# CSC Model Notation

## Model Indices and Sets

NotationDescription
$z \in \mathcal{Z}$$z denotes a zone and \mathcal{Z} is the set of zones in the network t \in \mathcal{T}$$t$ denotes an time step and $\mathcal{T}$ is the set of time steps
$t \in \mathcal{T}^{start}$This set of time-coupling constraints wrap around to ensure the output in the first time step of each year (or each representative period)
$t \in \mathcal{T}^{interior}$This set of time-coupling constraints wrap around to ensure the output in the inner time step of each year (or each representative period)
$d \in \mathcal{D}$Index and set of all DAC resources
$k \in \mathcal{K}$Index and set of all CO2 compression resources
$s \in \mathcal{S}$Index and set of storage resources in CO2 supply chain representing geological sequestration

## Decision Variables

NotationDescription
$x_{d,z,t}^{\textrm{C,DAC}}$this term represents CO2 captured by DAC resource $d$ in zone $z$ at time period $t$
$x_{k,z,t}^{\textrm{C,COMP}}$this term represents DAC-captured CO2 compressed by CO2 compression generation resource $k$ in zone $z$ at time period $t$
$x_{s,z,t}^{\textrm{C,INJ}}$this term represents CO2 injected into the CO2 storage resource $s$ in zone $z$ at time period $t$
$x_{i,z \rightarrow z^{\prime},t}^{\textrm{C,PIP}}$the CO2 pipeline flow decision variable representing CO2 flow via pipeline of type $i$ through path $z \rightarrow z^{\prime}$ at time period $t$
$y_{d,z}^{\textrm{C,DAC}}$capacity of DAC resources in the CO2 supply chain
$y_{k,z}^{\textrm{C,COMP}}$capacity of CO2 compression resources in the CO2 supply chain
$y_{s,z}^{\textrm{C,STO}}$capacity of CO2 storage in the CO2 supply chain
$y_{i,z \rightarrow z^{\prime}}^{\textrm{C,PIP}}$the CO2 pipeline construction decision variable representing newly constructed CO2 pipeline of type $i$ through path $z \rightarrow z^{\prime}$
$U_{i,z \rightarrow z^{\prime},t}^{\textrm{C,PIP}}$the CO2 pipeline storage level decision variable representing CO2 stored in pipeline of type $i$ through path $z \rightarrow z^{\prime}$ at time period $t$

## Parameters

NotationDescription
$\textrm{c}_{d}^{\textrm{DAC,INV}}$investment cost per tonne of DAC capture capacity
$\textrm{c}_{d}^{\textrm{DAC,FOM}}$fixed operation cost per tonne of DAC capture capacity
$\textrm{c}_{d}^{\textrm{DAC,VOM}}$variable operation cost per tonne of CO2 captured by DAC
$\textrm{c}_{g}^{\textrm{DAC,FUEL}}$fuel cost per tonne of CO2 captured by DAC
$\textrm{c}_{k}^{\textrm{COMP,INV}}$investment cost per tonne of CO2 compression capacity
$\textrm{c}_{k}^{\textrm{COMP,FOM}}$fixed operation cost per tonne of CO2 compression capacity
$\textrm{c}_{s}^{\textrm{STO,INV}}$investment cost per tonne of CO2 storage capacity
$\textrm{c}_{s}^{\textrm{STO,FOM}}$fixed operation cost per tonne of CO2 storage capacity
$\textrm{c}_{s}^{\textrm{INJ,VOM}}$variable operation cost per tonne of CO2 injected into CO2 storage by DAC
$\overline{y}_{d}^{\textrm{\textrm{C,DAC}}}$upper bound of capacity is defined,then we impose constraints on maximum DAC capacity
$\underline{y}_{d}^{\textrm{\textrm{C,DAC}}}$lower bound of capacity is defined,then we impose constraints on minimum DAC capacity
$\overline{y}_{k}^{\textrm{\textrm{C,COMP}}}$upper bound of capacity is defined,then we impose constraints on maximum CO2 compression capacity
$\underline{y}_{k}^{\textrm{\textrm{C,COMP}}}$lower bound of capacity is defined,then we impose constraints on minimum CO2 compression capacity
$\overline{y}_{s}^{\textrm{\textrm{C,STO}}}$upper bound of capacity is defined,then we impose constraints on maximum CO2 storage capacity
$\underline{y}_{s}^{\textrm{\textrm{C,STO}}}$lower bound of capacity is defined,then we impose constraints on minimum CO2 storage capacity
$\overline{x}_{s}^{\textrm{\textrm{C,INJ}}}$upper bound of rate is defined,then we impose constraints on maximum CO2 injection rate
$\overline{\textrm{R}}_{d,z,t}^{\textrm{C,DAC}}$For DAC where upper bound operation is defined, then we impose constraints on maximum operating capacity rate
$\underline{\textrm{R}}_{d,z}^{\textrm{C,DAC}}$For DAC where lower bound operation is defined, then we impose constraints on minimum operating capacity rate
$\overline{\textrm{R}}_{k,z}^{\textrm{C,COMP}}$For CO2 compression where upper bound operation is defined, then we impose constraints on maximum operating capacity rate
$\underline{\textrm{R}}_{k,z}^{\textrm{C,COMP}}$For CO2 compression where lower bound operation is defined, then we impose constraints on minimum operating capacity rate
$\overline{\textrm{R}}_{k,z}^{\textrm{C,INJ}}$For CO2 injection where upper bound operation is defined, then we impose constraints on maximum injection rate
$\underline{\textrm{R}}_{k,z}^{\textrm{C,INJ}}$For CO2 injection where lower bound operation is defined, then we impose constraints on minimum injection rate