Ind. Eng. Chem. Res. 1992,31, 543-549
Kcl, Kc2= gain of the diagonal controller C’ m = manipulated variable vector L = reflux flow rate q = feed liquid fraction
RGA(.)
Ail(.)
r = set-point vector TI1, TI,= integral time of diagonal controller U = left singular value decomposition matrix u 1 7 output singular vector of (.) associated to the maximum singular value u1 u2 7 output singular vector of (.) associated to the minimum singular value u2 V = right singular value decomposition matrix V = vapor flow rate vi(.) = input singular vector of (.) associated to the maximum singular value u1 v,(.) = input singular vector of (.I associated to the minimum singular value u2 y = output vector YHK,YD = heavy key component composition in the distillate XLK,XB = light key component composition in the bottom product ZLK = light key component feed composition ZHK = heavy key component feed composition ZH, = heavy component feed composition Greek Letters a = tuning parameter of the decoupler A = model errors matrix 6 = input error magnitude Aij = element ij of the relative gain array Z = diagonal matrix of singular values ul(.) = maximum singular value of matrix (.) u2(J = minimum singular value of matrix (.I
543
Literature Cited Bequette, B. W.; Edgar, T. F. Non-Interacting Control System Design Methods in Distillation. Comput. Chem. Eng. 1989, 13, 641-650. Brambilla, A.; Chen, S.; Scali, C. Robust Tuning of Conventional Controllers. Hydrocarbon Process. 1990,11,53-58. Bristol, E. H. On a New Measure of Interaction for Multivariable Process Control. ZEEE Trans. Autom. Control 1966,AC-11,133. Grosdidier, P.; Morari, M.; Holt, B Closed-Loop Properties from Steady-State Gain Information. Znd. Eng. Chem. Fundam. 1985, 24,221-235. Lau, H.; Alvarez, J.; Jensen, K. F. Synthesis of Control Structures by Singular Value Analysis: Dynamic Memures of Sensitivity and Interaction. AZChE J. 1985,31, 427-439. Luyben, W. L. Distillation Decoupling. AZChE J. 1970,16, 198. Mc Avoy, T.J. Interaction Analysis; ISA Monograph Series 6;ISA: Research Triangle Park, 1983;Chapter 6. Nett, C. N.; Manousiouthakis, V. Euclidean Condition and Block Relative Gain: Connections, Conjectures and Clarifications. ZEEE Trans. Autom. Control 1987,AC-32,405-407. Ray, H. W. Advanced Process Control; McGraw-Hill; New York, 1981;Chapter 3. Rosenbrock, H. H. Computer Aided Control System Design; Academic Press: London, 1974;pp 162-171. Shinskey, F. G. Distillation Control, 2nd ed.; McGraw-Hill: New York, 1984;Chapter 5. Skogestad, S.; Morari, M. Design of Resilient Processing Plants-IX. Effect of Model Uncertainty on Dynamic Resilience. Chem. Eng. Sci. 1987a,42, 1765-1780. Skogestad, S.; Morari, M. Implications of Large RGA Elements on Control Performance. Znd. Eng. Chem. Res. 1987b,26,2323-2330. Skogestad, S.;Morari, M. LV-Control of a High-Purity Distillation Column. Chem. Eng. Sci. 1988,43,33-48. Received for review April 1, 1991 Revised manuscript received September 16, 1991 Accepted September 30, 1991
Continuous Solidification/Stabilization Processing of Hazardous Wastes through Polymeric Microencapsulation Michael R. Powell? and R. Mahalingam* Department of Chemical Engineering, Washington State University, Pullman, Washington 99164-2710
The continuous solidification/stabilizationof a simulated aqueous hazardous waste stream through microencapsulation in a polyester matrix was evaluated in a static mixer/reactor and found to be feasible. For the emulsion formation step, the Sauter mean droplet size of the emulsion formed was found to vary with the stream total flow rate to the -0.87 power, the number of mixing elements to the -0.63 power, and the volume fraction of waste to the 0.2 power. Next, numerical simulation of the polymerization reaction step for the conditions investigated predicted that the degree of polymerization occurring inside the mixer/reactor was only on the order of a safe and desirable 0.2% of the total conversion, thus ensuring the absence of any premature gelling within the mixer/reactor; also, this resulted in only a negligible fluid temperature rise, these being verified by experimental observations and measurements. On these bases, exothermicity and solidification of the stream inside the mixer/reactor are hence not expected to be processing problems.
Introduction There are two major treatment pathways for hazardous waste streams. The first is chemical detoxification. This involves treating the waste in such a way that it becomes chemically inert. Obviously this is the preferred method of treatment from an ecological standpoint. Chemical
* Author to whom correspondence should be addressed. Present address: Battelle Pacific Northwest Laboratories, Richland, WA 99352. f
detoxification, however, is often prohibitively expensive or not currently possible. In such cases, the second method of treatment is invoked. These are the solidification and stabilization technologies. The approach here is to treat the waste stream in such a way that it can be safely transported, stored, or buried. An example of the solidification and stabilization technique is the polyester encapsulation process (Subramanian and Mahalingam, 1979). In this process, the waste stream is mixed with a polyester resin-in-styrene binding material until the waste is finely dispersed within the resin. If the
0888-5885f 92f 2631-Q543$Q3.QQ/Q 0 1992 American Chemical Society
544 Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992
waste is aqueous, the mixing results in a waste-in-resin emulsion. The resin phase is next polymerized resulting in the waste becoming encapsulated within the highstrength cross-linked resin shell. Previous studies, both in the laboratory and on the pilot plant, emphasized batch processing (Mahalingam et al., 1977; Mahalingam et al., 1981a,b) and evaluated the rheological characteristics of the emulsion, the waste types treatable (Subramanian and Mahalingam, 1979), and the properties of the solidified waste, for example, the leach characteristics and compressive strength. The present research (Powell, 1990) is aimed at converting the batch process into a continuous one through studies in a single continuous static mixer, in order to both emulsify the waste within the resin and to uniformly mix the polymerization initiator into the emulsion in order to achieve solidification,and to quantify the process parameters. This quantification was pursued along the following lines: determine the functional dependence of emulsion droplet size produced on process parameters such as emulsion (or feed streams) flow rate, number of mixing elements, and volume fraction of dispersed waste; next, simulate and verify the solidification/polymerization reaction; and, finally, relate these to the leach characteristics of the solidified waste product; this last aspect is discussed here only as relevant, although our studies on this are also extensive. Background Solidification a n d Stabilization Technologies. Solidification and stabilization ( S / S ) processes are intended for use in situations where chemical detoxification of a hazardous waste stream is either not possible or prohibitively expensive. S/S technologies are employed in treating the hazardous material in such a way that the resulting solid can be safely transported and either stored or buried. Two of the more popular current technologies for solidification/stabilization are grout processing and urea-formaldehyde binding, and these appear to be based more on economics than on leach characteristics. The polyester encapsulation process is a relatively new S/S technology. Here, the first step involves the emulsification of aqueous wastes into a polyester resin, to a maximum possible 7:3 ratio. Typical emulsion droplet sizes are on the order of 2-10 pm. In the next step, a small amount of free-radical initiator is added to begin the polymerization of the continuous resin phase. A highstrength monolithic solid results within about 10 min, the time interval being controllable by various process parameters. The aqueous wastes are thus effectively encapsulated within the 2-10-pm shells of the solidified resin. A full discussion on the process is available in Subramanian and Mahalingam (1979). Static Mixers. A static mixer achieves mixing by splitting, rotating, and recombining the flowing fluids. In laminar flow, the degree of mixing achieved is determined principally by the number of mixing elements present (Boss and Czastkiewicz, 1982). The enhancement of both mass and heat transfer provided by static mixers has been studied extensively (Grave, 1971; Morris, 1974; Nauman, 1979). Because of the continual redistribution of the velocity profiles provided by the mixing elements, it is possible to achieve very nearly ideal plug flow reactor conditions. This results in a more uniform product, particularly in the case of polymerization reactions where the open-tube velocity profiles can result in very high polydispersities. It should be added that for turbulent flow and low volume fractions of dispereed phase, the drop sizes produced in flow through a static mixer are expected to be an order of magnitude smaller than those produced by
similar flow through an open pipe (Middleman, 1974). The most important attribute of static mixers as they apply to the polyester process here is the high shear rates that can be achieved to facilitate the formation of a stable wastein-resin emulsion. Emulsion Rheology. The rheological characteristics of an emulsion are dependent primarily on the viscosities of the dispersed and continuous phases, the droplet size distribution, the volume fraction of the dispersed phase, and the rate of shear. Sherman (1968) investigated the dependence of the low-shear viscosity of water-in-oil emulsions on the mean drop diameter and found that for concentrated emulsions (volume fraction of dispersed phase 4 1 0.3) the apparent viscosity is inversely proportional to the mean drop diameter, up to about 15-pm size. A mean drop size larger than this was found to have little effect on the measured emulsion viscosity. The viscosity of an emulsion is also a strong function of the deformability of the dispersed-phase drops under shear (Sherman, 1968). The degree of deformability of these drops depends, to a great extent, on the characteristics of the adsorbed surfactants. Many emulsions are non-Newtonian; hence the apparent viscosity is also a function of the applied shear rate. The Na8O4(aq)-in-resinemulsion produced in the polyester encapsulation studies has been shown to be pseudoplastic, with a fluid flow behavior index (n)as low as 0.65 (Biyani, 1978). Model Development For purposes of understanding the process and scaling it up, it is desirable to develop a rigorous model for the continuous polymeric encapsulation of hazardous wastes. There are two distinct phases of the process that are amenable to modeling. The first is the emulsification of the waste into the polyester resin, and the second is the mixing/polymerization reaction that occurs upon injection of the initiator into the emulsion. In the emulsification step, the emulsion property that is most relevant is the mean emulsion droplet size. This is because previous work has shown the leach rate of the solidified product to be a strong function of droplet size (Subramanian and Mahalingam, 1979); thus, a theorybased model that predicts mean droplet size as a function of process parameters is desired. Middleman (1974), Strieff (1977), and Al Taweel and Walker (1983) have developed semiempirical relationships for Sauter mean droplet size as a function of Reynolds (Re) and Weber (We)numbers. D32,the Sauter mean drop size, is defined as
where f ( D )is a drop size distribution function which gives the number fraction of drops that are of size D. These relationships, however, are applicable for turbulent flow. Turbulent flow conditions are impractical for use in the polyester process here for the following reasons. Typical emulsion viscosities are on the order of 100-2000 cP, perhaps even higher. For static mixers (Komax Design Bulletin 103A), turbulent flow is achieved at Reynolds numbers greater than about 500. Even for an emulsion viscosity as low as 100 cP, the needed inlet pressure for this Reynolds number would be prohibitively large (AI' = 1000 psi for N = 30). There is also the phenomenon of shear-induced coalescence to consider. A t the onset of shear-induced coalescence the shear rate is high enough
Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992 545 that it tends to drive into phase separation any emulsion that is formed. On the basis of our experimental observations in the present work, shear-induced coalescence occurs at Re 1 ~ 2 0 It . is clear that the Kolmogoroff theory of isotropic turbulence cannot be applied to the laminar flow conditions prevailing in the polyester encapsulation process. On the basis of work done by Al Taweel and Walker (19831, an energy balance approach was selected for the modeling of the emulsication of waste into the resin. The basis of this model is the assumption that the flow energy of the input stream (APQE)times some mixer efficiency factor (7) is equal to the energy of the newly formed emulsion surface area. In terms of the Sauter mean diameter (D33,the total interfacial area per unit volume of an emulsion is given by A" = 64/D32 (2) where 4 is the volume fraction of dispersed waste. The energy balance is then f l q = 64a/D32 (3) where u is the interfacial energy between the waste and resin. From the literature (Komax Bulletin 103A),APfor a given tube size can be estimated by the empirical expression AP(N/m2) = 0.707QE(mL/min)p(cP)N (4) Substituting this into (3) gives
On the basis of (5), it should be possible to correlate D32 with emulsion volumetric flow rate QE,4, and N . Next, the modeling of the initiator mixing effects was carried out by the use of a simulated residence time distribution (RTD). RTD theory is frequently used to model the nonideal effects occurring in reactors. If the RTD is known for a reactor, it should be possible to obtain accurate information about the extent of reaction and heat generation. Unfortunately, there is no adequate theory that allows one to predict the RTD in a static mixer system a priori. For this reason, the RTD must either be determined experimentally (preferred method) or estimated by means of a semiempirical model. Nauman and Nigam (1985) have developed a model for the approximation of RTDs in static mixers. This model can be envisioned as an open tube along which there are a series of mixing planes evenly spaced. The fluid flowing through the mixer is assumed to flow as it would through an open tube (fully developed velocity profile) except at the mixing planes. At each of the mixing planes the fluid undergoes a mathematical transformation whereby the fluid that is originally close to the tube wall is transported instantly to the tube center and vice versa. In effect the flow is turned inside out. Nauman and Nigam determined that four Kenics static mixing elements are equivalent in action to that of a single mixing plane. The corresponding relationship for Komax elements is unknown; however, it could be expected to be of the same order. In the model development presented here, the approach of Nauman and Nigam was adopted for approximating the RTD. In their model, however, the simultaneous reaction and heat generation terms were not included. The model developed incorporate the simultaneousreaction and heat generation terms into the differential heat and mass balances of the fluid flowing within the mixing tube. Thus, the balance equations to be solved simultaneously are
In summary, the reaction and heat generation effects are modeled as occurring continuously along the entire length of the mixer/reactor; the mixing effects, however, are approximated by a series of mixing planes located at discrete points along the mixer/reactor. The associated boundary and initial conditions are
w, = wmo, T = Ti,
aT = 0 (adiabatic reactor), aY
at x = 0
awm - 0 -
aY
(8)
at y = 1 (10)
In (6) and (7), the axial and radial velocity profiles are respectively given as
-'
v,(r,z) = -a Jrrp(r,z) v,(r,z) dr rp(r,z) dz
(12)
Kinetic parameters for the polymerization reaction were taken from previously published results (Biyani, 1978; Biyani et al., 1980; Mahalingam et al., 1981a).
Experimental Section It was determined previously (Subramanian and Mahalingam, 1979) that the leach rate of waste encapsulated by the polyester process is a function of the emulsion droplet size. On the basis of this premise, it was decided that the primary parameter of interest in the present studies would be the mean emulsion droplet size. The experimental studies were carried out in two phases. The first phase involved the characterization of the Sauter mean emulsion droplet size with respect to changes in the number of Komax mixing elements (N), the volume fraction of dispersed waste (@),and the volumetric flow rate of the emulsion through the mixer (83. The second phase involved correlating the observed leach rates of waste from the solidified product with both the emulsion droplet size and the degree to which the initiator is mixed into the emulsion prior to solidification. The number of Komax mixing elements (N2)between the initiator injection point and the exit of the mixer/reactor was taken to be a measure of the degree of initiator mixing. The experimental unit consists of four basic sections. The first three are the flow arrangements for the resin, simulated waste, and polymerization initiator, and the fourth is the stainless steel static mixer/reactor. A schematic of the unit is given in Figure 1. The static mixer was obtained from Komax Mixing Systems (Wilmington, CA) in the form of 100 individual mixing elements. A fixed number of these elements were packed by hand into the 8.1-mm4.d. (9.5mm-0.d.) stainless steel tube, also supplied by Komax. The water-extensible resin that was used was Aropol WEP-662P polyester resin (Ashland Chemical, Columbus, OH). This resin consists of about 60% styrene, 35-40% polyester, and proprietary amounts of surfactants and
646 Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992
h
I
I
12,
0N=30 0 N=50 AN=72
A N=95
m w
A
I I I h1 I
04 0
200
400
600
I
800
Emulsion Flow Rate (ml/min)
Figure 2. Sauter mean drop size vs Q E for all 4's and Ilrs. ked
00=0.35
A - N2-blanketed resin reservoir
.0=0.40
B - simulated-waste reservoir C - N2-pressurized MEK peroxide reservoir
AQ=0.45
A @=0.50
D - nitrogen cylinder E solidification container F .Komax static mixer G .resin metering pump H - MEK peroxide rotameter I simulated-waste rotameter J - pressure gage K - check valves L .polymerization initiator injection pori locations ~
~
Figure 1. Schematic of experimental unit.
polymerization promoters (cobalt napthenate and dimethylaniline). The simulated waste solution used in all runs was a 20 w t % sodium sulfate solution. This is the principal component in low-level boiling-water nuclear reactor wastes (Krischer and Simon, 1984). Previous investigations have shown the polyester process to be well-suited for a wide variety of waste types (sodium sulfate, boric acid, filter aids, decontamination chemicals, heavy metals and mixed organics, organic chlorides, pigment sludges, mercury wastes, cyanide wastes, kepone, PCB, arsenic wastes, etc.); however, it is most effectively applied to aqueous solutions (Subramanian and Mahalingam, 1979). The polymerization initiator used was a solution of methyl ethyl ketone (MEK) peroxide in MEK (Delta X-9, Pennwalt). All experimentation was performed with all three process streams held at a temperature of 20 f 2 "C. The correlation between D32 and $, N, and QE was determined as follows. The flow rates of the resin and the waste were adjusted to give the desired $ and QE;QE)swere selected over the entire range that gave stable emulsions. No MEK peroxide initiator was used during this phase of the process characterization runs. The emulsion droplets were placed on a microscope slide and photographed at 400X magnification under a phase-contrast microscope (Nikon Diaphot). The second phase of the experimental work involved studying the effect of drop size and degree of initiator mixing on the leach rate of the encapsulated waste. Flow samples were collected at the exit of the mixer/reactor, at selected values of QE, $, and initiator mixing length N2 N2was varied by the appropriate placement of the initiator injection taps. One tap was installed at 15 mixing elements from the mixer exit and another at 30. The initiator injection porta consisted of 4 cm of 0.8-mm4.d. (1.6-mm-0.d.) stainless steel tubes that were tapped into the static mixing tube. For each set of N,, $, and 0 3 2 values, three samples were cast in the form of 3-cm-diameter right cylinderswith LID = 1.0. One of the samples was used in the ANS 1601 leach test (American Nuclear Society, 1986),another was
0
i 0
200
400
600
800
Emulsion Flow Rate (ml/min)
Figure 3. Sauter mean drop size vs Q E and 4 for N = 72.
used for scanning electron microscopy studies, and the third was kept as a spare. The leachate was analyzed for the amount of sodium ion present using an atomic absorption spectrophotometer (Perkin-Elmer 2280 U S ) . A Hitachi 5-570 scanning electron microscope was used to determine the average drop (cell) sizes for each of the solidified samples, after being cleaved to expose the encapsulated waste cells. For purposes of comparison with the emulsion drop sizes, the sizea from SEM measurements were recalculated to be also expressed as 0 3 2 , following a procedure described by Powell (1990). The electron micrographs showed the minimum thickness of the polymer shell surrounding each waste droplet is on the order of 0.1-0.5 pm, regardless of the volume fraction of waste and the drop size distribution. This shell thickness is the key parameter defining the strength of the solidified product.
Results and Discussion The results of the emulsion drop size studies are presented in Figure 2. This is a plot of the measured Sauter mean diameter versus emulsion flow rate (QE) for all the 6's and llrs studied. It should be noted that 0 3 2 decreases with increasing shear (as measured by QE) and with increasing N. Also, it was observed that, on the average, D32 increases with an increase in 4, but the magnitude of this effect is within the estimated uncertainty in the 0 3 2 measurements. For this reason, all 4's have been plotted together in Figure 2, whereas, for example, Figure 3 is a plot of D3, versus QE, for various $'s, for N = 72. It is seen that the effect of $ is in fact very small. The approximate 95% confidence intervals are f10% for the 0 3 2 measurements and f 1 2 mL/min for QE. A correlation was determined for the data in Figure 2. This correlation is D32(pm) = 5000Q~+'~87N-O~63$0~20 + 2.0 (13)
Ind. Eng. Chem. Res., Vol. 31, No. 2,1992 647 i
nnn.
1
---
0 N=30 0 N=50 AN=72 A N=95
0
8
h
0 250
25
0
50
75
100
125
200
0
400
600
800
Emulsion Flow Rote (ml/min)
Mixing Elements (N)
Figure 7. Mixer efficiency ( q ) as a function of QE and N.
Figure 4. Maximum attainable waste fraction vs N.
0.015
1 GOO
0N=30
0.750 --
0 N=50 A N=72 AN=95
B
X
E 0
1
0
a
z o
- -#- -15( - ,0500
~ A 0 - 0 D 3 2 = 7 6 p m . N2=15 0 - 0 D -7.7pm. N2=30 A A D 3 2 k p m N? = 15 A-A0$=6 Opm: N j = S O
0.250 4
0
200
400
600
I
800
-
0.000 0
5
10
Emulsion Flow Rate (ml/min)
Figure 5. Maximum attainable waste fraction vs QE and N.
15 Time (days)
20
25
3
Figure 8. Cumulative leachability vs time for #J = 0.55.
The variation of the static mixer efficiency parameter changes in N a n d QE, is given in Figure 7. It is seen that, in general, as N increases 9 decreases (u is practically constant based on experimental observations). This increase in mixing efficiency with decreasingN has also been observed by other workers. Al Taweel and Walker (1983) noted that the maximum efficiency is obtained by the first element in the mixer and then falls off rapidly as the fluid progresses through the mixer. Figure 8 shows the results of the ANS 16.1 static leach 1 2 0.000 4test for some of the solidifkd monoliths, and they correlate 3 4 5 6 7 0 well with the Sauter mean drop sizes. Drop Size ( p m ) Computer simulations of the conditions downstream of Figure 6. Sample drop size distribution from phase contrast mithe initiator injection point were performed on the basis croscopy: #J = 0.4, QE = 135 mL/min, N = 95, D, = 2.31 pm, D32= of simulated RTD discussed earlier. Equations 6 and 7 3.44 pm. were solved simultaneously in Advanced Continuous Simulation Language (ACSL), by the Method of Linea and the Similar correlations were observed for each value of N Gear Stiff Method of Integration. This simulation predicts studied, showing the consistency: a temperature increase of only about 0.15 "C between the D32(pm) = 4 6 5 O Q ~ ~ . ~ ~ N2.40 ~ . ~ ~N4=~30. ~ (14) ~ = 30, QE initiator injection point and the mixer outlet (N2 = 200 mL/min, 4 = 0.5) and matches the experimental Da2(pm)= 5600QE4~a76N+~63~0.20 2.70 N = 50 (15) observations. A parametric evaluation of the model was Ds2(pm) = ~ ~ ~ Q E ~ . 1.20 ~ ~ N~ = N 72 ~ (16) . ~ ~ next I carried $ ~ ~out,~in order ~ to obtain the effluent mixing cup as a function of both temperature and fractional Ds2(pm) = 4800QE+.s7N4.634023 + 1.10 N = 95 (17) the mean residence time inconversion the reaction section and the The dependence of the maximum attainable volume volume fraction of waste. The model predicts that the on N and Q E is not evident from fraction of waste (4mm) fractional conversion of the monomer is primarily a Figure 3. Figure 4 shows that as N decreases, r # in~ ~ ~function of the mean residence time, but also increases creases. This increase in C # J ~ =with decreasing N is only with an increase in emulsion entrance temperature. The observed down to about N = 20. Below this value no mixing cup temperature of the mixer/reactor effluent is emulsification takes place so 4- drops sharply to zero at predicted to be a function of both the mean residence time this point. Figure 5 gives the dependence of 4- on both and the waste volume fraction. QE and N. Figure 6 is a sample drop size distribution Figure 9 is a plot of the mixing cup temperature versus the mean residence time for sample cases of waste volume (DSD) histogram, based on phase contrast microscopy. The DSD is essentially log-normal, with the maximum fractions of 0.50 and 0.65. It is seen that as both the number fraction at a drop size around 2.0 pm for the residence time and 4 increase, the temperature also inconditions referenced. creases as to be expected since the extent of polymerization ( 9 ) for emulsification, with
1
~
+ + +
548 Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992
the static mixer are not expected to be problems in such an operation.
310
00=0.50
Acknowledgment M.R.P. was supported on a UNOCAL Fellowship. Material support came from Komax Mixing Systems and Ashland Chemical Go. I
298
@ 0
50
100 150 200 Mean Residence Time (sec)
250
Figure 9. Simulation of mixing cup temperature of mixer effluent. 0.200
,
I
00 = 0
5
0 150-
50
A0=0 65
>
5
0 100-
0 C
P c)
050
--
0
50
100 150 200 Mean Residence Time (sec)
250
Figure 10. Simulation of fractional conversion of resin.
increases and the heat of polymerization also results in a temperature increase. As 4 alone is increased, however, there is more waste per unit volume of emulsion that must be heated and this tends to keep the temperature down. Figure 10 shows the dependence of the fractional conversion of the monomer on the mean residence time and the waste volume fraction. In the absence of heat effects, the fractional conversion does not depend on the value of 4, because the value of the fractional conversion applies only to the resin phase and the conditions within the resin are independent of 4. As was shown in Figure 9, however, 4 does influence the temperature of the emulsion; thus 4 does have an indirect effect on the fractional conversion. For the residence times encountered in practice, it is seen that the fractional conversion achieved is the desirable low value; however, as the residence time increases the conversion also increases. For both Figures 9 and 10, the initiator concentration was set equal to 1.0 w t 70based on the weight of resin in the emulsion and the stream inlet temperature was held constant at 298 K. The parameters specified for determining the mean residence time were L = 0.2,1.0 m, QE = 100, 350 mL/min, and tube radius = 0.0041, 0.0080, and 0.0117 m. The number of mixing elements present in the mixer, which in turn determines the number of ideal mixing planes, was set by L and tube radius. Full details are available in Powell (1990). Temperature excursions and conversions in the solidification container, once the static mixer/reactor has been exited, are already well documented (Mahalingam et al., 1981a). Conclusions The results show that the continuous encapsulation process for aqueous hazardous wastes is a viable solidification/stabilization option. Through the use of a static mixer, it is possible to operate the process in the continuous mode. Exothermicity and premature gelling within
Nomenclature A , = interfacial surface area per unit volume C, = emulsion heat capacity D = droplet diameter D , = molecular diffusivity of resin in the emulsion D, = number mean droplet diameter D32= Sauter mean droplet diameter AH = heat of polymerization of resin k = thermal conductivity of the emulsion L = length of initiator mixing section LID = length to diameter ratio of cylinder n = power-law flow behavior index N = number of mixing elements N z = number of mixing elements downstream of initiator injection AP = pressure drop across mixer QE = emulsion volumetric flow rate Q, = emulsion mass flow rate r = radial position R = inside radius of the mixing tube R, = rate of polymerization of resin T = emulsion temperature u, = radial velocity u, = axial velocity w, = weight fraction of resin in emulsion x = dimensionless axial position y = dimensionless radial position z = axial position 7 = static mixer efficiency parameter 9 = volume fraction of waste in emulsion d,, = maximum attainable volume fraction of waste p = fluid viscosity p = emulsion density pa&) = emulsion density at position z , averaged across the radial plane ~7= interfacial energy between resin and waste Registry NO.MEK, 1338-23-4; hop01 WEP-662P, 97793-27-6; styrene, 100-42-5; dimethylaniline, 121-69-7; sodium sulfate, 7757-82-6.
Literature Cited A1 Taweel, A. M.; Walker, L. D. Liquid Dispersion in Static In-Line Mixers. Can. J . Chem. Eng. 1983, 61, 527-33. American Nuclear Society. “Measurement of the Leachability of Solidified Low-Level Radioactive Wastes by a Short-Term Teat Procedure”; American Nuclear Society, ANSI/ANS-16.1-1986, 1986. Ashland Chemical. ’Technical Data for AropolTMWEP 661P”; Ashland Chemical Co.: Columbus, OH, 1974. Biyani, R. K. Optimization of the Process Parameters and Economic Evaluations in Polyester Immobilization of Hazardous Wastes: M.S. Thesis, Department of Chemical Engineering, Washington State University, Pullman, WA, 1978. Biyani, R. K.; Subramanian, R. V.; Mahalingam, R. Polymerization with Redox Initiators. J . Appl. Polym. Sci. 1980, 25, 1257-60. Boss, J.; Czastkiewicz,W. Principles of Scale-up for Laminar Mixing Processes of Newtonian Fluids in Static Mixers. Znt. Chem. Eng. 1982, 22, 362-7. Grace. D. Static Mixinn and Heat Transfer. Chem. Process Ena. 1971, July, 57-59. Krischer. W.: Simon. R. Testing. Eualuation and Shallow Land BuriaZ of Lou, and Medium RaJioactiue Waste Form; Hardwood Academic: New York, NY, 1984. Mahalingam, R.; Juloori, M.; Subramanian, R. V.; Wu, W. P. Polyester Encapsulation of Hazardous Industrial Wastes; Proceedings of the 1977 National Conference on Treatment and Disposal of
-
I n d . Eng. Chem. Res. 1992,31, 549-561 Industrial Waste-waters and Residues; Information Transfer, Inc.: Rockville, MD, 1977; pp 97-106. Mahalingam, R.; Biyani, R. K.; Shah, J. T. Simulation of Solidification Temperature Profiles in the Polyester Process for Immobilization of Hazardous Wastes. Znd. Eng. Chem. Process Des. Deu. 1981a,20,8590. Mahalingam, R.; Jain, P. K.; Biyani, R. K.; Subramanian, R. V. Mixing Alternatives for the Polyester Process for Immobilization of Hazardous Residuals. J . Hazardous Mater. 1981b,5 , 77-91. Middleman, S. Drop Size Distributions Produced by Turbulent Pipe Flow of Immiscible Fluids through a Static Mixer. Znd. Eng. Chem. Process Des. Dev. 1974,13,78-83. Morris, W. D. An Experimental Investigation of Mass Transfer and Flow Resistance in the Kenics Static Mixer. Znd. Eng. Chem. Process Des. Dev. 1974,13,270-5. Nauman, E. B. Enhancement of Heat Transfer and Thermal Homogeneity with Motionless Mixers. AZChE J. 1979,25,247-58. Nauman, E. B.; Nigam, K. D. P. Residence Time Distribution of
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SEPARATIONS Pressure Drop Correlations and Scale-up of Size Exclusion Chromatography with Compressible Packings Abdul W. Mohammad, Donna G. Stevenson,and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
Pressure drop measurements were made for compressible gel packings Sephadex G-25 and G-100. A critical velocity at which pressure drop kept increasing was observed. Correlations were developed for pressure drop. Measurements of the chromatographic separation obtained for separating bovine serum albumin and nickel nitrate were correlated as measurements of H. A scaling procedure which keeps separation, pressure drop, and feed throughput constant was developed for each packing. The procedure and results for G-25 are similar to those developed previously for rigid packings. The use of smaller diameter packings can greatly reduce the amount of packing required. For G-100, which is quite compressible, the scaling procedure was different. Results of the scaling analysis for G-100 showed that there is little advantage to decreasing the particle size with very compressible packings. Size exclusion chromatography (SEC) separates molecules based on differential access to pores in the stationary phase and is used as a commercial method for large-scale separation of biomolecules (Janson and Hedman, 1982). SEC is most commonly used on a large scale for desalting usingdextran, polyacrylamide, and agarose based packings. Unfortunately, due to the highly porous nature of the packings which makes them compressible, the maximum flow rate is limited. Several different approaches for scaling of chromatographic systems have been proposed (e.g. Rudge and Ladisch, 1986; Wankat and Koo, 1988). The approach used by Wankat and Koo (1988) has also been used for adsorption and ion-exchange systems (Wankat, 1987) and adiabatic pressure swing adsorption processes (Rota and Wankat, 1990). This approach assumes that the existing old design is satisfactory. A new design, using a different particle size, will be developed while maintaining the same separation, pressure drop, and throughput. For chromatography with rigid particles it was found that reducing the particle size by half reduces the amount of packing
used and the cycle time by 75% if pore diffusion controls and by 60% if film diffusion controls. In order to develop scaling rules for SEC with compressible packings, it is important to develop correlations between pressure drop and measurable parameters such as flow rate, column diameter and length, and particle diameter. Previous works (Joustra et al., 1967; Davies and Bellhouse, 1989) have shown that the pressure drop correlation is highly nonlinear as opposed to the linear correlation for rigid particles (Bird et al., 1960). The previous experimental work measured pressure drop across the entire chromatographic system including tubing, valves, fittings,frits, and packing. Since the extracolumn pressure drop is significant, measurements of Ap across the column alone are needed. In this paper, the scaling approach will be extended to SEC with compressible Sephadex G25 and GlOO packings. The pressure drop correlations will be determined from the experimental data. Then using the experimental relationship for H and flow rates for the separation of bovine serum albumin (BSA) and nickel nitrate (NN), the scaliig
0888-588519212631-0549$Q3.QQ/Q 0 1992 American Chemical Society
