robust design for a sustainable future
TRANSCRIPT
Robust Design for a Sustainable FutureSolar Desalination for Food and Water Security
Dr. Matthew D. StuberCoFounder and DirectorWaterFX, Inc.
Seminar Outline
• Introduction to the Problem and Motivation
• Process Design and Modeling a Solution
• Mathematical Problem Formulation
• Robust Optimization, Semi-Infinite Programming Background and Relevance
• Solution Results and Discussion
• Conclusion
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Introduction and Motivation
• CA is home to the most productive agricultural region in the US
• Most recent crop report: $54B in revenue generated
• 99% of the nation’s supply and 50% of the world’s supply of raisins come from Fresno county
• 79% of human-used water goes to agriculture
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Introduction and MotivationSalt Imbalance
• Natural processes and agricultural irrigation operations accumulate salts in the region
• 275tons/hr (2001 report rate1)
• includes materials classified hazardous
• Unique soil conditions make groundwater shallow
• Water applied to the soil saturates crop root zones, dissolving salts, and become toxic to crops
• By 2030, 15% of arable land will need to be retired, 40% on the west side of the San Joaquin Valley2
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1. CA DWR, Water Facts: Salt Balance in the San Joaquin Valley, No. 20, 20012. R. Howitt, J. Kaplan, D. Larson, D. MacEwan, J. Medellín-Azuara, G. Horner, et al., The Economic Impacts
of Central Valley Salinity, Tech. rep., University of California Davis, 2009
Introduction and MotivationSummary
• Limited and unreliable water supply
• Climate change driven drought, economic and population growth
• Irrigation causes salt accumulation in soil
• Impairs soil, environmentally hazardous, reduces productivity
• Soil salinity control produces extraordinary quantities of saltwater
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Introduction and Motivation
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2H O impurities
, ,W Q h
sulfates,nitrates, phosphate
product
biomasssalt 0 0
dm d
dt dt waste
Introduction and Motivation
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2H O impurities
, ,W Q h
sulfates,nitrates, phosphate
product
biomasssalt 0 0
dm d
dt dt waste
Process Design and Modeling a SolutionObjective
• Primary Objective: Treat the saline wastewater to very high recovery, sequester the salts, and return freshwater
• Increase the overall water-use efficiency of the sector
• Reduce and eventually eliminate salt accumulation problem (and its effects)
• Increase the production efficiency of the land through sustainable drainage management
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Process Design and Modeling a SolutionDesign Criteria and Constraints
• Flexibility: varying feed quality/chemistry
• Robust: high salinity, scaling, crystallization, corrosion
• Reduced dependence on fossil fuels and grid power, reduced emissions
• Near-zero to zero liquid discharge, solids recovery
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Process Design and Modeling a Solution
• Basis for design: multi-effect distillation
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Single greatest source of entropy generation
Process Design and Modeling a SolutionWaste-Heat Recovery
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• 10-effect MED• Heat integration with inter-stage preheating and vapor absorption
Process Design and Modeling a SolutionConcentrated Solar
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2.56 3.87 5.44 6.53 7.67 8.58 8.55 8.14 7.2 5.81 3.99 2.930
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5
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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
MONTHLY AVG DNI
DNI [kWh/m2/day]
• Single-axis tracking large-aperture parabolic trough• Vacuum tube receiver• N-S orientation
• Solar resource data input from the NREL database• Specific coordinates• 8760h/year format
Mathematical Problem FormulationModel Considerations and Assumptions
• Without a solution, retire 10% growing region by 2035 due to salt impairment
• Continue irrigation and operate agribusiness
• Desalination for drainage reuse
• Prevent growing region retirement (salt impairment)
• Reduce water footprint of agriculture
• Generate a new income source for growers (M&I sales)
• Increase water for municipal use
19Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Mathematical Problem FormulationModel Considerations and Assumptions
• Desalinate all available drainage water: 22,500 acre-ft/yr (27.75M m3/yr)
• Fixed inflation on food/ag revenues and energy prices
• Debt financing, 10y amortization, 20y project
• Optimal design of solar field and storage for natural gas offset
• Water sales at market rates (parameter)
• Uncertainty in natural gas pricing (parameter)
20Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Logical constraint:
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water gas NPV, , : 0
C S dC C F N H F f
parameter (uncertainty) space
: design sp e
:
acC
d
F
F
NPV:f
Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Parametric Optimization
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S
water
gas
no. of PTCs per module
: no. of hours of thermal storage
water contract price $/acre-ft
: natural gas price $/ b u
:
t
:
mm
H
C
N
C
*
NPV water gas NPV water gas
water
a
,
g s
, , , , )
s.t. : 13 52
: 0 12
: 1800 2200
: 6 9
( ) max (s
s
s
N HC C H C C
N n
f f
n
h h
h c
c c
N
H
C
C
Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Simple Example:
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* 2
[ 5,5]( )
[ 2
a
,2
m x[ ]
]x
f x pp
p
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Simple Example:
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* 2
[ 5,5]( )
[ 2
a
,2
m x[ ]
]x
f x pp
p
𝑥
𝑓𝑥,𝑝
=−𝑥2−𝑝
2
0
2
p
p
p
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Simple Example:
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* 2
[ 2,2] [ 5,5]maxmin [ ]
p xx p
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Simple Example:
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* 2
[ 2,2] [ 5,5]maxmin [ ]
p xx p
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Parametric Optimization
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S
water
gas
no. of PTCs per module
: no. of hours of thermal storage
water contract price $/acre-ft
: natural gas price $/ b u
:
t
:
mm
H
C
N
C
*
NPV water gas NPV water gas
water
a
,
g s
, , , , )
s.t. : 13 52
: 0 12
: 1800 2200
: 6 9
( ) max (s
s
s
N HC C H C C
N n
f f
n
h h
h c
c c
N
H
C
C
Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Min-Max formulation
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water gas
*
NPV water gas,
water
gas
,, , , )
s.t. : 13 52
: 0 12
: 1800 2200
: 6 9
min max (s
sCC N
s
Hf H C C
N n n
N
h h
c c
c c
H
C
C
Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Semi-infinite programs:
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max ( )
s.t. ( , ) 0,p
g
f
x x
p
p X
2
[ 2,2] [ 5,5]maxm [ ]in
p xx p
*
[ 2,2],2
[ 5,5]
min
s.t. max[ ]p
xx p
*
[ 2,2],2
min
s.t. 0, [ 5,5]p
x xp
Mathematical Problem FormulationRobust Optimization and Worst-Case Feasibility
• Semi-infinite program reformulation
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*
,
NPV
min
s.t. ,( ) 0,P
f Dp
p d d
water gas( , )
( , )s
C
d
C C
N H
P F
FD
p
d
*
*
*
0 robust feasibility
0 not
0 further analysis required
Stuber, M D, Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse. Renewable Energy, 89, pp 552-563, 2016.
Solution Results and DiscussionParametric Optimal Design Performance
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* 30.15%sf
* 62.91%sf
* 58.09%sf
* 65.07%sf
Solution Results and DiscussionWorst-Case Feasibility
• Solving the semi-infinite program yielded a feasible design:
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Conclusion
• The worst-case economics support investment in solar desalination for a sustainable agribusiness
• On its own, desalinated water is considered “too expensive” by farmers
• Systems-view solution and optimal design methodology make it profitable
• Results provide further support for capital investment vs. uncertain futures (e.g., pay now for renewables or risk energy market volatility)
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