Environ. Scl. Technol. 1994, 28, 840-849
Fundamental Study of the Thermal Desorption of Toluene from Montmorillonite Clay Particles Brian R. Keyes and Geoffrey D. Sllcox'
Department of Chemical Engineering and Fuels Engineering, University of Utah, Salt Lake City, Utah 841 12 Nonisothermal desorption of toluene from individual montmorillonite clay particles was measured experimentally and modeled mathematically to elucidate details of the overall thermal desorption process. A single-particle reactor was used. It consisted of a porous, 2-6-mm clay pellet formed around a 0.05-mm diameter thermocouple in a 6- or 9-mm 0.d. glass tube. The tube was surrounded by a supplementary heater and placed in a GC oven. Desorption rates were obtained as a function of heating rate, clay type, particle size, and purge gas flow rate. In addition, the adsorption isotherms for two toluene/clay systems and one n-dodecanelclay system were measured and correlated using the Freundlich isotherm. At the conditions examined, the rate-controlling mechanism is associated with intraparticle diffusion. Isothermal desorption experiments using clay pellets of different sizes demonstrate that local desorption kinetics are not ratecontrolling. Toluene shows a slower desorption rate than n-dodecane at low concentrations. This is attributed to the hindered removal of toluene from interlamellar regions of the clay. Comparisons of single-particle reactor and pilot-scale rotary kiln results show that mass transport resistances associated with a bed of particles dominate the desorption process at rotary kiln conditions. Introduction Over the past decade, the cleanup of organically Contaminatedsoils has become a topic of increased interest. The discoveryof the numerous environmental catastrophes resulting from the improper disposal practices of the past has elevated public awareness and concern. This concern has manifested itself in the passage of a series of federal and state hazardous-waste-cleanup laws. Among the various options for remedial action, incineration or thermal desorption systems are considered most capable of the highest overall degree of destruction and control for the broadest range of hazardous waste streams. Consequently, the use of incineration and other thermal treatment methods is expected to grow (I). The purpose of this study was to investigate toluene (and dodecane) desorption from individual montmorillonite clay pellets. This study considered only the desorption of a single contaminant from dry clay. It was performed as the initial part of a larger work (2)that also considered moisture effects. In this study, the contaminant was adsorbed on the clay;no liquid phase was present. The goal was to identify and quantify the rate-controlling mechanisms operating on a particle level. Knowledge gained by this research is key to interpreting and modeling data from larger thermal treatment systems.
investigated the generation of transient puffs of volatile organic compounds (VOC)occurring when a contaminated sorbent was batch fed to a pilot-scale rotary kiln. The transient puffs of VOC's were attributed to the exposure of fresh sorbent surface area to the hot kiln environment as the sorbent bed underwent breakup and slumping motions caused by the kiln rotation. Wendt et al. ( 4 , 5 ) successfully modeled the characteristic behavior of the transient puffs via a bed-fragmentation model. Tognottl et al. (6)studied the adsorption and desorption of organic vapors on single sorbent particles with the aid of an electrodynamic thermogravimetric analyzer (EDTGA). Tognottl monitored the weight of a single particle levitated inside the EDTGA as the particle was subjected to both organically contaminated and clean nitrogen purge streams. Their results suggest that a finite percentage of the organic contaminant is tightly bound to the porous solids. Lighty et al. (7-10) reported the results of a parametric study on desorption of contaminants from soil in a benchscale particle-characterization reactor (PCR) and bedcharacterization reactor (BCR). They found that the desorption rate is a strong function of soil type and temperature and that, in complex hydrocarbon mixtures, the lighter components will be selectively desorbed first. Lighty et al. (11)mathematically modeled the desorption behavior in both the PCR and BCR environments by assuming equilibrium between local gas- and adsorbedphase contaminant concentrations. Lastly, Owens (12) conducted a parametric study of toluene desorption from montmorillonite clay particles during thermal treatment in a pilot-scale rotary kiln. Results showed that increased kiln rotation rate, increased kiln temperature, and decreased sorbent bed weight increase the overall toluene desorption rate. Owens et al. (13)also modeled the thermal desorption process for the rotary kiln. Their model included a first-order rate expression for the local generation term with an Arrhenius activation energy that was linearly dependent on adsorbedlayer concentration. A model sensitivity analysis showed that the local generation term was the most influential factor in determining the overall desorption rate. This finding suggested that the rate-controlling process for thermal desorption via rotary kiln incineration occurs on the individual particle level. The goal of the current study was to elucidate the particle-level desorption process by performing toluene desorption experiments using individual montmorillonite particles. Theory
* Primary contact for correspondence; e-mail address:
[email protected].
To make a fundamental assessment of the desorption process on a particle level, a model was formulated incorporating all probable mechanisms. Consider an individual spherical clay pellet as shown in Figure 1. Initially, the pellet is contaminated with a volatile organic species in thin adsorbed layers inside the porous particle.
840 Environ. Sci. Technol., Vol. 28, No. 5, 1994
0013-936X/94/0928-0840$04.50/0
Background The thermal treatment of organically contaminated solids has received attention in the past. Linak et al. (3)
0 1994 American Chemlcai Society
Local Adsorption Equilibria
External MassTranspon Resistance$
or Desorption Kinetics
---J
Qhn.
Surface diffusion
\
1ncn gas purge stream
Moleeular Diffusion and/or
If the relative rates of diffusion and mass transport in the system are fast with respect to the local adsorption/ desorption kinetics, then both eq 1 and eq 2 must he retained as separate equations within the governing set. However, if the relative rates of diffusion and mass transport in the system are slow with respect to the local adsorption/desorption kinetics, then a dynamic equilibrium will exist between the local adsorbed layer-phase and gas-phase concentrations. This condition is defined as local equilibrium. If local equilibrium exists, it is convenient to sum eqs 1 and 2 to eliminate the net adsorption rate RA:
Knudren Diffusion
Flgure I.Thermel desorption horn a slngle spherical porous particle.
The species' adsorbed-layerConcentrationis in equilibrium with the vapor-phase concentration in the gas-phase surrounding (and internal to) the porous clay pellet. At time t = 0, a clean inert purge gas stream begins sweeping awaythe organic-ladenvapors surroundingthe pellet. Due to the change in boundary conditions, concentration gradients are set up inside the pellet, and organic vapors diffuse toward the pellet's outer surface. The particle is also heated externally. The increasing pellet temperature shifts the adsorption equilibria toward lower adsorbedlayer concentrations. Organic molecules leave the adsorbed phase and enter the gas phase. This generation of vapor sweeps gases from the particle. The thermal desorption process continues until essentially all of the organic contaminant is removed. There are several mechanisms that apply to the overall thermal desorption process. These include heat transfer into the pellet, local desorption, bulk flow, pore diffusion (Le., gas-phase diffusion in porous media described by molecular diffusion and/or Knudsen diffusion), surface diffusion,and external mass transport (i.e., the transport of material across the gas boundary layer surrounding the pellet). In the governing equations, local desorption (or adsorption) acts as a generation term (i.e., a source or sink). The other mechanistic processes mentioned above (except heat transfer) characterize the transport of the desorbing materialaway from the initialsite of adsorption. When deriving the governing equations for any gasphase adsorption process, both the intraparticle gas phase and the adsorbed-layer phase must he considered. The vapor-phase speciescontinuityequation for a contaminant species A within the spherical particle is
where c is the total gas concentration (mol/m3);Y A is the mole fraction of species A, tp is the pellet void fraction; and N A is the molar flux of species A (mol m-2 8-l) in the vapor phase per unit area normal to the radius. The term -RA is the net rate for local desorption, which is commonly described by some prescribed reversible kinetic rate expression. The adsorbed layer-phase species continuity equation for species A is
where W A is the adsorbed-layerconcentration of species A (moVkg) per weight of sorbent; pp is the pellet density (kg/m3);and S Ais the molar flux of species A (mol m-* 8-l) per unit area due to surface diffusion.
Equation 3 has two dependent variables: Y A and OA.An equilibrium relationship (e.g., adsorption isotherm) must be used to link the two dependent variables when evaluating the system. The adsorption isotherm ultimately used in this investigation was the Freundlich (14) isotherm: WA
=
(4)
Additional information on adsorption isotherms is available elsewhere (15,16). In order for eq 3 to be integrated, constitutive equations for the molar fluxes N Aand S Amust be specified. Mason and Malinauskas (17) proposed the D u s t P C a s equation as a description of mass transport through porous media. Later, Gunn and King (18) independently derived a mathematically equivalent expression. For a binary system, the Dusty-Gas equation may be expressed as
-v(cyA) (5)
In eq 5, three mass-transport mechanisms are represented molecular diffusion, Knudsen diffusion,and pressure-driven bulk flow. Molecular diffusion is accounted for via the first term of eq 5 and includes the ratio of pellet void fraction cp to pore tortuosity T (also called the tortuosity factor). Multiplying the binary gas-phase diffusivity D m (mZ/s) by the ratio Cp/r results in an effectiue diffusiuity consistent with the Parallel-Pore model of Wheeler (19,20). G is defined G N A + Ne, which is the net advective flux in the gas phase. It is assumed that species B is nonadsorbing. Knudsen diffusion (21)is characterizedby the Knudsen diffusivitycoefficientDX, (m2/s). A theoreticalcorrelation for DK* in porous media containing only cylindrical pores is
where r,, is the pore radius and the quantity under the square root is the square of the average molecular velocity of species A. Pressure-driven bulk flow in porous media is the result of pressure gradients created by net local generation (or depletion) of gas species. Pressure-driven bulk flow is governed hy the ratio of the flow coefficient Bo (m2)over the meanfluidviscosityp (kgrn-'s-'). The flow coefficient Ewb'on. Scl. Tschnol.. Vd. 28. No. 5. 1994 64q
Bo is independent of temperature and is considered to be a property of the porous media alone. In addition to mass transport in the vapor phase, it is also possibleto transport material along the sorbent surface via surface diffusion. Smith (22) gave a constitutive equation for surface diffusion as (7)
where Dsa is the surface diffusivity of species A (m2/s). The surface diffusivityDsa is dependent on both adsorbedlayer concentration and temperature. The effect of temperature on DsA (assuming an activated process) is described by an Arrhenius-type expression (23): Ds, = ae-E,/RT
mass-transfer coefficientbetween the pellet's outer surface and the purge gas stream. In eq 15, external mass transfers enters the model as an algebraic boundary condition. At low mass-transfer rates,, the mass-transfer coefficient k, is function of the Reynolds number, Re(= 2pfURp/p),the Schmidt number, Sc(= pIpfDAB), and the flow geometry, i.e.
-2kpp
- f(Re, Sc, geometry)
(17)
CDAK
The dimensionless group on the left-hand side of eq 17 is the Sherwood number, Sh. The correlation given by Whitaker (24)for forced convection from a single sphere gives
(8)
Assuming the ideal gas law applies, eq 3 may be rewritten Here pUmand pels are the mean bulk fluid viscosities at the surrounding and sphere surface temperatures.
as
Experimental Procedures
Summing eq 9 over species A and (nonadsorbing) B of a binary system, the total continuity equation may be expressed as
Provided that the temperature profile within the spherical pellet is known, eqs 9 and 10 are the governing PDEs describing the thermal desorption process under the assumption of local equilibrium. The unknown dependent variables are the mole fraction YA and the total pressure P. If the temperature profile in the spherical pellet is unknown, then an energy balance must be included in the set of governing equations. In this study, the temperature profile was known by virtue of direct measurements. The boundary and initial conditions used in evaluating the governing equations were at t = 0: yA = yo
for all r where 0 Ir IR,
(11)
P = Pt
for all r where 0 5 r IR,
(12)
"'- O
for all t where t I O
(13)
-ar_ - 0
for all t where t 2 0
(14)
at r = 0: I -
ar
at r = R,: (8.4
* N.4 -
Y.4 G)lr=R,
= ky(YA\r=R,
YA,bulk)
for all t where t I O (15) for all t where t L 0 P = Pt (16) where yo is the initial mole fraction of species A at time t = 0; Pt is the total pressure of the purge gas flowing around the sphericalpellet;yA,bd is the mean mole fraction of species A in the purge gas stream; and ky is the external 842
Environ. Sci. Tschnol., Voi. 28,
No. 6,1994
Single-particledesorption experiments were performed to generate data for comparison with the mathematical model. A single-particle reactor (SPR) was constructed. It consisted of a clay pellet suspended inside a 6- or 9-mm 0.d. Pyrex tube, positioned inside the oven of a gas chromatograph. Figure 2 illustrates the experimental configuration. The Pyrex tube was attached to a Supelco four-port gas chromatography valve. The valve was also inside the oven of a Hewlett Packard 5790A Series gas chromatograph (GC). The other end of the tube extended through the wall of the oven where an 1/8-in. diameter vapor sampling probe (25) could be inserted. The probe was connected to a Finnigan MAT 700 ion-trap detector (ITD) (a type of mass spectrometer) by a 1-m glass capillary GC column encased in a heated stainless steel transfer line. The probe allowed precise, reproducible 220-ms bursts of sampled vapors to be introduced into the upstream end of the capillary column. The signals from the ITD were recorded on an IBM A T personal computer, and the integrated area under each signal was linearly proportional to the volume amount of that species in the vapor sample. Upstream of the SPR, equipment provided either a toluene-contaminated nitrogen stream or a clean nitrogen stream to the pellet. The toluene vapor generator consisted of two Pyrex gas washing bottles connected in series. The first gas washing bottle was maintained at room temperature; the second gas washing bottle was submerged in an ice bath at 0.0 "C. Following the gas washing bottles, the toluene-saturated nitrogen stream was further diluted with nitrogen to give an adjustable toluene concentration (10-10 000 ppm by volume). Inside the GC oven, a 1-m coil of glass tubing served as a mixing volume and preheakr for the toluene-laden nitrogen stream. Finally, a clean nitrogen stream was also plumbed into the GC oven. The four-port valve inside the GC oven could be positioned SO that either toluene-contaminated nitrogen or clean nitrogen would flow around the clay pellet. Two different montmorillonite clays were used. The first clay, hereafter referred to as "Smoky Joe" clay, was mined near a brick manufacturer in South Jordan, UT. The second clay, hereafter referred to as "commercial sorbent", was a commercial sorbent for chemical spills
Saturator 2. Slnek-particle
Ice Bath
reactw (SPR) experlmentsl setup fa investlgatbn of t h m a l desorption from IrdMdual cby pellets
Table 1. Physical Data of Sorbent Materials
material
BET surface area (mZ/g)
Smoky Joe clay commereial sarhent
17 3 80 t 5
*
aolid density
mean particle pore (kg/m3) porasity radius (A) 2.1 X 1Ds 2.5 X 108
0.4 0.5
49 89
(Moltan Co., Memphis, T N trade name, Safety Absorbent). The first clay had the advantage that it was a raw clay that could be mixed with water and formed into specific shapes. Other than drying, no special pretreatment of the mined clay was adopted. The second clay was calcined by the manufacturer and had a fixed nominal size. It was the same material used by Owens (12). Accurate particle temperatures were measured by embedding 0.05-mm (0.002-in.) type-K thermocouples inside the Smoky Joe clay pellets. This wasaccomplished by sifting the clay to assure a uniform particle size; only the finest particles, 538 Mm, were used. A mold was constructedusing astackof two, 2.4mm (3/32-in.)Teflon sheets. The top sheet had a 2.4-mm (3/32-in.) hole that served as the mold. Extending through the bottom sheet and positioned in the center of the mold was the thermocouple junction. The claywas combined with deionized water to form a paste consisting of 67 w t % clay and 33 wt % water. The paste was injected into a mold around the thermocouple and then scraped flush with the top of the Teflon sheet. The clay-filled mold was air-dried a t 110 OC and then baked overnight in an oven a t 540 O C (IO00 OF). What resulted was a partially calcined cylindricalclaypellet (2.1 X 2.1 mm diameter) with a 0.05-mm thermocouple embedded inside. Two other pellets (4.6 and 6.2 mm) were constructed in the same manner. The commercial sorbent particles used in this study did not contain internal thermocouples. The BET surface areas and other physical properties of both materials were measured prior to their use and are listed in Table 1. Before an experiment, the Smoky Joe clay pellet was positioned inside the SPR glass tube and was suspended from the lead wires of the thermocouple junction. The
lead wires were folded down at the top of the SPRs glass tube and along the outside. Teflon Swagelok ferrules and a nut were used to make the seal between the stainless steel fitting and the SPRs glass tube. Desorption tests were initiated by allowing atoluene-contaminatednitrogen stream (-100 mL/min) to flow around the clay pellet for 3-4 h until the system reached equilibrium. The temperature of the GC oven was maintained at 30 "C. To begin the desorption step of each experiment, the data acquisition systems for both the thermocouples and the ITD were started simultaneously. After 12.5 8, the four-port valve inside the GC oven was switched allowing apurenitrogengasstream(-l00mL/min) toflowaround the suspended clay particle. Then, 37.5 s after starting data acquisition, the power switch for the variable transformer connectedto the supplementalheater (surrounding the SPR) was turned on. Depending upon the setting of the variable transformer, the clay pellet experienced a heating rate from 0.5 to 1.8 OC/s. The pellet and gas temperatures and the toluene concentration at the exit of the SPR were recorded digitally versus time. A second thermocouple positioned next to the clay pellet was used to measure the purge gas temperature. After the toluene concentration at the SPR exit had dropped below the detection limit of the ITD (-1 ppm), the power to the supplementalheater was discontinuedand dataacquisition was terminated. The sorbent pellet was left in a nitrogen purge stream a t room temperature between experimental runs. In addition to the desorption runs, other SPR experiments using short columns of clay particles were conducted to determine the adsorption isotherms for the systems.
Results To establish the thermodynamics of both toluenelclay systems and the n-dodecanelSrnoky Joe system, a total of 65 adsorption isotherm points were measured at four different temperatures: 30, 65, 100, and 150 ' C . The weight of the clean Smoky Joe clay bed was 0.5941 g; the Envton. Sd.Techol.. Vd. 28. No. 5. 1004 84s
35
Table 2. Optimized Parameters Values for Freundlich Isotherm Model isotherm parameter x1 x2 x3 3c4
b 2
toluene adsorption Smoky Joe commercial clay sorbent
dodecane adsorption Smoky Joe clay
I
65C
A
100c
o
150C
0
'2
2e,
20
8
s 3
15
P8
10
a
(19)
where b = x1 exp(x,T)
(20)
z = x 3 + x,T
(21)
The values of the parameters xi for both the Smoky Joe clay and the commercial sorbent are listed in Table 2. The model's approximation of the adsorption isotherms is plotted in Figure 3. In the case of dodecane, the reciprocal of absolute temperature was used in the exponential of eq 20.
With adsorption equilibria quantified, attention was focused on obtaining desorption rate data. Approximately 50 nonisothermal desorption runs were performed at different heating rates, particle sizes, and purge gas flow rates. The initial contaminant loading level (24 mmol/kg for Smoky Joe and 79 mmol/kg for commercial sorbent) was fixed by the gas-phase toluene concentration during the adsorption process. In analyzing the SPR data, steps were taken to remove the direct dependency (due to dilution) of exit toluene concentration upon the purge gas flow rate. For each run, the exit toluene concentration was related back to the toluene flux leaving the sorbent pellet surface. Blank runs performed under similar conditions, except without sorbent pellets, established the influence of flushing the SPR tube free of contaminant vapors. The responses of these blank runs were subtracted from the SPR desorption runs. Figures 4 and 5 summarize the trends observed during the SPR desorption runs for toluene. Figure 4 shows Environ. Scl. Technol., Voi. 28, No. 5, 1994
4
o
v
weight of the clean commercial sorbent bed was 0.3055 g. The adsorption equilibrium data for the toluene/clay sorbent systems were plotted and analyzed to quantify the adsorption relationships. Figure 3 shows the toluene adsorption isotherm data for Smoky Joe clay. To correlate the adsorption data a number of different isotherms were tried: Langmuir (26),Freundlich (eq4),Temkin (27),BET (281, and Dubinin-Radushkevich (29). First, adsorption isotherms were fit to data at fixed temperatures. Next, simple functionalities were determined to describe the temperature variation of the isotherm parameters. Finally, the adsorption data was simultaneously fit across all temperatures using temperature-independent parameters. To determine optimal values of the isotherm parameters, the method of nonlinear least-squares via the LevenbergMarquardt Algorithm as implemented in LMDIF from the MINPACK library by More (30) was used. The resulting adsorption equilibrium model used for the SPR desorption simulations was
844
30 h
Smoky Joe clay
30C
25
2.819 X lo4 4.053 X lo6 1.891 X -2.759 X 10-2 -3.349 X 10-' 2.809 X -2.393X lo-' -4.305 X lo-' 9.165X lo-' 1.728X 2.633 X -1.529 X Values of Parameters b and 2 at 30 O C 6.57 15.80 19.99 0.45 0.28 0.37
= b (PA)'
I
Y
5
0 0
20
40 60 ao Toluene Partial Pressure (Pa)
100
120
Figure 3. Adsorption isotherms for toluene on Smoky Joe montmorillonite clay correlated uslng the Freundllch isotherm model.
results for SPR runs using a 6.2-mm particle of Smoky Joe at various heating rates. Figure 5 shows the results for toluene desorption from three different sizes of Smoky Joe pellets. Similar results were obtained with the commercial sorbent. A difference in the desorption patterns of toluene and dodecane on Smoky Joe was observed. This is illustrated by Figure 6, which shows the percent of initial contaminant remaining versus time for replicate SPR runs. In these runs, the dodecane started to desorb at higher temperatures than toluene (as expected), yet dodecane completed the desorption process in a shorter time than did toluene. Toluene exhibited longer elution times (at low concentration levels) compared to dodecane. To investigate specific questions of particle size effects independent of heating effects, four isothermal desorption runs were performed at 30 OC. Figure 7 shows two runs performed using a single 6.5-mm diameter Smoky Joe pellet and two other runs performed using 21 2.3-mm diameter pellets. In both cases, the overall mass was the same (0.225 g), and the smaller particles are decontaminated faster than the larger particles at isothermal conditions. Lastly, an SPR run was performed for a direct comparison of desorption rates with pilot-scalerotary kiln data. Figure 8 shows toluene desorption data generated in the SPR and data generated in a pilot-scale rotary kiln by Owens et al. (12). Both experiments used the commercial sorbent with similar heating profiles. The initial toluene loading levels were comparable: 0.7 wt % toluene for the SPR run and 0.25 wt % for the rotary kiln run. The SPR runs exhibited shorter decontamination times. Modeling Approach To facilitate interpretation and understanding of the SPR desorption for toluene, eqs 9 and 10 were solved numerically. Equations 9 and 10assume local equilibrium. This assumption was made for all simulations except for those explicitly based on desorption kinetics. The governing partial differential equations were solved by
I
I
I
I
I
1
I
Smoky Joe clay (6.2-mm dia.)
0 0
0.5
1.3 'CIS 0
1.0 'CIS
A
0.8 'CIS
0.6
I
-. r 3
2
v
0.4
?j VI
-a"
Simultaneous - model fit across all three data sets
0.3 5
e,
0.2
5 x
- 1.3 'CIS
L
0.1 2
g
0
"
0
100
200 300 Elapsed Time (s)
0
400
100
200 300 Elapsed Time (s)
400
g
500
Flgure 4. Comparison of heating rate for Smoky Joe SPR runs. Experimental and modeled data are compared for SPR toluene desorption runs using a 6.2-mm diameter Smoky Joe clay pellet and three different heating rates (0.8, 1.0, and 1.3 'CIS).
0.30
200
h
180
95b
ij 160
3
8
140
: 2
0
4 6-mmdia.
A
2 1-mmdia
1
0.25
l
-
9 3 EE
v
0.20 8
$ 3
VI Simultaneous model fit across 0.15 all three data sets
120
a
6 2-mmdia.
100
e,
0.10:
E 80
G
5
3
x
6.2-mm dia.; 0.55 'CIS 60
3
L
0.05 2
4 6-mm dia.; 0.56 "CIS
B
3
40 20 0
100
200 300 Elapsed Time (s)
400
0
100
200 300 Elapsed Time (s)
400
0 500
g
Flgure 5. Comparison of pellet diameter for Smoky Joe clay. Experimental and modeled data are compared for SPR toluene desorption runs using three different diameters (6.1, 4.6, and 2.1-mm) of Smoky Joe clay pellets. Heating rates were kept similar for all runs.
the method of lines. The system was integrated using LSODE from ODEPACK by Hindmarsh (31). An energy equation was not included in the set of governing equations solved because pellet temperatures were known from measurements. The radial temperature profile across the pellet radius at any instant of time was assumed to be parabolic between the internal and surface thermocouple readings. For heat transfer to solid spheres, at times away from t = 0, the radial temperature profiles are approximately parabolic. The assumption of a parabolictemperature profile is justifiable as long as the latent heat effects due to the heat of desorption are small in comparison with sensible heating of the clay pellet. The latent heat effects accounted for only 5 % of the total heat transferred. In solving the governing equations, not all of the quantities involved in the model were known a priori. Unknown quantities included the tortuosity r , the preexponential factor a,and the activation energy E, in eq 8. Other model parameters could be estimated from correlations, measured, or found in the literature. The external mass-transport coefficient 12, was computed via
eq 18. For the porous-media flow coefficient Bo,Mason (17) presented a theoretical relation which applies to Knudsen diffusion in cylindrica pores:
Mason's derivation for a porous matrix gives KO= (rpore/ 2)(ep/7) and
Initially, it was believed that values of the three unknown parameters (7, a,and E,) could be determined simultaneously by adjusting the values of the parameters to maximize the correlation of the math model with SPR data. Initial values for the unknown parameters were assigned, the model was evaluated, and the computed toluene flux leavingthe pellet's outer surface was compared to the measured flux. The values of the model parameters were to be adjusted via the Levenberg-Marquardt algorithm. The problem encountered with this approach was Environ. Scl. Technol., Vol. 28, No. 5, I994
845
3
t
40
A*ij
30
20
&
10
k,.. \'
I
I
200
400
0 0
.. . _ , :.-..
.
.,. . .
, . .- :,-. - .- - .- ..
800
600
i
. . . . ., .
IO00
,
1200
Time (s)
Flgure 6. Comparlson of toluene and Modecane desorption from Smoky Joe clay particles under similar condltions (6.2-mm diameter pellet; 1.2 OC/s heating rate).
0.9
0.8
5
rr
0.7
0.6 -$ 0.5 5
3
3
Replicate runs using twenty-one,
0.4
- 2 3-mm spherical Smoky Joe
i
3
."
pellets (0 2242 g net weight)
0.3
1-
. d
i!
O 2i I 01
Replicate runs using one, 6 5-mm i sphencal Smoky Joe pellet (0 2253 g net weight)
-I
0
4000
0
-2
I
,
8000 Time (s)
12000
16000
Flgure 7. Experlmentairesults from four isothermaltoluene desorption runs using two sizes (2.3 and 6.5-mm dlameter) of Smoky Joe clay pellets. All runs were performed at 30 O C .
that one transport mechanism tends to dominate the overall model for any given set of parameters. Conse180
G e 160 2
quentially, consistent values for model parametrs could only be determined for dominant transport mechanisms. Because this initial approach failed, a simpler modeling approach was taken in order to determine which mechanism acting by itself could best correlate the experimental SPR data. Figure 9 shows the results of fitting the model to the data for a SPR run using the 6.2-mm Smoky Joe pellet with 1.2 OC/s heating rate. Each of the five fits in Figure 9 was obtained with a single mechanism controlling the overall desorption rate. A listing of the optimized values for the model parameters from each simulation is given in Table 3. Note that bulk flow effects were included in the evaluations because the total continuity equation was retained. The results shown in Figure 9 indicate that, in practice, any one of the five mechanisms (including the mechanism of local desorption kinetics) could be used to correlate the SPR experimental desorption data. However, for reasons to be discussed below, not all five were theoretically probable as the dominate mechanism. For simplicity, it was decided to correlate the remainder of the SPR data using the parameter 7 with molecular diffusion in pores as the dominate mechanism. Values for 7 were determined by fitting experimental data simultaneously across multiple runs with either constant particle size or constant heating rate. Optimized values for 7 are listed in Table 4. Some comparisons between experimental and modeled data are shown in Figures 4 and 5.
Discussion As reflected by both the experimental and model data in Figure 4,increasing the sorbent-particle heating rate causes the peak in the desorption curve to become narrower, to become larger in magnitude, and to occur sooner. The integrated area underneath the desorption curve multiplied by the pellet's outer surface area is a measurement of the initial contaminant concentration. The integrated areas under the desorption curves within each plot were roughly the same. The material balance closure ranged from 70 to 130% based upon initial gasphase contamination levels and the adsorption isotherms given in Table 2. Evaluations of the model assumed closure.
c
1
0.8
0 0
I
0
Clay sorbent bed (rotary kiln)
Clay sorbent bed (rotarykiln)
__ Single clay pellet
Single clay pellet (SPR)
(SW
0 ' 0
!
200
'
1 0.2 I
I
400 600 800 0 200 400 600 800 1000 Elapsed Time (sec) Elapsed Time (sec) Figure 8. Comparison of single-partlcle reactor (SPR) data versus pilot-scale rotary kiln data. Identical commercial sorbent material was used In both runs. A 0.25 wt % toluene loading (8% flll fraction; 0.5 rpm rotation rate; see ref 13) was used for the rotary kiln; a 0.73 wt % toluene loading on a 3.8-mm diameter (0.0337 g) single sorbent pellet was used for the SPR experiment. 848
Envlron. Scl. Technol., Vol. 28, No. 5, 1994
Table 3. Optimized Values for Model Parameters from the Single-Mechanism SPR Desorption Models controlling mechanisms
optimized parameter values
local desorption kinetics surface diffusion
rd
0.6
k, = 0.125 X the value from eq 22
