Optimization of carbon dioxide sequestration in brine aquifers

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Optimization of carbon dioxide sequestration in
brine aquifers

• David Cameron Lou Durlofsky
• Smart Fields Seminar
• April 15, 2009

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Optimizing CO2 sequestration is similar to
optimizing oil production
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CO2 sequestration process

• Flue gas is separated to get pure CO2 stream
• CO2 is injected in brine aquifer as supercritical
  fluid
• A long equilibration phase (1000 yrs) follows
  injection
• CO2 is trapped in different ways

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Time scales for trapping mechanisms
(from Benson, 2007)
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Potential goal minimize mobile CO2

• Definition of mobile CO2
• Proportion of CO2 above residual saturation after
  equilibration
• Controlling parameters
• Well configurations
• Model parameters

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Contents of this talk

• Description of the reservoir model
• Formulation of optimization case study
• Optimization methods
• Optimization results from case study
• Summary and conclusions

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Reservoir model features
Base case parameters
Full reservoir model (to scale)

• Dimensions
• Grid
• Permeability
• Porosity
• Kv/Kh
• Max inj. per well
• Total injection
• Injection time
• Equilibration time

10 km x 10 km x 250 m 25 x 25 x 20 0.1 10000 md
(M 100) 0.15 to 0.35 0.1 50 000 STB/d (super
critical) 5 Mta (500 MW coal plant) 30 yrs 1 000
yrs
Inner section (not to scale)
Porosity
10 km
900 ft
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These figures were obtained using the preprocess
file
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Simulation features

• Used Stanfords General Purpose Research
  Simulator (GPRS)
• Two phase (water and CO2) compositional
• Peng Robinson EOS
• Hysteresis (Carlson method)
• No mineral trapping

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Case study 6 fixed wells Optimize using rate
control
Well configuration
Control parameters
The fraction of total injection rate at each well
(vectors over time) R1, , R6
Bounds
Constraint
Possible objective functions

• Mobile CO2
• CO2 under cap rock

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Base case equal injection rates
Base case phase distribution
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Base case equal injection rates
Base case phase distribution
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Base case saturation and dissolution snap shots
Base case dissolved CO2 (kg)
Base case CO2 saturation
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General Pattern Search (GPS) optimization method

• ADVANTAGES
• Gradient free
• Easy and robust
• Parallelizable
• DISADVANTAGES
• Local method
• Slow

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Mesh Adaptive Direct Search (MADS)optimization
method

• Generates random positive basis set
• Samples an area more densely than GPS

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Pattern search (N1) polling

• Fewer function evaluations per iteration
• Less likely to find global optimum
• GPS (N1) is biased

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Minimization of mobile gas phase with 6 unknowns
using different techniques
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Different methods converge to different solutions
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Minimization of mobile CO2 phase using more
unknowns
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Time updates tend toward bang-bang solutions
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Minimizing CO2 phase in the top layer
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Optimization with respect to mobile and top layer
CO2 give similar results
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Base case versus optimal solution
Optimized phase balance(18 par, mobile CO2)
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Cross sections for dissolution and saturation
Base case dissolution (1000 yrs)
Optimized dissolution (1000 yrs)
Base case saturation (1000 yrs)
Optimized saturation (1000 yrs)
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Summary and conclusions

• Summary
• Formulated CO2 sequestration as an optimization
  problem
• Designed a realistic synthetic model for CO2
  injection
• Optimal solutions reduced mobile CO2 by 30
• Solutions exhibit bang-bang behavior
• Conclusions
• Bang-bang injection increases dissolved and
  residually trapped CO2

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Future directions

• Test using more parameters
• Test more optimization methods
• Use position of wells as additional optimization
  variables
• Incorporate closed-loop optimization

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Acknowledgements

• Huanquan Pan for modeling and GPRS help
• Yaqing Fan for modeling and GPRS help
• David Echeverria for optimization and coding help