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Colorado Springs Utilities Case Study: Water System Calibration/Optimization

Istvan Lippai, Ph.D., P.E.1

Abstract

Colorado Springs Utilities (Utility) provides water service to a rapidly growing

population of 400,000. The Utility also owns and operates the Green Mountain Falls

(GMF) water system located several miles outside of city limits. The GMF water

system, serving 937 customers, is a separate water system consisting of small

diameter cast iron and ductile iron water pipes. A significant portion of pipes are of

unknown material. Fire flow was not considered when most of the system was

constructed; therefore the initial model results show hydrant discharge capacities as

low as 140 GPM (8.8 l/s). The first step to upgrade the existing system is the

development of an accurate water model. User demand is predicted from billing

records. Pipe roughness is estimated using a genetic algorithm-based optimization

procedure. This paper discusses the modifications to the optimizer to facilitate the

inverse model solution, the parameter estimation problem, and presents the results of

the modeling and calibration of the GMF water system.

Introduction

In the 1920’s, the town of GMF got into water rights dispute with a private water

company, called the Ute Pass Land Company (UPLC). UPLC had water rights and a

water delivery system on Catamount Creek upstream of GMF that served GMF,

Chipita Park, and other lands owned by UPLC. In the 1927 settlement of this dispute,

GMF agreed to drop its opposition to UPLC’s water rights case, and in exchange,

UPLC agreed to guarantee water service to GMF. In 1942, the Utility purchased

UPLC’s water rights and water system on the North Slope of Pikes Peak. The Utility

bought the water system to augment and firm up its North Slope water system and

water rights. In doing so, the Utility was obliged, as UPLC’s successor in interest, to

fulfill the 1927 agreement.

The GMF water system service area is characterized by steep terrain associated with

large pressure changes over short distances. The Ute Pass Reservoir Zone (UPRZ)

1 Water Resources Consultant, Castle Rock, Colorado, bpgclm@yahoo.com

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service level is between 7,450 ft and 7,880 ft (2,270 m and 2,400 m). The Ute Pass

Pump Zone (UPPZ) service level is between 7,800 ft and 8,050 ft (2,380 m and 2,450

m). See Figure 1.

Figure 1 – View of Green Mountain Falls Service Area

Model Development

The system, depicted in Figure 2, consists of 2 reservoirs, 388 junctions, 415 pipes, 2

pumps and 4 PRV’s.

UTE PASS PLANT RESERVOIR ZONE

RESERVOIR CAPACITY=0.6 MG

RESERVOIR OVERFLOW=7998'

RESERVOIR CAPACITY=0.25 MG

RESERVOIR OVERFLOW=8115'

UTE PASS PUMP ZONE

WTP CAPACITY = 2 MGD

HW

Y-24

UTE PASS WTP & RESERVOIR

HW

Y-2

4 T

O C

OLORADO S

PRIN

GS

28-GM

33-GM

38-GM

47-GM

52-GM

59-GM

66-GM

74-GM

75-GM

114-GM

115-GM

Figure 2 - Green Mountain Falls Water Model

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A 2-MGD (88 l/s) capacity water treatment plant (WTP) serves the GMF water

system. The WTP feeds the 0.6 MG (2,270 m3) capacity UPRZ reservoir. Two 300

GPM (19 l/s) pumps supply the 0.25 MG (950 m3) capacity UPPZ reservoir. Four-

pressure control valves (PRV’s) allow emergency and fire flow back-feed from UPPZ

to UPRZ.

The Utility uses H2ONet, which has the advantage of importing and exporting

EPANet data files. This feature was used to replace pipe sizes and pipe roughness

coefficients in the GMF water system model. The Utility maintains a detailed GIS

database of utilities and topographic information. A separate database contains the

name, address, user type, longitude and latitude, and the monthly water use of each

customer. An H2ONet model was developed using available GIS data. The

estimated maximum daily demand of 693 GPM (43.7 l/s) was allocated using

dynamic demand allocation (DDA) program (Lippai and Barbato 2003). The DDA

program reads a text file of customer billing records and assigns each customer’s use

to the nearest node as demand based on spatial location. The elevation of each

hydrant discharge nozzle selected for flow tests was measure by a ground survey.

The elevations of the remaining hydrant discharge nozzles were obtained from GIS

data. Most of the water lines are old, small diameter cast iron pipes that were installed

prior to acquisition of the system by the Utility. The combined lengths of 4-inch and

6-inch (100 mm and 150 mm) pipes comprise 63% of total system piping as seen in

Table 1.

Table 1 – Pipe Summary

Diameter Length Volume

inches mm ft m % gallons liters %

1 25 842 257 0.78 34 129 0.02

2 50 1,207 368 1.12 197 746 0.09

3 75 100 30 0.09 36 136 0.02

4 100 30,016 9,149 27.89 19,594 74,171 8.67

6 150 37,754 11,507 35.09 55,453 209,912 24.54

8 200 21,664 6,603 20.13 56,569 214,137 25.03

12 300 16,021 4,883 14.89 94,130 356,321 41.65

Total 107,604 32,798 100.00 226,013 855,552 100.00

Hydrants

The system has 111 hydrants. Most of these hydrants are old, dual 2-1/2 inch nozzle

hydrants. See Figure 3.

H2ONet’s “Fireflow” command is used to model fire flows from individual hydrants.

The headloss for a typical hydrant with 4-1/4 inch Main Valve is computed based on

a 2-1/2 inch Nozzle. See Figure 4.

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Figure 3 - Green Mountain Falls Hydrant

4" HYDRANT LATERAL

HYDRANT

2-1/2" NOZZLE

4" GATE VALVE

4" MAIN

0.24" Gate Valve

TotalHydrant Nozzle

3.52.5

Line to Branch TeeItem Description

0.8K

Minor Loss Coefficients

Figure 4 - Green Mountain Falls Hydrant Detail

The hydrant nozzle headloss coefficients were computed from discharge-headloss

curves supplied by hydrant manufacturers. The total hydrant headloss is computed as

the sum of minor headloss and hydrant lateral friction headloss to simulate fire flows.

Requests for flow tests were conducted with some hesitation because of the potential

for erosion over the steep terrain. Eleven (11) hydrants were tested and the results of

these tests are given in Table 2.

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Table 2 – Hydrant Flow Tests

Test Hydrant Node Pressure Discharge Date

Number Designation ID psi m GPM l/s Tested

1 28 - GM 10205 160 113 1250 79 08/03/04

2 33 - GM 10151 180 127 1160 73 09/21/04

3 38 - GM 10185 100 70 1340 85 08/03/04

4 47 - GM 10169 90 63 629 40 09/21/04

5 52 - GM 10141 155 109 480 30 08/03/04

6 59 - GM 10175 75 53 581 37 09/21/04

7 66 - GM 20061 65 46 240 15 09/21/04

8 74 - GM 20003 68 48 170 11 08/03/04

9 75 - GM 10190 65 46 823 52 09/21/04

10 114 - GM 10147 55 39 240 15 08/03/04

11 115 - GM 20010 30 21 710 45 09/21/04

Hydrants for flow tests were selected after careful consideration of the potential for

erosion based on location and elevation. Each hydrant was opened until the water ran

clear. Test Number 8 was discarded because a partially closed valve on the line

feeding the hydrant could not be located. Comparing modeled fire flows with results

shows that a number of tests are questionable. It is indicated by large errors. See

Tables 3 and 4.

Table 3 – Comparison of Model and Test Hydrant Pressure Results

Test Node Model Pressure Test Pressure Error

Number ID psi m psi m %

1 10205 156 110 160 113 2.5

2 10151 179 126 180 127 0.6

3 10185 97 68 100 70 3.0

4 10169 92 65 90 63 -2.2

5 10141 152 107 155 109 1.9

6 10175 76 53 75 53 -1.3

7 20061 69 49 65 46 -6.2

8 20003 71 50 68 48 -4.4

9 10190 64 45 65 46 1.5

10 10147 54 38 55 39 1.8

11 20010 31 22 30 21 -3.3

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Table 4 – Comparison of Model and Test Hydrant Discharge Results

Test Node Model Discharge Test Discharge Error

Number ID GPM l/s GPM l/s %

1 10205 1191 75 1250 79 4.7

2 10151 1107 70 1160 73 4.6

3 10185 1468 93 1340 85 -9.6

4 10169 613 39 629 40 2.5

5 10141 329 21 480 30 31.5

6 10175 892 56 581 37 -53.5

7 20061 293 18 240 15 -22.1

8 20003 303 19 170 11 -78.2

9 10190 749 47 823 52 9.0

10 10147 190 12 240 15 20.8

11 20010 1104 70 710 45 -55.5

Multi-objective Optimization with WinPipes

WinPipes (Lippai 1999) was developed for multi-objective planning and design

optimization of water distribution systems. WinPipes links a network solver with a

commercial optimizer. It uses the extended simulation (EPS) feature of EPANet

(Rossman 1994) to assign and specify optimization objectives in sequence. The

model can be tested against any number of objectives. Evaluation of pressure,

reliability, fire flow, simultaneous fire flow, pump operation, valve setting, tank

elevation, pumping life cycle costs, and component criticality have been implemented

and applied to the design of several Utility water systems. WinPipes was recently

modified for calibration of GMF water system model. The modified optimization

program compares actual and modeled pressures for selected hydrants. After

evaluating the system for the specified objectives, WinPipes returns the total penalty

for violating the objectives. The magnitude of the penalty increases with the

magnitude of the violation. The state of the system can be compared against the

normal pressure and seven hydrant flows by running the EPANet data file modified

for extended period simulation for each objective. See Figure 5.

The normal pressure at Node 10185 is 97.16 psi (68.36 m) and the residual pressure

with 1,340 GPM (84.5 l/s) discharging is 12.50 psi (8.79 m). Comparing the model

pressures to the tested pressures and converting to head in feet is the penalty assessed

for the hydrant at Node 10185.

Normal pressure penalty = abs(100.00-97.16)*2.308 =6.55

Hydrant flow pressure penalty = abs(12.50)*2.308 = 28.75

Total Penalty = 35.30

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Pressure for Node 10185

Tim e (hours)

11109876543210

Pre

ssu

re (

psi)

95.0

90.0

85.0

80.0

75.0

70.0

65.0

60.0

55.0

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

Figure 5 – Pre-calibration Pressure at Node 10185

The total system penalty is the sum of penalties assessed for all the hydrants. The

penalty is an indication error of initial pipe roughness estimates and the accuracy of

flow tests.

Calibration by Optimization

The goal is to adjust the pipe roughness coefficients, so that the resultant model

pressures under normal demand and during fire flows are close to actual pressures.

WinPipes penalty functions were modified for calibration. Penalty is computed as the

absolute value of the difference between actual and model pressures under normal

and fire flow conditions.

Calibration, estimation of pipe roughness coefficients from observed system pressures

and hydrant discharges, is an inverse problem (Willis and Yeh 1987). Unlike

optimization for project cost, optimization for parameter estimating is ill-posed and

even small errors of observed pressures and hydrant discharges can lead to large

errors in estimated pipe roughness coefficients. Consider an example of 6 inch-1000

ft (150 mm-305 m) and 4 inch-1000 ft (100 mm-305 m) old cast iron pipes in series.

The Hazen-Williams roughness coefficients of 6 inch and 4 inch pipes were

determined to be 93 and 87, respectively. At 200 GPM (12.6 l/s) the total headloss is

27.8 psi (19.6 m). Any number of roughness coefficient combinations can produce

the same total headloss along the curve in Figure 6. Selection of correct pair of

roughness coefficients is difficult. Isolating and testing for the roughness coefficient

of one pipe can be used to determine the roughness coefficient of the second pipe.

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Hazen-Williams Roughness Coefficient

80

90

100

110

120

130

140

150

30 40 50 60 70 80 90 100 110 120 130 140 150

6" Pipe Roughness

4"

Pip

e R

ou

gh

nes

ss

Figure 6 – Combination of Pipe Roughness at Constant Headloss

The instability of inverse problems can be further demonstrated by a simple case of

calibration by optimization. See Figure 7.

1000 GPM (63 l/s)

12"

8"

8"

8"

8"

8"

8"

8"

8"

8" 8"

27.09 psi (19.05 m)

Node 31

Node 23

11 12

21 22

31

110

111

112

113

121

122

42.14 psi (29.63 m)1000 GPM (63 l/s)

8" (203 mm)12" (305 mm)

Figure 7 – Simple Network

All pipe roughness coefficients of the simple network are 100. For calibration, all

initial pipe roughness coefficients were set to 90 and the optimizer was given a range

of pipe roughness coefficients between 70 and 130. The pressures at demand nodes

23 and 31 were matched with Hazen-Williams pipe roughness coefficients ranging

from 74 to 120. See Table 5.

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Table 5 – Calibration Results of Simple Network

Pipe Roughness Coefficient

Number Original Assumed Calibrated

11 100 90 74

12 100 90 90

21 100 90 110

22 100 90 90

31 100 90 96

110 100 90 118

111 100 90 120

112 100 90 113

113 100 90 90

121 100 90 90

122 100 90 90

The simple system calibration used exact “good” pressures based on the original pipe

roughness coefficients of 100, but the calibration optimization process managed to

reproduce the target pressures while returning a range of roughness coefficients that

are obviously incorrect. T he correct solution would have returned roughness

coefficients of 100 for every pipe. The problems encountered with the simple

example problem are magnified for the GMF water system because unconstrained

optimization allows pipe roughness coefficients to change in order to minimize the

difference between test and model pressures. An obvious constraint for the simple

network would have been to make the roughness coefficient of every pipe equal.

The solution space is an important factor to consider for calibration by optimization.

The solution space for optimization of above 11-pipe network for three discrete pipe

diameters is (311

) 1.77147x105. The solution space for calibration by optimization of

above 11 pipe network for 60 discrete pipe roughness coefficients is (6011

)

3.62797056x1019

, 2.048x1014

times increase in the number of computations required.

Similarly, the solution space for the 415 pipe GMF water system, still a small system,

would be (60415

) unmanageable. Grouping the pipes by material and diameter and

assigning the same roughness coefficient to each pipe within its material and diameter

group reduces the solution space to (607) 2.79936x10

12. Initial estimates of pipe

roughness coefficients were assigned to selected groups of pipe materials and

diameters. See Table 6.

Table 6 – Initial Roughness Coefficients by Diameter and Material

Diameter Initial Pipe Roughness

inches mm DIP CIP & UNK

4 100 99 74

6 150 104 81

8 200 107 85

12 300 110 N/A

Optimizing with the reduced solution space resulted in rapid convergence but the

results showed inconsistencies similar to the small network. See Table 7.

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Table 7 – Calibrated Roughness Coefficients by Unconstrained Optimization

Diameter Unconstrained Optimization

inches mm DIP CIP & UNK

4 100 77 54

6 150 109 30

8 200 114 111

12 300 157 N/A

Adding the constraint that the Hazen-Willams roughness coefficients of the pipes of

same material can only increase with increasing diameters increases the stability of

the solution convergence. Applying this constraint to 6 inch (150 mm) diameter CIP

& UNK pipes, the roughness would be increased from 30 to 54. Re-optimizing with

diameter based constraints produces a list of “reasonable” roughness coefficients.

See Table 8.

Table 8 – Calibrated Roughness Coefficients by Constrained Optimization

Diameter Costrained Optimization

inches mm DIP CIP & UNK

4 100 116 75

6 150 116 75

8 200 116 75

12 300 123 N/A

Understanding the hydraulic properties of pipes of different materials and diameters

was useful for guiding the heuristic search. These roughness coefficients include

minor losses at hydrants. The model is updated by replacing the initial pipe

roughness coefficients with the pipe roughness coefficients produced by constrained

optimization.

Conclusions and Recommendations

Calibration of pipe roughness coefficients by optimization should be used with

caution. The modeler needs to rely on experience and judgment and apply variable

constraints to eliminate numerically correct but physically meaningless solutions.

Where possible, determine the roughness coefficients of several representative pipes

by flow tests and use these roughness coefficients to guide the calibration by

optimization process.

Based on the updated pipe roughness coefficients, the fire flows were updated and the

optimal improvements needed to provide a minimum fire flow of 1,000 GPM (63

l/s)were identified using WinPipes. The improvements required are 8 inch-3,500 ft

(200 mm-1070 m) of new pipe, replacement of 4 inch-9,900 ft (100 mm-3020 m) and

6 inch-2,100 ft (150 mm-640 m) pipe with 8 inch (200 mm) pipe. See Figure 6 for

highlighted 8 inch (200 mm) new and replacement pipes proposed for meeting fire

flow requirements. Optimization was used to determine construction phasing of new

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pipes and replacement pipes to increase minimum fire flows to 500 GPM, 750 GPM

and 1,000 GPM (36 l/s, 47 l/s and 63 l/s).

NEW 8"

NEW 8"

NEW 8"

NEW 8"

NEW 8"

Figure 8 – Proposed New and Replacement 8 inch Pipes

Acknowledgement

Terry Foos, Engineering Support Coordinator, Colorado Springs Utilities, assisted in

the selection of suitable hydrants for flow tests. Len Wright, Ph.D., P.E., Water

Resources Engineer, Carollo Engineers, edited the paper.

References

H2ONet (2004). Graphical Water Distribution Modeling and Management Package,

MW Soft, Inc., Pasadena, CA.

Lippai, I. (1999). Robust Urban Water Distribution System Design. Doctor of

Philosophy Dissertation, University of Colorado, Boulder, CO.

Lippai I. and Barbato L. (2003). Dynamic Demand Allocation, 2003 AWWA DDS:

The Distribution & Plant Operations Conference, Proceedings, September 28-October

1, 2003, Portland, Oregon

Rossman, L. A. (1994). EPANET Users Manual. Drinking Water Research Division,

Risk Reduction Eng. Laboratory, U. S. Environmental Protection Agency, Cincinnati,

OH.

Willis, R. and Yeh, W. W-G. (1987). Groundwater Systems Planning and

Management, Prantice-Hall, Inc., Englewood Cliffs, New Jersey 07632, ISBN 0-13-

365651-9 025.