Fair, J. R., Lambright, A. J., Andersen, J. W., Ind. Eng. Chem., Process Des. Dev., 1, 33 (1962). Federal Water Pollution Control Act, as amended, 33 USC 1251, 1326 (a), Section 316 (a). Harmathy, T. Z., AIChEJ., 6, 281 (1960). Krabach, M. H., Marcello, R. A., “An Analysis of the Feasibility of Using Air Agitation to Reduce Gas Saturations in Seawater at Pilgrim Nuclear Power Station,” July 1976. Levenspiel, O.,“Chemical Reaction Engineering,” 2nd ed, Wiley, New York, N.Y.. 1972. Marcelio, R. A., Jr.. Krabach, M. H., Barllett, S . F., Evaluation of Alternate Solutions to Gas Bubble Disease Mortality of Menhaden at Pilgrim Nuclear Power Station, Yankee Atomic Electric Co., Oct 1975. Raymond, D. R., Zieminski, S . A., AIChEJ., 17, 57 (1971). Satterfield. C. N., J. Chem. Eng. Data, 6j4), 504 (1961).
Schweitzer, P. H., Szebehely, V. G., J. AppI. fhys., 21, 1218 (Dec 1950). Shulman, H. L., Molstad, M. C., Ind. Eng. Chem., 42, 1058 (1950). Silberman, E., “hoduction of Bubbles by the Disintegration of Gas Jets in Liquid,” Proceedings, 5th Midwestern Conference on Fluid Mechanics, University of Michigan, 1957. Sideman, S.,Hortacsu, O., Fulton, J. W., Ind. Eng. Chem., 58 (7), 32 (1966). Towell, G. D., et al., AIChE Int. Chem. Eng. Symp. Ser. 25, No. 10, 97 (1965). United States Environmental Protection Agency, Manual of Methods for Chemical Analysis of Water and Wastes, EPA-625/6-74-003, 1974.
Received for review February 16,1977 Accepted June 27,1977
Effect of Storage Tanks on Plant Availability Ernest J. Henley”’ and Hlromitsu Hoshino Computer Aided Design Centre, Cambridge, England
This paper develops a methodology for calculating the effect of storage tanks on plant availability (ratio of up- to downtime). The case where the tank acts as a pure time delay, i.e., where it can be filled immediately by upstream overcapacity or outside supply, is solved rigorously, and it is shown how existing computer codes can be used to obtain system steady- and unsteady-state availability changes. If the capacity of the upstream and downstream units is identical, then increases in availability can be obtained only if the tank is replenished during downstream repair or shutdown. The effects of this and other operating policies are analyzed and appropriate bounding theorems are suggested.
Introduction Storage tanks represent a considerable fraction of the invested capital in a chemical plant. The primary purpose of most storage tanks is to keep a process on-stream continuously or to permit an orderly shutdown in the case of equipment failure. Thus tanks sometimes decrease the plant unavailability, Q,which, for a repairable system, is defined so that Q/(1 - Q) is the ratio of downtime to uptime for a plant. We say “sometimes” because as will be demonstrated shortly, whether or not there is a decrease in Q depends on plant operating policy with respect to filling and emptying the tanks. Three previous papers are pertinent here. Ross (1973) published a result where tanks were treated as system time delays and a Monte Carlo analysis was performed. Rosen and Henley (1974) attempted to optimize intermediate storage for a nonrepairable system. In an unpublished paper presented in Birmingham, England, in September 1976, W. Holmes and F. E. Perris described “PATCH” and “BLOCK”, Imperial Chemical Industries’ in-house computer programs capable of steady-state Markov availability analyses of plants containing tanks which act as pure time delays, and tanks which can be filled on-line because of excess upstream capacity. These programs use a block reduction technique so that only overall process availability is calculated. Subsystems cannot be analyzed. The most comprehensive system reliability and availability analysis program now in use is the KITT code developed by Vesley and Narum (1972). Based on the kinetic tree theory Address correspondence to this author at the Department of Chemical Engineering, University of Houston, Houston, Texas 77004.
of Vesley (1970), this will compute all useful steady and unsteady state reliability parameters for systems, components, and cut sets. Since the application of this program to chemical process systems is limited somewhat by its inability to handle time delays and storage tanks, one of the major purposes of the investigation detailed here was to extend the usefulness of this very fine code.
Tank Operating Policy Failures do not occur instantaneously; there is always a finite time lapse between cause and consequence. In fault tree notation, this can be shown as in Figure 1. The delay can be of mechanical or electrical origin, or it may represent storage as in the case of a tank in a chemical plant. In general, delays uncouple units, thus blocking information transfer from upstream to downstream for a period of time. In Figure 2, for example, if the upstream (SU) and downstream (SD) flow rates are a t a steady state rate of 100 L h , and there is a storage tank which holds 100 L between the units, the downstream units will run for 1h after the upstream unit fails (providing the downstream units do not fail and the tank is fdl). The change in system availability due to a storage tank is a complex function of plant operating policy. For example, imagine that the capacity of the SU and SD units is exactly the same, that we start with a full tank, and operating policy A in the event of a SU failure is as follows. Policy A. (1) Run SD till the tank is empty or the SU failure is repaired. (2) Start up SU. (3) Fill the tank. (4) Start up SD. (5) Run till the next SD or SU failure. For Policy A, the storage tank will have no effect on the overall plant availability. However, starting with the same full tank and matched flows, imagine we adopt the following policy when SU fails. Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
439
Table I. Storage Tank Strategy Reason for Tank 1. Lack of feed to SD units poses a safety hazard (i.e.,SU units may be providing a coolant, inert blanket, dilutent etc.) 2. Quality of output from SU units is somewhat variable and product must be blended to maintain specs. 3. SD units difficult or costly to shut down (cracking furnaces, catalytic reactions, etc.) 4. SU units have excess capacity but are less reliable than SD units and availability increase is desired. 5. SD units have poor reliability but excess capacity and availability increase is desired. 6. SD and SU units have balanced reliabilities and capacity and availability increase is desired. 7 . SU units difficult or costly to shut down and/or overflow capability is required because of environmental pollution.
1
output
Operating Policy 1. Policy A. Always keep storage tank full if possible.
2. Policy A. Always keep storage tank full if possible.
3. Policy A. Always keep storage tank full if possible. 4. Keep storage tank full. Fill with both units on-line, or
when SD is down. 5 . Policy B. Keep storage tank empty, filling during SD
breakdown. 6. Keep tank half full, emptying and filling during shut-
downs.
I. Keep storage tank empty if possible, filling when SD is down.
I
N o flow from SD
Input
Figure 1. Delay gate. N o fluid i n tank
units SD
Q-) 1 Storage
Ups t re am u n i t s SU
(J A
Figure 2. Storage tank. Policy B. (1)Same as above. (2) Same as above. (3) Start up SD. (4)Run till the next SD or SU failure (with the tank empty). (5) Fill tank only while SD is down. Policy B will result in an increase in availability, since we never hold production for the purpose of filling the tank. Before attempting elaborate mathematical treatments of these and other possible operating policies, it might be sobering to consider the practical aspects of the situation. There are two major types of storage tanks in a chemical plant, and neither type is placed there strictly to obtain reliability or availability increases. (1) Product and raw material tanks-raw material supply, shipping, delivery, schedule, and production rates are the primary variables dictating size and configuration. (2) Intermediate storage tanks-here size, configuration, and operating policy depend on the purpose the tank is to serve. Table I details some typical storage tank functions and the associated operating policies. No gain in availability is obtained by policies 1,2,3, or 7 because here we fill or empty the tank immediately after plant startup, and the capacities SD and SU are matched. Policies 4, 5, and 6 result in an increase in availability providing we fill or empty during breakdown periods or we are able to fill or empty during 440
Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
I
(F)
Figure 3. Fault tree for storage delay. “normal” operation because of excess capacity SU or SD respectively. Table I does not, by any means, cover all of the reasons for having storage tanks. Tanks for the purpose of collecting overflows, effluents, off-spec materials, or streams from parallel or batch units also appear on plant sites, and each has a unique and optimal operating procedure. Time Delays We consider first Case 4 where the SU units have excess capacity, the tank can be filled instantaneously, and the mean time to failure of SU, MTTF(SU) >> T’, where T’ is the time to fill the tank. Thus, when SU fails, the tank is always full, and thus represents a pure time delay. Of course when SD fails, SU must shut down immediately. The fault tree for this situation is shown in Figure 3. The top event is no flow from
SD. In the development of the theory, we neglect the event “tank fails” and adopt the following notation: T = time to empty the tank, given no flow in after it starts to empty;
SU f a i l s
Tank empty
ST f a i l s
SU f a i l s
t
tl 1
\ Figure 4. Notation for interval T.
I
tl-T
t-t
Figure 5. Notation for interval t
W s ~ ( t= ) the expected number of events where the tank becomes empty at t per unit time due to SU failure at ( t - T ) . The subscript S T refers to a system conposed of tank and
1 -
- tl. SU i n f a i l e d s t a t e
SU f a i l s
su.
It is necessary to recognize that the tank becomes empty at t if and only if SU fails at ( t - T )and is not repaired by t , and that W S T ( ~is) not the same as the probability that the tank is empty. We now define Wsu(t) = the expected number of SU failures a t t per unit time; and P,( T ) = the probability of no upstream repair in time interval T . Thus, with reference
l-
1
t-t 2
Figure 6. Notation for interval t
- tz.
to Figure 4, and the above definitions W S T ( ~=) W s d t - T)Pr(T)
(1)
We assume an exponential repair distribution for the upstream units; thus the probability of no upstream repair in time T i s
Pr(T)= e-T/TSU(t)
W's for the above equations can be obtained from computer codes such as KITTI or 11. This code also calculates ASU, the probability of subsystem failure existing a t time t per unit time, given that subsystem failure has not occurred to time t . Thus we have the useful relationships
(2)
-
where S ~ Uis the upstream repair time. Substituting eq 2 into eq 1 we see that as t (steady state) WST = e - T / s s u W ~=~KWsu
(3)
--Qsu - ratio of expected downtime to expected uptime 1 - Qsu
(10)
Recognizing now that the downstream units fail when the tank is empty, we define the combined unavailability of the tank and upstream units at time t as Q s T ( ~ )=
S,t-TWsdt,)Pr(t - t i ) d t i
(12)
(4)
Figure 5 serves to clarify this equation. SU fails at t l and is not repaired by time t . An SU failure between t - T and t does not influence the failure of ST a t t . With reference to Figure 6, the unavailability of SU a t t is described by a relationship similar to eq 4.
Similarly, for the tank and SU
Combining eq 12 and 14 with eq 3 and 8 we see that a t steady state Since, in general, for constant repair times of
7
s
~
7SU
pr(t)= e--t/TSU
(6)
we substitute for Pr(t - t l ) in eq 4, and then using eq 5, we obtain for QST(t)
= 7ST
(15)
We now combine eq 13 with previously derived eq 1and 3 to obtain (16)
= (e-T/rsu)
Jt-T
W S U ( ~ ~ ) ~ - ( ( ~ - ~ ) -dt2 ~ ~ ) /( "7 S) U
= ( e - * / T s u ) ( Q ~ ~-( t5")) = KQsu(t
-T)
(8)
At steady state, this becomes QST = KQSU
This equation states that if SU is down a t t - T and not repaired in the interval T, ST is down at T . The failure of SU after t - T has nothing to do with the failure of ST a t t , because there is still some fluid left in the tank. The above equations, combined with some relationships inherent in the definitions, are sufficient to solve steady- or unsteady-state reliability problems involving complex systems containing storage which acts as a pure time delay. Q's and
At steady state AST = KAsu
We now apply these equations to test examples. Example 1. Obtain the MTTF and QST for a single SU unit XSU = 1 X TSU = 10 backed up by a storage tank, as a function of storage tank capacity in hours. Assume steady state. Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
441
SU system failure
No flow to SD units
o-(T) SU downtime
r? SU fails
00
Figure 7. Component data and structure example 2. X (failuresh) and T (repair time): 1, 1.0 X 10; 2, 2 X 40; 3, 3 X 60. Table 11. Reliability Parameters, Example 1
b s T x103
T
TI^
0 10 20 40
0 1 1 1.0 0.36788 0.36557 2.0 0.13534 0.13417 4.0 0.01832 0.01814
K
MTTF x 10-3, h Q~~ x 103 1
2.73546 7.45295 55.13413
9.90099 3.64236 1.34121 0.18151
Figure 8. SU failure plus tank example 2.
Table 111. Reliability Parameters, Example 2 io2
w x 103
A x 103
7
3.9756 7.79010 7.54726
2.00639 1.98378 2.02806
2.08946 2.15139 2.19362
19.8147 39.2735 37.21421
Qx
t 20 40 400
At steady state (Fussell, 1975)
Qsu = *-
Xr
+
h
wsu = 1 + Xr
1 AT' Substituting into eq 8 (this form of the steady-state equation was derived independently by G. Fussell, W. Johns, and ourselves)
Qm = KQsu = e - T / r Q S U Combining with eq 18 X
e
1
+ A T ) - AT
for X = 0.001 and T = 10. For a repairable system backed up by a tank which can be kept full, we note by Table I1 that the system availability and MTFF increases dramatically with tank size. Example 2. The fault tree of Figure 7 has the component characteristics as shown. In view of the repair times, we would expect steady state a t t > 200 h. The SU system parameters obtained by KITT are given in columns 2,3, and 4 of Table 111, and T was calculated by eq 12. Let us now examine the effect of introducing tanks 1and 2 representing time delays of 3.72 and 111.6 h, respectively (Figure 8). According to eq 2 this corresponds to K1= 0.90485 and Kz = 0.04979. The computer output in Table IV was obtained using an inhibit gate as a delay gate, with inhibit conditions K1 and K2. The results are consistent with our ex442
Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
su
SD
Figure 9. Case 1
pectations that the effect of the tanks is to increase the availability and reduce the number of system failures. Almost identical results are obtained if the SU system in Figure 8 is replaced by one component with system A and T'S from Table 111. One point of note is that the t's in Table IV are really ( t - 2"). O t h e r T a n k Policies We now examine the consequences of trying to keep the tank full, filling only while the downstream unit is under repair, and assuming exactly matched upstream and downstream production capabilities. We make the assumption of steady state and constant mean time to failure, MTTF, and mean time to repair, MTTR. Case I. Upstream Availability Greater T h a n Downs t r e a m Availability (Figure 9). Here, the downstream availability Ad is 20/23 = 0.87 and the upstream availability A, is 10/11 = 0.91. A good approximation to the system availability A, without the storage tank is A, = &A, = (0.87)(0.91) = 0.79. Since, however, we have excess upstream availability (or capacity) and the MTTR upstream is small compared to the tank size, the system availability is equal to Ad = 0.87, since the downstream unit never has to shut down because of lack of feed. Note that for a series system, to a first approximation, the system reliability A, is always bounded by A&, < A, < Ad (20) Case 11. Downstream AvailabiIity G r e a t e r T h a n Ups t r e a m Availability. It is quite obvious that in this case the tank is relatively useless since it will be empty most of the
Table IV. Reliability Parameters, Example 2
t'
K
Q X lo2
w x 103
20
0.90485 0.04979 0.90485 0.04979 0.90485 0.04979
3.59755 1.98041 x lo-' 7.05043 3.88295 X 10-1 6.83011 3.76285 X lo-'
1.81548 9.98922 X 10-2 1.79502 9.87665 x 1.83509 1.00971 X lo-'
40 400
time. Thus the system availability is simply the lower bound of A,, AdA,. Case 111. Equal Availability, Upstream, a n d Downstream. The limits on the system availability are given by eq 20. One simple way of obtaining an exact answer for this unrealistic case is to make a graphical time history for the system noting up- and downtimes and obtaining the availability this way. Conclusions We have shown in this article how the K I T T code can be used to calculate the change in availability for a system handling a storage tank which acts as a time delay, i.e. which can be filled "instantaneously" from an outside source or by upstream overcapacity. It has also been shown that where this outside source or overcapacity does not exist, tanks will have no effect on plant availability, or an effect which can be readily bounded, and closely approximated. Multiple tanks should provide no difficulties if they function as pure time delays. In the matched flow cases, multiple tanks represent a problem and system availabilities may become a function of the com-
A x 103
7
1.88232 1.00090 x 10-1 1.931184 9.91515 X 1.96962 1.013523 X
19.39589 19.92547 39.27772 39.31444 37.2195 37.2665
putational ordering. However, in the matched flow case, it seems prudent to use lower bound availability approximations anyway since plant operating policies may change. Acknowledgment The helpful suggestions of J. Fussell of the University of Tennessee, W. Johns of the London Polytechnic, and J. Grogan and F. E. Perris of IC1 are gratefully acknowledged. Financial support was provided by the National Science Foundation (ENG 75-17613). Literature Cited Fussell, J. B., /E€€ Trans. Reliab., R-24, 3 (1975). Rosen, E., Henley, E. J., Proceedings, AiCHElGVC Meeting, Munich, Oct 1974. Ross, R. C., Hydrocarbon Process., 75 (Aug 1973). Vesley, W. E., Nucl. Eng. Des., 13, 337-360 (1970). Vesley, W. E., Narum, R. E., "PREP and K I T , Computer Codes for the Automatic Evaluation of a Fault Tree", TID-4500 (1972).
Received f o r review December 13,1976 Accepted J u n e 10,1977
Infrared Spectroscopic Investigation of the Adsorption and Reactions of SO2 on CuO Steven A. Kent, James R. Kafzer, and William H. Manogue' Department of Chemical Engineering, University of Delaware, Newark, Delaware 1971 1
Infrared transmission spectroscopy at room temperature has shown that the equivalent of a monolayer of sulfur dioxide adsorbs on copper(l1) oxide at 20 OC forming three different surface species: chemisorbed sulfur dioxide, which was identified by a single band at 1360 cm-l; a nonplanar, chelating, sulfate group of less than CPusymmetry, identified by bands at 1200, 1140, 1050, 980, and
