# Presentation: 506431

## A New Model for Solute Mixing inPipe Junctions:Implementation of the Bulk Mixing Model in EPANET

**Clifford K. Ho and Siri Sahib S. Khalsa***Sandia National LaboratoriesAlbuquerque, NM
- *Student at the University of Virginia

***Presentation to EPA***

***Cincinnati, OH, October 11, 2007***

- Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000

## Overview

**Background**
**Introduction to Bulk Mixing Model**
**Comparisons with Experiments**
**Implementation in EPANET**
**EPANET-BAM Demonstrations**

## Background - Motivation

**Contaminant transport in water-distribution pipe networks is a growing concern**
**Mixing in junctions**
**Important for **
**Risk assessments**
**Vulnerability assessments**
**Inverse modeling (contaminant source detection, monitoring)**

## Background – Problem Statement

**Many water-distribution network models (e.g., EPANET) assume complete mixing at junctions**
**Previous studies have shown incomplete mixing in pipe junctions (experimental and computational)**
**van Bloemen Waanders et al. (2005)**
**O’rear et al. (2005)**
**Ho et al. (2006)**
**Romero-Gomez et al. (2006)**
**Webb and van Bloemen Waanders (2006)**
**McKenna et al. (2007)**

**from Orear et al. (2005)**

## Objectives

**Conduct physical and numerical simulations of contaminant transport in pipe junctions**
**Understand impact of parameters and processes on mixing behavior**
**Different flow rates**
**Effective mass transfer at impinging interface**
**Develop improved mixing models and incorporate into EPANET**

## Overview

**Background**
**Introduction to Bulk Mixing Model**
**Comparisons with Experiments**
**Implementation in EPANET**
**EPANET-BAM Demonstrations**

## Mixing in Pipe Junctions

**Bulk advective mixing caused by different flow rates**

**Turbulent mixing caused by instabilities at the impinging interface**

**(Webb and von Bloemen Waanders, 2006)**

**(Ho et al., 2006)**

## Bulk Mixing Model(Ho, 2007, J. Hydraulic Engr. in review)

**Honors conservation of momentum in the flow streams**

## Bulk Mixing Model

**Neglects mixing from turbulent instabilities**
**Provides lower bound to the amount of mixing that can occur in junctions**
**Complements the complete-mixing model in EPANET, which provides an upper bound to the amount of mixing that can occur in junctions**
**A scaling (mixing) parameter, 0 ****≤ s ≤ 1,**** can be used to combine the results of the bulk-mixing and complete-mixing models for more accurate estimation**
***C******combined***** = *****C******bulk***** + *****s***** (*****C******complete***** – *****C******bulk*****) **
**s = 0 (bulk mixing model)**
**s = 1 (complete mixing model)**

## Overview

**Background**
**Introduction to Bulk Mixing Model**
**Comparisons with Experiments**
**Implementation in EPANET**
**EPANET-BAM Demonstrations**

## Single-Joint Tests(Orear et al., 2005, Romero et al., 2006, McKenna et al., 2007)

**Cross-Joint**

## Single Cross-Joint Tests(Ho, 2007, J. Hydraulic Engr. in review)

- Note: Outlet flows equal

## Single Cross-Joint Tests(Ho, 2007, J. Hydraulic Engr. in review)

- Note: Inlet flows equal

## Multi-Joint Tests(3x3 Small-Scale Network, Orear et al., 2005)

**3x3 array of cross joints with 3-foot pipe lengths**
**Flow rates at inlets and outlets controlled**
**Pipe diameter:  0.5”**

## 3x3 Network Tests

## 3x3 Network Tests

## Mixing Parameter, s
0 ≤ s ≤ 1 (bulk mixing  complete mixing) bounds data
Dependence on junction geometry and fitting
Flush vs. press fit (expansion in junction)
s ~ 0.2 – 0.5 (for most flow ratios)
Network results
3x3 network
Diamond (converging) network
s ~ 0.4 – 0.5 (for most boundaryconditions and flow rates)

**0 ****≤ s ≤ 1 (bulk mixing ******** complete mixing) bounds data**
**Dependence on junction geometry and fitting**
**Flush vs. press fit (expansion in junction)**
**s ~ 0.2 – 0.5 (for most flow ratios)**
**Network results**
**3x3 network**
**Diamond (converging) network**
**s ~ 0.4 – 0.5 (for most boundary****conditions and flow rates)**

**Experimental Findings**

- Diamond converging network with 7 sequential cross junctions (SNL - M. Aragon, J. Wright, S. McKenna)

## Overview

**Background**
**Introduction to Bulk Mixing Model**
**Comparisons with Experiments**
**Implementation in EPANET**
**EPANET-BAM Demonstrations**

## EPANET-BAM Features(Bulk Advective Mixing)

**Fully compatible with EPANET 2.0**
**New versions of ‘Epanet2w.exe’ and ‘epanet2.dll’**
**GUI fully compatible**
**Mixing parameter can be adjusted at each junction**
**“****Valid” cross junctions are analyzed with bulk-mixing model**

## Mixing Parameter Storedin Input File

## EPANET-BAMValidation

**EPANET-BAM**

## EPANET-BAM Applications

**Hydraulic and water quality simulations with incomplete mixing at junctions (bulk mixing, s < 1)**
**Steady and transient**
**Bounding calculations for risk assessments**
**s=0, s=1**
**Integration with PEST (Parameter ESTimation Software; **_**[www.sspa.com](http://www.sspa.com/pest/)**__**[/pest/](http://www.sspa.com/pest/)**_**)**
**Calibration of mixing parameter at one or more junctions based on available concentration data**
**Contaminant source detection with sparse data**

## Implementation Issues

**Only cross junctions with adjacent inlets (and outlets) are currently analyzed for bulk mixing**
**All other junction configurations are assumed to yield complete mixing**

## Alternative Implementation of Incomplete Mixing in EPANET

**Can use regressions based on empirical or numerical data to correlate incomplete mixing with different flow rates at each junction**
**Collaboration with U. Arizona (Prof. Chris Choi)**
**Romero et al. (2006, WDSA), Austin et al. (2007, J. Water Resources Planning & Management)**
**Requires lots of data**
**Assumes simulated junctions are identical to those used to derive regressions**
**Corrosion products, different geometries, etc. may change mixing behavior**

## Overview

**Background**
**Introduction to Bulk Mixing Model**
**Comparisons with Experiments**
**Implementation in EPANET**
**EPANET-BAM Demonstrations**

## EPANET-BAM Demonstrations

**Exercise 1:  Steady contamination**
**Exercise 2:  Transient contamination**
**Exercise 3:  Source Detection**
**Exercise 4:  Gideon Network**

## Exercise 1Steady-State Contamination Scenario

- Note: simulated network is an up-scaled replica of a smaller network tested in the laboratory

**1000 mg/L of Chemical X enters the network through *****Contaminant Inlet***** **
**Predict the concentration of Chemical X at each neighborhood after the contaminant has spread completely throughout the network, assuming:**
**Complete mixing in cross junctions**
**Incomplete mixing (mixing parameter = 0.5) in cross junctions**
**Compare these predictions to laboratory measurements **

## Exercise 1Predicted Concentration Distributions

**Incomplete (Bulk) Mixing Model (s=0.5)**

**Complete Mixing Model**

## Exercise 1Concentration Differences

## Exercise 1Comparison to Laboratory Experiments

## Exercise 1Risk Assessment

**Each neighborhood is populated by 100 people, each of whom weighs 60kg**
**Assume each person consumes 2L of water per day**
**The lethal dose response curve of Chemical X is shown in Fig 2**
**Predict the number of deaths that will occur in each neighborhood after one day, assuming:**
**Complete mixing in cross junctions**
**Incomplete (bulk) mixing (mixing parameter = 0.5) in cross junctions**** **

## Exercise 1Risk Assessment: Complete Mixing

| Neighborhood | Concentration (mg/L) | Mass of X Ingested per Person per Day (mg) | Dose (mg/kg) | Predicted Mortality (%) | Predicted Deaths |
| --- | --- | --- | --- | --- | --- |
| N1 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N2 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N3 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N4 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N5 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N6 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N7 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N8 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N9 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N10 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N11 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
| N12 | 554.55 | 1109.10 | 18.49 | 5.97% | 5 |
|  |  |  |  |  |  |
|  |  |  |  | Predicted Death Toll: | 60 |

## Exercise 1Risk Assessment: Incomplete Mixing (s=0.5)

| Neighborhood | Concentration (mg/L) | Mass of X Ingested per Person per Day (mg) | Dose (mg/kg) | Predicted Mortality (%) | Predicted Deaths |
| --- | --- | --- | --- | --- | --- |
| N1 | 721.59 | 1443.18 | 24.05 | 50.66% | 50 |
| N2 | 777.27 | 1554.54 | 25.91 | 72.20% | 72 |
| N3 | 387.50 | 775.00 | 12.92 | 0.39% | 0 |
| N4 | 665.91 | 1331.82 | 22.20 | 28.87% | 28 |
| N5 | 777.27 | 1554.54 | 25.91 | 72.20% | 72 |
| N6 | 443.18 | 886.36 | 14.77 | 0.98% | 0 |
| N7 | 777.27 | 1554.54 | 25.91 | 72.20% | 72 |
| N8 | 331.82 | 663.64 | 11.06 | 0.15% | 0 |
| N9 | 331.82 | 663.64 | 11.06 | 0.15% | 0 |
| N10 | 777.27 | 1554.54 | 25.91 | 72.20% | 72 |
| N11 | 331.82 | 663.64 | 11.06 | 0.15% | 0 |
| N12 | 331.82 | 663.64 | 11.06 | 0.15% | 0 |
|  |  |  |  |  |  |
|  |  |  |  | Predicted Death Toll: | 366 |

## EPANET-BAM Demonstrations

**Exercise 1:  Steady contamination**
**Exercise 2:  Transient contamination**
**Exercise 3:  Source Detection**
**Exercise 4:  Gideon Network**

## Exercise 2Transient Contamination

**Consider the water distribution network subdomain of Exercise 1**
**In order to account for fluctuating demands throughout the day, the city adjusts the flow rates through the *****Outlet***** and the *****Contaminant Inlet***** every hour**
**Assume the flow adjustment pattern repeats itself**
**Assume the contamination of *****Contaminant Inlet *****occurs at 5 am.  Predict the concentration of Chemical X at neighborhoods N1, N6, and N11 at every hour over the 24 hours following the contamination event, assuming:**
**Complete mixing in cross junctions**
**Incomplete (bulk) mixing (mixing parameter = 0.5) in cross junctions **

## Exercise 2Transient Concentrations at N1, N6, and N11

## Exercise 2Concentration Differences

## Exercise 2Transient Risk Assessment

**As in Exercise 1, assume each neighborhood is populated by 100 people, each of whom weighs 60kg**
**Assume each person consumes 1/6 L of water per hour (2 L in 12 hours) and that a dose of Chemical X accumulates over 12 hours**
**Predict the number of deaths that will occur in each neighborhood due to ingestion of contaminated water from 8 am to 8 pm, assuming:**
**Complete mixing in cross junctions **
**Incomplete (bulk) mixing (mixing parameter = 0.5) in cross junctions**

## Exercise 2Transient Risk Assessment Results

|  |   | Complete Mixing |   |   | Incomplete (Bulk) Mixing (s=0.5) |   |
| --- | --- | --- | --- | --- | --- | --- |
| Neighborhood | Dose per person (mg/kg) | Predicted Mortality (%) | Predicted Deaths | Dose per person (mg/kg) | Predicted Mortality (%) | Predicted Deaths |
| N1 | 13.99 | 0.67% | 0 | 18.67 | 6.51% | 6 |
| N2 | 14.00 | 0.67% | 0 | 20.10 | 12.45% | 12 |
| N3 | 13.99 | 0.67% | 0 | 9.17 | 0.06% | 0 |
| N4 | 14.00 | 0.67% | 0 | 17.05 | 3.01% | 3 |
| N5 | 12.59 | 0.33% | 0 | 18.43 | 5.80% | 5 |
| N6 | 14.00 | 0.67% | 0 | 10.96 | 0.15% | 0 |
| N7 | 12.59 | 0.33% | 0 | 18.43 | 5.80% | 5 |
| N8 | 14.00 | 0.67% | 0 | 7.91 | 0.03% | 0 |
| N9 | 12.59 | 0.33% | 0 | 6.75 | 0.02% | 0 |
| N10 | 12.59 | 0.33% | 0 | 18.43 | 5.80% | 5 |
| N11 | 12.59 | 0.33% | 0 | 6.75 | 0.02% | 0 |
| N12 | 12.59 | 0.33% | 0 | 6.75 | 0.02% | 0 |
|  |  |  |  |  |  |  |
|  |  | Predicted Death Toll / 12 hours: | 0 |  | Predicted Death Toll / 12 hours: | 36 |

## EPANET-BAM Demonstrations

**Exercise 1:  Steady contamination**
**Exercise 2:  Transient contamination**
**Exercise 3:  Source Detection**
**Exercise 4:  Gideon Network**

## Exercise 3Source Detection

**Exercise 3****Source Detection**

**Consider the steady-state water distribution network subdomain of Exercise 1.  After the contaminant spreads completely throughout the network, residents report that the municipal water has a strange taste and smell. **
**In response to the complaints, city officials take two water samples, one from N1 and the other from N11, for analysis.  Chemical X is detected in the following concentrations*:**
**N1: 747.92 mg/L**
**N11: 319.73 mg/L**
**Determine the source node and the source concentration, assuming:**
**Complete mixing in cross junctions**
**Incomplete (bulk) mixing (mixing parameter = 0.5) in cross junctions**** **

- *Concentrations correspond to laboratory measurements from a down-scaled replica of the simulated network

## Exercise 3Source Detection Results

**Exercise 3****Source Detection Results**

**Each node in the network was simulated as a potential source and optimized for a source concentration in the range 0-2000mg/L using EPANET-BAM and PEST**
**The nodes are listed in increasing order of the objective function, “phi” (the sum of squared weighted residuals)**
**Only the first 10 nodes on these lists are listed in the tables below**
**Recall that the ****actual source was at “TracerIn” at 1000 mg/L**

## EPANET-BAM Demonstrations

**Exercise 1:  Steady contamination**
**Exercise 2:  Transient contamination**
**Exercise 3:  Source Detection**
**Exercise 4:  Gideon Network**

## Exercise 4Gideon Network

**Municipal water network in Gideon, MO (1993, pop. 1100)**
**Bird feces in “Tank 300” was believed to be source of *****Salmonella***** contamination**
**Due to reports of bad taste and smell, city decided to flush network through hydrants, releasing contaminated water from tank**

- (courtesy of L. Chandrasekaran, R. Herrick, R. Clark)

## Exercise 4“Tank 300 Demands”

## Exercise 4Model Comparisons – Junction 185 (Nursing Home)

## Exercise 4Model Comparisons – Junction 41 (Schools)

## Summary and Next Steps

## Summary

**Bulk Advective Mixing (BAM) Model**
**Allows incomplete mixing at pipe junctions**
**Provides lower bound**
**Complements existing complete-mixing model for bounding calculations**
**EPANET-BAM implements new model**
**Mixing parameter ****(0 ****≤ s ≤ 1) can be applied to any junction**
**Values of s ~ 0.2-0.5 yielded good matches to data**
**All EPANET features functional with new model**
**Integration with PEST allows calibration and optimization (e.g., source detection)**

## Next Steps

**Use EPANET-BAM to guide development of network experiments**
**Compare results with storage and transients**
**Demonstrate capability to calibrate and/or optimize parameters (e.g., source detection, monitoring)**
**Develop bulk mixing models for other junction configurations**
**Incorporate BAM into EPANET-MSX?**
**Release EPANET-BAM?**

## Acknowledgments

**Modeling**
**Steve Webb (SNL), Bart Van Bloemen Waanders (SNL), Glen Hammond (SNL), Pedro Romero (U. Arizona), Chris Choi (U. Arizona)**
**Testing**
**Lee O’Rear, Jr. (SNL), Jerome Wright (SNL), Malynda Aragon (SNL), Sean McKenna (SNL), Ryan Austin (U. Arizona), Chris Choi (U. Arizona)**
**Management**
**Ray Finley (SNL), Amy Sun (SNL)**