Ind. Eng. Chem. Res. 1987,26, 65-72 McCellan, A. L. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cerrito, CA, 1974; Vol. 11. McEachern, D. M.; Sandoval, 0.;Inigaze, J. C. J. Chem. Thermodyn. 1975, 7, 299. McHugh, M. A. In Recent Developments in Separation Science; Li, N. N., Carlo, J. M., Eds.; CRC: Boca Raton, FL, 1984; Vol. IX. Miller, K. J.; Savchik, J. A. J. Am. Chem. SOC.1979,101,7206-7213. Mollerup, T. Fluid Phase Equilib. 1981, 7 , 121-128. Oellrich, L. R.; Knapp, H.; Prausnitz, J. M. Fluid Phase Equilib. 1978,2, 163-171. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Rev. Chem. Eng. 1983, 1, 179. Peng, D.; Robinson, D. B. Znd. Eng. Chem. Fundam. 1976,15,59-62. Peter, S.; Brunner, G. Angew Chem., Znt. Ed. Engl. 1978, 17, 746-750. Prausnitz, J. M. Molecular Thermodynamics of Fluid Phase Equilibria; Prentice-Hall: Englewood, NJ, 1969. Prausnitz, J. M. Asilomar Conference Grounds, Pacific Grove, CA, 1977. Randall, L. G. Technical Paper No. 102,1985;Hewlett-Packard,San Diego.
65
Sanyal, N. K.; Ahmad, P.; Dixit, L. J . Phys. Chem. 1973, 77, 2552-2556. Schmitt, W. J.; Reid, R. C. presented at the AIChE Annual Meeting, San Francisco, 1984 Paper 103d. Schuyler, J.; Blom, L.; van Krevelen, D. W. Trans. Faraday SOC. 1953,49, 1391. Sengers, J. M. H. L.; Morrison, G.; Chang, R. F. Fluid Phase Equilib. 1983,14, 19-44. Taniewska, S. 0.;Goralski, P. J. Chem. SOC.Faraday Trans. 1 1981, 77, 969-974. Thomas, E. R.; Eckert, C. A. Znd. Eng. Chem. Process Des. Deu. 1984, 23, 194-209. Tijssen, R.; Billiet, H. A. H.; Schoenmakers, P. J. J. Chromatog. 1976, 122, 185-203. Whiting, W. B.; Prausnitz, J. M. Fluid Phase Equilib. 1982,9, 119. Wong, J. M.; Pearlman, R. S.; Johnston, K. P. J. Phys. Chem. 1985, 89, 2671. Ziger, D. H. Ph.D. Thesis, University of Illinois at Urbana, 1983.
Received for review April 19, 1985 Accepted May 1, 1986
Estimating Copolymer Compositions from On-Line Headspace Analysis in Emulsion Polymerization Miquel Alonso, Marcel Oliveres, Luis Puigjaner,* and Francesc Recasens Department of Chemical Engineering, Uniuersitat PolitBcnica de Catalunya, 08028 Barcelona, Spain
An improved methodology has been studied for the calculation of instantaneous copolymer compositions that occur during batch emulsion polymerization of monomers exhibiting partial water solubility, as in the case of styrene and acrylonitrile. T o achieve this, a newly designed chromatographic probe installed in the reactor gas space is operated periodically. T o accurately relate vapor compositions to copolymer compositions, the parameters that define the multiple phase equilibria (liquid-liquid-vapor) and the reactivity ratios must be obtained in separate experiments. Thus, liquid-liquid distribution coefficients, as well as monomer activity Coefficients and reactivities, were experimentally determined. By use of simple equilibrium and reaction models, it is thus possible to compute conversion and copolymer compositions from observed vapor analyses.
Introduction and Purpose Emulsion polymerization is an important process by which large amounts of plastics, rubbers and fibers are made. The kinetics and mechanism of the process have been elucidated in the past and are currently interpreted by the theory of Harkins-Smith-Ewart (Gardon, 1972). However, a rigorous extension of these theories to copolymers is not straightforward, although comprehensive models are appearing (Min and Ray, 1974; Ballard et al., 1981). The main subject of interest here is the emulsion polymerization of styrene (ST)and acrylonitrile (AN), where AN exhibits a significant solubility in water. In the general case of batch copolymer production, careful attention is needed in predicting and controlling the composition drift, as this adversely affects the properties and quality of the polymer. In the particular case of ST-AN, a dramatic improvement in product performance with the use of a composition control system has been shown (Hendy, 1975). Composition control can be carried out either by using off-line, time-dependent kinetic models (Haskell and Settlage, 1970; Johnson et al., 1981), time-independent composition models (Hanna, 1957), or off-line, temperature-conversion optimum profiles (Ray and Gall, 1969; Tirrell and Gromley, 1981). Recent work on emulsion polymerization shows the convenience of developing online sensing devices for conversion monitoring in the study of system dynamics (Schork and Ray, 1981; Kiparissides, 0888-5885/87/2626-0065$01.50/0
1980) and copolymer composition control (Hendy, 1975; Guyot et al., 1981; Abbey, 1981). The use of conversion or composition sensing devices requires a considerable amount of knowledge of the chemical nature of the reacting system. In the case of ST-AN, the water solubility of AN complicates the picture. Early studies reveal that, if liquid-liquid distribution equilibrium of AN is considered, bulk and emulsion copolymer curves almost coincide (Smith, 1948). Recent authors (Kikuta et al., 1976; Guillot and Rios, 1982) show that monomer-swollen polymer particles in equilibrium with the water phase determine the copolymer composition. Therefore, if on-line analysis of the global liquid is used for calculating copolymer compositions, the distribution of the feed monomers in the organic phase should be taken into account (Haskell and Settlage, 1970; Guillot and Rios, 1982). To implement a control system practical and robust enough for industrial use, it occurred to us to investigate how to relate the composition of the reactor headspace with that prevailing in the liquid phase responsible for the copolymer composition. In practice, vapor-phase sampling and analysis are much less troublesome than sampling a polymer emulsion, where fouling by coagulum occurs in the lines. Although much information and hardware on sampling techniques for headspace analysis are available (Kolb, 1980; Comberbach et al., 1984), the relationship between the vapor- and the organic-phase compositions 0 1987 American Chemical Society
66 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
a = xA0/xAw
for AN
(5)
p = xso/xsw
for ST
(6)
for water
(7)
6 = xwo/xww
A
B
Component mass balances in phases 0 and W are A = W x A W + MOXA' (8)
Figure 1. Liquid and vapor phases present in emulsion polymerization.
in the case of ST-AN is uncertain. It is also unknown if simple equilibrium relations can be used. The purpose of this paper is to demonstrate the feasibility of calculating the copolymer composition from the vapor composition during the batch emulsion copolymerization of ST-AN. For doing this, the multiple equilibria occurring in the system are first characterized under nonreacting conditions. Next, the effective reactivity raLios are determined. Following the practical approach of Kikuta et al. (1976), the evolution of copolymer composition vs. conversion can be made on the basis of previously determined parameters. A new chromatographic sampling device was designed and used to carry out the vapor analysis. Future work involves the use of a timedependent kinetic model (Alonso et d.,1983) that uses the signals from the vapor sensor presented here for operation and control purposes using proper algorithms.
Theory The reacting emulsion consists of the two stages, A and B, of Figure 1. They take place during the conversion of one after the other. To calculate the copolymer composition, situation A will include stages I, 11, and part of I11 of the classical theory of emulsion polymerization (Gardon, 1972). Stage A is characterized by the presence of an organic phase, 0, in contact with the aqueous phase, W. During situation A, the monomer compositions of phases 0 and W are assumed to be at equilibrium with each other and with the headspace vapor, V. As shown in the results, equilibrium between phases 0 and W still explains copolymer compositions, although monomer droplets are no longer present. Therefore, in situation A we make no distinction between stages I1 and 111. Situation B is reached during the late stages of the batch. During stage B, monomer adsorbed by the particles from the water phase can neither be described by an equilibrum between liquid phases nor by a liquid-solid adsorption equilibrium, as shown later. Copolymer Equation. The standard copolymer equation W S / W=A(Ms/MA)(rsMs + M A ) / ( M s+ rAM.4) (1) is assumed to hold, but it will be rewritten in terms of relative mass fractions as (rSmAfS2+ mSfSfA)/[rSmAfS2 + (mS
+ mA)fSfA + r A m s f A 2 1 (2) Recall that f A , f s , and Fs will change with conversion. Thus, Fs represents the instantaneous mass fraction of ST at conversion 2 in the copolymer when its relative mass fraction in the organic phase is f s . A t 2, component balances are -dS = FS(A0 + So) dZ (3) -dA = (1 - Fs)(Ao + So) dZ (4) Liquid-Liquid Equilibrium. AN and ST present in the organic phase will be assumed to distribute between phases 0 and W according to their partition coefficients FS =
S = W x S w + M0xSo
(9)
W = W x w W+ MoxWo
(10)
subject to
for i = A, S, and W. The relations of these with f A and f s are fA
=
xA0/(xAo
+ xs0)
f s = 1 - f~
112)
The initial conditions for the above system are S = So and A = A , at 2 = 0. The organic phase vanishes at limiting conversion or Mo = 0 at Z = ZL. Liquid-Liquid-Vapor Equilibrium. In order to calculate the composition of the headspace vapor, equilibrium will be assumed to exist between the two liquid phases and the vapor, all at the same temperature. For this to hold, mass transfer between the emulsion phases and the vapor must be much faster than reaction rate. This is generally the case in a batch system. Mole fractions will now be used. By setting the fugacities of each component to be equal in the vapor, water, and organic phases, one obtains PA = X I W y l W P 1 s a t = xloyloPISat
(13)
p s = X2Wy2WP28at = X*oy*OP*sat
(14)
where subscripts 1and 2 refer to AN and ST, respectively. If a gas chromatograph with a flame-ionization (FI) detector is used to analyze the headspace vapor, only the signals from AN and ST will be integrated. Therefore, only mole fractions of AN and ST will be calculated. Let Y A be the relative mole fraction of AN. Then, assuming that x20 = 1 - xl0, YA is obtained from eq 14 as Y A = X 1 ° P ~ s a t y ~ o / ( X 2 0 P 2 s a t ~ ~+o X 1 ° P l s a t y l O ) (16) where the activity coefficients are functions of the organic-phase composition (xl0, x 2 0 ) at the equilibrium temperature. A t a given conversion, eq 5-11 are solved for the eight unknowns (x?, xiw,Mo, and W ) .This provides values of xA0 and xso and f A and f s . By use of eq 2, FS is obtained and eq 3 and 4 can be integrated. With xl0 and x z o , the values of the activity coefficients, yl0 and yZo,are found and the relative composition of the vapor, YA,is obtained from eq 16. Parameters of the Model. Solution of the model described so far requires knowledge of reactivities, rs and r,, as well as those parameters that represent the liquid-liquid equilibrium, a , p, and 6. In order to predict the composition of the vapor phase, the activity coefficients of ST and AN in the organic phase must be known. Saturation or pure-component vapor pressures, P,sat, are taken from the literature. First, liquid-liquid equilibrium data were determined at the reaction temperature but under nonreacting conditions. From this study, distribution coefficients of AN,
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 67
Figure 2. Schematic of data acquisition system. 1, reactor; 2, reflux condenser; 3, temperature control bath; 4, vapor probe; 5, temperature contol relay; 6, pneumatic motors; 7, venturi; 8, GC oven; 9, FI detector; 10, GC microprocessor; 11, pneumatic-electric interface; 12, digital integrator.
ST, and water can be calculated. Assuming that these values hold during a polymerization run, the relative incorporation of ST vs. AN into the copolymer can be related to the corrected composition of the organic phase. In order to calculate the values of the reactivities, a modification of the current Fineman-Ross method was used (Fineman and Ross, 1950). To characterize the activity coefficients, monomer mixtures of AN and ST of varying composition were prepared at the reaction temperature. Activity coefficients were then determined by chromatographic headspace analysis and correlated with composition by use of the Van Laar equations.
Experimental Equipment and Procedures Chemicals. Commercial grades of ST and AN were used after purification. ST was distilled under reduced pressure at 327 K. AN was distilled at atmospheric pressure under nitrogen at 350 K. Soap (sodium lauryl sulfate) and initiator (K2S208)were analytical grade. Distilled water was used from laboratory facilities. Certified grade nitrogen (99.99%) was used for purging oxygen in polymerizations. Reactor. Reactions were carried out in an AIS1 316 stainless steel jacketed reactor equipped with a Pfaudler-type agitator impeller. Hot water, pumped through the jacket from a thermostat bath, was used to control the reaction temperature within *0.5 K. The upper part of the reactor consisted of a glass flange through which a thermometer, a glass reflux condenser, and the vapor sensor probe were inserted (see Figures 2 and 3B). Liquid samples could be taken through a bottom sampling valve. Polymerization runs were conducted at the conditions specified in Table I. A typical run was carried out as follows. Distilled water and soap were dissolved in the reactor and heated to the reaction temperature with agitation and N2 bubbling. Next, the monomer solution was slowly emulsified. After about 30 min, an aqueous solution of the initiator was added. At this moment, the stopwatch was started. Following the Course of a Reaction. Unconverted monomers were determined by gas chromatography using a DAN1 6800 apparatus equipped with a FI detector. Samples of the latex (1cm3) dissolved in dimethylformamide (15 cm3) containing ethylbenzene as internal standard were injected in the GC (1 pL). For the on-line analysis of the vapor phase over the reactor, the data acquisition system of Figure 2 was designed. The essential part of the system is the probe depicted in Figure 3A. It consists of a thin stainless steel tube (1-mm id.) that effects a programmed suction of
INJECTION SAMPLE
1
SAMPLING CARRIER
SAMPLE
I
7
I CARRIER
COLUMN
Figure 3. (A, top) Details of vapor probe, dimensions in mm. (B, bottom) Six-way valves. Table 1. Summary of ExDerimental Conditions A. Polymerization Runs temp, K 338 impeller speed, Hz 6 monomer concn, 9i vol 20 soap concn (SLS), kg/m3 0.85 initiator concn (K2S208), kg/m3 0.3 run no. 1 2 3 4 5 initial S T mass fraction 0.91 0.82 0.63 0.43 0.22 B. Ternary System AN-ST-Water at 338 K global mixtures, '70 mass AN water ST 64.5 0.0 35.5 5.8 11.6 17.5 23.5 29.7 35.8 42.2 48.5 55.0 61.6
35.7 36.0 36.3 36.6 36.9 37.2 37.5 37.8 38.1 38.4
58.5 52.4 46.2 39.9 33.4 27.0 20.3 13.7 6.9 0.0
reactor vapors at prefixed time intervals. The operation of the probe is controlled by the GC microprocessor, as described later. The dimensions of the probe and its location are those of Figure 3A. Inside the vessel, it was partially heated by the liquid mixture. Outside the vessel, on its way to the GC apparatus, it was heated externally by an electrical resistor provided with a temperature controller to maintain 473 K. This avoids condensation in the line.
68 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 10
*P.
, ,
,
.-7--,
i
1
TIME,min
Figure 4. Typical batch polymerizations. Effect of initial mass fraction of ST (see Table I). ZANis conversion of AN a t end of reaction.
The cyclic operation of the probe is as follows. Refer to Figures 2 and 3B. Sampling cycles were programmed by the GC microprocessor (10). This sent a signal to the interface (11),by which compressed air was admitted to the venturi (7). At the same time, pneumatic motors (6) turned the six-way sampling valves to the sampling position (Figure 3B). Depression a t the venturi ( 7 ) induced the flow of vapor to the sampling loop. Next, the six-way valves were switched to the injection position, and carrier gas swept the sample from the loop into the GC column. Simultaneously, the microprocessor (10) started the operation of the integrator (12) by means of the interface (11). The time taken for a complete cycle, including analysis, was only 5 min. The GC column (Supelcoport SP 1000, 2 m long) separated A N and ST a t 393 K. Peak areas provided by the integrator (12) were converted to relative mole fractions. Ternary System AN-ST-Water. In order to determine the ternary diagram, the global mixtures of Table I were prepared. Screw-capped glass tubes were shaken in a thermostated bath at 338 K and allowed to separate at the same temperature. Samples of the upper and lower equilibrium layers were taken by means of a long chromatography syringe. These were directly injected into a chromatograph equipped in this case with a thermal conductivity detector. Hence, the three components were analyzed in both layers. For these analyses, a Chromosorb 102 50-cm-longcolumn was used, operating at a programmed temperature.
Results and Discussion Determination of Parameters. Batch polymerizations were carried out at varying initial fraction of ST, ranging from 22 to 91 wt % ST, i.e., at both sides of the azeotropic composition. This is about 72% ST. Reacted monomers, as well as the polymer formed vs. reaction time, are represented in Figure 4 for four typical runs. As can be seen, ST is consumed a t a faster rate than AN. It is also observed that AN never reaches complete conversion although ST is almost completely used up, but the amount of unreacted A N increases as the initial fraction of AN is augmented. If the experimental instant fractions of ST in copolymer Fs are plotted vs. conversion (Figure 5 ) , it is observed that only run 3 gives a constant composition copolymer. For this run, Fs = 0.72 for a wide conversion interval. As the initial monomers composition is only 63% ST, this clearly
0
!&+&+A+& 0
02
R4
06
08
10
CONVERSION, Z
Figure 5. Instant ST mass fraction vs. global conversion. Arrows represent disappearance of droplets. Numbers on curves are runs of Table I.
Figure 6. Phase diagram for the system AN-ST-H,O a t 338 K. Continuous lines are from this study. Dotted ones are from Smith (1948).
indicates that substantial extraction of AN into water occurs. Experiments reported by other authors (Guillot and Rios, 1982) at decreasing water/monomer ratio show that the effects observed above tend to diminish, i.e., less AN unreacted and a normal position of the azeotrope. In order to correctly predict ST enrichment, as in runs 1 and 2, or AN enrichment, as in 4 and 5, information on the liquid-liquid system of ST-AN-H20 is needed first. This is also needed to determine the reactivity ratios. Figure 6 represents a phase diagram for the ternary system, AN-ST-H20 at 338 K, from which the distribution coefficients, a,p, and 6, can be calculated. Continuous lines are the ones obtained in the present study, while the dotted ones join data points obtained by Smith (1948) at temperatures 233-348 K. The latter were found by neglecting the solubility of ST in water and that of the water in the organic phase. Under these assumptions, the distribution coefficient of AN found by Smith would vary from 4.0 to about 12. In our study, precise measurements of the three components in the organic phase reveal that a and are both nearly constant. For all the mixtures examined (see Table I), a = 8.3 and 0 = 106, irrespective of the composition. Water, however, exhibits a variable degree of solubility in the organic phase. The distribution coefficient of water can be adjusted by means of an exponential as 6 =5X exp[3.02Ao/(Ao+ S o ) ] This expression indicates that, except at high AN mass fractions, the solubility of water in the oil will be very
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 69 I
01
10
,
,
,
,
,
,
. , ,
i
I
I
rs = 0.3
'A = 0.09
Ym=0.31
w
0
02
04
06
08
1
IO
J-VALUE
Figure 7. Kelen-Tudos plot of reactivity ratios. 0
small. For runs 1-4 of Figure 4,6 increases from 0.006 to 0.03. Also, the high value of p = 106 makes the solubility of ST in water negligible. After the liquid-liquid distribution coefficients are available, the reactivity ratios of ST and AN, rs and rA, can be determined by properly analyzing the relative conversions of ST and AN in the reaction runs. The classical method for determining reactivity ratios involves conducting polymerization reactions to low conversion, changing the initial fractions of the monomers. Copolymer is next isolated and analyzed for Fs, while the feed monomer composition, fs, is taken as that of the initial charge. Then, the Fineman-Ross method that is based on a linear form of eq 1 (Elias, 1977) is used to obtain the reactivity ratios. This procedure involves many reaction runs to have significant values of the reactivities. Instead, we used the chromatographic procedure based on all the kinetic curves of Figure 4. During a batch reaction it is possible to obtain as many values of dS/(dA + dS) as needed, while feed monomer compositions, fs, are obtained by solving the liquid-liquid distribution equations at every conversion. In principle, a single reaction run would be sufficient, provided enough composition drift occurs. Experiental error is less, however, if all reaction runs are taken together in the same plot. To obtain rs and PA,we used the method of Kelen-Tudos which is a modified version of the Fineman-Ross method (Kelen and Tudos, 1975) that allows for a more uniform weighing of the experimental data points as compared to the classical Fineman-Ross method. The values of rs and rAare obtained by plotting 7 = G / ( a m+ F) vs. 5 = F / ( a m F),according to
+
9 = rsf
- rA(1 - t ) / a m
(17)
and then making .$ = 1 and f = 0, respectively. cy, = (FminFmm)l/z is a known value. The results are shown in Figure 7. The values obtained by the least-squares regression are rs = 0.30 and rA = 0.09. These are close to those found for polymerization of ST and AN in a solution by Hatate, rs = 0.32 and r A = 0.12 (Hatate et al., 19711, and are used by Kikuta et al. (1976) in their simulation study. As the values of rs and rAare similar to those found in solution copolymerization, this constitutes a further check on the validity of the liquid-liquid partition coefficients. In order to predict the composition of the reactor vapor, the activity coefficients of AN and ST in the organic phase, yIo and yZ0,must be known. They were determined by a chromatographic method recently developed by Shaw and Anderson (1983), based on the classical headspace chromatographic techniques. Shaw and Anderson show that
0
02
OL
06
08
10
MOLE FRACTION OF A N
Figure 8. Activity coefficients of ST and AN in the organic phase.
the activity coefficient of component i in a homogeneous liquid mixture, where it has a mole fraction x i , is given approximately by yi = Ai/(xiAi')
(18)
where Ai is the chromatographic peak area of component i that results in sampling the vapor phase in equilibrium with the liquid in which component i has composition xi. Ai' is the peak area of the vapor when the liquid is the pure component, i, at the same temperature. In our case, monomer mixtures of AN and ST were prepared at 338 K with compositions from 0.15 to 0.73 mole fraction AN. yl0 and yzowere determined by the method explained above using the vapor sensor described in Experimental Equipment and Procedures. The results obtained are presented in Figure 8 where activity coefficients are plotted in the usual manner. The data points of Figure 8 were next correlated by the well-known Van Laar equations. In order to obtain the Van Laar constants, A12 and AZ1,a multiparameter optimization technique was used with solutions restrained by the condition that yl0 and yZ0are thermodynamically consistent. This condition is the one originally derived by Redlich and Kister (1948)
In our case, positive and negative values of the integral compensate each other within 1.8%. Best values of the Van Laar constants are Alz = 0,394 and Azl = 0.822 at 338
K. Copolymer and Vapor Compositions vs. Conversion. Before the headspace vapor composition is related to that of the forming copolymer, it is necessary to see how the measured copolymer composition compares with those calculated with the parameters determined so far. The evolution of the instantaneous copolymer composition with conversion is a more stringent test than the average copolymer composition. Experimental values of the instant composition are determined by the relative incremental incorporation of the components into the copolymer. Experimental values of Fs so obtained are presented in Figure 5, corresponding to the various polymerization runs. Continuous lines in Figure 5 represent the change in the instantaneous copolymer composition, with conversion obtained by integrating eq 2 to 12, using the values of rs and rA of Figure 7. As described in the Theory section, liquid-liquid equilibrium is solved at each
70 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 Table 11. Values of the Adsorption Equilibrium Constants in Late Stages initial ST ranges of mass run no. fraction conversion a' p' 1 0.91 0.96-1 17-3 900-200 2 0.82 0.94-1 17-3 900-10 3 0.63 0.83-0.92 17-3 900-300 4 0.43 0.63-0.82 22-2 1100-100 5 0.22
incremental conversion in order to calculate the monomer compositions prevailing in the organic phase. The values of a , P, and 6 used in the calculations were those obtained from the liquid-liquid distribution study. It is seen in Figure 5 that the agreement between experimental and predicted copolymer compositions is excellent for a wide range of conversions. However, some comments are in order. Conversions at which breaks on the curves appear mark the limit of validity of the present model. It is seen that, at limits, conversions decrease as AN in the copolymer increases. For instance, in run 1 where initial AN is 9%, the model works well up to about 90% conversion. However, in run 4 where AN is increased to 5770, the model is valid to about 62% conversion. In any case, these conversion limits are far above the conversions a t which monomer droplets have disappeared (end of stage I1 of the classical theory of emulsion polymerization). The arrows shown in Figure 5 correspond to conversions a t which monomer droplets are no longer present, according to the literature (Kikuta et al., 1976). For example, in run 2 (Figure 51, the present model allows a precise calculation of the copolymer composition up to 90% conversion, although monomer droplets disappeared at a conversion of about 42%. In summary, it seems that the presence or absence of an actual liquid phase (droplets) is quite irrelevant for the purpose of describing the copolymer composition. For the most part of the conversion interval, monomer-swollen polymer particles could be considered as a liquid phase in equilibrium with the water. Beyond the break points of Figure 5, the model equations for the liquid-liquid distribution reach a point a t which Mo = 0, and the calculation of the copolymer composition becomes impossible. In order to calculate the copolymer composition during these late stages beyond the break points, a liquid-solid adsorption equilibrium for the unconverted monomers is tentatively postulated as suggested by Kikuta (1976). In this case ST and AN would be adsorbed by the polymer particles from the water phase. Component balances during late stage B of Figure 1 become
s = PXSP + WXS" A = PXAP+ WXA" a' =
XAP/XAW
0' = xsp/xsw where P is the mass of polymer formed and W' is the mass of water. a' and p' are the adsorption equilibrium constants for AN and ST, respectively. Equations 19-23 replace eq 5-12 for conversion above the limiting ones for each run. Since an independent determination of a' and p' is difficult to do experimentally, these are taken as adjustable parameters for which adequate values can in principle be found by use of an optimization algorithm.
l
-
0. L 0 02
OL
06 08
10
CONVERSION, Z
Figure 9. Relative mole fraction of AN in vapor vs. conversion. Continuous lines are for model.
0
L0 2 + + d 04 0 6 0 8 IO
0
Ya Calcd Figure 10. Comparison between experimental and calculated mole fractions of AN in vapor for all runs of Table I.
The adjustment procedure shows, however, that no single set of optimum values of a' and p' exist for a given run; in general, a' and p' must be allowed to change with conversion. The best values of CY'and p' that have been found are listed in Table 11. The results of the calculation for the late stages of a batch are depicted by the steep lines in Figure 5 beyond the break points. The fact that a' and p' change so widely suggests that adsorption equilibrium during the late stages may be too much of a simplification. Qualitatively, it indicates a strong tendency for ST to be adsorbed by the particles, while AN tends to remain in the water phase. It also shows that more ST is drawn to the polymer phase the more AN is allowed to react. This has been observed also by other authors. The evolution of the relative mole fractions of AN, YA, in the reactor headspace are reported in Figure 9, corresponding to the same runs of Figure 5. Experimental values of Y Awere determined by using the vapor sensor during the operation of each run. The continuous lines of Figure 9 represent the calculated values of YAobtained by solution of the model with the activity coefficients of AN and S T determined experimentally. A comparison between calculated and experimental values of YAis made in Figure l O , , a l l runs of Figure 9 taken together in the same plot. The average mean-square deviation, considering all points, is below 6.4%. Hence, agreement is satisfactory. The calculation of the headspace composition in Figure 9 is carried out to conversions at which the liquid-liquid and liquid-vapor equilibria can be applied. Just as in the case of copolymer composition, liquid-vapor equilibrium can be safely assumed to hold for polymer conversions
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 71 Table 111. Summary of Results and Values of Parameters system ST AN parameters mi,kg/ kmol 104 53 saturation pressures a t 338 K, 6.66 67.9 kN/m2
02
0 AN
04
06
08
MOL FRACTION VAPOR,
10
determined parameters at 338 K reactivity ratios rs = 0.30 liq-liq distribution coeff (mass-fraction basis) for AN for ST for water
'fa
Figure 11. Relation between relative AN mole fraction in vapor and instantaneous mass fraction of ST in copolymer for all runs.
higher than those at which monomer droplets are no longer present. In this situation, monomers exist adsorbed by the polymer particles rather than as a separated liquid phase. However, they seem to exert their vapor pressures as if a polymer were not present. In other words, the activity coefficients of ST and AN do not seem to be much affected by the presence of the copolymer for a wide range of conversions. In summary, during wide conveersion intervals, the unreacted monomers can be assumed to distribute between the liquid phases and the vapor according to simple equilibrium relations, irrespective of the presence of polymer particles. Therefore, in principle it seems feasible to estimate the instantaneous copolymer composition from that of the headspace vapor. In Figure 11,the copolymer composition, Fs, estimated from the headspace vapor analysis, YA,is presented. The continuous line of Figure 11 represents calculated values of Fs as a function of YA, while experimental data points include all runs of this study. The agreement between experimental and calculated results is quite satisfactory. However, a word of caution is in place. As is seen in Figure 11,a t high values of YA, corresponding to runs 4 and 5, the sensitivity of Fs to changes in YAis very great. In this sense, caution is needed when using the present method for polymerizations at YAover 9070,corresponding to high AN copolymers. Summary and Conclusions The results of this investigation show that batch polymerization of ST and AN can be satisfactorily described by a model that takes into account the presence of an organic phase in equilibrium with the aqueous phase of the emulsion. The composition of the forming copolymer at a given conversion can be calculated from the monomer composition prevailing in the organic phase by using the standard copolymer equation. The results show that the conversions up to the limit at which the present equilibrium model no longer applies are higher than critical conversions at which monomer droplets disappear (end of stage 11). In order to follow the headspace vapor composition during a run, a new chromatographic sensor was developed and used for on-line data acquisition. The sensor is capable of cycled sampling and analysis of the reactor vapor space. A systematic study of the vapor, assumed in equilibrium with the liquid phases of the emulsion, allows an on-line calculation of the instantaneous copolymer composition with enough accuracy. Under the batch reaction mode employed here, the dynamics of the sensor are relatively unimportant, as suggested by the fact that experimental and estimated vapor compositions are in good agreement.
Van Laar const for system AN-ST (1 = AN, 2 = ST)
rA = 0.09 a = 8.3 p = 106 6 = 5 x io+ x
exp[3.02Ao/ (A, + &)I Ai2 = 0.394 A21 = 0.822
In order to estimate copolymer compositions from the values of the vapor analysis, a number of parameters of the system must be made available. Those parameters that characterize the liquid-liquid distribution of monomers, as well as their effective volatilities, have to be determined in separate experiments. Also, reactivity ratios of the monomers are needed. Table I11 summarizes the results obtained in the course of this study. Caution is suggested when extending the use of proposed strategy toward the extreme values of the vapor-phase composition for high AN copolymers. Progress is under way in this laboratory to improve the behavior of the vapor sensor presented here for the operation of semibatch and continuous emulsion polymerization of S T and AN. Acknowledgment The financial support of CAICYT Grant 4010/79 to this project is gratefully appreciated. Commercial monomers were provided free of charge by Arrahona, S. A. This is thankfully acknowledged. Nomenclature A = mass of AN remaining at conversion Z, kg A. = initial mass of AN in reactor, kg f A , fs = relative mass fraction of AN and ST in the organic phase, kg/kg of monomers F = X 2 / Y in Kelen-Tudos method, X = Ms/MA and Y = mS/dMA Fs = mass fraction of ST in instant copolymer, kg of ST/kg of polymer G = X(Y - 1)/ Y in Kelen-Tudos method mA, ms = molecular weights of AN and ST, respectively, kg/kmol MA, Ms = mole concentrations of AN and ST in the organic phase, eq 1, kmol/m3 M",W = total mass of organic and water phase, respectively, in reactor, kg P A , p s , pH.0 = partial pressures of AN, ST, and water, respectively, in reactor headspace at conversion Z, kN/m2 P = mass of polymer formed at conversion 2,kg PFt, P2gat, PHzOBat = pure component vapor pressures of AN, ST, and water, respectively, at reaction temperature, kN/m2 PA, rs = reactivity ratios of AN and ST S = mass of ST remaining at conversion Z, kg So = initial mass of ST in reactor, kg xA0,xs", xwo= mass fraction of AN, ST, and water, respectively, in organic phase xAW, xsw, xww = as above, in water phase xIo,xzo = mole fractions of AN and ST, respectively,in organic phase
Ind. Eng. Chem. Res. 1987, 26, 72-77
72
xIw,xZw = as above, in water phase XAp,Xsp = adsorbed mass of AN and ST, respectively, per
unit mass of polymer, kg/kg of polymer XAW, XsW= dissolved mass of AN and ST, respectively, per unit mass of water, kg/kg of water YA= p a / ( p A+ p s ) , relative mole fraction of AN in the vapor phase, mol of AN/mol of monomers 2 = global mass-fractional conversion ZAN = limiting conversion of AN in polymerization runs (Figure 4) Zr, = limit mass-fractional conversion Greek Symbols u, /3,6 = liquid-liquid distribution coefficients of AN, ST, and H,O, respectively, mass-fraction basis, eq 5-7 u’, p’ = adsorption equilibrium constants of AN and ST, mass basis, eq 21 and 22 ylo, y20, yH2O0 = activity coefficients of AN, ST, and H20, respectively, in organic phase yIw,yZw,T~~~~ = activity coefficients of AN, ST, and H20, respectively, in water phase 7,t , u , = in Kelen-Tudos method, defined in the text Superscripts
o = organic phase w = aqueous phase sat = saturation P = polymer Subscripts 1, A = acrylonitrile 2, S = styrene
L = limii min, max = minimum and maximum values in Kelen-Tudos method Registry No. (AN)(ST)(copolymer), 9003-54-7; ST, 100-42-5; AN, 107-13-1.
Literature Cited Abbey, K. J. ACS Symp. Ser. 1981, 165, 345. Alonso, M.; Oliveres, M.; Puigjaner, L.; Recasens, F. Proceedings of the 3rd Congress of International Information on Genie Chimique; Society of Chimie Industrielle: Paris, 1983; Vol. 1, p 47-1. Ballard, M. J.; Napper, D. H.; Gilbert, R. G. J . Polym. Sci., Polym. Chem. Ed. 1981, 19, 934. Comberbach, D. M.; Scharer, J. M.; Young, M.-Y. Chromatagr. Newsl. 1984, 12, 4. Elias, H.-G. Macromolecules; Wiley: New York, 1977; Vol. 2. Fineman, M.; Ross, S.D. J . Polym. Sci. 1950, 5, 259. Gardon, J. L. Symp. Polym. React. Eng. 1972, 137. Guillot, J.; Rios, L. Makromol. Chem. 1982, 183, 1979. Guyot, A.; Guillot, J.; Pichot, C.; Rios, L. ACS Symp. Ser. 1981, 165, 415. Hanna, R. J. Ind. Eng. Chem. 1957, 49(2),208. Haskell, V. C.; Settlage, P. H. Presented a t the AIChE Annual Meeting Chicago, 1970. Hatate, Y.; Nakashio, F.; Sakai, W. J . Chem. Eng. Jpn. 1971,4, 348. Hendy, B. N. Adv. Chem. Ser. 1975, 142, 115. Johnson, A. F.; Khaligh, B.; Ramsay, J. Presented at the National Meeting of the American Chemical Society, New York, Aug 1981. Kelen, T.; Tudos, F. J . Macromol. Sci., Chem. 1975, A9, 1. Kikuta, T.; Omi, S.; Kubota, H. J . Chem. Eng. Jpn. 1976, 9, 64. Kiparissides, C.; McGregor, J. F.; Hamielec, A. E. Can. J . Chem. Eng. 1980, 58, 48. Kolb, B. Applied Headspace Gas-Chromatography;Heyden: London, 1980. Min, K. W.; Ray, W. H. J . Macromol. Sci., Chem. 1974, C I l , 177. Ray, W. H.; Gall, C. E. Macromolecules 1969, 2, 425. Redlich, 0.; Kister, A. T. Ind. Eng. Chem. 1948, 40, 345. Schork, F. J.; Ray, W. H. ACS Symp. Ser. 1981, 165, 505. Shaw, D. A.; Anderson, T. F. Ind. Eng. Chem. Fundam. 1983,22,79. Smith, W. V. J . Am. Chem. Sac. 1948, 70, 2177. Tirrell, M.; Gromley, K. Chem. Eng. Sci. 1981, 36, 367.
Received for review April 22, 1985 Revised manuscript received January 21, 1986 Accepted March 13, 1986
Gaseous Mass Transport in Porous Media through a Stagnant Gas Ali Una1 Department of Metallurgy and Materials Science, Imperial College of Science and Technology, London, SW7 2BP England
An analysis is presented for gas-phase mass transport in porous media through a stagnant gas. The natural flux ratio rule for isobaric conditions, which requires that the fluxes be inversely proportional to the square roots of the molecular weights, is not met in this system. Accordingly, a pressure difference develops and this superimposes viscous flow upon diffusion. Equations are derived for the flux and the pressure difference, and it is shown that even when the pressure difference is small, the contribution of viscous flow to the flux can be considerable. Flux and pressure difference measurements carried out on the transport of carbon dioxide through stagnant nitrogen in a septum of coarse pores (average pore size 2.5 pm) are in agreement, within experimental error, with those predicted by the equations and hence provide support for the theories available for describing combined transport in porous media. Gas transport in porous media is an important factor in designing isotope separation equipment and nuclear reactors, in predicting reaction rates in catalysts and in gas and solid reactions, and in drying of porous solids. Accordingly, this field has received a considerable amount of attention over the past 2 decades, and the main problems appear to have been sorted out. ”The dusty gas model” developed by Mason and Malinauskas (1983) has been instrumental in the attainment of the present level of understanding. In transport under isobaric conditions (is., diffusion only), the fluxes of the components in a mixture are not
independent; they are related by CNi(Mi)1/2= 0 which, for binary mixture, becomes
(1)
Nl/N, = -t(M2/M1)1”2 (2) This relationship, first reported by Graham (1833), has been verified experimentally, and its applicability is not restricted to the Knudsen diffusion regime; it applies also in the transition and mutual diffusion regimes. Indeed, deviations from this ratio are frequently regarded as prime evidence of surface effects in mass transport.
0S88-5SS5/81/2626-0072~0~.50/00 1987 American Chemical Society
