Analysis of the Role of Stripping Agents in Polymer Devolatilization

Chemical Engineering Science, Vol. 43, No. 3, pp. 429-442. 1988. ooo5-2509/88 s3.00 + 0.00 Punted in Great Britain Q 1988 Pcrgamon Journals Ltd.

ANALYSIS OF THE ROLE OF STRIPPING AGENTS IN POLYMER DEVOLATILIZATIONt

K. RAVINDRANATH and R. A. MASHELKAR Polymer Science and Engineering Group, Chemical Engineering Division, National Chemical Laboratory,

Pune 411008, India

(Received 4 October 1986; accepted in revised form 25 May 1987)

Abstract-A comprehensive model has been developed to analyse the process of polymer melt devolatiliz- ation in the presence of a stripping agent, which performs the function of enhancing the molecular diffusion of the desorbing monomer and reducing the interfacial concentration. The problem leads to a coupled set of non-linear partial differential equations with time dependent boundary conditions. This problem has not been solved in the literature so far. The model enables the prediction of the influence of diffusivity ratios, relative volatility, hydrodynamic conditions, etc. on the devolatilizer performance and provides useful guidelines for the selection of a suitable stripping agent. The strategy developed in this work can be also used for related problems of multicomponent desorption in other systems.

1NTRODUCTlON

The problem of polymer devolatilization is frequently encountered in polymer synthesis and polymer proces- sing operations. Generally the aim is the removal of residual volatile monomer present in the polymer (Biesenberger and Sebastian, 1983). Invariably the polymer contains solvents, water and low molecular weight compounds. All these volatile components must be removed to improve the product quality, reduce the product cost and eliminate health hazards.

When the concentration of monomer is rather high polymer devolatilization is generally carried out by using flash evaporators. During this stage volatile components are removed through the formation of vapour bubbles. Newman and Simon (1980) and Amon and Denson (1984) have developed effective models for analysis this stage of devolatilization. In the final stages of polymer devolatilization, the concen- tration of monomer is further reduced to the desired level (usually to the ppm level). During this stage, the rate of monomer removal is limited by diffusional limitations. Therefore, single screw extruders and twin screw extruders, which can generate high interfacial areas and promote convective mixing, are widely used. A number of models have been developed for analys- ing the process of devolatilization in single screw extruders (Latinen, 1962; Coughlin and Canevari, 1969; Roberts, 1970; Biesenberger and Kessidis, 1982) and in twin screw extruders (Todd, 1974; Collins et al. 1985; Secor, 1986). All these models provide valuable guidelines for determining the efficiency of monomer removal rate. In addition, these models have been used for estimating the effective transport coefIicients and for examining the influence of screw extruder design parameters on the devolatilization process.

In many industrial operations, stripping agents (also known as carrier substances) are added to the polymer

t NCL Communication No. 4150.

to improve the devolatilization performance. For instance, for removing styrene from polystyrene, Werner (1980) found that addition of 3 “/, water helped in reducing the styrene content from 820 to 420 ppm under otherwise identical conditions. The effectiveness of addition of water as a stripping agent on desorption of ethylene from low density polyethylene melt in partially filled twin screw extruder can be seen from the data presented in Fig. 1 (Werner, 1980). In such cases desorption of the two volatile components occurs simultaneously and the simplified models developed in all the references cited in the foregoing cannot be used since they have not taken into account two major factors. In the presence of a stripping agent, the fractional free volume of the polymer is increased, which can lead to a significant increase in the diffusivity of the monomer which is supposed to be removed. Similarly, the partial pressure of the monomer is also reduced which again helps in removing the residual monomer. We will elaborate on these later.

It is important to mention here a recent interesting paper by Vrentas et al. (1985) which tackles a related problem. They developed a model for devolatilization occurring in a film. In their model the film is initially assumed to contain a small amount of monomer and the film is then exposed to a gas stream containing a stripping agent. During this process the absorption of stripping agent and the desorption of the monomer is assumed to take place simultaneously. After a par- ticular time the gas stream is replaced by an inert stream, so that desorption of both the components can take place. They found that the stripping agent can substantially aid the monomer removal process. Their model is not directly applicable, when the stripping agent is added in the beginning of devolatilization process.

The devolatilization of a polymer melt is generally carried out in a partially filled screw extruder under high vacuum and the stripping agents are added in the beginning of the operation itself. In such a case, the

429

K. RAVINDRANATH and R. A. MASHELKAR

16 i I I Illll I I 10' 2 3 5 102 2 3 5 10s

PRESSURk,mbar

1. Enhancement of devolatilization of low density polyethylene by using a stripping agent (Werner. 1980).

exact extent of vacuum applied plays an important role

and the interfacial concentrations cannot be assumed to be zero or for that matter to have a constant finite value independent of time. In fact the interfacial concentrations will change with time and a time depedent boundary condition at the interface has to be used. An additional complication arises due to the great sensitivity of the value of molecular diffusivity of small solutes in polymeric media to small changes in the concentration of volatiie components. Indeed a small change in the fractional free volume in the molten polymer as a result of the presence of a small molecular weight monomer can alter the diffusivities by an order of magnitude (Duda and Ni, 1978).

A realistic model for monomer removal from poly- mer melts in the presence of a stripping agent requires incorporation of al! the above-mentioned complexities, whereas none of the earlier papers consider these aspects. There are no guidelines available in the open literature regarding selection of suitable stripping agents. The influence of the concentration of the stripping agent, diffusivity and the vapour pressure of the stripping agent on the devolatilization process has not been quantitatively examined in the past. We believe that our work provides important guidelines in this regard.

There are two additional motivations behind this work. Ravindranath and Mashelkar (1984, 1985, 1986)

have analysed the final stages of polycondensation involved in the manufacture of polyethylene tereph- thalate. They show that in the presence of side reactions, the rate of polycondensation is actually enhanced, rather than reduced. This is essentially due to the augmentation of the desorption of the key volatile component in the presence of other volatile components which are formed as a result of side reactions. One expects similar phenomena to occur in the presently considered case of simultaneous desorp- tion of two volatile species from a polymeric melt. Additionally, and perhaps more surprisingly, there appear to be no prior analysis of the case of simul- taneous desorption of two volatile species even in the case of low molecular weight systems. The present study thus serves the general purpose of providing framework for analysing these cases too.

MATHEMATICAL MODEL FOR DEVOLATILIZATION IN A

MOLTEN POLYMER FILM

Any model developed for devolatilization in a single screw or a twin screw extruder should incorporate the

following specific aspects:

-Desorption from the flowing melt pool and from the film deposited on the barrel wall

-The presence ofcirculatory flow of the polymer melt - The influence of backmixing.

Stripping agents in polymer devolatilization 431

In the present work a mathematical model will be developed mainly for the process involved in the first step mentioned above, namely devolatilization in a thin stagnant film. This model can then be used for developing a complete model for single screw or twin screw extruders.

Consider a thin stagnant molten polymeric film of a finite thickness placed on a solid impermeable surface. Initially the polymer film has a thickness L and it contains a small amount of monomer (pl 0) and stripping agent (pzO). At time t = 0, the polymer film is exposed to vacuum, which assigns a specific value of concentration of monomer and stripping agent at the interface (x = L). The thickness of the film is assumed to be very small. Hence the monomer and the stripping agents are assumed to be removed only through the interface. In the present analysis of ternary diffusion process, it is assumed that p, and p2 are sufficiently small so that the cross diffusion coefficients can be neglected compared to the principal diffusion coef- ficients (Vrentas et al., 1985). Then the mass balance equations for unsteady state diffusion in a finite film can be written as

a~, a apI -=- D,-

at ax ( > ax

dP2 a -=_ at dX ( > D dp2

2 ax

(1)

Here p1 is the mass density and D, is the diffusivity of component 1. Subscript 1 refers to the monomer and subscript 2 refers to the stripping agent. The boundary conditions are

p, = p,,; p2 = p20; t = 0, 0 Q .X 6 L (3)

3PI -=o; +o: t>o,x=o at (4)

PI = Pli; P2 = PZii t > 0, x = L. (5)

pIi and pzi refer to the concentration of components 1 and 2 at the interface. The gas phase resistance is assumed to be negligible due to the low pressures employed in the devolatilization process. The concen- tration of the monomer and the stripping agent will be assumed to be small. Therefore the variation of film thickness with time is neglected. The self diffusion coefficients D1 and D2 depend on the concentration of the diffusing species. These are given by Vrentas et al. (1985).

exp - (WI @: +w,P:

D, = D,,exp - (WI p: &/<I 3 + WI2 p;I + w3 Vf 523)

VFFilY

V FH- Y

- +,, + T- T,,)w,

+f+& + T-T&w,

++(K2 + T- T&w,. (8)

Here D, 1 is the pre-exponential factor for component I, w1 is the mass fraction of component I and @ is the specific critical hole free volume of component I for a jump. Here subscript 3 refers to the polymer. P,, is the average free volume per gram of mixture and y is the overlap factor for free volume. The parameters K, ,, K 21, K~I. Kzz, K,, and K2, are free volume par- ameters, which can be determined from the solvent and polymer viscosity data (Duda et a[., 1982). T is the temperature and T,, is the glass transition temperature for component I. 5 1 3 and tz3 are the ratios of critical molar volume of components 1 and 2 to the critical molar volume of jumping unit of polymer.

Equations (lk(5) are nondimensionalised using the following variables

B = D;/D:

0: = D, (pl = 0; ,u2 = 0)

0; = Dz(pl = 0; pr = 0).

Equations (l)-(5) are now converted to

(13)

(14)

(15)

(18)

aM* ---=Q aM2 all

-=Q e>o; q=o 3’T

(19)

The mass fractions of component 1 and 2 were calculated by using the following equations:

Ml W ‘=M,+M,+M,

M, w2 = M,+M1+M3

(21)

(22)

where Mj = V,. (23)

To proceed with the actual calculations, the initial mass fractions of component 1 and 2 were fixed and pIo and pzo are calculated from the following

432 K. RAVINDRANATH and R.A. MASHELKAR

expression:

WlO PI0 =

w20 Pzo = -

v/lw,.+ Vzw,,+ Psw,,' w

The solution of eqs (16) to (20) can be found, once the values of the following parameters are known: PI, P:, K>,/Y (K>,+ T-T&~,,,<z~, B,w~~/w~~,w~*/w~“,P~i and pZi. Vrentas et al. (1985) have discussed the possible range of values for 8,, fit, K Jy (K2, + T

- r,,), 5 1 3 and tz3 and these have been used in the present work (see Table 1). The value of p depends on the type of stripping agent used. w10/w30 and w20/w30 are the input parameters. pli and pZi depend on the applied vacuum.

Cakulation of interfacial concentrations (p ,i and p,,) In the limit of very low concentrations of p ,iand pZi,

we assume that the Flory-Huggins theory for binary mixtures (Biesenberger and Sebastian, 1983) can be used to describe the theormodynamics of the ternary system. Then the partial pressure of component 1 and 2, in the simplified form, can be written as

PI =P?+I exp(l+X,)=P~P,p,iexp(l+X,) (26)

p2 = Pz$Z exp(1 +x,) = PT vZ pZi exp(l +x,). (27)

Here Py is the pure component vapour pressure, 41 is the volume fraction and x1 is the polymer-solvent interaction parameter for component I. Rearranging eqs (26) and (27) and expressing p1 and pz in terms of the applied vacuum (P), we get

and

(29)

where CL = PIPye +XI and 6 = Pyel+xz/Pyel +x1. While analysing the devolatilization process of a

single component, all the previous workers (Latinen, 1962; Coughlin and Canevari, 1969; Denson, 1983) have assumed p ,i to zero. With such an assumption, the exact effect of vacuum on devolatilization cannot be analysed. In addition for a fixed applied vacuum, pli and pzr are not constant for the case of desorption of

Table 1. Typical properties of monomer, stripping agent and polymer (Vrentas et al., 1985).

Property

Stripping Monomer agent Polymer

1 2 3

P: (cm3/d 0.90 0.90 3; (cm3/g)

0.80 1.20 1.20 0.90

K,,lY w,, + T- T,,)

(cm”/iz) 0.40 0.40 0.05 513 0.75 0.75 -

x1 0.5 0.5

Table 2. Some typical systems where simultaneous desorp- tion of two comoonents is encountered

System Desorbing volatile components

1.

II.

Removal of reaction byproducts (1) Polyethylene terephthalate (2) Polybutylene terephthalate (3) Nylon 6 Removal of residual monomer (1) Polystyrene

(2) Polymethyl methacrylate

(3) Low density polyethylene

Ethylene glycol, water and acetaldehyde Butanediol, water and tetrahydrofuran Caprolactum and water

Styrene and water (stripping agent) Methyl methacrylate and water (stripping agent) Ethylene and water (stripping agent)

two components. Indeed they vary with time. The interfacial concentrations (eqs 28 and 29) depend on the vapour composition, which is in turn determined from the desorption rates of components 1 and 2. But the individual desorption rates can vary with time due to the continuous change in diffusivity value and also due to the continuous change in the concentration profile of the components in the film. Therefore, p1, and pZi will change with time. We now propose a new procedure for calculating pl, and pzi as a function of time. If p 11 and pZi values at time f3 are known, p li and pr, at 0 + A8 can be determined by proceeding the following steps.

(1) Assume p ,, and pZ, values at 8 + A6, based on the values at time 8.

(2) Calculate the desorption rates of components 1 and 2 from the following equations.

N, =; s t+At _-D ap, dt

@fAO

’ L?x = ___ __

f x=L

(3)

(4)

D, aM, --~ 0: h- q=,

d6, (30)

s

t+At OfAO

____

I

(31)

Because of the sharp gradients at the interface a specially developed method (described in the Appendix) is used for calculating N, and N,. With these values of N 1 and N z, calculate the mole fraction of the components in the vapour phase from

N1 ” = N,+N2

N2 y2 =Nl+N,’

Calculate p ,i and pzi using eqs (28) and (29).

(32)

(33)

Stripping agents in polymer devolatilization

(5) If the calculated and assumed values of p ,, and pzi are not within a prescribed error bound ( 4 0.1 “/,), repeat steps (1) to (4).

While writing eqs (32) and (33), it is assumed that the vapours are removed at the same rate as they are formed and there is no backmixing in the vapour phase. This is true only for devolatilization in a thin stagnant film considered in the present work. For devolatilization in an extruder, the calculation of p li and pZi is more involved, since the vapours formed at time f are mixed with those formed at time t + At. Therefore the vapour at the outlet or the extruder will represent as average composition of the vapours formed at different times. This important fact has to be taken into account for developing a complete model for screw extruders.

RESULTS AND DISCUSSION

It has been customary to analyse the performance of a devolatilization process in terms of the fraction of extractable components remaining unextracted, fi 1.

6 1

= PI-Pli

PlO -P,,’ (34)

As we have already pointed out earlier, pi, is assumed to change with time. Hence eq. (34) is not useful for presentation of the results. Therefore we shall analyse the effectiveness of the devolatilization process in terms of the following parameters.

433

s 1

M, = MI dv; (35) 0

1

iii, = s

Mzdv. 0 (36)

Here A, represents the fraction of the monomer remaining in the polymer. R, represents the ratio of the amount of stripping agent in the polymer to the initial amount of monomer. In the present work, all the calculations are performed assuming that the polymer contains initially one percent of monomer (w,~/w~~ = 0.01).

influence of stripping agent on desorption (a = 0) As mentioned earlier, the previous workers have

assumed pli to be zero, which is equivalent to the assumption of c1 = 0 in the present work. The effect of the initial concentration of a stripping agent on i\;i, is shown in Fig. 2 for cc = 0 and p = 0. When /I = 0, the diffusivity of the stripping agent is zero and it is not removed from the system. With an increase in the initial concentration of the stripping agent, the free volume of the polymer increases (see eq. 6), hence D, /Dy also increases. Therefore, R, decreases dra- matically with an increase in the stripping agent concentration as shown in Fig. 2.

However, such a dramatic reduction cannot occur when the finite diffusivity of the stripping agent is taken into account (p # 0). The influence of the molecular diffusivity of stripping agent is shown in

Fig. 2. Effect of stripping agent concentration on fi,, u = 0, fi = 0.

434 K. RAVINDRANATH and R.A. MASHELKAR

0 0.1 0.2 o-3 o-4 O-5 0.6 0.7 0.6 0.9 1.0

8

Fig. 3. Effect of diffusivity ratio (8) on M,; M,, = 2, x = 0.

Fig. 3 for the specific case of a = 0 and for a fixed initial concentration of the stripping agent. Larger values of /3 imply faster removal of the stripping agent too. Such rapid removat implies in turn that the contribution of the stripping agent towards the in- crease of overall free volume would decrease as time progresses. This would mean that the favourable influence of the presence of stripping agent in enhanc- ing the diffusivity of the monomer would reduce too. One concludes that stripping agents with large values of p offer no long term advantage, and stripping agents which have low to moderate values of ,!I must be used. In the latter case, the stripping agent will remain in the molten polymer for extended periods and aid in the process of monomer removal. Note that this obser- vation is valid only in the case of OL = 0. When 01 is finite, we get different results depending on the devolatiliz- ation time, as we shall see later.

Influence of applied vacuum or desorptionfor a single component system (a =finile)

In Figs 2 and 3, the effect of applied vacuum on M, is not taken into account. Its influence on M, is now shown in Fig 4. The value of cr depends both on the applied vacuum as well as on the pure component pressure (eq. 28). For typical polystyrene-styrene system, the value of cc changes from 0.001 to 0.01 at 171°C (Biesenberger and Sebastian, 1983), when the applied vacuum is varied from 1 to 10 kPa (which are

typical operating pressures of single screw extruder). As intuitively expected, increasing the vacuum (lower values of a) helps in decreasing A, at a faster rate. Depending on the applied vacuum (u), the final value of M, at longer times is fixed due to equilibrium considerations. For obtaining very low values of M,, the devolatilization process has to be operated at high vacuum.

Simultaneous itxjiuence of applied vacuum and stripping agent on desorption

ti, can be reduced effectively by adding small amounts of stripping agents. This is shown in Fig. 5 for a fixed applied vacuum (x = 0.003). M, decreases continuously with an increase in &?,,. The addition of stripping agent leads to a decrease in the effective partial pressure of monomer in addition to influencing the overall free volume of the polymer. This aids the desorption process. However, the concentration of the stripping agent cannot be increased continuously since the heat input for vaporizing the stripping agent in the devolatilizer will also increase. The effect of a stripping agent on the devolatilization process for different values of a is shown in Fig. 6. It can be seen that the influence of stripping agent is more pronounced at lower levels of vacuum (higher c() in comparison to that at higher levels of vacuum (lower r). This important observation can be explained as follows. At higher values of CL, the stripping agent is effective both in

Stripping agents in polymer devolatilization

3 I I

2

o*oi 0 o-1 0.2 0.3 0.4 0.5 0.6 0.7 O-6 0.9 1.0

Fig. 4. Effect of operating vacuum on 8,; MzO = 0

1-o

s

3

2

xi, 0.1

5.

3

o-01 0 0.1 0.2 0.3 o-4 O-5 O-6 0.7 O-8 0.9

Fig. 5. Effect of stripping agent concentration on M,; o! = O.W3, fl = I,6 = 1.

CES 43:3-c

436 K. RAVINDRANATH and R. A. MASHELKAR

2

0.01 0 o-1 o-2 o-3 0.4 o-5 O-6 o-7 0.6 o-9 I.0

0

Fig. 6. Effect of operating vacuum on ml with (-- ) and withouttPPP) stripping agent; Mzo = 2, p = 1, 6 = 1.

increasing the free volume of the polymer and in reducing the partial pressure of monomer. As c( -+ 0, p ,i approaches zero and the stripping agent is effective only in increasing the free volume of the polymer. Therefore the stripping agent is less effective as c( + 0. The effectiveness of stripping agent in reducing the monomer concentration to a very low level can be seen from Fig. 6. For instance at 6 = 1 (fixed residence time in extruder) and c( = 0.001 (fixed vacuum) we can reduce A, from 0.113 to 0.06 by addition of a stripping agent.

Influence of the diffuusit;ity of‘ stripping agent on desorption

Another important parameter in the devolatilization process is the ratio (fi) of the diffusivity of-the stripping agent to the diffusivity of the monomer. Earlier (see Fig. 3), we examined the influence of /? for a = 0. There we concluded that stripping agents with low values of p are preferable. Now the influence of fi for the case of finite LY ( = 0.003) is shown in Fig. 7. When b = 0, we see that &f, reduces rapidly initially and then reaches a plateau of A, = 0.237. The initial rapid decrease is ascribed to the increased diffusivity of the monomer due to the enhanced free volume contribution by the stripping agent. However, when p = 0, the stripping agent is not removed from the system and the contri- bution of the stripping agent towards the reduction of partial pressure is zero. Thus at longer times (Q > 0.4)

the minimum value of n;i, is determined by vapourliquid equilibrium considerations alone and reaches a plateau.

For moderate values of fi( = 0.1 and l), the stripping agent also continuously desorbs from the system. While it is present in the system it contributes both to enhancement of free volume (leading to enhanced diffusivity of monomer) and also to reduction of partial pressure of the monomer, the latter effect is predominant particularly at longer time scales. Hence M, continues to decrease continuously. For high finite values of p( = lo), we have a curious observation. Due to the high diffusivity of the stripping agent in comparison to that of the monomer, it is rapidly removed at short times. Its effectiveness, therefore, in contributing to the enhancement of monomer desorp- tion rate is negligible.

The above observations offer important clues for the selection of a stripping agent, in that agents with very low or high values of/i should not be selected but those with moderate values of ,8( = 0.1 to 1) are the preferred ones.

Influence of stripping agent in the very low concen-

tration regime In the results discussed so far, we have considered

the effect of stripping agent both on the free volume of the system (leading to a change in the diffusivity of the monomer) and also the change in partial pressure.

Stripping agents in polymer devolatilization

Fig. 7. Effect of diffusivity ratio (fi) on &f,; A?,, = 2, OL = 0.003, 6 = 1.

Recent environmental regulations imply that one has to reduce the monomer concentration to very low levels (few ppm). In such cases, the amount of stripping agent added itself will be negligible and its influence on the free volume of the system will also have to be neglected. It is instructive to consider such a case.

When the free volume contribution of the stripping agent is neglected D, E 0’: and D, = D;.Now the role of the stripping agent is only in decreasing the partial pressure. When the diffusivity of the stripping agent is less than the diffusivity of monomer (namely p < 1), the partial pressure contribution of the stripping agent is not significant as compared to the case when @ = 1. Therefore &f , values for /? = 0.1 are always higher in comparison to those for p = 1 as shown in Fig. 8. For j? = 10, the contribution of the stripping agent is maximum up to a certain time and j%f 1 becomes smaller when compared to the results for j3 = 1. During this time, most of the stripping agent is removed and its contribution at longer times decreases. In the case of p = 1, the contribution of the stripping agent is significant even at longer times. Therefore L@, is minimum for /Y = 1 even at longer times compared to the corresponding results obtained with finite p values considered in this work. For selecting the stripping agent, not only its diffusivity but also the time for devolatilization should be taken into account. There is a limiting design value for p in such cases, in that the

diffusivity of the stripping agent should equal to the diffusivity of the monomer.

be at least

Znfluence of vapour pressure of the stripping agent

(6 + 1) In all the previous calculations, the ratio of vapour

pressures of stripping agent to the monomer is taken as unity (i.e. 6 = 1). The influence of change of 6 on ti, is shown in Fig. 9. In the case of 6 + 0, the stripping agent has very low vapour pressure and therefore it con- tinues to remain in the system. The qualitative trend in this case is similar to the one in the case of p + 0 including the attainment of a plateau. On the other hand for finite values of 6, as expected, the desorption is more rapid.

Influence of periodic mixing of the-film So far, the film was considered to be stagnant (or

unmixed) during the devolatilization process. In actual practice, the film is mixed at definite intervals (depend- ing on the screw speed in the extruder). Therefore it is important to examine the influence of mixing on the devolatilization process.

We assume that the film remains stagnant and it is exposed to the vacuum for a fixed interval of time (@,), and then the film gets mixed. At the end of each such mixing operation, the average concentration of the film was calculated by averaging over the length of the film.

438 K. RAVINDKANATH and R. A. MASHELKAR

O-01 0 0.1 o-2 0.3 o-4 0:5 0.6 0.7 O-6 o-s 1-o

8

Fig. 8. Effect of diffusivity ratio (8) on A%, without considering free volume contribution; MZO = 2, a=0.003,6= 1.

3

2

O-01 I 1 0 0.1 0.2 0.3 o-4 0.5 O-6 0.7 O-6 0.9 t-0

8

Fig. 9. Effect of vapour pressure of the stripping agent on M,; M,, = 2, a = 0.003, 6 = 1.

Stripping agents in polymer devolatilization

0.01 \ 0 0.1 0.2 0.3 o-4 0.5 O-6 0.7 0.0 0.9 1.0

8

Fig. 10. Effect offilm mixing on M, ; MzO = 2, a = 0.003, fi = I,6 = 1; (a) ideal&d penetration theory; (b, c, d) present model.

This average concentration provided the starting con- centration for the next intervals. The results obtained are shown in Fig. 10. In all the cases examined here mixing is shown to help in decreasing the A, value. By mixing at regular intervals, large concentration gradients are created at the interface, which are essential for attaining high desorption rates.

It may be mentioned that recently Sector (1986) has developed a mass transfer model for a twin screw extruder by using periodic mixing of a film. The calculations provided here can be easily incorporated in such a model to enable the development of a complete model for a devolatilizing extruder (see, however, the discussion on the limitations of such an approach in certain regimes presented later).

The role of time dependent boundary conditions in the two component desorption problem

As pointed out earlier, the concentration of the monomer (pJ at the interface is expected to change with time. When B = 0, however p ,i remains constant (Fig. 1 l), since the stripping agent does not contribute towards reduction of the partial pressure of the monomer. Similarly for /3 = I, p 1, remains constant since the desorption rates of the monomer and the stripping agent at any time remain proportional to the initial concentrations of the monomer and stripping agent. For /I < 0.1, p Li increases in the beginning and

then decreases as shown in Fig. 11. The desorption rates of monomer and stripping agent depend on the value of difTusivity and on the concentration gradient at the interface. In the beginning, for p = 0.1, the desorption rate of monomer is greater than that of the stripping agent. The mole fraction of monomer in the vapour phase increases and hence p ,i increases (see eq. 28). When a part of the monomer is removed from the system the rate of desorption of monomer will be less than the rate of desorption of the stripping agent. Therefore, p li will then decrease as shown in Fig. 11. Similar explanation can be offered in the case of the results obtained with B = 10 also.

In desorption processes occuring in low molecular weight systems, the influence of stripping agent on free volume is negligible and only the diffusivity ratios (p) and vapour pressure ratios (6) for the two components need to be considered. When /3 - 1 and 6 - 1 the problem is decoupled and the time invariant boundary conditions at the interface can be safely used. However, in the case when the diffusivities or the vapour pressures of the two components are not equal (p # 1, 6 # 1) the interfacial boundary conditions will change as a function of time, and then the methods developed in this work have to be used,

Limitations of the penetration theory approach A majority of the workers (Latinen, 1962; Roberts,

440 K. RAVINDRANATH and R. A. MASHELKAR

I-C )-

I-

i ,_

I

p 0.1

10

5 I-

3

2

0.01 L

/ I 1 1 I I

/

0 o-1 o-2 o-3 o-4 o-5 0.6 0.7 O-6 C

8

Fig. 11. Effect of diffusivity ratio (/?) 017 M,, pl,/p,o; = 2, a = 0.003, 6 = 1.

1970; Denson 1983; Secor, 1986) analysing the per- formance of the devolatilization equipment have used the penetration theory. It is instructive to compare the model results of the present work with those obtained by using the penetration theory. The penetration theory predicts that the rate of desorption is given by

(37)

Here t, is the exposure time, a is the interfacial area, and D, is the diffusion coefficient of the desorbing monomer. D, can be assumed to be constant only in the case of very low monomer concentration regime. D, otherwise will be a function of monomer concen- tration. Hence it is both time and position dependent.

The interfacial concentration /3,i is constant only for the single component desorption process and it is determined by the applied vacuum alone. For a two component desorption process, p ,i will vary with time depending on the diffusivity of the second volatile component. In fact most of the previous workers (Latinen, 1962; Roberts, 1970; Secor, 1986) have as- sumed pli to be equal to zero for analysing the devolatilization data. What errors can such simplified assumptions introduce in the model predictions? This can be illustrated by using D, = 07 and p ,i = 0.

Equation (37) for the rate of desorption then reduces to

J 40’: y.

e

Following Secot (1986) the material balance for vol- atile component 1 after the first exposure is given by

p*o = p: + t,N,. (39)

Substituting eq (38) in (39) gives

Pt _l_ 40, PlO :‘- 7t

(40)

where 0, = DytJL’. Assuming that the film is mixed after every exposure, the concentration of volatile component after n exposures is given by

ii;&_ /40,\ PI0 \ \i 7t /

where n = 0/G,. The left hand side of eq. (41) is equal to ti, by

definition (eq. 35). We now plot the predictions from eq. (41) in Fig. 10 for Be = 0.01. Wecompare the results of eq. (41) with our results for 0, = 0.01. When Q -C 0.15, eq. (41) predicts higher values of &?f, com- pared to our results and for 8 > 0.15 the reverse is true. This observation can be explained as follows. At small

Stripping agents in polymer devolatilization 441

values of 8, we have D1 > 0’: due to the free volume contribution of the monomer and the stripping agent. The rate of desorption calculated based on our model is higher compared to that calculated from eq. (38). Therefore &Ii, values are lower for our model in the beginning. At longer times p r -+ /, ti because of equilib- rium considerations and the rate of desorption ap- proaches zero. Hence ti, reaches a plateau level. In the derivation of eq. (41), p ,i is taken as zero. Therefore the rate of desorption is significant even at longer times and ti, values continues to decrease.

Subscript zero indicates the initial values distance in the x-coordinate polymer-solvent interaction par- ameter for components 1 and 2 mole fraction of monomer and strip- ping agent

CONCLUSION Stripping agents are commonly added to aid the

process of devolatilization in polymer melts. These agents have a dual function of enhancing the molecular diffusivity of the desorbing monomer and also in reducing the interfacial concentration of the monomer. Proper incorporation of these factors leads to a set of coupled equations with time variant boundary con- ditions, a problem that has not been tackled in the prior literature. The present work develops a mathe- matical model and also a solution strategy which could be used in a broad range of problems. More specifically the model results can be used for ascertaining the influence of diffusivity ratios, relative volatilities, etc. on the process of devolatilization and consequently also for selection of suitable stripping agents. The present model can be easily incorporated in more comprehensive models of total systems, such as twin

screw devolatilizers.

a

DI, Dz

fim n NI, N,

NOTATION

interfacial area diffusion coefficients for monomer and stripping agent limiting values of D, and Dz at p1 = 0 and p2 = 0 thickness of the film dimensionless parameters as defined in eqs (9), (10) and (23). fraction of monomer remaining in the polymer ratio of the amount of stripping agent present in the polymer to the initial amount of monomer value of M, at 0 = 0 number of exposures desorption rates of monomer and stripping agent average desorption rate applied vacuum vapor pressure of monomer and strip- ping agent devolatilization time exposure time molar volume of monomer, stripping agent and polymer weight fraction of monomer, stripping agent and polymer, respectively.

Greek symbols

cc

PI? P2

3;

Subscripts

0 i 1 2

3

parameter as defined in eqs (28) and (29) parameter as defined in eq. (13) parameter as defined in eq. (29) dimensionless film thickness ( = x/L) dimensionless time as defined in eq.

(12) dimensionless exposure time ( = D:t,/L2)

mass density of monomer and strip- ping agent average mass density of monomer after n exposures

values at H = 0 values at the interface (x = L) monomer stripping agent polymer

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of foam growth; analysis of the growth of closely spaced spherical bubbles. Po[ym. Engng Sci. 24, 10261034.

Biesenberger, J. A. and Kessidis, G., 1982, Devolatilization of polymer melts in single screw extruders. Polym. Engng Sci. 22, 832-835.

Biesenberger, J. A. and Sebastian, D. H., 1983, Polymerization Engineering, pp. 573-659. Wiley, New York.

Collins, G. P.. Denson, C. .D. and Astarito, G., 1985, Determination of mass transfer coefficients for bubble free devolatilization of polymeric solutions in twin screw extruders. A.1.Ch.E. J. 31, 1288-1296.

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La&en, G. A., 1962, Devolatilization of viscous polymer systems. Adv. Chem. Ser. 36, 235-246.

Newman, R. E. and Simon, R. H. M., 1980, A mathematical model of devolatilization promoted by bubble formation.

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Ravindranath, K. and Mashelkar, R. A., 1985, Recent adv- ances in polyethylene terephthalate manufacture, in Developments in Plastic Technology-2 (Edited by A. Whelan and J. Craft), pp 142. Applied Science Publishers. U.K.

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442 K. RAVINDRANATH and R. A. MASHELKAR

Roberts, G. W., 1970, A surface renewal model for the drying Integration of eq. (Al) with respect to 6, yields of polymers during screw extrusion, A.I.Ch.E. J. 16, 1

878-882. 1

-J ~+A@D, akf, s+AeaM,

-__ Secor. R. M.. 1986. A mass transfer model for twin screw AtJ B 07 aq “=I

dt, =A JJ

---ddBdq 0 B ae

ext&der, J&lym. ‘Engng Sci. 26, 647652. Todd, R. B., 1974, Sot. Plast. Engng Tech. Papers 20, 472.

1 ’ =-

s A0 o (Ml le+ao -MI Is) ds WV

Vrentas, J. S., Duda, J. L. and Ling, H.-C., 1985, Enhancement of impurity removal from polymer films. J. appl. Polym. Sci. and

D:P,o 1

J ’ 30, 449945 16.

Wcrncr, H., 1980, in Deuofntilization of Plastics, pp. 99-131. Verrin Deutscher Ingenieure Dusseldorf. VDI- Gesselschart Kunststoftechnik.

N,=p- (A3) L.

W,le---Mle+& dtl. A0 o

Similarly by integrating eq. (17). We obtain

P 4 e+AO D2 dM1 -__ APPENDIX A@ * DZO atl g=1

dH = & s

I (Mz Iti+Ae - Mz le)drl

0

Equation (16) can be integrated with respect to n leading to (A4) and