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EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
On-line Condition Assessment and Control of Water Distribution
and Gas Pipeline Networks
B. S. Murty Department of Civil Engineering
I.I.T. MADRAS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
ACKNOWLEDGEMENT
Dr. H. Prashanth Reddy (Civil)Dr. S. Mohan Kumar (Chem.)Prof. Shankar Narasimhan (Chem.)
I.I.T. MADRAS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
INTRODUCTION
Water distribution networks - pipes, tanks, reservoirs, pumps, and valves.
Water scarcity – need for increasing the efficiency and
reliability of supply in these networks.
– Leads to the studies on
• Monitoring
• Management and control
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
INTRODUCTIONINTRODUCTION
Natural gas to be transported from producing regions to consumption regions.
The biggest problem with the safe operation of the oil and natural gas pipelines is development of rupture leaks.
Delay in detecting leaks leads to loss of property and human life in fire hazards.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
INTRODUCTIONINTRODUCTION
LDS can be classified as Software based automatic leak detection systems and field investigative leak detection systems.
SCADA based LDS is inexpensive and continuously monitors gas pipelines.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Hardware based techniques: Can detect small leaks,but expensive
Software based techniques: Cannot detect small leaks,but inexpensive
Inverse Transient methods: Computationally intensive,not suitable for on-line app.
Frequency analysis methods: Require suspension of normal operationsNot tested for complex networks
Most of the methods: Developed for WDN and not for gas pipelines
Problems with existing Methods
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
1
Node without demand
Delivery node
Sourcenode
2 3
4 5
6 7 8
[1] [2]
[3]
[4]
[5]
[6]
[7]
[8] [9]
Fig. 1: schematic of network
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
SIMULATION
Given
Pipe Characteristics
Source Pressure {function of time)
Demands {function of time}
Gas Composition {function of time}
Determine
Pressures & Flow rates
at all the points in the system
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
HOW DO WE DO THIS?
0)/( 2 =∂∂
+∂∂
tpcA
xM
01)2/(/)sin( 222 =∂∂
+++∂∂
tM
ApDAMMccpg
xp λθ
Continuity & Momentum Eqs.
For a Pipe Inclined at an Angle
Continuity Equation at a junction
Pressure Equality at a Junction
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Solve the PDEs
Appropriate Numerical Method (FD / FV)
For Specified Boundary Conditions
(Specify Temporal
Pressure Variation at Source
& Demand Variation)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
WHAT IS THE PROBLEM ?
FD Methods:
Time consuming !
Not Suitable for On-Line Applications(Leak Detection)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
LEAK DETECTION
Assume a leak location & corresponding leak magnitude
Run the FD model for the above using pressure at source node and demand variation (Leak is treated as demand!)
Obtain Simulated pressures and flows at all the desired points where measurements are available
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
LEAK DETECTION (Contd.)
Determine the RMS error between measured & simulated pressures & flows
Solve the Optimization problem for leak magnitude & location such that the RMS error is minimized
This involves thousands of calls to the simulation code
Too much CPU time !!! (2 hours for a 1000 s run of one simulation, DT = 1 s)
Measurement noise is not factored into the methodology
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
STATE ESTIMATION
All we need for simulation: Pressure variation at source nodes and Demand variation at demand nodes
But we may have more measurements than this
All the above come with measurement noise
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
STATE ESTIMATION (Contd.)
Which measurements shall I consider in simulations ?
How do I know that the considered measurements are noise free?
State estimation reconciles all the measured data and gives out the expected (mean) state of the system which satisfies the governing equations
Absolutely important in leak detection via hypothesis testing
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
WHAT IS A TRANSFER FUNCTION MODEL?
Transfer functions relate M1 & P2 at any instant to M2 & P1 at that instant & Past values of M2 and P1
Using an approximation of Governing Equations
There is no need to discretize the pipeline as in FD methods
1 2
PipelineM1 & P1 M2 & P2
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Linearize governing equations
Analytical solution in Laplace domain
Get transfer functions in Laplace domain
Take inverse Laplace in time domain
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Down stream pressure equation in time domain
( )*
2 1 11
( )*
2 21
( )*2 2
21
( * ) * *(1 )* ( * )
* *(1 )* ( * )
* *(1 ) ( * )*
s s
s s
s s
T TN N iT T
s si
T TN N iT T
si
T TN N iT T
si
p N T k e e p i T
k e e M i T
k T e M i T eT
− − −
=
− − −
=
− − −
=
⎡ ⎤∆ = − ∆ +⎢ ⎥
⎣ ⎦⎡ ⎤− − ∆ −⎢ ⎥⎣ ⎦
⎡−− ∆
⎣
∑
∑
∑ 2 22* ( * )s
k T M N TT
⎡ ⎤⎤+ ∆⎢ ⎥⎢ ⎥
⎢ ⎥⎦⎣ ⎦
(11)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Upstream flow equation in time domain
( )*
1 21
( )*1
11
11
( * ) * (1 ) * ( * )
T - * (1 ) * ( * ) *T
T + * ( * )T
s s
s s
T TN N iT T
s si
T TN N iT T
si
s
M N T e e M i T
e p i T e
p N T
− − −
=
− − −
=
⎡ ⎤∆ = − ∆ +⎢ ⎥
⎣ ⎦⎡ ⎤⎡ ⎤
− ∆⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦
∆
∑
∑
(12)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
TskF PP +
=1
111,2 Ts
sTF PM +
=1
11,1 Ts
F MM +=
11
2,1 TssT
kF MP ++
−=1
)1( 222,2
Ψ=ek1
⎟⎠⎞
⎜⎝⎛ Ψ+= Ψ 22/
2 2411u
DALek λ
⎟⎠⎞
⎜⎝⎛ Ψ+Ψ−= Ψ 2
2
22/
241
611
2 cD
uLeT λ
⎟⎠⎞
⎜⎝⎛ Ψ+= Ψ 2
22/
1 2411
c
ALeT
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Ψ+
+=
241
161
22
2
2cD
uL
uDT
λ
λ
22
sin2 c
gL
c
uu
DL θλ
−=Ψ
By expanding Transfer functions
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Complete discrete model in the time domain for the entire network:
Combine above Eqs.(11) and (12) for all the pipe elements with
Continuity equation and pressure equilibrium equations at thejunctions
Continuity equation and pressure drop equation at valves
Continuity equation and equations describing compressor operation.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Formulation of the State Estimation Problem
Resulting system of equations for the entire network: Linear
Ax + Bu = 0 (13)
vector x: All measured variables (corresponding to time instants (N-n)T to NT,
vector u: All unmeasured variables (corresponding to time instants (N-n)T to NT).
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
The matrices A and B depend on the pipe parameters, sampling period, compressibility factor and friction factor.
Matrices A and B are time dependent
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
The best estimates of variables x and u, for a given set of measurements y for the variables x, can be obtained by solving the following weighted least squares estimation problem
Minimize
Subject to Ax + Bu = 0
Matrix Q is the covariance matrix of errors in measurement
Standard reconciliation problem
Crowe’s Projection Matrix technique
)()( 1 xyQxy T −− −
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Obtain the state estimate for the current time instant NT in a recursivemanner by utilizing the estimates obtained for all the previous times
The constraint Eq. (13) is re-cast as given below.
where
Measured and unmeasured variables corresponding to the current time instant NT
and
are the corresponding sub-matrices of A and B.
Ax Bu c+ =, x u
,A B
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Vector c : Weighted sum of the estimated flows and pressures at the previous time
Just enough variables are specified
Solution: objective function value = 0simulation problem
More measurements (specifications) than the minimum required to solve the problem are given:
Formulation gives a best fit solution
Takes into account the inaccuracies
state estimation
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION
• Second order MacCormack explicit FD method is used to validate the proposed TF model.
• Network (fig. 1) consists of 8 nodes and 9 pipe elements
• Slow transient caused by variation of demand at one of the demand node is simulated with Bench mark model (FD model) and proposed model
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
1
Node without demand
Delivery node
Sourcenode
2 3
4 5
6 7 8
[1] [2]
[3]
[4]
[5]
[6]
[7]
[8] [9]
Fig. 1: schematic of network
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Demand Variation with with time at node 8
0.60.70.80.9
11.11.21.31.4
0 1000 2000 3000 4000 5000 6000
Time (sec)
Dem
and
(MM
SCM
D)
Fig. 2 Specified Demand variation at node 8
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
58.8
58.9
59
59.1
59.2
59.3
59.4
0 1000 2000 3000 4000 5000 6000
Time (sec)
Pres
sure
(kg/
cm2 )
Bench mark model Proposed model (dt = 1 sec) Proposed model (dt = 15 sec)
Comparison of pressure at node 8
RESULTS AND DISCUSSION RESULTS AND DISCUSSION –– DYNAMIC DYNAMIC SIMULATIONSIMULATION
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Fig. 12: True and estimated mass flow rates at node 1: Case-2
1.175
1.275
1.375
1.475
1.575
1.675
1.775
0 1000 2000 3000 4000 5000 6000
Time (sec)
Mas
s flo
w ra
te (M
MSC
MD
)
Estimated mass flowrate without redundancy Estimated mass flowrate with redundancyTrue mass flow rate
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Fig. 14: True and estimated demands at node 5: Case – 2
0.485
0.49
0.495
0.5
0.505
0.51
0.515
0 1000 2000 3000 4000 5000 6000
Time (sec)
Dem
and
(MM
SCM
D)
Estimated demand without redundancy (dark blue)Estimated demand with redundancy (pink)True demand (yellow)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
0.014620.02116P8
0.016820.02365P7
0.017520.02444P6
0.0010.00313D5
0.017030.02393P5
0.0001230.001087F4
0.017090.02394P4
0.018370.02521P3
0.0001880.004563F2
0.018680.02480P2
0.0001060.05489F1
0.004920.01000P1
Redundant Measurements with noiseJust specified with noiseVariable
Table 5: Reduction in RMS error with increased redundancy
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
0.30.350.4
0.450.5
0.550.6
0.650.7
0.75
0 1000 2000 3000 4000 5000 6000
Time (sec)
Dem
and
(MM
SCM
D)
Fig. 17 Estimation of unknown demand at Node 5
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
CONCLUSIONS CONCLUSIONS –– STATE ESTIMATIONSTATE ESTIMATION
Test problems on the example network indicated that the proposed method is 25 times faster than the explicit finite-difference approach.
It was also demonstrated that the proposed approach can be used to estimate unknown demands.
The above features, coupled with the computational efficiency, make the approach ideally suited for on-line leak detection and identification.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
LEAK DETECTION METHODOLOGYLEAK DETECTION METHODOLOGY
In order to detect a leak online, we will call state In order to detect a leak online, we will call state estimator at each sampling time instant.estimator at each sampling time instant.
ObjFunction > Threshold => possible leakObjFunction > Threshold => possible leak
We will hypothesize a leak in every branch of the We will hypothesize a leak in every branch of the pipeline network and determine best fit Dpipeline network and determine best fit DLL, X, XLL based on based on measurements [t, t+WT] in each branch. measurements [t, t+WT] in each branch.
The hypothesis that best fits the data among all the The hypothesis that best fits the data among all the hypotheses then determines the branch, location and hypotheses then determines the branch, location and magnitude of the leak magnitude of the leak
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
LEAK DETECTION METHODOLOGYLEAK DETECTION METHODOLOGY
PP11,M,M11
11
PP22,M,M22
22
Branch iBranch i
xxii LL--xxii
bbll = unknown leak magnitude= unknown leak magnitude
xxiiLL--xxii
PP11,M,M11PP22,M,M22
Branch iBranch i11 Branch iBranch i22PPLL,M,MLL
Unknown demand DUnknown demand DLL
Leak pipe modelLeak pipe model
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Leak detection hypothesis Leak detection hypothesis –– optimization problemoptimization problem
1
m ,uM in ( ) ( )
Ty m Q y m
Sub jected toA m B u c
−− −
+ =
The DThe DLL is unknown and it is part of u vector is unknown and it is part of u vector
LEAK DETECTION METHODOLOGYLEAK DETECTION METHODOLOGY
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
hypothetical series pipelinehypothetical series pipeline
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING SIMULATIONSDETECTION USING SIMULATIONS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING SIMULATIONSDETECTION USING SIMULATIONS
Available instrumentation:Available instrumentation:
Pressure and flow measurements are available at both Pressure and flow measurements are available at both the ends.the ends.
Intermediate pressure measurements are available at SVIntermediate pressure measurements are available at SV--1, SV1, SV--4, SV4, SV--5 and SV5 and SV--7.7.
Total Total six pressure measurementssix pressure measurements and and two mass flow two mass flow measurementsmeasurements..
This is the basic instrumentation level considered for leak This is the basic instrumentation level considered for leak detection simulations but additional pressure detection simulations but additional pressure measurements added to improve the leak isolation measurements added to improve the leak isolation efficiency.efficiency.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Discretized form of hypothetical series pipelineDiscretized form of hypothetical series pipeline
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING SIMULATIONSDETECTION USING SIMULATIONS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING SIMULATIONSDETECTION USING SIMULATIONS
Natural gas composition used isNatural gas composition used is:: CHCH44 93.42, N93.42, N22 0.12, CO0.12, CO22
2.36, C2.36, C22HH66 1.76, Propane 1.35, i1.76, Propane 1.35, i--Butane 0.31, nButane 0.31, n--Butane Butane 0.32, i0.32, i--Pentane 0.01, nPentane 0.01, n--Pentane 0.08, nPentane 0.08, n--Hexane 0.01.Hexane 0.01.Dynamic Viscosity of the natural gas was taken as Dynamic Viscosity of the natural gas was taken as 0.0000125 N s m0.0000125 N s m--22..Boundary conditions for the transient test:Boundary conditions for the transient test:P1 (Pressure at nodeP1 (Pressure at node--1) = 45.0 kg/cm1) = 45.0 kg/cm22;;Normal demand at consumption node is 60500 SCMH but Normal demand at consumption node is 60500 SCMH but is a function of time to create unsteady flow conditions;is a function of time to create unsteady flow conditions;
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING SIMULATIONSDETECTION USING SIMULATIONS
With noise + no filter + PT at every nodeCategory-6
With noise + no filter + additional ten PT’s to existing instrumentation
Category-5
With noise + filter (90% (90% weightageweightage to past to past data) data) + existing instrumentation
Category-4
With noise + filter (80% (80% weightageweightage to past to past data) data) + existing instrumentation
Category-3With noise + existing instrumentationCategory-2
Without noise + existing instrumentationCategory-1Test DescriptionS. No
CATEGORIES OF TESTS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING SIMULATIONSDETECTION USING SIMULATIONS
Improvement in the leak detection results with extra nineteen Improvement in the leak detection results with extra nineteen pressure measurements added to the existing instrumentationpressure measurements added to the existing instrumentation
151.26123.760500.42195.08195.59
33102723.930250.94194.56195.58
12815.71020.712102.89192.61195.57
184.36310.160500.5103.56103.066
4914.83472.530250.77103.83103.065
18015.21393.612100.91102.15103.064
212.46193.860500.2453.9753.733
529.62735.330250.5253.2153.732
17531.91596.312100.8952.8453.731
(SCMH)(SCMH)(km)(km)
Delay in leak detection time (sec)
% error in estimated leak magnitude
Estimated leak magnitude
Magnitude of leak tested
Error in leak location
Estimated leak location
Leak location (km)
S. No
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
CONCLUSIONS CONCLUSIONS -- LEAK DETECTION LEAK DETECTION USING SIMULATIONSUSING SIMULATIONS
Proposed methodology is validated for 2%, 5% and 10% Proposed methodology is validated for 2%, 5% and 10% leaks using a series pipeline and a pipeline network.leaks using a series pipeline and a pipeline network.
Accuracy of the proposed method decreases when Accuracy of the proposed method decreases when measurement noise is present. measurement noise is present.
Results for a total of 66 numerical runs indicated that the Results for a total of 66 numerical runs indicated that the proposed methodology works very well if noise level in proposed methodology works very well if noise level in the measured data is low. In case of noisy data, the the measured data is low. In case of noisy data, the proposed method performs well if there is a sufficient proposed method performs well if there is a sufficient redundancy in the measurements.redundancy in the measurements.
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING LAB EXPERIMENTSDETECTION USING LAB EXPERIMENTS
Experimental setup
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION -- LEAK LEAK DETECTION USING LAB EXPERIMENTSDETECTION USING LAB EXPERIMENTS
Network7.656.026.7124.68206.9200250
Network13.0212.0103.0499.68203.5200250
Network10.059.075.0674.68203.8200200
Network4.836.056.949.68227.2200150
Series7.386.030.9224.68204.4200250
Series12.1312.0100.4299.68201.5200250
Series9.729.075.0574.68203.6200200
Series6.346.045.9449.68206.3200150
EstimatedActualEstimatedActualEstimatedActual
Pipelineconfiguration
Leak Magnitude(SLPM)
Leak Location from inlet end (m)
Time of Leak (sec)Flow rate(SLPM)
Validation of proposed leak detection methodology using laboratory experimental data
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
CONCLUSIONS CONCLUSIONS –– LAB EXPERIMENTSLAB EXPERIMENTS
A total of 72 experiments were conducted by changing initial flow rate, leak location, leak magnitude, and network configuration (series and network).
In series pipeline, the error in the magnitude estimation was less than 10% in 65% of the cases and the error in the magnitude estimation was less than 15% in 78% of the cases. Maximum error in estimation (31%) occurred in one test.
The proposed method located the leak within 3 m (2.5% error based on the total length of the pipe) from its actual location of occurrence in most of the cases (32 out of 36 tests). (series pipeline)
The estimated leak location was within 3 m (2.5% error based on the total length of the pipe) from its actual location of occurrence in 17 out of 36 cases. (network)
The magnitude error in the estimation was less than 10% in 50% of the cases. The magnitude error in the estimation was less than 15% in 72% of the cases. (network)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
The leak detection and identification method was implemented on-line on the LANCO pipeline, owned and operated by the GAIL (India) Ltd.
The pipeline is used to supply natural gas from Tatipaka to the LANCO power plant at Kondapalli.
The existing instrumentation consists of six pressure sensors one each at Tatipaka, Dindi (SV-1), Mortha (SV-4), Tadepalligudem (SV-5), Koppaka (SV-7) and Kondapalli, a gas chromotograph at Kondapalli, mass flow meters at Kondapalli and Tatipaka, and temperature sensors at Kondapalli and Tatipaka.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION –– FIELD LEAK FIELD LEAK DETECTION TESTSDETECTION TESTS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Hypothetical Series pipeline systemHypothetical Series pipeline system
Pipeline characteristics:Pipeline characteristics:
LengthLength = = 204.7 km204.7 km
DiameterDiameter = = 0.443 m (ID)0.443 m (ID)
RoughnessRoughness = = 250 microns250 microns
Natural gasNatural gas is flowing through the systemis flowing through the system
Average temperatureAverage temperature = = 302 K302 K
Flow measurements sampling intervalFlow measurements sampling interval = = 10 seconds10 seconds
RESULTS AND DISCUSSION RESULTS AND DISCUSSION –– FIELD LEAK FIELD LEAK DETECTION TESTSDETECTION TESTS
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION –– FIELD LEAK FIELD LEAK DETECTION TESTSDETECTION TESTS
Schematic of LANCO pipeline
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
RESULTS AND DISCUSSION RESULTS AND DISCUSSION –– FIELD LEAK FIELD LEAK DETECTION TESTSDETECTION TESTS
3 4.6717.51:58 PM1:51 PM6
6 125.1139.06:35 PM6:06 PM5
10 66.061.91:07 PM12:55 PM4
3 113.4139.07:31 PM7:07 PM3
10 162.1139.06:49 PM6:25 PM2
1.5 63.661.910:20 AM10.20 AM1
EstimatedActualEstimatedActual
Estimated Leak Magnitude
(% of total flow)
Leak Locationfrom Tatipaka (km)
Time of LeakField Test No.
Validation of the proposed leak detection methodology using field tests
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Objectives
Overall objective - develop techniques for monitoring and control of water distribution networks.
The specific goals are to
– Monitor the health of the pipes by online estimation of pipe roughness coefficient
– Develop an online control strategy for optimal operation of water distribution network
– Validate the developed methods through simulation of large scale networks
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
State Estimation
State estimation – estimate flows, pressure, outflows from noisy measurements.
– Nonlinear constrained optimization problem
Objective
Constraints– Continuity (flow balance) equation at each node– Loop equations that relate the pressure drop variables – Correlation for energy losses due to friction (Hazen- Williams
correlation is used here)
( ) ( )YYYYMinT ˆ~ˆ~ 1 −∑−= −φ
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
MethodologyMethodology
Derive reduced optimization problem using graph theoretic concepts
Reduced number of constraints is equal to number of independent loops
Reduced optimization problem is then solved using Successive
Quadratic Programming technique
Gradient of objective function and reduced constraints are derived
analytically
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Schematic diagram of Tiruppur network
Network Details
Pipes = 71
Nodes = 46
Source Node = 1
Demand node = 45
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Case Studies – Tiruppur network
No
Yes
Yes
Yes
All 45 nodes
All 45 nodes
All 45 nodes
All 45 nodes
1
1
1
1, 35 to 46
-
-
1 to 12
1 to 12
1
2
3
4
Demand at nodes
Pressures at nodes
Flows in pipes
Noise(Yes/No)
Measured variables
Case
1001001005.0
9594942.0
8877771.0
6865480.5
2621150.1
Case-4Case-3Case-2% pipes (flow)% error
less than
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Unknown Demand Estimation
0.20.002980.0029727
3.60.000520.0005119
6.30.001180.0012616
15.70.004320.0037337
5.20.00120.0012616
16.10.004330.003733613.40.004230.0037335
% ErrorEstimated demand(m3/s)
Actual demand,
(m3/s)
Demand unknown at
nodesCase
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Parameter Estimation in WDN
Given measurements flows, pressures and outflows estimate pipe roughness coefficients
State estimation is extended to perform combined state and parameter estimation
Step-1: Reduce number of parameters by grouping pipes
– K-means clustering algorithm used to group pipes based on pipe diameter and age
Step-2: Estimate states and reduced set of pipe coefficients
– Graph theoretic reduction procedure extended
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Case studies for parameter estimation
1201206-9, 24-28,34-55, 70, 71
9012010-23, 29-33, 57-69
601201-5, 56
Case - 11Cases- 8,9 and 10
Pipe No’s
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Measurements for different cases
YesAll 45 nodes1, 23-321-2411
YesAll 45 nodes1, 23-321-2410
YesAll 45 nodes1, 23-321-159
YesAll 45 nodes1, 23-261-58
Demandat nodes
Pressuresat nodes
Flowsin pipes
Noise(Yes/No)
Measured variablesCase
For cases 8,9,10 and 11– noise added 1% of the true value
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Comparison of actual and estimated HWC
4.59125.519.15109.0236.2676.481206-9,24-28,34-55,70,71
8.331304.03115.168.3313012010-23,29-33,57-69
4.3114.846.46112.246.79111.851201-5,56
Error %
Estimated HWC
Error %
Estimated HWC
Error %
Estimated HWC
Case-10Case-9Case-8Actual HWC
Pipe No’s
8.331301206-9, 24-28,34-55, 70, 71
18.72106.859010-23, 29-33, 57-69
7.3064.38601-5, 56
Error %Estimated HWC
Actual HWC
Pipe No’s
Case-11
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Control of water distribution network
Control objective
Equitable distribution of water
Manipulated variables -
valve openings - continuous valves
Solution strategy – Model predictive control
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Control problem formulation
0 < U < 1 for continuous valvesLoop constraintsMinimum pressure specifications
Constraints
Inferential Scheme
Objective
for P time periods
( )1
2
, ,... 1 1
ˆ ˆmind
k k M
N Psp pmmi k j i k j ku u i j
f d d d+ −
+ += =
= − −∑∑
ˆ ˆpmmk k kd d d= −
| 1 |ˆ ˆ ˆpm m
k k k k kd d d−= −
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Control strategy – Flow chart
Modular implementation in C interfaced with FORTRAN optimizer
Control Algorithm Process(WDN)
StateEstimator
Valve settings
Measurements
Demand setpoint profile External disturbances
Disturbance estimated,States estimated
Extended Period Simulation
Valve settings(M-time period)
States(P-time period)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Sample network with only continuous valves
Continuous valves = 11 and 12Demand nodes = 5 and 11
Insufficient2
Sufficient1
Water available in
reservoir
Case
Case studies
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Case- 1: Control algorithm results
Demand at nodes are met since sufficient water available
Demand at node - 5
00.00050.001
0.00150.002
0.00250.003
0.0035
0 2 4 6 8 10 12 14 16 18 20 22 24
Time, hr
Dem
and,
m3 /s
Demand Estimated outflow (M=1,P=1)
Demand at node - 11
00.0010.0020.0030.0040.0050.0060.007
0 2 4 6 8 10 12 14 16 18 20 22 24
Time, hrD
eman
d, m
3 /sDemand Estimated outflow (M=1,P=1)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Case- 1: Control algorithm results
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Case- 2: Control algorithm results
Demand at nodes are not met since sufficient water is not available
Demand at node-5
0
0.002
0.004
0.006
0.008
0.01
0.012
0 2 4 6 8 10 12 14 16 18 20 22 24
Time, hr
Dem
and,
m3 /s
Demand Outflow (M=1,P=1) Outflow (M=1,P=5)
Demand at node-11
0
0.005
0.01
0.015
0.02
0.025
0 2 4 6 8 10 12 14 16 18 20 22 24
Time, hr
Dem
and,
m3 /s
Demand Outflow (M=1,P=1) Outflow (M=1,P=5)
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Case- 2: Control algorithm results
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.
Demand at node-5
00.00050.001
0.00150.002
0.00250.003
0.0035
0 2 4 6 8 10 12 14 16 18 20 22 24
Time, hr
Dem
and,
m3 /s
Demand With disturbance correctionWithout disturbance correction
Demand at node-11
0
0.001
0.002
0.0030.004
0.005
0.006
0.007
0 2 4 6 8 10 12 14 16 18 20 22 24
Time, hrD
eman
d, m
3 /sDemand With disturbance correctionWithout disturbance correction
EWRE Division, Indian Institute of Technology Madras, Chennai- 36.