704
I n d . Eng. Chem. Res. 1990, 29, 704-70;
Predicting Drying Cycle Times of Thixotropic Material in Nauta Dryers Nauta processing technology has been evaluated for drying of a n organic salt. T h e thixotropic rheological properties of the material varied considerably depending on the temperature and water level. The uniqueness of this application is that significant variation in density, rheology, heat-transfer rates, a n d available heat-transfer area was occurring during drying. A dynamic simulation model was developed a n d used as a predictive tool during t h e testing a n d scale-up work. T h e computer algorithm predicts, with good accuracy, these pilot through production scale tests. T h e model, while accurately predicting drying rates over t h e nonlinear 20-fold increase in scale, accounts for severe variation in density a n d heat transfer during the batch drying cycles. There are a number of cited cases in the chemical, pharmaceutical, and food industries where "Nauta" processing equipment is being used in special mixing and, in some cases, drying applications (Shevlin, 1978; Updegrove, 1977; van den Bergh and Scarlett, 1984). The literature, however, is void of any reported work on drying applications when significant changes in volume, heat-transfer rates, and product rheology are occurring. Recently the drying of an organic salt solution required scale-up evaluation. This material had unique thixotropic rheological properties which varied extensively depending on the temperature and water level. Over the 72-257'' water composition range, the organic salt passed through three distinct rheological forms (thixotropic slurry. sticky, and claylike) before becoming a free-flowing powder. The volume (and available heat-transfer area) also varied significantly during drying. In addition to an extensive experimental program, a dynamic simulation model was developed and used as a predictive tool in this study. The model is sensitive to the nonlinear geometric scale-up, to density variation, to severe changes in available heattransfer area, and to alternate heat-transfer systems.
Nauta Equipment Design The Nauta mixer/dryer is a cone-shaped agitated vessel which, for drying applications, can be equipped with a full cone jacket. The agitator is an internal screw which is rotated in the upward or lift direction while traversing around the inner circumference a t a slow angular velocity. The unique cone design, plus the lifting motion of the screw agitator, results in gentle mixing. A drawing illustrating a typical Nauta mixer/dryer is shown as Figure 1. Most of the important geometric relationships such as the cone half-angle, jacket surface area at a given volume, screw diameter, and pitch are similar among equipment manufacturers. In scale-up applications, larger units become "taller" with an identical lower design as the smaller pilot models (Le., constant cone angle). Scale-up in drying applications for cone-shaped vessels becomes a challenge. It is the nonlinear interaction of the variable heat-transfer area compounded by volume and density changes that presents the opportunity to the process engineer. An additional factor is that the overall heat-transfer coefficient may vary as much as 10-fold through the drying cycle. When the drying duty is significant, as in the present case, an understanding of these fundamental relationships is essential for accurate scale-up. This nonlinearity of scale can best be described by a surface/volume function valid for the Figure 1 design. This relationship, developed for a typical commercially available unit, is shown as Figure 2. The surface area available for heat transfer is a complex nonlinear function of dryer height. The problem becomes even more complex if the total distillate-to-feed weight ratio is significant. This implies that volume (and perhaps even density) variation will occur during the drying cycle. T o illustrate this point, Figure 3 shows the actual, available surface area relative 0888-5S85/90/2629-0704$02.50/0
to the initial amount in a volume reduction case. The present model incorporates both of these nonlinear scale-up and application concepts.
Dynamic Simulation Model 1 . Energy Balance. For applications where a large amount of water is removed during drying, sensible heat effects are small, leaving a heat balance given by Q = m X = UAAT (1) where m is the distillate mass flux per unit time. The heat balance can be expressed in differential form and integrated to give the total drying time, 0, needed to remove the desired weight of volatiles, M,:
Calculating the integral can be a challenge because of nonlinear and time-variant functionalities in U and A during the batch drying cycle. 2. Geometric Description. Based on the geometric definitions shown on Figure 1, three important geometric functions to define the slant height ( h J ,heat-transfer area (A3), and volume (V,) are shown below: h3 - hz --d3 - dz h s = -cos - cy 2 sin CY ~ ( d 3 '- d,'! A' = 4 sin cy
(3)
(4)
- dI31
(5) 24 tan cy A convenient mechanism for defining the moisture concentration in the Nauta dryer is through the weight fraction removed during drying, #: =
v 3
$,=-
c; - c
1-C where the total amount of volatiles removed at any point in time, M , is equal to Wi$. Knowing the distillate profile, one can independently determine the mass in the dryer. The solids bulk density can then be used to calculate the dryer volume. In many applications, the density may not be constant and will require experimental data for defining this functionality. The volume is thus (7)
and at this volume level, the dryer height is given by h(c) =
(
3V(C) T
+ v,
tan2 a
}
1'3
Equation 8 is valid assuming no angle-of-repose factors 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 705
.......................
d
3
accuracy. Since eqs 9 and 4 become equivalent, the only requirement is to experimentally determine the heattransfer coefficient function, U(C). The test equipment facilities available at vendor sites vary in design. When vendor test data are collected, it is necessary to correct for any effects due to alternate jacket heating fluids to facilitate a common basis for comparison of the results. The overall heat-transfer coefficients (as measured in any of the tests) are actually a summation of the inverse resistances as given below:
.....................
Figure 3. Heat-transfer area function in volume reduction applications.
In order to correct for alternate jacket heating designs, it is necessary to specify outside and wall resistance values in order to determine the desired inside coefficient profile. When mixing effects upon scale-up may be important (powder applications), a more extensive experimental program should be considered. In this case, solids bulk density (hence, porosity) will affect the boundary-layer thermal diffusion rates, which is expected to be the controlling mechanism. Agitation variation in scale-up would thus play an important role. Such systems also lend themselves to augmenting drying rates by partial fluidization. The reader is referred to Shevlin (1978) and Updegrove (1977) for further insight into this technique. In solids drying applications, where the material retains a claylike form throughout the drying cycle, agitation levels necessary to maintain bulk-phase mixing are important (see van den Bergh and Scarlett (1984)),but variation on scale-up will not necessarily be significant. In these cases, the controlling mechanism is one of diffusion both within the “clay” and more importantly through the expected wall “skin” layer. The scale-up procedures as outlined above are expected to yield reasonable results in these cases as well. 4. Drying Time: Complex Systems. The simplifying assumption of a constant volume system is not always valid. In these cases, a numerical solution of eq 4 may be necessary. A FORTRAN algorithm was written for the solution to eq 4. This algorithm uses center-difference logic to approximate the differential equation functions in question and requires two subroutines for inputting the density and heat-transfer coefficient functionality relative to the drying cycle. The user is prompted for appropriate boundary conditions and equipment dimensions. Further information on this algorithm is available from the author. The iterative calculations done by the program are summarized as follows: (1)increment mass removed, (2) calculate 9, (3) calculate C, (4) read U from data or function, (5) read p . (6) use appropriate value for A. (7) use desired AT, (8) calculate V (volume), (9) calculate h (height), (10) calculate A (area), (11)calculate incremental t (time), (12) determine average incremental time (center difference), (13) s u m time to trace total, and (14) compare conclusion or 9 with boundary value; return to (1) or end.
(Le., for free-flowing solids that maintain a minimum height during the drying cycle). The available area is 4[h(c) tan .I2 - ?rdZ2 A(c) = (9) 4 sin a 3. Drying Time: Simplified Systems. The total drying time, as calculated from eq 2, is trivial in cases where volume variation can be neglected. Furthermore, for scale-up evaluation, the decaying functionality between S I V and dryer size (see Figure 2) can be used with good
Model Application: Drying of an Organic Salt Slurry Recovery by drying of a product intermediate provided the impetus for developing and testing this model. An organic salt slurry needed to be dried from 72% to 25% water by weight. The algorithm was used to predict pilot-plant and vendor tests (including scale-up) and to aid in the design specifications for two commercial scale units. The overall heat-transfer data collected in the pilot-plant work as a function of product moisture are summarized
t
I
I
I
I
I Y,
S/V
1.4
-
1.3
-
-I
BLO
I ns
i
(mi1.2 -
1.1
1.0
I 1.0
I 0.8
I
I 0.6
I
I 0.4
I
1 0.2
V/Vi
706 Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 IB0
Table 11. Sam& Proeram 1
Outout"
REWIRES; DRYER H A L F ANGLE ( D E G R E E S ) , DRYER BOTTOM OR CUT OFF O F F D I W E T E R ( I N C H E S ) , H E I G H T TO 6OTTCM O F J A C K E T ( I N C H E S ) , A'4D t i E I G t I T TO TOP O F JhCK!ZT (:&CIIESI, 17.0, 1 4 . 0 , 4 . 9 , 140.0 1 C D E F I N E T l i E DRYER GECMCTRY T H I S PROGi?AM
(11 THE I21 Trli ( 3 1 TtiE ( 4 1 THE
c L 100
~
t-
ViiiiiT RR5 TIIS I N i T I A L W 3 F I t < A L WATER C O N C . VALUES
(WT P E R C E N T ) ?
65.546, 3 5 . 0 w i i m I S T I I E F E E D WEIGHT
r_
ILBSI ?
16O62.0 k A S A U S E R D E F I N E D VACUUM F U N C T I C N BEEN D E F I N E D (0-NO, S E L E C T HEAT T R W S F E R BASIS, U i C l OR H I i C ) ? I0 U ( O V 6 R A L L C O E F . ) , 1- H I I I N S I D E COEF.) 1
-
20
I 75
l
70
I
1
I
I
I
50
60
C (conc.)
1
l
40
(nt
30
I
wiirg:
20
I S HO IOU:S;DE
COEF. i ?
1cc0.0
:: water)
i
Figure 4. Heat-transfer coefficient function.
case size. ft3 pilot-plant 10 test dataa test 1 10
test 3 test 4 test 5 productn unit 1 productn unit 2
10 10 18 50 229 229
jacket fluid steam
S3 F T 99 cu ET O R WATER WATER
Table I. Simulation Results
test 2
l-YES)?
o
time, h C;. % C,. % Dredicted actual 72 25 56.0
--
i a 7 o . i ~GAL 65.546 35.000
1
L B S WATER R E M I N I N G LBS S O L I D S OUT
I
F I N A L WT
LBS WATER REMOVED BY D I S T N
-
oil steam steam oil steam steam
61 60 69 50 72 45 72 66 66
25 35 42 28 25 24 23 35 35
5.2 6.8 5.4 6.9 6.0 3.0 12.6 5.9 5.9
5.0 6.2 5.8 6.5 5.6 3.0 12.5 5.5 5.9
Basis for model development.
in Figure 4. These data were determined from analysis of dryer temperatures, internal height of solids, and collected distillate (see eq 1). In the development of the drying technology, several vendor tests were conducted to augment the pilot-plant data base. A comparison of predicted versus actual drying times for all of the runs is given in Table I. The tests encompassed a 5-fold scale increase which provided important scale-up testing for the model. The variability in the tests (hot oil, water, and steam systems) is often encountered when using vendor test facilities. In all cases, the agreement between predicted and measured drying times was excellent. The final utilization of the model was in specifying two dryers for a commercial scale plant. The predictions of the model agree very well with this final scale-up. The program is conversational in order to allow the user to specify geometric and system data and select the desired output format. A sample output is shown as Table 11. Summary A dynamic simulation model has been developed to predict drying rates in Nauta mixerldryers. Although the model can be used in connection with many types of Nauta drying applications, it is especially valuable when dealing with solids drying where significant density or volume variation occurs. The neglection of sensible heat changes in the energy balance is consistent with this scope. It necessarily encorporates a time-variant geometric description of the Nauta dryer. The model is also sensitive to cases involving differing jacket heat-transfer system designs. Excellent agreement has been demonstrated between predicted and measured drying times over a wide data base.
DRY TIME
1123 CONC
MASS
LOSS
3.53
0.655 0. 0.05 0 . 6 5 4 76. 3.13 0.652 152. 0.43 3.638 762. 0.72 0.623 1 3 7 2 . 3.99 0.607 1982. 1 . 2 7 0 . 5 8 9 2592. 1.57 0.113 3202. 1 . 9 0 5.548 3 8 1 2 . i.28 0.521 4 4 2 2 . 2.73 0 . 4 9 8 5032. 3.27 3 , 4 6 3 5642. 2.91 3 . 4 3 6 6252. 4.12 0.398 6 8 6 2 . 5.71
3 355
i1i2.
5.il
5 353
75(8.
.v.,:i
PRC;;C.CD
DRYER )IT
VOL FT3
130.6 130.3 130.1 127.8 125.4 122.9 123.3 117.5
209.4 208.3 207.2 198.0 188.7 179.5 170.0 ;60.3
114.6
150.6
111.3 127.8
140.0
104.1
:in,a iCR.3 90.1 89.1 87 9
1OC 2 96.2
UHYII:; 5 . 8 5 2 HRS
92.1 9i.9
2379.85 5531.00
8513.85
7548.15
E t i i E H 2 FOR F U L L OUTPUT, 1 FCR TREND, 1
water
--
129.6
0 FOR SUMMARY
MEA FT2
161.3 160.7 160.1 155.2 150.1
145.0 133.6 134.1 128.4 122.; 115.7 138.9 1C2.1
?5,2 e5.0 80 2
ti
153.0 152.7 152.5 149.4 145.8 141.7 134.4 123.7 110.7 92.8 70.6 58.3 16.9
SPEC
DEL T
GRAV
DEG
1.23
63.9 54.2 61.6 88.3 99.8 109.1 114.7 117.9 121.8 132.9 147.2
1.23 1.23 1.24
1.25 1.26 1.27 1.28
1.30 1.33 1.36
1.40 1.45 1.50
29.C 32.7
1.54
3i.9
1.55
F
167.1
lR0.6 152.0 182.0 162.0
PRESS MM
760.0 737.7 717.0 455.5
322.3 279.9 250.3 234.8 225.1 173.8 100.8
64.9 45.0 43.1 40.3
43.0
.:?2
This is a simulation program for nauta process drying evaluation by D. M. Johns.
Nomenclature A , S = surface area available during drying, function of concentration, ft2 A,, A, = outside and inside jacket wall heat-transfer area, ft2 A , = mean wall heat-transfer area, ft2 C = weight fraction of water d , = bottom diameter, ft d 2 = diameter at jacket bottom, ft d3 = initial dryer interface diameter, f t h = height of material in dryer, function of concentration, f t h , = projected height from apex to dryer bottom, ft h2 = projected height to jacket bottom, ft h3 = projected height to initial dryer interface, ft h, = slant height, ft h,, h, = outside and inside wall heat-transfer coefficients, BTU/(h ft2 "F) ho,E,hi,f = fouling coefficient, BTU/(h ft2 O F ) K , = wall thermal conductivity, BTU/(h ft "F) m = mass removed per unit time, lb/h M = weight of volatile (water) removed, related to solids moisture concentration,independent variable in integration, lb M , = specified weight of water to be removed, lb Q = heat flux, BTU/h t = time, h AT = thermal driving force, O F U = overall heat-transfer coefficient, BTU/(h ft2 O F ) U, = U calculated based on the outside jacket wall, BTU/(h ft2 O F )
Ind. Eng. Chem. Res. 1990, 29, 707-709
V1 = projected volume from apex to dryer bottom, ft3 V , = initial dryer volume, ft3 Wi = initial dryer charge, lb x , = wall thickness, ft a = projected cone angle, deg 8 = total drying time, h h = latent heat of vaporization, -1000 for water, BTU/lb J. = weight fraction removed based on initial charge
Literature Cited Shevlin, E. J. The Day-Nauta Mixer-Processor. Pharm. Technol. 1978, March, 56-59.
707
Updegrove, L. B. Batch Drying in a Nauta Mixer. Chem. Eng. Prog. 1977, April, 107-112. van den Bergh, W. J. B.; Scarlett, B. Some Improved Scale-up Rules for a Conventional Nautamixer. Zntl. Symp. Mixing 1984, 537-546.
Dennis M. Johns Agricultural Chemicals Process Research 969 Building The Dow Chemical Company Midland, Michigan 48667 Receiued for reuieui December 13, 1989 Accepted January 18, 1990
'H NMR Composition Analysis of Styrene-a-Methylstyrene-Butadiene Terpolymer A method for the determination of styrene-a-methylstyrene-1,2- and 1,Cbutadiene terpolymer based on 'H NMR spectrometry data is developed. Lacking any reference method, t h e accuracy and reproducibility were examined for t h e mixture of appropriate homopolymers. T h e method is additionally verified by analyzing the dependence of the obtained results for terpolymer compositions upon the conversion as well as upon the chemical composition of t h e starting monomer mixtures. T h e observed regularities as well as the standard deviation and the difference of the average confirm the applicability of the developed method for terpolymer analysis. Composition and configuration of copolymers affect their physical properties and use. These data are also important for the study of copolymerization reactions. Styrene (S)-a-methylstyrene (MS)-butadiene (B) terpolymers are difficult systems for composition analysis due to the structural similarity of styrene and a-methylstyrene. Most analytical methods are not applicable in that case. As far as 'H or 13C NMR spectrometry is considered, there are many papers dealing with styrene-a-methylstyrene and styrene-butadiene copolymer analysis but none dealing with styrene-cu-methylstyrene-butadiene terpolymer analysis. This is a very specific case as far as 'H NMR spectrometry is considered due to the almost complete overlapping of signals of S, MS, and B in the aromatic and aliphatic parts of the spectra, and thus, a different approach in the analysis is required. In this paper, a method for the determination of S, MS, 1,2B, and 1,4B terpolymer based on 'H NMR spectrometry data is presented. Lacking any standard method, the accuracy and reproducibility were examined based on a mixture of appropriate homopolymers. The terpolymer spectrum is not a simple superposition of homopolymer spectra, due to the impact of distribution of individual monomer units on the chemical shift. Thus, it was necessary to check the applicability of the method on terpolymer samples. This was done by analyzing the dependence of the obtained results on conversion as well as on the chemical composition of starting monomer mixtures. The observed regularities only served to validate the presented analytical method, without intending to explain the reactivity ratios.
Experimental Data Samples. Homopolymers polystyrene, poly(a-methylstyrene), and polybutadiene, prepared by suspension (PS) or emulsion (PMS, PB) polymerization, were precipitated (benzene/methanol) and dried under vacuum until constant weight. Their limiting viscosity numbers [?] determined in toluene at 25 "C were 0.50 for PS, 0.20 for PMS, and 1.39 dL/g for PB. 0888-5885/90/2629-0707$02.50/0
Terpolymers were prepared from three different mixture of monomers: S/MS/B 20/10/70,10/30/60, and 10/60/30 mol % . Reactions were performed in a 1-L autoclave using a "cold" (at 5 "C) emulsion process initiated by the hydroperoxide-iron-sodium formaldehyde sulfoxylate system. Samples of the terpolymers, taken out at different conversions, were terminated, purified by coagulation, precipitated, and dried under vacuum until constant weight was reached: reaction system S, 59 g; MS, 33.4 g; B, 108 g; water, 405 g; potassium myristate, 1.8g; Dresinate 515, 6.75 g; Orotan N, 0.3 g; tert-dodecylmercaptan, 0.3 g; 2,4,4-trimethylpentyl-2-hydroperoxide, 0.253 g; FeS0,-7H20, 0.3 g; EDTA, 0.06 g; sodium formaldehyde sulfoxylate, 2.4 g. NMR Spectrometry. The 'H NMR spectra are recorded on a Varian EM-390 NMR spectrometer (90 MHz) at room temperature. CCl, was used as the solvent (-20% w/v) and Me,Si as the internal standard.
Results and Discussion Figure 1 presents the 'H NMR spectrum of the styrenea-methylstyrene-butadiene terpolymer. The protons of the styrene and a-methylstyrene aromatic rings resonate from 6.8 to 7.4 ppm. Assignations of the olefinic part of the spectra were performed according to Mochel (1967): from 4.6 to 5.0 ppm resonating 2.5 protons on the double bond of 1,2-butadiene; from 5.0 to 5.7 ppm resonating 0.5 proton on the double bond of 1,2-butadiene and 2 protons on the double bond of 1,4-butadiene. The protons of the methyne, methylene, and methyl groups of the aliphatic part of all monomer units, more or less mutually covered, resonate in the area from 0.9 to 2.9 ppm. The signal of the methyl group of a-methylstyrene at 1.2 ppm is the least overlapped by other signals. Therefore, it is used in the analysis of the terpolymer as the characteristic signal for a-methylstyrene. It is better resolved in the terpolymer spectrum, and it resonates at weaker field than in the pure homopolymer spectrum. The areas of the aforementioned regions were denoted by a, b, c, and d respectively (Figure 1). 0 1990 American Chemical Society
