I
R. N. BARTHOLOMEW and R. M. CASAGRANDE Shell Oil Co., Inc., Houston, Tex.
Measuring Solids Concentration in Fluidized Systems by Gamma-Ray Absorption In process control, radioisotopes can be used to measure density of opaque materials and solids concentration in fluids. They are compact and cheap, and need no adjustment or calibration
IN
PROCESS C O h T R O L , recent avaiialiliiy of suitable radioisotopes has focuwd attention on radiation absorption for measuring densities and detecting density differences in opaque materials. A growing number of industrial applications use bera or gamma radiation; the radioactive sources are cheap. conipact, and need no adjustment or calibration. However, special handling- and storage facilities are required for ptwonne1 protection. Gamma-ray absorption has been used successfully to measure density of concrete slabs and control pipeline movements and levels in storage and surge tanks (d, 9 ) ; a beta-ray device is used t o control the thickness of paper during its manufacture (7). This method has general utility and because the equipment is mounted esternally, it does not interfere with the system under stiid>.--a feature of particular value for resrarch. Knowledge of solids concentration is often necessary for the design and operation of processes embodying fluidization of particles under static or transport conditions. I n a fluidized fixed lied! the average solids holdup is approximately equal to the pressure drop per unit length through the bed (3, ,7). tliough nothing is said about solids distribution lvithin the bed. Poor solids distribution in a catalytic reaction pro cause undesirable effects such as high catal)-st inventory, low conversion. excessive side reactions, or reduced capacity. Estimates of solids holdup in fluidized transport systems from pressure-drop measurements over vertical sections are usually of limited reliability because a substantial part of the pressure drop occurs through energ)- consumption for particle acceleration and various frictional effects. Space r.elocir!.; a n im-
428
porta111 catal!-iic reaction process variable! is especially difficult to dererrnine under conditions of catalb-st traIiSpJI't ivithout a direct measuremc~ntof catal:-st Iiolduli and distribution. Fluid dynaniics studies of 1irterogrnr.ous ilo\v s!.sterns are facilitated if t h r x phase concrntrations art>kno\vn, becausc a n ~ o ~ n c n t u i balance ri gives tht. value of the tvall friction coafficirnt. The gammara!' absoiplion tcchniqur has been rstended to quantitative nieasureriient (,I solids concentrarion and distribution i n fluidized s!.stcnis, particularly 1hr dispersed phase. but the applicabk q u a tions art: valid for an!- liererogcnc*ous system An in\~stigationof dense phiis(, fluidization by means of s-rays has r e cently 1Jet.n reported (i). Ganinia radiation. btiing elcctroniagnetic, is ;issiiinr.d to obey tlir .ivell-kno\vii Lamlx%rt-Reer'slaiv of' esponcntial a b sorption in a lioinogeneous ~nedium(.;. 0). This l a i v is espressed ~nathematically fur monoenerqetic radiation as
r.
=
-w
J,,~
(1
~
\vherc. I , is incident inrriisit!.; Z,. subsident iniensitv; L , a b ~ o ~ , lthickn ~rr ' and ,u. linear at)soq)tion coefficicn compir;ibl(. expression for rnultieii radiation is morc complex and dc Icad to the desired simple rrhtionship. The numerical value of p depends 011 the physical and chemical state of the absorber. Ratio I.I p . !\.here p is al)sorber density. called mass absorption coefficient. a? is independent of state b ~ i t not composition ol' the absorber. Eci~iiition 1 t h u s becomes
I,
=
I,e-wL
(21
For several homogeneous absorbing media in series, relationships are derived as folloivs: .iftcr radiation passes through the first
INDUSTRIAL AND ENGINEERING CHEMISTRY
The ratio of I, to I , is then O’I4
However. La = L,
+ Lu
O.‘*
J d
(9)
b L
0.10
ci
Combination of Equations 8 and 9 gives
> t
m
Mav OF RADIATION
i Z
w
uLL
0.00
L
W
0 0
T h e mean solids density over the chosen path is
z 0
0.06
!i m m
a
UJ m
Elimination of L p from Equations 10 and 11 and solution for p m gives
a
0.04
I 1.02
1.36
0.02-
%PP
which is a general form valid for solidliquid or liquid-gas systems as well as for solid-gas systems. The term for gammaray absorption in air can be neglected without appreciable error. When density of the fluidizing medium is negligible and ctapa is approximately equal to aupu, the simplified equation thus obtained
is usually satisfactory as a basis for experimental work. Grohse ( 5 ) also used zero and flow measurements in his x-ray studies of fluidized beds. However, he made a series of zero measurements for varying thicknesses of a standard absorber of known density inserted in the radiation path, to establish a density calibration curve with the aid of Equation 4. Average bed densities were determined directly from flow measurements by means of the calibration curve. This procedure is equivalent to using Equation 13 but requires more physical measurements. Particle mass absorption coefficient ap is a function of gamma energy used, degree of source and detector collimation, and geometry of the system, in addition to composition of the absorbing medium. With highly collimated arrangements and monoenergetic sources, cu, is practically independent of geometry and from the data of Davisson and Evans (7), can be estimated within 1 3 % . Typical curves of mass absorption coefficient as a function of atomic number and gamma energy appear in Figure 1. T h e effect of geometry is associated with back-scattered radiation from the
6
2.04
16
26 36 ATOMIC NUMBER OF
. 46 ABSORBING
56
66
-
/
76
MEDIUM
Figure 1. Effect of atomic number and energy of radiation on mass absorption coefficient
surroundings and parts of the system not directly in the absorption path. I t is usually advisable to determine CY, experimentally in order to minimize errors caused by various assumptions made in the derivation of Equation 13; deviations of 20% or more from the theoretical value of a, may occur under some experimental conditions. An ideal gamma source for density measurements should have a long half life and emit monoenergetic radiation in the range of 0.5 to 1.5 m.e.v. Below 0.5 m.e.v., strong sources are required for sufficient radiation to penetrate the walls of a large apparatus, and in addition, ct, varies considerably with atomic number; above 1.5 m.e.v., radiation absorption is so small that obtaining precise data under typical experimental conditions is difficult. Cobalt-60 (1.1 and 1 . 3 m.e.v.) and cesium-137 (0.66 m.e.v.) are readily available and have proven satisfactory. Radiation intensity is measured by any practicable means. Both GeigerMuller tubes and scintillation crystals are suitable detectors, but special consideration of their limitations is necessary for each application. Sensitivity to gamma rays, temperature, voltage fluctuations, and vibration are the chief factors, but initial cost, bulk, and useful life also may affect the choice. I n general, GeigerMuller tubes have the advantage of simplicity, but scintillation crystals have much higher gamma sensitivity.
A scintillation counter (crystal plus photomultiplier tube) is particularly useful with a linear amplifier and a pulse height analyzer-the entire apparatus constitutes a gamma ray spectrometer. Adjustment of the instrument to determine only attenuation of the primary photoelectric peaks eliminates the need for collimation-only necessary source shielding is required. I n field application, use of an input-line voltage regulator will improve the results materially ; in some instances, additional, extremely fine regulation of the high voltage supply to the photomultiplier tube is desirable. Temperature control is maintained by means of a jacket, heated or cooled as necessary, placed around the scintillation counter. Experimental Results Since 1951, the gamma-ray absor‘ption principle has been used to determine density patterns in transverse sections of fluidized systems in transfer lines and vessels ranging from 6 inches to 40 feet in diameter. Studies have been made on pilot plant and commercial units in both dense and dispersed phase fluidization. Results of these chemical engineering studies made with the gamma ray technique will be published separately. I n order to demonstrate this method, a n example of its application to a particular unit is given. Data for calculating the cross-sectional VQL. 49, NO. 3
a
MARCH 1957
429
counting rates \\ere 10, 3, and l";, respecrivrly; the averagt. ratio o f I , t o I , \vas 1.2. On this basis, stat1dar.d deviation of path densities is estiiri;itc.d a s 13';. Densit!. distribution a t
T
(1.5)
\ihich is valid unl!, o v r r tlic r c y i o i i ('11c.losed ti!. the bou1idaric.s o f tht: crms r w t i o n . I k n s i t y surface, is i n t i \.rrtical p1ant.s coi.resi~ondinq 11) 1 1 d t I i 5 chosrn for exixriniental d e nirrits. I n the arbitrarily dinatt s!.strm, thcac: plaiic-s a r c IVIIIY~srnted by equations of t h c f o r l l l \
Figure 2.
p,, =
430
ilccording t u this equation, efi'ecr on patti dtnsity of errors in the counting r a t e depends on the ratio bet\vecn the counting rates under nonfloLv and Ho\r conditions. :\ high ratio is desirable to minimize error in the density measurements: therefore, medium-energy qarnina sources are prei'errrd because a qreater percentage of the radiation is absorbed. L'nder experimental conditions. estimated errors in the mass absorption coefficient, path irngths. anti
Table I,
N
(10)
t
OUllt.
+ + + + ?(I. + C\'
1 MI11
( rllllll-
SIIIl
P l t 11 I )l>ll.ltJ 1,lJ ( ( 1 1 1 1
K 5
1.53 1.59 0.93 1.69 1.51 0.95 1.44 0.98 1.53 1.69 1.56 0.97
11.9 8.9 6.0 6.7 5.5 4.8 7.5 4.9 8.9 5.7 6.7 7.0 3.8 5.8 7.1 6.6 7.9 9.9
14 mm. steel 170 mm. water
0.046 0.56
Determination of a p 2700 1680 2908 1417
487 62.4
G1 G 2 G 11 G 11.75
K1 K Z K 3 9 4
INDUSTRIAL AND ENGINEERING CHEMISTRY
t
/,I]
(1')
+
-
4528 6244 731 1 6349 5405 7388 6567 7475 4714 7002 6406 5290 6866 5795 7024 7107 6776 5250
El
