PBMO: The Comprehensive Physics-Based Flow, Transport, and Management Optimization

Tool-kit*Larry M. Deschaine, Peter Huyakorn, Varut Guvanasen, and

Theodore Lillys

Presented at the NDIA: Environment, Energy, & Sustainability Symposium & Exhibition

Colorado Convention Center Denver, CO June 14th – 17th, 2010.

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Presentation Outline

Optimization Benefits Introduction to Physics-Based Modeling

Optimization (PBMO) and Applicability PBMO Medallion Methodology and

Implementation HTRW, Water Resources and Energy

Application Examples Benefits to Restoration Programs Summary and Conclusions

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Why Optimization?

Increased Reliability

Increased Stakeholder Confidence

Accelerated Site Closure

Reduced Project Performance Risk

Results in Cost Savings and Minimizing Long-term Liabilities

PBMO maintains or improves stakeholder required level of certainty

by employing best designs and analysis.

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PBMO MedallionTM Approach

Approach

Structured and Produces Credible Solutions

Systematically Integrates Optimization Algorithms and Physics-Based Models

• Realistic Capturing of Important Site Physics, Financial Constraints and uses Effective Optimization Methods

Systematic Integration and Coherent Interpretation of Disparate Site Data Using all Relevant Information

Benefits:

Optimal Solutions Honor Site Physics; Transparent and Reviewable

Results in Updated Real-time Estimates of System Performance with Quantified Knowledge Uncertainty

Considers Availability of Project Funds

• Optimal Strategies Maximize Return for the Dollar

PBMO Medallion technology enables professionals

Optimization Specification Input

Modeling Requirement Input

Scenario Specification Input

System Performance Prediction

Optimal

Decision

Strategy

PBMO Medallion™ Coupling Concept

Stakeholders

Graphical

User

Interface

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MedallionTM-Environmental Remediation System (ERS) Optimization Applicability

HTRW Sites:• Plume Delineation (PD) and Long Term

Monitoring (LTM): Finding, tracking and LTM optimization

(LTMO)• Remedial Design (RD) Optimization:

New or Remedy-in-place (RIP) optimization• Source Finding (SF):

LNAPL and DNAPL

PBMO code has modular design, produces investment grade solutions, and has

applicability at any stage in the CERCLA Process

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Sitewide ERS Optimization Tool kit

See Deschaine, L. M., 2008. Simulation and Optimization of Large Scale Subsurface Environmental Impacts: Investigations, Remedial Design and Long Term Monitoring. WM2008 Conference, February 24th – February 28th, 2008, Phoenix, AZ and references therein.

DNAPL Source Finding

Provides optimal estimate of source location.

Combines physics-based models and human insight

Critical for ensuring the proper areas are investigated and remediated

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MedallionTM Water Resources Support (WRS) Tool-kit Optimization Applicability

Water supply systems Design of hydraulic structures

• Reservoirs• Dams• Levees• Pump storage

Selection of alternative water resource management options• Control of salt water intrusion in coastal aquifers• Watershed and groundwater source allocation, distribution and reuse• Well field design and operation• Design of water quality monitoring networks• Thermal distribution and impacts

Renewable energy• Integrated hydropower energy generation and resource planning• Solar salt ponds

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MedallionTM-ERS and WRS Tools, Models and Algorithms

Top Half of Medallion:

Optimization: Lipschitz Global

Optimization (LGO) HGL_Opt Outer Approximation (OA) Kalman Filter (KF) Linear Programming (LP) Heuristic / Evolutionary

Genetic Algorithms (GA) Evolutionary Strategies Tabu Search Simulated Annealing

Bottom Half of the Medallion

Physics-based Fate &Transport models: MODFLOW-SurFact MODHMS PTC, UTCHEM MODFLOW-MT3DMS HEC Family of codes

MEC (Inversion) Geophysical Data Fusion

Machine Learning Response Function-writers Equation-writers

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PBMO’s modular design facilitates linking the appropriate physics-based

simulator with the best global optimization algorithm(s). This combination is then

used to develop a credible optimal strategy.

PBMO Application Flow Chart

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Phase 1: Feasible Optimal Solution

Analysis & Review

Phase 2: PBMO Implementation

Process follows EPA and Industry Optimization Standards and Guidelines

Global Optimization

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Global Minimum

A Local Minimum

Illustrative Objective Function (Response Surface) and Decision Variables. The feasible set is the 2-D rectangle formed by the range of the decision variables, the objective (cost) function f(x) is theheight of the response surface

The objective of global optimization is to find the absolutely best solution, in the possible presence ofa multitude of local sub-optimal solutions.

Cost of Decision: f(x)

LGO Solver Suite for Nonlinear Optimization

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LGO is a suite of global and local nonlinear optimization methods in an integrated framework

Global search methods (solver options):• Continuous branch-and-bound• Adaptive random search: single-start or multi-start• Exact penalty function applied in global search phase• Mixed integer nonlinear model: extension in progress

Local optimization follows from:• Best global-search based point(s)• User-supplied initial point• Optimization by the generalized reduced gradient method

Key reference: Pintér (1996) Global Optimization in Action”, KluwerAP / Springer monograph and later works

Lipschitz Global Optimization

General model formulation:

Minimize the objective function f(x)

Subject to the constraints x D :={xl x xu; g(x) 0}

Lipschitz continuity:

• The slope (variability) of the function values is bounded with respect to the system input variables (x)

Key generic feature of our optimization models and solvers:

• For all “reasonable” model input arguments the model function values can be computed

• LGO does not require higher-order model function information

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Global Optimization Using LGO

An example: Complex response function successfully solved by LGO

LGO is able to analyze and to solve complex nonlinear models, under minimal analytical assumptions.

Computable values of continuous or Lipschitzmodel functions are needed only, without requiring access to higher-order information

handled by LGO.

Broad application scope meets the

needs of real-world optimization

“Theorists interested in optimization have been too willing to accept the legacy of

the great eighteenth and nineteenth century mathematicians who painted a clean world of [linear, or convex]

quadratic objective functions, ideal constraints and ever present derivatives.

The real world of search is fraught with discontinuities, and vast multi-modal, noisy search spaces...”

D. E. Goldberg, genetic algorithms pioneer

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Objective Function Surface:Umatilla Case 2

Top Surface View View of Bottom of Surface

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Using MODFLOW-SF, HGL developed an analysis of the Umatilla case used in the ESTCP Optimization Study. The objective function surface is presented above. Random search produced as good a remedial design as the published GA solution.

Cost

In

creasi

ng

Cost

Incre

asin

g

PBMO-ERS Application Examples

With Focus on HTRW Sites

Example 1: Anniston Army Depot, Anniston, AL

Site Details: Army Base whose operations released waste materials into the public drinking water aquifer

Focus Issue: DNAPL source with TCE diffusion in fractured rock matrix

• Complex karstic hydrogeology• Remediation time frame estimate

> 100 years

Objective: • Optimize LTM program

PBMO Medallion-ERS Tool-box:• Top Half: Kalman Filter,

geostatistics, GA• Bottom Half:

Regional Model: MODFLOW Focused model: PTC

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Long Term Monitoring Well Optimization Results

Stakeholder Reviews:• Stakeholder group comprised of representatives from EPA, State of

Alabama, community, COE and AEC

PBMO Result:• Number of groundwater monitoring well samples per year reduced from

119 to 41 • Recommendation implemented and performing as designed since 2004

Acceptance:Analyses and conclusions were accepted by EPA and State regulators

ROI Cost Savings:• Cost of Analysis (Incremental): $50K• Savings to date: $2.76M• Previous sampling program

119 samples/yr ($842K/yr or NPV = $17.5M at 5% discount rate)• Optimized sampling program

41 Samples/year ($290K/yr or NPV = $6.04M at 5% discount rate)• ROI: 229:1

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Example 2: DOE Pantex Plant, Amarillo, TX

Site Details: Nuclear Material Plant. Processing wastewaters entered the subsurface environment

Focus Issue: TCE detection in the sole source Ogallala Aquifer upgradient of public well field

Objective: • Evaluate if existing monitoring

well network sufficient for TCE migration detection

• Prepare Contingency Remedial Design; train site personnel on use

PBMO Medallion-ERS Tool-box:• Top Half:, Outer Approximation,

Kalman Filter, geostatistics• Bottom Half:

Regional Model: MODFLOW-SF Focused model: PTC

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TCE Monitoring Well Assessment for the Ogallala Aquifer TCE Detection

Stakeholder Reviews:• Independent Review Team Recommends formation of Technical Advisory

Group • Technical Advisory Group Formed, includes Plant Personnel, University

Representatives, Regulators, Stakeholders and Industrial Representatives• TAG Unanimously Recommends what has become the PBMO Medallion Tool

for Plant Evaluation (Risk Assessment & Corrective Measures Study)• Application of Plume Delineation module initiated

PBMO Result: The plume delineation technology assessed that:• The existing MW network reduced uncertainty by 93.4%. Optimal by 98%• Only 1-2 additional optimally located wells required versus the initial 6-12

deep (~ 600 ft) wells envisioned by the stakeholders

Acceptance: All analyses and conclusions were accepted by DOE, EPA and State regulators

• High confidence in analyses

ROI Cost Savings:• Cost of Analysis: $96K.• Well avoidance costs: $2M• ROI: 20:1

Similar analysis performed for RDX issue for potential migration of RDX from perched water to Ogallala, similar acceptability results

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Example 3: Standard Chlorine of Delaware

EPA Region III National Priority List (NPL) Superfund Site

Investigation, chemical removal, and remediation costs to date: over $100M

IssuesOver 570,000 gallons of chlorobenzenes released

Natural attenuation not a viable option

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Optimization Approach:Hydraulic Gradient Flow Control

General Concept:

• The selection of a design strategy that minimizes (or maximizes) an objective function while satisfying specified design constraints (constrained optimization)

• The objective function and the constraint equations are defined in terms of decision variables

• When the objective function and the constraint equations are linear in terms of the decision variables, then the problem is a linear programming (LP) problem

• When the objective function or the constraint equations are non-linear in terms of the decision variables, then the problem is a non-linear programming (NLP) problem

• NLP models are most typical in the area of remediation design unless strong simplifying (modeling) assumptions are made

• In generic simulation and optimization approach as a rule leads to NLP and mixed integer (MI) NLP

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Optimization Problem Formulation

Goal is to contain the chlorobenzenes at least cost (minimum) by pumping from extraction wells

Subject to:Total flow rate less than existing treatment plant capacity of 95 gpm

Inward hydraulic gradients where specified

Upward hydraulic gradients specified within entire area surrounded by slurry wall

Dashed line: specification region for

gradient control constraints

Extraction well location

(Containment Wall)

Example 4: Integrated Groundwater-Surface Water Simulation and Management Optimization Tools

Primary Challenges

• Interaction of surface and subsurface flow systems over a basin

• Drought and land surface subsidence

• Wetlands and ecosystem health

• Water quality

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Candidate Scenarios for Optimization of Regional Water Resources

Quantify spatial/temporal distribution of subsurface recharge, surface-subsurface interactions in streams and wetlands

Impacts of subsurface water extraction on surface water

Effects of urbanization/land-use/climate change on water quantity & quality, health of aquatic ecosystems

Restoration of adversely-impacted streams, wetlands, etc.

Subsurface versus overland

migration pathways of

contaminants & pathogens26

Examples 5 & 6: Energy and the EnvironmentIntegrated Simulation and Optimization

Power Grid Performance Optimization (2009)

Global Energy Transition Model (2010+)

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Simulation / optimization of integrated systems with transmission constraints,

resource distance from point of use, and water, energy, agriculture and transportation synergies and competition

Example 7: When Models are not Available: Derive Functions Using Machine Learning

Inputs

Site-specific inputs include any aspect deemed important by the design team

Genetic programming (GP) is utilized to uncover the relationships necessary to understand the process

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1 2 3 4 5 6 7 8 9

Ax

is T

itle

Axis Title

Chart Title

Target

Model

Rank-ordered data

% C

onta

min

ant

Resp

onse

Actual vs. GP Model Predictions

Bioremediation Response: Predictive Model Code

Complete Model Code (developed in Fortran):

Model Attributes & Value Developed using GP Procedure

• Inductive algorithms design program structure and constants concurrently

• Provides important inputs• Provides an understandable

relationship for peer review and acceptability

Predictive module can be used as stand-alone or incorporated into flow and transport model

LGO is used to optimize the estimates of the model parameters, the system performance and decisions

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real function model(d)

real, intent(in) :: d(0:18)

real, parameter :: G1C0 = 2.450073real, parameter :: G1C1 = -1.999177real, parameter :: G2C0 = 9.462036real, parameter :: G2C1 = 6.572907real, parameter :: G3C0 = -3.264129real, parameter :: G3C1 = -3.080017real, parameter :: G4C0 = -5.827912real, parameter :: G4C1 = -5.046691

real :: varTempvarTemp = 0.0

varTemp = ((d(7)/d(14))-(log(d(16))-d(0)))varTemp = varTemp + (((d(13)+d(13))-

(((d(16)*G2C1)+(d(18)*G2C0))*d(17)))**(1.0/3.0))varTemp = varTemp + (G3C0/d(5))varTemp = varTemp + ((G4C0/d(14))-(d(2)-d(0)))

model = varTemp

end function model(d)

GP derived

relationship

Converts to mathematical equation for

interpretation, acceptance, or refinement

Benefits to Restoration Programs

Summary and Conclusions

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Benefits

PBMO Medallion-ERS & WRS provides solutions applicable for both groundwater and surface water issues including energy and carbon footprint analysis

The integrated physics-based optimization approach considers more relevant factors than any previous technology

PBMO Medallion-ERS & WRS applies to all sites, contaminants, and impacts that the community needs to address

PBMO Medallion-ERS & WRS incorporates a graded approach - only applications with sufficient ROI is warranted/conducted

On a site basis, cost savings resulting from optimization will vary depending on tool applicability. Results have ranged from $2.4M to $20M+

Summary and Conclusions

Optimal Physics-Based Solutions:

• Transparent, defensible, and peer reviewable.

• Documented cost savings concurrent with increased stakeholder confidence.

• FOS ensures PBMO used only when merited value warrants application

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Additional References

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Deschaine, L. M., Simulation and Optimization of Subsurface Environmental Impacts; Investigations, Remedial Design and Long Term Monitoring of BioNAPL Remediation Systems, Chapter 9, in In-Situ Bioremediation of Chlorinated Ethene DNAPL Source Zones: Case Studies, Prepared by The Interstate Technology and Regulatory Council, Bioremediation of Dense Non-Aqueous Phase Liquids (Bio DNAPL) Team, 2007. www.itrcweb.org/Documents/bioDNPL_Docs/BioDNAPL-2.pdf

Deschaine, L. M., Simulation and Optimization of Large Scale Subsurface Environmental Impacts; Investigations, Remedial Design and Long Term Monitoring. Journal of "Mathematical Machines and Systems", National Academy of Sciences of Ukraine, Kiev. No 3, 4. 2003. Pages 201-218. http://www.immsp.kiev.ua/publications/eng/2003_3_4/index.html

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Thanks for your attention!

Questions and comments welcome.

Please contact us for further information:

ldeschaine@hgl.com

+1 (703) 663-0064