Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
107
Steady-State Study of a Titanium Dioxide Rotary Kiln Guy Dumont and Pierre R. Belanger' Department of Electrical Engineering, McGill University, Montreal, Canada H3A 2A 7
This paper describes a mathematical model of a rotary kiln used for the calcination of titanium dioxide. The purposes of the model are a better understanding of Ti02 calcination and an improvement of kiln efficiency. The model is based on heat and mass transfer equations. The temperature profile along the kiln given by simulation is compared with actual measurements. The results are also used to derive conclusions about a possible scheme of control and to provide an explanation of kiln behavior which has so far remained unexplained. Finally, the optimization results permit us to see that an appreciable improvement of the efficiency of the kiln's operation is possible.
Introduction Titanium dioxide (TiOz) is a substance used as a pigment or whitener in paints, paper, textiles, plastics, and other products. The raw material is mostly available in a crystalline form known as anatase; unfortunately, it is another form, rutile, which has the right pigmentary properties. The conversion is achieved in a rotary kiln fed with a slurry of water and Ti02 in anatase form. The aim of the calcination is to produce Ti02 pigment with a rutile content around 98%. Given the important properties of rutile, this operation is crucial for the quality of the final product. The first objective of this study is t o improve kiln control. Typically, only 65% of the product has a rutile percentage within specifications. The steady-state analysis presented here represents the first stage of the study. I t is meant to answer questions relating to the basic structure of the control system, such as the identification of the principal perturbation variables and the selection of effective measured and manipulated variables. The possiblity of operating point optimization is also explored, in order t o assess the existence of optimum points. A model need not have the precision of, say, a process design model to provide useful answers to such questions. All that is needed is to structure the control system, which can then be tuned on-line. The use of rotary kilns is a feature of several industries; the cement kiln, in particular, has already been studied several times (Spang, 1972; Saas, 1967). The Ti02 kiln differs from the cement kiln in a t least one important aspect: the principal reactions are endothermic. The only study known to the authors that deals with a kiln with endothermic reactions is that by Manitius et al. (1974), for an aluminum oxide kiln. The Ti02 is sufficiently different to warrant its own investigation. In any case, for the Ti02 kiln we have to take into account the effect of the combustion chamber on the kiln. The analysis presented here is based on the usual heat and mass balances. The combustion chamber is modeled, as far as the rest of the kiln is concerned, as a radiating disk. Profiles are computed for two different kilns, one in Sorel, QuBbec, and one in Calais, France, for which some temperature measurements were available. A rapid sensitivity analysis to disturbances reveals that, unlike the cement kiln, this kiln cannot be adequately regulated by temperature control. This fact is confirmed by empirical knowledge of the plant. The model also indicates that two material temperature measurements along the kiln might give useful information about the length of the drying zone. Finally, a rapid and rather crude optimization scheme indicates that substantial improvements in kiln economics could result from a better setting of the primary and secondary air flows. 0019-7882/78/1117-0107$01.00/0
Description of the Kiln and Assumptions The calcination of the titanium dioxide is one of the most important stages in the processing of this pigment. This operation has two main purposes: (1) dry a slurry composed mainly of Ti02 and water and dissociate the sulfuric acid contained in it; (2) transform the Ti02 from anatase to rutile. These two operations are carried out in a single rotary kiln, 36-60 m in length, 2-4 m in diameter rotating a t the rate of 4-8 rotationdh. (See Figure 1.) Schematically the kiln can be divided into three parts: (1) drying zone which itself can be considered as consisting of three subzones: (a) preheating section until the slurry temperature reaches 100 "C; (b) constant rate drying section where the slurry behaves like a pure body a t constant temperature; (c) falling rate drying section where the temperature of the slurry starts to rise even though water is still evaporating; (2) heating zone where the solid temperature increases rapidly until it reaches the point where the rutilization is initiated; (3) rutilization zone where the crystalline transformation occurs. A percentage of 98% of rutile in the discharge product is generally required. Experience shows that it is sometimes difficult if not impossible to keep this percentage stable. In order to construct the model it is assumed that: (1)All parameters in a cross section of the kiln are constant. (2) Axial heat transfer due to conduction and radiation (except radiation from the combustion chamber) is insignificant. (3) Conduction except radial through the kiln lining does not occur. (4)There is no axial mixing of the solid (no axial diffusion). (5) The presence of sulfuric acid and chemical additives in the slurry does not significantly affect the heat balance. (6) The transformation from anatase to rutile follows the Arrhenius law. The conversion is first order with respect to anatase. The first four assumptions, aimed a t the simplification of the complex heat transfer equations, are common in the literature about kiln simulation. Assumption 5 is justified by the fact that the sulfuric acid is present in small amount. In the model it is assimilated to water. The chemical additives are present in infinitesimal parts. The sixth assumption is more intuitive. Only one reference (Barksdale, 1966) gives an indication about the order of the reaction: it is claimed to be second order. However, in the absence of more information, a simple first order will be tried. The results of the simulation will later show that a first order gives results in concordance with the actual plant. Mass Transfer Equations a. Distribution of the Material in a Cross Section. I t is assumed that the material is distributed in a crescent-like section with fixed ends; the angle is considered as constant
0 1978 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
108
b
-
-
q
-
---+
LDOLEI(
7
Figure 1. Scheme of the kiln. Figure 3. Heat fluxes.
CCMBUmlON
Figure 4. Effect of the combustion chamber. Figure 2. Cross section of the kiln. and equal to 120' around the particular fillage of the kilns studied here (see Figure 2). For given throughput rate and material velocity, R , can be determined. The velocity of the material V , is assumed to be proportional to the rotary speed (RPM), the kiln diameter, D, and its inclination from the horizontal, (3.
V, = K,(RPM)PD
(1)
K , is estimated from the residence time of the material in the kiln.
b. Rate of Drying. The critical moisture content is assumed t o be 10%on a wet basis. Saas (1967) and Manitius e t al. (1974) assume that the constant drying rate does not depend on the gas temperature. Making the same assumption, from Perry (1973) we can write for the constant rate zone
or using 1 = V,t
where A is the anatase content, AH the activation energy of the reaction, /Iis the material temperature, and k is a constant. d. Tertiary Air Flow. Due to the temperature and velocity of the hot gas stream inside the kiln, the inner pressure is less than the atmospheric pressure. Hence by Bernoulli's theorem there exists an uncontrollable air flow originating a t various orifices such as the discharge end. Applying the Bernoulli theorem for the main stream inside the kiln, the negative pressure l p inside the kiln a t the hot end can be expressed as
where p g is the gas density a t temperature T and Vis the gas velocity a t temperature T. Assuming the ideal law holds, we can write Pg
-aQh - -- -373h
ai V , ~ E L , Qp where h is defined as the total heat transfer coefficient, p is the bulk density of the dry material, E is the bed thickness, and L , is the water latent heat. The Q's are flow rates, the subscript h denoting the water, p denoting the dry product. In the falling rate zone the rate of drying is equal to
(3) where kh is a constant determined a t the boundary between the two drying zones, knowing the critical moisture and dQh/di from (2) a t that point. e. Rutilization. As stated before, the transformation from anatase to rutile is assumed to follow the Arrhenius law. For a first-order reaction, the rate of transformation can be written as dA - = -kA exp at or (4)
= Po
rTi7
(6)
The velocity of the tertiary air flow through an orifice of areas is
v = C d B a t To
(7)
PO
Hence, the tertiary air flow can be expressed as AT = spou. Knowing that V = Qg/pgS,where S is the kiln gas flow crosssection area and from ( 5 ) ,(6), (7) AT is given by
-
AT = KQg
T dg T,
(8)
where K = Cs/S. K is easily determined by measuring the percentage of oxygen in the output gases and knowing the kiln operating point. For instance, it was found that for kiln C, if AT is in m3/min and Qg in kglh, K = 0.0204 for T o = 293. By this method it has been shown that in some cases the tertiary air flow can reach up to 30-40% of the secondary flow. Heat Transfer Equations a. Kiln. The following heat fluxes are considered (see Figures 3 and 4):& , from gas to material; I $ ~from ~ , gas to inner wall; dwm,from inner wall to material; dWo,from inner wall to ambient air. These four heat fluxes appear all along the kiln.
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
109
In addition the following are considered in the drying zone: dgg,from gas to the water vapor produced by drying of the slurry; 4ev,consumed by evaporation. In the rutilization zone, located in the last few meters of the kiln, we have to account for the combustion chamber influence and the crystalline reaction: 4eg,from combustion chamber to gas; dem,from combustion chamber to material; &, consumed by rutilization. The first four heat fluxes can be expressed by the rather common formulas
4gm= agLp(T - 8)
+ u L ~ t , t ~ (-T 04) ~
(9)
+ uL3cwtg(T4- Tw4)
(10)
4wm= awL1(Tw- 8) + ~ L z t ~-( tg)tm(Tw4 l - 6')'
(11)
4gw= agLs(T - T,)
dwo= Uwo(Tw- To)
(12)
where L1, Lp, L3 are arc lengths as defined in Figure 2. The heat transfer coefficients cyg, aw,and Uwoand the emissivities cg, em, and cw are given in Appendices (a) and (b),respectively. u is the Stefan constant. T , 8, and T , are the temperatures of the gas, material, and inner wall, respectively. The heat flux +gg is computed assuming the temperature of the water vapor rises instantaneously from 373 K to the gas temperature T
where cv is the vapor specific heat as given in Appendix (c). The heat flux @r is assumed to be proportional to the rate of reaction &=-Q,-Aexp V,
AHM R8 79.9
0 -
4cm= a L ~ t , t , (T G , ~ o4)F
(15) (16)
where TG,is the chamber gas temperature; F and F1 are form factors defined in Appendix (d). Under these conditions, the heat balance equations can be written as
a
ai
+ d g w + 4gg +
a (4cg)
(17)
The temperatures and flow rates depend on the space variable 1. The heat fluxes depend on the temperatures in a nonlinear fashion. b. Combustion Chamber. The state of the combustion chamber is assumed to be independent of that of the kiln and can be treated separately. The following assumptions are made: (i) The flame is a cylindrical body whose temperature is uniform and determined solely by the fuel rate and the primary air flow. (ii) The temperature of the lining as well as that of the gas in homogeneous. The following heat fluxes are considered (see Figure 5): 4b, from flame to chamber inner wall; &,, from flame to chamber gas; dbc, from chamber wall to chamber gas; @bo,from chamber wall to ambient air. These heat fluxes are expressed by 4% = (rSfFficf(1 - cc)cb(Tf4 - T b 4 )
where Tf and T b are the temperatures of the flame and the chamber wall, respectively. Ffi is a form factor and sfand s b are the flame and wall lateral areas, respectively. The flame temperature, from assumption (i) can be computed by
F,P
=
(Tf- 2 9 3 ) ~ f [ ( P-f P,)F,
+ A,]1.29
(24)
where F, and A, are the fuel rate and the primary air flow. P , P f , and P, are the heat constant, the gas generation, and the air consumption per kilogram of fuel. The combustion chamber heat balance is then
- 293) = dfc + 4 b c 0 = 4% - 4 b c - @bo
QcCc(TGc
(25) (26)
where Q, is the combustion gas flow given by
T o simplify the model, the effect of the combustion chamber is likened to that of an equivalent disk located a t the open end of the chamber radiating toward the kiln as illustrated in Figure 4. The resulting heat fluxes are
- [QgCgTl = 4 g m
Figure 5. Heat fluxes in the chamber.
(20)
Q, = [(Pf - PJF,
+ A, + AJ1.29
(27)
where A, is the secondary air flow. Algorithm The computation of the state of the combustion chamber requires the solution of a system of two nonlinear algebraic equations, (25) and (26). The solution is computed by means of the Newton-Raphson algorithm. The inputs to the chamber, Le., the fuel rate F,, the primary air flow A,, and the secondary air flow A,, appear in (24) and (27). The state of the combustion chamber is characterized by three temperatures: Tf, Tb, and TGC. The computation of the conditions inside the kiln is much more complex. The steady-state model is a set of two interdependent nonlinear first-order differential equations, (17) and (18), and one algebraic equation (19). The integration method used is an implicit method known as J/TP (Jorgensen, 1969). We have a two-point boundary value problem: the boundary conditions are the cold material temperature, O(0)and the hot gas temperature T(L).The algorithm is designed by assuming an initial cold gas temperature T(0) and then integrating forward for both gas and material. If the boundary value a t the hot end is not hit, then the cold gas temperature is modified and the process repeated until the hot boundary condition is satisifed. The algorithm is summarised as follows. Step 1. Given F,, A,, A,, compute Q,, Tf, TG,, and T b using eq 24,25,26, and 27. Then, using Q, and TG,,compute AT by eq 8. Compute the hot gas boundary T ( L )= T L ,knowing Q,, AT, and TG, and assuming that temperature of the tertiary air flow increases from T o to TLand the temperature of the hot gas stream decreases from TG,to TL. Step 2. Compute the material velocity and the distribution of the material in the cross section.
110
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
Table I Simulation Actual Plant Cold gas temperature, T ( 0 ) Material temperature at point C, OC
Material temperature at point a, OA % HzO at point C % Rutile
I
i1
\
5
10
is
to
DISTMCE FROM COLD END
15
,I
*)
m
Figure 6. Computed temperature and conversion degree profiles along kiln: a, Calais; b, Sorel.
Step. 3. Assume cold gas temperature T ( 0 ) .Knowing O(O), compute TJO) using (19). Step 4. Integrate in the forward direction the system (17)-(18)-(19), using J/TP. The integration step will be taken as 0.5 m. This yields T(1),O ( 1 ) and T,(1) for 1 = 0, L. I t is also necessary to compute Q h ( l ) as well as Ru(l). Step 5. Compare T ( L )with T L .If the hot boundary T Lis hit within 5 "C, stop. If not, assume a new cold gas temperature. This algorithm was shown to coverage in 3 to 4 iterations. Computed Results a. Temperature and Concentration Profiles. The basic result yielded by the simulation is the temperature profile along the kiln. The simulation was run for two different types of kiln: kiln C ( L = 56.50 m) and kiln S ( L = 39.50 m). The measurements available on both kilns are the combustion , cold gas temperature, chamber gas temperature, T G ~the T(O),the rutile percentage a t the discharge of the kiln, R U G ) , and the residence time, t . In addition on kiln C the following are available: the material temperature at point C (1 = 40 m), Oc*, the moisture content (measured by loss a t 100 "C as a sample grabbed from a hole drilled through the kiln lining) a t point C, and the material temperature a t point A ( I = 54 m), OA.
Knowing the rutile percentage a t the discharge and assuming AH has the value given in the literature (Samsonov, 1973),k of eq 4 can be adjusted, so that the rutile percentage issued from simulation and the actual one correspond. 12 seems to depend on E , the bed thickness. After several simulation runs, on both kilns k = 2280/E seems to give a good approximation of the discharge rutile percentage (f2%). The parameter K , of eq l is estimated from the residence time. The total heat transfer coefficient h of eq 2 is determined for kiln
426 "C 159 "C
415 "C 150-200 "C
795 "C
800 "C
3.5%
97.2%
4-6% 96.5-99.5%
C from the moisture content of point C. It is assumed to have the same value for kiln S. Figure 6 pictures the profiles obtained by simulation of kilns C and S. Table I compares theoretical values with experimental data for kiln C. Some of the difference between the calculated and the actual cold gas temperature can be explained by the fact that the temperature is actually not measured exactly a t the end of the kiln but in the duct through which the gases go to the gas treatment system. A potentially interesting measurement point is located in the material temperature high slope region, before the rutile content starts to increase significantly. The high-temperature slope implies that changes in the length of the kiln zones would likely result in significant temperature changes a t that point. This point, called point X, is located at 1 = 44 m for kiln C, Ox N 550 "C. For kiln S the points corresponding to C, X, and A, Le., where OC N 150-200 "C, OX in the high slope region, and OA N 800 "Care located as follows: point C, 1 = 28.5 m; point X, 1 = 30.5 m; point A, 1 = 38.0 m. The temperature profiles do not seem to be very sensitive to changes in heat transfer coefficients, except that the gas heat transfer coefficient cyg affects them more noticeably. However, the rutile conversion is affected in greater proportions by heat transfer coefficient variations. The algorithm seems to give a fairly realistic representation of the two kilns studied. By comparing a skin temperature profile (Figure 7 ) ,which is the only additional available data for kiln S, with the profiles on Figure 6b, we can see that the end of the drying zone seems to be well approximated. However crude this model is, we must bear in mind that it is not intended for kiln design. We will now study the response of the model to feed slurry changes and material velocity changes as well as its sensitivity to AH. b. Responses to Changes in Feed Slurry. The responses to changes in throughput rate and feed slurry moisture (see Figure 8) show that the material temperature seems to be most sensitive to these changes just after the end of the drying zone, Le., between points C and X. Beyond point X, the change is not significant. Therefore we can think of the material temperature measurement around point C and X as a good indication of the drying zone length. The effect of slurry moisture content on the rutile percentage is quite significant, 1%change in the moisture of the pulp (which is frequent) yielding a 1%change in discharge rutile content. However, dry product throughput rates have practically negligible effect on rutile percentage. c. Sensitivity to AH. The rutilization activation energy is one of the most important parameters of the model. It seems natural to investigate the sensitivity of the model to AH variations. Figure 8 depicts the computed results. First, we note that the rutile content responds significantly to changes in AH; a 10%change in AH produces an 18%change in rutile percentage. Secondly, we observe that the temperature changes in the rutilization zone corresponding to an increase in AH may be either positive or negative, depending on exactly where one looks. Thirdly, we see that the temperature a t point A undergoes an increase for either an increase or decrease in
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
200
150
+
0
RIIn
SI
'
h)In
SI11
-
a -
Mean Volur
.. /
100
-
~, . .
J
..
.
/
.
111
-.
, .
DISTWCE FROM cou) END
m
Figure 7. Sore1 skin temperature profile.
I
I
'
change content 10duerutile i o 10% L o % InCrenSe
/"
n
-25
?*
Figure 8. Response, vs. distance, to changes in feed moisture, feed rate, and heat of rutilization.
AH. These facts indicate that the temperatures in the rutilization zone are near a mathematical minimum with respect to AH; this is further confirmed by the relatively small temperature changes observed, 0.6-4% for a 10% AH change. Physically, an increase AH implies a drop in the reaction rate. Because of the endothermic nature of the reaction, this tends to produce a temperature rise, which tends to restore the rate, hence the temperature. These results appear to explain a phenomenon often observed on Ti02 kilns, where a rutile percentage drop to 80% is observed with no appreciable temperature changes. We hypothesize that this is due to sudden AH changes attributable perhaps to catalyst percentage or its distribution in the crystal, acting directly on the rutile percentage without going through the thermal inertia dynamics. Thus, in contrast to the situation in a cement kiln, the rutilization zone temperature is not a valid indicator of composition, since it fails to respond to what seems to be the principal disturbance variable. A control strategy aimed at keeping this temperature constant will regulate against inlet charges, but it will not counteract AH perturbations. Since the temperature a t point C is an adequate indicator of inlet conditions and is easier to get than at A or X, it only is retained.
Optimization In this section, we address the question: Is it worthwhile to search for an optimal operating point? The variable to be optimized is the fuel rate; at given throughput, we wish to adjust the air flow so as to meet the product specification with the lowest possible fuel rate. No claim is made here that the values found are in fact the optimal settings: the present model is not capable of that kind of precision. We do claim, however, that the model can confirm the existence of a minimum and give order-of-magnitude results. a. Optimization with Constant Primary Air/Fuel Ratio. We shall keep assumption (i) of the preceding three sections; i.e. we shall neglect the air entrainment by the flame. For a given throughput rate we want to find the combination of fuel (the primary air flow is given by the fuel rate) and of secondary air that for the model minimizes the fuel rate and satisfies the following constraints. (i) The rutile percentage at the operating point must be within specifications. For the example treated here, a rutile percentage between 97.7% and 98.3% is acceptable. (ii) The cold gas temperature T ( 0 )must not exceed 47 "C;otherwise we face risks of corrosion within the gas treatment system. (iii) The temperature of the gas in the combustion chamber must not exceed 1350 "C to guarantee a good durability to the refractory bricks of the chamber. Figure 9 shows the computed results of the simulation. It pictures for a given range of secondary air flow rates the minimal fuel rate satisfying the three previous constraints for three different throughput rates for kiln C. The existence on the model of an optimal secondary air flow rate appears clearly on the actual kiln C, for Qp = 1.06, a decrease in secondary air flow led to a decrease in fuel rate; for Qp = 1.16, on the other hand, the same secondary air flow proved to be low, an increase leading to a decrease in fuel rate. This confirms the existence of the minimum. b. Optimization with Varying Primary Air/Fuel Ratio. Keeping the same assumptions as previously leads to ridiculously low fuel rate when the excess air decreases. This is due to the fact that we still assume that only the primary air flow enters the combustion, a decrease in primary air flow leads to a drastic increase in flame temperature. In fact, when the primary air/fuel ratio decreases, the flame length and its temperature increase while the secondary air flow becomes of the same order as the primary air flow. The air entrainment by the flame can no longer be neglected.
112
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
'GC
1300
1
I
1500
'1:
t
I-
1
OK
,
,
+;
:A
e
127:
I A
S
1100
+
A
P
I
1.4
1.2
E 1.2
l
1.6
1.4
a
IOoP
1
= 290
I
1.6
b
\QP=l.
90
80
60
100
SECONDARY AIR FLOW
Figure 9. Optimization of fuel rate.
The flame, due to its inner gas velocity and temperature, creates a depressure in the combustion chamber. Due to this phenomenon, part of the secondary air stream is mixed with the primary air in the flame thus increasing the actual air/fuel ratio. Consequently, the flame temperature decreases, thus diminishing the benefits of working with a lower air excess figure. Unfortunately, very little quantitative knowledge is available about such factors as the influence of flame length, its temperature, density, and effect of turbulence in the chamber. However, to get some understanding of the phenomena involved, it is possible to formulate the problem more or less intuitively, knowing that the results will be more qualitative than quantitative. The expressions presented below are simply functions intuitively derived to try to reproduce the qualitative behavior of the phenomena, rather than exact physical descriptions. They are based on the work of Beer and Chigier (1972). The flame length L f increases with the fuel rate and decreases with the actual air/fuel ratio, and may be expressed as
Lf = K1 log
[14- In (R,) F C
+KZ
(28)
where R , represents the actual air/fuel ratio in Nm3/kg, and K1 and K z are constants. The amount of secondary air entrained by the flame can be expressed by K,A, with
aL$ + b(A,/A,)' (7+f)1'z (29) 1 aL$ + b ( A , / A p ) 2 where a, b, and c are constants. The total air entering the combustion is then K, =
+
At, = A ,
+ KeAs
(30)
The flame temperature is computed using A t , instead of A , in (24). The system (24), (28), (29), (30) is solved for Lf, At,, and Tfby a trial and error method. Now, we must notice that the influence of the chamber on the kiln is given by two variables only: TG,and Q, (this is true if we neglect the direct radiation from the chamber wall and
+
A 5
1100
I
'
1
= 313
A
13? A
S
P
'
6
e
l
l
w
"
"
+
A
F
'
1
= 333
~
e
i
the flame to the kiln). We dispose of three actuated inputs to achieve this set of two values. Obviously, there are several combinations leading to the same TG,and Q,, one of them yielding to a minimal fuel consumption. Now, if we neglect the difference between the soot formation and the stoichiometric ratio of the fuel, we can replace Q, by A , A,, Le., the operating point is given by TG,and ( A , A,). Figure 10 pictures for four different total air flows the effect of the air excess on the combustion chamber temperature for various fuel rates. From the previous section we had the following operating for Q, = 1.00: A , A , = 270; F , = 935; e = 1.53; TG, = 1445 K. This point is also found on Figure 10a for e = 1.53 and F , = 935. I t is seen that this temperature TG,can also be obtained with lower fuel rates, the minimal one being F , = 830, for e = 1.25. Below that air excess figure, the air entrainment becomes important, reducing the efficiency of the combustion. These results indicate that experimentation with varying air-fuel would be in order.
+
+
+
Conclusions The model seems to be reasonably consistent with the experimental results, given the uncertainty of the parameter values. This model, written as the first step in the design of a control, scheme yields three measurements: the rutile percentage, the material temperature a t the end of the drying zone 0c, and the material temperature in the high slope region 0x. Material temperature measurements in the rutilization zone do not seem to be helpful in controlling the rutile percentage. The optimization study indicates that there exists a substantial potential improvement in the economics of kiln operation.
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
The next step in the design of a control scheme is a dynamic simulation of the kiln. This was in fact done and is presented, together with actual results of the consequent control scheme of the kiln, in a paper submitted elsewhere. Acknowledgments We would like to thank Tioxide S. A. (France) and Tioxide of Canada Ltd., for having allowed us to study their kilns and used their data. Appendix. Formulas Used to Compute Coefficients (a) Heat Transfer Coefficients (Derived from Manitius et al., 1974). a , = 0.8 d0.238 X 2225 X RPM X a,
where a, = 1
+ 2.5 X 10-4(T, Ng
=
- 273)
0.00689Qf 01.5
(b) Emissivities (Derived from Perry, 1973). c, t,
+ 3.5 X 10-4(B - 423)
< < 1423 K = 0.5 + 1.35 X 10-4(T, - 900) 400 < B < 1900 K tg = 0.85 - 5 X 10-4T 673 < B < 1300 K = 0.5
423
113
(2) Specific to Kiln C. a = 0.008
b=l c = 1767 D = 3.2 m K = 0.0204 K1 = 4.608 K2 = 5.215 K , = 6.1 L = 56.5 m L k c = 0.8 m P = 10300 kcal/kg P, = 11.34 Nm3/kg P f = 12.10 Nm3/kg RPM = 0.07 (3) Specific to Kiln S. D = 2.38 m K = 0.003 Km = 5.6 L = 39.5 m Lk, = 0.8 m P = 12315 kcal/kg P, = 12.50 Nm3/kg Pf = 13.75 Nm3/kg RPM = 0.11 N.B.: For confidentiality purpose, flow rates are not given.
( c ) Heat Capacities. c, = (8.22
Nomenclature
+ 0.00015T + 0.00000134T2)/18 (Perry, 1973)
cp is computed as follows c, = a
+ bT - c / T 2
(J/kg mol "C)
where a, b, and c are shown in Table I1 (Samsonov, 1973) Table 11. Coefficients for Comwtine: cn Tvue
Rutile Anatase
1
a
b X lo3
c x 10-5
75294.3 74707.7
1173.2 2093.8
18226.5 17723.7
+ 0.00260)T - 273)(Qg- Qh) + Qhc,) 4.18
1 ~f
kcal/kg
(d) Form Factors F , F1.
+
F = - T ( L L H T- 1)R3 [R2f ( L LHT - I)]' F1
=
+
+
TR2
( L LHT- 1)' (e) Values Assigned to Coefficients. ( 1 ) Common to Both Kilns. C, = 0.275 kcal/kg "C cf = 0.300 kcal/kg "C h = 490 kcal/m2 "C h k = 2280/E L , = 540 kcal/kg u b o = 12.5 kcal/h "C U,, = 5 kcal/h m "C p = 2" AH = -17 929 kcal/kmol tb t, tf
=1 = 0.15 = 0.5
6 = 120" p
= 4000 kg/m3
A = anatase content, % A , = primary air flow, m3/min A , = secondary air flow, m3/min AT = tertiary air flow, m3/min A,, = total air flow entering the flame, m3/min a, b, c = coefficients of air entrainment in eq 29 C = orifice coefficient in eq 7 c, = combustion chamber gas specific heat, kcal/kg "C c f = combustion gas specific heat, kcal/kg "C c g = kiln gas specific heat, kcal/kg "C e , = material specific heat, kcal/kg "C c, = water vapor specific heat, kcal/kg "C D = kiln diameter, m E = material bed thickness, m e = air excess ratio F , F1, F f b = form factors for radiative heat transfer F, = fuel rate, kg/h g = 9.81 m/sz h = total heat transfer in equation 2, kcal/m2 "C h K = coefficient for computation of tertiary air flow K1, K2 = coefficients in eq 28 K , = coefficient of dependence of air entrainment in secondary air flow K , = coefficient for computation of material velocity in eq 1 k = rate of conversion to rutile k h = rate of drying in falling rate zone L = kiln length, m L1, Lz, L3 = arc lengths defined in Figure 2, m L , = water latent heat, kcal/kg L f = flamelength,m L k c = gap between kiln and chamber, m 1 = distance from cold end, m P = heat content of fuel, kcal/kg P, = stoichiometric ratio of fuel, Nm3/kg Pf = soot formation of fuel, Nm3/kg Qc = chamber gas flow, kg/h Qg = kiln gas flow, kg/h Q h = water flow rate, kg/h Q, = material flow rate, kg/h Q, = dry product throughput rate, kg/h R = perfect gas constant, kcal/kmol '(2, R , = actual primary air/fuel ratio, Nm3/kg
114
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
RPM = rotary speed of kiln, turns/min S = gas flow cross section area, m2 s b = chamber wall lateral area, m2 Sf = flame lateral area, m2 s = tertiary air entry orifice section, m2 T = gas temperature, K T I = hot gas boundary, K Tb = chamber wall temperature, K Tf = flame temperature, K Te, = chamber gas temperature, K To = outside temperature, K T , = kiln wall temperature, K u h_. o = heat transfer coefficient through - chamber lining, -. kcal/h "C = heat transfer coefficient through kiln lining, kcal/h
u,,
m ___
O C.~ :
V = kiln gas velocity, m/h u = tertiary air entry velocity, m/h Vm = material velocity, m/h
Greek Symbols a , = heat transfer coefficient in eq 22, kcal/h m2 "C a f = heat transfer coefficient in eq 21, kcal/h m2 "C ag = heat transfer coefficient in eq 9 and 10, kcal/h m2 "C aw = heat transfer coefficient in eq 11,kcal/h m2 "C @ = kiln axis inclination angle AH = rutilization activation energy, kcal/mol deg Ap = negative pressure inside kiln, atm t b = chamber wall emissivity t, = chamber gas emissivity tf = flame emissivity tg = kiln gas emissivity
= material emissivity = kiln wall emissivity 4 = central angle as in Figure 2 tm t,
4gwr dwm, 4gg,dew 4cm, dr = heat fluxes as defined in the text, kcal/h m 4, , $fi, dfc, 4bc, $bo = heat fluxes as defined in the text, \cal/h p = dry material bulk density, kg/m3 po, pg = gas densities at T oand T , respectively, kg/m3 u = Stefan constant, kcal/h m2 "C4 O = material temperature, K OA, Ox,OC = material temperature a t points A, X, and C respectively, K 4gF,
Literature Cited Barksdale, J., "Titanium. Its Occurrence, Chemistry 8 Technology", Ronald Press, New York. N.Y., 1966. Beer, J., Chigier, N. C., "Combustion Aerodynamics", 1972. Jorgensen, P.. Onde Eiectr., 4a, 823 (1969). Manitius. A,, Kurcvusz, E.,Kawecki, W.. ind. Enq. Chem. Process. Des. Dev., 13, 132 (1974): Perry, J. H., Ed., "Chemical Engineer's Handbook", McGraw-Hill, New York, N.Y., 1973
Saab,':, Ind. Eng. Chem. Process Des. Dev., 6, 532 (1967). Samsonov, G. V., "The Oxide Handbook", IFI/Plenum, New York, N.Y., 1973. Spang, H. A,, 111, Automatica, 8, 309 (1972)
Received for review M a y 17, 1976 Accepted December 27,1977
T h i s work has been made possible by the financial aid of the Canada Counci1.
The Kinetics of the Reaction of Sulfur Dioxide with Methane over a Bauxite Catalyst John J. Helslrom and Glenn A. Atwood' Department of Chemical Engineering, The University of Akron, Akron, Ohio 44325
The reaction between sulfur dioxide and methane over a bauxite catalyst was studied between 500 and 650 O C at 1 atm. The methane and sulfur dioxide concentrations were varied from 0.02 to 0.28 atm and from 0.04 to 0.79 atm, respectively. The space time, kg min L-', was varied from 0.9 to 3.9. Both a single-site model and a dual-site model correlated the data equally well. The single-site model is RcH4= [Pc~,4490 exp(-6190/T) /[1 P ~ o ~ ( 6 . 8X5 exp(l1 500T)], and the double-site model is R C H= ~ [Pc~~2 000 2 exp(-3130/T)]/[ 1 -k Ps0,(3.13 X exp(8850/T)]*], where the rate, RCH4,has the units of standard liters of methane reacted per kilogram of catalyst per minute, the temperature Tis in K, and the partial pressures are in atmospheres.
r'
+
Introduction The number of methods being proposed and evaluated for the control of sulfur dioxide pollution continues to proliferate under the steady pressure from the federal governments, the state governments, and citizens groups to clean up the environment. Many of these control methods, especially in electric power production and the smelting industries, involve the removal of the sulfur dioxide from the flue gas. The majority of the processes utilize the absorption of the sulfur dioxide, the adsorption of the sulfur dioxide, or the catalytic oxidation of the sulfur dioxide to the trioxide which is then removed as sulfuric acid or a sulfate. Some of the adsorption and absorption processes generate large amounts of essentially worthless materials which are discarded; others regenerate
the sulfur dioxide in a concentrated state for subsequent treatment which may involve oxidation to sulfur trioxide for the production of sulfuric acid or reduction to elemental sulfur. The reduction methods usually employ hydrogen sulfide, carbon monoxide, or some form of solid carbon (Rosenburg et al., 1975). The reduction of sulfur dioxide with methane and other hydrocarbons has been known at least since the beginning of this century (Young, 1915). By 1940, a pilot plant capable of producing five tons of sulfur per day using natural gas had been built a t Garfield Utah (Fleming and Fitt, 1950). Since World War 11, a large number of papers have appeared in the literature concerning the use of methane and natural gas as reductants in both pilot plant and laboratory studies. However, information concerning the heterogeneous catalytic re-
0019-7882/78/1117-0114$01.00/0 0 1978 American Chemical Society
