Ind. Eng. Chem. Res. 199434, 255-262
265
Natural Gas Desulfurization by Adsorption: Feasibility and Multiplicity of Cyclic Steady States E. S. Kikkinides, V. I. Sikavitsas, and R. T. Yang* Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14260
The feasibility of simultaneous removal and concentration of H2S from natural gas by pressure swing adsorption (PSA) is established. The predried feed contains 1000 ppm HzS and 5% C02. The purified adsorption product contains below 1ppm HzS at methane product recoveries above 95%. At the same time a desorption product with 2% HzS is obtained which can be readily converted into sulfur by known processes. In the PSA system, there is a region of feed velocities where two stable cyclic steady states and an unstable steady state exist. Under the same PSA conditions considered, the product impurities in the two stable steady states are approximately 100 and 1 ppm HzS, depending on the initial bed conditions. Upon examining the differences between the HzS concentration profiles in the bed at the two steady states, the lower steady state is described by a single wave kept short from breaking through the bed, while the upper steady state is described by a combined wave with transfer zones a t each end of the bed, connected by a “middle” constant zone.
Introduction The removal of HzS from natural gas is being accomplished in industry by gas-liquid absorption processes using amines as the solvent. These processes are costly and energy intensive. Pressure swing adsorption (PSA) has been recently studied for simultaneous removal and concentration of trace components from gas mixtures (Ritter and Yang, 1991; Kikkinides and Yang, 1991, 1993b; Ruthven et al., 1994). PSA has the potential of being an economic and more energy efficient alternative for HzS removal and recovery from natural gas. Although considerable research effort has been made in sweetening sour natural gases, not many systematic studies have been reported on the dynamic performance of molecular sieves in natural gas purification processes. An experimental study of natural gas purification using a 5A zeolite was done by Chi and Lee (1973). In their work it was suggested that this sorbent could be used in an adsorption process t o remove H2S from natural gas. The scope of the present work is to examine if and under what conditions HzScan be removed from natural gas using PSA. At the same time it will be desirable to be able to concentrate H2S in the desorption product so that it can be used for production of sulfur via commercial processes. The goal is to remove H2S to below 10 ppm and to produce a desorption stream with more than 2% HzS. The sorbent selected for this separation was 5A zeolite following the suggestions in the work of Chi and Lee (1973). As in the work of Chi and Lee (19731, the use of a zeolite requires dehydration of the free gas prior to the PSA separation, or alternatively, a guard bed containing a desiccant can be used to be practical commercially (Yang, 1987). The model natural gas mixture contained 1000 ppm HzS, 5% COO,and the balance CHI. Equilibrium adsorption isotherm data for these three gases on 5A zeolite were obtained from Union Carbide molecular sieves data sheets, as well as from the work of Chen et al. (1990). The data were correlated by the Langmuir isotherm and the Langmuir
* Author t o whom correspondence
should be addressed.
Table 1. Langmuir Parameters and Heats of Adsorption of HzS, COz, and C&, on 5A Zeolite compok1 kz k3 k4 AH nent mmoVg moVgK atm-I K kcaVmol 198.767 7.83 HzS 15.0364 3.37 x lo-‘ 148.966 2.46 x 1196.25 5.98 COz 11.1370 2.16 x 2.43 x 2075.74 3.31 CH4 2.6396 8.4 x lo-*
parameters obtained are given in Table 1. These results were used as input parameters to an equilibrium PSA mathematical model which was solved numerically to predict if and under what conditions H2S can be removed from natural gas and at the same time concentrated in the desorption product. The subject of multiple steady states in cyclic adsorption processes is an interesting and also practically important one. Davis et al. (1988) discussed the possibility of multiplicity for thermal swing adsorption with two dilute adsorptive components. A subsequent analysis on the same system by LeVan (1990) identified regions of operation where multiplicity could exist, and also a discrimination was made between stable and unstable steady states. These results were confirmed by Croft and LeVan (19921, using the direct determination method to converge on the periodic states (LeVan and Croft, 1991; Smith and Westerberg, 1992; Croft and LeVan, 1994a). For pressure swing adsorption, two cyclic steady states were suggested for different systems studied by Farooq et al. (19881, by Suh and Wankat (19891, and by Ritter and Yang (1991). However, the PSA cycle studied by Ritter and Yang did converge into one final steady state after approximately lo5 cycles, and the PSA cycle studied by Farooq et al. also converged into a single steady state (Croft and LeVan, 1994b). The stability of multiple states for both thermal and pressure swing cycles has been discussed more recently by Croft and LeVan (1994b). Suh and Wankat (1989)presented a novel PSA cycle involving a combined cocurrent and countercurrent blowdown step. By fixing the sorbent productivity but changing both feed velocity and purge/feed ratio, they obtained two different product recoveries at the same product purity. It should also be noted that for purification with a simple two-step PSA cycle, it is possible to calculate directly the cyclic steady state (Sundaram, 1993) using the simulated counterflow analogy (Suzuki, 1985). It should also be
Q888-5885I95/2634-Q255$09.QQl~0 1995 American Chemical Society
256 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
noted that numerical techniques are now available with which all multiple solutions can be located for systems of nonlinear equations (Seader et al., 1990). For the PSA system in this study, true multiplicity was observed and an analysis similar to that of LeVan was made to identify regions of operation for multiplicity.
where qm and b are the Langmuir parameters and are functions of temperature
qm = k,
- k,T;
b = k,exp[k,/Tl
(6)
The bed boundary conditions are of the following form:
PSA Cycle Description A five-step PSA cycle is used in this study. In this cycle, each bed undergoes the following cycle steps: (I) pressurization with feed, (11)high-pressure adsorption, (111) cocurrent depressurization, (IV)countercurrent blowdown, and (V) countercurrent purge with adsorption product (at low pressure). Earlier work in similar types of separations has suggested the inclusion of the cocurrent depressurization (CD) step following adsorption in order to improve the recovery of the strongly adsorbed component (Kikkinides and Yang, 1991, 1993b). This is because the CD step increases the concentration of the strong adsorptive in both gas and adsorbed phases by lowering the pressure in the voids (Yang, 1987).
at Z k = 0 and
a t Z k = L. Note that the index k corresponds to the step number in the PSA cycle and for each step we have. Step 11: High-pressure adsorption. 211= Z;
?Yi
a2yi
- - DL--
at
az2
+
?Yi uaz
,2111
RgT
+ --- 1is a necessary condition for a "pure" thermal wave to appear ahead of the concentration wave. In the present case, this condition is met for the H2S concentration wave. Therefore as can be seen from Figure 6, and in comparison with Figure 3, the thermal wave has almost traveled completely out of the bed while the H2S concentration wave remains inside. As a result, most of the bed is cooled to the feed temperature and the temperature rises only near the exit. This behavior is found in both cyclic steady states, although the temperature is slightly higher when starting from a clean bed than when starting from a saturated one. During the ensuing cocurrent depressurization steps (Figures 7 and 8) the temperature decreases uniformly along the bed, and reaches nearly 0 "C at the end of the blowdown step. Note that the temperature is lower when starting from a clean bed than when starting from a saturated bed. This again is because the temperature wave depends mainly on the COz (and CHI) concentration waves and is not significantly affected by the H2S adsorption. Thus since more C02 is desorbed when starting from a clean bed, it is expected that the temperature will be lower in that case. During the purge step, the temperature profile remains constant and near the feed temperature at the end of this step. Again, this is because most COS is desorbed during the two preceding steps so there is no other physical reason for the temperature to be further decreased. Since the temperature of the purge gas is 25 "C, it is expected that at the end of this step the temperature of the bed will be 25 "C as well. Figure 10 shows the temperature profiles at the end of the feed pressurization step, The temperature rise
Figure 11. Transient behavior of HzS concentration in the adsorption product starting from different initial bed conditions (equilibrated with various H2S concentrations up to 1000 ppm).
is caused by the adsorption of mainly C 0 2 and H2S. Since the feed end of the bed is already saturated at the beginning of the step, further feeding does not result in heating. The result is a monotonically increasing temperature profile along the bed. Multiplicity of Cyclic Steady States. It has been proven (Gavalas, 1966)that, in general, for distributed parameter systems with chemical reactions and heat and mass transfer, there exist an odd number of possible steady states. Among the 2n 1steady states the ones with an even subscript are unstable, while the other are asymptotically stable (Luss and Amundson, 1967; h i s , 1968). For the case of a first-order chemical reaction, with heat and mass transfer in a non-isothermal reactor, multiplicity greater than 3 is possible only in a nonadiabatic reactor (Hlavacek et al., 1971; Varma and Amundson, 1973). For more complicated cases an excellent review exists (Jensen and Ray, 1981). Thus in the present study we expect that, for the same value of uf,there should be at least one more steady state in the region between the two stable ones. If this steady state is unstable, then most likely there should only be three steady states. If it is stable then there should be two more unstable steady states each of which should be located between the two stable ones. Since in our present study we approach the cyclic steady state by solving the transient equations starting from different initial conditions we are not able to evaluate the unstable steady state solution (Hlavacek and Hofmann, 1970). However, we can determine its existence and find its upper and lower bounds by the following procedure: For the same value of uf (for which two different steady states are already found) we run the model equations starting from different initial conditions between the two steady states. This is illustrated in Figure 11, for uf= 85 c d s . It can be seen that for initial conditions of H2S close to its lower steady state value, the system converges to that steady state. On the other hand, for higher values of initial H2S concentrations, the system converges to the upper steady state. Near the middle zone between the two steady states there exists a repulsion-type curve. As a result, starting slightly above that curve the transient solution will
+
Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 261 converge to the upper steady state whereas starting slightly below it the transient solution will converge to the lower steady state. This curve can be determined accurately if one computes for a large number of initial conditions for HzS concentration. There should exist the third steady state which is obviously an unstable one. Since our system is adiabatic we should not expect more than three steady states (Hlavacek et al., 1971; Varma and Amundson, 1973). In addition it is known from bifurcation theory that different integral curves should not cross each other (Iooss and Joseph, 1980). Thus from Figure 11it is very unlikely to have more steady states at that specific value of uf.For uf= 85 cm/s, there exist three steady states foryH2S: two stable ones at 1.2 and at 65.5ppm and an unstable one between 5 and 10 PPm. It should be noted that when starting from different initial conditions the corresponding value of COz initial concentration was between 3%and 3.5%(except for the two standard cases of initially clean and initially saturated (with feed) beds where it was 0% and 5%, respectively). However, an accurate value of COz initial concentration was not critical for the convergence of the system to a steady state mainly because COz is in bulk quantities and is always breaking through the bed. Although the origin of multiplicity is not clear and is a subject of further research, it appears that there are at least two factors that may be responsible for this behavior: (1)non-isothermality and (2) large adsorption amounts and nonlinear mixture isotherms with at least one component having a high Henry’s law constant.
Conclusions Pressure swing adsorption can be used to remove HzS from natural gas. When starting from a feed with 1000 ppm HzS and 5% C02 the HzS concentration is reduced t o 1 ppm while the CH4 recovery is above 95%. At the same time, concentrated HzS around 2% is obtained in the desorption product and can be used for sulfur production by well-known commercial processes. In the present system under study, there is a region of feed velocities where two stable and one unstable cyclic steady states exist. Departing from the lower velocity on the upper branch of this region toward lower values of uf,the upper steady state becomes unstable for a short range of uf values and disappears as one moves further to lower values of uf. Similarly, departing from the high velocity on the lower branch of the multiplicity region toward higher values of uf,the lower steady state becomes unstable for a short range of uf values and disappears as one moves further to higher values of uf. Under the same PSA conditions being considered, the product impurities in the two stable steady states are approximately 100 ppm and 1ppm HzS, depending on the initial bed conditions. For the given velocity the lower steady state (producing the 1 ppm HzS product) is reached from beds initially equilibrated with a gas phase containing 100 ppm or less H2S, whereas the higher steady state is reached starting from a gas phase with 200 ppm or higher HzS. The middle unstable steady state can be located by following the transient behavior of the bed. When examining the differences between the HzS concentration profiles in the bed a t steady state, it appears that the lower steady state is described by a single wave kept short from breaking through the bed, while the upper steady state is described by a combined
wave with two transfer zones at each end of the bed, connected by a “middle” constant zone.
Acknowledgment This work was supported by NSF under Grant CTS9212279 and the Petroleum Research Fund administered by the American Chemical Society.
Nomenclature a = parameter in the pressure history curve, l/s b = Langmuir parameter, atm-l defined by eq 5 cpg= heat capacity of the gas phase, cal/(g K) c, = heat capacity of the solid phase, c d ( g K) DL= mass axial dispersion constant, cm2/s
L = length of the bed, cm N = total number of components in the mixture P = pressure, atm q = adsorbed amount, moVg (1 = volume-averaged adsorbed amount, moVg qm = saturated amount adsorbed, defined by eq 5, moVg R, = gas constant, (atm cm3)/(molK) T = temperature, K t = time, s u = interstitial velocity, c d s y = mole fraction in the gas phase z = axial position in the bed, cm Greek Letters E
= fractional void in the bed
LL = mass axial dispersion constant, cm2/s @b =
density of the bed, g/cm3
Subscripts
b = bed
CD = cocurrent depressurization f = feed H = high i = species i j = speciesj K = step number in PSA cycle L = low p = product Q = (-AH) = heat of adsorption, cal/mol Superscript
* = equilibrium Literature Cited A r i s , R. On Stability Criteria of Chemical Reaction Engineering.
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IE940249N Abstract published in Advance ACS Abstracts, December
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