This model was used in: Jan F. Wiegner, Alexa Grimm, Lukas Weimann, and Matteo Gazzani (2022): Optimal Design and Operation of Solid Sorbent Direct Air Capture Processes at Varying Ambient Conditions, Industrial & Engineering Chemistry Research 61 (34), 12649-12667, DOI: 10.1021/acs.iecr.2c00681

Dependencies

Obligatory:

• YALMIP
• any MILP solver compatible with YALMIP (can be from the Matlab optimization toolbox)
• Matlab Statistics and Machine Learning Toolbox

Nice to have:

• Gurobi or CLEX as external solvers

Package content

Main: Loads and sets data and performs optimization.

Data:

AirInletCooling contains data on the cooling effect of spraying water into the inlet air of the DAC unit

DAC_Data_5_ConstOP contains data on the process performance at constant operating parameters and different ambient conditions

DAC_Data_5 contains data on the process performance at optimized operating parameters and different ambient conditions

In Input_DAC you can specify economic data and emission factors for the optimization:

• Demand is in t of CO2
• Module Investment cost is in EUR/module
• Lifetime is in years
• Maintenance Cost in % of annualized investment costs
• Carrier prices are in EUR/kWh
• Emission Factors are in t/kWh
• Eta_elth depicts the electric efficiency of the ohmic heating

Settings contains general data on the model assumptions:

• Constant demand 1: demand needs to be met as specified in demand 0: demand needs to be met over the full period
• D specifies the number of typical days. Input data is clustered by k-means respectively.
• N specifies the number of total days
• K specifies the number of time intervals per dayo
• Size min is the minimal number of modules that need to be built
• Size mas is the maximal number of modules that can be built
• Optimization type (1: minimize cost, 2: minimize emissions, 3: minimize cost at emission constraint. You can set an emission constraints by specifying Settings.EmissionConstraint to a certain value)
• ElThTradeOff (1: Ohmic heating allowed, 2: Ohmic heating turned off)
• Nr_bp: number of breakpoint on DAC performance curve (leave it at 2)
• ConstantOP (1: keep operating parameters constant, 0: allow for optimized operating parameters in each time slice)
• RHadapt (0: no inlet water spraying, 1: allow inlet water spraying)
• RHdiscrete: how many discrete point to consider for inlet water spraying

Solver_Options: sdpsetting from YALMIP adapted to the model

Functions

DAC_Standalone_6: main function to perform the optimization

DACOutput_4: performs the fitting of the performance parameters based on the given RH and T vector (for variable operating parameters)

DACOutput_4_ConsPar: performs the fitting of the performance parameters based on the given RH and T vector (for constant operating parameters)

PLR: Performs a piece-wise linear regressio

Results

Contains a file with the optimization results for the DAC Standalone case for different temperature-humidity combinations. n