Ind. Eng. Chem. Res. 1988,27, 1229-1235
1229
Periodic States for Thermal Swing Adsorption of Gas Mixtures Mark M. Davis, Russell L. McAvoy, Jr., and M. Douglas LeVan* Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22901
A theoretical study of periodic states approached in the adsorption of mixed vapors of benzene and cyclohexane in a n adiabatic fixed bed of activated carbon is reported. T h e adsorption cycle has a n adsorption step, a heating step, and possibly a cooling step. T h e feed for the adsorption step contains dilute adsorbates in nitrogen. Heating is with hot nitrogen. Adsorption and heating steps occur countercurrently. Parameters in a mathematical model are varied to determine how the heating time and the temperature and pressure of the feed for heating affect the periodic state. The results show t h a t at modest or high regeneration pressures the heavy component, benzene, does not accumulate in the bed over repeated cycles. Instead, the cycle operates with the bed enriched in the light component. T h e stability of periodic states and the economic efficiency of energy utilization are also examined. This paper considers the thermal swing adsorption of two components. The study pertains to an adsorption cycle operated for the purpose of recovering both components (as opposed to separating the Components from one another). The cycle may involve two or three steps: adsorption, heating, and possibly cooling. Heating is accomplished by passing a hot, noncondensable purge gas through the bed in the direction countercurrent to the flow direction for the adsorption step. The hot gas performs two tasks. First, it adds energy to the bed which increases the volatility of the adsorbate and supplies the latent heat for desorption. Second, it sweeps the desorbed material out of the bed. The aim of this work is to outline the influence of process parameters, specifically heating time and regeneration pressure and temperature, on the behavior of an adsorption bed a t the periodic state (or so-called cyclic steady state) when two adsorbable components are present. The economic efficiency of a periodic state is evaluated and compared to other possible periodic states. We consider a limited class of problems where the two components are distributed nonuniformly in the bed a t the start of regeneration. Previous studies of cyclic behavior of fixed-bed sorption systems have been relatively few. Most have been concerned either with an isothermal process having two steps (saturation and regeneration) or a single, isothermal cycle step beginning with a nonuniform initial loading (see, for example, Rhee et al. (1970, 1986), Helfferich and Klein (1970), Dodds and Tondeur (1974),Grevillot et al. (1974), Ruthven (1978), Bailly and Tondeur (1981), Rhee and Amundson (1982), Gelbin et al. (1983), Costa and Rodrigues (1985), and Frey (1986)). For nonisothermal adsorption, while elegant theory has been developed for treating single cycle steps beginning with uniform conditions (e.g., Rhee and Amundson (1970) and Pan and Basmadjian (1971)),little previous work has been carried out on the analysis of cyclic behavior. Previous work on thermal swing adsorption has been restricted to single-component adsorption. Carter (1975) has considered a heating step beginning with a bed having a nonuniform initial loading of a single adsorbate. A study of the cyclic operation of an adsorption bed with thermal regeneration has been presented in the thesis of Chao (1981), a detailed account of which has been given by Ruthven (1984). Chao considered the adsorption of a single component in a two-step cycle (adsorption and heating). Both steps were considered to occur isothermally,
with the time for heating the bed neglected. Thus, the bed was assumed to be a t a constant high temperature throughout the regeneration step. More recently, Kumar and Dissinger (1986), following Basmadjian et al. (1975), have considered the nonisothermal purge of a single adsorbate from a fixed bed. They proposed an equation for a characteristic feed temperature for which energy consumption was a minimum. Davis and LeVan (1987) have analyzed complete adiabatic adsorption cycles for singlecomponent adsorption. Historically, two approaches have been taken in solving the conservation equations for nonisothermal fixed-bed adsorption. The classical approach considers the limiting behavior of an adiabatic bed, with local equilibrium existing between the fluid and solid phases. For large deep beds, solutions obtained by this approach indicate all of the qualitative features of performance. The second approach involves the development of a full rate model for the rigorous simulation of the performance of a bed; particle size and shape, velocities, and other parameters must be specified to determine mass- and heat-transfer characteristics. Since the aim of this work is to outline the influence of the major process parameters and experimental data are currently lacking, we have opted for a simplified model. We have assumed local equilibrium between the fluid and solid phases and adiabatic behavior, thus greatly simplifying the calculations. Our analysis of periodic behavior is based on integral properties of the solution to a mathematical model. At least for a deep bed, these properties are relatively insensitive to mass- and heat-transfer resistances. The system considered is benzene and cyclohexane adsorbed on activated carbon. Nitrogen is the carrier gas.
Mathematical Model The mathematical model consists of conservation equations and the adsorption equilibrium relationships. We assume that the bed operates isobarically and adiabatically. Furthermore, we have ideal gas behavior, plug flow, and local equilibrium with no dispersion. Material balances for components 1 and 2 are of the form
The energy balance for an adiabatic bed is
* Author to whom correspondence should be addressed. 0888-5885/88/2621-1229$01.50/0
0 1988 American Chemical Society
1230 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988
where us =
(cs
+ Ca191 + C a 2 9 2 ) ( T - T r e 3 - X I ~ I- 1 2 4 2 (3) Uf
= hf - P / P f
hf = cp(T- T,,f)
(4) (5)
The adsorption equilibrium relation is the binary Langmuir isotherm, which is given by
with (Rhee et al., 1972)
Ki= KioT1/2exp(Xi/RT)
(7)
In solving the equations, the following dimensionless variables were introduced:
p = z/L
(9)
u* = u / u o
(10)
The dimensionless velocity u* was calculated assuming a constant inert flux in a dilute system. This gives u* = T/To
(11)
The fluid-phase accumulation terms were found to be small compared to the corresponding solid-phase terms (see Friday and LeVan (1982)) and were discarded. As mentioned previously, the process modeled has an adsorption step, a heating step, and possibly a cooling step. In general, regeneration is not carried out to completion. The bed profile a t the end of the adsorption step is the initial condition for the heating step. Similarly, the bed profile a t the end of the heating step (or cooling step, if it exists) is the initial condition for the adsorption step. Adsorption and heating steps are analyzed rigorously below. The effect of a cooling step on the overall cycle can be inferred from previous results (Davis and LeVan, 19871, as discussed briefly below. For the heating step the gas is passed into the bed in a direction opposite to that for the adsorption step. The cooling gas may be passed into the bed in either direction, and its temperature is taken to be the same as that of the feed for the adsorption step. If the cooling step is omitted, the bed will be cooled early during the adsorption step (see Basmadjian (1975) and Davis and LeVan (1987)). The adsorption step is treated by using simple wave theory. This step ends when the first material transition reaches the end of the bed. The state of the bed at the end of this step will be such that all interactions between shocks and simple waves will be complete (see Rhee et al. (1970,1986) and Davis and LeVan (1987)). The bed will contain two shocks: a single-component shock breaking through at the end of the bed and a two-component shock a t some intermediate position in the bed. From eq 1, 2 and 8-10 and if the fluid-phase accumulation terms are neglected, simple wave theory gives for a shock
where the differences are taken between the states on either side of the shock. Given the quantities of undesorbed solute in the bed a t the start of the adsorption step,
Table I. Physical and Thermodynamic Properties components benzene cyclo(1) hexane (2) c,, kJ/(mol K) 0.140 0.152 Pb, kg/m3 A, kJ/mol 43.5 32.6 c p , kJ/(kg K) c,, kJ/(kg K) 4.4 3.0 Q,mol/kg KO,m3/(mol K1iZ) 3.88 X 1.04 X IO4 Trer,K
480 1.06 1.05 298
eq 12 can be solved for the compositions in the bed and the locations of the shocks. The heating step is analyzed using finite differences. Equations 1 and 2 are solved by replacing the spatial derivative with a backward difference approximation and then integrating the resulting set of ordinary differential equations by using a Gear’s method solver (Hindmarsh, 1980). Integral properties of the solution, discussed below, are then obtained. To reduce the dependence of these properties on the backward difference approximation, Richardson’s differed approach to the limit is used (Richardson, 1927; Finlayson, 1980). This involves obtaining properties a t two or more spatial step sizes and then plotting the properties versus the inverse of the number of steps. A straight line is passed through the points. The intercept of the line with the y axis represents the value of the property for an infinitesimal step size. Only integral properties of the solutions were extrapolated; breakthrough curves shown below were obtained using 200 divisions of the axial coordinate, with 100 equal-sized divisions placed on either side of the two-component shock. Values chosen for the parameters appearing in the model are shown in Table I. Physical properties were assigned typical literature values. The parameters in the isotherm relation are those of Rhee et al. (1972), which were determined from the data of James and Phillips (1954). Benzene is the “heavy” component and cyclohexane is the “light” component as determined by their heats of desorption. In Table I and in equations and figures which follow, benzene and cyclohexane are indicated by the subscripts 1 and 2, respectively. Approach The study consists of choosing a base case for the heating of the bed and then varying the heating temperature, the heating pressure, and the extent of accumulation of the heavy component in the bed to obtain their influence on the periodic state. We let feed for the adsorption step be a t 1 MPa and 298 K and contain the adsorbable components a t 5% of their pure-component vapor pressures. Thus, P = 1 MPa, T = 298 K, 41 = 0.05, and +2 = 0.05, where 4 is the fractional degree of saturation of the vapor phase with a component. For the base case heating step, solute-free gas at 1 MPa and 373 K is passed into the bed until both adsorbable components have been removed completely. This is described mathematically by P = 1 MPa, T = 373 K, 41 = 0, and 42 = 0. On the basis of the definition of 4, partial pressures are determined from P L = $iPL,sat (13) where the pure-component vapor pressure Pi,sat is calculated by using the Antoine equation. Solving eq 12 for an initially clean bed indicates that at the end of the adsorption step, when cyclohexane has just broken through the bed, benzene has penetrated 49.9 % of the way through the bed. The bed profiles at the end of this adsorption step are shown in Figure 1. p1 marks the depth of penetration of benzene into the bed. The values of gl, g2,and T shown in the figure are independent of the location of 5;. For < ll,the bed is in equilibrium with the feed for the adsorption step. For { > the values
cl,
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1231 299
T 298
i
q l = 298 mollkg
I
I
I
r-I ] I 298.54 K
298 K
1
I
I
I
I
-- -,qL= - -2-36_ /ml; - kg- -
qp=069moi/kg
_-_________
0 0
02
04
b
06
08
IO
Figure 1. Benzene (l), cyclohexane (2), and temperature profiles a t the start of the heating step for the base case. Flow for the previous adsorption step was from left to right; flow for heating is from right to left. At the end of the adsorption step, cyclohexane had just reached the end of the bed a t { = 1. The two-component shock is located a t { = = 0.499. Solute-free gas left the bed prior to breakthrough at a temperature of 299.65 K.
where chi is the time-dependent effluent concentration of component i during the heating step and c,. is the constant feed concentration of component i for the adsorption step. Since only a single value of 7, exists, eq 14 can be evaluated for either component. For our purposes, we consider the optimal periodic state to be such that a minimum of energy is required in heating the hot gas. Since the dimensionless times are measured in terms of superficial column volumes fed to the bed, the performance at the periodic state is evaluated by the ratio of the number of column volumes of hot gas fed to the bed during regeneration to the number of column volumes fed during the adsorption step. Thus, we seek to minimize the ratio 7h/7,. It should be pointed out that other criteria of optimality may certainly be appropriate depending on the purpose of the adsorption cycle and detailed costs. We have previously discussed the importance of condenser operation in solvent recovery applications (LeVan et al., 1987). (The point should be made that a bed can be regenerated completely with clean gas and no heating in a simple purge step. However, process constraints on time or a requirement that effluent concentrations be large enough to permit efficient recovery of desorbed solutes by condensation usually make heating a necessity.)
280 300
200
Figure 2. Breakthrough curves for benzene (l),cyclohexane (2), and temperature for heating step. Parameters are those of the base case with = 0.499. 1.51
of q2 and T are determined from eq 12. In addition to varying pressure and feed temperature for the heating step, we vary fl. Thus, we treat as a parameter the depth of penetration of the heavy component in the bed over repeated cycles. Our approach involves determining the heating times that are consistent with a chosen fl, as follows. A periodic state requires closure of the material balance; i.e., for each component, the amount removed from the bed during regeneration is equal to the amount that accumulates in the bed during the adsorption step. (Note that this condition is satisfied for the base case.) For our purpose, the condition for a periodic state is satisfied when components have been removed from the bed during heating in the same proportion a t which they are present in the feed for the adsorption step. We monitor the ratio of moles of cyclohexane to moles of benzene eluted during the heating step as a function of the dimensionless heating time q,. When this ratio is equal to the ratio of concentrations in the feed for the adsorption step, a periodic state has been found. Then, knowing the dimensionless heating time, the dimensionless adsorption time (7,)is calculated by material balance using quantities of undesorbed solute or quantities eluted. For the latter we have
I
I
100
I
I
I
I
I
E
0
400
800
I200
Th
Figure 3. Effluent ratio as a function of heating time for various feed temperatures for heating. Remaining parameters are those of the base case.
Results and Discussion The feed for the adsorption step will be the same for all examples. In order to simplify the discussion, we define an effluent ratio E as mol of 2/mol of 1 removed during heating E= (15) cA2/cA1in feed for adsorption Again, components 1 and 2 are benzene (heavy) and cyclohexane (light), respectively. Figure 2 shows breakthrough curves for the heating step of the base case. This is the solution to eq 1 and 2 for the initial loading shown in Figure 1. For heating, the hot gas would flow from right to left in Figure 1. The initial concentrations in the effluent, before the bed outlet for heating becomes warm, are approximately equal and are simply those of the feed for the adsorption step. At longer times, two waves are apparent. (The true wave character of the solution is disguised by the nonuniform initial loading of the bed. Other waves and wave interactions are present.) At ‘h = 34, the first wave emerges with the effluent concentrations and temperature increasing abruptly. The concentration of the light component increases somewhat more than the concentration of the heavy component. Slightly thereafter, however, the second wave begins to breakthrough and the concentration of the light component drops relative to that of the heavy component. It remains lower until Th = 280. The adsorbates are completely removed from the bed by 721 = 1070. Figure 3 is a plot of the effluent ratio E versus 711 for the base case and for variations in hot feed temperature about the base case. A periodic state occurs a t any point where the curve intersects the dashed line, indicating E = 1. When the curve lies above the dashed line, more of the
1232 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 151
I
I
I
I
I
1
I
I
T
- 360 340
-
Y
2
I
300
I
200
100
1
I
1
400
1
800
I
320
U
I
05;
I-
280 300
I 1200
r, Figure 4. Effluent ratio as a function of heating time for various pressures for heating. Remaining parameters are those of the base case.
light component has been removed from the bed. Similarly, if the curve lies below the dashed line, a larger quantity of heavy component has been removed. The curve for the base case, labeled 373 K in Figure 3, indicates the existence of three periodic states: (1)for 7 h < 34, prior to the appearance of the first wave at the bed outlet; (2) a t 7h = 60; and (3) for Th > 1070, after complete removal of the adsorbates from the bed. For thermal swing adsorption, the first periodic state is discounted because the bed has not been regenerated thermally. Thus, in the discussion which follows, we will refer to the second and third periodic states as the short-time and long-time periodic states, respectively. We will show later that the short-time periodic state for the base case is unstable. The curves in Figure 3 for other temperatures behave as one might expect. High feed temperatures regenerate the bed quickly. Temperatures above 398 K could not be investigated due to formation of saturated vapors and the resulting failure of the equilibrium relation (see Friday and LeVan (1982, 1984)). Figure 4 shows the behavior of the effluent ratio for variations in the pressure for the heating step. 5; is held constant at 0.499. Again, a t the base case pressure of 1 MPa, the long-time periodic state is at 7h = 1070. As the pressure is reduced first to 0.5 MPa and then to 0.3 MPa, this periodic state, corresponding to complete removal of the adsorbates from the bed, remains a t 7 h = 1070. This periodic state is approached in Figure 4 from beneath the E = 1 line. This means that the heavy component is removed from the bed more quickly and that the last adsorbate to be removed is the light component. On the basis of equilibrium theory, the rate of propagation of the last trace of the light component through the bed is determined by the slope of the pure-component isotherm of the light component at infinite dilution. Because this velocity is independent of pressure, the long-term periodic states for 1.0,0.5, and 0.3 MPa all occur at the same value of 711. At low pressures the character of the behavior changes. The curve for 0.1 MPa in Figure 4 never drops below the E = 1line. This indicates that the last component to be removed from the bed completely is the heavy one. For P = 0.1 MPa and the given parameters, periodic states exist only for values of C1 1 0.499. For regeneration times shorter than that for complete regeneration, the heavy component will accumulate preferentially in the bed. The general shape of the curves in Figures 3 and 4 gives an indication of where other periodic states lie. If heating were stopped at a Th not corresponding to a periodic state, then one of the components would have accumulated in
I'
I
Y
-G Figure 6. Effluent ratio as a function of heating time for various depths of penetration of heavy component into bed. Remaining parameters are those of the base case. E = 1 is not reached for J; = 0.6 at long times.
the bed relative to the other. As the cycle continues, a new periodic state would be approached, exhibiting either a deficiency or a surplus of, say, the light component in the adsorbed phase. Consider, for example, the base case. If heating were stopped at any time between 711 = 60 and 1070, then from Figure 3 and 4 more of the heavy component would have been removed. A periodic state would be approached after repeated cycles for which the bed contains, throughout the adsorption step and a t the end of the heating step, more of the light component than the heavy component. For this case, the heavy component does not penetrate as far into the bed during the adsorption step; the value of Cl would be less than 0.499. Breakthrough curves for precisely this case are shown in Figure 5. All parameters are those for the base case except for which is now equal to 0.2. Compared to the base case, at long times the effluent concentrations for the heavy and light components are much less and somewhat greater, respectively. Figure 6 shows the dependence of the effluent ratio on heating time for several different depths of penetration of the heavy component into the bed during the adsorption step. Pressure and feed temperature for heating are those of the base case. Note that for 5; = 0.2, the last occurrence of E = 1 is at 7h = 120. Thus, no periodic state consistent with the parameters exists for a longer heating time. If heating is allowed to occur for a t h e greater than Th = 120, then the cycle would move toward a new periodic state with the bed containing more of the heavy component. For example, from Figure 6, if 711 were changed from 120 to 430, then 5; would advance from 0.2 to 0.4.
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1233
0'50 1 040i
I 05
1
0
h
\
06
I
I 400
-+
800
1200
[h
Figure 7. Effluent ratio as a function of heating time for P = 0.3 MPa and various depths of penetration of heavy component into the bed. Remaining parameters are those of the base case.
The stability of the short-time periodic states near Th = 60 can be considered using Figure 6. The structure of the c w e s in this vicinity is such that the cycle would move away from these states toward the long-time periodic states. For example, consider how the cycle might approach the short-time periodic state a t 3; = 0.4, for which Th = 55. Th is set to 55 and the system is allowed to cycle toward a new periodic state. Let tl for the current periodic state, prior to setting Th to 55, be 0.499. Thus, in order to approach the new periodic state, the quantity of benzene in the bed relative to cyclohexane must be reduced. For the first heating step we find that the curve for t1 = 0.499 lies above the E = 1 dashed line a t Th = 55. Thus, the heating step removed more cyclohexanethan benzene from the bed. The cycle is not moving toward the desired state but away from it. (For this example, the cycle will not approach a long-time periodic state since none exist for 5; > 0.499. A stable short-time periodic state corresponding to a large 5; exists and is approached.) As a second example, consider the approach to the same periodic state but from a current periodic state having ll = 0.3. At 7 h = 55, the curve for S; = 0.3 lies below the E = 1 dashed line. Thus, during the first heating step, more benzene than cyclohexane will be removed from the bed. 5; will decrease further rather than move toward the target periodic state. A stable (long-time) periodic state will be approached having shallow penetration of benzene into the bed (S; = 0.05). It appears that in general a periodic state is stable if, in the vicinity of the periodic state, tl increases in passing vertically downward across the E = 1line. Such states are shown near Th = 300 in Figure 7, which pertains to the base case except the pressure has been changed to 0.3 MPa. Under these circumstances, stable short-time solutions exist for 5; > 0.43, where curves begin to dip below the E = 1 line. The manner in which a periodic state is approached is further illustrated in Figure 8. This figure shows rigorous calculations of cyclic performance for the base case with Th = 200. For the first adsorption step, 2803 column volumes of feed are fed to the bed prior to breakthrough and benzene penetrates to 3; = 0.499. Thereafter, roughly 1450 column volumes are sufficient to saturate the bed. The periodic state is approached reasonably quickly, with S; approaching 0.27, consistent with Figure 6. At the periodic state, 94% of the benzene and 42% of the cyclohexane in the bed a t the end of the adsorption step are removed during heating. Figure 9 shows rh/Ta, the performance criteria, plotted versus l1.Curves for different pressures represent loci of
I
I
I
I
3
4
5
6
Cycle Number
Figure 8. Approach to the periodic state for the base case with a heating time of T~ = 200. 125
0
_I _ _I _I _ _I
02
I
I
I
I
7-------4
04
06
08
I
IO
4 Figure 9. Dependence of performance criterion on depth of penetration of heavy component into the bed.
stable periodic states. The feed temperature of the heating gas is 373 K for all curves. (As shown by Figure 3, temperature does not have the pronounced effect on the qualitative features of the cycle that pressure does.) Two dashed lines are shown in Figure 9. The vertical line is at ll = 0.499. To the left and right of this line, the bed is enriched in the light and heavy component, respectively. The horizontal line represents the periodic state that occurs a t the outset of the heating step, before the bed outlet becomes warm. In this regime, one column volume of hot feed gas a t 373 K shrinks isobarically as it is cooled to the initial bed temperature of 298 K. It carries the components out of the bed at their feed concentration for the adsorption step. Thus, a column volume of hot gas removes the amounts of the components present in 2981 373 column volumes of feed for the adsorption step. T h / T a , being the ratio of column volumes, is therefore equal to 3731298. The curve for 0.1 MPa lies to the right of 5; = 0.499. Thus, the cycle is operated with an accumulation of the heavy component in the bed. Along this locus of periodic states, the value of Th decreases in moving away from ll = 0.499. The curve goes through a minimum near 5; = 0.6, a t which point Th is approximately 1300. This is the op-
1234 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988
timal heating time for the cycle from the standpoint of minimizing heating requirements. For the larger pressures of 1.0,0.5, and 0.3 MPa, longtime periodic states lie to the left of the C1 = 0.499 dashed line. Furthermore, the curves share a common point on that line. (This is consistent with the periodic states for complete regeneration shown in Figure 4.) Values of both Th and T, decrease in moving along the curves from the l1 = 0.499 dashed line. The minimum in the curve for P = 1.0 MPa occurs near = 0.2, where 7 h = 120. For the pressures of 0.5 and 0.3 MPa, a wide range of stable short-time solutions exist also. These are represented by the nearly horizontal branches which cross the ll = 0.499 line. Concluding Remarks Our results show that a high-pressure heating step tends to favor the removal of the heavy component from the bed and that a low-pressure heating step favors the removal of the light component. Displacement of benzene by cyclohexane plays a role because of the nonuniform initial bed loading. However, the behavior can be explained satisfactorily simply in terms of the two tasks performed by the hot gas, the addition of energy to the bed and the sweeping of desorbed material out of the bed. At high prc ssures the bed is heated quickly. This increases the volatility of both components, but the partial pressure of the heavy component is increased by a greater percentage as can be seen from the Clausius-Clapeyron-type equation for isosteric heat of adsorption:
Thus, the component with the larger heat of adsorption will have the larger percentage change in partial pressure an heating. (Equivalently, the observed behavior can be explained by the selectivity or relative volatility becoming closer to unity as temperature is increased.) Once the bed is heated, the heavy component is removed from the bed at a greater rate than the light component relative to their proportions in the feed for the absorption step. The periodic state is such that the cycle operates with the bed enriched in the light component, with enough of it removed to lead to closure of the material balance. At low pressures the bed is heated slowly. The sweeping of desorbed components from the bed becomes very important. Because of the manner in which the bed is loaded, as shown in Figure 1,the reverse flow heating desorbs the light component from the region .t > Cl and deposits some of it in the region { < fl where both components are removed. As time progresses, the concentration of the heavy component in the effluent drops relative to that of the light component. The material balance is satisfied after the concentration of the light component finally drops, as it must, relative to that of the heavy component. The bed is left enriched in the heavy component. In Figure 9 it was shown that the curves for the performance criterion T h / T , are relatively flat near the minima. The corresponding optimal regeneration times occur roughly when the major thermal transition leaves the bed (see Figures 2 and 5). Thus, in the absence of any other information, if a regeneration time is chosen such that this transition just leaves the bed, the process should be near optimal from the standpoint of energy utilization. This paper has not considered in any detail the removal of adsorbate from the bed during a cooling step. A lowpressure cooling step with flow in the same direction as the heating step can effectively remove a considerable amount of adsorbate from the bed if the cycle step is timed
properly. This can be incorporated in the current study in a qualitative way. For the benzene-activated carbon system, Davis and LeVan (1987) have shown that roughly 55 column volumes of cooling gas at 1.0 MPa are sufficient to cool the bed. For the first 45 of these column volumes, there is no indication at the bed outlet that the bed is being cooled. Thus, in some cases, it is possible to significantly reduce heating requirements beyond those reported here. For example, results similar to those of the cycle considered in Figure 8 should be obtained for a cycle with roughly 50 fewer column volumes for heating, using instead a cooling step at 1.0 MPa. Cooling at lower pressure can further increase energy efficiency. Acknowledgment This research was supported by the National Science Foundation under Grant CBT-8417673. Nomenclature c = gas-phase concentration of solute, mol/m3 cd = heat capacity of adsorbate i, kJ/(mol K) cp = heat capacity of gas phase, kJ/(kg K) c, = heat capacity of adsorbent, kJ/(kg K) E = effluent ratio, eq 15 hf = enthalpy of gas phase, kJ/kg K = constant in Langmuir isotherm, m3/mol L = bed length, m P = total pressure, MPa q = adsorbed-phase concentration, mol/kg Q = Langmuir isotherm monolayer capacity, mol/ kg R = gas constant t = time, s 5" = temperature, K ut = internal energy of gas phase, kJ/ kg u , = internal energy of stationary phase, kJ/kg u = interstitial velocity, m/s uo = interstitial velocity of feed, m/s u* = dimensionless velocity z = axial coordinate, m Greek Symbols = void fraction of packing E' = local voidage of bed including pore space [ = dimensionless axial coordinate 5; = depth of penetration of heavy component into bed X = heat of desorption, kJ/mol P b = bulk density of packing, kg/m3 pf = density of gas phase, kg/m3 T = dimensionless time = fractional saturation of vapor phase t
+
Subscripts
a = adsorption step h = heating step i = component index 1 = heavy component, benzene 2 = light component, cyclohexane Literature Cited Bailly, M.; Tondeur, D. Chem. Eng. Sci. 1981, 36, 455. Basmadjian, D. Can. J . Chem. Eng. 1975, 53, 234. Basmadjian, D.; Ha, K. D.; Pan, C. Y. Ind. Eng. Chem. Process Des. Deu. 1975, 14, 328. Carter, J. W. AIChE J. 1975, 21, 380. Chao, J. Ph.D. Dissertation, University of New Brunswick, Fredericton, N.B., Canada, 1981. Costa, C.; Rodrigues, A. AZChE J. 1985, 31, 1655. Davis, M . M.; LeVan, M. D. AZChE J . 1987, 33, 470. Dodds, J . A,; Tondeur, D. Chem. Eng. Sci. 1974,29, 611. Finlayson, B. A. Nonlinear Analysis in Chemical Engineering; McGraw-Hill: New York, 1980; p 110. Frey, D.D. Ind. Eng. Chem. Process Des. Deu. 1986, 25, 70.
Ind. Eng. Chem. Res. 1988,27, 1235-1241 Friday, D. K.; LeVan, M. D. AZChE J. 1982,28,86. Friday, D. K.; LeVan, M. D. AZChE J. 1984, 30,679. Gelbin, D.; Bunke, G.; Wolff, H. J.; Neimass, J. Chem. Eng. Sci. 1983,38, 1993. Grevillot, G.; Tondeur, D.; Dodds, J. A. J. Chromatogr. 1974, 102, 421. Helfferich, F.; Klein, G. Multicomponent Chromatography;Marcel Dekker: New York, 1970; pp 105-272. Hindmarsh, A. C. ACM-SIGNUM Newsletter 1980, 15(4), 10. James, D. H.; Phillips, C. S. G. J. Chem. SOC.1954, 1954, 1066. Kumar, R.; Dissinger, G. R. Znd. Eng. Chem. Process Des. Dev. 1986, 25, 456. LeVan, M. D.; McAvoy, R. L., Jr.; Davis, M. M.; Dolan, W. B. In Fundamentals of Adsorption; Liapis, A. I., Ed.; Engineering Foundation: New York, 1987, pp 349-358. Pan, C. Y.; Basmadjian, D. Chem. Eng. Sci. 1971, 26, 45.
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Received for review August 12, 1987 Accepted February 22, 1988
Absorption Characteristics of Sulfur Dioxide in Water in the Presence of a Corona Discharge Niraj Vasishtha and Arun V. Someshwar* Department of Chemical Engineering, University of New Hampshire, Durham, New Hampshire 03824
The absorption characteristics of sulfur dioxide into a stagnant body of distilled water are investigated in the presence of point-plane ionic discharges in a closed chamber a t 30 f 0.1 "C. SO2 removal is seen t o be enhanced when the liquid surface is subjected t o the discharge, with the bulk of the enhancement resulting in acidic deposition within the chamber. Gas-phase oxidation of SO2 in the absence of liquid water is seen t o be minimal. T h e effects of varying the discharge intensity and polarity and gas oxygen content on the observed absorption rate enhancements are reported. The removal of sulfur dioxide from effluent gases emanating from coal-fired electric-generating plants in ways that are efficient and inexpensive continues to be a problem of paramount concern. Existing flue gas desulfurization (FGD) technologies make use of expensive scrubbers with alkaline reagents as the principal scrubbing medium. Extreme levels of corrosion caused by these reagents have necessitated the use of expensive corrosion-resistant scrubber materials, resulting in high capital costs. The problem of waste disposal of the alkaline sludge is an additional unwelcome factor. In recent years, several researchers (Koppang, 1977; Pilat and Raemhild, 1977; Marks, 1970) have observed that when liquid water is sprayed from electrified nozzles its SO2absorption capacity increases dramatically. While the experimental evidence presented by these authors points clearly in the direction of an advanced technique for SO2 removal, the precise nature of these charge-induced effects is as yet unclear. Considering that spray dryers using liquid reagents are still the dominant FGD method of operation, a further elucidation of the fundamental underlying parameters is imperative.
Background Previous work related to enhanced, charge-induced, SOz absorption can be grouped into three categories. The first category comprises mainly pilot-plant studies in which a liquid absorbent was sprayed from nozzles maintained at a high electric potential into a flowing gas stream containing SOz. Koppang (1977) and Pilat and Raemhild (1977),while working primarily with particulate emission control, found that charged liquid water droplets issuing from electrified nozzles were capable of removing substantial amounts of SO2, far exceeding even that attributable to saturation. Marks (1970) provides further experimental evidence of the superior absorption capabilities of charged aerosols for certain noxious gaseous species. 0888-5885/88/2627-1235$01.50/0
The second category of researchers was primarily interested in accounting for possible enhancements in mass-transfer rates of SO2 absorption into liquid absorbents. Uchigasaki et al. (1967) conducted a detailed laboratory study looking into the absorption of SOz (among other gases) into water and 1 N NaOH in a wetted wall column and in the presence of a wire-cylinder electric discharge. The SOz concentrations studied in this work were typically over 2 mol % or 20000 ppm, which far exceeds the levels commonly found in effluent gases from coal-fired power plants (typically 0 to 3000 ppm). This study was conducted under various conditions of discharge density, polarity, and SO2 and Oz content in the gas stream. On the basis of their results, the authors have suggested that the enhanced removal of SOz in a short-contact-time apparatus was due primarily to a vast improvement in the overall mass-transfer coefficient in the presence of the discharge. However, they also seem to indicate that the enhancement of the transfer coefficient is a strong function of the gas Oz content (being negligible in the absence of 0,) and that the discharge leads to partial oxidation of the SOz with the resulting HzS04being detected in both the exiting gas and liquid phases. Uchigasaki and Endo (1969) and Asano and Uchigasaki (1970) have also reported on significantly enhanced absorption rates of SOz into other alkaline solutions such as N,N-dimethylamine and aqueous Ca(OH), solution. Sheldstad et al. (1974) have also corroborated the observations of increased absorption rates of SO2 into water and several other alkaline reagents in the presence of a wire-cylinder discharge identical with the one used by Uchigasaki et al. (1967). They concluded that the largest effect of the corona occurs in those liquids which give the highest absorption rate without corona (primarily the most alkaline liquids). Carleson and Berg (1983) investigated the absorption of pure SO2 into water droplets formed by electrified nozzles in an attempt to observe any enhanced mass0 1988 American Chemical Society
