Ind. Eng. Chem. Process Des. Dev. 1981,
2. The use of oleum instead of concentrated sulfuric acid does not increase the conversion to m-toluenesulfonicacid appreciably. 3. If the acid concentration and the reaction temperature are both high, the conversion decreases. 4. The reactant ratio and the time of acid addition do not significantly affect the conversion to m-toluenesulfonic acid. Nomenclature A = acid addition time, min b = regression equation constants to be estimated C = feed acid concentration expressed in normality N = normality, mol of hydrogen ion/L R = mole ratio of acid to toluene T = reaction temperature, “C
20,85-90
85
Y = conversion to m-toluenesulfonic acid, % 8 = time of reaction, h
Literature Cited Box, G. E. P. et ai. “Deslgn and Analysis of Industrial Experiments”, 0. L. Davies, Ed., Hafner Publishing Co.: New York, 1963. Broyles, A. R.; Eckert, R. E. Ind. Eng. Chem. Rocess Des. Dev. 1973, 72, 295. Cerfontain. H.; Slxma, F. L. J.; Voiibracht. L. Recl. Trav. Chem. Pays-8as 1963a, 82, 659. Cerfontain, H.; Duin, H. G. J.; Voiibracht, L. Anal. Chem. 1083b, 35 1005. Engiund, S. W.; Aries, R. S.; Othmer, D. F. Ind. Eng. Chem. 1953, 45, 189. Holleman, A. F.; Caland, P. Ber. 1911, 44, 250. Morrison, R. T.; Boyd, R. N. “Organic Chemistry”. Aiiyn and Bacon, Inc.: Boston, 1973; pp 339-341. Patwardhan, V. S. M.S. Thesis, Purdue University, West Lafayette, IN, 1971. Spryskov, A. A. Zh. Obshch. Khlm. 1960, 30, 2449.
Receiued for review April 12, 1979 Accepted October 20, 1980
Simulation of Solidification Temperature Profiles in the Polyester Process for Immobilization of Hazardous Wastes R. Mahallngam,” R. K. Biyanl, and J. T. Shah Deparfmnt of Chemical Engineering, Washington State University, Pullman, Washington 99 164
As part of the development of a process for immobilizing hazardous wastes in a polyester matrix, an analysis is provided here for the prediction of temperature profiles during curing of the emulsion, by consideration of reaction exotherms and polymerization kinetics. Such anaiyses should be helpful in the optimal design of burial containers.
Introduction The dominant feature of current industrial development is an increasing concern to prevent pollution of the environment by hazardous industrial wastes. Until the seventies the operating philosophy was basically to treat the waste as necessary to meet the operating conditions while not exceeding existing regulations. A basic approach in waste management is to develop processes for the conversion of hazardous residuals in the form of liquids or semi-solid sludges to solids for safe handling, transportation, and storage with minimal potential for contamination of the environment. Immobilization (Neilson, 1977) of the waste is primarily concerned with the incorporation of the waste into a solidification agent. The basic operations are waste collection, waste pretreatment, solidification-agent mixing, packaging, and waste package handling. Pretreatment is primarily directed toward reducing waste volume, dewatering sludges, and adding chemicals for pH adjustment and foam prevention. The solidification operation is the most important stage of the immobilization process. A monolithic free-standing solid is formed by using solidification agents such as bitumen, hydraulic cement, absorbents, and organic polymers. If 100% retention of a waste for its hazardous lifetime is the goal of shallow land disposal, better waste processing techniques must be adopted. Recently, the feasibility of immobilizing hazardous wastes in a polyester matrix has been demonstrated by our research team, both in the laboratory and on the pilot plant 0196-4305/81/1120-0085$01.00/0
(Subramanian and Raff, 1975; Juloori, 1976; Wu, 1978; Jain, 1978; Mahalingam et al., 1977; Subramanian et al., 1977; Biyani, 1978; Washington State University, 1977). By finely dispersing the waste solution, slurry, or solids in a water-extensible polyester resin, each waste particle or droplet is individually encapsulated inside a thin skin of the resin matrix. Addition of an initiator polymerizes this resin matrix to produce a rigid monolithic solid suitable for land burial. One of the objectives in our pilot plant studies has been to develop a computer model, based on thermal analyses and polyermization kinetics, to predict temperature profiles during the curing of the emulsion; this should enable one to arrive at an optimum LID ratio for burial containers of various sizes. Some discussion is available in the literature on problems of nonuniform reaction due to heat transfer and the reaction exotherm (Horn, 1960; Lee and Neville, 1967; Doyle, 1969; Hills, 1971). Mathematical analyses, however, are limited. More recently, Progelhof and Throne (1975) have carried out one-dimensional transient heat conduction analyses of reactive, unfilled polymers and epoxies, showing that isothermal heat generation rates underestimate the nonisothermal values by more than an order of magnitude. Broyer and Macosko (1976) showed through their one-dimensional transient analyses that for cyclic processes, such as thermoset injection molding and reaction injection molding, it may be more desirable to control the heat flux through the mold walls rather than the wall temperature. Adabbo et al. (1979) have expanded the above work to include, among 0 1980 American Chemical Society
88
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
others, a description of the evolution of temperature and conversion within the sample and on the influence of the wall temperature on the process behavior and the heat of reaction. A recent review on nonisothermal polymerization processes in which the chemical reaction occurs with thermal self-acceleration is provided by Stolin et al. (1979). Background Unsaturated Polyester and Emulsions. Unsaturated polyesters (Wu, 1978) are composed of three basic types of structural units: unsaturated acids, saturated acids, and glycols. They are dissolved in a solvent such as styrene. During the curing, styrene serves to cross-link the polyester chains thus forming a rigid three-dimensional structure. A commercial water-extensible polyester resin, Aropol WEP 661-P (Ashland Chemical Co., Columbus, Ohio), which contains 60% styrene, has been used for all the pilot runs. A water-in-oil emulsion is formed by dispersing the waste solution as micron size droplets into the continuous resin phase. WEP 661-P contains proprietary emulsifying agents which considerably lower the energy requirements (Ashland Tech. Bull., 1968) for forming a stable “waterin-resin” emulsion. This emulsion has a shelf life of up to 4 months. Free Radical Polymerization and Reaction Rate. One of the objectives in the present study is to simulate on the computer the temperature profiles experimentally observed during the curing of the emulsion; it is necessary to review here, briefly, the free-radical polymerization kinetics of styrene. This review highlights the inadequacies in existing data and the need for additional experimentation, which has been conducted as part of this study but reported elsewhere (Biyani, 1978; Biyani et al., 1980). Once a free radical is generated-from whatever source-subsequent reactions follow the traditional freeradical polymerization kinetics (Odian, 1970). The rate of polymerization in the (MEKP-DMA) initiated system is then given as
COMPRESSED AIR-%&--?--,
RESIL
I3
+.------
INITIATOR 4
Figure 1. Pilot plant flow sheet-polyester process for immobilization of hazardous wastes: 1. waste preparation tank; 2. steam coil; 3. variable-speed paddle mixer; 4. variable speed TEEL screw pump; 5. rotameter;6.3-way ball valve with pneumatic actuator;7. a,b, flow control valves; 8. emulsiication tank; 9. variable-speedturbon mixer; 10. air motor; 11. variable-speed MOYNO screw pump; 12. a,b, ball valves with pneumatic acturaton; 13. resin tank; 14. resin metering pump; 15. a,b, diaphragm valves; 16.4-way solenoid valve; 17. timer; 18. solidification can; 19. variable speed helicone mixer; 20. diaphragm pump; 21. initiator tank. r R E S I N
-
CHARGED MANUALLY
O ~ W A S T ESTREAM COMMENCED-RECYCLE STARTED ~ M W . I N G STARTED 13% TM, 120 RPM)**
I
b S T A S L E EMULSION FORMED
I RESIN STREAM COMMENCED SPEED OF MIXER INCREASED TO 1050 RPM
CANNING
-z
30
g
40
5
I
I
50
*I
CAN iI1 GAL)
2
1
2-
3
4
.i
FFEED STREAMS STOPPED
-
4-
5-
4-1
I
5-
1
4 I
STARTED
1
+
* S,”d*,4*’:,
MIXING AND CANNING
60 LSTDPPED
I
6d 7-
END OF RUN @ 6 0 M I N
where k, = propagation rate constant, kt = termination rate constant, kd = dissociation rate constant (for peroxide), f = initiator efficiency, a = concentration of promoter (DMA), b = concentration of peroxide (MEKP), and M = concentration of monomer. The WEP 661-P contains 60% styrene monomer (Ashland Tech. Bull., 1968) and, as such, the curing reaction can be well approximated by the polymerization of styrene to form polystyrene which cross-links the polyester chains. Since the resin composition is proprietary, precise numbers for the promoter concentration are not available. Realistic approximate figures based on the published literature (Pennwalt Corp. Bull., 1973) have been used in computations discussed later. The other parameters which need to be determined for the computations are k,, kt,kd, and f. k, has been evaluated (Walling, 1957) for styrene and is not likely to change for the resin reaction. Values for the termination constant kt have also been reported for bulk styrene, but k, is a strong function of viscosity (Odian, 1970) of the system (Tramsdorff effect). High viscosity hinders the diffusion of polymer chains and termination is reduced. It is estimated that typical kt values for bulk styrene polymerization are reduced by several orders of magnitude for viscceities encountered during the curing of the waste-in-resin emulsion. Values for f and the dissociation constant, kd, for the system MEKP-DMA-cobalt napthenate are not
* Emulr an
6OmDleS
t* Type o f mixer,
collected
for isc cosily meaiuwnenis
rpm
Figure 2. Operations schedule for run 34.
available in the literature. Laboratory experiments were, therefore, performed based on the procedure described by O’Driscoll and McArdel (1959). Equation 1differs from that used by O’Driscoll and McArdel (1959) by a factor of 2. The reason for this (Odian, 1970) is that one peroxide molecule yields only one radical capable of initiating polymerization. The calculations and results are described in Biyani (1978) and Biyani et al. (1980) and are used in Appendix 11. Pilot Plant Runs General Description of the Runs. The pilot plant process flowsheet (Figure 1)is described in detail in the work of Jain (1978) and Biyani (1978). A brief outline of the general operation of the pilot plant is given here (Figure 2). To start off, a batch emulsion in the desired ratio of resin to waste is prepared in the emulsification tank. Continuous streams of resin and waste in the correct proportions are then fed into this emulsion base in the emulsification tank. Emulsion samples are frequently drawn for rheological characterization and for droplet size distribution determination. Additionally, once pumping into cans is started for purposes of solidification, samples for subsequent
Ind. Eng. Chem. Process Des. Dev., Vol. 20, I2500
SYMBOL
7500
1
5000
-
2500
-
,oooo
2 E
0
2.5
RPM
A
5.0
RPM RPM
10.0
Table I. Results for Run 34
f l
SPINDLE SPEED
waste used resin used planned waste to resin ratio (wt basis) initiator used temperature of waste solution, " C temperature of resin, "C flow rate of waste solution, g/min
-
3 E W z
z
-
CAN *I I
IO
20
l
I
l
50
40
30
I
6 I
70
60
80
TIME (MINI
Figure 3. Apparent viscosity vs. time elapsed since the commencement of emulsification, run 34.
I
APEAKEXOTHERM ~
35
i-
II j
-
03
05
07
09
No. 1, 1981 87
I1
INITIATOR CONCENTRATION 1WT.h SASED ON RESIN I
Figure 4. Effect of initiator concentration on peak exotherm and time to peak exotherm for run 34.
leaching tests (Biyani, 1978) of the solidified product are also withdrawn and allowed to solidify in 40-mL plastic vials. Experimental Results. A sampling of results is presented in Table I. The viscosity of the emulsion samples at different spindle speeds is plotted (Figure 3) as apparent viscosity vs. time elapsed since the beginning of emulsification. In the polymerization reaction encountered here during solidification, the peak exotherm and setting times can be controlled by the amount of initiator added. Thus,the measured peak exotherms and the corresponding times to peak exotherm are plotted (Figure 4) as a function of initiator concentration. Simulation of Cure Temperature Profiles The curing reaction of the emulsion is exothermic (17 kcal are released (Brandrup and Immergut, 1966) for every mole of styrene polymerized), and a peak exotherm is associated with the solidification process. Much concern (National Conference, 1977; WSU, 1977) has been expressed over this heat generation and dissipation, especially for the case where, in industry, larger containers of up to 100 ft3 (2.832 m3) are used for solidification. Cans of up to 10 gal (0.038 m3) have been used (Jain, 1978) for solidification purposes on the pilot plant and exotherms measured. Exotherms in larger containers thus remain to be determined. One approach is to perform a computer simulation to generate the peak exotherms based on thermal and polymerization rate data. The upper limit for the peak exotherms can be determined by assuming an adiabatic reaction condition in the cure container. The calculations which are quite simple and presented by Biyani (1978) show the temperatures to be safe (less than 100 "C) even
sodium sulfate, 20% by weight Aropol WEP 661-P 65:35
Lupersol Delta-X 55 20 1368 for 18.5 min, then 260 flow rate of resin, g/min 140 batch of resin, kg 13.4 flow period of waste and resin, min 24 mixer type and speed, rpm 3B, Turbon; 1850 canning cycle time, min 6 filling time per can, min 1 amount of initiator per can, mL 6-14 duration of mixing in can, min 3 time for emulsification, min 8 type of mixer for initiator Helicone 6 total number of cans density of waste, mg/mL 1.14 density of resin, g/mL 1.02 waste t o resin ratio (wt basis 66:34 achieved) quality of emulsion uniform, viscous, and stable initiator concentration, g/100 g of 0.49-1.15 resin in emulsion peak temperature, " C 54-71 time t o reach peak exotherm, min 22-36 compressive strength, N/mmz 14.9 ?r 0.53 % leached in 84 days 0.5 7-0.86 characteristics of the solidified pro- good encapsulation duct and good mechanical integrity; good curing and hard set; uniform appearance with no free water
under adiabatic reaction conditions. The approach to develop more realistic heating/cooling curves is described below. A heat balance on the element of a cylindrical shell yields (Kreith, 1976) the following differential equation
a2T -++-+ 1a2T - + + =d2T =- + -1aT ar2 r ar r2a42 a z 2
4 k
PCPaT k at
(2)
The following assumptions are made: (1)The temperature T is assumed to be independent of C#J without loss of accuracy. (2) C, and p are independent of temperature. (3) Thermal conductivity, k, is uniform. A. One-Dimensional Model. Neglecting the z-direction changes, eq 2 can be written as (3)
IC: at t = 0, for all r, T = To = 70 O F ; BC 1: for all t , at r = 0, aT/ar = 0; BC 2: for all t, at r = R, -Iz(dT/ar) = h(T - 70). Case I: Uniformly Constant Heat Generation. The above differential eq 3 is solved using numerical procedures. As a first approximation, the rate of heat generation is assumed to be uniformly constant. The time to peak exotherm is assumed to be the total time for completion of the reaction. Typical values (Jain, 1978) of the time to peak exotherm are taken as 0.5 and 1.0 h. The values of some of the thermophysical quantities used in the computations are presented in Appendix I. The results for the 0.5 and 1.0 h cases are summarized in
88
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
Table 11. Exotherm Calculations for Various Sized Containers (One-Dimensional Model)
item Case I. uniformly constant heat generation
container size 1 gal 55 gal 50 ft3 1 gal 55 gal 50 f t 3
peak exotherm,a "F 152.4152.4+ 152.4+ 152.4+ 152.4+ 152.4+
1gal 55 gal 50 f t 3
128.1+ 128.4+ 128.4+
Case 11. time dependent heat generation
surface temp at time to time to peak peak exoexotherm, h therm, "F
1.0 1.0 1.0
time step, h
0.5 0.5 0.5
143.3 148.9 150.6 146.7 150.6 151.5
0.10 0.10 0.10 0.05 0.05 0.05
1.02 1.48 1.48
119.6 122.5 125.2
0.02 0.02 0.02
The peak exotherms listed are for any point along the longitudinal axis. The initial temperature of the emulsion for all cases is 7 0 ° F . (I
Table 111. Exotherm Data for a 1-Gal Can for Various Values of k t a
k,, Limo1 s
0.3
X
los
0.3 x 103
0.3
X
10'
time t o peak exo- peak exotherm, "F therm, h 88 121 128
23.5 5.5 1.02
time step, h 0.50
130
0.10
1;
Z=022FT
0.02
The k , for pure styrene polymerization (Walling, 1957) is 0.3 x 10' L/mol s.
0132 H O U R
L/D
LL
:I
O0
0732 H3LR TIME
a
Table I1 with k, value drawn from Table 111. Temperature profiles leading to a peak exotherm are obtained. For obtaining the cooling curves, the heat generation term is deleted from eq 3 during the computations. Case 11. Time-Dependent Heat Generation. As a more realistic approach to evaluating the exotherms, the rate of heat generation should be evaluated as a function of time and temperature, as opposed to being linear with time only. More precisely, the heat generation term q / k , in eq 3, is dependent upon the reaction rate. The derivation of this term and its application in the simulation of temperature profiles-with the aid of a computer program-is presented in Appendix 11. The results again are summarized in Table 11. The salient features regarding the heat generation term and the applicability of the computer program are the following (1)The reaction rate has been evaluated for an initiator concentration of about 1% by weight of resin. (2) The k d and f have been evaluated for a promoter concentration approximately that in WEP 661-P. (3) It is assumed that k,2/kt is a function of temperature alone and is averaged for the effect of percent conversion. The k, is taken to be the same as for bulk styrene polymerization even though the cross-linking reaction involves radical addition to polyester and styrene double bonds. The k , is usually (Pennwalt Corp. Bull. 1973) reduced by several orders of magnitude due to the high viscosity of the emulsion and gel. The determination of k, for a highly viscous emulsion turning into a cross-linked gel is complicated; even an order-of-magnitude prediction may be widely off. As an alternative approach, k , may be determined to within an order of magnitude by comparing the temperature profiles for a 1-gal can for various parametric values of kt (Table 111) with those obtained in the experiments. For higher values of k,, larger time steps could be used without significant loss of accuracy since the times to peak exotherm were higher. From Table 111, it could be concluded that for the WEP 661-P-MEKP system, k, is of the order of 3 L/mol-s. Once
,
n w
.A
0
0 093
0 186
0 28
DISTANCE FROM AXIS, FT
Figure 5. Development of radial temperature profiles on a fixed axial plane with progress in time.
this is ascertained, temperature profiles for various size containers are simulated (Table 11). (4) The accuracy of the finite difference techniques in approximating continuous temperature profiles is lmited by the size of the time and space steps. (5) All the assumptions listed under eq 2 apply to the program. (6) Heat loss from the reaction vessel is accounted for with a calculated natural convection coefficient of 1.09 Btu/h ft2 O F . This causes the temperature to drop rather slowly with time (Biyani, 1978). I t should be recognized that higher values of natural convection coefficient do exist in practice (Kreith, 1976). B. Two-Dimensional Model. By including the variations in z dimension, eq 2 can be written as a2T laT -+--+ -+ ar2 r dr
a2T
-4= - -PCPaT
az2
k
k at
(4)
IC: at t = 0, for all r , T = To = 70 OF; BC 1: for all t , at r = 0, aT/ar = 0; BC 2: for all t , at r = R, -k(aT/ar) = h (T - 70); BC 3: for all t , at 2 = L, -k(dT/dz) = h (T 70). The solution of the above equation in terms of T = T(r,z,t) has been obtained using Heating 5, Oak Ridge (1977). Figure 5 typically shows the development of the radial temperature profiles at a given axial plane (fourfifths from the center), with progress in time. Figure 6 shows the radial temperature profiles at various planes
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 89 Table IV. Exotherm Calculations-Effect of Time Step (Two-Dimensional Model) time t o container peak exopeak exoitem size therm, OF therm, h Case I. uniformly constant heat generation Case 11. time dependent heat generation a
surface tempa at time t o peak exotherm, " F
time step, h
1 galb
151.74+
1
141.7+
0.1
1galb
135.41 135.32 135.32
0.50 0.51 0.51
129.02 128.82 128.82
0.1 0.01 0.00033
Surface temperature varies with distance z ; however, the indicated temperature is maximum.
LID = 1.365.
Table V. Exotherm Calculations-Effect of LID Ratio (Two-Dimensional Model, Time-Dependent Heat Generation surface time t o temp at peak time to peak exoexoexotherm, therm,'F therm, h "F
LID 0.2 0.75 1.00 1.365 3.00 4.00
134.26 135.29 135.29 135.41 134.88 134.74
136
-
135
I30
::
0.332 0.532 0.532 0.50 0.432 0.432
time step
130.75 129.11 128.82 129.02 128.86 : 128.61
At,
h 0.1 0.1 0.1 0.1 0.1 0.1
:
-=
-
2
i
00, 056
Y r 3
t
5
TIME
I N I T I A L TEMP: 70'F
L 125
loa -
--
1
107
0532 HOUR
L/D = I O
-
-
-
2 : 0 0 TO 066
4
TlME 001 HOUR
"* 0
I O
L / 20 D
30
Figure 7. Effect of container L I D ratio on peak exotherm time (peak temperature at the center, 135 OF).
-
-
I
0093 0 106 DISTANCE FROM AXIS, F T
0 28
Figure 6. Radial temperature profiles at varius planes across the axis.
drawn across the axis. Table IV shows the effect of computational time step on the accuracy of the computations while Table V summarizes the effect of varying the container L I D ratios on the exotherm. These results are plotted in Figure 7. Discussion A summary of results from the five cases considered is presented in Tables 11, IV, and V. These tables show that temperature profiles for containers up to 50 ft3 are not much different from those for 1-gal cans. This is to be expected because the adiabatic exotherm (
