INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1951
restrictions on the degrees of freedom encompassed in the terms R’ and R must be adjusted for any work in this direction. The equations derived should have application t o design, instrumentation, and general energy and material balance work. Table I1 presents a summary of the pertinent equations together with their uses and limitations. The cost of material and energy balances can be placed a t a minimum by observation of the equations. In addition, the chemical engineering teacher who is forever confronted with devising problems that can be solved by the student may find the equations and conceptions of help.
,
k
= sets of streams, each set having a common analytical
L
=
m
=
M’ = M
nt
=
ntp = N = P =
Q
Xomenclature applies at the boundary of the system = number of ultimate component concentrations set in all b k’ sets C‘ = ultimate component mass fraction concentration I d’ = sets of k’ sets having all stream rates fixed d = sets of k sets having all stream rates fixed 6 = ntp - nt A = maximum minus actual number of saturated streams e = number of electrical transfers E = rate of electrical energy transfer fl = frequency an ultimate component stream composition occurs more than once fo = frequency an analytical component stream composition occurs more than once fp = frequency a pressure occurs more than once f8 = frequency a stream rate occurs more than once ft = frequency a temperature occurs more than once F‘ = material balance degrees of freedom F = material and energy balance degrees of freedom FG = Gibbs degrees of freedom F; = material balance design degrees of freedom F I = material and energy balance design degrees of freedom go = gravitational constant gi = local acceleration of gravity ho = number of chemical homogeneous equilibria H = specific enthalpy k‘ = sets of streams, each set having a common ultimate component composition
=
na = nu =
(I
NOMENCLATURE
1811
= =
r
=
s
=
S T v B
= =
R‘ = R =
w
W,
y
2
= =
= =
= =
component composition number of linkages between unit systems sets of heterogeneous equilibria number of independent material balance variables a t a linkage number of independent material and energy balance variables at a linkage number of analytical components in a stream number of ultimate components number of defining thermodynamic components total thermodynamic components in an equilibrium number of single phase streams number of phases number of heat transfers rate of heat transfer sets of streams having common stream rates number of material balance restrictions number of material and energy balance restrictions specific surface energy mass rate of flow of a stream from system number of unit systems sets of streams having common temperature velocity of stream number of shaft works rate of mechanical shaft work sets of streams having common pressure height of stream above datum plane
Subscripts i = “ith” stream, system, ete.
j = “th” ultimate component a, b, c , etc. = ultimate components 1 , 2 , 3 , etc. = stream numbers, system numbers etc. LITERATURE CITED
(1) Dodge, B. F., “Chemical Engineering Thermodynamics,” p. 11,
New York, McGraw-Hill Book Co., 1944. (2) Findlay, A,, “The Phase Rule and Its Application,” London. Longmans, Green and Co., 1931. (3) Gilliland, E. R., and Reed, C. E., IND. ENG.CHEM.,34, 551 (1942). RECEIVED May 11, 1950.
locating Fluidized Solids Bed level in a Reactor
Enggtring Process
HOT WIRE METHOD
I
G. L. OSBERG NATIONAL RESEARCH COUNCIL, OTTAWA, ONTARIO, CANADA
A n alternative to the usual pressure drop method of locating the fluidized solids bed level in a reactor is often desirable, because plugging of pressure taps which are in contact with the bed is encountered unless special preventive measures are taken. The hot wire method described here exploits the excellent heat transfer properties of a fluidized solids bed. The thermally sensitive elements are a part of a thermal conductivity bridge and are mounted in a probe. Details of construction and performance in a laboratory unit are given. This type of level probe should be particularly useful in high pressure units. The probe could readily be incorporated in automatic bed level control equipment.
A
HOT wire method for locating the fluidized solids bed level in a reactor offers a practical alternative to the pressure drop method commonly employed for determining and controlling bed depth. The hot wire method described here is based on the well-established observation that the heat transfer rate from a hot surface is much higher in a fluidized solids bed than in a fixed bed or in gas alone (1). Thus, when a hot wire, which has a large positive resistivity temperature coefficient, is submerged in a fluidized solids bed, its temperature will be lowered, and hence its resistance will be less, compared with its temperature and resistance in air alone. The hot wire is made a branch of a Wheatstone bridge circuit, so that changes in its resistance alter the balance of the bridge. A somewhat similar application of a thermal conductivity
1872
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
bridge has been suggested for determining liquid levels b>-Becker et al. (a). They propose the use of a thermistor as the detect,ing element. Thermistors have large negative temperature coefficients of resistivity but are limit,ed t o appl+ations employing temperatures of less than 300' to 400' C. Hot wire elements, if made of platinum for example, could be employed a t somewhat higher temperatures. This paper describes the results of experiments with a hot wire probe that was used to determine the bed level of a fluidized solids bed in a laboratory unit. EXPERIMENTAL METHOD
The hot wire probe is illustrated in Figure 1. The probe consists of two hot wire elements which were made by threading 0 . 0 0 5 - i n c h diameter piano steel wire back and forth through a thin mica sheet. 0 The mica sheet was held between two slotted stmeel plates, one of which was brazed to a '/$-inch steel pipe. Copel A wire leads, insuhted by p o r c e l a i n beads, were brought through the center of the pipe. H The steel wire was joined to Copel wire with silver solder. Copel wire \Tas used only for the part of t,he connecting wire that mould be exposed t o temperatures above room temperature; copper was used for connecting wire a t room t,emperature. MICA The Wheatstone bridge circuit is STEEL shown in Figure 2. C and D are fixed, 20-ohm manganin wire resistanceE. B and E are 100-ohm vario m able resistances which were used to lYC ES - Y __ keep the bridge in balance when the Figure 1. Hot Wire fluidized solids bed temperature Probe was being changed. G and H are the wire elementsof the probe; these have a resistance of about 2 ohms each a t room temperature. Since G and H plus the connecting leads are almost identical the voltage drop across the bridge is substantially independent of
Vol. 43, No. 8
fluctuations in fluidized solids bed temperature. The current to the bridge is supplied by a 6-volt lead storage battery; it is adjusted by means of a variable resistance, I , and measured with an ammeter, A . A 100-ohm potentiometer type resistance, F , is connected across the bridge so that only 10 to 20% of the voltage drop is fed to a Leeds and Sorthrup recording potentiometer. R h e n used, the probe was lowered into a fluidized solids bed until resistances G and H were totally immersed. ThP bridge output was adjusted so that the trace was recorded a t the lefthand side of the strip chart by altering variable resistances R and E. The probe was then raised until G was just below the surface of the fluidized solids bed. Then, by lifting the probe in 1-cm. steps, a record similar to that shown in Figure 3 mas obtained. The bed depth is computed from these data. I t was more convenient to move the probe than actually to change the bed depth. The fluidized solids unit used in this experiment was a 3-inch diameter stainless steel unit which was electrically heated. The bed consisted of a sample of - 100 to 150 Tyler mesh foundry sand, and it was maintained a t a temperature of 480" C. The superficial air velocity a t this temperature Tas computed to br 0.45 foot per second. The current to the bridge was held constant a t 0.70 ampere. The voltage change across the bridge under these conditions, when G was raised above the bed, compared a i t h G totally immersed, \vas about 50 millivolts.
+
59.6 60.8 61.3
62.6
2.c
63.7 64.7 65.6 66.6
vi
68.1
I I W
z
6 7.0
1.c 66.0 65.1 64.1 63.1
6 1.9
60.9
I
2
3 4 M I L L IV O L T S
5
6
7
Figure 3. Strip Chart of Bridge Voltage at Various Probe Depths
i TO L N.RECORDER
F
Figure 2. Wheatstone Bridge Circuit for Hot Wire Probe
DISCUSSIOS OF RESULTS
The strip chart illustrated in Figure 3 is typical of the rehults obtained with a hot vire depth probe. The fluctuations of the trace a t a particular depth setting are due to variations in heat transfer rate caused by the turbulent surface and by the irregular movements of the particles within the bed. The fluctuations recorded in Figure 3 are not true reproductions of the bridge voltage variations, however, since the recording met,hod employed w-as too slow to follow the rapid changes in bridge voltage. The mid-point of the trace in Figure 3 was estimated, and its displacement from an arbitrary line on the left side of the chart was measured. This displacement was plotted against the position of the probe relative t o the top of the unit. The resulting curve (Figure 4) shows a satisfactory correlation between the immersed depth of the probe and the change in bridge output voltage.
August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
The sensitivity of the probe depended to a large extent on the details of construction. Fine wire in each element of the probe was essential because it permitted a high hot wire temperature at a reasonable bridge current. It was necessary also t o prevent possible damage t o the wire elements from the fluidized solids bed, by supporting them and in such a way 8 s to minimize heat losses to the support. This was accomplished satisfactorily by threading the wire back and forth through holes in a sheet of mica, so that the wire touched only a t the holes in the mica sheet.
1873
Equations 1 and 2 were divided by At, At1, respectively, then subtracted from each other and rearranged to yield the expression (3) The voltage change across the bridge, when the current to the bridge is held constant and G is raised above the fluidized bed, is given by
Substituting in ( A t 1 - A t ) from Equation 3 an expression for Ao is obtained. In this step, as in Equation 3, ( Z R - A R ) = ZR is assumed.
Av =
PIot of Recorded Bridge Voltage Depth
us.
Probe NOMENCLATURE
The dependence of bridge voltage on wire temperature and size of wire was derived for a somewhat idealized case. It was assumed t h a t no heat was transferred t o the mica sheet, that the connecting leads and the air above the bed were a t the fluidized solids bed temperature, and t h a t a steady state heat flow from t h e wire was obtained. It was also assumed t h a t resistance G is equal t o H when both are immersed in the bed and t h a t the effective resistance of ratio arms C and B and D and E are equal. When the probe is completely immersed in a fluidized solids bed, the heat generated in the wire is removed by heat transfer t o the fluidized bed and by heat conduction along the connecting wire; thus
&RT
= hbAAt
+ 2ka 1At
(1)
where hb is used as a n over-all heat transfer coefficient. The processes by which the fluidized solids bed removed heat from the hot wire are not specified. When the probe is raised so that G only is exposed t o air, the energy removed from G is given by a n analogous expression
ci2Rt1= haA At'
+ -1 u At' 2k
where
Rt'
Rt[l
+ a(At'
-
-
( A t ) (At') A (hb ha) ZR 4 ~ i o(1 - 01 At) Ri
Equation 5 shows the importance of using a high temperature difference between the wire and the fluidized bed. The magnitude of the temperature difference At and At1 can be estimated from Equations 1 and 2 or computed from hot wire resistance, if the appropriate temperature resistance data are available. It should be noted t h a t hb is substantially greater than ha. Baerg et al. (1)report maximum values of hbfrom 80 to 100 B.t.u./hour/ square foot/" F. and a value of ha equal t o about 4 B.t.u./hour/ square foot/" F. Preliminary experiments on heat transfer rate in a fluidized bed with a hot wire probe similar in principle to the one described here, yielded values of hb three t o four times higher than those reported by Baerg.
MILLIVOLTS
Figure 4.
01
At)]
(2)
A = surface area of wire element, G, sq. ft. a = cross-sectional area of wire, sq. ft. i = current flowing through G, amperes io = current to bridge, amperes
c = a constant 3.413 B.t.u./hour/watt ha = heat trandeer c3efficient in air, B.t.u./hour/sq. ft./' F. ha = heat transfer coefficient in fluidized solids bed, B.t.u./ hour/sq. ft./' F. k / l = thermal conductivity coefficient, B.t.u./hour/sq. ft./
F./ft. T , = temperature of air a k v e bed, ' F. Ta = temperature of bed, F. T,, = temDerature of wire G in bed. O F. T,i = temperature of wire G in air, F. At = T , - Tb At1 = T u 1 - T a RT = resistance of hot wire G a t Tu, ohms RT~ = resistance of hot wire G at T w l ,ohms R1 = effective resistance of a r m C and B or D and E, ohms ZR = 2R1 Ro RH,ohms AR = R T ~ RT CY = resistivity temperature coefficient in range T , t o T,' 0 = bridge output voltage O
+ +
LITERATURE CITED
(1) Baerg, A., Klassen J., Gishler, P. E., Can. S.Research, 28F,287 (1950). (2) Becker, A., Green, C. B., Pearson, G. L., Am. Inst. Elec. Engrs., 65,711 (1946). RECEIVED February 3, 1951.
