EPA/600/R-17/264 I September 2017
www.epa.gov/homeland-security-research
United States
Environmental Protection
Agency
oEPA
Water Network Tool for Resilience
(WNTR) User Manual
WNTR
Water Network Tool for Resilience
Office of Research and Development
Homeland Security Research Program
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EPA/600/R-17/264
August 2017
Water Network Tool for Resilience (WNTR) User Manual
by
Katherine A. Klise, David B. Hart and Dylan Moriarty
Sandia National Laboratories
Geoscience Research and Applications
Michael L. Bynum
Purdue University
Davidson School of Chemical Engineering
Regan Murray, Jonathan Burkhardt, and Terra Haxton
U.S. Environmental Protection Agency
Office of Research and Development
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Contents
1 Overview
1
2 Installation
3
3 Software framework and limitations
6
4 Units
9
5 Getting started
11
6 Water network model
12
7 Water network controls
13
X NetworkX graph
16
9 Hydraulic simulation
18
10 Water quality simulation
22
11 Simulation results
24
12 Disaster scenarios
27
13 Resilience metrics
30
14 Stochastic simulation
34
15 Copyright and license
36
16 Software quality assurance
37
17 References
39
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Disclaimer
The United States Environmental Protection Agency through its Office of Research and Development funded and
collaborated in the research described here under an Interagency Agreement # DW89924502 with the Department
of Energy's Sandia National Laboratories. It has been subjected to the Agency's review and has been approved for
publication. Note that approval does not signify that the contents necessarily reflect the views of the Agency.
Mention of trade names products, or services does not convey official EPA approval, endorsement, or
recommendation. The contractor role did not include establishing Agency policy.
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and
Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S.
Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.
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List of Tables
1 WNTR Subpackages 6
2 Classes in the network Subpackage 6
3 Classes in the son Subpackage 7
4 EPANET Hydraulic Unit Conventions 9
5 EPANET Water Quality Unit Conventions 10
6 EPANET Energy Unit Conventions 10
7 Description of WNTR Example Files 11
8 Condition Classes 14
9 Topographic Resilience Metrics 31
10 Hydraulic Resilience Metrics 32
11 Water Quality Resilience Metrics 32
12 Water Security Resilience Metrics 33
13 Economic Resilience Metrics 33
iv
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List of Figures
1 WNTR code repository on GitHub, integrated development environment using Spyder, and sample
graphics generated by WNTR 1
2 Flowchart illustrating four example use eases 2
3 Opening a Python console from a command prompt 3
4 Opening a Python console using Spyder 4
5 Example directed mulligraph 16
6 Example relationship between pressure (p) and demand (d) using both the demand-driven and pres-
sure dependent demand simulations 20
7 Example relationship between leak demand (d) and pressure (p) 20
8 Conceptual representation of Panels used to store simulation results 24
9 Example time-series graphic 25
10 Example network graphic 26
11 Example state transition plot and network graphic used to visualize resilience 30
12 Example fragility curve 35
v
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Abbreviations
API: Application programming interface
EPA: Environmental Protection Agency
IDE: Integrated development environment
SI: International System of Units
US: United States
WNTR: Water Network Tool for Resilience
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Acknowledgements
The U.S. Environmental Protection Agency acknowledges the technical review of the WNTR software and
manual and/or technical editing provided by the following individuals:
Eun Jeong Cha, University of Illinois
Sudhir Kshirsagar, Global Quality Corp
Marti Sinclair, Alion Science and Technology, for Attain
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1 Overview
Drinking water systems face multiple challenges, including aging infrastructure, water quality concerns,
uncertainty in supply and demand, natural disasters, environmental emergencies, and cyber and terrorist attacks.
All of these have the potential to disrupt a large portion of a water system causing damage to infrastructure and
outages to customers. Increasing resilience to these types of hazards is essential to improving water security.
As one of the United States (US) sixteen critical infrastructure sectors, drinking water is a national priority. The
National Infrastructure Advisory Council defined infrastructure resilience as "the ability to reduce the magnitude
and/or duration of disruptive events. The effectiveness of a resilient infrastructure or enterprise depends upon its
ability to anticipate, absorb, adapt to, and/or rapidly recover from a potentially disruptive event" [11].
Being able to predict how drinking water systems will perform during disruptive incidents and understanding how
to best absorb, recover from, and more successfully adapt to such incidents can help enhance resilience. Simulation
and analysis tools can help water utilities to explore the capacity of their systems to handle disruptive incidents and
guide the planning necessary to make systems more resilient over time [17].
The Water Network Tool for Resilience (WNTR, pronounced winter) is a Python package designed to simulate and
analyze resilience of water distribution networks. Here, a network refers to the collection of pipes, pumps, nodes,
and valves that make up a water distribution system. WNTR has an application programming interface (API) that
is flexible and allows for changes to the network structure and operations, along with simulation of disruptive
incidents and recovery actions. WNTR can be installed through the United States Environmental Protection
Agency (US EPA) GitHub organization at https://github.com/USEPA/WNTR. An integrated development
environment (IDE), like Spyder, is recommended for users and developers. Figure 1 shows the GitHub webpage,
Spyder IDE, and sample graphics generated by WNTR.
Pull requests Issues Gist
USEPA/WNTR
Spyder (Python 3.6)
File Edit Search Source Run Debug Consoles Projects Tools View Help
Q & @ IS @ ~ 9 in
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Add response/repair/mitigation strategies including leak repair, retrofitted pipes, power restoration, and
backup generation
Simulate network hydraulics and water quality using pressure dependent demand or demand-driven
hydraulic simulation, and the ability to pause and restart simulations
Run probabilistic simulations using fragility curves for component failure
Compute resilience using topographic, hydraulic, water quality/security, and economic metrics
Analyze results and generate graphics including state transition plots, network graphics, and network
animation
These capabilities can be linked together in many different ways. Figure 2 illustrates four example use cases, from
simple to complex.
Simple
Complex
START
Generate a water
network model
Modify the
network structure
and operations
Modify the
network
structure
Save the modified
network as an
EPANET INP file
Compute
topographic
metrics
Recompute
topographic
metrics
Run a hydraulic and
water quality
simulation
Compute resilience
metrics
Add a disruptive
incident and recovery
action based on
historical data
Rerun the hydraulic
and water quality
simulation
Recompute resilience
metrics
END
Analyze results and
generate graphics
Define fragility curves
for failure and
available resources
for recovery
'
r
Simulate
environmental change
from a disaster
V
J
'
'
Add a disruptive
incident and recovery
action based fragility
curves and available
resources
Run a hydraulic and
water quality
simulation
Compute resilience
metrics
OJ
Q.
Figure 2: Flowchart illustrating four example use cases.
While EPANET includes some features to model and analyze water distribution system resilience, WNTR was
developed to greatly extend these capabilities. WNTR provides a flexible platform for modeling a wide range of
disruptive incidents and repair strategies, and pressure dependent demand hydraulic simulation is included to
model the system during low pressure conditions. Furthermore, WNTR is compatible with widely used scientific
computing packages for Python, including NetworkX [6], Pandas [10], Numpy [19], Scipy [19], and Matplotlib
[7]. These packages allow the user to build custom analysis directly in Python, and gain access to tools that analyze
the structure of complex water distribution networks, analyze time-series data from simulation results, run
simulations efficiently, and create high-quality graphics and animations.
2
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2 Installation
WNTR can be installed as a Python package using standard open source software tools.
Step 1: Setup your Python environment
Python can be installed on Windows, Linux, and Mac OS X operating systems. WNTR requires
Python (versions 2.7, 3.4, or 3.5) along with several Python package dependencies. Python
distributions, such as Anaconda, are recommended to manage the Python environment. Anaconda can
be downloaded from https://www.continuum.io/downloads. General information on Python can be
found at https://www.python.org/.
Anaconda includes the Python packages needed for WNTR, including Numpy, Scipy, NetworkX,
Pandas, and Matplotlib. For more information on Python package dependencies, see Requirements.
Anaconda also comes with Spyder, an IDE, that includes enhanced editing and debug features along
with a graphical user interface. Debugging options are available from the toolbar. Code documentation
is displayed in the object inspection window. Pop-up information on class structure and functions is
displayed in the editor and console windows.
To open a Python console, open a command prompt (cmd.exe on Windows, terminal window on Linux
and Mac OS X) and run 'python', as shown in Figure 3, or open a Python console using an IDE, like
Spyder, as shown in Figure 4.
| Command Prompt - python
C:\Users>python
Python 3.6.0 |Anaconda 4.3.1 (64-bit)| (default, Dec 23 2916, 11:57:41) [MSC v.1900 64 bit (AMD64)] on Win32
Type "help", "copyright", "credits" or "license" for more information.
>>>
Figure 3: Opening a Python console from a command prompt.
Step 2: Install WNTR
The installation process differs for users and developers. Installation instructions for both types are
described below.
For users: Users can install WNTR using pip, which is a command line software tool used to install
and manage Python packages. It can be downloaded from https://pypi.python.org/pypi/pip.
To install WNTR using pip, open a command prompt and run:
pip install wntr
This will install the latest stable version of WNTR from https://pypi.python.org/pypi/wntr.
Note: A WNTR installation using pip will not include the examples folder, which is referenced
throughout this manual.
Users can also download a zip file that includes source files and the examples folder from the US EPA
GitHub organization. To download the master (development) branch, go to
https://github.com/USEPA/WNTR, select the "Clone or download" button and then select "Download
ZIP." This downloads a zip file called WNTR-master.zip. To download a specific release, go to
https://github.com/USEPA/WNTR/releases and select a zip file. The software can then be installed by
running a Python script, called setup.py, that is included in the zip file.
To build WNTR from the source files in the zip file, open a command prompt and run:
unzip WNTR-master.zip
cd WNTR-master
python setup.py install
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Figure 4: Opening a Python console using Spyder.
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For developers: Developers can install and build WNTR from source using git, which is a command
line software tool for version control and software development. It can be downloaded from
http://git-scni.com.
To build WNTR from source using git, open a command prompt and run:
git clone https://github.com/USEPA/WNTR
cd wntr
python setup.py develop
This will install the master (development) branch of WNTR from https://github.coni/USEPA/WNTR.
More information for developers can be found in the Software quality assurance section.
Step 3: Test installation
To test that WNTR is installed, open a Python console and run:
import wiitr-
If WNTR is installed properly, Python proceeds to the next line. No other output is printed to the
screen.
If WNTR is not installed properly, the user will see the following ImportError:
Import-Error: No module named wntr
2.1 Requirements
Requirements for WNTR include Python (2.7, 3.4, or 3.5) along with several Python packages. The following
Python packages are required:
Numpy [19]: used to support large, multi-dimensional arrays and matrices, http://www.niiiiipy.org/
Scipy [19]: used to support efficient routines for numerical integration, http://www.scipy.org/
Net workX [6]: used to create and analyze complex networks, https://net workx.github.io/
Pandas [10]: used to analyze and store time series data, http://pandas.pydata.org/
enum34 (for Python 2.7): used to add enumerated type support for Python 2.7,
https://pypi.py tlion.org/pypi/eninii34
These packages are included in the Anaconda Python distribution.
2.2 Optional dependencies
The following Python packages are optional:
Matplotlib [7]: used to produce figures, http://matplotlib.org/
Plotly [15]: used to produce interactive scalable figures, https://plot.ly/
xlwt [22]: used to read/write to Microsoftฎ Excelฎ spreadsheets, http://xlwt,readthedocs.io
Numpydoc [19]: used to build the user manual, https://github.com/nunipy/numpydoc
nose: used to run software tests, http://nose.readthedocs.io
These packages are included in the Anaconda Python distribution.
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3 Software framework and limitations
Before using WNTR, it is helpful to understand the software framework. WNTR is a Python package, which
contains several object-oriented subpackages, listed in Table 1. Each subpackage contains modules which contain
classes, methods, and functions. See the online API documentation at htl:ps://wnti.readtiiedocs.io for more
information on the code structure. The classes used to generate water network models and run simulations are
described in more detail below, followed by a list of software limitations.
Table 1: WNTR Subpackages
Subpackage
Description
epanet
Contains EPANET 2 compatibility functions for WNTR.
metrics
Contains methods to compute resilience, including hydraulic, water quality, water security, and
economic metrics. Methods to compute topographic metrics are included in the
wntr.network.graph module.
network
Contains methods to define a water network model, network controls, and graph representation
of the network.
scenario
Contains methods to define disaster scenarios and fragility/survival curves.
sim
Contains methods to run hydraulic and water quality simulations using the water network
model.
graphics
Contains methods to generate graphics.
utils
Contains helper functions.
3.1 Water network model
The network subpackage contains classes to define the water network model, network controls, and graph
representation of the network. These classes are listed in Table 2. Water network models can be built from scratch
or built directly from EPANETINP files. Additionally, EPANETINP files can be generated from water network
models.
Table 2: Classes in the network Subpackage
Class
Description
WaterNetworkModel
Contains methods to generate water network models, including methods to read
and write INP files, and access/add/remove/modify network components. This
class links to additional model classes (below) which define network
components, controls, and model options.
Junction
Contains methods to define junctions. Junctions are nodes where links connect.
Water can enter or leave the network at a junction.
Reservoir
Contains methods to define reservoirs. Reservoirs are nodes with an infinite
external source or sink.
Tank
Contains methods to define tanks. Tanks are nodes with storage capacity.
Pipe
Contains methods to define pipes. Pipes are links that transport water.
Pump
Contains methods to define pumps. Pumps are links that increase hydraulic
head.
Energy
Contains attributes for specifying global energy prices and global pump
efficiencies.
Valve
Contains methods to define valves. Valves are links that limit pressure or flow.
Curve
Contains methods to define curves. Curves are data pairs representing a
relationship between two quantities. Curves are used to define pump curves.
Source
Contains methods to define sources. Sources define the location and
characteristics of a substance injected directly into the network.
TimeControl
Contains methods to define time controls. Time controls define actions that start
or stop at a particular time.
ConditionalControl
Contains methods to define conditional controls. Conditional controls define
actions that start or stop based on a particular condition in the network.
WaterNetworkOptions
Contains methods to define model options, including the simulation duration
and time step.
6
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3.2 Simulators
The sim subpackage contains classes to run hydraulic and water quality simulations using the water network
model. WNTR contains two simulators: the EpanetSimulator and the WNTRSimulator. These classes are listed in
Table 3.
Table 3: Classes in the sim Subpackage
Class
Description
EpanetSimulator
The EpanetSimulator uses the EPANET 2 Programmer's Toolkit [13] to run
demand-driven hydraulic simulations and water quality simulations. When using the
EpanetSimulator, the water network model is written to an EPANET INP file which is
used to run an EPANET simulation. This allows the user to read in INP files, modify
the model, run an EPANET simulation, and analyze results all within WNTR.
WNTRSimulator
The WNTRSimulator uses custom Python solvers to run demand-driven and pressure
dependent demand hydraulic simulation and includes models to simulate pipe leaks.
The WNTRSimulator does not perform water quality simulations.
3.3 Limitations
Current software limitations are noted:
Certain EPANETINP model options are not supported in WNTR, as outlined below.
Pressure dependent demand hydraulic simulation and leak models are only available using the
WNTRSimulator.
Water quality simulations are only available using the EpanetSimulator.
WNTR reads in and writes all sections of EPANET INP files. This includes the following sections:
[BACKDROP], [CONTROLS], [COORDINATES], [CURVES], [DEMANDS], [EMITTERS], [ENERGY],
[JUNCTIONS], [LABELS], [MIXING], [OPTIONS], [PATTERNS], [PIPES], [PUMPS], [QUALITY],
[REACTIONS], [REPORT], [RESERVOIRS], [RULES], [SOURCES], [TAGS], [TANKS], [TIMES], [TITLE],
[VALVES], and [VERTICES],
However, the following model options cannot be modified/created in WNTR:
[BACKDROP] section
Efficiency curves in the [CURVES] section
[DEMANDS] section (base demand and patterns from the [JUNCTIONS] section can be modified)
[EMITTERS] section
[LABELS] section
[MIXING] section
[REPORT] section
[VERTICES] section
While the EpanetSimulator uses all EPANET model options, several model options are not used by the
WNTRSimulator. Of the EPANET model options that directly apply to hydraulic simulations, the following
options are not supported by the WNTRSimualtor:
[DEMANDS] section (base demand and patterns from the [JUNCTIONS] section are used)
[EMITTERS] section
D-W and C-M headloss options in the [OPTIONS] section (H-W option is used)
Accuracy, unbalanced, demand multiplier, and emitter exponent from the [OPTIONS] section
Speed option and multipoint head curves in the [PUMPS] section (3-point head curves are supported)
Head pattern option in the [RESERVOIRS] section
7
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Volume curves in the [TANKS] section
Rule timestep, pattern start, report start, start clocktime, and statistics in the [TIMES] section
PSV, FCV, PBV, and GPV values in the [VALVES] section
Future development of WNTR will address these limitations.
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4 Units
All data in WNTR is stored in SI (International System) units:
Length = to
Diameter = to
Water pressure = to (this assumes a fluid density of 1000 kg /to3)
Elevation = to
Mass = kg
Time = s
Concentration = k g/m3
Demand = to3 / s
Velocity = to/s
Acceleration = g (1 g = 9.81 to/s2)
Energy = J
Power = W
Pressure = Pa
Mass injection = kg/s
Volume = to3
WNTR is compatible with all EPANET unit conventions. When using an EPANETINP file to generate a water
network model, WNTR converts model parameters using the units defined in the Units and Quality options of the
EPANET INP file. These options define the mass and flow units for the model. Some units also depend on the
equation used for pipe roughness headloss and on the reaction order specified. Table 4, Table 5, and Table 6
provide information on EPANET unit conventions (modified from [13]).
Table 4: EPANET Hydraulic Unit Conventions
Hydraulic parameter
US customary units
Sl-based units
Flow
flow can be defined as:
flow can be defined as:
CFS: ft3 /s
LPS: L/s
GPM: gal/min
LPM: L/min
MGD: million gal/day
MLD: million L/day
IMGD: million imperial
CMH: m3 /hr
gal/day
CMD: m3 /day
AFD: acre-feet/day
Demand
flow
flow
Diameter: pipes
in
mm
Diameter: tanks
ft
m
Elevation
ft
m
Hydraulic head
ft
m
Length
ft
m
Emitter coefficient
flow / sqrt(psi)
flow / sqrt(m)
Friction factor
unitless
unitless
Minor loss coefficient
unitless
unitless
Pressure
psi
m or kPa
Roughness coeff: D-W
10 3 ft
mm
Roughness coeff: H-W, C-M
unitless
unitless
Velocity
ft/s
m/s
Volume
ft'3
m 3
9
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Table 5: EPANET Water Quality Unit Conventions
Water quality parameter
US customary units
Sl-based units
Concentration
mass /L where mass can be defined
mass /L where mass can be defined
as mg or ug
as mg or ug
Bulk reaction coefficient: order-1
1/day
1/day
Wall reaction coefficient: order-0
mass /ft2 /day
mass /m2 /day
Wall reaction coefficient: order-1
ft/day
m/day
Reaction rate
mass /L/day
mass /L/day
Source mass injection rate
mass /min
mass /min
Water age
hours
hours
Table 6: EPANET Energy Unit Conventions
Energy parameter
US customary units
Sl-based units
Energy
kW-hours
kW-hours
Efficiency (pumps)
percent
percent
Power
hp (horse-power)
kW
When running analysis in WNTR, all input values (i.e., time, pressure threshold, node demand) should be specified
in SI units. All simulation results are also stored in SI units and can be converted to other units if desired. The
SymPy Python package can be used to convert between units [9].
10
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5 Getting started
To start using WNTR, open a Python console and import the package:
rt wntr
A simple script, getting_started.py, is included in the examples folder. This example demonstrates how to:
Import WNTR
Generate a water network model
Simulate hydraulics
Plot simulation results on the network
rt wntr
# Create a water oclel
inp_file - "netwc inp"
wn = wntr.network,WaterNetworkModel(inp_file)
# Graph the network
wntr,graphics,plot_network(wn,
title=wn.name)
# Simulate hydraulics
sim = wntr.sim.EpanetSimulator
results = sim.run_sim()
(wn)
# Plot results on the network
pressure_at_5hr = results.node
wntr.graphics.plot_network(wn,
title=
loc["pressure", 5*3600, :]
node_attribute=pressure_at_5hr, node_size=30,
Pressure at 5 hours")
Additional examples, listed in Table 7, are included in the examples folder.
Table 7: Description of WNTR Example Files
Example file
Description
water_network_model.py
Generate and modify water network models
networkx_graph.py
Generate a NetworkX graph from a water network model
hydraulic_simulation.py
Simulate hydraulics using the EPANET and WNTR simulators
water_quality_simulation.py
Simulate water quality using EPANET
simulation_results.py
Extract information from simulation results
disaster_scenarios .py
Define disaster scenarios, including power outage, pipe leak, and changes to
supply and demand
resilience_metrics .py
Compute resilience metrics, including topographic, hydraulic, water quality,
water security, and economic metrics
stochastic_simulation.py
Run a stochastic simulation
fragility_curves .py
Define fragility curves
interactive_graphics .py
Create interactive network and time series graphics
animation.py
Animate network graphics
Several EPANETINP files are included in the examples/network folder. Example networks range from a simple 9
node network to a 3,000 node network. Additional network models can be downloaded from the University of
Kentucky Water Distribution System Research Database at http://www.iiky.edii/WDST/dalabaseJitnil.
11
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6 Water network model
The water network model includes junctions, tanks, reservoirs, pipes, pumps, valves, demand patterns, pump
curves, controls, sources, simulation options, and node coordinates. Water network models can be built from
scratch or built directly from an EPANETINP file. Sections of EPANETINP file that are not compatible with
WNTR are described in limitations. The example water_network_model.py can be used to generate, save, and
modify water network models.
A water network model can be created by adding components to an empty model:
wn = wntr.network,WaterNetworkModel()
wn.add pattern('pat 1 " , [1 ] )
wn.add pattern("pat2" , [1,2,3,4,5,6,1,8,9,10])
wn.add_junction('nodel", base_demand==0.01, demand pattern name="pat 1",
elevation=100.0, coordinates^(1,2))
wn.add_junction('node2', base_demand==0,02, demand pattern name="pat2",
elevation=50.0, coordinates^(1,3))
wn,add pipe ( 'pipel', "nodel", "node2", length-304.8, diameter-0.3048, roughness-100,
minor_loss=Q.0, status^"OPEN")
wn.add_reservoir("res", base_head=125, head_pattern_name="pat 1", coordinates^(0,2) )
wn.add pipe(1pipe21, "nodel", "res", length-100, diameter0.3048, roughness-100,
minor_loss=0.0, status^"OPEN")
wn.options.duration = 2 4*3600
wn,options.hydraulic_timestep = 15*60
wn,options.pattern_timestep = 60*60
A water network model can also be created directly from an EPANET INP file:
inp_file - "networks/Net3.inp"
The water network model can be written to a file in EPANET INP format. By default, files are written in LPS units.
The EPANET INP file will not include features not supported by EPANET (i.e., pressure dependent demand
simulation options).:
wn.write_inpfile("filename.inp")
For more information on the water network model, see WaterNetworkModel in the API documentation.
12
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7 Water network controls
One of the key features of water network models is the ability to control pipes, pumps, and valves using simple and
complex conditions. EPANET uses "controls" and "rules" to define conditions [13]. A control is a single action
(i.e., closing/opening a link or changing the setting) based on a single condition (i.e., time based or tank level
based). A rule is more complex; rules take an IF-THEN-ELSE form and can have multiple conditions and multiple
actions in each of the logical blocks. WNTR supports EPANET's rules and controls when generating a water
network model from an INP file and simulating hydraulics using the EpanetSimulator. WNTR includes additional
options to define controls that can be used by the WNTRSimulator.
The basic steps to define a control for a water network model are:
1. Define the control action
2. Define the control or rule using the control action
3. Add the control or rule to the network
These steps are defined below. Examples use the "Net3.inp" EPANET INP file to generate the water network
model object, called wn.
7.1 Control actions
Control actions tell the simulator what to do when a condition becomes "true." Control actions are created using
the Control Act ion class. A control action is defined by a target link, the property to change, and the value to
change it to. The following example creates a control action that opens pipe 330:
>>> import wiitr. network . controls as controls
>ป 11 = wn . get_link ( " 330 " )
>ป actl = controls. ControlAction (11, '"status", 1)
>ป print (actl)
set Pipe('330').status to Open
7.2 Simple controls
Control objects that emulate EPANET's [CONTROLS] section are defined in two classes:
ConditionalControl and TimeControl. When generating a water network model from an EPANET INP
file, a ConditionalControl or TimeControl will be created for each control.
Conditional controls: ConditionalControl objects define tank level and junction pressure based controls.
Conditional controls require a source, operation, threshold, and a control action. The source is defined as tuple
where the first value is a water network model component and the second value is the attribute of the object. The
operation is defined using NumPy functions such as np.greater and np.less. The threshold is the value that triggers
the condition to be true. The control action is defined above.
In the following example, a conditional control is defined that opens pipe 330 if the level of tank 1 goes above
46.0248 m. The source is the tank level and is defined as a tuple with the node object nl and the attribute level. To
specify that the condition should be true when the level is greater than the threshold, the operation is set to
np.greater and the threshold is set to 46.0248. The control action actl from above is used in the conditional control:
>>> nl = wn.get_node('1' )
>ป threshl = 46.0248
ปป ctrll = controls . ConditionalControl
(nl, "level"), np.greater, threshl, actl)
>>> ctrll
cConditionalControl: , 'level
), , 4 6.0248,
->-, ' status
, 'Open'>>
To get an EPANET-like description of this control, use the print function:
ป> P rint (ctrll)
LINK 330 Open IF NODE 1 Above 46.0248
13
-------
Time-based controls: TimeControl objects define time-based controls. Time-based controls require a water
network model object, a time to start the condition, a control action, and additional flags to specify the time
reference point and recurrence. The time flag is either SIM_TIME or SHIFTED_TIME\ these indicate simulation or
clock time, respectively. The daily flag is either True or False and indicates if the control should be repeated every
24 hours.
In the following example, a time-based control is defined that opens Pump 10 at hour 121. The time flag is set to
SIM_TIME and the daily flag is set to False. A new control action is defined that opens the pump:
>>> time2 = 121 * 60 * 60
>ป timeflag2 = "SIM TIME"
>ป dailyflag2 = False
>ป pump2 = wn . get_link ( ' 10 " )
ปป act2 = controls . ControlAction (pump2 , "s
: at: u s " , 1)
ปป ctrl2 = controls . TimeControl (wn, time2 ,
timeflag2, dailyflag2, act2)
>ป print (ctrl2)
LINK 10 Open AT TIME 121:00:00
Note that the EpanetSimulator is limited to use the following pairs: time_flag='SIM_TIME' with daily_flag=False,
and time_flag='SHIFTED_TIME' with daily_flag=True. The WNTRSimulator can use any combination of time
flag and daily flag.
7.3 Complex rules
Control objects that emulate EPANET's [RULES] section are defined in the If ThenElseControl class. When
generating a water network model from an EPANETINP file, an IfThenElseControl will be created for each rule.
An IfThenElseControl is defined using a ControlCondition object and a ControlAction object.
Condition classes are listed in Table 8.
Table 8: Condition Classes
Condition class
Description
TimeOfDayCondition
Time-of-day or "clocktime" based condition statement
SimTimeCondition
Condition based on time since start of the simulation
ValueCondition
Compare a network element attribute to a set value
RelativeCondition
Compare attributes of two different objects (e.g., levels from tanks 1 and 2)
OrCondition
Combine two WNTR Conditions with an OR
AndCondition
Combine two WNTR Conditions with an AND
All of the above conditions are valid EPANET conditions except RelativeCondition.
In the following example, the previous simple controls are recreated using the IfThenElseControl:
>>> condl = controls.ValueCondition(nl, "level", ">", 46,0248)
>ป print (condl)
Tank ( '1') .level > 46.0248
>>> rulel = controls.IfThenElseControl(condl, [actl], name-"control1')
>ป print (rulel)
Rule controll := if Tank('1').level > 46.0248 then set Pipe('330').status to Open
>>> cond2 = controls.SimTimeCondition(wn, ' = ", "121:00:00")
>ป print (cond2)
sim____time = 435600 sec
>>> rule2 = controls.IfThenElseControl(cond2, [act2], name-'control2")
>ป print (rule2)
Rule control2 := if sim_time = 435600 sec then set Pump ('10') .status to Open
More complex rules can be written using one of the Boolean logic condition classes. The following example
creates a new rule that will open pipe 330 if both conditions are true, and otherwise it will open pipe 10. This rule
will behave very differently from the rules above:
14
-------
>>> cond3 = controls.AndCondition(condl, cond2)
>ป print (cond3)
( Tank ( ' 1 ' ) .level > 46.0248 && sim_time = 435600 sec )
>>> rule3 = controls.IfThenElseControl(cond3, [ actl ], [ act2 ], priority=3, name
<-+' wei rd" )
>>> print(rule3)
Rule weird := if ( Tank ( ' 1 ' ) .level > 46.0248 && sim_time = 435600 sec ) then set^
^Pipe ('330'). status to Open else set Pump('10').status to Open with priority 3
Actions can also be combined, as shown in the following example:
>>> cond4 = controls.OrCondition(condl, cond2)
>ป rule4 = controls.IfThenElseControl(cond4, [actl, act2])
>ป print (rule4)
Rule := if ( Tank ( ' 1 ' ) .level > 46.0248 | | sim_time = 435600 sec ) then set Pipe ('330
status to Open and set Pump ('10'). status to Open
The flexibility of the IfThenElseControl combined with the different ControlCondition classes and ControlActions
provides an extremely powerful tool for defining complex network operations.
7.4 Adding controls to a network
Once a control is created, they can be added to the network. This is accomplished using the add_control
method of the water network model object. The control should be named so that it can be retrieved and modified if
desired:
>>> wn.add_control('NewTlmeControl', ctrl2)
>ป wn . get_control ( " NewTlmeCont rol" )
cTimeControl: model, 435600, 'SIM_JTIME', False, cControlAction: , 'status
, ' Open ' >>
15
-------
8 NetworkX graph
WNTR uses NetworkX data objects to store network connectivity as a graph. A graph is a collection of nodes that
are connected by links. For water networks, nodes represent junctions, tanks, and reservoirs while links represent
pipes, pumps, and valves.
Water networks are stored as directed multigraphs. A directed multigraph is a graph with direction associated
with links and the graph can have multiple links with the same start and end node. A simple example is shown in
Figure 5. For water networks, the link direction is from the start node to the end node. The link direction is used as
a reference to track flow direction in the network. For example, positive flow indicates that the flow direction is
from the start node to the end node while negative flow indicates that the flow direction is from the end node to the
start node. Multiple links with the same start and end node can be used to represent redundant pipes or backup
pumps. In WNTR, the graph stores the start and end node of each link, node coordinates, and node and link types
(i.e., tank, reservoir, valve). WNTR updates the graph as elements are added and removed from the water network
model.
Figure 5: Example directed multigraph.
NetworkX includes numerous methods to analyze the structure of complex networks. For more information on
NetworkX, see https://networkx.github.io/. WNTR includes a custom Graph Class, WntrMultiDiGraph. This
class inherits from NetworkX MultiDigraph and includes additional methods that are specific to WNTR. The
example networkx_graph.py can be used to generate a graph from a water network model.
A copy of the graph can an be obtained using the following function:
G = wn . get_graph_deep_copy ()
The graph is stored as a nested dictionary. The nodes and links (note that links are called edges in NetworkX) can
be accessed using the following:
node_name - '12 3'
print (G.node [node__name] )
print (G. edge [node__name] )
The graph can be used to access NetworkX methods, for example:
:t networkx as nx
node_degree = G,degree ()
between = nx.betweenness__centrality (G)
wntr . graphics , plot_network (wn, node_att ribute==bet_cen, node_size = 30,
title='Betweenness Cent rality')
Some methods in NetworkX require that networks are undirected. An undirected graph is a graph with no
direction associated with links. The following NetworkX method can be used to convert a directed graph to an
undirected graph:
uG = G.to_undirected()
Some methods in NetworkX require that networks are connected. A connected graph is a graph where a path
exists between every node in the network (i.e., no node is disconnected). The following NetworkX method can be
used to check if a graph is connected:
16
-------
print(nx.is_connected(uG))
Some methods in NetworkX can use weighted graphs. A weighted graph is a graph in which each link is given a
weight. The WNTR method weight_graph can be used to weight the graph by any attribute. In the following
example, the graph is weighted by length. This graph can then be used to compute path lengths:
length = wn.query_link_attribute('length")
G.weight_graph(link_attribute = length)
17
-------
9 Hydraulic simulation
WNTR contains two simulators: the WNTRSimulator and the EpanetSimulator. See Software framework and
limitations for more information on features and limitations of these simulators.
The EpanetSimulator can be used to run demand-driven hydraulic simulations using the EPANET 2 Programmer's
Toolkit. The simulator can also be used to run water quality simulations, as described in Water quality simulation.
A hydraulic simulation using the EpanetSimulator is run using the following code:
epanet_sim = wntr.sim.EpanetSimulator (wn)
epanet_sim_results = epanet_sim.run_sim()
The WNTRSimulator is a pure Python hydraulics simulation engine based on the same equations as EPANET. The
WNTRSimulator does not include equations to run water quality simulations. The WNTRSimulator includes the
option to simulate leaks, and run hydraulic simulations in either demand-driven or pressure dependent demand
mode. A hydraulic simulation using the WNTRSimulator is run using the following code:
wntr_sim = wntr.sim.WNTRSimulator(wn)
wntr_sim_resuits = wntr_sim,run_sim()
The example hydraulic_simulation.py can be used to run both simulators.
More information on the simulators can be found in the API documentation, under EpanetSimulator and
WNTRSimulator.
9.1 Options
Hydraulic simulation options are defined in the WaterNetworkOptions class. These options include duration,
hydraulic timestep, rule timestep, pattern timestep, pattern start, default pattern, report timestep, report start, start
clocktime, headloss, trials, accuracy, unbalanced, demand multiplier, and emitter exponent. All options are used
with the EpanetSimulator. Options that are not used with the WNTRSimulator are described in Limitations.
9.2 Mass balance at nodes
Both simulators use the mass balance equations from EPANET [13]:
53
-------
For q < 0:
hL = -10.667C,~1'852cr4'87:LL|9|1'852
For q > 0:
hL = 10.667C,"1'852^4'871L|g|1'852
These equations are symmetric across the origin and valid for any q. Thus, this equation can be used for flow in
either direction. However, the derivative with respect (o q a(<\ 0 is 0. In certain scenarios, this can cause the
Jacobian of the set of hydraulic equations to become singular (when q = 0). To overcome this limitation, the
WNTRSimulator splits the domain of q into six segments to create a piecewise smooth function.
9.4 Demand-driven simulation
In demand-driven simulation, the pressure in the system depends on the node demands. The mass balance and
headloss equations described above are solved assuming that node demands are known and satisfied. This
assumption is reasonable under normal operating conditions and for use in network design. Both simulators can
run hydraulics using demand-driven simulation.
9.5 Pressure dependent demand simulation
In situations that lead to low pressure conditions (i.e., fire fighting, power outages, pipe leaks), consumers do not
always receive their requested demand and a pressure dependent demand simulation is recommended. In a pressure
dependent demand simulation, the delivered demand depends on the pressure. The mass balance and headloss
equations described above are solved by simultaneously determining demand along with the network pressures and
flow rates.
The WNTRSimulator can run hydraulics using a pressure dependent demand simulation according to the following
pressure-demand relationship [20]:
where d is the actual demand (m3/s), Df is the desired demand (m3/s), p is the pressure (Pa), Pf is the pressure
above which the consumer should receive the desired demand (Pa), and P0 is the pressure below which the
consumer cannot receive any water (Pa). The set of nonlinear equations comprising the hydraulic model and the
pressure-demand relationship is solved directly using a Newton-Raphson algorithm.
Figure 6 illustrates the pressure-demand relationship using both the demand-driven and pressure dependent
demand simulations. In the example, Df is 0.0025 m3/s (39.6 GPM), /'/ is 30 psi, and / , is 5 psi. Using the
demand-driven simulation, the demand is equal to Df regardless of pressure. Using the pressure dependent demand
simulation, the demand starts to decrease when the pressure is below Pf and goes to 0 when pressure is below I',.
9.6 Leak model
The WNTRSimulator includes the ability to add leaks to the network. The leak is modeled with a general form of
the equation proposed by Crowl and Louvar [4] where the mass flow rate of fluid through the hole is expressed as:
where dieak is the leak demand (m3/s), Cd is the discharge coefficient (unitless), A is the area of the hole (m2), p is
the gauge pressure inside the pipe (Pa), a is the discharge coefficient, and p is the density of the fluid. The default
discharge coefficient is 0.75 (assuming turbulent flow), but the user can specify other values if needed. The value
of a is set to 0.5 (assuming large leaks out of steel pipes). Leaks can be added to junctions and tanks. A pipe break
is modeled using a leak area large enough to drain the pipe. WNTR includes methods to add leaks to any location
along a pipe by splitting the pipe into two sections and adding a node.
Figure 7 illustrates leak demand. In the example, the diameter of the leak is set to 0.5 cm, 1.0 cm, and 1.5 cm.
19
-------
0.0030
0.0025
0.0020
"e 0.0015
TS
0.0010
0.0005
0.0000
Dema n
Pressur
d-driven
e dependent
demand
10
15 20
P (psi)
25
30
35
Figure 6: Example relationship between pressure (p) and demand (d) using both the demand-driven and pressure
dependent demand simulations.
0.0030
0.0025
0.0020
Leak dlameter = 0.5 cm
Leak diameter = 1.0 cm
Leak diameter = 1.5 cm
C.CC 15
C.CCIC
C.CCC5
C.CCOC
Figure 7: Example relationship between leak demand (d) and pressure (p).
20
-------
9.7 Pause and restart
The WNTRSimulator includes the ability to
Reset initial values and re-simulate using the same water network model. Initial values include tank head,
reservoir head, pipe status, pump status, and valve status.
Pause a hydraulic simulation, change network operations, and then restart the simulation
Save the water network model and results to files and reload for future analysis
These features are helpful when evaluating various response action plans or when simulating long periods of time
where the time resolution might vary. The file hydraulic_simulation.py includes examples of these features.
21
-------
10 Water quality simulation
Water quality simulations can only be run using the EpanetSimulator. As listed in the Software framework and
limitations section, this means that the hydraulic simulation must use demand-driven simulation. Note that the
WNTRSimulator can be used to compute demands under pressure dependent demand conditions and those
demands can be used in the EpanetSimulator. The following code illustrates how to reset demands in a water
network model using a pressure dependent demand simulation:
sim = wntr.sim.WNTRSimulator(wn)
results = sim.run_sim()
wn,reset_demand(results.node["demand"], "PDD")
sim = wntr,sim,EpanetSimulator(wn)
results_withPDdemands = sim.run_sim()
After defining water quality options and sources (described in the Options and Sources sections below), a hydraulic
and water quality simulation using the EpanetSimualtor is run using the following code:
sim = wntr,sim,EpanetSimulator(wn)
results = sim.run_sim()
The example water_quality_simulation.py can be used to run water quality simulations and plot results.
10.1 Options
Water quality simulation options are defined in the WaterNetworkOptions class. Three types of water quality
analysis are supported. These options include water age, tracer, and chemical concentration.
Water age: Water quality simulation can be used to compute water age at every node. To compute water
age, set the 'quality' option as follows:
wn.options,quality - "AGE"
Tracer: Water quality simulation can be used to compute the percent of flow originating from a specific
location. The results include tracer percent values at each node. For example, to track a tracer from node
'111', set the 'quality' and 'tracer_node' options as follows:
wn.options,quality - "TRACE"
wn.options,quality_value = "111"
Chemical concentration: Water quality simulation can be used to compute chemical concentration given a
set of source injections. The results include chemical concentration values at each node. To compute
chemical concentration, define sources (described in the Sources section below) and set the 'quality' options
as follows:
wn.options.quality = "CHEMICAL"
To skip the water quality simulation, set the 'quality' options as follows:
wn.options.quality = "NONE"
Additional water quality options include viscosity, diffusivity, specific gravity, tolerance, bulk reaction order, wall
reaction order, tank reaction order, bulk reaction coefficient, wall reaction coefficient, limiting potential, and
roughness correlation. These parameters are defined in the WaterNetworkOptions API documentation.
When creating a water network model from an EPANETINP file, water quality options are populated from the
[OPTIONS] and [REACTIONS] sections of EPANET INP file. All of these options can be modified in WNTR and
then written to an EPANET INP file.
22
-------
10.2 Sources
Sources are required for CHEMICAL water quality analysis. Sources can still be defined, but will not be used if
AGE, TRACE, or NONE water quality analysis is selected. Sources are added to the water network model using
the add_source method. Sources include the following information:
Source name: A unique source name used to reference the source in the water network model.
Node name: The injection node.
Source type: Options include 'CONCEN,' 'MASS,' 'FLOWPACED,' or 'SETPOINT.'
- CONCEN source represents injection of a specific concentration.
- MASS source represents a booster source with a fixed mass flow rate.
- FLOWPACED source represents a booster source with a fixed concentration at the inflow of the node.
- SETPOINT source represents a booster source with a fixed concentration at the outflow of the node.
Strength: Baseline source strength (in mass/time for MASS and mass/volume for CONCEN,
FLOWPACED, and SETPOINT).
Pattern: The pattern name associated with the injection.
For example, the following code can be used to add a source, and associated pattern, to the water network model:
wn.add pattern("Source?at:tern", start_time-2*360 0, end_time-15*3600)
wn.add_source("Source!', '121', "SETPOINT", 1000, "SourcePattern')
In the above example, the pattern is given a value of 1 between 2 and 15 hours, and 0 otherwise. The method
remove_source can be used to remove sources from the water network model.
When creating a water network model from an EPANETINP file, the sources that are defined in the [SOURCES]
section are added to the water network model. These sources are given the name 'INP#' where # is an integer
related to the number of sources in the INP file.
23
-------
11 Simulation results
WNTR uses Pandas data objects to store simulation results. The use of Pandas facilitates a comprehensive set of
time series analysis options that can be used to evaluate results. For more information on Pandas, see
http://pandas .pydata.org/.
Results are stored in Pandas Panels. A Panel is a 3-dimensional database. One Panel is used to store nodes results
and one Panel is used to store link results. The Panels are indexed by:
Node or link attribute
Time in seconds from the start of the simulation
Node or link name
Conceptually, Panels can be visualized as blocks of data with 3 axis, as shown in Figure 8.
Link Name
Link Name
Link Name
Q-
Link Attribute
Node Name
Node Name
Node Name
Q.
Node Attribute
Figure 8: Conceptual representation of Panels used to store simulation results.
Node attributes include:
Demand
Expected demand
Leak demand (only when the WNTRSimulator is used)
Pressure
Head
Quality (only when the EpanetSimulator is used for a water quality simulation. Water age, tracer percent, or
chemical concentration is stored, depending on the type of water quality analysis)
Type (junction, tank, or reservoir)
Link attributes include:
Velocity
Flowrate
Status (0 indicates closed, 1 indicates open)
Type (pipe, pump, or valve)
The example simulation_results.py demonstrates use cases of simulation results. Node and link results are
accessed using:
print(results.node)
print(results.link)
24
-------
The indices can be used to extract specific information from the Panels. For example, to access the pressure and
demand at node '123' at 1 hour:
print(results.node.loc[['pressure' , 'demand'], 3600, '123'])
To access the pressure for all nodes and times (the notation returns all variables along the specified axis):
print(results.node.loc['pressure' , :, :])
Attributes can be plotted as a time-series, as shown in Figure 9:
pressure_at_nodel2 3 = results.node.loc['pressure',
: ,
'123 ' ]
pressure_at_nodel2 3.plot()
50
49
48
47
46
45
0
100000
200000
300000
400000
500000
600000
Figure 9: Example time-series graphic.
Attributes can be plotted on the water network model, as shown in Figure 10. In this figure, the node pressure at 1
hr and link flowrate at 1 hour are plotted on the network. A colorbar is included for both node and link attributes:
pressure_at_lhr = results.node.loc['pressure', 3600, :]
flowrate_at_lhr = results.link.loc['flowrate' , 3600, :]
wntr.graphics.plot_network(wn, node_attribute=pressure_at_lhr,
link_attribute=flowrate_at_lhr)
Network and time-series graphics can be customized to add titles, legends, axis labels, etc.
Panels can be saved to Excel files using:
results.node.to_excel('node_resuits.xls')
results.link.to_excel('link_results.xls')
25
-------
Figure 10: Example network graphic.
-------
12 Disaster scenarios
Drinking water utilities might be interested in examining many different disaster scenarios. They could be acute
incidents like power outages and earthquakes or they could be long term issues like persistent pipe leaks,
population fluctuation, and changes to supply and demand. The following section describes disaster scenarios that
can be modeled in WNTR. The example disaster_scenarios.py demonstrates methods to define disaster scenarios.
12.1 Earthquake
Earthquakes can be some of the most sudden and impactful disasters that a water systems experiences. An
earthquake can cause lasting damage to the system that could take weeks, if not months, to fully repair.
Earthquakes can cause damage to pipes, tanks, pumps, and other infrastructure. Additionally, earthquakes can
cause power outages and fires.
WNTR includes methods to add leaks to pipes and tanks, shut off power to pumps, and change demands for fire
conditions, as described in the sections below. The Earthquake class includes methods to compute peak ground
acceleration, peak ground velocity, and repair rate based on the earthquake location and magnitude. Alternatively,
external earthquake models or databases (e.g., ShakeMap [21]) can be used to compute earthquake properties and
those properties can be loaded into Python for analysis in WNTR.
When simulating the effects of an earthquake, fragility curves are commonly used to define the probability that a
component is damaged with respect to peak ground acceleration, peak ground velocity, or repair rate. The
American Lifelines Alliance report [1] includes seismic fragility curves for water system components. See
Stochastic simulation for more information on fragility curves.
Since properties like peak ground acceleration, peak ground velocity, and repair rate are a function of the distance
to the epicenter, node coordinates in the water network model must be in units of meters. Since some network
models use other units for node coordinates, WNTR includes a method to change the coordinate scale. To change
the node coordinate scale by a factor of 1000, for example, use the following code:
wn.scale_node_coordinates(10 00)
The following code can be used to compute peak ground acceleration, peak ground velocity, and repair rate:
epicenter - (320 00,1500 0) # x,y location
magnitude = 6.5 # Richter
depth = 100 00 # m, shallow
earthquake = wntr.scenario.Earthquake(epicenter, magnitude, depth)
distance = earthquake.distance_to_epicenter(wn, element_type==wntr,network.Pipe)
pga = earthquake.pga_attenuation_model(distance)
pgv = earthquake.pgv_attenuation_model(distance)
repair_rate = earthquake.repair_rate_model(pgv)
12.2 Pipe breaks or leaks
Pipes are susceptible to leaks. Leaks can be caused by aging infrastructure, the freeze/thaw process, increased
demand, or pressure changes. This type of damage is especially common in older cities where distribution systems
were constructed from outdated materials like cast iron and even wood.
WNTR includes methods to add leaks to junctions and tanks. Leaks can be added to a pipe by splitting the pipe and
adding a junction. To add a leak to a specific pipe:
wn,split_pipe_with_junction('123', "12 3_A", "123_B', "123_leak_node')
leak_node - wn.get_node('123_leak_node')
The method add_leak adds time controls to a junction which includes the start and stop time for the leak.
27
-------
12.3 Power outage
Power outages can be small and brief, or they can also span over several days and effect whole regions as seen in
the 2003 Northeast Blackout. While the Northeast Blackout was an extreme case, a 2012 Lawrence Berkeley
National Laboratory study [5] showed the frequency and duration of power outages are increasing by a rate of two
percent annually. In water distribution systems, a power outage can cause pump stations to shut down and result in
reduced water pressure. This can lead to shortages in some areas of the system. Typically, no lasting damage in the
system is associated with power outages.
WNTR can be used to simulate power outages by changing the pump status from ON to OFF and defining the
duration of the outage. To model the impact of a power outage on a specific pump:
# Defint
ver c.
utSiCTe at Cl
mp
?'? 5 '
The method add_pump_outage adds time controls to a pump to start and stop a power outage. When
simulating power outages, consider placing check bypasses around pumps and check valves next to reservoirs.
12.4 Fires
WNTR can be used to simulate damage caused to system components due to fire and/or to simulate water usage
due to fighting fires. To fight fires, additional water is drawn from the system. Fire codes vary by state. Minimum
required fire flow and duration are generally based on building area and purpose. While small residential fires
might require 1500 gallons/minute for 2 hours, large commercial spaces might require 8000 gallons/minute for 4
hours [8]. This additional demand can have a large impact on water pressure in the system.
WNTR can be used to simulate fire fighting conditions in the system. WNTR simulates fire fighting conditions by
specifying the demand, time, and duration of fire fighting. Pressure dependent demand simulation is recommended
in cases where fire fighting might impact expected demand. To model the impact of fire conditions at a specific
node:
# Define fire conditions at node '197'
fire_flow_demand = 0.252 # 4000 gal/min = 0,252 ni.3/s
time_of_fire = 10
duration_of_fire = 4
remainder = int (wn , options.duration/3 600-time_of_fire-duration_
_of_fire)
fire flow pattern = [0]*time_of_fire + [1]*duration_of_fire +
0]^remainder
wn.add pattern('fire_flow", fire flow pattern)
node = wn.get_node("197')
original_base_demand = node.base_demand
original_demand_pattern_name = node.demand pattern name
node.base_demand = original_base_demand+fire_flow_demand
12.5 Environmental change
Environmental change is a long term problem for water distribution systems. Changes in the environment could
lead to reduced water availability, damage from weather incidents, or even damage from subsidence. For example,
severe drought in California has forced lawmakers to reduce the state's water usage by 25 percent. Environmental
change also leads to sea level rise which can inundate distribution systems. This is especially prevalent in cities
built on unstable soils like New Orleans and Washington, DC which are experiencing land subsidence.
WNTR can be used to simulate the effects of environmental change on the water distribution system by changing
supply and demand, adding disruptive conditions (i.e., power outages, pipe leaks) caused by severe weather, or by
adding pipe leaks caused by subsidence. Power outages and pipe leaks are described above. Changes to supply and
demand can be simple (i.e., changing all nodes by a certain percent), or complex (i.e., using external data or
correlated statistical methods). To model simple changes in supply and demand:
# Reduce supply, imcrea.se demand
for reservoir_name, reservoir in wn.reservoirs():
reservoir,base_head = reservoir.base_head*0,9
for junction_name, junction in wn,junctions():
28
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12.6 Contamination
Water distribution systems are vulnerable to contamination by a variety of chemical, microbial, or radiological
substances. During disasters, contamination can enter the system through reservoirs, tanks, and at other access
points within the distribution system. Long term environmental change can lead to degradation of water sources.
Contamination can be difficult to detect and is very expensive to clean up. Recent incidents, including the Elk River
chemical spill and Flint lead contamination, highlight the need to minimize human health and economic impacts.
WNTR simulates contamination incidents by introducing contaminants into the distribution system and allowing
them to propagate through the system. The example water_quality_simulation.py includes steps to define and
simulate contamination incidents.
Future versions of WNTR will be able to simulate changes in source water quality due to disruptions.
12.7 Other disaster scenarios
Drinking water systems are also susceptible to other natural disasters including floods, droughts, hurricanes,
tornadoes, extreme winter storms, and wind events. WNTR can be used to simulate these events by combining the
disaster models already described above. For example, tornadoes might cause power outages, pipe breaks, other
damage to infrastructure, and fires. Floods might cause power outages, changes to source water (because of
treatment failures), and pipe breaks.
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13 Resilience metrics
Resilience of water distribution systems refers to the design, maintenance, and operations of that system. All these
aspects must work together to limit the effects of disasters and enable rapid return to normal delivery of safe water
to customers. Numerous resilience metrics have been suggested [17]. These metrics generally fall into five
categories: topographic, hydraulic, water quality, water security, and economic. When quantifying resilience, it is
important to understand which metric best defines resilience for a particular scenario. WN'I'R includes many
metrics to help users compare resilience using different methods.
The following sections outline metrics that can be computed using WNTR, including:
Topographic metrics (Table 9)
Hydraulic metrics (Table 10)
Water quality metrics (Table 11)
Water security metrics (Table 12)
Economic metrics (Table 13)
While some metrics define resilience as a single system-wide quantity, other metrics define quantities that are a
function of time, space, or both. For this reason, state transition plots [3] and network graphics are useful ways to
visualize resilience and compare metrics, as shown in Figure 11. In the state transition plot, the x-axis represents
time (before, during, and after a disruptive incident). The y-axis represents performance. This can be any time
varying resilience metric that responds to the disruptive state. State transition plots are often generated to show
time varying performance of the system, but they can also represent the time varying performance of individual
components, like tanks or pipes. Network graphics are useful to visualize resilience metrics that vary with respect
to location. For metrics that vary with respect to time and space, network animation can be used to illustrate
resilience.
State Transition plot for time-series metrics Network graphic for spatially distributed metrics
Original State
Recovered State
Incident
Disrupted
State
Resilience Action
Figure 11: Example state transition plot and network graphic used to visualize resilience.
The example resilience_metrics.py demonstrates how to compute these metrics.
13.1 Topographic metrics
Topographic metrics, based on graph theory, can be used to assess the connectivity of water distribution networks.
These metrics rely on the physical layout of the network components and can be used to understand how the
underlying structure and connectivity constrains resilience. For example, a regular lattice, where each node has the
same number of edges, is considered to be the most reliable graph structure. On the other hand, a random lattice
has nodes and edges that are placed according to a random process. A real world water distribution system
probably lies somewhere in between a regular lattice and a random lattice in terms of structure and reliability.
NetworkX includes a wide range of topographic metrics that can be computed using the WntrMultiDiGraph.
WNTR includes additional methods/metrics to help compute resilience. These methods are in the
WntrMultiDiGraph class. Commonly used topographic metrics are listed in Table 9. Information on additional
topographic metrics supported by NetworkX can be found at https://networkx.github.io/.
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Table 9: Topographic Resilience Metrics
Metric
Description
Node degree
Node degree is the number of links adjacent to a node. Node degree is a measure
of the number of branches in a network. A node with degree 0 is not connected to
the network. Terminal nodes have degree 1. A node connected to every node
(including itself) has a degree equal to the number of nodes in the network. The
average node degree is a system wide metric used to describe the number of
connected links in a network. Node degree can be computed using the NetworkX
method degree. Terminal nodes can be found using the method
terminal_nodes.
Link density
Link density is the ratio between the total number of links and the maximum
number of links in the network. If links are allowed to connect a node to itself, then
the maximum number of links is ra2, where n is the number of nodes. Otherwise,
the maximum number of nodes is n(n 1). Link density is 0 for a graph without
edges and 1 for a dense graph. The density of multigraphs can be higher than 1.
Link density can be computed using the NetworkX method density.
Eccentricity and diameter
Eccentricity is the maximum number of links between a node and all other nodes
in the graph. Eccentricity is a value between 0 and the number of links in the
network. Diameter is the maximum eccentricity in the network. Eccentricity and
diameter can only be computed using undirected, connected networks. Network X
includes a method to convert directed graphs to undirected graphs,
to_undirected, and to check if graphs are connected, is_connected.
Eccentricity and diameter can be computed using the NetworkX methods
eccentricity and diameter.
Simple paths
A simple path is a path between two nodes that does not repeat any nodes.
NetworkX includes a method, all_simple_paths, to compute all simple
paths between two nodes. The method links_in_simple_paths can be used
to extract all links in a simple path along with the number of times each link was
used in the paths. Paths can be time dependent, if related to simulated flow
direction. The method weight_graph can be used to weight the graph by a
specified attribute.
Shortest path lengths
Shortest path lengths is the minimum number of links between a source node and
all other nodes in the network. Shortest path length is a value between 0 and the
number of links in the network. The average shortest path length is a system wide
metric used to describe the number of links between a node and all other nodes.
Shortest path lengths and average shortest path lengths can be computed using the
following NetworkX methods shortest_path_length and
average_shortest_path_length.
Betweenness centrality
Betweenness centrality is the fraction of shortest paths that pass through each node.
Betweenness coefficient is a value between 0 and 1. Central point dominance is the
average difference in betweenness centrality of the most central point (having the
maximum betweenness centrality) and all other nodes. These metrics can be
computed using the NetworkX methods betweenness_centrality and the
method central_point_dominance
Closeness centrality
Closeness centrality is the inverse of the sum of shortest path from one node to all
other nodes. Closeness centrality can be computed using the NetworkX method
closeness_centrality.
Articulation points
A node is considered an articulation point if the removal of that node (along with
all its incident edges) increases the number of connected components of a network.
Density of articulation points is the ratio of the number of articulation points and
the total number of nodes. Density of articulation points is a value between 0 and
1. Articulation points can be computed using the NetworkX method
articulation_points.
Bridges
A link is considered a bridge if the removal of that link increases the number of
connected components in the network. The ratio of the number of bridges and the
total number of links in the network is the bridge density. Bridge density is a value
between 0 and 1. The method bridges can be used to find bridges in a network.
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13.2 Hydraulic metrics
Hydraulic metrics are based upon variable flows and/or pressure. The calculation of these metrics requires
simulation of network hydraulics that reflect how the system operates under normal or abnormal conditions.
Hydraulic metrics included in WNTR are listed in Table 10.
Table 10: Hydraulic Resilience Metrics
Metric
Description
Pressure
To determine the number of node-time pairs above or below a specified
pressure threshold, use the query method on results.node['pressure'].
Todini index
The Todini index [16] is related to the capability of a system to overcome
failures while still meeting demands and pressures at the nodes. The Todini
index defines resilience at a specific time as a measure of surplus power at each
node and measures relative energy redundancy. The Todini index can be
computed using the todini method.
Entropy
Entropy [2] is a measure of uncertainty in a random variable. In a water
distribution network model, the random variable is flow in the pipes and
entropy can be used to measure alternate flow paths when a network
component fails. A network that carries maximum entropy flow is considered
reliable with multiple alternate paths. Connectivity will change at each time
step, depending on the flow direction. The method weight_graph method
can be used to weight the graph by a specified attribute. Entropy can be
computed using the entropy method.
Fraction of delivered volume
Fraction of delivered volume is the ratio of total volume delivered to the total
volume requested [12], This metric can be computed as a function of time or
space using the f dv method.
Fraction of delivered demand
Fraction of delivered demand is the fraction of time periods where demand is
met [12], This metric can be computed as a function of time or space using the
fdd method.
Population impacted
Population that is impacted by a specific quantity can be computed using the
population_impacted method. For example, this method can be used to
compute the population impacted by pressure below a specified threshold.
13.3 Water quality metrics
Water quality metrics are based on the concentration or water age. The calculation of these metrics require a water
quality simulation. Water quality metrics included in WNTR are listed in Table 11.
Table 11: Water Quality Resilience Metrics
Metric
Description
Water age
To determine the number of node-time pairs above or below a specified water
age threshold, use the query method on results.node['quality'] after a
simulation using AGE.
Concentration
To determine the number of node-time pairs above or below a specified
concentration threshold, use the query method on results.node['quality'] after
a simulation using CHEM or TRACE.
Fraction of delivered quality
Fraction of delivered quality is the fraction of time periods where water quality
standards are met [12], This metric can be computed as a function of time or
space using the f dq method
Average water consumed
Average water consumed is computed at each node, based on node demand and
demand patterns [18]. The metric can be computed using the
average_water_consumed method.
Population impacted
As stated above, population that is impacted by a specific quantity can be
computed using the population_impacted method. This can be applied to
water quality metrics.
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13.4 Water security metrics
Water security metrics quantify potential consequences of contamination scenarios. These metrics are documented
in [18]. Water security metrics included in WN'I'R are listed in Table 12.
Table 12: Water Security Resilience Metrics
Metric
Description
Mass consumed
Mass consumed is the mass of a contaminant that exits the network via node
demand at each node-time pair [18]. The metric can be computed using the
mass_contaminant_consumed method.
Volume consumed
Volume consumed is the volume of a contaminant that exits the network via node
demand at each node-time pair [18]. A detection limit can be specified. The metric
can be computed using the volume_contaminant_consumed method.
Extent of contamination
Extent of contamination is the length of contaminated pipe at each node-time pair
[18]. A detection limit can be specified. The metric can be computed using the
extent_contaminant method.
Population impacted
As stated above, population that is impacted by a specific quantity can be computed
using the population_impacted method. This can be applied to water security
metrics.
13.5 Economic metrics
Economic metrics include network cost and greenhouse gas emissions. Economic metrics included in WNTR are
listed in Table 13.
Table 13: Economic Resilience Metrics
Metric
Description
Network cost
Network cost is the annual maintenance and operations cost of tanks, pipes,
vales, and pumps based on the equations from the Battle of Water Networks
II [14]. Default values can be included in the calculation. Network cost can
be computed using the cost method.
Greenhouse gas emissions
Greenhouse gas emissions is the annual emissions associated with pipes
based on equations from the Battle of Water Networks II [14]. Default
values can be included in the calculation. Greenhouse gas emissions can be
computed using the ghg_emissions method.
Pump operating energy and cost
The energy and cost required to operate a pump can be computed using the
pump_energy method. This uses the flowrates and pressures from
simulation results to compute pump energy and cost.
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14 Stochastic simulation
Stochastic simulations can be used to evaluate an ensemble of hydraulic and/or water quality scenarios. For
disaster scenarios, the location, duration, and severity of different types of incidents can be drawn from
distributions and included in the simulation. Distributions can be a function of component properties (i.e., age,
material) or based on engineering standards. The Python packages Numpy and Scipy include statistical
distributions and random selection methods that can be used for stochastic simulations.
For example, the following code can be used to select N unique pipes based on the failure probability of each pipe:
N = 2
failure_probability - { 'pipel' : 0.10, ' pipe2 ' : 0.20, 'pipe3': 0.25, "pipe4": 0.15,
ฆpipeS': 0.30}
pipes_to_fail = np.random.choice(failure_probability.keys(), N, replace False,
p=failure_probability,values())
The example stochastic_simulation.py runs multiple realizations of a pipe leak scenario where the location and
duration are drawn from probability distributions.
14.1 Fragility curves
Fragility curves are commonly used in disaster models to define the probability of exceeding a given damage state
as a function environmental change. Fragility curves are closely related to survival curves, which are used to define
the probability of component failure due to age. To estimate earthquake damage, fragility curves are defined as a
function of peak ground acceleration, peak ground velocity, or repair rate. The American Lifelines Alliance report
[1] includes seismic fragility curves for water network components. Fragility curves can also be defined as a
function of flood stage, wind speed, and temperature for other types of disasters.
Fragility curves can have multiple damage states. Each state should correspond to specific changes to the network
model that represent damage, for example, a major or minor leak. Each state is defined with a name (i.e., 'Major,'
'Minor'), priority (i.e., 1, 2, where higher numbers = higher priority), and distribution (using the Scipy Python
package). The distribution can be defined for all elements using the keyword 'Default,' or can be defined for
individual components. Each fragility curve includes a 'No damage' state with priority 0 (lowest priority).
The example fragility_curves.py uses fragility curves to determine probability of failure:
from scipy.stats import lognorm
FC = wntr,scenario,FragilityCurve ()
FC.add_state('Minor', 1, {'Default'
lognorm
0.5, scale==-Q .
>) })
FC.add_state('Major', 2, {'Default'
lognorm
0.5, scale==-0 .
?) })
Figure 12 illustrates a fragility curve based on peak ground acceleration with two damage states: Minor damage
and Major damage. For example, if the peak ground acceleration is 0.5 at a specific junction, the probability of
exceeding a Major damage state 0.25 and the probability of exceeding the Minor damage state is 0.85. For each
stochastic simulation, a random number is drawn between 0 and 1. If the random number is between 0 and 0.25,
the junction is assigned Minor damage. If the random number is between 0.25 and 0.85, then the junction is
assigned Major damage. If the random number is between 0.85 and 1, then the junction is assigned No damage.
After selecting a damage state for the junction, the network should be changed to reflect the associated damage.
For example, if the junction has Major damage, a large leak might be defined at that location.
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Fragility curve
Minor
Major
Peak Ground Acceleration (g)
Figure 12: Example fragility curve.
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15 Copyright and license
The WNTR Python package is copyright through Sandia National Laboratories. The software is distributed under
the Revised BSD License. WNTR also leverages a variety of third-party software packages, which have separate
licensing policies.
15.1 Copyright
Copyright 2015-2017 Sandia Corporation.
Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
the U.S. Government retains certain rights in this software.
15.2 Revised BSD license
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Sandia National Laboratories, nor the names of
its contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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16 Software quality assurance
The following section includes information about the WNTR software repository, software tests, documentation,
examples, bug reports, feature requests, and ways to contribute.
16.1 GitHub repository
WNTR is maintained in a version controlled repository. WNTR is hosted on US EPA GitHub organization at
https://github.coni/USEPAAVNTR.
16.2 Software tests
WNTR includes continuous integration software tests that are run using Travis CI. The tests are run each time
changes are made to the repository. The tests cover a wide range of unit and integration tests designed to ensure
that the code is performing as expected. New tests are developed each time new functionality is added to the code.
Testing status (passing/failed) and code coverage statistics are posted on the README section at
https://github.coni/USEPA/WNTR.
Tests can also be run locally using the Python package nose. For more information on nose, see
http://nose.rea.dtliedocs.io/. nose comes with a command line software tool called nosetests. Tests can be run in the
WNTR directory using the following command:
nosetests -v with-coverage cover-package=wntr wntr
16.3 Documentation
WNTR includes a user manual that is built using the Read the Docs service. The user manual is automatically
rebuilt each time changes are made to the code. The documentation is publicly available at
http://wnti.readtliedocs.io/. The user manual includes an overview, installation instructions, simple examples, and
information on the code structure and functions. WNTR includes documentation on the API for all public
functions, methods, and classes. New content is marked Draft.
16.4 Examples
WNTR includes examples to help new users get started. These examples are intended to demonstrate high level
features and use cases for WNTR. The examples are tested to ensure they stay current with the software project.
16.5 Bug reports and feature requests
Bug reports and feature requests can be submitted to https://github.com/USEPA/WNTR/issues. The core
development team will prioritize and assign bug reports and feature requests to team members.
16.6 Contributing
Software developers, within the core development team and external collaborators, are expected to follow standard
practices to document and test new code. Software developers interested in contributing to the project are
encouraged to create a Fork of the project and submit a Pull Request using GitHub. Pull requests will be reviewed
by the core development team.
Pull requests must meet the following minimum requirements to be included in WNTR:
Code is expected to be documented using Read the Docs.
Code is expected to be sufficiently tested using Travis CI. Sufficient is judged by the strength of the test and
code coverage. 80% code coverage is recommended.
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Large files (> 1Mb) will not be committed to the repository without prior approval.
Network model files will not be duplicated in the repository. Network files are stored in examples/network
and wntr/tests/networks_for_testing only.
16.7 Development team
WNTR was developed as part of a collaboration between the United States Environmental Protection Agency
National Homeland Security Research Center, Sandia National Laboratories, and Purdue University. See
https://github.coni/USEPAAVNTR/graphs/contributors for a list of contributors.
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17 References
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Report for the American Lifelines Alliance, ASCE (Ed.) Reston, VA: American Society of Civil
Engineers. April 2001.
[2] Awumah, K., Goulter, I., and Bhatt, S.K. (1990). Assessment of reliability in water distribution
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[3] Barker, K., Ramirez-Marquez, J.E., and Rocco, C.M. (2013). Resilience-based network component
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[4] Crowl, D.A., and Louvar, J.F. (2002). Chemical Process Safety: Fundamentals with Applications, 3
edition. Upper Saddle River, NJ: Prentice Hall, 720p.
[5] Eto, J.H., LaCommare, K.H., Larsen, P.H., Todd, A., and Fisher, E. (2012). An Examination of
Temporal Trends in Electricity Reliability Based on Reports from U.S. Electric Utilities. Lawrence
Berkeley National Laboratory Report Number 5268E. Berkeley, CA: Ernest Orlando Lawrence
Berkeley National Laboratory, 68p.
[6] Hagberg, A.A., Schult, D.A., and Swart P.J. (2008). Exploring network structure, dynamics, and
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[9] Joyner, D., Certik, O., Meurer, A., and Granger, B.E. (2011). Open source computer algebra systems,
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http://www.dhs.gov/xlibrary/assets/mac/mac_critical_inlTastructurejresilience.pdf.
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of the water networks II - Problem description. Water Distribution Systems Analysis Conference
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https://eiiips.exeter.ac.iik/iiiedia/iiniversit.yofexeter/eiiips/research/cws/downloads/
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[15] Sievert, C., Parmer, C., Hocking, T., Chamberlain, S., Ram, K., Corvellec, M., and Despouy, P.
(2016). plotly: Create interactive web graphics via Plotly's JavaScript graphing library [Software].
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[18] United States Environmental Protection Agency. (2015). Water Security Toolkit User Manual.
Washington DC: U.S. Environmental Protection Agency. U.S. Environmental Protection Agency
Technical Report, EPA/600/R-14/338, 187p.
[19] van der Walt, S., Colbert, S.C., and Varoquaux, G. (2011). The NumPy array: A structure for efficient
numerical computation. Computing in Science and Engineering, 13, 22-30.
[20] Wagner, J.M., Shamir, U., and Marks, D.H. (1998). Water distribution reliability: Simulation
methods. Journal of Water Resources Planning and Management, 114(3), 276-294.
[21] Walk, D.J., Worden, B.C., Quitoriano, V., and Pankow, K.L. (2006). Shakemap manual, Technical
manual, users guide, and software guide. United States Geologic Survey, Retrieved on April 25, 2017
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[22] xlwt contributors. (2016, November 18). xlwt documentation. Retrieved on April 25, 2017 from
https://xlwt.readtliedocs.io.
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vvEPA
United States
Environmental Protection
Agency
PRESORTED STANDARD
POSTAGE & FEES PAID
EPA
PERMIT NO. G-35
Office of Research and Development (8101R)
Washington, DC 20460
Official Business
Penalty for Private Use
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