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130 CHAPTER 6. SUMMARY, CONCLUSIONS AND FUTURE WORK Nomenclature Greek Symbols vector of time-averaged top layer mobility error ∆ variables characterizing leaks in the cap rock η ˆ Λ measure of the similarity of leaked CO2 between two models ˆ λ CO2 mobility Ω feasible region for optimization variables φ porosity scaling parameters θ vector of K-L parameters ξ Variables a constant in permeability/porosity relationship b constant in permeability/porosity relationship dobs observed injection and monitoring well data F expected error from approximate history match forward model for flow simulation f (il, jl ) grid block indices for a leakage site J optimization objective function Jλ time-averaged total CO2 mobility in the top layer over 500 years Jave time-averaged mobile CO2 over 1000 years J1000 mobile CO2 at 1000 years J100 mobile CO2 at 100 years K number of brine cycling events k permeability 132 CHAPTER 6. SUMMARY, CONCLUSIONS AND FUTURE WORK krg relative permeability of gas (CO2 ) phase krw relative permeability of water phase kz,l grid block permeability for a leakage site L number of leakage sites ℓ number of K-L parameters cycling duration variables l M number of time intervals for CO2 injection geological model parameters, e.g., porosity m N number of CO2 injection wells n number of optimization variables Nb number of grid blocks in model Np number of PSO particles brine cycling proportion variables p R number of geologic realizations for optimization with uncertain geology CO2 injection rate variables r ˆ S misfit function cycling start time variables s Sg gas phase (CO2 ) saturation optimization variables u weighting matrix W data weight parameters w location variables for injection wells x sensor location variables y Bibliography Adler, PM, & Brenner, H. 1988. Multiphase flow in porous media. Annual Review of Fluid Mechanics, 20(1), 35–59.

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