Ind. Eng. Chem. Res. 1988,27, 2139-2148
2139
significantly due to the decrease in the dispersion of Pt crystallites from 88% to 17%. The redispersion of sintered Pt crystallites in air at 500 "C for 2 h restored 80% of the oxygen-enrichmentcapability of fresh Pt/ y-alumina. The processes of the redispersion of sintered Pt/ y-alumina and the adsorption of the oxygen on redispersed Pt/y-alumina occurred simultaneously. This will decrease the duration of adsorption-desorption cycles. However, it took 2 h to redisperse the sintered Pt crystallites satisfactorily. Acknowledgment I
I
1
3 4 Time ( h r l
I
5
G
We thank the Korean Trader's Scholarship Foundations for a research fund to pursue this research. Registry No. 02, 7782-44-7; Pt, 7440-06-4.
Figure 10. Effect of oxygen adsorption time a t 500 "C on the amounts of oxygen desorbed (Qo= the amounts of oxygen desorbed when adsorption time is 1 h Q = the amounts of oxygen desorbed for various adsorption times).
4 times as much as that of oxygen adsorption a t 10 min. This result indicated that the redispersion of sintered Pt crystallites and the adsorption of oxygen on them occurred simultaneously and that the redispersion was nearly completed within 2 h in oxygen atmosphere at 500 "C. The concentration of the oxygen in air enriched with Pt/y-alumina after it was redispersed in air a t 500 "C for 2 h is presented in Figure 7E. Compared with Figure 7A, 80% of the capacity of oxygen enrichment was restored. The inability of the sintered Pt crystallites to be redispersed completely to the dispersion of fresh Pt crystallites was not a serious problem to the commercial applications but the time needed (2 h) for redispersion was. Further research is required to solve this problem.
Conclusions The enrichment of air with oxygen up to 25% was obtained with 1wt % Pt/y-alumina, when the oxygen in air was selectively adsorbed on Pt/y-alumina at 500 "C for 30 min and desorbed for 14 min by raising the temperature of the Pt/y-alumina column to 640 "C a t a rate of 10 "C/min. Four cycles of adsorption and desorption with Pt/ y-alumina decreased the extent of oxygen enrichment
Literature Cited Benson, J. E.; Hwang, H. S.; Boudart, M. J. Catal. 1973,30, 146. Berry, R. J. Surf. Sei. 1978,76, 415. Birke, P.; Engels, S.; Becker, K.; Neubauer, H. D. Chem. Technol. 1979,31,473. Birke, P.; Engels, S.; Becker, K.; Neubauer, H. D. Chem. Technol. 1980,32, 253. Bond, G. C. Catalysis by Metal; Academic: London and New York, 1962;Chapter 5. Brennan, D.; Hayward, D. 0.; Trapnell, B. M. W. Proc. R. SOC. London, Ser. A 1960,A258,81. Cochran, S. J. J. Chem. Soc. Faraday Trans. 1 1985,81,2179. Flynn, P. C.; Wanke, S. E. J. Catal. 1974,34,390. Foger, K.; Jaeger, H. J. Catal. 1985,92, 64. Foger, K.; Hay, D.; Jaeger, H. J. Catal. 1985,96,154. Graham, T. Phil. Mag. J. Sei. 1866,32, 401. Johnson, M.F. L.; Keith, C. D. J. Catal. 1963,68,473. Kim, H.C.; Woo, S. I.; Kim, Y. G. Hwahak Konghak 1988,26,337. Mastard, D.G.; Bartholomew, C. H. J. Catal. 1981,67,186. Mitchell, J. K. J. R. Inst. Chem. 1831,2, 101. Rutheven, D. M. Principles of Adsorption and Adsorption Pi.0cesses; Wiley: New York, 1984. Schwarzenbek, E. F.; Turkevich, J. US Patent 3400073,1968. Straguzzi, G. I.; Aduriz, H. R.; Gigola, C. E. J . Catal. 1980,66,171. Yang, R. T.Gas Separation by Adsorption Processes;Buttenvorths: New York, 1986.
Received for review August 17,1987 Revised manuscript received June 22, 1988 Accepted July 6, 1988
A Characterization of Diffusion Distillation for Azeotropic Separation J a m e s K. McDowell and J a m e s
F. Davis*
Department of Chemical Engineering, T h e Ohio S t a t e University, 140 W e s t 19th Avenue, Columbus, Ohio 43210
T h e use of a n inert gas filter represents a n alternative t o the conventional methods of separating azeotropic mixtures. Fullarton and Schlunder demonstrated the concept in terms of behavior at a single point in their diffusion distillation experiments and modeling. This study extends the investigation and the description of the process behavior t o an integral column via computer simulation, by making use of additional raw data reported by Fullarton and Schlunder, unused in their analysis. T h e study exposes process parameters for diffusion distillation that are not evident from the differential analysis and provides insight into already established parameters. Results demonstrate purification levels beyond those presented in the work of Fullarton and Schlunder. T h e model presented shows an improvement over the model of Fullarton and Schlunder through more careful property calculations and a better process description. Recent algorithms for dealing with multicomponent mass-transfer coupling interactions are incorporated in the simulation. An inert gas can be used to separate azeotropes by taking advantage of differences in relative rates of diffusion. Such a process, making use of what is referred to as an inert gas filter, offers an alternative to conventional azeotropic separation based on vapor-liquid equilibrium. 0888-5885/88/2627-2139$01.50/0
Separation based upon differences in relative rates of diffusion through a gas introduced into the system have been applied in several areas. Both mass diffusion (Benedict and Boas, 1951) as well as sweep diffusion (Cichelli, 1951) use a carrier gas to separate a binary gaseous mix0 1988 American Chemical Society
2140 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988
ture. While similar in strategy, these reports provide little information for understanding the key parameters important in a liquid mixture separation. They do, however, point out that mass-transfer coupling can be important in modeling such separations. A closely related phenomenon, diffusion of evaporating vapors through an inert gas, was explored in an early work concerning lacquer films (Lewis and Squires, 1937). The objective of the report was to emphasize that such behavior was different from constant boiling mixtures. As a result, several features of the phenomena were not explored, and the notion was not discussed as a means of separation. Recently, the point behavior a t the azeotrope of a coupled inert gas filterheat-transfer process, called diffusion distillation, was discussed and experimentally demonstrated by Fullarton and Schlunder (1983). With an emphasis only on the point behavior, the work offers a partial description of diffusion distillation and, more broadly speaking, some insight into the notion of the inert gas filter for azeotropic separations. Fullarton and Schlunder, fortunately, reported the raw experimental data which included composition and temperature data above and below the azeotrope. These additional data, which was not used in the point behavior analysis, provide the experimental data used in this research for extending the analysis of diffusion distillation and further exploring the notion of the inert gas filter. In the experimental apparatus of Fullarton and Schlunder, the inert gas was contained in the annular gap between two concentric wetted-wall columns. Evaporation occurred a t one wall, while condensation occurred at the opposite wall. The azeotropic mixture was separated by filtering or preferentially passing one of the components through the inert gas. Experimentally, the apparatus was operated differentially by maintaining large internal flow rates. This mode of operation provided negligible composition changes over the length of the column and the data taken therefore approximated behavior a t a single point. The experimental results demonstrated the viability of enriching the 2-propanol fraction of an 2-propranolwater mixture beyond the azeotropic composition using air as an inert gas. With emphasis on the azeotropic separation a t a single point, the analysis of Fullarton and Schlunder did not completely describe the nature of the process nor did the results give an indication of the extent of the separation. The consideration of a practical implementation of this concept for azeotropic separation has motivated the need for further analysis of diffusion distillation in its present wetted-wall configuration. In this paper, we discuss the results of the extended analysis and the viewpoint of the Fullarton and Schlunder experiments, which allows us to use the data. Building around their experimental results, the single-point behavior is extended to an integral column. The model developed in this study permits the investigation of changes in composition, flow rate, and temperature along the column length. This enhanced analysis provides a more thorough description of diffusion distillation and exposes additional important parameters that are not apparent from a differential point of view. The computer model developed for this study takes advantage of recent developments in modeling mass-transfer coupling. Model performance is improved over that presented by Fullarton and Schlunder and also shows strong agreement with the raw experimental data.
centric wetted walls. A stagnant inert gas fills the annular space between the walls. During the operation of the process, a liquid mixture enters the top of the column and flows as a film on the inside of the outer tube. Evaporation occurs at this wall and a vapor mixture forms at the gasliquid interface. The composition of this vapor is a function of the liquid film temperature and composition. Under a composition gradient, components diffuse through the inert gas and condense on the outside of the inner tube. The temperature of the condensing wall is cooled with flowing cooling water. Cooling of the inlet mixture from evaporation is prevented by applying a constant heat flux to the outer tube wall. In the experiments of Fullarton and Schlunder, the tube diameters were such that the annular gap can be regarded as a planar slot. In order to make use of the raw data reported by Fullartun and Schlunder, the azeotropic system chosen for this study is 2-propanol and water, with air as the inert gas. 2-Propanol will be represented by component 1,water by component 2, and air by component 3. Differential Balances. The following equations are presented to describe the changes in process variables along the length of the column. Variables of interest include flow rates, compositions,and temperatures. AU mass and heat transfer is assumed to be in a direction normal to the liquid layer. The prime symbol, I,will denote a variable on the evaporating wall. Variables on the condensing wall will be denoted with a double prime, ”. The change in flow rate over a differential height, dz,is related to the flux of material leaving or arriving a t the film interface. For the evaporating liquid film, the change in L’ over dz can be written as dL’/dz = -NT (1)
Modeling The Physical System under Study. The separation column used by Fullarton and Schlunder (1983) to carry out the diffusion distillation process consists of two con-
(7)
The minus sign indicates that the material is leaving the evaporating film. L’is a perimeter flow rate. Similarly, for the condensing film flow rate, the change in L”over dz is dL”/dz = NT (2) This equation expresses the fact that the flux of material leaving the evaporating film condenses on the condensing side and there is no accumulation of material in the inert gas. The condensing liquid layer flows downward, concurrently with the evaporating liquid layer. The change in mole fraction, x;, over dz is derived from the equation for the component flow, L1’, defined as L1’ = X1’L’ (3) From the definition of the derivative of a product, the change in L,’ over dz can be written as dL’ dxi 1’ - = xl’ - + L‘(4) dz dz dz This quantity is also related to the component molar flux, N,,by d L l ’ / d ~= -N1 (5) By use of the relation in eq 5, eq 4 can be written as dxl’ -1 dz = -(Nl L‘ + x i dz
”)
A similar equation can be written for xi”:
values of x2’ and x i ’ along the column are directly calculated by using the binary relation. x 2 = 1 - xl.
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2141 The change in the evaporating liquid layer temperature depends upon the net energy transfer to the liquid layer. The constant heat flux into the evaporating wall represents the heat input and is denoted as Q‘. The heat loss by the liquid layer is due to latent losses from mass diffusion and losses from sensible heat effects. With these heat losses denoted as Q’, the change in T‘ over dz is dT‘ = Q f - Q ” L’c (8) pL dz The variation in the coolant temperature, T,, is directly related to Q” as (9)
Multicomponent Mass-Transfer Model. The concept of the inert gas filter is centered around the preferential diffusion of certain gas-phase components through a nondiffusing inert gas. This process is necessarily multicomponent, involving three or more components. Because of the widely varying diffusivities, interactions or coupling between diffusing species can be expected. Coupling refers to the diffusion of a t least one of the components in a mixture being affected by the concentration gradients of other components present. In extreme cases, coupling can cause reverse diffusion, osmotic diffusion, or diffusion barriers (Toor, 1957). Coupling has been shown to occur in systems where two or more components are diffusing through an inert gas (Krishna and Panchal, 1977; Krishna et al., 1976; Webb and Sardesai, 1981). Additionally, Fullarton and Schlunder (1983) showed binary models that do not account for coupling and that poorly described the performance of diffusion distillation. Coupling models reported in the literature are based on film theory solutions of the one-dimensional StefanMaxwell equations. These models fall into three categories based on the solution approach: the exact solution (Krishna and Standart, 1976); the linearized solution (Toor, 1964; Stewart and Prober (1964); and explicit solutions (Krishna 1979a,b; Taylor and Smith, 1982). The exact solution of Krishna and Standart contains the fewest assumptions and requires a computer solution for the component molar fluxes. Although, the original algorithm is reported to have convergence and stability problems (Burghardt, 1984; Taylor and Webb, 1981), Taylor and Webb (1981) present a new algorithm with some significant numerical modifications to the original exact solution algorithm. The result is a very robust and efficient procedure that eliminates these numerical problems. The Taylor and Webb version of the exact solution is used to model the multicomponent diffusion and calculate the component molar fluxes for this study. Process Behavior at a Point. In order to calculate the molar fluxes using the Taylor and Webb algorithm, the vapor compositions on each side of the annulus must be determined. These compositions form the driving forces for diffusion through the inert gas filter. The boundary compositions a t a given point are established by the vapor-liquid equilibrium at each of the interfaces. The evaporating liquid layer is assumed perfectly mixed across the lateral cross section with respect to composition and temperature. This implies that xl,’ = x i and that T,’ = T’. The subscript I denotes the variable at the interface. The perfectly mixed assumption has been shown to be successful in the modeling of fractionating evaporators (Davis et al., 1984; Dribika and Sandall, 1979; Honorat and Sandall, 1978; Rohm 1980). Given the compositions xl’ and x i and the temperature T’, the vapor compositions
a t the evaporating film interface are calculated from the phase equilibrium. Assuming the total pressure of the system is low and the gas phase is ideal, the vapor compositions yl’ and y i are calculated by using y : = Tixi’pi*/PT (10) riis the liquid activity coefficient and Pi*is the component vapor pressure. P T is the total pressure and is assumed constant along the length of the column. Once yl’ and y i are calculated, y i , the mole fraction of the inert gas at the interface is calculated from the sum of mole fractions relation: y3/ = 1 - y1’
- y;
(11) The equilibrium relationships a t the condensing interface are analogous to those a t the evaporating film. However, the condensing interface conditions are a function of the evaporating film conditions as well as the cooling water flow rate and temperature. As a result the liquid composition and the interface temperature are not known beforehand, and relationships must be developed to determine the values of xl,” and Ti‘. In condensation, the liquid layer has been treated previously in two ways. One approach is to assume that the liquid layer is well-mixed. This assumption implies that there is no mass-transfer resistance in the liquid layer and gives rise to the relationship
(12) As previously stated, this assumption is applied to the evaporating liquid f i i and has also been used in modeling fractionating condensers and wetted-wall distillation columns (Davis et al., 1984; Dribika and Sandall, 1979; Honorat and Sandall, 1978; Rohm, 1980). The other approach is to assume the liquid layer is totally unmixed, implying the mass-transfer resistance in the liquid layer is infinite. This case gives xl,” in the following form: XI,”
XI?
= XI’’
= Nl/NT
(13)
Equation 13 necessarily must describe the composition for the first drop of condensate on the condensing wall. In a study of multicomponent condensation by Webb and Sardesai (1981),these two liquid layer models were compared, with the results showing little difference between these assumptions. As a result, eq 13 is used in the model presented here to describe the point behavior at the top of the column since it defines the mole fraction of the first drop of the condensate. The mixed model is used to describe the interface composition a t all other points along the column. The interface temperature is calculated from an energy balance on the condensing interface. Energy leaving the condensing interface is removed by the flowing coolant. Q”, the heat removed by the coolant, can be defined in terms of the interface temperature, T,”, as Q” = ho(T,” - T,) (14) where T, is the coolant temperature and ho is the heattransfer coefficient for the liquid film and the condensing wall. Equation 14 has been used successfully in the modeling of heat transfer in multicomponent condensers (Krishna and Panchal, 1977; Krishna et al., 1976; Webb and Sardesai, 1981). Changes in the condensing layer enthalpy in the longitudinal direction are neglected. Since the heat leaving the evaporating interface must equal the heat transferred to the condensing interface, Q” also denotes the heat input to the condensing interface. As a heat input, Q”consists of latent heat and sensible heat contributions. In multicomponent condensers that involve
2142 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988
a gas stream flowing parallel to the liquid interface, the sensible heat transfer is described by forced convection. However, in the case of diffusion distillation, the inert gas is stagnant and there is no forced convection. Heat transfer due to free convection is possible but not easily analyzed, and probably insignificant as shown by the following argument. The ratio of latent heat to heat transfer due to free convection would be bracketed by the ratio of latent heat to heat transfer under forced convection and by the ratio of latent heat to thermal conduction. A comparison of latent and sensible heat contributions in a condenser with forced convection heat transfer was made by Onda et al. (1970). They found that the latent heat contribution was 100 times greater than the sensible heat transfer. Sample calculations with values from the experimental data of Fullarton and Schlunder (1983) show the ratio of latent heat to heat transfer by thermal conduction to be approximately 1000. With these limits, it is assumed that the sensible heat-transfer contribution due to free convection can be neglected. Thus, Q”is described in terms of its latent heat component only. This conclusion combined with an ideal gas assumption allows the heat input to the condensing interface to be expressed in the following form:
Q” = EHu,Nt
(15)
Niis the component molar flux and Huiis the component heat of vaporization at T‘. Equations 14 and 15 can now be combined to form an expression for TI” as shown:
T,” = (CHuNi)/h,+ Tc
(16)
Simulation Conditions and the Sequence of Calculations. Before we begin the calculations, several initial variables must be specified, namely L’, T’, xl’, Q’, L,, and T,. The composition, q’, is chosen to be 0.68, since we are interested in separation through the azeotrope. T’values are chosen from the conditions in the experiments of Fullarton and Schlunder, as is the value for T,. Q’ is set at a value that maintains a relatively constant T’along the length for the column. A value of L, was not provided by Fullarton and Schlunder. An appropriate value was estimated from similar wetted-wall condensation systems (Krishna and Panchal, 1977; Webb and Sardesai, 1981) and L, was assigned 0.03 kmol/(m s). There is a possible division by zero in both eq 6 and 7. In eq 6, L’ = 0 implies that the evaporation liquid layer has been completely transferred and the wall is dry. This condition should be avoided both in the experimental operation and the computer simulation since no separation occurs. Fullarton and Schlunder (1983) do not report the values of L’used in their experiments; thus, values for the simulations were chosen with the dry out condition in mind. With respect to eq 7, L1” = 0 presents a different problem. This condition is an initial condition at the top of the column and makes the use of eq 7 impossible. This situation can be eliminated by combining the overall and component material balances over the differential section. The method is outlined in the following equations: L”(dz) = L’(0) + L”(0) - L’(dz) (17) xl”(dz) = (xl’(0)L’(0) + x l”(0)L”(0) - X I ’ (dz)L ’( dz))/ L ”( dz) (18) Condensate is assumed to form at the top of the column, z = 0. The composition of this material, however, is of little consequence since L”(0) = 0 ensures that the product
xl”(0)L”(O) is zero. The use of the material balances eliminates the need to integrate eq 2 and 7 at the top of the column or at any subsequent position.
3 1f f u s I o n
d i s t I Is t i o r i I
c c)I u m r i
\
L
-
_ _
i
ToTdensote
storage
+or k
kaSd
‘J’I
Figure 1. Material flows in the experiments of Fullarton and Schlunder.
Once the values of L‘, T‘, Q’, xl’, L,, and T, have been specified, the calculations can proceed. The simulated column was arbitrarily chosen to be 1 m in length. For the integration of the differential equations discussed, the column is divided into 100 sections. The computations for the simulation proceed as follows: 1. The vapor concentrations at the evaporating interface are calculated by using eq 10 and 11. 2. An initial value for T,” is calculated. 3. An initial value for xl” is calculated. 4. The vapor concentrations at the condensing interface are calculated by using Equations 10 and 11. 5. The component molar fluxes are calculated using the model of Taylor and Webb (1981). 6. A new value of xl” is computed with eq 13. If the value has not converged, return to step 4 with a new value of XI”. 7. A new value of Ti’ is computed by using eq 16. If the value has not converged, compute a new value by using the method of bisection and return to step 4. 8. Equations 1, 6, 8, and 9 are integrated by using the Adams method. 9. Calculate L” and xl” with the material balances. 10. The above steps are repeated a t each integration. This sequence gives column profiles for flow rates, liquid and vapor compositions, temperatures, and molar fluxes. The simulation was coded in VAX Fortran under VMS and was executed on a VAX 111780.
Model Validation at a Point The results presented by Fullarton and Schlunder (1983) represent process behavior at the azeotropic composition. These single-point results can be used to validate the single-point description developed in the previous section. A simplified depiction of Fullarton and Schlunder’s experimental setup is shown in Figure 1. The feed tank contains a mixture of 2-propanol and water. The feed enters the top of the column and flows down the evaporating wall. As detailed in the model description, material diffuses through the inert gas layer to the opposite wall and condenses. The condensate flows along the length to the bottom of the column. Both liquids flowed as falling films and were sampled for composition analysis as they exited the bottom of the column. The evaporating film flow was recycled to the feed tank, while the condensate was collected separately in a storage tank. The compositions of the evaporating film at the top and the bottom of the column differ negligibly, because the
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2143 Table I. Experimental Values of the Azeotropic Selectivity"
T',"C
SAZ
T'," C
SAZ
30 40 50
0.155 0.158 0.145
60 70 76
0.115 0.076 0.042
Table 111. Condensate Flow Rates at Various Evaporation Temperatures" T',"C n, mol/h T',"C n. mol/h 30 3.57 60 28.87 40 8.14 70 53.83 50 14.94 76 85.57
nFullarton and Schlunder. 1983.
Fullarton and Schlunder, 1983. Table IV. Total Molar Fluxes at Various Evaporation Temperatures
Table 11. Percent Relative Error in SA.Predictions T',"C this model F/S model -7.48 30 4.73 -16.27 40 -1.87 50 -5.48 -20.83 -29.22 60 -12.42 70 -14.50 -30.79 -30.71 76 -13.46
T', "C 30 40 50
S))lO6
17.88 40.78 74.84
NTI
T',
(kmol/(m2
"C 60 70 76
144.62 269.66 428.66
s))106
40 ,:q
Table V. Percent Relative Error in N APredictions T',"C % re1 error T',"C % re1 error 30 33.50 60 23.72 40 30.51 70 17.72 50 23.36 76 9.56
0 15
"
NTI
(kmol/(m2
500
X
0 10
curve
r
0 05
Values
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..........C u r v e
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5
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"
v
"
x
20
30
40
5c
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/'
60
(CEG
70
8L
C ,
Figure 3. Total molar flux at various values of T'.
trends in the azeotropic selectivity. Table I1 compares the relative errors in the prediction of Sm for each of the models. This improvement in predictions can be attributed to a better description of the interface conditions and more precise property calculations. Prediction of the Total Flux. A second test for the model was provided by the measurements of the condensate flow rate. Since the condensate is formed only from material diffusing through the inert gas, it represents a direct measure of the total flux. Table I11 presents condensate flow rates a t xl' = 0.68 determined from experimental data for various values of T'. Given the condensate flow rates, the total flux can be calculated by dividing by the area for mass transfer. The area of transfer for the concentric wetted walls is given in eq 21 (Fullarton and Schlunder, 1983). The length, 2, in A = ?TdLMZ (21) Fullarton and Schlunder's column is 0.580 m, and dLMis the log-mean diameter. The total molar fluxes for the flow rates in Table I11 are presented in Table IV. The transfer area used to calculate the values in Table IV is 0.055 45 m2. Values of NT at specific T'values and a xl' composition of 0.68 are available from the simulation results. Figure 3 compares the experimental values with those from the simulation. The simulation results follow the trend exhibited by the experimental data. Notice that the total
2144
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988
m Series of differential columns
m
Long
single
Column
U
Figure 4. Comparison of a single column with recycle to a series of single-pass columns.
Figure 5. Comparison of a series of single-pass columns to a long single-pass column.
flux grows significantly with an increase in evaporation temperature. This behavior is justified since the vapor pressure is proportional to T” (n > 1) and the diffusivities are in general proportional to the vapor pressure. The relative errors of the predictions are presented in Table V. The percent relative error decreases with an increase in temperature. The predictions are best when the condensate flow rates are high. The increase in error a t the lower temperatures could be due to the difficulty in measuring the lower flow rates. Fullarton and Schlunder (1983) show identical trends in the relative error of their transfer efficiency predictions.
ture of the condensing film was maintained between 15 and 30 O C . In this temperature range, the vapor compositions of water and 2-propanol are less than 0.10, and the equilibrium curves are very flat. The vapor compositions change very little with any change in liquid film composition. As a result, the conditions at the condensing film interface are nearly invariant to changes in temperature and liquid composition. Thus, the experimental measurements made by Fullarton and Schlunder over time, within a very small error, correspond to measurements taken along the long of a very long single-pass column. The raw dynamic data of Fullarton and Schlunder are presented in xl’, xl” pairs a t unknown time intervals for various combinations of evaporating film temperature, annular width, and inert gas. From a mass balance on the condensation side in a differential column, Fullarton and Schlunder (1983) presented the following equation:
Process Extension beyond the Azeotropic Composition The point behavior reported by Fullarton and Schlunder has been used to test the model performance a t the azeotropic composition. However, these results do not extend the characterization of diffusion distillation. It is the unused raw data reported by Fullarton and Schlunder that makes possible the extension of diffusion distillation to an integral column. When a comparison is established between the dynamic behavior of the experimental differential column and the simulated integral column, these raw data provide experimental information for validating our model a t compositions beyond the azeotrope. This comparison is made by recognizing that the operation of the differential column with recycle can be viewed as a series of single-pass differential columns as shown in Figure 4. This analogy is possible because there is a negligible composition difference between the recycle stream and the feed tank. If Fullarton and Schlunder’s experiment were run for an extended period of time, all the contents of the feed tank would eventually be transferred to the condensate storage tank. Similarly, if the number of columns in the series configuration were sufficiently large, again the feed would be entirely transferred to the condensate tank. Samples taken from the differential column with recycle a t some point in time correspond to the sampling of some individual column in the series of differential columns. In the case of the series of differential columns, the condensate is drawn off at each stage. A condensate liquid film is always present in the case of a long single column. If the effects of the condensing side temperature and liquid composition are negligible, then the series of columns behaves as a long single column. These configurations are compared in Figure 5. In the experiments, the tempera-
The boundary vapor composition of the evaporating film is fixed by T‘ and x i . As discussed earlier, these vapor compositions give rise to the component molar fluxes. The values of T’ and xl’ are descriptive of the behavior a t a point in the column. Based on the assumptions of the comparison, the values of T’and xl’ for all practical purposes determine the ratio Nl/NT. This triplet (T’, xl’, Nl/NT)is the means of comparison between the simulation results and the lab data of Fullarton and Schlunder. Raw dynamic data (xl’,N 1 / N T )with air as the inert gas and an annular width of 0.0025 m are used for the comparison. The raw data and the simulated profiles are presented in Figure 6. The agreement is quite good. The consistent prediction shown a t the higher temperature is likely due to free convection enhancements to mass transfer that were not accounted for in the model. Free convection is driven by the temperature gradient across the annular gap. At lower T’values, the gradient would be less and the free convection effect would be reduced, resulting in the better predictions at T‘ = 40 “C.
Discussion of Results Notion of the Selectivity. As shown in eq 22, N1/NT and xl” are interchangeable in a differential column. By use of this relation, the selectivity and the azeotropic selectivity can be redefined as S X I ’ - N1/NT (23)
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2145 n
r-
0
+
V a l u e s from Fullorton & X V a l u e s from Fullorton & ........... S i m u l a t i o n s ot 4 0 C Simuictions O t 7 0 C
Schlunder Schlunder
Ot Ot
40 C 70 C
-Values
from
simulation
..... Volues
from
experiment
-
xx x
YX
+
+
+
+
+ 0
0
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"
20
0
0 60
0 65
0 75
0 70
0 80
"
'
30
"
"
'
'
40
Figure 7. S
"
50
Temperature
0 85
x:
"
"
'
60
(DEG
'
'
'
70
~
'
80
C)
~versua T T'.
Figure 6. Dynamic point behavior at T' = 40 and 70 O C .
This restated definition is a difference between a composition and a flux fraction. In the case of an integral column, the composition of the condensation layer would not necessarily be equal to the flux ratio, N l / N T . For a differential column, with no condensate flow at the top of the column, eq 19 is valid; however, for an integral column with an established condensate flow, it does not describe the selectivity. As a result, eq 23 represents a more general definition of the selectivity, because the flux fraction represents the composition of the material leaving the evaporating film. The amount and composition of material leaving the evaporating film determines how the evaporating film composition will change. These equations represent an improvement over the original definitions presented by Fullarton and Schlunder (1983). Equations 19 and 20 are not valid in the general case. The importance of the flux fraction is emphasized by considering the limits of the selectivity. By use of eq 24 as an example, SAZ would be a maximum if N1/NT = 0. This implies that only water is transferred through the inert gas filter. On the other hand, the azeotropic selectivity would be zero if Nl/NT = 0.68. When a component in the mixture is removed in a ratio that is the same as its composition, then the selectivity will be zero and there will be no change in composition. Viewing eq 24 with these thoughts in mind, it is possible to reexamine the trends in Figure 2. The maximum occurs because N1f NT goes through a minimum. At T'= 40 "C, the boundary vapor compositions and relative diffusivities are such that the transfer of water is maximally preferred. As T'increases beyond 40 "C, the relative transfer of water decreases because the vapor composition driving force for 2-propanol increases since it is the more volatile component. The Definition of the Enrichment. The goal of the separation is to enrich the material coming into the column in 2-propanol. Thus, of principle interest is the change in 2-propanol composition of the evaporating liquid film along the length of the column. The enrichment will be defined as the change in 2-propanol mole fraction over a differential length. This change in composition of the evaporating film was defined in the discussion of the differential balances as eq 6. By use of the relation in eq 1, eq 6 can be rewritten as
Solving eq 23 for Nl results in Nl = -(S + xl')NT (26) Combining eq 25 and 26 results in an expression for the
enrichment in terms of the selectivity and the total flux, namely,
A t the azeotropic composition, the enrichment is defined as
Both the selectivity and the total flux are factors in the enrichment. Notice the enrichment is also a function of L', the perimeter flow rate of the evaporating layer. This aspect is not brought out in the analysis of a differential column. Sensitivity of L'in a Differential Column. From the definition of the enrichment in eq 28, it is possible to write and expression for the flow rate, L', namely,
L' = SA&T(l/(dn
