7
Ind. Eng. Chem. Res. 1994,33, 7-13
Modeling Reaction Quench Times in the Waste Heat Boiler of a Claus Plant Linda V. Nasato,t Kunal Karan, Ani1 K. Mehrotra, and Leo A. Behie' Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, Alberta, Canada T2N IN4
At the high temperatures found in the modified Claus reaction furnace, the thermal decomposition and oxidation of H2S yields large quantities of desirable products, gaseous hydrogen (Hz) and sulfur (SZ).However, as the temperature of the gas stream is lowered in the waste heat boiler (WHB) located downstream of the furnace, the reverse reaction occurs leading to reassociation of HZ and SZmolecules. To examine the reaction quenching capabilities of the WHB, a rigorous computer model was developed incorporating recently published intrinsic kinetic data. A sensitivity study performed with the model demonstrated that WHBs have a wide range of operation with gas mass flux in the tubes from 4 to 24 kgl(m2-s). Most important, the model showed that it was possible to operate WHBs such that quench times could be decreased t o 40 ms, which is a reduction by 60% compared to a base case scenario. Furthermore, hydrogen production could be increased by over 20% simply by reconfiguring the WHB tubes.
Introduction The separation of sulfur compounds from natural gas is usually accomplished by a selective absorption process that produces an acid gas feed for a Claus sulfur recovery unit. The acid gas contains as its major components,HzS, CO, and HzO; and as its minor components,hydrocarbons, Nz, and COS. The basis of the modified Claus process is the production of elemental sulfur via a two-step reaction. In the first step or thermal stage, one-third of the HzS is completely oxidized to SO2 in the reaction furnace, located at the front end of plant. A benefit that also occurs is the production of significant quantities of elemental sulfur (SZ)from the thermal decomposition of HzS. In fact, the sulfur produced in the furnace is 50-60 % of the total sulfur condensed in the plant. Well-known equilibrium curves, such as those published in the GPSA Data Book (1987) or by Paskall (1979), show that the sulfur conversion increases with flame temperature, from about 68% at 926 "C to about 75% at 1260 "C. The main HzS oxidation reaction is
-
H,S + 3/20,SO, + H,O (1) Note that a number of other reactions occur in the furnace (Paskall, 1979) including
-
+ '/,O, S + H,O 2H,S + SO, 3/2S,+ 2H,O ~ H , S+ 3/20, 3/2S, + 3H,O H,S
(2)
(3)
(4) The reaction furnace is followed by the waste heat boiler (WHB), where heat is recovered by cooling the furnace product gases. In the second step or the catalytic stage, unreacted HzS is then combined with SO,, produced via eq 1, over an alumina catalyst to form elemental sulfur in fixed bed reactors by the following reaction: 2H2S + SO, s 3/xS, + 2H,O (5) Sulfur formed in each stage of the Claus plant is condensed and recovered to achieve maximum conversion ~
~
~~~
~
* To whom correspondence may be addressed.
+ Present
Address: Goar, Allison and Associates Inc., Tyler,
TX. 0888-588519412633-0007$04.50/0
in the catalytic reactors. The unrecovered sulfur, in elementalor combined form (HzS,COS, CSz),is combusted to SO2 in the tailgas incinerator which is then emitted to the atmosphere. Tailgas clean-up units are added sometimes prior to incineration to increase the sulfur recovery and minimize emissions. Role of the WHB. The Claus furnace and the WHB together are treated normally as a single unit. The Claus furnace WHB is a shell and tube heat exchanger (see Figure 1) in which product gases from the furnace a t 9W1300 "C are cooled to 250-300 "C in one or two tube passes and high-pressure steam is generated on the shellside. The Claus furnace product is a mixture of gases; in addition to the expected sulfur compounds (SZ,HzS, and SO,), combustion products (H2O and COz), and inerts (Nz and Ar), four other compounds often appear (H2, CO, COS, and CSz). Field tests conducted at the Ultramar Refinery (Wilmington, CA) by Sames et al. (1990)indicate that a reduction in S2,Hz, and CO contents and an increase in H2S and COS contents of the product gas takes place along the WHB tube. Hydrogen, although not present in the feed gas to the furnace, was reported to be present at the outlet of the single tube pass WHB. Its presence was attributed to the thermal decomposition of HzS into H2 and SZ.The thermal decomposition of H2S is a reversible reaction for which the forward reaction is favored a t high temperatures encountered in the Claus reaction furnace,while the reverse reaction or reassociation of H:! and SZis favored at the lower temperatures in the WHB. The disappearance of CO in the WHB tube is attributed to its reaction with SZ to form COS. The following two reactions are thus believed to occur in the WHB tubes:
+ '/,S,s H,S co + 1l2S, * cos H,
(7)
Located just after the reaction furnace, the WHB plays an important role in the overall design of the Claus plant. The reactions given as eqs 6 and 7 had never been considered to occur in the WHB prior to the study by Sames et al. (1990). In fact, the gas composition at the inlet and the outlet of waste heat boiler have been assumed to be the same for design purpose, leading to an incorrect and overly conservative design. Thus, it is not surprising 0 1994 American Chemical Society
8 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 REACTION FURNACE
WASTE HEAT BOILER ( W H B ) PROCESS GAS TO CONDENSER NO. 1 HIGH PRESSURE
FUEL GAS TO S E A L POT
BOILER FEED WATER
Figure 1. Schematic diagram of a reaction furnace and the waste heat boiler (WHB).
that the primary aim of the WHB was considered to cool or quench the gas and not to quench the two reactions that occur in the tubes. However, an improved and optimized design of a WHB, taking into account the two reactions, can reduce the quench, time and increase the production of potentially valuable H2 and S2. Quenching of the Hz-Sz reassociation reaction (eq 6) in the WHB would result in an increase in available H2. Hydrogen, although present only in small quantities, offers several benefits to the overall process. A number of commercially available tailgas clean-up processes require the reduction of tailgas sulfur compounds (Le. COS, CS2, S, and ,902) to produce H2S prior to further treatment. Hydrogen is usually produced by the reforming of methane; hence, it involves additional capital and operating costs that become an integral part of the cost of the tailgas treatment process. An increase in a continuous source of hydrogen from the thermal stage, thus implies a reduction in requirement of additional Ha, and thus a lowering of the capital investment. The quenching of the H2S formation reaction would also result in a decrease in H2S output from the WHB outlet. In turn, this implies a reduction in the HS/S02 ratio, which is to be maintained at a stoichiometric ratio of 2:l for the catalytic reactions that occur in the downstream reactors. Maintaining this ratio would decrease the SO2 output from the furnace. This will require oxidizing a reduced amount of H2S in the furnace which can be achieved by lower air or oxygen throughput to the furnace. For air-based operations, this results in hydraulically unloading the downstream sulfur recovery unit. In oxygen-based operations, this results in a reduced oxygen requirement for the furnace and consequently a lower cost involved in its production. Contrary to belief, most of the COS in the Claus process is formed in the WHB and not in the reaction furnace. The presence of COS in the product gases is undesirable due to the difficulty of its hydrolysis to H2S in the downstream catalytic reactors. The COS, although present only in small quantities at the WHB exit, contributes significantly to sulfur emissions if not hydrolyzed to H2S. The quenching of the COS formation reaction will result in a reduction of COS output from the WHB exit. This implies a reduction in sulfur loss or an enhancement in sulfur recovery.
Model Development Model Equations Development. A rigorous onedimensional model of a WHB tube has been developed
(Nasato, 1993). Plug flow is assumed in the WHB tubes, implying negligible radial concentration and temperature gradients. Other assumptions include steady-state operation and ideal gas behavior. Finally, it has been assumed that a constant tube-wall temperature is maintained as saturated water vaporizes to form high-pressure steam on the shellside of the WHB. The effects of the hydrodynamic and thermal entrance regions have been neglected which Nighswander et al. (1989)found to be a good assumption. Although a number of reactions may occur in the WHB tube, the reactions between H2 and SZand CO and S2 were considered to be most important. This is justfiable in view of the findings by Sames et al. (1990).The reactions given by eqs 6 and 7 are reversible, homogeneous gasphase reactions and are first order with respect to the concentrations of the species involved, namely H2, CO, S2, H2S, and COS. Material Balance. The component mass balance equations for j = 1, ..., n, components and i = 1, ..., N , reactions are dFj/dz = A C s i j r i j j = 1,..., n, The main secondary sulfur species reactions are as follows (Sames et al., 1990):
-s, - s,
3s2 452
(9)
(10) These reactions have been ignored for two reasons. First, this paper establishes that the key chemical reaction is quenched at a temperature (T,) of 900 OC near the entrance of the WHB tube. Above a temperature of 900 "C, sulfur vapor is present as S2. Secondly,no sulfur vapor condenses in the WHB tube because the gas temperature is always above the sulfur dew point temperature. Moreover, the heat of reaction for the two reactions (eqs 9 and 10)is only about 20% of the total heat duty (GPSA DataBook, 1987). Energy Balance. The energy balance equation is given by dT/dz = [ A ( ( - m R 1 ) r 1 + (-mR2)rZ) TDU(T - Tw)l/[~FjCpj1 (11) Pressure Drop. The pressure drop is obtained from momentum balance: dP/dz = -2fG2/pD (12) where f = Fanning friction factor for tubes at Re > 5000,
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 9 which is calculated from
and
f = 0.079Re-0.025 (13) Residence Time. Assuming ideal gas behavior, the actual mean residence time in the tubular reactor is given by
Heat Transfer. The overall heat-transfer coefficient, U , is defined as follows: -1= f f i + - + - 1
X
8
+-+-D
Off,
(15)
U hi k m D ~ t Doh0 Do where f f i and f f , are fouling factors and were obtained from Perry et al. (1984) as 1.77 X lo4 and 8.81 X m2.K/W, respectively. Since U is in the range of 30-40 W/(m2.K), any uncertainty in the fouling factors, f f i and ff,, will be insignificant. The tube outside heat transfer coefficient for steam generation, h,, is assumed to be large in comparison to the inside coefficient, hi, making the fourth term of eq 15 negligible. The local inside heat transfer coefficient, hi, was calculated from the Dittus-Boelter equation (Welty et al., 1976):
(Nu,) = 0.023(Re,)0~8(Prz)0~33
(16) The thermodynamic, physical, and transport properties of gases were calculated rigorously using pure component properties and appropriate mixture formulae, as summarized in Appendix A. Reaction Kinetics. The rate expression for the reversible homogeneous gas-phase reaction between H2 and So (eq 6) is given by the following equation:
The kinetic parameters for the reassociation reaction were derivedfrom the work of Dowling et al. (1990)by modifying their rate expressionto a convenientlyusable form (Nasato, 1993).
k, = (45.48 X 106)e'-26000/Rn
(18)
k, = (3.779 x i09)e(a/Rn
(19) The rate expression for the homogeneous gas-phase reaction between CO and S2 (eq 7) may be approximated as follows (Nasato, 1993): (-reo) = k1CCOCS, - k2CCOS
(20)
where (-reo) is the rate of disappearance of CO with units kmol/(m3.s). Applying the first-order rate constant developed by Klemm and Davis (1974) to eq 20 results in the rate constant for the reverse reaction as follows:
The forward and reverse rate constants, kl and 122, respectively, are related by the equilibrium constant, K (in m3/kmol), as follows (Bichowsky, 1936):
K
I
k /k 1
- e(22500-36.0T)/RT
2-
(22)
Equation 22, as given by Bichowsky (19361, has been modified slightly in order to predict the data more accurately (Nasato, 1993). The final kinetic expression, by combining eqs 20 and 22, for the reaction between CO
S2
to form COS may be written as (-reo) = kl(CcoCsz - C,o,/K)
(23)
Design Constraints. There are two major constraints involved in the design of the Claus furnace WHB, the pressure drop across the tubes and the heat flux. i. Pressure Drop. The Claus plant operates at close to atmospheric pressure which leaves little freedom in terms of allowable pressure drop. The overall pressure drop across the plant is restricted by the pressure of the inlet stream, which is normally in the range of 160-175 kPa. Since the pressure at the plant outlet is atmospheric, the maximum possible pressure drop across the plant is generally in the range of 60-75 kPa. The maximum allowable pressure drop across the WHB tubes is, thus, in the range of 6-8 kPa. Although a typical value of pressure drop is 4 kPa, the maximum allowable pressure drop for the model simulation was set to 6 kPa. ii. Heat Flux. The process of quenching, requiring rapid removal of heat from the system, implies a high heat flux, defined as U(T - Tw). However, the maximum possible value of heat flux in a system that involvesboiling of a liquid is restricted by the critical heat flux (CHF). Mechanical failures, in the form of tube burnout, can result if the heat flux approaches the CHF. The CHF value is a function of a number of parameters, the pressure of the boiling liquid (saturation pressure) being one of them. Dykas and Jensen (1992) studied the CHF phenomenon in a bundle of horizontal tubes. They reported the CHF values at zero steam quality for saturation pressures of 150 and 500 kPa as 160 and 240 kW/m2,respectively. The CHF value increases with an increase in saturation pressure. Since the minimum saturation pressure, for the purpose of model simulation, is 1740 kPa, which is more than 500 kPa, the maximum allowable heat flux value of 175 kW/m2 can be safely assumed. Model Simulation and Solution Method. Equations 8,11,12, and 14 represent a system of first-order ordinary differential equations. The solution to these equations was obtained through the use of a computer program written in the Advanced Continuous Simulation Language (ACSL) installed on IBM 6000 RISC computer at The University of Calgary. Results Definition of Quench Time. The time taken to quench a reaction such that its rate becomes insignificant is termed the quench time. In order to determine the quench time, the quench temperature (T,) must be known first. The quench temperature is the temperature at which the rate of reaction becomes relatively insignificant. Hence, a dimensionless temperature, 8, is defined as
e = (T - T,)/(T,- T,)
(24)
According to eq 24, 0 = 1 at T = Tf (at the tube inlet); conversely, 6 = 0 at T = Tp' For this study, the reactions are considered to be essentially ceased when the reaction rates are decreased by 95% of their values at the WHB inlet. At the 95% level, almost 99% of the hydrogen conversionis complete (Nasato, 1993). Therefore, the time at which 8 falls to zero is defined as the quench time. Base Case Conditions. A base case set of operating conditions for the WHB were selected from Sames et al. (1990) and are given in Table 1. The flow rate, inlet composition,and temperature were obtained from Western Research's Ultramar Field Test 1, as shown in Table 2 (Sames et al., 1990). The feed composition was assumed
10 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994
Table 1. Base Case Conditions for the Ultramar Refinery WHB (Sames et al.. 1990)
20,
~
feed temperature (Tf), K tube-wall temperature (Tw), K total molar flow rate, kmol/h mass flux (G),kg/(m2.s) kPa feed pressure (Po), tube length, m tube inside diameter (D), mm tube outside diameter (Do), mm number of tubes (single pass)
1594.0 487.6 298.9 6.7 162 8.23 43.99 50.80 240 I
Table 2. Inlet Feed Molar Flow Rates to the WHB (Sames et al., 1990) molar flow rates (F;). kmol/h test 1 test 2 test 3 test 4 test 5 WHB feed temp (Tf), "C Hz
1321
1224
s2
10.04 7.94 134.10 146.10 2.07 2.74 5.88 6.43 9.66 10.31 0.29 0.47 4.30 5.67 95.30 82.78 33.86 28.97
total
298.9
Nz
co coz HzS
cos so2
HzO
1208 3.86 88.67 1.32 4.80 6.37 0.24 3.28 45.60 20.96
1285
01 200
1488
5.78 11.18 92.52 113.00 3.52 2.07 6.60 6.34 11.52 9.82 0.42 0.60 6.17 4.11 61.47 121.40 28.91 40.02
175.1
211.4
L I
I
I
I
400
600
800
I
1200
1000
1400
Gas Temperature ("C)
Figure 2. Predicted molar flow rates for evaluation of the quench temperature in the WHB (base case conditions). 1400
I
I
i200
,-.
0 1000
O
287.9
/
R
314.0
constant and oxygen-enriched air (32 %) was utilized. A constant wall temperature was assumed since saturated steam is produced on the shellside of the WHB. The simulations were performed using the base case parameters and data from the Ultramar Refinery Field Test 1. Figure 2 represents a plot, for one WHB tube, of the molar flow of Hz and HzS for the base case conditions where the gases enter the WHB tube at 1320 "C and are predicted to leave at 250 "C. The quench temperature is approximately 900 "C (1173 K). Secondly, the axial temperature profile inside the WHB tube is plotted in Figure 3 and the actual residence time (eq 14) inside the tube is plotted in Figure 4 for the base case conditions. The results of the base case analyses indicate that the reaction between Hz and S2 is quenched in 67 ms which occurs in the first 1 m of the tube.
Discussion of Results The effect of varying tube diameter, while maintaining the mass flux (G)constant, on the temperature profile is presented in Figure 5. The mass flux was maintained at the base case condition of 6.7 kg/(m2-s)by varying the number of tubes. The results indicate that use of a smaller tube diameter reduces the quench time. For example, a tube diameter of 25.4 mm (1.0 in.) results in a decrease in quench time from 67 to 25 ms, or a 63% reduction for the reaction between Hz and S2. This corresponds to an increase in H2 recovery of 21% and a decrease in H2S production of 15%. Increasing the tube diameter to 3.0 in. results in an increase in residence time from 67 to 122 ms. This corresponds to only a 6.7 % reduction in H2 and a 2.7% increase in H2S production. Figure 6 shows that an increase in mass flux from 6.7 to 12.0 kg/(m2-s)results in approximately 35% decrease in quench time from 67 to 44 ms. This corresponds to a 7.2% increase in Hz recovery and a decrease of 3.4% in HzS production. For a reduction of mass flux to 4.0 kg/ (m2.s),the quench time increased by 53% from 67 to 104 ms. This corresponds to a 4.6 % reduction in H2 yield and a 2.1% increase in H2S production. For a mass flux of 23.6 kg/(m2.s), the quench time decreased from 67 to 24 ms, which is a 65% reduction. For this case, the increase
c
.......................................
Thbe Wa!l I
c
i
1
I
1
I
I
I
1
2
3
4
5
6
7
a
Tube - e r s t h (m)
Figure 3. Predicted temperature profile in the WHB tube (base case conditions).
in mass flux resulted in an increase of H2 production of 19.6% and a reduction in H2S production of 8.5%. The pressure drop increases with the mass flux (eq 12); however, within the range of mass flux evaluated, the pressure drop did not exceed the maximum allowablevalue of 6 kPa. Figure 7 illustrates the effect of mass flux on the pressure profile through the WHB tube. The pressure drop for a mass flux of 6.7 kg/(m2.s)is about 100 Pa, which increases to about 500 Pa for the mass flux of 12.0 kg/ (m2.s). Finally, the pressure drop of 2000 Pa is predicted for amass flux of 23.6 kg/(m2.s). Note that mass velocities in the range 10-30 kg/(m2.s)are recommended for WHBs by Goar (1990). Another important variable that is affected by gas mass flux is the heat flux. Figure 8 presents plots of heat flux along the WHB tube for four values of gas mass flux. An increase in the gas mass flux by a factor 3.5 leads to a 3-fold increase in maximum heat flux. This is due to the fact that an increase in mass flux implies an increase in Reynolds number and in turn an increase in hi (eq 16). Nonetheless, all of the heat flux values in Figure 8 are far below the CHF of 175 kW/m2. A plot of the molar flow rates of H2, H2S, CO, and COS, as a function of the WHB tube length, is given as Figure 9. The results in Figure 9 illustrate that, as the hot effluent gas stream from the reaction furnace enters the WHB and begins to cool, the recombination of H2 and S2 to form H2S is favored. As the gas stream cools in the WHB, the forward and reverse reactions are quenched and the composition remains essentially unchanged.
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 11 163
1000
-:
. - _.4.0 k g / r n 2 s
- 6.7 k g / m
800
2
s (Base C a s e )
c-\
v
0
a
e,
Y
E 600 ._ +
162
w
?
a, 0
v)
400
C
v)
e,
161
2 200
.... 12 0 kg/rn2 s 23.6 k q / r n 2 s 160
0 0
1
2
3
4
5
6
7
0
8
1
2
3
4
5
6
7
8
Tube L e n g t h ( m )
Tube L e n g t h ( m )
Figure 4. Predicted gas residence time in the WHB tube (base case conditions).
Figure 7. Effect of mass flux on pressure profile for 43.99-mm (2.0in.) WHB tube diameter.
z 1.0 h
E c
y
0.8
Q
6 7
kg/rn2s
4
5
(Base Case)
E r
0.6
0
C
u
6 0.4 v)
Lo
a -
.-
0.2
v)
t
u
.c 0.00
0 20
40
60
80
100
120
Residence Time (ms)
Figure 5. Effect of tube diameter on quench time predictions at mass flux of 6.7 kg/(m2.s) (base case conditions).
2
3
6
7
8
Tube L e n g t h (m)
Figure 8. Effect of mass flux on local heat flux for 43.99-mm (2.0in.) WHB tube diameter. 4
20
h
m
1
140
v
1.0
E F
0.8
23 6 k g / r n 2 s
Y
-6 7 ---- 4 0
E, t-
3
12 0 k g / m 2 s
a
kg/m2s
0 0
(Base Case)
kg/rn2 s
0
0.6
2 2 0 0
1 0
C a,
v)
0.4 m
1
v)
a, -
0.2 .-: Lo C
0
a, E
'6 0.0
~
0
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
0
Tube L e n g t h ( m )
Figure 9. Variation of predicted molar flow rates of H2, H2S, CO, and COS along the WHB tube (base case conditions).
In Figure 10, the molar flow rates for all components (Hz, Sz, HzS, CO, and COS) are compared with the Ultramar Refinery field test data; the calculated results agree fairly well with the measured data.
Design Recommendations The results from the model presented here can be used beneficially in the design and operation of a commercial WHB. Within the physical limits of a typical WHB, three
variables may be adjusted to optimize the production of the desirable components, Hz and Sz and, at the same time, retard the production of the undesirable components, HzS and COS. The three variables are the tube diameter, the gas mass flux, and the pressure of the steam generated on the shellside of the WHB. Each variable and the resulting benefits are discussed below. i. Tube Diameter. If a new unit is being designed, an optimum tube diameter should be selected to allow for rapid quenching of the reactions without exceeding the allowable pressure drop. All other factors being equal, it
12 Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994
-
I
35, Ul*rorncr Refinery Test Data ( S o r n e s et 0 1 1990)
‘1. 30
Res, is ‘ram Model Simulation
5 25
v
2
4..
20
0
K
I l5
-
LL
10
0 -
2
5 0
H,
S,
HS ,
CO
COS
Figure 10. Comparison of simulation resulta for the molar flow rates of Hz, SZ,HgS, CO, and COS at the WHB outlet with measured data from Ultramar Refinery Field Test 1 (Sames et al., 1990).
was shown that reducing the tube size from 2.0 to 1.0 in., for the Ultramar Refinery, results in approximately 60 % reduction in the reaction quench time, allowing for a 21 ?6 increase in Hz production. I t is recommended the tube size be dictated primarily by the pressure drop constraint (Le. a typical design pressure drop of 4 kPa). The tube diameter should not be oversized, as this has the effect of retarding the quenching of the reactions. ii. Gas Mass Flux. For a new unit, it is possible to adjust the gas mass flux by either increasing or decreasing the number of tubes in the WHB. In an existing unit, the mass flux can only be increased by decreasing the effective number of tubes in the WHB. A higher mass flux allows for a more rapid quenching of the reactions (faster by 21-42%); however, very large values of mass flux may be limited by the CHF. Over the 10-30 kg/(m2.s) range of gas mass flux recommended for WHBs (Goar, 19901, the CHF generally decreases with the steam quality (Dykas and Jensen, 1992). Therefore, it is recommended that the gas mass flux be set at an optimum level to allow for a rapid quenching of the reactions without exceeding the recommended mass flux. As was shown, increasing the mass flux by a factor of 3.5 results in approximately 20 ?6 increase in Hz production without any significant effect on the production of COS. iii. Steam Pressure. The tube wall temperature is set by the pressure of saturated steam generated on the shellside of the WHB. It was determined that lower wall temperatures, hence lower steam pressures, allow for more rapid quenching of the reactions (Nasato, 1993). Within the range of steam pressure analyzed, 345-3450 kPa (50500 psig), an increase or decrease in quench time does not result in a significant change in Hz, HzS, or COS production (Nasato, 1993). The pressure of steam generated in the WHB usually ranges between 2400-4100 kPa (350-600 psig). Normally,345-520 kPa (50-75 psig) saturated steam is produced in all sulfur condensers, except in the final condenser, which may produce 100-140 kPa (15-20 psig) steam (Goar, 1990). Therefore, it is recommended that the steam pressure, hence the wall temperature, be dictated by the plant utility steam requirements and not as a means for promoting rapid quenching of the reactions. Conclusions A rigorous mathematical model has been developed for the evaluation of kinetic and heat transfer characteristics of a WHB in a modified Claus sulfur recovery unit. The operating mass flux of 6.7 kg/(mz.s) (Sames et al., 1990)
is below the recommended range of 10-30 kg/(m2*s)(Goar, 1990). An enhancement in sulfur recovery can be achieved by increasing the mass flux, possibly by plugging some of the tubes in an existing WHB. It is shown that quench times are in the range of 25 to 75 ms for the quenching of reaction furnace effluent gases in the WHB. Reactions must be quenched rapidly in the front end of the WHB to prevent the reassociation of hydrogen and sulfur to produce hydrogen sulfide, and to suppress the formation of undesirable carbonyl sulfide from carbon monoxide and sulfur. It was determined that the WHB in the Ultramar Refinery is capable of quenching the reaction gases in a time as low as 25 ms. For new designs, smaller tube diameters and a higher mass flux should be investigated within the constraints of the allowable pressure drop and critical heat flux, Also, the production of lower pressure steam on the shellside of the exchanger can provide a small reduction in quench time. The extent of the reassociation of Hz and Sz to form HzS, and the reaction of CO and SZto form COS depends on the relative kinetics and the residence time/temperature profile in the WHB, which would vary with the particular design. Incorporating these considerations into the design of a WHB reduces the potential for these reactions to occur. This translates into a higher concentration of potentially useful HZ in the tailgas, thus reducing the requirement for Hz in commercial tailgas clean-up processes. Eliminating the formation of COS in the WHB will result in a significant decrease in sulfur emission from the downstream incinerator. Also, an increase in the overall sulfur conversion within the furnace results in a higher efficiency for 02 usage in oxygen-enrichment operations. Acknowledgment Financial support was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). Nomenclature A = cross-sectional area of the tube (=lrD2/4),m2 C, = heat capacity at constant pressure, J/(kmol.K) C, = heat capacity at constant volume, J/(kmol.K) D = tube diameter, m D L= ~ log-mean tube diameter, m f = Fanning friction factor for tubes ff = tube fouling factor, (mz-K)/W F = molar flow rate, kmol/s G = gas mass flux, kg/(m2.s) h = heat transfer coefficient, W/(mZ.K) PHR = heat of reaction, J/kmol K = equilibrium constant for COS formation reaction, m3/
kmol = forward rate constant, krnol/(m%atm2) kz = reverse rate constant, kmol/(m3.s.atm) km = thermal conductivity of tube material, W/(mK) M = molar mass, kg/kmol NU = Nusselt number (=hiDIXm) p = partial pressure, Pa P = pressure, Pa Pr = Prandtl number (=Cp&dXm) R = universal gas constant (=8314 Jl(kmo1.K)) Re = Reynolds number (=GD/pm) r = rate of reaction, kmol/(m3.s) si, = stoichiometric coefficient of component j in reaction i T = temperature, K Tr = WHB feed gas temperature, K Tq= quench temperature, K kl
Ind. Eng. Chem. Res., Vol. 33, No. 1, 1994 13
T,= reduced temperature T, = tube-wall temperature, K tR = gaa residence time in tube, s U = overall heat transfer coefficient, W/(m2.K) xw = tube-wall thickness, m y = mole fraction z = axial distance, m Greek Letters F = inverse of reduced viscosity, pP-1 8 = dimensionless quench temperature p = mass density, kg/m3 X = thermal conductivity of gas, W/(mK) p = dynamic viscosity, Pes q = viscosity in eq A l , KP &j = mixing parameter Subscripts c = critical i = inside i = ith reaction j = jth component m = mixture o = outside z = local
Appendix A Dynamic Viscosity. The correspondingstates method, by Lucas, was used to estimate the pure component viscosity (Reid et al., 1986): q[ = 0.807c 'la
- 0.357e4*4gTr+ 0.340e44.068Tr + 0.018
(AI) where [ = 0.176 (T&4Pc4)1/6. The gas mixture viscosity was calculated from Wilke's method (Reid et al., 1986): n
where 4ij 4ji-l = (Mj Mi-1)1/2,as given by Herning and Zipperer (Reid et al., 1986). Thermal Conductivity. The pure component thermal conductivities were calculated using a method by Steil and Thodos (Reid et ai., 1986): 2.03 X M - 1.15 + --
4
C,JR
(Cp)j were obtained from Himmelblau (1982) with the mixture heat capacity as (Cp)m= Cyj(Cp)j. Heat of Reaction. The standard heat of reaction data (-AHR)were obtained from Himmelblau (1982).
Literature Cited Bichowsky, R. F. The International Critical Tables; Reinhold Publ.: New York, 1936;Vol. I.. Dowling,N.I.;Hyne, J.B.;Brown,D.M.KineticaofReactionbetween Hydrogen and Sulfur Under High-Temperature Claus Furnace Conditions. Ind. Eng. Chem. Res. 1990,29,2327. Dykas, S.; Jensen, M. K. Critical Heat Flux on tube in a Horizontal Tube Bundle. Exp. Therm. Fluid Sci. 1992,5,34. Gas Processors Suppliers Association (GPSA). Engineering Data Book; GPSA Tulsa, OK, 1987;Chapter 22. Goar, B. G. Design Considerations for Modified-Claw Sulphur Recovery Plants. In Sulphur Recovery; Western Research Calgary, Alberta, Canada, 1990. Himmelblau, D. M. Basic Principles and Calculations in Chemical Engineering, 4th ed.; Prentice-Hall: New Jersey, 1982. Klemm, R. B.; Davis, D. D. A Flash Photolysis-Resonance FluorescenceKineticStudyof theReaction S(sP)+OCS.J. Phya. Chem. 1974, 78,1137. Nasato, L. V. Modelling of Quench Times in the Waste Heat Boiler of a Modified Claus Plant. M. Eng. Thesis, Univ. of Calgary, Calgary, Alberta, Canada, 1993. Nighswander, J. A.; Huntrods, R. S.; Mehrotra, A. K.; Behie, L. A. Quench Time Modelling in Propane Ultrapyrolysis. Can. J. Chem. Eng. 1989,67, 608. Paskall, H. G. Capabilityof theModified-C1ausProcess;Department of Energy and Natural Resources: Edmonton, Alberta, Canada, 1979; Chapter IV. Perry, R. H.; Green, D. W.; Maloney, J. 0. Perry's Chemical Engineers' Handbook, 6th ed.; McGraw-Hill: New York, 1984. Reid, R. C.; Prausnitz, J. M.; Poling, B.E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1986. Sames, J. A.; Paskall, H. G.; Brown, D. M.; Chen, M. S. K.; Sulkowski D. Field Measurements of Hydrogen Production in an OxygenEnriched Claus Furnace. Proceedings of Sulfur 1990International Conference, Cancun, Mexico, April 1-4, Conference sponsor: British Sulfur Corp. Ltd.,1990;pp 89-105. Welty,J. R.; Wicks,C. E.; Wilson,R. E. FundamentakrofMomentum, Heat and Mass Transfer,2nd ed.; John Wiley: New York, 1976.
Wilke's method was used for the mixture thermal conductivity (Reid et al., 1986): n
n
i=l
j-1
Received for review July 6 , 1993 Revised manuscript received September 22, 1993 Accepted October 5, 1993. ~
Heat Capacity. The pure component heat capacities
~~
Abstract published in Advance ACS Abstracts, December 1, 1993. @
