken from Ducret’s work
(Ducret, 1995). Three artificial slags and one industrial slag are considered. The three iron saturated artificial slags have a Fe/SiO
2
ratio at 1.7, and they are: slag A, without any MgO

or CaO; slag B, with 6 wt% MgO; slag C, with 3 wt% MgO and 3 wt% CaO. The viscositytemperature relations are shown in Figure 1. The temperature at the interface of solid and liquid slag layers are set to the liquidus temperatures. The other physical properties of the slags are assumed to be similar for all slags (Elli, 2008). These physical properties are shown in Table 1. The gas phase temperature is set at 1700 K.
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1450 1500 1550 1600
Temperature (K)
1650 1700 1750 slag A slag B slag C industrial
Figure 1. Viscosity-temperature relation and the liquidus temperature for different slags: slag A (Fe/SiO
2
=
1.7, 0 wt% CaO, 0 wt% MgO), TL(liquidus temperature) = 1476 K, 1 .
2651 e 4 * exp( 9 .
3715 e 3 / T ) ; slag
B (Fe/SiO
2
= 1.7, 0 wt% CaO, 6 wt% MgO), TL = 1616 K, 4 .
4643 e 9 * exp( 2 .
622 e 4 / T ) ; slag C
(Fe/SiO
2
= 1.7, 3 wt% CaO, 3 wt% MgO), TL = 1481 K,
TL = 1566 K, 4 .
5209 e 4 * exp( 8 .
9482 e 3 / T ) .
2 .
6432 e 4 * exp( 7 .
6089 e 3 / T ) ; industrial,
Table 1. Properties of nickel matte melting slag
Density (kg/m
3
)
Thermal conductivity, k (W/m-K)
Specific heat C p
(J/kg-K)
Emissivity
Mass flow rate m (kg/s-m)
2800
1
1200
0.8
0.6
4. RESULTS AND DISCUSSION
For the four different slags, the thickness and the surface temperature of running layer were first calculated. Then the heat flux through the slagging wall was obtained. The results are shown in Table 2 with the liquidus temperature of the slag. The viscosity influences the thickness of the running layer. The industrial slag which has the highest viscosity gives the largest thickness. The heat flux increases when the liquidus temperature decreases, because

the gas phase temperature is fixed. The magnitude of the heat flux is reasonable; however, more adequate properties of the slag will ensure more accurate results.
Table 2. Thickness, surface temperature of the running slag layer and heat flux through the slagging wall for the four different slags
TL (K)
Slag A
1476
T outer
(K) 1543 f
(mm) q (kW/m
2
0.55
) 7.6
Slag B
1616
1640
0.48
3.2
Slag C
1481
1540
0.47
7.8
Industrial
1566
1614
0.68
4.4
5. CONCLUSIONS
A slag model was used to calculate thickness and surface temperature of the running slag layer with the data for nickel matte smelting slags. Three artificial slags and one industrial slag were tested. The magnitude of heat flux through the slagging wall is reasonable, which proves the applicability of the model in the calculation for flash smelting slags. The model can be implemented as a subroutine and be used in CFD analysis of an uptake shaft. It can also be used in other combustion applications.
6. ACKNOWLEDGEMENT
This work has been part of the activities of the Åbo Akademi Process Chemistry Centre funded by the Academy of Finland in their Centres of Excellence Program. Financial support obtained from Outotec Oyj and by the National Technology Agency of Finland in the research project “INTER” is gratefully acknowledged.
7. REFERENCES
Bird, R.B., Stewart, W.E., Lightfoot, E.N. (1960). John Wiley, New York.
Ducret, A.C. (1995).
Doctoral thesis , Department of Chemical Engineering, the University of Melbourne.
Ducret, A.C., Rankin, W.J. (2002).
Scandinavian Journal of Metallurgy , 2002, 31: 59-67.
Elli, M. (2008).
Doctoral thesis , Faculty of Chemistry and Material Science, Helsinki
University of Technology.
Seggiani, M. (1998).
Fuel , 77(14), 1611-1621.
Yang, Y. (1996).
Acta Polytechnica Scandinavica , Chemical Technology Series No. 242.
Yang, Y., Jokilaakso, A., Taskinen, P. and Kytö, M. (1999).
JOM , Vol. 51, No. 5, pp.36–
39, 47.