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]
$e(I)=||E(I)||=\left||\sum _{f\in I}a(f)E_{up}(f)|\right|$ = process input energy [J]
$e(G)=||E(G)||=\left||\sum _{f\in G}a(f)E_{up}(f)|\right|$ = 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]
$E{m}_{up}(f)=(a(VOC),a(CO),a(NOx),a(PM10),a(PM2.5),a(SOx),a(CH4),a(N2O),a(CO2))$ = energy vector associated with emissions to produce [g/J,g/g,g/l]
$Enem=(E,Em)$ = energy-emissions vector
$Ene{m}_{up}(f)=(E_{up}(f),E{m}_{up}(f))$ = 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 $p$
$E{m}_p$ = 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