Ind. Eng. Chem. Res. 1994,33,2651-2655
265 1
Including Radiative Heat Transfer and Reaction Quenching in Modeling a Claus Plant Waste Heat Boiler Kunal Karan, Ani1 K. Mehrotra, and Leo A. Behie' Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
Due to increasingly stringent sulfur emission regulations, improvements are necessary in the modified Claus process. A recently proposed model by Nasato et al. for the Claus plant waste heat boiler (WHB) is improved by including radiative heat transfer, which yields significant changes in the predicted heat flux and the temperature profile along the WHB tube, leading to a faster quenching of chemical reactions. For the WHB considered, radiation accounts for approximately 20% of the heat transferred by convection alone. More importantly, operating the WHB at a higher gas mass flux is shown to enhance reaction quenching, resulting in a doubling of the predicted hydrogen flow rate. This increase in hydrogen flow rate is sufficient to completely meet the hydrogen requirement of the H2S recovery process considered, which would eliminate the need for a hydrogen plant.
Introduction Due to increasingly stringent sulfur emission regulations, there has been an added focus on enhancing the overall sulfur recovery or decreasing sulfur emissions from the modified Claus process. This popular process for sulfur recovery from acid gases needs further improvement to meet the new stringent emission standards. Basically, the modified Claus process is a twostage process in which one-third of H2S is first oxidized to SO2 in the reaction furnace (RF) and the remaining H2S is then reacted catalytically with SO2 to form elemental sulfur in fixed-bed reactors. From an emissions point of view, the RF is perhaps the most critical piece of equipment in a Claus plant due to the fact that up to 70% of the total sulfur production in straightthrough plants is generated in the RF. Hence, small improvements in the RF, coupled with those in a waste heat boiler (WHB), can yield significant benefits in terms of reducing total sulfur emissions from a Claus plant. Despite the fact that the modified Claus process has been in existence for over half a century, a thorough understanding of all of the reactions occurring in the RF and the WHB still eludes us. Recently, Monnery et al. (1993) and Nasato et al. (1994) provided important insights into the role of reaction kinetics in the design of the RF and the WHB of a Claus plant. Until pointed out recently (Sames et al., 19901, the following two chemical reactions were ignored altogether in designing the WHB:
+ 'I2S2== H2S co + lI2S2* cos H2
(1) (2)
Both of these reactions proceed at appreciable rates at the WHB inlet temperature (-1300 "C), but are essentially quenched a t temperatures below 900 "C (Nasato, 1993). For the WHB, there are three direct consequences of reactions given as eqs 1and 2: (a) the elemental sulfur formed in the RF is consumed via eqs 1and 2, (b) H2S is formed by the reassociation reaction *To whom correspondence (
[email protected]).
may
be
addressed
0888-588519412633-2651$04.5010
(eq l),and (c) COS, an undesirable byproduct, is formed via eq 2. All of these affect the efficiency and the economy of the Claus process directly or indirectly. Implication of the COS and H& Formation Reactions. A rapid quenching of the H2S formation reaction (eq 1)in the WHB, located immediately after the RF, will result in a saving of elemental sulfur as well as substantial amounts of hydrogen. A saving in sulfur simply implies increased sulfur recovery at the end of the WHB. Furthermore, hydrogen is an important component of the tail gas clean-up units (TGCUs) that use an H2S recovery process. In H2S recovery processes, all forms of sulfur (pure or combined) are hydrogenated or reduced to H2S. The H2S thus formed is then either removed by absorbing in amine solutions such as in the SCOT, ARCO, Beavon-MDEA, and Sulften processes or recovered as sulfur in the Stretford unit such as in the Beavon-Stretford process (GPSA, 1987). The hydrogen needed for hydrogenation imposes additional burden on the capital required for a Claus plant with a H2S recovery unit because a hydrogen plant is required. However, if a sufficient amount of H2 could be produced in the RF and if the H2S reassociation reaction (eq 1)could be quenched in the WHB, then the H2 requirement for the H2S recovery process in the TGCU can be met partially or even completely. In fact, the calculations of Nasato et al. (1994) showed that, by decreasing the WHB quench time t o 40 ms, the hydrogen production could be increased by as much as 20%. Rapid quenching of the COS formation reaction (eq 2) has two important benefits: it will decrease the amount of COS formed while preserving the amount of sulfur produced. It is important to note that any COS a t the exit of the WHB that is not hydrolyzed in the catalytic converters following the WHB represents a major sulfur loss from the plant. A significant amount of sulfur in the form of COS (i.e., as much as 15%of the total sulfur emissions) has been reported to be present in tail gas emissions. Sames et al. (1990) showed that most of the COS in the tail gas is formed in the WHB via eq 2, which is contrary to the earlier belief that COS was formed in the RF. Clearly, a rapid quenching of the reactions in the WHB will lead to lesser amounts of COS in the WHB exit gases. That is, a substantial
0 1994 American Chemical Society
2652 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
reduction in sulfur loss (or an enhancement in sulfur recovery) can be achieved by carefully designing the WHB. Intrinsic Reaction Rate Expressions. The rate expressions for the homogenous gas phase reactions, eqs 1 and 2, are given as (Nasato et al., 1994): -rHz
= klPHPSz - k2PHzS
(3)
-‘CO
= k3CCOCS, - ‘4‘COS
(4)
where -rHz and -reo denote the rates of disappearance of Ha and CO, respectively. The reaction rate constants in the above rate expressions are (Nasato et al., 1994)
(11) The kinetic rate expressions for the reactions were given above as eqs 3-8. The constraints for the maximum allowable pressure drop and heat flux were given by Nasato et al. (1994). With the inclusion of radiative heat transfer, the energy balance equation of Nasato et al. (1994) is modified as follows:
In eq 12, qc and q r denote the rate of heat transfer per unit tube length due to convection and radiation, respectively: 4, = JcDU(T- T,)
qr = noD(gGP- aGTw4)
(7) where R is the universal gas constant. Nasato (1993) related the forward and reverse rate constants k3 and k4 in eq 4 via an equilibrium constant, K (in m 3 h o l ) , as follows:
Radiative Heat Transfer Effects. In the WHB model presented by Nasato et al. (1994), heat transfer calculations were made by considering only convection. Radiative heat transfer in boilers becomes important if the flowing gases are nontransparent at high temperatures. In fact, a number of components in the RF product gases are nontransparent, e.g., C02, H20, , 9 0 2 , and CO. These gases absorb and emit radiation energy, and thus contribute additional heat flux through the tube wall. While a higher heat flux may be beneficial as far as gas quenching is concerned, exceeding the critical heat flux (CHF) for the boiling of water on the shell side can be detrimental to the safe operation of the WHB because of the increased likelihood of the tube burnout (Dykas and Jensen, 1992). Since the total heat flux (due t o convection and radiation) will always be higher than the convective heat flux, there is a risk that design calculations based only on convective heat transfer may cause the operation of the WHB at conditions approaching or exceeding the CHF value. Model Equations As mentioned previously, a rigorous one-dimensional model, including the intrinsic reaction kinetics, for the WHB tube was presented by Nasato et al. (1994). The model of Nasato et al. (1994) assumes steady state plug flow (i.e., neglects radial concentration and temperature gradients), constant outer tube-wall temperature, and ideal gas behavior. The mathematical expressions for material balance, pressure drop and residence time over an element of the WHB tube are given below as eqs 9, 10 and 11, respectively. dFQ= ACs,rij
i = 1, ..., N,;j = 1, ..., n, (9)
(13) (14)
The procedure for estimating the convective heat transfer rate, qc in eq 13, was given by Nasato et al. (1994). The expression for qr in eq 14 implies some simplifying assumptions, including all nontransparent gases to be “gray” and the tube inner-surface to be “black. Furthermore, any radiative exchange between the RF combustion chamber (i.e., the flame and the refractory surfaces) and the WHB inlet tube end is neglected due to a small view factor. The gas-mixture emissivity ( C G ) and absorptivity (m) were estimated as follows (Perry et al., 1984): EG
(ECO,
+ E H , o ~ H , o ) ( ~- C d + €so,
(15)
a, = (acoz + aHzoCH20)(l - C,,) + aso, (16) where C,, is a small correction due to spectral overlap of H20 and CO2, and C H ~ O is a correction factor to account for the total pressure being different from 1atm andor the partial pressure of H2O ( P H ~ o being ) nonzero. For the WHB calculations, all of these correction factors were estimated from the plots (Perry et al., 1984;Hottel, 1954) at the average partial and total pressures in the tube. Further details of the calculation procedure for the emissivity and absorptivity of individual gas components are given in the Appendix. Solution Method. The coupled nonlinear differential equations, eqs 9-12, were solved using the Gears algorithm of the Advanced Continuous Simulation Language (ACSL) installed on the AIX network of the University of Calgary. Base Case Conditions. The calculations were performed to simulate the operating conditions for the Claus plant WHB at the Ultramar Refinery in California (Sames et al., 1990). As reported by Nasato et al. (19941, the WHB is a single-pass shell-and-tube heat exchanger consisting of 240 tubes, each 8.23 m in length with 43.99 mm inside diameter and 50.8 mm outside diameter. Field Test 1 of Sames et al. (19901, selected as the base case for model simulations, was performed at a molar gas-mixture flow rate of 298.9 kmol/h, through the tube side of the WHB at an inlet temperature of 1594 K and a pressure of 162 kPa, which corresponds to a tube mass flux of 6.7 kg/(m2*s).On the shell side of the WHB, the generation of saturated steam yields a constant tube-wall temperature of 487.6 K. The feed composition for Field Test 1 was taken as (in mol
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2663 1400 I
35
I
Z 7 Ultramar Refinerv Test Data
30
Simulation Results
d
b)
E 3 Convection only 25 20
3 15
2 2
lo
-..-.-------~-....--.-.-----.--~-.----.-----.-~-.~ $ 5
Tube Wall 0
0
1
2
3
4
5
Tube Length (m)
6
7
0
8
Figure 1. Predicted temperature profile in the WHB tube with and without radiative heat transfer (base case conditions).
S,
H,
H,S
CO
COS
Figure 3. Comparison of simulation results, with and without radiative heat transfer, for the molar flow rates of Hz, SZ,HzS, CO, and COS at the WHB exit with the data from the Ultramar Refinery Field Test 1of Sames et al. (1990) (base case conditions).
40 c.I
$ 3 20 3
0
i
0
1
2
3
4
5
Tube Length (m)
6
7
8
0.0
Figure 2. Variation of predicted local heat flux in the WHB tube, with and without radiative heat transfer, and the contribution of radiative heat flux to the total heat flux (base case conditions).
%) H2 = 3.36, N2 = 44.86, CO = 0.92, C02 = 2.15, H2S = 3.45, COS = 0.16, SO2 = 1.90, H2O = 31.88, and S2 =
11.32.
Discussion of Results Figure 1presents the predicted axial gas temperature profile along the WHB tube for two cases. The first case reproduces the calculations of Nasato et al. (1994)where the heat removal from gas to tube wall was considered to be only by convective heat transfer. In the second case, both convective and radiative modes of heat transfer are considered. Note that the temperature profiles in Figure 1 differ significantly; for example, a temperature difference of approximately 100 "C is predicted at a distance of 2 m from the WHB inlet. To further demonstrate the contribution of the radiative heat transfer in the WHB tube, the local heat flux along the tube length is plotted in Figure 2. Also plotted in Figure 2 is the fraction of heat flux (of the total) due to radiative heat transfer. The radiative heat transfer contributes as much as 28% of the total heat flux a t the WHB tube inlet where the gas temperature is the highest. Even at the WHB exit, where the temperature is much lower (approximately 500 K), the model predicts the radiative heat transfer to be 13%of the total. Thus, over the WHB tube length, radiation accounts for an average of 20% of the heat transferred by convection alone. The reaction quench time is predicted to be approximately 50 ms, compared to 67 ms with convection alone. That is, the gas quenching in the WHB is predicted to be even faster than that estimated by Nasato et al. (1994).
0
1
2
3
4
5
6
7
8
Tube Length (m) Figure 4. Effect of gas mass flux on reassociation of Hz and SZ into HzS along the WHB tube length; results for the base case conditions and the maximum gas mass flux.
Figure 3 shows a comparison of the predicted molar flow rates of the five reacting components a t the WHB exit for the base case. The predicted flow rates for the two cases (i.e., with and without the radiative heat transfer) differ slightly. Nonetheless, the molar flow rate predictions obtained by including radiative heat transfer are somewhat closer t o the test data reported by Sames et al. (1990). Effect of Gas Mass Flux. An increase in gas mass flux yields a larger value of the heat transfer coefficient, which results in a faster quenching of the two important reactions (eqs 1 and 2). The maximum value of gas mass flux, however, is limited by the CHF considerations as well as the maximum allowable pressure drop in the WHB tube. On the basis of the recommended gas mass flux range for the WHBs (Goar, 19861, the maximum gas mass flux was taken to be 29.7 kg/(m2*s). At this maximum gas mass flux, the predicted heat flux was below the maximum recommended heat flux of 175 kW/m2and the pressure drop across the WHB tube was well within the 4-6 kPa allowable limit. Presented in Figure 4 are the molar flow rates of H2S and Hz along the WHB tube length for two scenarios: the base case, where the gas mass flux is 6.7 kg/(m2.s), and the maximum gas mass flux. The results demonstrate that quenching of the Hz-S2 reassociation reaction (eq 1)is complete in the first 2 m of the WHB tube. The results in Figure 4 show conclusively that the WHB should be operated at a higher gas mass flux,leading to an appreciable reduction in the HzS flow rate by retarding the reassociation of H2 and S2.
2654 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
for sulfur (eq 15) =
2 x 0.0193 kmoyh = 0.04 kmoVh for SO, (eq 16) = 3 x 0.567 kmoVh = 1.70 kmoVh
P I
From Figure 5 , the hydrogen available at a gas molar rate of 4.1 kmol/h in the WHB exit (corresponding to the maximum allowable gas mass flux) is more than sufficient to meet the 3.01 kmofi requirement in the TGCU. The increase in gas mass flux in the WHB could be accomplished by either decreasing the number of tubes or choosing a smaller tube diameter.
1 ' O
58%0
2
0
10
2o 2 Gas Mass Flux (kg/(m .s))
30
Conclusions
Figure 5. Variations in the predicted molar flow rates of H2 and H2S at the WHB exit with the gas mass flux.
In Figure 5, the predicted molar flow rates of H2 and H2S at the WHB exit are plotted against the gas mass flux. It should be noted that the H2 flow rate a t the WHB exit is almost doubled from 2.2 to 4.1 k m o f i when the gas mass flux is increased from the base case condition of 6.7 to 29.7 kg/(m2.s). Estimation of Hz Requirement in H2S Recovery Process. In this section, simple mass balance calculations are described for estimating the H2 requirement in H2S recovery processes or the TGCU. The purpose of these calculations is to show that the increase in H2 molar rate, which could be accomplished by using the maximum gas mass flux in the WHB, is sufficient t o completely meet the hydrogen requirement of a typical H2S recovery process. The implication of this is very important since a hydrogen plant would not be needed. In the TGCU for the recovery of HzS, large amounts of Hz are required for the following reactions involving the reduction of sulfur species:
+ H, - CO + H2S S, + 2H, - 2H2S SO, + 3H, - H,S + 2H20 COS
(17)
(18) (19)
For estimating the hydrogen requirement in the TGCU, the COS concentration is taken as that a t the W H B exit in the base case, i.e., Field Test 1of Sames et al. (1990). That is, it is assumed that COS does not react in the catalytic converters. Next, the entrained sulfur amount is assumed to be 0.5% of that formed in the RF. The conversion of SO2 into sulfur (in catalytic converters) is assumed to be only 90%. Recognizing that conversions higher than those assumed here would take place in an actual unit, these calculations represent a worst case scenario. On the basis of the above, the molar rates of the sulfur species entering the TGCU are:
COS to be reduced = COS at the WHB exit = 1.27 kmoVh entrained sulfur = 0.005 x sulfur at the WHB inlet = 0.0193 kmoVh unconverted SO, = 0.1 x 5.67 kmoVh = 0.567 k m o m For the above rates, the total H2 requirement is estimated to be 3.01 kmoVh as follows: for COS (eq 14) = 1 x 1.27 kmoVh = 1.27 kmoVh
The effect of radiative heat transfer in the WHB of a Claus plant was simulated by modifying the mathematical model presented by Nasato et al. (1994). It was shown that radiative heat transfer contributes significantly to the total heat transfer. Its inclusion causes noticeable changes in the heat flux and the temperature profile along the WHB tube, which in turn affect the quenching of the two important reactions. It was found that the radiative heat transfer contributes from about 28% (at the WHB tube inlet) to 13%(at the WHB tube exit) of the total heat flow. The calculations also showed that a H2 saving of 1.9 kmovh can be achieved by increasing the gas mass flux from 6.7 (base case) to 29.7 kg/(m%). Preliminary mass balance calculations showed that this increase in H2 is sufficient t o meet entirely the hydrogen requirement of the H2S recovery process considered.
Acknowledgment We thank Mr. Wayne D. Monnery for helpful discussions and comments. Financial support was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). Nomenclature A = cross-sectional area of the tube (=nD2/4),m2 c = concentration, km0Ym3 C, = heat capacity at constant pressure, J/(kmol*K) C,, = correction factor to account for spectral overlap of CO2 and HzO = correction factor to account for P * 1 atm and/or PHlO # 0 D = tube diameter, m F = molar flow rate, kmol/s f = Fanning friction factor for tubes G = gas mass flux,kgl(rn2.s) AHR = heat of reaction, J h o l K = equilibrium constant, m3/kmol kl = reaction rate constant, kmol/(m3watm2) kz = reaction rate constant, kmol/(m3.s.atm) k3 = reaction rate constant, m3/(kmol.s) k d = reaction rate constant, s-l L = mean beam length for volume radiation, m N , = number of reactions n, = number of components P = pressure, Pa p = partial pressure, Pa or atm qc = convective rate of heat transfer per unit tube length, W/m qr = radiative rate of heat transfer per unit tube length, W/m R = universal gas constant ( 4 3 1 4 J/(kmol*K)or 1.987 cay
(mol-K) ) r = rate of reaction, kmol/(m3.s)
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2655 = stoichiometriccoefficient of componentj in reaction i T = gas temperature, K T, = tube-wall temperature, K t R = gas residence time in tubes, s U = overall (convective)heat transfer coefficient, W/(rnLK) z = axial distance, m sij
perature (T,) and atpjL (=p&TdT). The absorptivities of COZ and H2O are related to the emissivity by the following equations (Perry et al., 1984):
Greek Letters
a = absorptivity E = emissivity Q = mass density, kg/m3 u = Stefan-Boltzmann constant (4.672 x
W/(mLK4))
Subscripts
G = gas mixture i = ith reaction j =jth component
Appendix. Calculation of Emissivity and Absorptivity of Gases at the WHB Conditions The emissivity and absorptivity of a gas are a h c t i o n of its partial pressure @j), its temperature (T), and the shape of the bounding surface confining the gas volume. The shape of the bounding volume dictates the mean beam length (L) for volume radiation. For the 2-in.diameter WHB tube, the volume confining the gas can be approximated as an infinite cylinder, for which LID = 0.9 corresponds to L = 0.04 m. The emissivity and absorptivity of a gas mixture are obtained from the summation of the single gas emissivity and absorptivity, respectively. At elevated temperatures encountered in the WHB, the radiative heat transfer is of importance mostly for heteropolar gases; the gases with symmetrical molecules (such as H2, N2, etc.) are assumed commonly to be transparent to radiation with negligible emissivity. The concentrations of CO and COS in the gas mixture are small (< 1mol %); hence these were neglected in radiation calculations. Thus, only CO2, H20, H2S, and SOZ were included in emissivity and absorptivity calculations. Due to a lack of data, H2S was assumed to have the same emissive and absorptive properties as those of HzO because of their molecular similarity. Hence, the partial pressures of H20 and HzS were added in obtaining P H , ~ . Emissivity. Plots for estimating the emissivities of C02, H20, and SO2 are available from Perry et al. (1984) and Hottel (1954). Over the temperature range of interest (i.e., 480 K < T < 1600 K), the emissivity values, at the average p& for each of COZ,HzO HzS and S02, were read from the respective plot and fitted to the following correlations for the purpose of interpolation at varying gas temperatures along the tube length.
+
log E H , ~= -0.824 - 5.10 x 10-4T log 6co, = -1.676
+ 1.99
~o-~ 2.2 T
(All
10-~p (Az)
log cso, = -1.871 - 3.40 x 10-4T - 1.2 x l O - ' p (A3) The average values ofpJ used in obtaining eqe Al-A3 are p H z & = 2.16 kPa m (0.07 atm-R),pco& = 0.14 kPa m (0.0045 atm-ft), andpSo& = 0.12 kPa m (0.004 atmR). Absorptivity. The determination of gas absorptivity (a)requires the values of emissivity at the wall tem-
A similar relation for the absorptivity of SO2 could not be found; hence, SO, was assumed to be related to the emissivity in a form similar to that in eqs A4 and A5 for ace, and aHzo,except the temperature correction was assumed as (T/Tw)0.50:
Once again, the emissivity values at the wall temperature (T,= 487.6 K) and several values ofp& were read from the respective plots for each gas (Perry et al., 1984; Hottel, 1954) and fitted to the following correlations in terms of gas temperature in the WHB tube.
E ~ ~ , ( T ~ , ~ ~ ~ ,= LT 9.2 . +x, / T )
+ 11.5lT - 12601p (A7)
cH o(Tw,pH2,LT.+,/T) = 7.6 x
+ 50.417" - 6 8 3 0 l p (A8)
cso,(Tw,pso,LT.+,/T) = 2.2 x
+ 3.55lT
(A9)
Literature Cited 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 Criteria for Basic Sulfur Plant Designs; Goar, Allison and Associates Inc.: Tyler, Tx, 1986. Hottel, H. C. Radiant-Heat Transmission. In Heat Transmission, 3rd ed.; McAdams, W. H. Ed.; McGraw-Hill: New York, 1954; Chapter 4. Monnery, W. D.; Svrcek, W. Y.; Behie, L. A. Modelling the Modified Claus Process Reaction Furnace and the Implications on Plant Design and Recovery. Can. J. Chem. Eng. 1999,71, 711. Nasato, L. V. Modelling of Quench Times in the Waste Heat Boiler of a Modified Claus Plant, M.Eng. Thesis, University of Calgary, Calgary, Alberta, Canada, 1993. Nasato, L. V.; Karan, K.; Mehrotra, A. K.; Behie, L. A. Modeling Quench Times in the Waste Heat Boiler of a Claus Plant. Znd. Eng. Chem. Res. 1994, 33, 7. Perry, R. H.; Green, D. W.; Maloney, J. 0. Perry's Chemical Engineers' Handbook, 6th ed.; McGraw-Hill: New York, 1984, pp 10:60-68. Sames, J. A.; Paskall, H. G.; Brown, D. M.; Chen, M. S. K.; Sulkowski, D. Field Measurements of Hydrogen Production in an Oxygen-Enriched Claus Furnace. Proceedings Sulfur 1990 Znternational Conference, Cancun, Mexico; British Sulphur Corp. Ltd.: 1990; pp 89-105. Received for review February 7, 1994 Revised manuscript received June 23, 1994 Accepted July 22, 1994@ Abstract published in Advance ACS Abstracts, October 1, 1994. @
