Robust Design for a Sustainable Future

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

2

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

3

Introduction and MotivationCalifornia’s Unprecedented Drought

June 2014 June 2015 June 2016

4

Introduction and MotivationSalt Imbalance

5

accumulation = in – out + generation - consumption

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

6

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

7


8

2H O impurities

, ,W Q h

sulfates,nitrates, phosphate

product

biomasssalt 0 0

dm d

dt dt waste


9

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

10

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

11

Process Design and Modeling a Solution

• Basis for design: multi-effect distillation

12


• Basis for design: multi-effect distillation

13

Single greatest source of entropy generation

Process Design and Modeling a SolutionWaste-Heat Recovery

14

Process Design and Modeling a SolutionWaste-Heat Recovery

15

• 10-effect MED• Heat integration with inter-stage preheating and vapor absorption

Process Design and Modeling a SolutionConcentrated Solar

16

2.56 3.87 5.44 6.53 7.67 8.58 8.55 8.14 7.2 5.81 3.99 2.930

1

2

3

4

5

6

7

8

9

10

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


17

Process Design and Modeling a SolutionLarge-Scale Deployment

18

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:

21

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.


• Parametric Optimization

22

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



• Simple Example:

23

* 2

[ 5,5]( )

[ 2

a

,2

m x[ ]

]x

f x pp

p


• Simple Example:

24

* 2

[ 5,5]( )

[ 2

a

,2

m x[ ]

]x

f x pp

p

𝑥

𝑓𝑥,𝑝

=−𝑥2−𝑝

2

0

2

p

p

p


• Simple Example:

25

* 2

[ 2,2] [ 5,5]maxmin [ ]

p xx p


• Simple Example:

26

* 2

[ 2,2] [ 5,5]maxmin [ ]

p xx p


• Parametric Optimization

27

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



• Min-Max formulation

28

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



• Semi-infinite programs:

29

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


• Semi-infinite program reformulation

30

*

,

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


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 DiscussionParametric Optimal Design Economics

32

Solution Results and DiscussionWorst-Case Feasibility

• Solving the semi-infinite program yielded a feasible design:

33

Solution Results and Discussion

34

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)

35

Thank YOU!

36

Any Questions?

37

Process Design and Modeling a SolutionSolar Thermal Energy Storage

38

• Single-tank packed-bed thermal storage• Spherical concrete packing• 12” tank insulation• Reverse-flow charging/discharging

Documents

Robust Design for a Sustainable Future