Ind. Eng. Chem. Res. 1988,27, 636-642
636
SEPARATIONS Influence of Hydrodynamics on Physical and Chemical Gas Absorption in Packed Columns John R. Lindner, Craig N. Schubert, and Robert M. Kelly* Department of Chemical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218
A model for physical and chemical gas absorption in a packed column was developed to investigate the influence of hydrodynamics on mass transfer. The model can simulate systems with gas- and liquid-phase axial dispersion, as well as liquid-phase static holdup. Two systems were chosen for investigation: the C02-water system and the C02-H2S-MDEA system. The C02-water system provides an example of physical absorption. The C02-MDEA system gives an example of absorption accompanied by a moderately paced chemical reaction. The H,S-MDEA system gives an example of absorption accompanied by an instantaneous chemical reaction. Results show that nonideal flow in the column has the largest effects on physical absorption and on absorption with instantaneous reaction. In some cases, this effect is shown to lead to an error of greater than 40% in the designed height of a packed column. It is also shown that hydrodynamics can be an important consideration in scale-up from small packings. Significant progreas has been made in understanding the complex hydrodynamics associated with separations conducted in packed columns as well as with catalytic reactions carried out in trickle flow systems. As a result, many models have been proposed that attempt to describe departures from plug flow in these systems. However, little progress has been made in determining the implications of these models to situations with complex mass transfer, such as chemical absorption. Perhaps the best way to characterize the many proposed models for packed column irrigation is to separate them into discrete and continuous representations. In either case, some degree of deviation from plug flow is used to describe the influence of hydrodynamics on mass transfer. Mixing cell models, which are based on a discrete representation of packed columns, have been used by many to describe packed column trickle flow hydrodynamics (van Swaaij et al., 1969; Shulman et al., 1971;Baldi and Sicardi, 1975). These models are based on either a tanks-in-series approach or a series of mixing planes. Each mixing cell is described by a set of variables including temperature and concentrations. Continuous models for packed column hydrodynamics also have been proposed. These models involve the solution of differential equations that may include capacitance and axial dispersion parameters. Because continuous functions are used to represent column behavior, these models are amenable to solution with an efficient computation scheme based on orthogonal collocation. One of the earliest representations of packed column hydrodynamics, which is still used, separates the total liquid holdup into dynamic and static fractions (Shulman et al., 1955). Liquid moves through the dynamic holdup in plug flow with interchange between the static and dynamic holdups. For fast chemical reaction and physical absorption, the static holdup is less effective than the dynamic holdup because it quickly becomes saturated (Joosten and Danckwerts, 1973). The static holdup be-
comes completely effective for moderately paced chemical reaction and evaporation. While this model has been widely used to correlate absorption data, tracer experiments have shown that consideration of capacitance effects alone is not sufficient to describe packed column hydrodynamics (Bennett and Goodridge, 1970; Schubert et al., 1987). Bennett and Goodridge (1970) extended the static holdup model to include dispersed plug flow in the dynamic liquid holdup. Through tracer experiments involving step decreases in salt concentration in the liquid feed to the column, they were able to measure static and dynamic holdups, interchange rates between the holdups, and the liquid-phase Peclet number all in a single experiment. Their model, which was similar to one proposed by van Swaaij et al. (1969), compared favorably to experimental data. Patwardhan (1978) simplified the model proposed by Bennett and Goodridge (1970) so that solutions could be more easily obtained in systems with complex mass transfer, such as those found with chemical absorption. This "extended cross-flow'' model incorporates static holdup but assumes there is no axial dispersion in the gas and liquid phases. This model was used to account for the relationship between hydrodynamics and chemical absorption for several different reaction regimes in both the static and dynamic holdups. In addition to capacitance (static holdup) and liquidphase axial dispersion, several workers have examined the effect of axial dispersion in the gas phase. Burghardt and Bartelmus (1980) looked at gas-phase dispersion alone, while Dunn et al. (1977) examined dispersion in both the gas and liquid phases. Both investigations lead to the result that nonidealities in the hydrodynamics can have a significant effect on absorption column operation. Suenson et al. (1985) combined liquid- and gas-phase dispersion in a packed column model, which was solved using orthogonal collocation, and compared it to experi-
Q888-5sBs/Bs/2627-Q636$01.5Q/Q 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 637
--
Table 1. Reactions in the Aqueous MDEA-H2S-C02 System COP + HzO HCOZ- + Ht COZ COz + OHHC03COS- + Ht (instantaneous) HCOy (instantaneous) H2S H2S HS- + Ht (instantaneous) HS- S' + Ht MDEA R3N + H+ R3NH+ (instantaneous) HzO H20 OH- + Ht (instantaneous)
---
used to eliminate the reaction rate terms in the liquidphase equations for those components which are assumed to react infinitely fast. For the sulfur compounds in the system, the equations for the dynamic liquid phase become
-
mental data for chemical absorption/stripping of C02. However, dispersion was included in the model mainly to eliminate oscillations they observed in their numerical solutions; the dispersion coefficients used did not change the results significantly from plug flow. The relationship between mass-transfer and column hydrodynamics is sometimes a critical consideration in the design and operation of packed column gas absorbers and strippers. While there are instances in which nonideal flow effects can be considered negligible (Brittan and Woodburn, 1966), there are also many cases in which they be significant. The work presented here addresses this issue through a simulation model that can incorporate the features of previous efforts to model packed column hydrodynamics in a mass-transfer framework.
Packed Column Model A model similar to the capacitance-liquid-phase axial dispersion model of Bennett and Goodridge (1970) was chosen for this study but was expanded through the addition of gas-phase axial dispersion. With several adjustable parameters, this approach gives enough generality to be used for several types of hydrodynamic models. For example, with gas dispersion disabled, Bennett and Goodridge's (1970) original model is obtained. By disabling both gas- and liquid-phase dispersion, Patwardhan's (1978) extended cross-flow model can be simulated. The static holdup can exchange mass with both the dynamic liquid holdup and the gas phase. Mass transfer between the static and dynamic portions is assumed to be caused by bulk flow between the two phases (Kan and Greenfield, 1983). Including the gas absorption term, and the term for bulk chemical reaction, the overall balance for the static phase becomes Qs(ci - si) + aspi
+ 4srsi = 0
(1)
Kan and Greenfield (1983) assumed that the static phase did not transfer with the gas and could only transfer mass with the dynamic liquid. This assumption can also be incorporated into the present framework by setting the static interfacial area to zero, effectively eliminating gas absorption into the static liquid phase. The balance for the dynamic holdup requires terms for axial dispersion, bulk flow, exchange with the static holdup, absorption from the gas phase, and bulk reaction. Incorporation of these terms leads to
The gas-phase balance has terms for dispersion, bulk flow, and absorption. Summing these gives
Absorption with Chemical Reaction. Absorption with instantaneous chemical reaction can also be analyzed within this framework. The gas-phase equations remain unchanged. The method developed by Olander (1960) is
(4)
Dl(d2[H2S]c/d~2 + d2[HS-],/dz2 + d2[S=]c/d~2) + QL(d[H,S],/dz + d[HS-],/dz + d[S=],/dz) + ad("H2S + ~ H S -+ as=) Q,([H$ls lHS-1, + [s'], [H2Slc- lHS-1, - [S=lc)= 0 (6) Table I show a list of the reactions in the C02-H2S-MDEA system. Each of the instantaneous reactions is treated similarly. Boundary Conditions. One difficulty in using the dispersed plug flow model for liquid and gas flow through the packed column is choosing appropriate boundary conditions. In order to satisfy conservation of mass at the inlet and outlet, the Langmuir-Danckwerts boundary conditions must be used (Nauman and Mallikarjun, 1983). For the liquid phase, these conditions can be written as Qlc(t,L-) = Qlc(t,L+) - D1 dc/dzl,,i dc/dzl,=O = 0
(7)
(8)
These boundary conditions, however, predict a discontinuity at the inlet of the column ( z = L). A possible modification to these boundary conditions was suggested by Nauman and Mallikarjun (1983), which brings the dispersed plug flow model in closer agreement with experimental data but requires several adjustable parameters. However, since the Langmuir-Danckwerts conditions have only one adjustable constant (the axial dispersion coefficient) which can be readily obtained in the literature, they were chosen for this work. Absorption Rates. Several analytical approximations for determining mass-transfer rates in the MDEA-H2SC02system have been developed. However, because of the complexity of the equations involved, it is not practical to determine an analytical solution which addresses all of the issues in this work, including the nonideal liquid phase, reversibility of all reactions, and depletion of MDEA at the interface. The only practical method for including all of these effects is to numerically solve the system of equations governing the mass transfer. The drawback to using a numerical solution technique rather than an analytical solution is that the calculations become more time consuming. Thus, much effort has been spent on development an efficient solution method to the mass-transfer equations. The final method developed is based on orthogonal collocation and uses a pseudo-Newton-Raphson iteration technique. A summary of the reactions governing the aqueous MDEA-H2S-C02 system is shown in Table I. (Where an equation applies to tertiary amines in general, the notation R3N is used. MDEA is used where the result is specific to methyldiethanolamine.) All of the reactions, except those involving C02, are proton transfers, which are regarded as instantaneous. The method of Olander (1960) was used to treat these instantaneous reactions. The film model is used to compute the mass-transfer rates. While this model is generally accepted to be less accurate than surface renewal models, the film model is
638 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 Table I1
temp pressure liquid flow rate gas flow rate liquid holdup gas mole fraction of co*
40 "C 5 atm 1.4-4.5 kg/(m*-s) 4 mol/("%) 0.22 m3/m3 0.4 for static holdup and gas-phase dispersion 1.0 for liquid-phase dispersion
used here because the slight decrease in accuracy is outweighed by a large improvement in computational efficiency. The equations governing mass transfer in the film are derived from the reactions in Table I. In addition, two boundary Conditions are required for each component. For the liquid bulk boundary, the boundary conditions require that the film side concentrations are the same as the bulk side concentrations. The equations at the gas boundary are made more complicated by the presence of instantaneous reactions. However, they can be handled by requiring mass conservation at the boundary and equilibrium for the instantaneously reacting components, as was done by Cornelisse et al. (1980). The resulting equations for the system are [H+] + [R,NH+] - [HCOS-] - 2[CO3'] - [HS-] 2[S=] - [OH-] = 0 (29) Note that the gas-phase concentrations appearing in eq 20 and 23 are those at the interface, not in the bulk gas phase. These interfacial concentrations are related to the bulk gas composition and the transfer rate by eq 30 (Treybal, 1980). Equation 30 is solved with the other equations governing the film to compute the final solution for the file profile of each component.
[H+] + [RSNH'] - [HCOS-] - 2[CO3'] - [HS-] 2[S=] - [OH-] = 0 (18) The boundary conditions at the liquid bulk are all of the form shown in eq 19, which sets the concentration in the film at the film-bulk liquid interface equal to the concentration in the bulk liquid:
[clIx=O
= [Cllbulk
(19)
The boundary conditions at the gas interface are derived from the mass conservation equations, vapor-liquid equilibrium, and the equilibrium equations for the instantaneously reacting species. These are shown in eq 20-29.
Orthogonal Collocation. Orthogonal collocation on finite elements (Finlayson, 1980) is used to solve two systems of differential equations: the system describing the overall mass balances in the column, and the system governing interphase transport for the MDEA-H2S-C02 system. ,The differential equations were converted to nonlinear equations which were then solved with the pseudo-Newton-Raphson iteration technique described by Broyden (1965). Model Parameters. A key problem that is encountered while attempting to develop a packed column model is the choice and availability of appropriate modeling parameters. The model developed here uses parameters that have been correlated previously and have been used in several packed column modeling efforts. A discussion of their use in this model follows. Axial Dispersion Coefficients. The axial dispersion coefficients for the gas and liquid phases have been measured by several workers but show wide disagreement (Burghardt and Bartelmus, 1980). In this model, representative values for gas and liquid dispersion coefficients were chosen. Liquid-phase dispersion coefficients were taken from Bennett and Goodridge (1970) because their work also included an analysis of static holdup. Dunn et al. (1977) reported values for gas-phase dispersion coefficients based on a relatively large data base, and these
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 639 were chosen for use in the model for this reason. Mass-Transfer Coefficients and Interfacial Areas. Mass-transfer coefficients for both gas and liquid phases and interfacial area were determined from the correlation developed by Onda et al. (1968). This correlation has been tested for some physical absorption cases by Kelly et al. (1984) and was shown to be better than several other reported in the literature. The correlation is easily programmed and is dimensionally consistent. Static Holdup. The parameters associated with the static holdup are especially difficult to obtain. Several approaches have been suggested for the measurement of the amount of static holdup and the interchange rate with the dynamic holdup. Shulman et al. (1955) measured the static holdup by draining experiments. The column was irrigated and then allowed to drain. The liquid that remained in the column was attributed to static holdup. Bennett and Goodridge (1970) and Schubert et al. (1987) have used tracer experiments to measure both the amount of static holdup and the interchange rate. These experiments show a much smaller static holdup than the drainage-type experiments. The interfacial area of the static holdup is also difficult to obtain. Joosten and Danckwerts (1973) and Puranik and Vogelpohl (1974) have attempted to measure this parameter by measuring the interfacial area under different regimes, one in which the static holdup is completely effective (e.g., evaporation) and one in which it is completely ineffective (e.g., physical absorption). The difference between these two is taken as the static interfacial area. However, this approach does not take into account other nonideal flow effects present in the system. For example, the presence of axial dispersion will also cause an apparent change in the amount of interfacial area available for absorption for different absorption regimes. Since there is wide disagreement on the values of the parameters for static holdup, the values used in this work have simply been chosen to be representative of the ranges presented in the literature. The values will give some idea of the effect that can be expected from a system with liquid-phase static holdup present. Phase Equilibria. Two systems are examined in this work: COz in water and HzS and COz in aqueous MDEA. Phase equilibria for the COz-water system are readily available. However the MDEA-HzS-CO2 system presents some problems. Jou et al. (1982) measured total solubilities for HzS and COz in MDEA at varying pressures and MDEA concentrations. However, the concentration of the free H a and C 0 2 in the solution, rather than the total acid gas content, is needed to predict mass-transfer rates. In order to predict the concentrations of the individual species in solution, expressions for the activity coefficients in the liquid and the fugacity coefficients in the gas phase are needed. For the gas phase, the Redlich-Kwong equation of state is used. However, there is no generally accepted equation of state available for the liquid phase. In this work, the method developed by Edwards et al. (1978) is used. The binary interaction parameters were fit to the solubility data of Jou et al. (1982, 1986). The resulting parameters (Lindner, 1988) are able to correlate the available data with an average error of about 10%. Reaction Kinetics for COzin Aqueous MDEA. The kinetics of COP reaction in aqueous MDEA have been studied by several workers. Barth et al. (1984) considered the effect of liquid-phase activity coefficients, but they were limited by their experimental method to MDEA concentrations of less than 0.2 M. Yu et al. (1985) worked
Table I11 temperature pressure liquid flow rate gas flow rate liquid holdup gas mole fraction of cop MDEA concn
40 "C 5 atm 1.4-4.5 kg/(m%) 4 mol/ (m2-s) 0.22 m3/m3 0.4 for static holdup and gas-phase dispersion 1.0 for liquid-phase dispersion 3m
Table IV temperature pressure liquid flow rate gas flow rate liquid holdup gas mole fraction of HpS MDEA concn
40 "C 5 atm 1.4-4.5 kg/(m2.s) 6 mol/(m2.s) 0.22 m3/m3 0.2 3m
with MDEA concentrations of up to 2.5 M but did not include liquid-phase activity coefficients in his analysis of the data, nor did Blauwhoff et al. (1984). For use in the present model, the data of Yu et al. (1985) have been reexamined. The current mass-transfer framework and VLE data were used to determine the apparent rate constant for the COZ-MDEA reaction (Lindner, 1988).
Results The systems under examination, COz-water, and C02-H2S-MDEA, span a broad range of absorption rates. COz in water gives a physical absorption case, where absorption rates are low. COz in MDEA gives moderately paced absorption rates, with a reaction close to pseudo-first order in the film. HzS-MDEA gives high absorption rates with instantaneous reaction. Each of these types of absorption shows a different interaction with the packed column hydrodynamic models examined in this work. The conditions used in this work are shown in Tables II-IV. The results are put in a form that shows the error in predicted height that would be incurred by ignoring hydrodynamic effects. This error in predicted height is given by E Hactual/Hideal (31) where Haad is the packed height predicted for the model when hydrodynamic effects are included, and Hidedis the predicted packed height when plug flow is assumed in the column. For this work, 0.00635-m ceramic intalox saddles were used as a representative model packing (Schubert et al., 1987). This is an important size for laboratory scale work and is expected to show more of an effect than larger packing sizes, since axial dispersion coefficients and static holdup are both larger for smaller packings. C02-Water. Effect of Axial Dispersion. The effect of liquid-phase axial dispersion on the absorption of COz in water is shown in Figure 1. For high specified absorption of COz, Hactudis almost double Hideal. A large effect is expected in this system, since the capacity of the solvent for COz is small. The small changes in the concentration profile caused by axial dispersion have a large impact on absorption. Gas-phase axial dispersion, however, has almost no effect on the predicted packing height. Since absorption rates are low in this system, the gas-phase concentration of COz changes only slightly between the inlet and the outlet. Therefore, there is little driving force for gas dispersion. The maximum error in the predicted packed height for the
640 Ind. Eng. Chem. Res., Vol. 27, No. 4,1988
/'
/
I
/
,
I Figure 1. Effect of liquid-phase axial dispersion in the Cop-water system on the predicted packed height for the conditions given in Table 11. The error in the packed height is calculated by eq 31.
range of conditions shown in Table I1 is less than 2%. Effect of Static Holdup. As has been mentioned in several works (Joosten and Danckwerts, 1973; Patwardhan, 1978), the static holdup is ineffective for physical absorption because it is rapidly depleted, the solvent has little capacity for absorbed gases. Since 20% of the liquid inventory has been assumed to be static, a completely ineffective static holdup would lead to a 20% error in packed height. The error is less than this maximum, however, since even for physical absorption, the static holdup is still partially effective. For the conditions in Table I1 and COz absorption rates in the column up to 0.05 mol/(m2-s),the error (given by eq 31) was approximately constant at 11% C02-MDEA. Effect of Axial Dispersion. Neither gas- nor liquid-phase axial dispersion has a significant effect on C02absorption into MDEA. For the conditions shown in Table 111, the difference between the predicted height including dispersion effects and that for plug flow was never greater than 2 94. This result is expected for a compound absorbing near the pseudo-first-order regime. Since the absorption rate is nearly constant throughout the column, the concentration gradients of each of the species in the system are also nearly constant. Under these conditions, axial dispersion will have very little effect. These conditions correspond numerically to small second-derivative terms in eq 2 and 3. Effect of Static Holdup. Static holdup is expected to have the least effect on absorption with moderately paced chemical reaction (Joosten and Danckwerts, 1973). The static holdup remains effective for absorption since the absorption rate is low, but the capacity of the solvent is high. To examine this, it was assumed that 20% of the liquid inventory in the column was static, and the results of these runs were compared to previous runs in which the entire inventory was assumed to be dynamic. The predicted height of packing for the static holdup cases was never more than 2% higher than the predicted height assuming plug flow in the column for the range of conditions in Table 111. H,S-MDEA. Effect of Axial Dispersion. Unlike the C02-h4DEA case, HzSshows a large effect for liquid-phase axial dispersion. Figure 2 shows the error in predicted height for this system. The error is small for low removal requirements but grows to over 30% for a specification of 2% H$ in the outlet gas at the lower liquid flow rate. This effect is due to the high absorption rates of H2Sand the large difference in absorption rates between the top and bottom of the column. Adjacent portions of the column have large differences in the gradients of H2S and HS-
-
- - -
Figure 2. Effect of liquid-phase axial dispersion in the H2S-aqueous MDEA system on the predicted packed height for the conditions given in Table IV. The error in the packed height is calculated by eq 31.
.
,
+-
-
~
':c2
ic;cJi;ic
c,tlet
3 2 6
C C . L
gas
TC.E
~-__ 3 :
3 c a
- r a c t ~ c n2 '
-,S
Figure 3. Effect of gas-phase axial dispersion in the H2S-aqueous MDEA system on the predicted packed height for the conditions given in Table IV. The error in the packed height is calculated by eq 31.
concentration, and this gives a large driving force for axial dispersion. A t the higher liquid flow rate, the errors are much smaller. In this case, the liquid is less saturated, so dispersion has less of an effect on the absorption rate. Gas-phase axial dispersion also has a large impact on the H2S-MDEA system, for much the same reasons. Figure 3 shows the error in predicted height for this system. For the set of conditions in Table IV, the maximum error at the lowest liquid flow rate is about 12%, but the maximum error at the highest flow rate is almost 40%. Here, the higher liquid flow rates cause the H2Sin the gas phase to be absorbed more rapidly. The rapid change in the absorption rate of HzS through the column provides a large driving force for axial dispersion. Effect of Static Holdup. The static holdup is generally ineffective for the absorption of H2Sinto MDEA. The MDEA in the static holdup is rapidly depleted because of the high absorption rate of HzS. Figure 4 shows the error in predicted height for the low flow rate conditions given in Table IV. It is approximately constant at 6 % . In this case, the low gas-phase concentration of H2S limits the absorption rate, making the static holdup partially effective.
Discussion It is still not clear which elements should be incorporated into a hydrodynamic model for gas absorption in packed columns. Given a sufficient number of adjustable param-
Ind. Eng. Chem. Res., Vol. 27, No. 4,1988 641 small packing used in this work. For larger packing sizes, these effects will be of less significance. However, since many of the larger columns are designed from data measured in smaller equipment, these considerations could be very important for the scaling of data from pilot plants to larger installations.
;
Acknowledgment
---
This work was supported through National Science Foundation Grant CPE-8307023. J. R. Lindner gratefully acknowledges the support of the W. R. Grace Company.
O o 4 1
0021
0
I
1
0 0 02 0 04 0 06 0 08 Specified o u t l e t g a s m o l e fractlon oi
0 1 +i2S
Figure 4. Effect of liquid-phase static holdup in the H2S-aqueous MDEA system on the predicted packed height for the conditions given in Table IV,with a liquid flow rate of 1.4kg/(m*.s). The error in the packed height is calculated by eq 31.
eters, most frameworks described in the literature can be made to work, at least over a limited range of conditions. The approaches used by Shulman et al. (1955) and Patwardhan (1978) are supported by experiments measuring effective interfacial area, such as those summarized by Puranik and Vogelpohl (1974) and by Joosten and Danckwerts (1973). These hydrodynamic models are able to explain the variation in effective interfacial area with changes in absorption regime. For physical and instantaneous absorption, these methods predict a lower interfacial area, since the static holdup is not effective for gas absorption in these regimes. For absorption with a slowpaced chemical reaction, they predict that both the static and dynamic holdup contribute to the total effective interfacial area. Several problems arise with these approaches, however. They require accurate determination of the static holdup and associated interfacial area; these parameters are difficult to measure directly. Also, given the small amount of static holdup that has been measured under dynamic conditions (Bennett and Goodridge, 1970; Schubert et al., 1987), dispersion-based models may be more useful for packed column simulations. It should be noted that a column model based on axial dispersion behaves similarly in some respects to one based on a static holdup approach. For liquid-phase axial dispersion, the deviation from plug flow is largest for the physical absorption and instantaneous reaction cases and is lowest for moderately paced chemical reaction. This is the same result expected for a packed column model based on static holdup. Because the results are similar, models of either type could be used to account for nonideal flow conditions in a packed bed. However, axial dispersion based models have some distinct advantages. (1)Axial dispersion models require fewer parameters than static holdup models. (2) The parameters that are required are more accessible to experimental measurement. (3) Models based on axial dispersion have fewer variables. Static holdup models require liquid concentrations for both the dynamic and static holdup, increasing the computational effort required. (4)The existing data base for the parameters necessary in an axial dispersion model is larger than that for static holdup. Hydrodynamic effects can have a serious impact on packed column performance. This effect is largest for the
Nomenclature a d = interfacial area for the dynamic liquid, m2/m3 a, = interfacial area for the static liquid, m2/m3 aH20= activity of water c, = dynamic liquid concentration of component i, mol/L D, = gas-phase axial dispersion coefficient, m2/s D,= liquid-phase axial dispersion coefficient, mz/s D,= diffusivity of component i Fg= gas-phase mass-transfer coefficient, mol/(m2.s) L = height of packing in column, m N = rate of mass transfer, mol/(m2.s) P = pressure, atm Qg = gas flow rate, mol/(m2-s) Q1 = dynamic liquid flow rate, m3/(m2.s) Q, = exchange rate from static to dynamic phase, l / s rdL= rate of production of component i in dynamic liquid phase by bulk reaction, mol/(m3.s) r8, = rate of production of component i in static liquid phase by bulk reaction, mol/(m3.s) s, = static liquid concentration of component i, mol/m3 T = temperature, K 1: = position in liquid film, m y, = gas-phase mole fraction of component i z = position along column, m Greek Symbols a,= absorption rate of component i into dynamic liquid, mol/s
fl, = absorption rate of component i into static liquid, mol/s b = thickness of liquid mass-transfer film, m y t = liquid activity coefficient for component i & = fractional holdup of dynamic liquid & = fractional holdup of gas & = fractional holdup of static liquid di = fugacity coefficient of component i Registry No. MDEA, 105-59-9; COP,124-38-9H2S,7783-06-4.
Literature Cited Baldi, G.; Sicardi, S. Chem. Eng. Sci. 1975,30,617. Barth, D.; Tondre, C.; Delpuech, J.-J. Chem. Eng. Sci. 1984,39,1753. Bennett, A.; Goodridge, F. Trans. Znst. Chem. Eng. 1970,48,T232. Blauwhoff, P.M. M.; Versteea, - G . F.; van Swaaii, W. P. M. Chem. Eng. Sci. 1984,39,207. Brittan. M. I.: Woodburn. E. T. AZChE J. 1966.12. 541. Broyden, C. G. Math. Cohput. 1965,19,577. Burghardt, A.; Bartelmus, G. Znt. Chem. Eng. 1980,20,117. Cornelisse, R. A. A.; Beenackers, C. M.; van Beckum, F. P. H.; van Swaaij, W. P. M. Chem. Eng. Sci. 1980,35,1245. Dunn, W. E.; Vermeulen, T.; Wilke, C. R.; Word, T. T. Ind. Eng. Chem. Fundam. 1977,16, 116. Edwards, T . J.; Maurer, G.; Newman, J.; Prausnitz, J. M. AIChE J. 1978,24,966. Finlayson, B. A. Nonlinear Analysis in Chemical Engineering; McGraw-Hill: New York, 1980. Joosten, G. E. H.; Danckwerts, P. V. Chem. Eng. Sci. 1973,28,453. Jou, F.; Mather, A. E.; Otto, F. D. Znd. Eng. Process Des. Dev. 1982, 21,539. Jou, F.;Otto, F. D.; Mather, A. E. Presented 1986 Annual Meeting of AIChE, Miami Beach, FL, 1986,Paper 140b. Kan, K.; Greenfield, P. F. AZChE J. 1983,29, 123. Kelly, R. M.; Rousseau, R. W.; Ferrell, J. K. Ind.Eng. Chem. Process Des. Deu. 1984,23,102. ,
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Lindner, J. Ph.D. Thesis, The Johns Hopkins University, Baltimore, MD, 1988. Nauman, E. B.; Mallikarjun, R. Chem. Eng. J. 1983,26, 231. Olander, R. D. AIChE J. 1960, 6 , 233. Onda, K.; Takeuchi, H.; Okumoto, Y. J . Chem. Eng. Jpn. 1968, 1 , 56. Patwardhan, V. S. Can. J. Chem. Eng. 1978,56, 56. Puranik, S. S.; Vogelpohl, A. Chem. Eng. Sci. 1974,29, 501. Schubert, C. N.; Lindner, J. R.; Kelly, R. M. AIChE J. 1987,32,1920. Shulman, H. L.; Ulrich, C . F.; Wells, N. AIChE J . 1955, 1, 253. Shulman, H. L.; Mellish, W. G.; Lyman, W. H. AIChE J . 1971,17,
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Received for review May 19, 1986 Revised manuscript received November 5, 1987 Accepted November 27, 1987
Multicomponent Batch Distillation. 1. Ternary Systems with Slop Recycle William L. Luyben Process Modeling and Control Center, Department of Chemical Engineering, Mountaintop Campus, 111 Research Drive, Lehigh University, Bethlehem, Pennsylvania 18015
The capacity factor methodology developed by Luyben for binary batch distillation is extended to the separation of ternary mixtures. The processing strategy of recycling the two slop cuts back into the next batch is used. The effects of both design and operating parameters are explored by using digital simulation: number of trays, reflux ratio (both fixed and variable), initial still charge, relative volatility, and product purity. The capacity factor can be used to determine the optimum number of stages and the optimum reflux ratio. Results show little difference in capacity between an optimum fixed reflux policy and a variable reflux policy. Capacity increases with increasing number of trays and increasing relative volatility. Batch processing is becoming increasingly important in many chemical companies as the trend to specialty, small-volume, high-value chemicals continues. Batch distillation columns are frequently an important part of these processes. Batch distillation has the advantage of being able to produce a number of products from a single column. Even though batch distillation typically consumes more energy than continuous distillation, it provides more flexibility and involves less capital investment. A single column can also handle a wide range of feed compositions, number of components, and degrees of difficulty of separation. Since energy costs are not too significant in small-volume, high-value products, batch distillation is often attractive for this class of products. The batch distillation process is characterized by a large number of design and operating parameters to be optimized: the number of trays, the size of the initial charge to the still pot, and the reflux ratio as a function of time (during the product withdrawal periods and during the slop cut periods). In binary separations, there are two products and one slop cut. In ternary separations, there are three products and two slop cuts. Batch time is established by the time it takes to produce the two distillate products and the heavy product left in the still pot at specified purity levels. Most of the work on batch distillation has been limited to the separation of binary mixtures: for example, Luyben (1971),Kerkhof and Vissers (1978),and Gonzalez-Velasco et al. (1987). Ternary batch distillation was studied by Stewart et al. (1973),both theoretically and experimentally. They showed the effects of reflux ratio and number of trays on a measure of separation performance called the average product composition. Van Dongen and Doherty (1985) studied multicomponent, azeotropic, batch distillation. The slop cut in a binary separation can usually be recycled back to the next batch since its composition is often
not much different from that of the feed. The slop cut is the distillate that is removed during the period when the overhead contains too much heavy component to be used in the light product and the material left in the still pot and column still contains too much light component to meet specifications for the heavy product. For ternary systems, there could be two slop cuts. The first will contain mostly the light component and the intermediate component. The second slop cut will contain mostly the intermediate component and the heavy component. In this paper, we assume that both of these slop cuts are recycled back into the next still pot charge. Clearly, this makes little sense from a thermodynamic viewpoint. Alternative operating strategies should be able to improve the efficiency of the system. These include (1) saving up a number of slop cuts and doing binary batch distillations on each of the slop cuts; (2) charging fresh feed to the still pot and feeding the slop cuts into the column at an appropriate tray and at an appropriate time during the course of the next batch; and (3) using the first slop cut to fill up reflux drum (and perhaps the column) prior to the start-up under total reflux conditions in the next batch cycle. The only operating policy to be considered in this paper is recycle of all slop cuts. Although this operation may not be the most efficient, it is certainly the most simple and most widely used in practice. Therefore, it has been used in the initial studies of multicomponent batch distillation. Studies of alternative schemes will be reported in a future paper. Another aspect of batch distillation that becomes much more complex as we move from binary up to multicomponent systems is the question of finding the optimum operating reflux ratio policy. Work on binary systems (Coward, 1967) showed little improvement in going from a constant reflux ratio operation to a more complex constant composition operation or even to the sophisticated
0888-5885/88/2627-06~2~0~.50/0 0 1988 American Chemical Society
