65
Ind. Eng. Chem. Prod. Res. Dev. 1986, 25, 65-68
Solvent Removal from Ethylene-Propylene Elastomers. 2. Modeling of Continuous-Flow Stripping Vessels Frank J. Matthews, James R. Fair, Joel W. Barlow, and Donald R. Paul Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
Charles Corewith' Exxon Chemical Company, Linden, New Jersey 07036
The diffusion model presented in part 1 of this series was applied to correlation of results from a commercial-scale, continuous-flow solvent stripper. A very good correlation was found, with the model accounting for the effects of the major operating variables. Finally, a set of transport, energy, and material balance equations was developed which permits the effect of operating conditions to be estimated and solvent removal to be optimized.
In part 1 of this series (Matthews et al., 1986) reference has been made to commercial approaches to the removal of solvent from synthetic elastomers. Elastomers that are produced by solution polymerization are usually separated from the solvent by steam stripping in a series of stirred tanks, as shown in Figure 1. Most of the solvent is removed in the first tank (coagulator) where the elastomer is precipitated in the water phase as porous, spongy particles ("crumb") typically containing 5-15 wt % solvent. The water slurry of rubber particles is then transported to the other tanks (strippers) in the train where additional solvent stripping occurs. Any solvent remaining in the rubber after the stripping process is normally lost to the atmosphere during the extrusion drying process, which removes water from the crumb and yields the final, dried product. Thus good solvent removal in the stripping vessels is essential for avoiding both solvent loss and atmospheric emissions. The design of effective stripping systems requires an understanding of the solvent diffusion process in rubber crumb suspended in hot water. For hexane in ethylene/propylene rubber (EPR), the laboratory studies described in part l of this series led to an expression for the diffusion coefficient and a mathematical model for a crumb particle that allows calculation of diffusion rates. In this part of the series we describe the application of the model to correlating data from a commercial-scale, continuousflow stripper and develop equations from which performance can be optimized. Continuous-Flow Stripper Diffusion Equation The laboratory study showed that a single porous particle can be modeled as an assemblage of spheres characterized by an effective radius, R , with the diffusion rate given by dC/dt = ( l / r 2 )d[D(C)r2dC/dr]/dr
(1) It is more convenient to express the solvent content of the rubber as weight percent rather than as concentration. Accordingly, C was replaced by X in eq 1by assuming that for the low levels of solvent generally existing in a stripper, the solvent concentration is equal to pX/lOO, where p is the density of the pure rubber. Because of the concentration dependence of the diffusion coefficient in polymer systems, eq 1 is not easily integrated to a form convenient for data-correlation pur-
poses. For this reason, we assume that D can be approximated by a constant value given by the integral average
D =
---Ix" xi-x, x, 1
dX
where Xi and X , represent the weight percent of solvent in the rubber entering and leaving the stripper, respectively. With the linear concentration dependence for D described in eq 4 of part 1, D is given by
D
+ 3.00pX)
(3)
+ 1.5p(Xi + X,))
(4)
= D(O)(1
Integration of eq 2 yields
D
= D(O)(l
Replacement of D in eq 1 by D allows integration to the result (Xi - XJ / (Xi - Xeq) = m
1 - (6/7?)
C (exp(-Dn2&/R2)/n2) ( 5 ) n=l
For a continuous-flow stripper, eq 5 must be averaged over the crumb residence time distribution to obtain the mean solvent concentration in the particles leaving the vessel. In the absence of experimental data, we assume that the vessel is perfectly mixed with a particle residence time distribution given by
E ( t ) dt = ( e - t / B / O ) dt
(6)
The mean exit concentration of solvent in the rubber is thus equal to
X, = Jm(X,e-t/R/O) dt
(7)
Combining eq 5 and 7 and integrating give the final result for calculating solvent diffusion rates in a stripping vessel: (Xi - Xe)/ (Xi - Xeq) = m
1- ( 6 / x 2 ) n=l
l / [ ( D O / R 2 ) n 4 ~+2 n2] (8)
Data Analysis Equation 8 was applied to the correlation of data obtained in a commercial-scale, continuous-flow stripping vessel for three different EPR grades of varying molecular
0196-4321/86/1225-0065$01.50/00 1986 American Chemical Society
Table I. Effective Crumb Diameter Determination av deviation,
PoI yme r SOlUtlOn
-
grade
A B C
I-.-
,-___
L'*=,
,
-,
crumb size, cm 0.71-1.4 0.93-1.08 0.72-1.82
mol wt, wt av 160000 210000 370000
X , (meas)-X, El. cm 0.082 f 0.011 0.051 1 0 . 0 0 7 0.075 0.010"
*
(wed) 0.28 0.14 0.34
"From laboratory diffusion data R = 0.095 cm for 0.635-cm diameter crumb; R = 0.138 cm for 1.27-cm diameter crumb.
Table 11. Variation of Solvent Content With Particle Size ~~~~~~
sieve fraction size, cm greater less than av than 2.54 1.13 1.84 1.13 0.673 0.90 0.673 0.475 0.57 0.475 3.236 0.36 0.236
~
Figure 1. Steam-stripping process.
I
10
I
.20
.40
.60 30 1.0
'
Grade B
b
Grade C
,
2.0
4.0
DBIR'
Figure 2. Fit of experimental results to diffusion equation.
weight over the following range of operating conditions: temperature 87-101 O C ; pressure 67-100 kPa (abs); crumb residence time 14-37 min; inlet hexane concentration 2-18 wt 7'; and mean crumb size 0.7-1.8 cm. The vessel investigated was the second in the stripping train and was fed with an aqueous slurry of crumb particles. The values of the independent and dependent parameters in this equation were established as follows. The crumb residence time was calculated from the flow rates by assuming the crumb concentration in the vessel was the same as in the feed. This is almost never the case for solid/liquid mixing in continuous-flow vessels; however, no data were available that could provide a more accurate estimate. To account for the slight temperature dependence of D(0) indicated in Table I1 of part 1, an Arrhenius relationship between D and temperature was assumed, and the data points a t 105 and 115 "C were used to obtain the constants in the equation D ( 0 ) = 3.048
X
lo-* exp[-2815/T (K)]
(9)
The value of fi was then calculated from eq 4. The equilibrium solvent concentration, X,, was calculated from the Flory-Huggins relationship In (Ph/Ph)= In V
+ (1 - VI + x ( I - VI2
(10)
with a value of the Flory-Huggins parameter x = 0.28 as reported by Newman and Prausnitz (1973). Finally, X, and X , were measured by dissolving crumb particles in toluene and determining the amount of hexane present by GC analysis. By fitting these parameters to eq 8 with a nonlinear least-squares computer program, the value of R (the effective diffusion radius) was obtained. As shown in Table I, R is essentially the same for polymers A and B and somewhat smaller for polymer C. The 20. limit on R is about 13% of its value, and the average deviation between measured and predicted X e ranges from 0.14 to 0.34 wt % , indicating that eq 8 correlates the data quite well.
cumulative wt 9c 21 70 87 98 100
hexane content, wt O/c 1.71 1.42 1.03 0.84
This is also shown in Figure 2 by the comparison of measured values of fractional solvent removal with the predictions of eq 8. Over the range of DdlR2 investigated (0.25-1.5) the slope of the curve in Figure 2 is quite flat, from which it would appear that R cannot be determined accurately. However, the least-squares correlation procedure was actually carried out to give a best fit to X e which varied from 0.4 to 2.1 wt % and depends more strongly on Dd/R2than does the fractional hexane removal. The weight mean particle size, as determined by sieve analysis, differed by about a factor of 2 over the course of the experimental program for grades A and C but reqained relatively constant for grade B (see Table I). In deriving eq 8 it was assumed that R is not a function of particle diameter despite the dependence seen in the laboratory study of part 1. The consequences of this approximation are discussed in more detail later on. The laboratory crumb stripping was done with an EPR very similar to polymer B, and the R values from the lab scale batch equipment and commercial-scale flow vessel are in reasonable agreement. The laboratory study was done some time after the crumb samples were obtained. Crumb particles usually densify to some extent on standing, which can explain the lower porosity and higher R in the laboratory diffusion rate measurements. Although R is essentially an emipirical parameter when calculated from the diffusion equation, it should be related to the porosity of the crumb particle. A t constant conditions in the first stripping vessel where the particles are formed, we would expect the porosity to depend initially on the rheology of the polymer solution fed to the vessel. However, changes can occur in the crumb as its age increases due to polymer flow, and low molecular weight polymers at high temperature and long residence time could lose appreciable amounts of surface area. The data in Table I indicate that R is not a function of polymer molecular weight. Thus for these particular EPR's porosity is probably not strongly affected by flow. Although the laboratory work showed that R is dependent on particle size, increasing by 40% for a doubling of particle diameter, this effect was ignored in correlating the data from the continuous-flow vessels. A plot of residuals (measured value - predicted value) from the correlation vs. mean particle size (see Figure 3), as determined by sieve analysis, indicates that neglecting this dependency does not produce a bias in the correlation. Nevertheless, the solvent content does decrease with particle size, as shown in Table I1 by the hexane analysis of the size
Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, No. 1, 1986 I
Table 111. Effect of Pressure on Stripper Operation with SuDerheated Feed" 4.5
hexane removal pressure, kPa (abs) 130 120 100 80 60
temp,
X,,,
"C
wt %
106 104 100 93 86
0.71 0.50 0.27 0.163 0.104
D, cm2/s 0.179 X 0.169 X 0.152 X 0.134 X 0.114 X
%
78.1 80.8 83.1 83.5 82.6
% of equil 88.6 88.1 87.1 85.8 84.1
G
B
e c n
+ S$,, + G J g ,
+ P,
-0.5
093l
0 -.91
I
4.5
?93
Grade A
I
I
7
m a
.6
.8
1.0
1.2
1.4
1.6
Water, W, Rubber, 0 , Hexane, X,
Water, W, Rubber, G, Hexane, X.
I
Steam, S,
(11)
Figure 4. Stripper operating parameters.
but no additional steam. As pressure is decreased, temperature drops, which decreases the diffusion coefficient and tends to reduce diffusion rate. However, more water flashes into the vapor phase, which reduces the hexane partial pressure and thus X,. This increases the driving force and tends to raise diffusion rates. As a result of these two competing trends, hexane removal goes through a maximum with pressure. For the particular set of operating conditions represented in Table IV, the optimal operating pressure is about 80 kPa. Decreasing the amount of hexane in the crumb entering the stripper causes similar opposing effects on the diffusion rate. On the one hand, X is lowered, which gives a higher diffusional driving forcexut due to the effect of solvent concentration on D , diffusivity is decreased. The results in Table IV show that the effect on the diffusion coefficient is the more important factor for initial hexane contents of 2-15 wt % , and the fractional hexane removal decreases as less solvent is present in the feed. Of course, the total amount of hexane in the crumb leaving the stripper does go down as less hexane is added to the stripper.
(13)
Table IV. Effect of Feed Hexane Content on Stripper Operation"
xe,,
"C
wt %
99.0 99.5 100.0 100.0
0.67 0.451 0.270 0.082
1.8
Mean Crumb Size, Cm
After expressing all physical properties as appropriate functions of temperature, eq 8 (diffusion), 10 (equilibrium), 11 (heat balance), and 13 (vapor composition), along with the appropriate material balance relationships, can be solved to give the stripper temperature and hexane content of the crumb leaving the vessel as a function of the feed rates, composition, and temperature. A computer algorithm for solving simultaneous, nonlinear algebraic equations is used to perform the calculations. As an example of stripper optimization, predicted hexane removal as a function of pressure is shown in Table I11 for a stripper fed with a superheated aqueous slurry
temp,
I
I
Figure 3. Effect of crumb size on correlation residuals.
If there is no liquid solvent present in the vessel, the ratio of hexane to water is given by
hexane in feed, wt % 15.0 10.0 6.0 2.0
1
a
.4
(12)
H,/S, = (P/Pw- 1)/0.21
'
0
s
The small amount of solvent present has been neglected in eq 11. The ratio of solvent to water in the vapor phase can be obtained from the pressure equation
P = Ph
I
a
al
Stripper Optimization With a model for the diffusion calculation established, we can now proceed to a mathematical model for the stripping vessel as a whole. We will only consider strippers that are fed with an aqueous slurry of rubber particles and not a polymer solution. For the flows shown schematically in Figure 4,the vessel heat balance is = WJ,,
I
IX.
fractions from sieving. Note, however, that the first two size fractions are quite close in hexane content and comprise about 70% of the total sample. Also, more than a factor of 2 difference in diameter is needed to produce a substantial difference in the amount of solvent present. The relatively narrow particle size distribution and the variation of average particle size by a factor of 2.5 at most (for grade C)in a series of experiments combine to make the calculated value of R insensitive to particle size. However, in general the applicability of eq 8 is limited to a narrow range of crumb diameters, and the effect of diameter on diffusion rate must be accounted for if a broad range of crumb sizes is present.
+ SiEsi+ GiE,i
I
B
"Feed temperature = 110 "C; hexane in feed = 6.0 wt %; residence time = 22 min.
WiE,,
t
I
Grade C
67
D,
xe,
cm2/ s 0.330 X 0.232 X 0.152 X 0.066 X
wt%
"Feed temperature = 110 "C; residence time = 22 min; pressure = 100 kPa.
1.61 1.31 1.01 ,545
hexane removal 70 of 70 esuil 89.3 93.4 86.9 91.0 83.1 87.1 72.7 75.9
68
Ind. Eng. Chem. Prod. Res. Dev. 1986, 25, 68-72
Conclusions The diffusional model for solvent removal from porous rubber particles in aqueous slurries that was derived from batch laboratory experiments gives a good correlation of data obtained in a commercial-scale, continuous-flow vessel. The model accounted for the effects of the major operating variables. Also, the value of the effective crumb radius, the only parameter in the model, was in reasonable agreement between the batch and continuous experiments. However, three simplifying assumptions were required for the analysis of the continuous flow data: (1)the crumb in the vessel is perfectly mixed; ( 2 ) the rubber concentration is the same in the vessel as in the feed; and (3)the crumb size does not affect R , the effective crumb radius for diffusion. Approximation of the crumb residence time distribution by an exponential probably does not lead to serious error. But for the particular vessels used in this investigation, suspension of buoyant, large particles tends to give lower particle concentrations in the vessel than in the feed and, consequently, assumption 2 leads to overestimation of crumb residence time. This in turn would lead to an underestimation of R, but the magnitude of the effect cannot be easily estimated a t present. The assumption of R independent of crumb size causes little error over a twofold variation in mean particle diameter as long as the parameter D8 / R 2 is greater than about 0.007. For larger size variations or smaller values of D8/R2,the diffusion model should be corrected to account for the decrease in R with crumb size. The same is true if the particle size distribution is very broad. Finally, a set of transport, energy, and material balance equations for a continuous-flow stripper is presented that allows the effect of operating conditions to be estimated and solvent removal to be optimized.
Nomenclature C = solvent concentration in rubber, g/cm3 D = diffusion coefficient, cm2/s Q ( 0 ) = diffusion coefficient at 0 solvent concentration D = integral average diffusion coefficient E, = rubber enthalpy E, = steam enthalpy E , = water enthalpy G = rubber flow, wt/time H = hexane flow rate, wt/time P = stripper pressure, kPa absolute Ph = hexane partial pressure, kPa absolute Ph = hexane vapor pressure, kPa absolute P, = water vapor pressure, kPa absolute r = radial position in spherical particle H = effective crumb radius, cm S = steam flow, &/time t = time, s V = solvent concentration in rubber, volume fraction W = water flow, wt/time X = solvent concentration in rubber, wt % 0 = residence time, s p = rubber density, g/cm3 x = Flory-Huggins parameter
Subscripts e = outlet stream from stripper i = inlet stream to stripper eq = equilibrium value Registry No. Hexane, 110-54-3.
Literature Cited Matthews, F. J.; Fair, J. R.; Barlow, J. W.; Paul, D. R.; Cozewith, C. Ind. Eng. Cbem, Prod. Res. Dev. 1986, preceding paper in this issue. Newman, R. D.; Prausnitz, J. M. AIChE J , 1973, 19, 704.
Received for revieu August 16, 1984 Accepted August 29, 1985
Explosives Synthesis at Los Alamos Michael D. Coburn," Betty W. Harris, Klen-Yin Lee, Mary M. Stineclpher, and Helen H. Hayden Explosives Technology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
During the past two decades, the explosives synthetic effort at Los Alamos has been directed toward energetic heterocyclic compounds and has produced some useful thermally stable explosives. The recent evolution of crystal-density predictive methods is guiding our current efforts toward ultrahigh performance explosives. Much of our effort is now on the development of new methods for preparing unique nitro compounds that are inaccessible by conventional techniques. This paper will review the Los Alamos synthetic program with emphasis on the development of novel thermally stable explosives, and current efforts to synthesize high-density/performance explosives will be discussed.
Introduction The need for a viable explosives synthesis effort is evident when the historically changing requirements of explosives are considered. Since it generally requires about 10 years from the time a useful new explosive is synthesized to qualify it for application, the synthesis effort must be vigorously pursued now or there may be serious deficiencies in our ability t o meet explosives requirements of the next decade. Since the future requirements are not
defined, an inventory of explosives with a broad range of chemical and physical properties is needed. The common explosives 2,4,6-trinitrotoluene (TNT), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), octahydro1,3,5,7-tetranitro-l,3,5,7-tetrazocine (HMX), and pentaerythritol tetranitrate (PETN) were considered adequate for all weapons needs until the requirement for an insensitive high explosive (IHE) was implemented. Fortunately, 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), which had
0196-4321/86/1225-0068$01.50/00 1986 American Chemical Society
