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</math>] for gases, [J/sh tn] for solids
$\rho (f)\,$ = density [g/gal] for liquids, [g/$l$] for gases, does not exist for solids