Ind. Eng. Chem. Process Des. Dev. 1980, 19, 465-469 465

show that for equal power requirement per unit volume, the same K,a will not be obtained in two different scales and the larger column gives the larger value of K,a. By taking these advantages of MVDC’s over conventional extractors, a higher efficiency of extraction can be ex- pected. Nomenclature A = amplitude of disk vibration, m a = interfacial area, m2/m3 dd = vibrating disk diameter, m dh = diameter of hole in partition plate, m dd = column inside diameter, m d, = drop diameter, m d,, = volume-surface mean diameter, m D, = continuous phase diffusivity, mz/s Dd = dispersed phase diffusivity, m2/s F = main flow rate through the hole of the partition plate,

f = frequency, l / s or Hz Fr = Froude number defined by eq 4 H = stage height, m HETS = height equivalent to a theoretical stage, m K, = overall mass transfer coefficient based on the continuous

k , = continuous phase mass transfer coefficient, m/s kd = dispersed phase mass transfer coefficient, m/s rn = equilibrium constant N , = defined by eq 5! nAf = maximum vibirating velocity, m/s P , = maximum power requirement per unit volume, W/m3 q = back flow ratio between the interstages q’ = back flow ratio between the intrastages R e = Reynolds number ( d p U p / p ) Sc = Schmidt number (c(/pDc) U = slip velocity of the drop, m/s u, = superfacial velocity of continuous phase, m/s ud = superfacial velocity of dispersed phase, m/s VE = volumetric efficiency defined by eq 13 W e = Weber number defined by eq 3 Greek Let ters

m3/s

phase, m/s

pd, q = dispersed phase holdup pc = continuous phase holdup, 1 - q d p = viscosity of continuous phase, Pa s u = interfacial tension, N/m p = density of continuous phase, kg/m3 Ap = density difference, Ipc - kg/m3 ‘1 = extraction factor, u,/mud Literature Cited Akai, J., Masters Thesis, University of Osaka Prefecture, 1979. Billerbeck, C. J., Farguhar, J., Reid, R. C., Bresee, J. C., Hoffman, A. S., Ind.

Calderbank, P. H., Trans. Inst. Chem. Eng., 38, 443 (1958). Calderbank, P. H., Moo-Young, M. B., Chem. Eng. Sci., 18, 39 (1961). Chantry, W. A., Von Berg, R. L., Wiegant. H. F., Ind. fng . Chem., 47, 1153

Chen, H. T., Middleman, S., AIChf J., 13, 989 (1967). Coulaloglou, C. A,, Tavlarides, L. L., AIChE J., 22, 289 (1976). Hu, S., Kintner, R. C., AIChE J. , 1, 42 (1955). Ioannou, J., Hafez, M., Hartland, S., Ind. Eng. Chem. Process Des. Dev., 15,

Karr, A. E., AIChE J., 5. 446 (1959). Klee, A. J., Treybal, R. E., AIChE J. , 2, 444 (1956). Miyanami, K., Tojo, K., Yano, T., Miyaji, K., Minami. I., Chem. fng . Sci., 30,

Miyanami, K., Tojo, K., Yano, T., Chem. Eng. Sci., 33, 601 (1978). Miyauchi, T., Ohya, H., AIChf J., 11, 395 (1965). Mlynek, Y., Resnick, W., AIChE J. , 18, 122 (1972). Ritcey, G. M., Lucus, B. H., I . Chem. E. Symp. Ser., No. 42 (1975). Roger. W. A., Trice, V. G., Rushton, J. H., Chem. Eng. Prog., 52, 515 (1956). Smoot, L. D., Babb, A. L., Ind. Eng. Chem. Fundam.. 1, 93 (1962). Sprow, O., Chem. fng . Sci., 22, 415 (1967); AIChE J. , 15, 995 (1969). Szabo, T. T., Lloyd. W. A., Cannon, M. R., Speaker, S. S., Chem. Eng. Prog.,

Takeba, K., Shirai, Y., Kimoto, R., Preprint of the 10th General Symposium of

Thornton, J. D., Dept. Chem. €4. J., Newcastle-upon-Tyne, No. 2, 25 (1966). Tojo, K., Miyanami, K., Yano, T., J . Chem. Eng. Jpn., 8, 122 (1975a). Tojo. K., Miyanami, K., Yano, T., J . Chem. Eng. Jpn., 8, 165 (1975b). Tojo, K., Miyanami, K., Yano, T.. to be submitted, 1979. Tojo, K., Miyanami, K., Yano, T., Chem. Eng. J., 11, 101 (1976). Tojo, K., Ph.D. Thesis, University of Osaka Prefecture, 1975. Tojo, K., Miyanami. K., Yano, T., Chem. fng . J., 17, 211 (1979). Van Dijck, W. J. D., US. Patent 2011 166 (Aug 13, 1935). Vermeulen, T.. Williams, G. M., Langlois. G. E., Chem. Eng. Prog.. 51, 85F

Wellek, R. M., Ozsoy. M. U., Carr, J. J.. Thompson, D., Konkle, T. V., Ind. Eng.

Received for review August 22, 1979 Accepted March 24, 1980

Eng. Chem., 48. 183 (1956).

(1955).

469 (1976).

1415 (1975).

80(l), 66 (1964).

the Society of Chemical Engineers, Japan, p 124, 1971.

(1955).

Chem. Process Des. Dev., 8, 515 (1969).

Absorption of Microwave Energy by Oil Shale; Effects of Shale Richness, Placking Factor, and Frequency

Arvlds Judzis, Jr., Ralph E. Hiatt, Brymer Wllliams, and Arnls Judrls’

Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48 109

The diielectric behavior of Green River oil shale from the Piceance Creek Basin was studied in the microwave frequency ran e as a function of organic content, frequency of radiation, and packing factor. Shale containing 42 to 317

relative permittivity from 0.034 to 0.155 at a frequency of 500 MHz. The measurement of permittivity may, therefore, be an1 alternate and powerful assaying method for oil shale. A broad spectrum of frequencies may be used to assay shale because orientation polarization was observed to disperse molecular dipole relaxation over two decades of frequency.

cm f oif oil/kg of shale (10 to 76 gallton) as determined by Fischer assay exhibited increasing values of the imaginary

Introduction The assaying of oil shale to determine organic content

has been traditionally accomplished by the shale being heated in a specified. manner to evolve a liquid product

from it. The most widely used procedure is the modified Fischer assay described by Stanfield and Frost (1949). Its success is largely due to the accuracy and reliability of the oil yield determinations which are within 2.1 cm3 of oil/kg

0196-4305/80/1119-0465$01.00/0 0 1980 American Chemical Society

466

of shale (0.5 gal/short-ton) for lean and intermediate richness shales.

Microwave radiation may be an alternative means of measuring the organic content of oil shales. There exists a strong correlation between the dissipation of microwave energy in shale and its organic richness. In this study, the dielectric behavior of Green River oil shale in the micro- wave frequency range and its dependence on shale rich- ness, frequency of radiation, and density were considered.

Oil shale samples studied came from the Piceance Creek Basin in the Green River formation of Colorado. The rock is a layered marlstone, consisting predominantly of do- lomite, with a solid organic substance, kerogen, imbedded within the inorganic matrix. Other types of mineral matter include calcite, nahcolite, dawsonite, silica, clays, and some inclusions of pyrite. Theory

Microwaves are electromagnetic radiation with a fre- quency in the range of 0.3 to 300 GHz (Parsons, 1975). The instantaneous field strength of such an oscillating field can be described a t a fixed location in space by

where Eo = amplitude of the field strength, v = frequency of electromagnetic radiation, t = time, and j = (-1)ll2,

The incident electromagnetic radiation induces a dis- placement of dipoles, generally out of phase with the field, in the irradiated medium. The disturbance is similarly described a t the same location in space by

(2) where Do = amplitude of dipole displacement and 4 = phase angle. Alignment of the dipoles in the irradiated medium with the oscillating electric field may be perfect, rendering the phase angle, r p , zero; it may be completely random if the field is changing too quickly, again producing a zero phase angle; or it may exhibit a behavior between the two extremes. A maximum absorption of energy will occur when the dipoles resonate between the extremes of perfect alignment and total nonalignment (when dipole relaxation time is too small to follow the applied field). The thermodynamic tendency of dipoles to stay aligned with the field is sometimes called dipole relaxation.

The complex relative permittivity, or normalized di- electric constant, tr, is a measure of the ability of a material to store electric energy. It can be split into two terms, the real and imaginary parts

er = €* / to = e’ - jtr‘ (3) where e* = complex permittivity, eo = permittivity of free space (8.85 X 10-l2 F/m), t’ = (Do/e,,Eo) cos 4, and t” = (Do/ea0) sin 4. The imaginary term, often called the loss factor, is proportional to the ratio of Do to E,,, which is 90” out of phase. It is an index of the amount of energy ac- tually absorbed by the irradiated material and subse- quently dissipated as heat. The dielectric constant is a function of both the frequency of the electromagnetic field and the nature of the shale.

The microwave frequency range of 0.3 to 300 GHz en- compasses the vibrational and rotational frequency range of typical organic bonds (Bauman, 1962). The polar nature of kerogen enhances dipole relaxation effects and, hence, the observed energy dissipation. Furthermore, the nu- merous sulfur-, nitrogen-, and oxygen-hetero atoms present in kerogen (Robinson et al., 1963) greatly augment the polarizability of this substance. Such high molecular weight polymers usually exhibit “orientation polarization” where segments of the macromolecule change orientation rather than the entire molecule itself. This produces a

Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980

E = EJ?e[exp(j(~mt))] (1)

D = D&e[exp(j(2avt - $))I

-,

1422cm 0 635 cm

.::--I-;@, ....._ -~ ~- ,yJ - ~ ~ _ _ _

4 - Figure 1. Slotted line sample holder assembly.

distribution of relaxation time values and, consequently, energy loss is fairly constant over a wide range of fre- quencies. Experimental Section

Modified Fischer Assays. The mine-run oil shale samples from the Anvil Points and Colony mines in Col- orado (both in the Piceance Creek Basin) were assayed with the modified Fischer retort described by Stanfield and Frost (1949) of the United States Bureau of Mines.

Sample Preparation for Microwave Measurements. Two techniques to prepare the shale samples to proper dimensions for microwave analysis were developed. The sample holder attached at the right end of the slotted line, the device used in this study and described later, was designed for a sample filling the annular space as shown in Figure 1.

Samples prepared as “natural oil shale” were obtained first by coring a rock specimen with a 15.9 mm ( 5 / 8 in.) 0.d. diamond coring drill. Each core was then placed in a jig and drilled through the center with a size “C” carbon steel drill bit or a smaller 6.0 mm (15/M in.) diamond coring drill. All samples were dried at 105 “C 2.5-3 h to remove moisture before the microwave measurements were made.

The second method of producing samples deals with compaction of shale fines into the required shape. Shale was crushed by hand to an arbitrarily chosen -149-pm (-100 mesh) size and placed in a split mold with a doughnut-shaped cavity. Mold release was sprayed on the molds interior surface to minimize binding. The mold was then compressed at pressures up to 434 MPa with a manually operated hydraulic press.

The physical nature of a compacted sample made by this method may be described by several variables including density, porosity, and packing factor. It is especially im- portant to keep one of these constant when comparing shales of different richness or organic content. The “packing factor” is quite fundamental as it describes the percent the sample’s specific gravity is of that shale’s specific gravity found naturally in the Piceance Creek Basin. A maximum packing factor of 86% was achieved in this study, the theoretical packing limit for uniformly sized spheres being 74%. Pressures up to 434 MPa (63 OOO psi) were used in the compaction procedure. Packing fadom greater than 74% were possible through compaction of shale powders at pressures exceeding the compressive strengths of the particles. In addition, particles smaller than 149 pm would fill the voids created by the close packing of 149 pm size particles.

The advantages of the compaction technique in making the samples are that inhomogeneities in highly stratified rock specimens disappear as a large amount of crushed powder may be riffled together. In addition, a larger and more representative portion of a rock is assayed for its potential oil yield. A disadvantage is the lower limit for the packing factor obtainable by this method. Samples with a packing factor below 62% crumble with the slightest handling. No cementing agent was added to the shale powder, as it would interfere with the microwave mea- surements.

Measurement of Complex Permittivity. Permittivity measurements were taken with a General Radio 874-LB slotted line, fitted with a 200-ohm crystal detector and an

Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 467

I I ~ ?. I Sample M~ \* c-...

MICROWAVE GENERATOR ATTENUATOR SLOTTED LINE

wavelength

_ _ _ _ _ _ _ 2 I14

Figure 2. Permittivity measurement apparatus.

adjustable stub attenuator. The microwaves were gener- ated with a Hewlett-Packard Model 612A UHF signal generator externally modulated by an oscillator. A standing wave indicator was used to measure voltage standing wave ratios (VSWR) and to locate wave minima in the slotted line tube. The VSWR is the ratio of the maximum voltage to the minimum voltage in the trans- mission line. Sucher and Fox (1963) describe various techniques to measure permittivity.

Data is taken with the sample backed, first, by a “short circuit” and, then, by an “open circuit” (see Figure 2, Judzis et al., 1977). .4 homemade variable position short facilitated the measurements with the short one-quarter wavelength behind the sample. An Ames gauge ensures accurate length measurements in the slotted line. Low pass filters, placed in the transmission line immediately after the signal generator, reduced the chance of higher har- monics occurring in the slotted line.

Mathematical manipulation to compute the dielectric constant from raw data involves complex variables and is easily handled by a computer program. Impedances are first calculated by the following relationship

( l / p - PO) - j tan (2nl/A0) z = - (4) 1 - j U / p - l/pO) tan (27d/Ao)

where p = measuredl VSWR with the slotted line con- taining a sample (either open or short circuit mode), p o = measured VSWR without a sample, 1 = null position shift (either mode), and A. = wavelength. Transmission line losses are compensated for by the insertion of p o in the calculation of the complex impedance. The complex permittivity is then calculated from

j X o arctanh (Zsc/Zoc)1/2 e * = & - (5) 27rd (Z,,.Z0,) 1’2

where d = sample length. Permittivity measurements a t frequencies in excess of

500 MHz on the described apparatus are inaccurate and not reproducible. The major problems were ineffective shorts that terminated the transmission line. This resulted in significantly higher transmission power losses, charac- terized by low pols. As the true VSWR = ( l / p - l /p0)-l , accuracy suffers as p o approaches p . At frequencies less than 500 MHz, the slotted line was too short to measure the wavelength of the transmission or to locate minima for both termination modes. Alternate equipment for ob- taining the complex dielectric constant, though, was used for these other micrlowave frequencies. Therefore, in- strumental artifacts limited the study of oil shale richness effects on cfr to the slpectral region around 500 MHz. Results

Oil Shale Richness. The richness of Green River oil shale from the Piceance Creek Basin as determined by Fischer assay correlates strongly with the imaginary term of the shale’s relative dielectric constant a t 500 MHz. Figure 3 (Judzis et al., 1977) shows this relationship for cores. Accuracy is estimated to be &14 cm3/kg (3.4 gal/ ton) using a confidence level of 90%. Replicate mea- surements on five 138 cm3/kg (33 gal/ton) shale samples

SHALE RICHNESS, cm3/kg (Fischer assay) 0 50 to0 150 200 250 300

I l l ’ “1 ‘I Natural Shale ,/ I Inorganic Matrix

O.I 0.1 0 t P I

Ob t b 20 30 40 50 $0 710 80’ SHALE RICHNESS, GPT (Fischer assay)

Figure 3. Imaginary term of the relative complex dielectric con- stant, e * / ~ ~ = c’ - $‘, vs. Fischer assay richness of Green River oil shale.

were used for this statistical analysis. The sensitivity of this relationship with respect to shale richness is partially responsible for its accuracy in such potential applications as assaying. The imaginary dielectric constant, for exam- ple, increases by a factor of 6 as shale richness increases from 42 to 334 cm3/kg (10 to 80 gal/ton). The real di- electric constant varies between 3.5 and 4.7 with no ap- parent pattern as shale richness changes at the measure- ment frequency of 500 MHz.

Though d’ is a direct measure of the concentration of kerogen, a linear relationship is not observed for the im- aginary dielectric constant plotted against shale richness. The distribution of the organic matter about or within the inorganic matrix must play a crucial role in this nonlin- earity. From physical strength information and Green ‘ River Oil shale’s behavior under compression (Needham, 1976), it is apparent that lean shales consist of a continuous phase of inorganic marl, the richer varieties, a continuous phase of kerogen. The transition appears to take place a t a richness of 113 cm3/kg (27 gal/ton), but slowly.

The smaller “slope” in the lean oil shale regime suggests that a hindrance effect may be taking place. The phe- nomenon of dipole resonance in the kerogen macromole- cule is hindered by surrounding marl, unable to rotate or vibrate freely a t the interface. As the kerogen nodules increases in size and begin meeting one another, this hin- drance is reduced. The growing of the organic matter into the continuous phase further enhances dipole relaxation as new interactions are born with the merging of the before isolated kerogen nodules. Thus, a more sensitive depen- dence of e r r on richness takes place, exhibited by a greater slope, as kerogen is united. Increasing polarity of more largely sized kerogen phases is also a possible cause of the observed increase in slope.

The imaginary dielectric constant of “zero richness” shale may be evaluated by knowing the values of err for the major constituents of Green River oil shale. Schulman (1976) presents an overall average composition of the in- organic matrix: dolomite, 32 wt %; calcite, 16%; silica, 15%; and clays, 35%. The remaining 2% is distributed among nalcolite, dawsonite, siderite, ferroan, and others in trace amounts. The values of t” for dolomite and calcite were determined experimentally, whereas the values for silica and clays appear in the literature (Von Hippel, 1954). After converting the composition to a mole basis, the weighted permittivity values are simply added, resulting in an imaginary dielectric constant of 0.029. Table I summarizes the permittivities of Green River oil shale matrix constituents.

488 Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980

Table I. Inorganic Matrix of Green River Oil Shale permittivity

constituent wt % mol % E l E I ‘

dolomite 3 2 28 .00 6.33 0.039 calcite 16 25 .78 7.34 0.061 silica 1 5 40.28 3.78 0 . 0 0 0 2 clays 35 5.94 2 .31 0.040

a z & 002

at 500 MHz ond 2 4 O C

O ’ ” 60 70 80 90 to0 h I I I I

PACKING FACTOR, percent

Figure 4. Complex dielectric constant of 138 cm3/kg (33 gal/ton) shale as a function of packing factor.

Packing Factor. Permittivity measurements were made on Green River oil shale samples compacted from -149 pm powder. Oil shale with a 138 cm3/kg (33 gal/ton) richness was used. Problems associated with the expansion of the doughnut-shaped samples upon removal from the mold introduced some error in the measurement of the packing factor. Figure 4 shows the dependence of both the imaginary and real dielectric constants on this com- paction parameter. A least-squares fit was used for both linear relationships in the packing factor regime shown. The 100% data do not come from a compacted sample as that would be impossible, but rather from the naturally occurring sample.

These plots show a trend not a t all unexpected. Con- cerning the imaginary term of the dielectric constant, the index of a material’s “lossiness”, the less the kerogen concentration in the sample, the less the energy dissipation is. Kerogen undergoes dipole relaxation which accounts for this dissipation. The inorganic marl matrix does not exhibit such a phenomenon. This is evident from the previous parameter study when e” and shale richness correlated well. In the regime studied, both e’ and e’’ vary linearly with packing factor. At lower packing factors, however, the relationships are nonlinear, with e” ap- proaching zero and ef approaching 1. These values ap- proximate the dielectric constant of air.

The trend for the real dielectric constant agrees with Fender e t al. (1962), who have studied various terrestrial and extraterrestrial rocks, in that “the relative permittivity is to first order a linear function of the packing factor.”

Frequency. The dependence of the complex permit- tivity upon measurement frequency was also determined for frequencies in the range from 250 MHz to 10 GHz. An oil shale sample of 138 cm3/kg (33 gal/ton) richness was compacted from -149 pm powder to a packing factor of 86%. Actual permittivity measurements were made by the Air Force Avionics Laboratory at Wright-Patterson Air Force Base. The slotted line technique was used; however, the data collection procedure is automated as is the fre- quency scan.

Figure 5 shows the results of measurements of both the real and imaginary permittivities. The real term of the dielectric constant, which is approximately 4 in the entire

138 cm3/kg l 33GPT) shale 86% pocking foctor

Imaginary, e”

i 138 cm3/kg l 33GPT) shale 86% pocking foctor

Imaginary, e”

, L I I 01 0 2 0 4 0 6 0 8 10 2 0 4 0 6 0 a o to

Figure 5. Complex dielectric constant of 138 cm3/kg (33 gal/ton) shale with a packing factor of 86% as a function of frequency.

frequency range investigated, agrees quite well with the previous study when a sample with a packing factor of 86% and a richness of 138 cm3/kg (33 gal/ton) has a real di- electric constant of 3.7. The oscillations a t frequencies greater than 3 GHz are due to noise and instrument in- accuracies.

The imaginary term of the relative dielectric constant is reasonably constant over the frequency range studied. It should be noted that the accuracy of df is one or two orders of magnitude less than in the two previous variable studies, shale richness and packing factor. ef’ cannot in reality be a negative quantity, indicating some errors in measurement when e” drops below zero. Overall trends, however, of how El‘ varies with frequency were sought when the frequency dependence was ascertained.

Orientation polarization is clearly evident as the ad- sorption of microwave energy does not peak in a narrow frequency range. Kerogen, a large macromolecule, exhibits a variety of relaxation times during dipole relaxation as its segments change orientation independently rather than the entire molecule itself. A broad spectrum of choices in frequencies is, therefore, available in developing oil shale assaying correlations.

Conclusions Green River oil shale does indeed absorb electric energy

from microwave transmissions. Such a phenomenon was observed by studying the dielectric behavior of this ma- terial with a slotted line. The specific findings are as follows.

(1) (a) The imaginary relative dielectric constant for oil shale from the Piceance Creek Basin increases from 0.034 to 0.155 as shale richness increases from 42 to 319 cm3/kg (10 to 76 gal/ton) a t a frequency of 500 MHz and a tem- perature of 24 “C. (b) The real term of the relative di- electric constant varies between 3.5 and 4.7 with no pattern as richness changes. (c) The complex magnetic permea- bility is consistently near 1 for all Colorado shales studied at 500 MHz. The shales are, therefore, nonferritic and are not susceptible to magnetically induced electric currents.

(2) Orientation polarization disperses molecular dipole relaxation of kerogen over the studied frequency range of 250 MHz to 10 Ghz. The imaginary permittivity is, therefore, fairly constant in this range. The inorganic marl matrix is relatively “transparent” to microwaves.

(3) The strong correlation between shale richness as determined by Fischer assay and the shale’s loss tangent (ratio of imaginary to real permittivity) a t 500 MHz and 24 “C enables one to assay Piceance Creek shale for its organic content by the measurement of its complex per-

FREQUENCY, GHz

Ind. Eng. Chem. Process Des. Dev. 1980, 79, 469-477 469

mittivity. Since the dielectric constant is an inherent physical property of' a material, it is independent of the method of measurement. Accuracy of the prescribed technique from this study is f14 cm3/kg (3.4 gal/ton) at 90% level of confidence. Accuracy improves as richness increases.

(4) Two techniques to fabricate samples for slotted line permittivity and permeability measurements were devel- oped: (a) coring of inatural shale samples perpendicular to the strata with coring drills, and (b) pulverization of the shale to -149 I.tm powder and subsequent compaction of the fines in a mold with pressures up to 434 MPa (63 000 psi).

(5) This study of the dielectric behavior of Green River oil shale lays the groundwork for future research endeavors in (a) continuous analysis of shales, and (b) production of oil and combustible gasses by high power microwave transmissions.

Literature Cited Bauman, R. P., "Absorption Spectroscopy", Chapter VII, pp 264-313, Wiiey,

New York, 1962. Fender, W. D., Knott, E. F., Ole, A., Siegel, K. M., "The Moon", p 545, Kopal

and Mikhailov, Ed., Academic Press, 1962. Judzis, A., Jr., Williams, B., Hiatt, R. E., "Assaying Green River Oil Shale wlth

Microwave Radiation", p 207, Tenth Oil Shale Symposium Proceedings, Colorado School of Mines. 1977.

Needham, R. B., "Prediction of the Permeability of a Fragmented 011 Shale Bed During In-Situ Retorting wlth Hot Gas", presented at 51st Annual Soclefy of Petroleum Engineers of AIME Meeting, New Orleans, La., Oct 3-6, 1976.

Parsons, R. W., SOC. Pet. Eng. J., 15, 302 (1975). Robinson, W. E., Lawior, D. L., Cummins, J. J., Fester, J. I., U . S . Bur. Mines

Rep. Invest. 6166 (1963). Schulman, B. L., AIChE Symp. Ser., 72, No. 155 (1976). Stanfieid, K. E., Frost, I. C., U.S. Bur. Mines Rep. Invest., 4477 (1949). Sucher, M., Fox, J., '"endbook of Microwave Measurements", Voi. 11, Chapter

IX, pp 495-546, Polytechnic Press of the Polytechnic Institute of Brooklyn, N.Y., 1963.

Von Hippei, A. R., Ed., "Dielectric Materials and Applications", Chapter V, pp 301-314, Wiley, New York, 1954.

Received for review J u n e 22, 1978 Accepted October 25, 1979

Determination of Interfacial Area by Chemical Absorption and by Power Measurement

Shlrlni I. El-Shawatby and Sherlf H. Eissa'

National Research Center, Cairo, Egypt

In a mechanically stirred tank the rates of absorption accompanied by fast reactions of carbon dioxide-air mixtures into aqueous sodium hydroxide solutions have been measured. Suitable models were chosen for calculating the effective interfacial area in addition to the Danckwerts plot which is used for simultaneous evaluation of interfacial area and mass transfer coefficient. In a pure carbon dioxide-water system the volumetric mass transfer coefficients were determined using the concept of fractional approach to equilibrium. A novel method was proposed for the evaluation of interfacial area for air-water systems based on power consumption data. Average gas bubble diameters were estimated from gas holdup and interfacial area. This area for physical absorption was also calculated by a proposed method which, when coupled with the volumetric mass transfer coefficients obtained before, offered a good means for predicting the mass transfer coefficients.

\

Previous Work Although many authors published values of the volu-

metric mass transfer coefficient in stirred tanks, only few values of the specific: interfacial area were reported.

Vermeulen and co-workers (1955) were the first to measure specific area in gas-liquid systems by the light transmission technique. Calderbank (1958,1959) extended this technique and gave correlations for interfacial area, gas holdup, and bubble size at relatively low specific power input for different liquids like water, aqueous solutions of glycol or glycerol, and organic solvents. For the nonelec- trolyte solutions or pure liquids, Calderbank (1958) found that the specific interfacial area a was dependent on the agitation power being correlated by

(1) in the range 260 I P/ V I 2600 W/m3. For air dispersions in pure, nonelectrolyte liquids a t 15 "C, the maximum integral average value of a reported was about 110 m-l. Calderbank and Moo-Young (1961) presented generalized

u = Ao(P/V)0.4*(Vs/VJ0.5 - p ,0 .2*~o .6

* F a c u l t y of Engineer ing, R i y a d h Un ivers i ty , R iyad, S a u d i Arabia.

correlations applicable to pure liquids or solutions of nonionic solutes in which kL was shown to be independent of the agitation power input, being solely dependent upon the physical properties of the phases according to

N S h = kLdb/DL = 2.0 + 0.31[db(p~ - pg)g/@~D~]1'3 (2)

for small bubbles where db < 2.5 mm and

NSh = 0.42(Nsc)1'2.(NGr)1'3 (3) for large bubbles where db > 2.5 mm.

These two equations show that kL is independent of d b It was found also by Calderbank and Moo-Young (1961) that 5 X I kL I 5 X m/s for small bubbles and that 5 X I kL I 11 X lo-* m/s for large bubbles. The results of these studies showed that the change in kLa with changing P/ V solely was due to changes in a, kL remaining constant as long as the average bubble diameter distinctly remained in either the small or the large category.

For carbon dioxide absorption in viscous aqueous solu- tions of glycerol, Calderbank and Moo-Young (1961) showed that there is a trasitional bubble regime where 0.5 I db I 2.5 mm in which kL decreased with decreasing db. Hence, in general, as P/ V is increased, kL remains constant until db decreases to a value of about 2.5 mm, then to

0196-4305/80/1119-0469$01.00/0 0 1980 American Chemical Society