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Reliability analysis of desalination equipment
Desdinatton,32(1980)225-231 OEhvierScientific Publishing Company,&mskdam-RintsdinTbeNatharIauds
RELIABILITY ANALYSIS OF DESALINATION EQUIPMENT
A. UNIONB, E. BURNS, AND A. HUSSEINY Science APplications. Inc., 5 Palo Alto Square, Suite 200, Palo Alto, California and 507 Main, Ames, Iowa
Using fault tree logic. the reliability and availabi,lityof water systems in-
cluding desalination units are examined using field data whenever possible. Also, an assessment is made of factors impacting availability and safety‘of MSF desalination plants.
SYMBOLS
Q
Total yearly amount of water available to the water district (cubic meter/ year1
QD Design daily capacity of the water system (cubic meter/day) qi Unavailability
of a portion of the water system output
fi The fraction of district requirements which can be met with the diminished water system capacity
SCENARIOS
Availability of desalination plants when used as the main supply of fresh water is of prime importance in selection of desalination processes.
Using avail-
ability as a basic design criterion would assure the use of high quality equipment
and provide for a highly cost-effective process.
Several techniques of
availability and reliability analysis can be employed to diagnose the performance of desalination systems.
One such technique is fault tree logic which traces
a specific fault to its basic causes.
The probability of equipment or unit fail-
ure is then used to estimate the system unavailability by employing the roles of
Boolean algebra. A typical water system based on MSF desalination processes as that shown in Figure 1 will be analyzed.
Two scenarios are considered in which the system is
assumed to supply water to a self-sustained village and to a town. Relevant parameters for the system and the two scenarios are listed in Table 1. 225
The water system
226
uNIoNEmAL
has no backup for supplying water to the city or village.
However, the reservoir
acts as a semi-redundant feature of the water system since it can supply water to the town even if the desalination plant is unavailable. MIXING
METERING
WATER
AND
y;y”STAT’o
II-II
Ii
It is limited in size
II
ii
DESALINATION
PLANT
il
TO IRillGATlON DISTA ICT
Ill Fig. 1.
Small town water supply system.
TABLE 1 Water/power requirements for a dual purpose generation/desalination system
PLANTELBCTRIC
POWERCAPACITY
5-8 MW
DISTILLED WATER CAPACITY
1,893 C&ID*
BLENDING RATIO WITH 3,000 PPM BRACKISH WATER
4/l
TOTAL WATER SYSTEM UJTPUT
2,536 CMD*
PER CAPITA POWER CONSUM'TION RATE [Demand includes personal use, desalination plant pump loads and centralized vapor compression cooling load.)
2-4 KW
PER CAPITA DCMESTIC USE OF WATER
322 CMD*
PER CAPITA IRRIGATED WATER REQUIREMENT (Based on crops which include citrus, potatoes, beans, tomatoes, other vegetables, wheat and alfalfa_ Watering is assumed to be required for 6-8 months per year and plant is sized for this requirement.)
348 CMD*
Low Sustained Need Requirement DOMESTIC USE REQUIREMENT
(Self-Sustaining Village)
(2,000 Persons)
IRRIGATION WATER FOR FOOD PRODUCTION (4,000 Persons) FRACTIONAL WATER SYSTEM CAPACITY REQUIRED High Sustained Need Requirement
-81
(Town)
DOMESTIC USE REQUIREMENT (7,300 Persons) FRACTIONAL WATER SYSTEM CAPACITY REQUIRED *Cubic Meter/Day
644 CMD* 1,393 CMD'
2,415 CMI' -93
UNIONE
227
Er_AL
to approximately 7 days Supply of water for the village.
Given that the desali-
nation plant is operating at partial capacity, there is a time period in which the reservoir can make up the difference between water supply requirements
and
desalination plant output, after which there is a dropoff in water system output. If we assume that the desalination. plant is composed of five semi-independent units each supplying 20% of the plant's output, the time which the plant can be operated at a given output before reservoir depletion is shown in Table 2.
TABLE 2 Reservoir depletion as a function of water system capacity
Fresh Water output (Cubic Meter/Day)
MSF Units Available
Fraction of Overall SUPPlY f
T RESD Reservoir Depletion Time (days)
Low Need Case
High Need Case
4
2,006
.8
3
1,514
.6
3i3 26.2
51.7 19.9
2
1,022
.4
13-7
10.8
1
492
-2
9.3
7.9
0
0
0
7
7
WATER SYSTEM AVAILABILITY Two criteria
may be used for judging the adequac)- of the water supply system.
First, the ability of the water supply system to supply the minimum daily requirements of the water district may be assessed and the expected shortfall [if any) estimated_
A second and more conservative approach is to determine the
probability of a water system shortfall, determine a maximum probability for the occurrence, and whether or not the
system
meets
established operability
limits
(Figure 2).
Good Poor
system system
Performante
performance
Acceptabrllty ltmits for system operation. ie , the system rs not to be unavarlable for greater than x days with a probability of y D-Days
Fig. 2.
I”
Which
Water
is Unavailable
System reliability mapping.
m_oNEETAL
228
Using the fault tree logic illustrated in Figure 3, the loss of function (partial or complete) for the water system can be diagrammed as shown in Figure 4(a-c).
Un-
availability of subsystems in the water system down stream of the reservoir is assumed to result in total unavailability
of the water supply.
upstream components is equivalent to total unavailability The contribution of EISF unit unavailability
Unavailability
of
of the desalination system.
to a water system shortfall is shown
in Figure 4(c) for loss of 100% of plant output for more than seven days.
Similar
diagrams may be plotted for partial loss of plant output.
I
Eva A
Top
4
Event
L
4
Systsm FSllUKl3 c 1 subsystem A Component
gate logic
0
OR
@
AND gale logic
Fig. 3.
I
TOP
1 0 4 0 0
FAULT
FAULT EVENT caused by l camblnation of faults acting through logic gates AND
OR
GATE
GATE
BASIC
FAULT
FAULT not devatoped
to its causes
A
TRANSFER
IN
A
TRANSFER
OUT
Fault tree logic and symbols
Given the minimum average water district requirements for two end use scenarios, it is of interest to know, on a yearly basis, what the sustained capacity of the water system is as a function of subsystem availability.
Effective capacity for
the district water supply system can be defined in terms of availability by the equation _Q
J65QD
= 1 -
Gl
: qi(l-fi) i=O
For the water system shown in Figure 1 with five semi-independent MSF desalination units, the output of various degraded system states is shown in Table 2. Notably, for the low village requirement case, the system can supply the full water district requirement
(on the average) almost indefinitely and
SO
a single
redundant MSF unit becomes a design feature. Total system unavailability can be defined in terms of subsystem availabilities using the event names of Figure 4, that is, q0 = %!s + 'MS 'GPL + 'MS pGPL qRgS
qups
(2)
229
Fig,
4(a] ,_ Loss af effectiveness
of water
supply
system.
Fig. 4@3.
Fig.
4(c).
133
SPS =
q1PL + %PL qTP + %PL -"TP%ES
qDES-
%zP + 'EP qSD - pEP psD qPRE + pEP PSD pPRE %.on
c "1 'EP 'SD T P_% ~~O~{~SF
(43
IJNIONEETdL
230 The partial water supply unavailability qi =
qMSF'n-il
In equations 3 and 5,
states are given by the set of equations
qRES(i)
i = 1,2,3,4
n=S
refer to the unavailability
qRESot0qES5
as a result of the depletion of various MSF operating
(51
of the reservoir
units.
Reservoir unavailability may be modeled by the probability that equipment upstream from the reservoir remains unrepaired for a sufficient duration to deplete the reservoir.
For the partial operational states, the repair time of interest
is that of the multistage flash units, rMSF [days). Approximatingthe probability of no repair with an exponential distribution, yields the relationship -rRESD(i)'rMSF
(61
qRES(i) = e
For the case where no NSF units are operating, or where the entire desalination plant output is unavailable because of another upstream failure, we can approximate reservoir unavailability -7/r qRESO
= e
by
ups
(71
Where, using the nomenclature of Figure 4 *ups =
(‘EISF
+ *IPL
Unavailabilities
+ ‘EP
+ %D
+ TSD
+ ‘ION
+ =PRE1’7
of each of the major water supply system components other
than the desalination plant are given in Table 3 along with supporting data and data sources.
TA3LE 3 Subsystem failure rates and unavailabilities
(9)
mmmm
231
The metering station is assumed tc be made up of redundant valving, metering control equipment and bypass lines. by equipment malfnnctions
Its unavailability,
therefore, is dominated
such as valve failures and calibration drafts and human
errors committed during maintenance.
Maintenance is assumed to be monthly requiring
Human failures include miscalibration
exercise by the bypass valving.
to remove the system from isolation after maintenance.
and failure
The pretreatment system
for the desalination plant is assumed to be identical from a reliability standpoint. Piping failures resulting in a total catastrophic break are rare occurrences. Rather more likely is a significant leak requiring repair or a leak in a sensitive location.
Piping failure rates are mainly based upon field experience in high
quality industries(l), and a one-mile stretch of piping is assumed to be at risk. It is assumed that leaks can be repaired in 72 hours, but that a catastrophic failure would require far longer. The pumping station consists of one or more high capacity low-head motor pumps [1_33/sec required flow).
The pump is a dominant outage contributor.
assumed to be maintained monthly with an I-hour outage required.
It is
Given a failure
to run or start, a mean repair time of 20 hours is usually required.
Unavailability
is calculated i?or a single pump design and with the assumption of a two-pump redundant system. An on-site power supply consists of a gas turbine or oil-fired boiler which supplies power to the town as well as to the desalination plant.
The unit may be
intertied with a grid to provide increased redundancy, but in some cases, a grid intertie may not be available. assumed to be a gas turbine.
For reliability estimating purposes, the unit is Failure rates for gas turbine equipment can be found
in several sources and an average unavailability average, 0.137, for U.S. equipment.
of 0.13 is close to the national
Unavailability
of electric power is calculated
assuming that the gas turbine is an isolated source and assuming that off-site interties are available. Steam delivery is provided by heat recovery from the power generation unit. For added reliability, a package boiler might be installed to provide steam in the absence of heat delivery from the electric power cycle, assuming, of course, that electricity is available from off-site sources.
The reliability of the package
boiler and its maintenance policy would be similar to that of the electric power steam delivery system.
Failure of the steam delivery system with no package
boiler is a common-mode failure of the electric power supply. existence of the package boiler, unavailability
Assuming
the
is the "intersection" of loss of
steam from heat recovery and failure of the package boiler.
It is assumed that
both the package boiler and power delivery system would not be in maintenance simultaneously. The ion exchange system is assumed to be basically passive in natuxe and dominated by its maintenance requirement.
lJNIONEETAT4
232 Substitution of the unavailability Eqs. 2-S
contributions of Table 3 into the availability
yields the set of availabilities
depletion time is halved.
shown in Table 4.
Notably, the reservoir
This is to account for the fact that other failures may
have occurred previously which partially depleted the reservoir. viewed, the system
may have
Alternately
had more units unavailable previously and the state
which it is now is a transitional state.
In the absence of a clear prior, a value
of 0.5 for the fractional reservoir capacity is assumed. system unavailability are given.
Two equations for total
One (qDL) assumes that the system, other than the
NSF units, is highly reliable with redundant transfer pumps, steam sources, and off-site power ties.
The other (qoL) estimates the reliability of water system
equipment very conservatively.
TABLE 4 Summary of partial and total unavailability navailability
q0
contributors excluding MSF unavailability
Low Water District Need
qoL
= 4.6 x 10m4 + e
High Water District Need
I
-7/T ups
2.5 x 10
-2
[
+ (%,sF)5
-7/r 'OH
ups
= 4.6 x 10m4 + e
-4.65/r&lSF
4 q1
q1 = 'MSF 'MSF
q2
92 = lo &SF2
x 10-l + (q&5
e
4 -3.95/r*MSF q1 = ' 'MSF gMS.F e
-6.9/'tk*sF
2
3
-13-1/T~isF e
93
43 = lo %lSF
%SF
94
94 = S %lSF4 'MSF e
-5'4'T&ISF
2 92 = lo pMSF
qMSF3 e
1 1
%SF3
e -9.95/T,,,,
2 93 = 10 P&fSF3 qMSF
-1S6.S/rMsF
4 44 = ' &SF
e -25-8/Tb*sF
%fSF e
To provide a clearer understanding of the effect of MSF unit unavailability fractional water system
capacity (Eq. l), the problem is solved parametrically.
Figure 5 shows a plot of effective water nation unit unavailability maintenance)
on
for several
system
values
capacity of MSF unit
as a function of desalirepair
times
(including
given a low water district need scenario.
The minimum average water svstem requirement for the system is shown (SIN). For the low use scenario, the system exceeds minimum functionability requirements by a significant amount for all cases except high unit unavailability average repair times.
and long
Figure 6 shows a similar set of plots for the high water
district requirement scenario.
Except for the lowest average repair time case,
higher MSF unit unavailabilities will result in a fresh water shortfall.
1.0
-.i
.aI-
(Days: TMSF
Plot -+-+-c
5
-_._.--__.
3
qf
7 ?4
ql ON
3
qh (cl
7
q,, cc)
14
q,, cc)
ZL ------
.7
.l
I
2
.3
CM
91 CW
+ .eI-
Q
I-
_4
.5
qh4SF
Fig.
5.
Effective water system capacity (dimensionless) as a function of MSF unit unavailability - low average district need-case
1.0
.9
Plot
3
qg(bl
_..._..- ..
7
9
-----
4
o,
3
q,,c=)
7
qh
14
qh
a .a
---e--e-
.7
q
LSF@=
\ I
.l
Fig. 0.
2
.3
.4
a-
.5
Effective water system capacicy_(dimensionless) as a function of MSF unit unavailability - high average district need case
234
Notes to Figures 5 and 6: (a) Minimum average water system capacity meeting water district requirements. QJ) 9, - unavailability of subsystems other than MSF units calculated using high redundancy and/or unit reliabilities. co> qn - unavailability of subsystems other than MSF units calculated using conservative estimates, (d) Estimate of unit unavailability this study. (e) Unit availability for 1.25-year period (Reference 5). It is of interest to estimate the unavailability fox &f!3F units from available data in order to estimate the adequacy of the hypothesized water system design. Figure 7 illustrates in fault logic form the major sources of unavailability for a "typical" MSF desalination unit. Active failures are mainly those involving moving mechanical equipment such as pumps and motorized valves. Passive failures include heat exchangers and condensers, as well as piping. Scheduled maintenances are assumed to take place every 500 hours. Of particular interest are externally caused failures which include intake problems, a major source of lost output in coastal units.
.(a) - Includes leakage and mpture of piping heat exchangers and process vessels for ali reasons Cb3 - Includes unscheduled clltagecontributors such as vibration and corrosion, based on a population of 20 pumps per unit
EC3 - Assumed to he scheduledmaintenance for scale control, cleaning, and active equipment overhaul (packing and lubrication) Cd3 - Includes failures of active control equipment, calibration drifts in control equipment and monitoring instrumentation,assumes a risk population of 50 units Gel
- Includes maintenance failures such as equipment left off-line. equipment trips, and improper calibrations
Cfl - Includes Such effects as silting up of equipment as a result of tidal variations and seaweed clogging of equipneat Fig. 7.
Categorical breakdawn of outage contributors for a single M5F unit.
A quantification of unavailability contributions by source is given in Table 5. The sources of unavailability data include a year's worth of operating experience for an early U.S. unit(s). The evaluations are necessarily conservative since
the
fault
txee
is not drawn to detail and the data is incomplete. Using the avail-
abfe data, calculated system unevailahility is approximately 0.2b.
&en
compared
to the overalL desalination unit unavailability of 0.295 from Reference 5, the agreement is xeasoneble. On Figures s and 6 the two est%m&es of unavailability are shown, Clearly, the expected unit availability is adequate for the LOW district need scenario except for the case of extended repair times. For the high district need scenario, the adequacy of the designed system is more questionable since average repair times of less than seven days are required. Analysis of repair times used in fhe NSF unit unavcilebiItityealculatjionwould imply an average 'iMSF2 3 days, but no error bounds or variance for this data could be calculated from the sparse data available. TARLE5 EiSFunit unavailability contributors
Figure 8 shows for comparison the effective water system capacity for a single MSF system consisting of one unit with the same capacity as the five MSF units in the analyzed design. Clearly, the effect of increased NSF unavailability, in cese of single units. is more severe. Also it should be noted that, based on the calculated estimates of unit unavailability, the system would be inadequate for the high district need scenario. Even 5%~ the low end case, the system is inadequate for the case where other subsystem components are exhibiting high unavaifabilities
Q,,,(
estKnate1
best
PI01
7
I ------
7
-+-+-
-__
_
__-__-
.l
1
unit
equtvalent
q,,
1
unit
eqwvalent
qL,
low
v#llaQe
need
low
vlllaqe
need
qL
*
qt,
,
qr
s h’Q”
wilage
need
hlQh
vtllage
neea
q,,r
i
I
.2
q
7M.W
.3
-4
.5
qMSF
Fig. 8.
Comparison, effective water system capacity (dimensionless) for five unit system and equivalent single unit system.
CONCLUSIONS The above discussion plants.
has focused on reliability considerations
for desalination
The emphasis has been on integrating the plant into a water supply system
such that the district fresh water requirements are met or exceeded.
The results
of this preliminary analysis indicate that 1.
Required equipment reliability is a function of the system design characteristics and the expected demand.
2.
Using average water system capacity as a function of component availabilities and daily water demands, failure models of MSF desalination systems and reliability data on desalination equipment can be conveniently incorporated into estimates of unit effectiveness.
3.
NSF desalination equipment reliability and maintainability analyzed using existing availability methodology.
The above results are limited in scope by several factors.
problems can be
Reliability
estimates for desalination equipment have not been systematically analyzed using logic models and no central bank of reliability data exists which is specifically tailored to desalination equipment.
Also, the use of average capacity and demand
criteria may not suffice for the treatment of problems such as transient water demands and cannot give credit for demand fluctuations and conservation measures. Several recommendations are in order.
First, a system model should be avail-
able which can treat transient demands and output changes of the entire water
UNIONEFiTAL
237
system, relating these variables to unit design, component reliability and maintenance procedures.
Performance simulation models incorporating component avail-
ability are already in use to estimate the performance effectiveness of nuclear safety equipment and can be readily adapted for use on desalination equipment. Second, in-depth fault tree logic should be developed for current NSF designs to provide a framework for availability estimates and a vehicle for diagnosing performance loss problems.
Finally, a retrievable data bank should be established for
desalination equipment to provide a ready source of reliability data and establish equipment reliability standards within the industry. As NSF desalination units become more universally accepted as a means of providing fresh water for community development,
it is imperative that the focus of
developmental effort be on improving performance by increasing unit availability and safety. systems
Similar studies must also be conducted for alternate desalination
such as reverse osmosis.
The analysis of the water system, in this
case, will be similar to the situation presented here.
Nevertheless,
the unavail-
ability calculations for the RO units will be of different nature due to differences in the structure of the process.
REFERENCES 1. 2. 3. 4. 5. 6.
U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, "Reactor Safety Study, Appendix III - Failure Rate Data," NUREG 75/014, October 1975_ Edison Electric Institute, "EEI Unit Availability Summary Report, Equipment Availability in the Period 1966-1976," EEI 77-64, December 1977. J. E. Kelly, R. C. Erdmann, K. Gilbert, "Fault Tree Analysis for Reliability Prediction of Gas Turbine Power Plants," EPRI AF-811, June 1978. Institute of Electrical and Electronics Engineers, "IEEE Nuclear Reliability Data Manual." ANSI/IEEE STDSOO-1977 Wiley-Interscience 1977. U.S. Department of the Interior, "First Annual Report, Saline iiater Conversion Demonstration Plant, San Diego, California," PB 181684, February 1964. R. R. Fullwood, E. T. Burns, and D. Harris, "Preliminary LPG Terminal Risk Study for Los Angeles," SAI-138-79-PA, April 1979.
RELIABILITY ANALYSIS OF DESALINATION EQUIPMENT
A. UNIONB, E. BURNS, AND A. HUSSEINY Science APplications. Inc., 5 Palo Alto Square, Suite 200, Palo Alto, California and 507 Main, Ames, Iowa
Using fault tree logic. the reliability and availabi,lityof water systems in-
cluding desalination units are examined using field data whenever possible. Also, an assessment is made of factors impacting availability and safety‘of MSF desalination plants.
SYMBOLS
Q
Total yearly amount of water available to the water district (cubic meter/ year1
QD Design daily capacity of the water system (cubic meter/day) qi Unavailability
of a portion of the water system output
fi The fraction of district requirements which can be met with the diminished water system capacity
SCENARIOS
Availability of desalination plants when used as the main supply of fresh water is of prime importance in selection of desalination processes.
Using avail-
ability as a basic design criterion would assure the use of high quality equipment
and provide for a highly cost-effective process.
Several techniques of
availability and reliability analysis can be employed to diagnose the performance of desalination systems.
One such technique is fault tree logic which traces
a specific fault to its basic causes.
The probability of equipment or unit fail-
ure is then used to estimate the system unavailability by employing the roles of
Boolean algebra. A typical water system based on MSF desalination processes as that shown in Figure 1 will be analyzed.
Two scenarios are considered in which the system is
assumed to supply water to a self-sustained village and to a town. Relevant parameters for the system and the two scenarios are listed in Table 1. 225
The water system
226
uNIoNEmAL
has no backup for supplying water to the city or village.
However, the reservoir
acts as a semi-redundant feature of the water system since it can supply water to the town even if the desalination plant is unavailable. MIXING
METERING
WATER
AND
y;y”STAT’o
II-II
Ii
It is limited in size
II
ii
DESALINATION
PLANT
il
TO IRillGATlON DISTA ICT
Ill Fig. 1.
Small town water supply system.
TABLE 1 Water/power requirements for a dual purpose generation/desalination system
PLANTELBCTRIC
POWERCAPACITY
5-8 MW
DISTILLED WATER CAPACITY
1,893 C&ID*
BLENDING RATIO WITH 3,000 PPM BRACKISH WATER
4/l
TOTAL WATER SYSTEM UJTPUT
2,536 CMD*
PER CAPITA POWER CONSUM'TION RATE [Demand includes personal use, desalination plant pump loads and centralized vapor compression cooling load.)
2-4 KW
PER CAPITA DCMESTIC USE OF WATER
322 CMD*
PER CAPITA IRRIGATED WATER REQUIREMENT (Based on crops which include citrus, potatoes, beans, tomatoes, other vegetables, wheat and alfalfa_ Watering is assumed to be required for 6-8 months per year and plant is sized for this requirement.)
348 CMD*
Low Sustained Need Requirement DOMESTIC USE REQUIREMENT
(Self-Sustaining Village)
(2,000 Persons)
IRRIGATION WATER FOR FOOD PRODUCTION (4,000 Persons) FRACTIONAL WATER SYSTEM CAPACITY REQUIRED High Sustained Need Requirement
-81
(Town)
DOMESTIC USE REQUIREMENT (7,300 Persons) FRACTIONAL WATER SYSTEM CAPACITY REQUIRED *Cubic Meter/Day
644 CMD* 1,393 CMD'
2,415 CMI' -93
UNIONE
227
Er_AL
to approximately 7 days Supply of water for the village.
Given that the desali-
nation plant is operating at partial capacity, there is a time period in which the reservoir can make up the difference between water supply requirements
and
desalination plant output, after which there is a dropoff in water system output. If we assume that the desalination. plant is composed of five semi-independent units each supplying 20% of the plant's output, the time which the plant can be operated at a given output before reservoir depletion is shown in Table 2.
TABLE 2 Reservoir depletion as a function of water system capacity
Fresh Water output (Cubic Meter/Day)
MSF Units Available
Fraction of Overall SUPPlY f
T RESD Reservoir Depletion Time (days)
Low Need Case
High Need Case
4
2,006
.8
3
1,514
.6
3i3 26.2
51.7 19.9
2
1,022
.4
13-7
10.8
1
492
-2
9.3
7.9
0
0
0
7
7
WATER SYSTEM AVAILABILITY Two criteria
may be used for judging the adequac)- of the water supply system.
First, the ability of the water supply system to supply the minimum daily requirements of the water district may be assessed and the expected shortfall [if any) estimated_
A second and more conservative approach is to determine the
probability of a water system shortfall, determine a maximum probability for the occurrence, and whether or not the
system
meets
established operability
limits
(Figure 2).
Good Poor
system system
Performante
performance
Acceptabrllty ltmits for system operation. ie , the system rs not to be unavarlable for greater than x days with a probability of y D-Days
Fig. 2.
I”
Which
Water
is Unavailable
System reliability mapping.
m_oNEETAL
228
Using the fault tree logic illustrated in Figure 3, the loss of function (partial or complete) for the water system can be diagrammed as shown in Figure 4(a-c).
Un-
availability of subsystems in the water system down stream of the reservoir is assumed to result in total unavailability
of the water supply.
upstream components is equivalent to total unavailability The contribution of EISF unit unavailability
Unavailability
of
of the desalination system.
to a water system shortfall is shown
in Figure 4(c) for loss of 100% of plant output for more than seven days.
Similar
diagrams may be plotted for partial loss of plant output.
I
Eva A
Top
4
Event
L
4
Systsm FSllUKl3 c 1 subsystem A Component
gate logic
0
OR
@
AND gale logic
Fig. 3.
I
TOP
1 0 4 0 0
FAULT
FAULT EVENT caused by l camblnation of faults acting through logic gates AND
OR
GATE
GATE
BASIC
FAULT
FAULT not devatoped
to its causes
A
TRANSFER
IN
A
TRANSFER
OUT
Fault tree logic and symbols
Given the minimum average water district requirements for two end use scenarios, it is of interest to know, on a yearly basis, what the sustained capacity of the water system is as a function of subsystem availability.
Effective capacity for
the district water supply system can be defined in terms of availability by the equation _Q
J65QD
= 1 -
Gl
: qi(l-fi) i=O
For the water system shown in Figure 1 with five semi-independent MSF desalination units, the output of various degraded system states is shown in Table 2. Notably, for the low village requirement case, the system can supply the full water district requirement
(on the average) almost indefinitely and
SO
a single
redundant MSF unit becomes a design feature. Total system unavailability can be defined in terms of subsystem availabilities using the event names of Figure 4, that is, q0 = %!s + 'MS 'GPL + 'MS pGPL qRgS
qups
(2)
229
Fig,
4(a] ,_ Loss af effectiveness
of water
supply
system.
Fig. 4@3.
Fig.
4(c).
133
SPS =
q1PL + %PL qTP + %PL -"TP%ES
qDES-
%zP + 'EP qSD - pEP psD qPRE + pEP PSD pPRE %.on
c "1 'EP 'SD T P_% ~~O~{~SF
(43
IJNIONEETdL
230 The partial water supply unavailability qi =
qMSF'n-il
In equations 3 and 5,
states are given by the set of equations
qRES(i)
i = 1,2,3,4
n=S
refer to the unavailability
qRESot0qES5
as a result of the depletion of various MSF operating
(51
of the reservoir
units.
Reservoir unavailability may be modeled by the probability that equipment upstream from the reservoir remains unrepaired for a sufficient duration to deplete the reservoir.
For the partial operational states, the repair time of interest
is that of the multistage flash units, rMSF [days). Approximatingthe probability of no repair with an exponential distribution, yields the relationship -rRESD(i)'rMSF
(61
qRES(i) = e
For the case where no NSF units are operating, or where the entire desalination plant output is unavailable because of another upstream failure, we can approximate reservoir unavailability -7/r qRESO
= e
by
ups
(71
Where, using the nomenclature of Figure 4 *ups =
(‘EISF
+ *IPL
Unavailabilities
+ ‘EP
+ %D
+ TSD
+ ‘ION
+ =PRE1’7
of each of the major water supply system components other
than the desalination plant are given in Table 3 along with supporting data and data sources.
TA3LE 3 Subsystem failure rates and unavailabilities
(9)
mmmm
231
The metering station is assumed tc be made up of redundant valving, metering control equipment and bypass lines. by equipment malfnnctions
Its unavailability,
therefore, is dominated
such as valve failures and calibration drafts and human
errors committed during maintenance.
Maintenance is assumed to be monthly requiring
Human failures include miscalibration
exercise by the bypass valving.
to remove the system from isolation after maintenance.
and failure
The pretreatment system
for the desalination plant is assumed to be identical from a reliability standpoint. Piping failures resulting in a total catastrophic break are rare occurrences. Rather more likely is a significant leak requiring repair or a leak in a sensitive location.
Piping failure rates are mainly based upon field experience in high
quality industries(l), and a one-mile stretch of piping is assumed to be at risk. It is assumed that leaks can be repaired in 72 hours, but that a catastrophic failure would require far longer. The pumping station consists of one or more high capacity low-head motor pumps [1_33/sec required flow).
The pump is a dominant outage contributor.
assumed to be maintained monthly with an I-hour outage required.
It is
Given a failure
to run or start, a mean repair time of 20 hours is usually required.
Unavailability
is calculated i?or a single pump design and with the assumption of a two-pump redundant system. An on-site power supply consists of a gas turbine or oil-fired boiler which supplies power to the town as well as to the desalination plant.
The unit may be
intertied with a grid to provide increased redundancy, but in some cases, a grid intertie may not be available. assumed to be a gas turbine.
For reliability estimating purposes, the unit is Failure rates for gas turbine equipment can be found
in several sources and an average unavailability average, 0.137, for U.S. equipment.
of 0.13 is close to the national
Unavailability
of electric power is calculated
assuming that the gas turbine is an isolated source and assuming that off-site interties are available. Steam delivery is provided by heat recovery from the power generation unit. For added reliability, a package boiler might be installed to provide steam in the absence of heat delivery from the electric power cycle, assuming, of course, that electricity is available from off-site sources.
The reliability of the package
boiler and its maintenance policy would be similar to that of the electric power steam delivery system.
Failure of the steam delivery system with no package
boiler is a common-mode failure of the electric power supply. existence of the package boiler, unavailability
Assuming
the
is the "intersection" of loss of
steam from heat recovery and failure of the package boiler.
It is assumed that
both the package boiler and power delivery system would not be in maintenance simultaneously. The ion exchange system is assumed to be basically passive in natuxe and dominated by its maintenance requirement.
lJNIONEETAT4
232 Substitution of the unavailability Eqs. 2-S
contributions of Table 3 into the availability
yields the set of availabilities
depletion time is halved.
shown in Table 4.
Notably, the reservoir
This is to account for the fact that other failures may
have occurred previously which partially depleted the reservoir. viewed, the system
may have
Alternately
had more units unavailable previously and the state
which it is now is a transitional state.
In the absence of a clear prior, a value
of 0.5 for the fractional reservoir capacity is assumed. system unavailability are given.
Two equations for total
One (qDL) assumes that the system, other than the
NSF units, is highly reliable with redundant transfer pumps, steam sources, and off-site power ties.
The other (qoL) estimates the reliability of water system
equipment very conservatively.
TABLE 4 Summary of partial and total unavailability navailability
q0
contributors excluding MSF unavailability
Low Water District Need
qoL
= 4.6 x 10m4 + e
High Water District Need
I
-7/T ups
2.5 x 10
-2
[
+ (%,sF)5
-7/r 'OH
ups
= 4.6 x 10m4 + e
-4.65/r&lSF
4 q1
q1 = 'MSF 'MSF
q2
92 = lo &SF2
x 10-l + (q&5
e
4 -3.95/r*MSF q1 = ' 'MSF gMS.F e
-6.9/'tk*sF
2
3
-13-1/T~isF e
93
43 = lo %lSF
%SF
94
94 = S %lSF4 'MSF e
-5'4'T&ISF
2 92 = lo pMSF
qMSF3 e
1 1
%SF3
e -9.95/T,,,,
2 93 = 10 P&fSF3 qMSF
-1S6.S/rMsF
4 44 = ' &SF
e -25-8/Tb*sF
%fSF e
To provide a clearer understanding of the effect of MSF unit unavailability fractional water system
capacity (Eq. l), the problem is solved parametrically.
Figure 5 shows a plot of effective water nation unit unavailability maintenance)
on
for several
system
values
capacity of MSF unit
as a function of desalirepair
times
(including
given a low water district need scenario.
The minimum average water svstem requirement for the system is shown (SIN). For the low use scenario, the system exceeds minimum functionability requirements by a significant amount for all cases except high unit unavailability average repair times.
and long
Figure 6 shows a similar set of plots for the high water
district requirement scenario.
Except for the lowest average repair time case,
higher MSF unit unavailabilities will result in a fresh water shortfall.
1.0
-.i
.aI-
(Days: TMSF
Plot -+-+-c
5
-_._.--__.
3
qf
7 ?4
ql ON
3
qh (cl
7
q,, cc)
14
q,, cc)
ZL ------
.7
.l
I
2
.3
CM
91 CW
+ .eI-
Q
I-
_4
.5
qh4SF
Fig.
5.
Effective water system capacity (dimensionless) as a function of MSF unit unavailability - low average district need-case
1.0
.9
Plot
3
qg(bl
_..._..- ..
7
9
-----
4
o,
3
q,,c=)
7
qh
14
qh
a .a
---e--e-
.7
q
LSF@=
\ I
.l
Fig. 0.
2
.3
.4
a-
.5
Effective water system capacicy_(dimensionless) as a function of MSF unit unavailability - high average district need case
234
Notes to Figures 5 and 6: (a) Minimum average water system capacity meeting water district requirements. QJ) 9, - unavailability of subsystems other than MSF units calculated using high redundancy and/or unit reliabilities. co> qn - unavailability of subsystems other than MSF units calculated using conservative estimates, (d) Estimate of unit unavailability this study. (e) Unit availability for 1.25-year period (Reference 5). It is of interest to estimate the unavailability fox &f!3F units from available data in order to estimate the adequacy of the hypothesized water system design. Figure 7 illustrates in fault logic form the major sources of unavailability for a "typical" MSF desalination unit. Active failures are mainly those involving moving mechanical equipment such as pumps and motorized valves. Passive failures include heat exchangers and condensers, as well as piping. Scheduled maintenances are assumed to take place every 500 hours. Of particular interest are externally caused failures which include intake problems, a major source of lost output in coastal units.
.(a) - Includes leakage and mpture of piping heat exchangers and process vessels for ali reasons Cb3 - Includes unscheduled clltagecontributors such as vibration and corrosion, based on a population of 20 pumps per unit
EC3 - Assumed to he scheduledmaintenance for scale control, cleaning, and active equipment overhaul (packing and lubrication) Cd3 - Includes failures of active control equipment, calibration drifts in control equipment and monitoring instrumentation,assumes a risk population of 50 units Gel
- Includes maintenance failures such as equipment left off-line. equipment trips, and improper calibrations
Cfl - Includes Such effects as silting up of equipment as a result of tidal variations and seaweed clogging of equipneat Fig. 7.
Categorical breakdawn of outage contributors for a single M5F unit.
A quantification of unavailability contributions by source is given in Table 5. The sources of unavailability data include a year's worth of operating experience for an early U.S. unit(s). The evaluations are necessarily conservative since
the
fault
txee
is not drawn to detail and the data is incomplete. Using the avail-
abfe data, calculated system unevailahility is approximately 0.2b.
&en
compared
to the overalL desalination unit unavailability of 0.295 from Reference 5, the agreement is xeasoneble. On Figures s and 6 the two est%m&es of unavailability are shown, Clearly, the expected unit availability is adequate for the LOW district need scenario except for the case of extended repair times. For the high district need scenario, the adequacy of the designed system is more questionable since average repair times of less than seven days are required. Analysis of repair times used in fhe NSF unit unavcilebiItityealculatjionwould imply an average 'iMSF2 3 days, but no error bounds or variance for this data could be calculated from the sparse data available. TARLE5 EiSFunit unavailability contributors
Figure 8 shows for comparison the effective water system capacity for a single MSF system consisting of one unit with the same capacity as the five MSF units in the analyzed design. Clearly, the effect of increased NSF unavailability, in cese of single units. is more severe. Also it should be noted that, based on the calculated estimates of unit unavailability, the system would be inadequate for the high district need scenario. Even 5%~ the low end case, the system is inadequate for the case where other subsystem components are exhibiting high unavaifabilities
Q,,,(
estKnate1
best
PI01
7
I ------
7
-+-+-
-__
_
__-__-
.l
1
unit
equtvalent
q,,
1
unit
eqwvalent
qL,
low
v#llaQe
need
low
vlllaqe
need
qL
*
qt,
,
qr
s h’Q”
wilage
need
hlQh
vtllage
neea
q,,r
i
I
.2
q
7M.W
.3
-4
.5
qMSF
Fig. 8.
Comparison, effective water system capacity (dimensionless) for five unit system and equivalent single unit system.
CONCLUSIONS The above discussion plants.
has focused on reliability considerations
for desalination
The emphasis has been on integrating the plant into a water supply system
such that the district fresh water requirements are met or exceeded.
The results
of this preliminary analysis indicate that 1.
Required equipment reliability is a function of the system design characteristics and the expected demand.
2.
Using average water system capacity as a function of component availabilities and daily water demands, failure models of MSF desalination systems and reliability data on desalination equipment can be conveniently incorporated into estimates of unit effectiveness.
3.
NSF desalination equipment reliability and maintainability analyzed using existing availability methodology.
The above results are limited in scope by several factors.
problems can be
Reliability
estimates for desalination equipment have not been systematically analyzed using logic models and no central bank of reliability data exists which is specifically tailored to desalination equipment.
Also, the use of average capacity and demand
criteria may not suffice for the treatment of problems such as transient water demands and cannot give credit for demand fluctuations and conservation measures. Several recommendations are in order.
First, a system model should be avail-
able which can treat transient demands and output changes of the entire water
UNIONEFiTAL
237
system, relating these variables to unit design, component reliability and maintenance procedures.
Performance simulation models incorporating component avail-
ability are already in use to estimate the performance effectiveness of nuclear safety equipment and can be readily adapted for use on desalination equipment. Second, in-depth fault tree logic should be developed for current NSF designs to provide a framework for availability estimates and a vehicle for diagnosing performance loss problems.
Finally, a retrievable data bank should be established for
desalination equipment to provide a ready source of reliability data and establish equipment reliability standards within the industry. As NSF desalination units become more universally accepted as a means of providing fresh water for community development,
it is imperative that the focus of
developmental effort be on improving performance by increasing unit availability and safety. systems
Similar studies must also be conducted for alternate desalination
such as reverse osmosis.
The analysis of the water system, in this
case, will be similar to the situation presented here.
Nevertheless,
the unavail-
ability calculations for the RO units will be of different nature due to differences in the structure of the process.
REFERENCES 1. 2. 3. 4. 5. 6.
U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, "Reactor Safety Study, Appendix III - Failure Rate Data," NUREG 75/014, October 1975_ Edison Electric Institute, "EEI Unit Availability Summary Report, Equipment Availability in the Period 1966-1976," EEI 77-64, December 1977. J. E. Kelly, R. C. Erdmann, K. Gilbert, "Fault Tree Analysis for Reliability Prediction of Gas Turbine Power Plants," EPRI AF-811, June 1978. Institute of Electrical and Electronics Engineers, "IEEE Nuclear Reliability Data Manual." ANSI/IEEE STDSOO-1977 Wiley-Interscience 1977. U.S. Department of the Interior, "First Annual Report, Saline iiater Conversion Demonstration Plant, San Diego, California," PB 181684, February 1964. R. R. Fullwood, E. T. Burns, and D. Harris, "Preliminary LPG Terminal Risk Study for Los Angeles," SAI-138-79-PA, April 1979.