Reliability Engineering and System Safety 42 (1993) 21-27

Water distribution valve topology for reliability analysis

T h o m a s M. Walski Wilkes University, PO Box 111, Wilkes-Barre, Pennsylvania 18766, USA

This paper points out the importance of adequate valving in providing water distribution system reliability and the problems in assessing the reliability of a water distribution system, using a link-node representation commonly found in pipe network models. The paper suggests using an approach involving 'segments' of a distribution system that can be isolated with valves as the basic unit for assessing reliability, and illustrates the use of a graphical approach to analyze the adequacy of valving.

INTRODUCTION

Most techniques for quantitatively analyzing water distribution system reliability have at their heart some type of hydraulic pipe network model. The hydraulic model represents the real water distribution system as a collection of links (pipes) and nodes (junctions). While this representation is very good for hydraulic analysis, it has some weaknesses when used to evaluate the reliability of a system.

The key weakness in the l ink-node representation is correctly describing what happens when a pipe breaks and must be isolated for maintenance or repair. Most investigators represent a pipe being out of service by removing the link associated with that pipe from the hydraulic model. For example, Goulter and Coals I equate a link with a pipe in a network model. Ormsbee and Kessler 3 and Tung et al.3 use the word 'components' when discussing reliability, but equate a water distribution component with a link in a pipe network model. The remainder of this paper will demonstrate that the l ink-node representation can be misleading and will propose and illustrate an alternative representation for identifying how valving effects the portion of the system that is out of service.

Bouchart and Goulter 4 are the only researchers to consider valve location explicitly in a reliability analysis. They assumed that each pipe link initially had a valve at each end and they determined the number of 'interior valves' to improve reliability. They found that the first few valves significantly

Reliability Engineering and System Safety 0951-8320/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England.

increased reliability, but the impact diminished with each new valve added.

21

PROBLEMS WITH LINK-NODE REPRESENTATION

Importance of valves

The most important problem with the l ink-node representation is that it fails to account for the way that pipes are connected in real water distribution systems and how they are isolated for repair. Pipes are isolated by closing valves along a pipe. In real water distribution systems these valves are not necessarily located at the end of each pipe. Instead of removing a single link when a pipe is taken out of service, the utility removes an irregular shaped collection of links and nodes. (A related problem is that not all valves can be located and operated even if they did exist.) Valves are the key to providing water distribution system reliably. A system without valves would be completely crippled during every pipe break or maintenance event requiring a shutdown. Not enough attention has been given to the importance of valves and their placement in distribution systems.

Bouchart and Goulter 4 and other researchers assumed that individual pipe links could be isolated with valves at each end. This is not current practice in the water industry. If there are n pipe links coming into an intersection, there will almost always be fewer than n valves in that intersection.

To quantify the error introduced by assuming each pipe link has a valve at each end, the author examined

22 Thomas M. Walski

the l ink-node representation for a detailed pipe network model of a portion of the Austin, Texas, water distribution system (Sheet F-37). Of the 59 links in that area, 34% had no valves, 42% had one valve, 16% a valve at each end, 3% had two valves (but not at each end) and 3% had three valves. This section is typical of the author's experience with many other water systems. Therefore, assuming that it is possible to isolate individual pipe links is incorrect.

Simple intersection

Consider the intersection of pipes 1, 2, 3 and 4 in Fig. 1. If one of the pipes connected at that intersection should fail and must be shut down, the l ink-node representation would only be accurate in case A in which each link had an operable valve at each end. As demonstrated above, this is generally not the case.

In practice, most design engineers would not place four valves at a cross-type intersection as shown in Fig. 1. Two or three valves at such an intersection are about all that are usually included, as shown in case B where a failure in pipe 1 will take portions of links 2, 3 or 4 out of service. In case B, a failure in pipe 1 would also take the intersection of the four pipes out of service.

Another way of connecting pipes in an intersection is case C in which the pipes are in separate planes and are connected by a short 'dogleg' connection with a valve. In this case a shutdown of pipe 1 would automatically take out link 3, but would not take out links 2 and 4, and would leave links 2 and 4 connected.

Grid system

Now consider a more common situation of a gridded pipe network shown in Fig. 2(A). As shown in Fig. 2(B), a pipe failure at point X would remove four links and three nodes from the pipe network. An eight-valve shutoff for a single pipe repair is not a

M O D E L

2

/\ B C

Fig. 1. Alternative vaiving at node.

I - I I

A I -~- I

I I

I

I

I

I

B

I I I I I

It--><-~-I

+, +,

C

I - I I I

A B

I I I-~t

i i

I

I I

I 1

X

- - - - LINE IN SERVICE

. . . . . LINE OUT OF SERVICE

VALVE IN LINE

BREAK LOCATION

Fig. 2. Extent of outage due to piping break.

desirable situation, but does occur regularly, espe- cially in systems without regular valve maintenance. Figure 2(C) shows that if valves are installed and operable at points A and B, then the failure would only take one link and no nodes out of service.

Transmission versus distribution

The representation of the distribution system in the model is especially difficult in the case of a pipe network model that combines large transmission mains with smaller distribution mains. Just as interstate highways have no intersections or traffic lights, large transmission mains have few connections with the water distribution grid and few valves.

Figure 3 shows such a case where a 36 in (900 mm) water transmission main shares the north-south right-of-way with an 8 in (200 mm) distribution main. In good design, the two sets of pipes are somewhat isolated so that a failure of the 36 in has little direct effect on the distribution grid while a failure in the

Water distribution valve topology 23

8"

A J

+~

8" 36" i"

6"

12"

SYSTEM MODEL

Fig. 3. Example with distribution and transmission mains in same right-of-way.

distribution grid would have little impact on the 36 in pipe. For convenience, though, many modelers would represent each intersection as a single node as shown in the model representation on the right of the figure (or might even eliminate the 8in north-south pipe because its carrying capacity is negligible when compared with the 36 in).

Hydraulically, the model representation in Fig. 3 would work very well. Now suppose that a break occurred at point A as shown in the smaller illustration. The model would need to be broken as shown. A link and node would need to be removed. The implication is that the topology of the system changes with each pipe outage and the traditional way of representing this interaction is inaccurate.

The above examples illustrate that the key factor in analyzing the hydraulics of a distribution system during an outage is knowing the location of operable valves and reorganizing the system to reflect the extent of the shutdown due to the outage. Simply removing a pipe link from a model is misleading.

Importance of laterals

Another problem is that, in determining the reliability of an individual pipe link, most investigators assume that a pipe has a failure rate associated with a single diameter and is made of a uniform material. The 36 in pipe in Fig. 3 would have a very low break rate associated with it because of the low break rate generally associated with large mains.

However, many large transmission mains often have drain hydrants at low points so that the pipe can be drained for maintenance. A typical such installation is shown in Fig. 4. The reliability of the entire 36 in (91.4 cm) pipe is reduced by the fact that a failure in the 6in (15.2cm) hydrant lateral can take a large section of the 36 in line out of service. (Because of

S 36" PIPE

y 6" PIPE

S VALVE

' HYDRANT

Y Fig. 4. Example showing lateral as part of transmission

main.

their cost, valves are used very sparingly in large transmission mains; e.g. a 36 in gate valve costs in the order of $40 000). Reliability analysis needs to account for the chance of an outage in laterals and service lines that cannot be isolated from the large main.

ALTERNATIVE TOPOLOGY

The preceding section demonstrated that the location and condition of isolating valves significantly impact the extent of an outage due to a pipe failure or other maintenance event which may require taking a pipe out of service. Simply removing a link from a hydraulic model does not capture the effect of a pipe outage in most instances.

Distribution system segments

What is needed is a way of describing the portion of a water distribution system that can be isolated by closing valves. This author has used the word 'segment' to describe such a pipe or collection of pipes 5 and to highlight the difference between a segment and a network model link. Figure 5 shows the network for Fig. 2 broken into segments.

Segments provide a way for a water utility to assess quickly the susceptibility of a system to a single pipe break. Figure 5 shows that a break in segment 2 would require turning a large number of valves to achieve a shutout and would leave a fairly large number of customers without water.

If the segments could be shown in color on a map or a computer monitor, it would be very easy to identify segments that are likely to magnify a small pipe break into a major shutdown. A color graphics display of segments would be helpful to a utility in determining if the distribution system has adequate valving.

24 Thomas M. Walski

1 1 _: . . . . . . . . . . . . 2

_ L , t b l i I i i . . . . . . . . . . --4!. ..... L{_ ~4- t _ , t 43

!6 : , ~1 ,.5

Fig. 5. Distribution segments in example.

-(

Fig. 6. Graph of segments shown in Fig. 5.

In addition, the delineation of segments makes it possible to apply graph theory to pipe networks. Each segment can be represented as a node while each valve can be represented by an arc. The utility can bring to bear the power of graph theory to identify weaknesses in the system. Figure 6 shows such a representation of the pipe network in Fig. 5.

At first, representing a valve as an arc seems couterintuitive because valves are small and are located at a single point, and would seem best represented by nodes. However, a valve has two ends like an arc while a segment may have many valves associated with it like a node.

'Segments' as used in this paper differ from what Bouchart and Goulter 4 refer to as distribution segments. They defined a new segment as starting whenever the demand along the link or the diameter changed. Such a definition is contrary to this author's intent because it obscures the purpose of segments (i.e. to provide a way to identify which portions of a distribution system can be isolated). This author suggests use of the word 'subsegment' for what Bouchart and Goulter called segments.

Example of valving problem

Some systems may look to be highly reliable looped water distribution systems when they are viewed on system maps. However, because of the lack of valves, there may be very few segments, so that the reliability is very low.

Consider the distribution system shown in Fig. 7. A

2 / t'

Fig. 7. Example distribution system.

Fig. 8. Graph of segments from Fig. 7.

customer at point A may feel fairly secure in that he is located on a loop served by another loop. However , suppose there is a break at point X. The customer would be without water because of the lack of valves. The graph of that system in Fig. 8 shows that segments 2 and 7 need additional valving to make the system reliable. This situation could not be readily identified from a map of the distribution system.

A P P L I C A T I O N

Manual versus automated analysis

At present, manually identifying segments in a real water distribution system for all but the simplest systems is tedious. However, it can be very helpful in identifying potentially troublesome situations. Linking software to automate this process with standard graphics packages shows promise as a reproducible method to assess the adequacy of valves in the future.

Graphing segments of a distribution system can help identify which segments are critical because they are the only path to some portion of the system. In addition, the number of arcs attached to a segment indicates the number of valves that must be operated to isolate the segment. This number should not be too great because a shutdown will be time consuming and

Water distribution valve topology 25

the probability that one of the valves not working is high.

Until software is developed to automate valve graphs, design engineers will be required to draw segments manually and use old rules of thumb such as 'no more than four valves should be needed to isolate any pipe break' and 'no single pipe outage should be capable of wiping out all feeds to a given area'.

Identifying critical segments

Once the graph has been constructed, it is not too difficult to examine manually the graph for critical nodes. In addition, algorithms from graph theory can be applied to find critical segments quickly.

One, approach to determine if a node is critical is to conduct a 'breath-first' search 6 of each tree emanating from a segment (node). If one of the trees located during these searches is disjoint (i.e. has no nodes in common with other trees from this node), then that node is a critical node. This can easily be extended to pairs of nodes that are connected by combining them into one node to simulate the case where a valve is unavailable (i.e. exists but is not operable).

Design implications There is no rigid rule that says a distribution segment should be able to be isolated with the turning of four valves or less. Instead, it is simply a case that the probability of being unable to isolate a segment increases with the number of valves in that segment. The tradeoffs between the cost of valves and the increase in reliability they provide should prove to be a good research topic.

The fewer valves that need to be turned, the more likely a segment will be isolated successfully. If a valve cannot be operated, the size of the area that must be shutdown grows and the probability that another inoperable valve will be encountered means that a shutdown for a single maintenance event can involve many customers.

For example, if the probability that a valve cannot be found or used is 0-1, the probability of not being able to operate both valves for a two-valve shutdown is 0.19. The probability of not being able to operate four valves for a shutdown is 0-34 and the probability of not being able to operate eight valves is 0.57.

Component reliability

Unfortunately, not many data exist on the availability of distribution system valves. This author has worked with numerous systems and would estimate that this value can range from 0.02 (2% unavailable) to 0.33 (one-third of valves unavailable). These availabilities are inversely related to the extent of valve maintenance and exercising practiced by the utility

and the age of the system. Work is needed to quantify these relationships.

Cullinane 7 summarized data from the Environmen- tal Protection Agency on valve availability and found gate valves in wastewater treatment plants to have reliability in excess of 0.999. These data are not consistent with the author's experience of water distribution valves. This is due to (1) the treatment plant valves being used routinely, and (2) the relative newness of treatment plant valves in comparison with many distribution systems. Wastewater treatment plant valves tend to be less than 20 years old, while distribution system valves are often older than 50 years old.

Data presented by Cullinane 7 showed a mean time between failures for gate valves of the order of 1 year and a mean time to repair of the order of 4 h. While these numbers are not unreasonable for above ground valves, they do not include the time to locate and identify inoperable valves which can be many hours in most water distribution systems. There are no data on the inability to locate valves.

LARGE SCALE EXAMPLE

To determine if the concepts presented above are applicable to real water distribution systems, a graph of valves and segments was prepared for a roughly one square mile (2-59 km 2) portion of Austin, Texas, water distribution system, as shown in Fig. 9. (The actual distribution system map (Sheet F-37) is too complicated to show in this paper.)

This portion of the system is made up primarily of 6 and 8 in (150 and 200 mm) pipes, which are fed from a few loops of 12 in (300 mm) pipe. (The 12 in valves are the arcs with the heavy line thickness.) Flow reaches this area from the bottom and right side of the figure. The example illustrates several good features of this approach to assessing the adequacy of valves.

The first point is that segments 1, 100 and 101 are the only way to serve the nodes in the 100s. This is because the segments in the 100s are part of a municipal utility district that purchases its water from Austin through a master meter located in segment 100. From the map of the system, this feature is not obvious, but from the graph in Fig. 9, it can readily be identified. In this case, having all of the flow pass through a single segment is intentional. Usually, having all the flow to an area pass through a single segment is highly undesirable, but often missed.

The next interesting segments are segments 33 and 34. Segment 33 is a fairly important pipe while segment 34 is a small circle off the main street. The map of the actual piping in that area is shown in Fig. 10(A). Having two feeds to segment 34 is not helpful if segment 33 should be taken out of service. A better

26 Thomas M. Walski

< 12 IN. VALVES

12 IN, VALVES

Fig. 9. Full-scale application.

arrangement is shown in Fig. 10(B) where a valve is installed, breaking segment 33 into two segments so that 34 could be fed even if there is a shutdown for one portion of 33. In general, having two segments

~ 33

(a)

34•_ 33B

33A

(b)

Fig. 10. Map of the actual piping.

connected by more than one valve is a poor use of valves.

Figure 9 shows a number of segments with only a single source. In general, this is not good design, but in this case it is acceptable in that these represent small cul-de-sac type streets. For example, segments 47 and 48 have a total of 12 homes served by the segments. Cul-de-sacs and dead ends are a result of modern development patterns which shy away from grid layouts. While this may be esthetically pleasing, it reduces the reliability of the water supply to customers living on these dead ends.

The most interesting feature of Fig. 9 is segment 1, which shows that there are nine valves connected to this segment. Actually it would require operation of eight of the valves to be shut to isolate this segment because there are no sources in the area beyond segment 100.

However, eight valves is too many to have to operate to shut off such an important segment. Segment 1 is also a half mile (0-8 km) long which means there is a high probability of a pipe break. To make matters worse, a few of the fire hydrants along segment 100 do not have isolating valves, so that a car

Water distribution valve topology 27

striking a hydrant can cut off water for about one-third of the customers in Fig. 9.

One or two additional valves in semgnet 1 would greatly improve the utility's ability to shut down an area for repair without depriving water to all the customers in segments 100 and greater. The only other segments requiring a five-valve shutoff are 32, 107 and 112 and none of those segments are quite as critical at 1.

SUMMARY

The link-node representation is not a completely acceptable way of analyzing water distribution systems for reliability because it does not account for the importance of valves in the distribution system and their effect on isolating or exaggerating the impact of a pipe break or maintenance event. Valves are the key to providing system reliability.

Identifying 'segments', which are a portion of the water distribution system that can be isolated by valves, provides a way to identify if adequate valving is present in a water distribution system. An approach to evaluate graphically the adequacy of valving is proposed and demonstrated.

ACKNOWLEDGEMENT

The author wishes to acknowledge the help of Dr Jie Wang of the Wilkes University Department of Computer Science.

REFERENCES

1. Goulter, I. C. & Coals, A. V., Quantitative approaches to reliability assessment in pipe networks. J. Transport. Engng., 1121 (3) (1986) 287.

2. Ormsbee, L. E. & Kessler, A., Optimal upgrading of hydraulic network reliability. J. Water Resources Planning and Manage., 116 (6) (1992) 784.

3. Tung, Y. K., Mays, L. W. & Cullinane, M. J., Reliability analysis of systems. In Reliability Analysis of Water Distribution Systems, ed. L. W. Mays. ASCE, New York, 1989, pp. 260-98.

4. Bouchart, F. & Goulter, I. C., Improvements in design of water distribution networks recognizing valve location. Water Resources Res., 27 (12) (1991) 3029.

5. Walski, T. M., Discussion of 'Quantitative Approaches to Reliability Assessment in Pipe Networks. J. Transport. Engng, 113 (5) (1987) 585.

6. Horowitz, E. & Sahni, S., Fundamentals of Computer Algorithms, Computer Science Press, 1978.

7. Cullinane, M. J., Reliability and maintainability data for water distribution system components. In Reliability Analysis of Water Distribution Systems, ed. L. W. Mays. ASCE, New York, 1989, pp 190-225.