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Ind. Eng. Chem. Fundam. 1983, 22, 502-503
to be some differences in the values of the diffusion coefficient used by Kumar et al. (1980) and by us. This factor also may account for a portion of the discrepancy and indicates the need for reliable and accurate ways for measuring or calculating diffusion coefficients for nonNewtonian fluids because of their importance in the development of a successful model. Conclusions Mass transfer from benzoic acid spheres to pseudoplastic fluids has been investigated in the creeping flow region. The Sherwood number increased with Peclet number but tended to vary by as much as a factor of 4 in comparison with theoretical predictions. The effect of pseudoplasticity on transfer may have been concealed by the contribution of the natural convection mechanism, which seemed to increase as the continuous phase approached Newtonian behavior. Nomenclature Cb = solute concentration in bulk fluid (ML-3) C, = solubility of solute in fluid D , = sphere diameter ( L ) D , = diffusivity ( L 2 T 1 ) k , = mass transfer coefficient ( L T l ) K = power law consistency index (ML-"P-2) n = power law index of determination N = mass flux (ML-2T1) Npe = Peclet number = ( V D J D ) N R =~ Reyonolds number = ( P % - ~ D , " / K )= (pVDs/we) NS, = Schmidt number = (we/pDv) Nsh = Sherwood number = ( k $ J D , ) Nsb = S h e r w d number for diffusion and natural convection V = mean velocity (LT')
p = density (ML-9 ke = effective viscosity
(ML-lT') = K ( D , / V)l-n
Literature Cited Bhavaraju, S. M.; Mashelkar, R. A.; Blanch, H. W. AIChE J . 1978, 2 4 , 1063. Bowman, C. W.; Ward, D. M.;Johnson, A. I.; Trass, 0. Can. J . Chem . Eng , 1961. 3 9 , 9. Friedlander, S. K. AIChE J . 1957, 3 , 43. Friedlander, S. K. AIChE J . 1961, 7 , 347. Garner, F. H.; Hoffman, J. M. AIChE J . 1960, 6 , 579. Garner, F. H.; Hoffman, J. M. A I C M J . 1961, 7 , 148. Garner, F. H.; Keey, R. B. Chem. Eng. Sc/. 1958, 9 , 119. Garner, F. H.; Keey, R. B. Chem. Eng. Sci. 1959, 9 , 218. Garner, F. H.; Suckling, R . D. AIJ . 1958, 4 , 114. Gurkan, T.; Wellek, R. M. Ind. Eng. Chem. Fundam. 1976, 15, 45. Hirose, T.; Moo-Young, M. Can. J . Chem. Eng. 1969, 4 7 , 265. Hlrose, T.; Moo-Young, M. Ind. Eng. Chem. Fundam. 1972, 1 1 , 281. Kawase, Y.; Ulbrecht, J. J. Chem. Eng. Commun. 1981, 8 , 213. Kumar, S.; Tripathi, P. K.; Upadhyay. S. N. Lett. Heat Mess Transfer, 1980, 7, 43. Kumar, S.; Upadhyay, S. N. Ind. Eng. Chem. Fundam. 1980. 19, 75. Lochiel, A. C.; CaMerbank, P. H. Chem. Eng. Sci. 1964, 19, 471. Runikis, J. 0.;Hall, N. A.; Rising, L. W. J . Am. Pharm. ASSOC.1958, XLVII, 758. Shirotsuka, T.; Kawase, Y. J . Chem. Eng. Jpn. 1973, 6.432. Slkdar, S. K.; Ore', F. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 722. Steele, L. R.; Geankoplls. C. J. AIChEJ. 1959, 5, 178. Steinberger, R. L.; Treybal, R. E. A I C M J . 1960, 6 , 227. Wet, G. C.; Leppert, G. J . Heat Transfer 1961, 83. 163. Ward, D. M.; Trass, 0.; Johnson, A. I. Can. J . Chem. Eng. 1962, 4 0 , 164. Wellek, R. M.; Gurkan, T. A I C M J . 1976, 22, 484. Wellek, R. M; Huang, C-C. Ind. Eng. Chem. Fundam. 1970, 9 . 480.
Chemical Engineering Department University of Lowell Lowell, Massachusetts 01854
Michael A. Hydet Alfred A. D o n a t e l l i *
Receiued for review October 10,1981 Revised manuscript received June 13, 1983 Accepted July 8,1983 'General Foods Corp., Woburn, MA 01801.
Neutron Attenuation: A Novel Approach to Residence Time Studfes in Coal Hydrogenation Reactors A novel approach to the measurement of resldence time distributions (RTD) in chemical reactors is described. The technique involves the attenuation of neutrons by tracers and is particularly sukable for obtaining residence time measurements in coal hydrogenation reactors.
Introduction The successful scale-up and optimization of continuous reactors for coal hydrogenation will rely heavily on generalized kinetic data obtained in laboratory-scale and pilot-scale reactors. Residence time distribution (RTD)data are essential for such generalizations to be made with confidence. Previous attempts to measure RTD's in coal hydrogenation reactors have involved the use of techniques which are not applicable to studies of reaction kinetics (Barreto et al., 1977; Vasalos et al., 1979). Standard optical and spectrophotometric methods are also unsuitablemainly because of the thickness of reactor walls, the difficulties and hazards associated with having optically transparent windows in high pressure-high temperature reactors, and the opaqueness of reaction products. We have developed a technique which involves the attenuation and scattering of neutrons by tracers and which is particularly suitable for the measurement of RTD's in coal hydrogenation reactors. Several elements, including boron, cadmium, and gadolinium, have markedly different neutron absorption cross sections to carbon and hydrogen which are the major reaction species in coal hydrogenation.
Other atoms such as deuterium and helium have different neutron scattering cross sections to hydrogen. Hence any of these elements is distinguishable from the reactants and is thus a potential tracer in coal hydrogenation reactors. The technique is readily adaptable to reaction processes other than coal hydrogenation and also has potential in the area of powder technology where determinations of material homogeneity and effectiveness of mixing are required. Experimental Section The results presented here were obtained by passing thermal (very low energy) neutrons through a section of a simulated three-phase reactor. Since little obstruction to neutron flux is provided by the stainless steel reactor walls or the surrounding heaters and insulation, the degree of attenuation of neutrons by the reaction components can be monitored by the detection and counting of emergent neutrons. The apparatus used in this study is shown schematically in Figure 1. The energy of neutrons radiating from the h / B e source is reduced (thermalized)by the surrounding wax. The howitzer produces a directed flux of thermalized 0 1983 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983 503
wax,
I
Cadmium screen aprrture\
with
Neutron h/Be
source
/
Sluq o f tracer f 8 896
2-
.Neutron detector
o
I
I
I
I
40
60
eo
loo
I
I
120
140
Figure 3. Response-time data, using air as tracer, for simulated gas-phase plug flow conditions in a laboratory-scale continuous reactor for coal hydrogenation. The data shown correspond to a 3-mm long air bubble.
Material flow
Figure 1. Apparatus for determining residence time distributions by the neutron attenuation technique.
5 % Boron 010 010
20
I
20
Time l m i n )
Neutron "Howitzer"
0
t
892 I
40
60 Time
80
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Boron Boron
I20
(minl
Figure 2. Response-time data, using boron as tracer, for simulated liquid-phase plug flow conditions in a laboratory-scale continuous reactor for coal hydrogenation. The data shown correspond to a mean liquid residence time of 70 min, i.e., tracer is injected at reactor inlet at time, t = 0.
neutrons, which are further collimated by an aperture in the cadmium screen. The neutron flux indicated by the detector is related to the concentration of tracer passing the aperture. Tracers may be injected as a pulse or step input, and their dispersion on passing through the reactor can be analyzed to evaluate the residence time distribution. The exact nature of the detector response will depend on a number of factors, such as the type and concentration of tracer used and the reaction medium in which the tracer studies are being performed. Results The results presented in Figures 2 and 3 were obtained with a model system which had the same geometry and construction materials as the CSIRO laboratory-scale continuous reactor for coal hydrogenation. Boron and air were used as tracers. Paraffin wax, with similar neutron attenuation properties to coal/oil slurries, was cast inside lengths of thin-walled glass tube. Plugs of known boron
concentration and air bubbles of known dimensions were formed in the wax. The wax sections were then moved through the reactor tube to simulate the flow of a coal/oil mixture under ideal plug flow conditions. For safety during the simulation studies, a low activity neutron source (50 mCi Am/Be) was used, resulting in a data acquisition rate 209 times slower than that necessary for on-line measurements in the CSIRO continuous reactor (for which a 100-pg 262Cfsource is to be used). Consequently, the speed at which the wax sections were passed through the reactor was of the linear velocities expected in nonsimulated applications. Therefore, each data point in Figures 2 and 3 represents the counts accumulated in 600 s (which would correspond to a 3 s count period in the on-line version of this technique). The data show quite clearly that tracers (in this case boron) at concentrations as low as 0.5% w/w can be detected. The response to an air slug is indicative of the sensitivity of the technique to gas tracers with low neutron attenuation cross sections. Thus, for example, if a deuterium or helium tracer was injected into a high-pressure hydrogen stream, the tracer could be distinguished from any gaseous or liquid hydrocarbon present. The response data presented are significant at the 99% confidence level for boron and the 95% confidence level for air. The results presented in Figure 3 suggest that in addition to providing a means of obtaining RTD data for liquid and solid phases, the technique will provide a means of monitoring flow regimes in multiphase reactors. This study shows that the use of neutron-attenuating tracers should provide a viable method for determining residence time distributions in coal hydrogenation reactors. Acknowledgment We thank Mr. R. Meakins, Dr. R. Holmes, and Mr. J. Marshall for technical advice. Registry No. Neutron, 12586-31-1; boron, 7440-42-8.
Literature Cited Barreto, F.; Anderson, S. J.; Goldstein, B. R.; Moor, S. S. "Three-Phase Flow Characteristics bf Cylindrical Vessels"; ORNL/MIT-257, Oak Rldge Net. Labs., Sept 23, 1977. Vasalos, I. A.; Bild, E. M.; Taterson, D. F. "Modeling the Fluid Dynamics of the H-Coal Reactor", Amoco Research Centre, Napervllle, IL CONF. 790822-3, 1979.
CSIRO Division of Fossil Fuels North Ryde, N S W 2113 Australia
Keith N. Clark* Neil R. Foster Ron G. Weiss
CSIRO Division of Mineral Physics Gerald R. Newman North Ryde, N S W 2113 Australia Received for review April 26, 1982 Revised manuscript received April 29, 1983 Accepted June 10, 1983
