# Notations

$\eta \,$ = efficiency [J/J]
$f\,$ = material [Tag]
$B\,$ = set of basic resources (coal,ng, oil, uranium ore, wind, hydro, solar, etc.) [Tags]
$e(f)\,$ = energy content of a material $f$ [J]
$a(f)\,$ = amount of a material $f$ [J,g,l,$] $f_{O}\,$ = main output [Tag] $f_{p}\,$ = co-product material [Tag] $l(f)\,$ = Energy loss of a material $f$ [J] $fl\,$ = Feed Loss [J] $I\,$ = List of all of the process inputs [List] $P\,$ = List of all of the process Copruducts [List] $G\subset I\,$ = List of all of inputs in a group (amount or efficiency group) [List] $S\subset G\,$ = List of all of inputs in a group which have share (amount of efficiency) [List] $E=(e(b_{1}),e(b_{2}),...,e(b_{n})),\ b_{i}\in B\,$ = energy vector [J] $||E||=e(b_{1})+e(b_{2})+...+e(b_{n})\,$ [J] $E_{up}(f)\,$ = energy vector associated with upstream energy to produce $f\,$ [J/J, J/g, J/l] $e(I)=||E(I)||=\left|\left|\sum _{f\in I}a(f)E_{up}(f)\right|\right|\,$ = process input energy [J] $e(G)=||E(G)||=\left|\left|\sum _{f\in G}a(f)E_{up}(f)\right|\right|\,$ = group energy [J] ${\hat {e}}(I)=\sum _{f\in I}e(f)\,$ = process input energy without upstream (energy used by the process) [J] ${\hat {e}}(G)=\sum _{f\in G}e(f)\,$ = group energy without upstream [J] $Em=(a(VOC),a(CO),a(NOx),a(PM10),a(PM2.5),a(SOx),a(CH4),a(N2O),a(CO2))\,$ = emission vector [g] $Em_{up}(f)=(a(VOC),a(CO),a(NOx),a(PM10),a(PM2.5),a(SOx),a(CH4),a(N2O),a(CO2))\,$ = energy vector associated with emissions to produce [g/J,g/g,g/l] $Enem=(E,Em)\,$ = energy-emissions vector $Enem_{up}(f)=(E_{up}(f),Em_{up}(f))\,$ = energy-emissions upstream vector vector $E_{p}\,$ = energy vector associated with main output production at process $p\,$ $E_{loss}\,$ = energy vector associated with process losses $p\,$ $Em_{p}\,$ = emissions vector associated with main output production at process $p\,$ $e_{p}=||E_{p}||\,$ = total process energy associated with main output production [Tag] $t\,$ = technology [Tag] $m\,$ = mode of transportation (rail, barge, etc.) [Tag] $ei\,$ = energy intensity [J/g/m] $Ef(f,t)=(a(VOC),a(CO),a(NOx),a(PM10),a(PM2.5),a(SOx),a(CH4),a(N2O),a(CO2))\,$ = emission factors vector for fuel $f$ and technology $t\,$ [g/J] $Ef(f,m)\,$ = emission factor for process fuel $f$ and transportation mode $m$ $d\,$ = distance [m] $T\,$ = list of technologies $M\,$ = list of transportation modes $s(f)\,$ = share for the process fuel $s(f,t)\,$ = technology share for the process fuel $hv(f)\,$ = heating value [J/gal] for liquids, [J/$l[/itex]] for gases, [J/sh tn] for solids
$\rho (f)\,$ = density [g/gal] for liquids, [g/$l$ ] for gases, does not exist for solids