Ind. Eng. Chem. Res. 1987,26, 2192-2195
2192
BHRA Fluid Engineering: Cranfield, Bedford, England. 1979; Vol. I, pp 15-36. Mukataka. S.: Kataoka., H.:. Takahashi. J. J.Ferment. Technol. 1980. 58(2), 155l161. Nagata, S. Mizing, Principles and Applications; Kodansha: Tokyo, 1975; Chapter 3. Oosterhuis, N. M. G.; Kossen, N. W. F. Biotechnol. Bioeng. 1983,26, 546-550. Oosterhuis, N. M. G.; Kossen, N. W. F. Biotechnol. Lett. 1981,3(11), 645-650. Revill, B. K. Proceedings, 4th European Conference on Mixing; BHRA Fluid Engineering: Cranfield, Bedford, England, 1982; pp 11-24.
Literature Cited Brennan, D. J.; Lehrer, H. I. Trans. Inst. Chem. Eng. 1976, 54, 139-152. Bryant, J.; Sadeghzadeh, S. Proceedings, 3rd European Conference on Mixing; BHRA Fluid Engineering: Cranfield, Bedford, England, 1979; Vol. I, pp 325-336. Cooker, B.; Mitchell, F. R. G.; Nedderman, R. M. Chem. Eng. 1983, 392, 81-83. Costes, J.; Couderc, J. P. Proceedings, 4th European Conference on Mixing; BHRA Fluid Engineering: Cranfield, Bedford, England, 1982; pp 25-34. Einsele, A,; Finn, R. K. Ind. Eng. Chem. Process Des. Deu. 1980,19, 600-603. Khang, S. J.; Levenspiel, 0. Chem. Eng. Sci. 1976, 31, 569-577. Mann, R.; Mavros, P. P.; Middleton, J. C. Trans. Inst. Chem. Eng. 1981, 59, 271-278. Middleton, J. C. Proceedings, 3rd European Conference on Mixing;
Received for review January 18, 1984 Revised manuscript received April 21, 1986 Accepted May 10, 1986
Measuring the Liquid Circulation Time in a Large Gas-Liquid Contactor by Means of a Radio Pill. 2. Circulation Time Distribution Jan van Barneveld* and Willem Smit Akzo Corporate Research Department, P.O. Box 60, 6800 A B Arnhem, The Netherlands
Nico M. G . Oosterhuis Suiker Unie Research, 4709 R A Roosendaal, T h e Netherlands
Hans J. Pragt Akzo Engineering bu, 6800 A B Arnhem, The Netherlands
Circulation time distribution data for a radio pill in a 20-m3 two-stirrer gas-liquid contactor have been measured. An interpretation model for the pill circulation is given. The model assumes the liquid to circulate through five compartments; the radio pill follows the liquid flow and is subject to a constant rate of fall, depending on the gas fraction. Applying this model, the circulation time distribution data of the pill are correlated. T h e simple five-compartment model gives a good fit for the mean and the tailof the radio pill circulation time distribution data; the fit for short circulation times is not as good. If the rate of fall for the pill is set to zero, the liquid circulation time distribution is obtained from the model. 1. Introduction
The liquid circulation time is defined here as the time interval between successive passages of a liquid element through the same or a corresponding point in a stirred vessel. We have been measuring the liquid circulation time distribution in a 20-m3reactor provided with two Rushton disk turbines and four baffles. The experiments have been carried out in water, applying both ungassed and gassed conditions. We used a radio pill and two aerials for our measurements. In part 1 of this paper (Barneveld et al., 1987), assumptions and data on the flow pattern and on the mean circulation time have been given. In part 2, the circulation time distribution measurements will be reported. 2. Equipment and Procedure Detailed information on the experimental setup is given in part 1 of this paper. The dished bottom reactor, T = 2.50 m, was provided with four baffles and two central six-blade Rushton disk turbines (D = 0.8 m) (see Figure 1). Two aerials, each consisting of an isolated steel cable loop, were mounted concentrically around the two turbines in the impeller plane. OSSS-5SS5/S~/2626-2192$01.50/0
The applied flow follower was a 3-cm spherical radio pill, designed to be neutrally buoyant in water. The influence of the gas holdup on the buoyancy of the pill is given in part 1. The signal of the pill was picked up by the two aerials and processed by two radio receivers. By applying a squelch circuit, the receivers could be adjusted in such a way that an output signal appeared only if the strength of the received signal exceeded a certain level. So a detection volume around each aerial could be adjusted. The output signals were fed to a tape recorder and processed off-line with t h e aid of a hybrid computer. The experiments were carried out in tap water at room temperature. The stirrer speed was kept constant at 2.6 s-l. Experiments were performed at a liquid volume of 19 m3 and superficial gas (air)velocities of 0, 1.5, and 2.6 cm/s, respectively. Under these conditions, gas holdups were, respectively, 2.9%) 9.1%) and 12.5%. One experiment was made at a liquid volume of 11 m3 without gas sparging. Here only the lower impeller was in contact with the liquid. All the 19-m3 experiments were run for at least 51/2 h, resulting in 2.000-10.000 passages of the pill along each aerial. 3. Model As stated in part 1, it is assumed that the reactor consists
of five well-mixed compartments, compartments 1,3, and t 3 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2193 L
T
V e s s e l diameter Number o f impellers Impeller diameter Impeller b l a d e w i d t h Impeller s p e e d B a f f l e width P o s i t i o n o f l o w e r impeller P o s i t i o n o f u p p e r impeller
I
1 n
250m 2
0 W
O32T 020
N
26s'' 009 T 035 T 105 T
Ob HL
Hu
Figure 2. Flow diagram for the radio pill.
Figure 1. Reactor dimensions.
5 being situated below the lower impeller, in between the two impellers, and above the upper impeller, respectively. Compartments 2 and 4 are the detection zones around the two impellers (see Figure 1). The fluid as well as the radio pill circulate through the five compartments. In accordance with the results given in part 1, it is further assumed that the two impellers have equal liquid circulation capacities, Qc,l, and that the liquid flow from each impeller divides itself equally over the lower and the higher compartment. The radio pill is assumed to be subject to the liquid flow movement and also to a constant rate of fall, the latter being determined by the gas fraction. In general, the pill can leave a compartment in two ways: by following the liquid or by falling to a lower compartment. The frequency, f l , for following the liquid flow is f l = 1/71) 71 being the mean residence time of a liquid element in the compartment. This mean residence time is determined by the liquid volume in the compartment, Ve) and the impeller pumping capacity, Qc,l. The frequency for falling out is = 1/.z (1) where 7, = mean falling height in a compartment divided by the rate of fall of the pill. It is assumed that the pill enters a compartment at half its height, Hi, and that the rate of fall, uz, is constant for a given gas holdup. (The relationship between falling rate and gas fraction has been determined experimentally.) Assuming this holdup to be uniform throughout the fermentor gives
For each compartment the following "pill balance" can be given: accumulation = in - out (4) in which q' = probability that the pill is present in compartment i (analogous to the amount of tracer after the injection of a tracer pulse) and f = fkequency with which the pill, being in compartment i, moves to compartment '-J
j.
The relevant frequencies,f "j, for the five compartments are given below. All other frequences are zero.
compartment 1: compartment 2:
f 1-2 = l / T 1 l 1 0.5 f2-I = -
+
7:
f2-3
compartment 3:
f3-2
. 7z1
Hi =24
(2)
If the pill passes n times through a compartment, then a fraction (p) of n leaves the compartment by falling down to a lower one while a fraction (1- p ) of n follows the liquid flow 71
P=-
+ 7, The pill circulation is given in Figure 2. 71
=
0.5/~: 1 +0.5 =7:
fz
compartment 4:
f4-3
f5'4
(6)
(7)
713
1 +0.5 =7:
compartment 5:
712
(5)
714
1 +1 =-
72
7:
The mean liquid residence time is for compartments 1and 5: .=2ve Q~J
For compartments 2, 3, and 4,
(3)
The time intervals between successive passages of the radio
2194 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 Table I. Observed Mean Circulation Times and Calculated Liauid Circulation Capacities liquid vol, m3 11 19 19 19 19 19 19 superficial gas rate, u,, 0 0 0 0 2.6 2.6 2.6 cm/s vol gas holdup, 1 - c, % 2.9 2.9 2.9 2.9 12.5 12.5 12.5 obsd mean, fc,p2: s 2.6 4.0 3.1 circulation, &p4, s 8.0 26.2 times of the radio, pill, 2.3 2.7 fc,p2+4, s calcd liquid circulation 2.85 2.39 2.57 2.73 1.68 1.68 1.69 capacity, Qc,l, m3/s
nfc,pi = observed mean circulation time of the pill related to compartment i. In all the experiments given in the table, the maximum detection distance was 32 cm. c5
10
,.
-L. 0
20
08
EO 15
06
0 10
01
0 05
02
h
; E
".
2
8
L
12
-
0
20
16
i
e
12
2C
'6
sec
set
Figure 5. Circulation time distributions of pill and liquid: liquid volume, 19 m3; two impellers; zero gas flow; detection with aerial in compartment 4.
10
05
05
10
04
08
1 c
h 0 4 1
-H
08
1
-
33
0:
0'
02
0
2
L
6
8
03
06
02
OL
01
10
2
-
1
>
E
2
06 f
-
3
02
04
01
02
02
C
2
4
6
sec
8
'0 set
2
i
Figure 3. Circulation time distributions of pill and liquid: liquid volume, 11m3; one impeller; zero gas flow; detection with aerial in compartment 2. 35
z3
L
6
8
1
2
0
0
L
6
8
sei
10
Sec
Figure 6. Circulation time distributions of pill and liquid liquid volume, 19 m3; two impellers; zero gas flow; detection with aerials in compartments 2 and 4.
10 10
-
02
01
0:
r8k.: I
I 0
-
9
2 1 6 2 0 set
0
L
8
'2
20
16
Figure 4. Circulation time distributions of pill and liquid: liquid volume, 19 m3; two impellers; zero gas flow; detection with aerial in compartment 2.
pill through the detection zones have been measured. Each circulation of the pill can be simulated by the following boundary conditions. At t = 0, the pill leaves the detection zone (compartment 2 or 4,respectively). In case the pill leaves compartment 2, the following starting conditions are valid: q2 = q4 = q5 = 0 and q' q3 = 1. The ratio between q1 and q3 is given by the pill flow from compartment 2 to compartments 1 and 3 in the stationary situation (see Figure 2). At time t , the probability that the pill has passed through or is present in the detection compartment 2 is q2 (f2'l and f2'3 = 0). By simple numerical forward integration with small steps, the q' values for the various compartments can be calculated as a function of time. For compartments 2 and 4,the thus calculated q values can be compared with the measured values. The model has only one parameter left. In part 1 of this paper, this parameter has been calculated from the observed mean circulation time of the radio pill. In the lower part of Table I, the thus calculated values of Qc,l are given. With these values and with the model, the pill circulation time distributions for the various ex-
+
0
sec
2
4
6
8
1
0
0
10
i0
30
50
40
sec
SFl
Figure 7. Circulation time distributions of pill and liquid liquid volume, 19 m3; two impellers; gas rate, 2.6 cm/s; detection with aerial in compartment 2.
-"
1ii
10 1
* 0 20
08
I
LIRUIO
0 10
0 10
105
Ob5
0
20
40
60
80
100 set
4 10
01
-
-
z2
4Oi
v 0
06
$
20
30
50
LO sec
Figure 8. Circulation time distributions of pill and liquid: liquid volume, 19 m3; two impellers; gas rate, 2.6 cm/s; detection with aerial in compartment 4.
periments were calculated, assuming the liquid in each compartment to be ideally mixed. The frequency distribution of the pill circulation time (C.T.D.) with respect to compartment 2 is given by C.T.D. = dq2/dt (15) In the same way, the C.T.D. for compartment 4 and com-
I n d . Eng. C h e m . Res. 1987,26, 2195-2204 0 25
10
g
-k0 20
-
-
h
08 06
e i
04
02
0
2
4
6
8 1 0 set
2
10 r
08
:
g e
&O 15
06
0 10
04
0 05
02
0
4
8
12
$
-
20
16 Set
Figure 9. Circulation time distributions of pill and liquid liquid volume, 19 m3; two impellers; gas rate, 2.6 cm/s; detection with aerials in compartments 2 and 4.
+
partments 2 4 has been calculated. Finally the circulation time distribution of the liquid was calculated in the same way by setting the rate of fall to zero. The observed and the calculated distributions of the pill as well as the calculated distributions of the liquid are given in Figures 3-9.
2195
for interpreting our measurements. Such a model contains a large number of ideal mixers in series and parallel and is likely to be capable of fitting both short and long circulation times. After some modifications, the presented model can be used for the calculation of gas holdup, residence time distribution in solid-liquid dispersions, etc.
Acknowledgment The mechanical construction of the radio pill and the aerials was designed and developed by H. van Dam. The electronics were designed and built by L. P. de Meulmeester, who made a major contribution to the measurements.
Nomenclature = frequency with which the pill, being in compartment i, moves toward compartment j , s-l f, = frequency for a pill leaving a compartment with liquid flow, s-1 f, = frequency for a pill leaving a compartment by falling out, fi+j
S-1
4. Discussion The simple five-compartments model gives a good fit for the tail of the circulation time distribution of the pill. In all cases, the fit for the short circulation times is not as good. There is a time lag in the beginning of the observed pill circulation time distribution curves, which is not explained by the model. Apparently the assumption of the liquid phase in each compartment being ideally mixed is too simple. The pill, having left a detection compartment, has at least a minimum residence time in the next compartment before reentering the same aerial compartment. In all experiments, the observed pill circulation time distribution shows one or more peaks; this will also be caused by the nonideality of the mixing in the various compartments. In our model, we assume that the probability for the pill to leave a compartment by falling out or by following the liquid flow is independent of the path the pill has been following before entering the compartment. For a nonideally mixed system, this will not be completely true. The shape of the observed distribution curves is the same as the shape of the curves reported by Mann et al. (1981). After including two impellers and a rate of fall for the pill, their structured stochastic flow model may be useful
Hi= height of compartment i, m p , = falling probability of a pill q’ = probability that the pill is present in compartment i QCJ= liquid circulation capacity of an impeller, m3/s t p time, s tcf = time between two successive passages of a liquid element through compartment i, s tc,: = time between two successive passages of the pill through
compartment i, s v , = superficial gas velocity, m/s v , = rate of fall of a pill within a compartment, m/s V = compartment volume, m3 Greek Symbols t ,= volumetric liquid fraction T I , = mean residence time of the pill in compartment i, s T{ = mean residence time of a liquid element in compartment i, s T: = mean time for the pill to fall out of a compartment, s
Literature Cited Barneveld, J. v.; Oosterhuis, N. M. G.; Pragt, J. J.; Smit, W. Znd. Eng. Chem. Res. 1987, preceding paper in this issue. Mann, R.; Mavros, P. P.; Middleton, J. C. Trans. Znst. Chem. Eng. 1981,59,
271-278.
Received for review April 21, 1986 Revised manuscript received May 19, 1987 Accepted June 11, 1987
Screening of Process Retrofit Alternatives Wayne R. Fisher, Michael F. Doherty, and James M. Douglas* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
A systematic procedure for developing and screening process retrofit opportunities is presented. The procedure considers both modifications in the structure of the flow sheet and in equipment sizes for a fixed flow sheet. Also, a systematic way of identifying “bottlenecking” equipment is described. The results of case studies indicate that retrofitting to reduce raw materials costs often is much more important than retrofitting to save energy. Expert systems and “intelligent” computer codes have the potential of making a dramatic impact on the practice of chemical engineering. As a minimum, we expect that solution strategies for various types of problems will be combined with hierarchies of algorithms to make it possible 0888-5885/87/2626-2195$01.50/0
to explore more process alternatives quickly and inexpensively. A t present, “knowledge engineers” attempt to capture solution strategies by interviewing experts and watching them work. However, it is possible to develop hierarchical, “top-down”, “least-commitment” strategies 0 1987 American Chemical Society
