Equations

for transparency and educational purposes, this section presents the equations used in the application to perform emission calculations, which are also available in the annexes of the cbam implementing regulation the equations are numbered as they appear in the regulation 🏭 installation's total emissions \text{equation 4 } \quad \text{em} {\text{inst}} = \sum {i=1}^{n} \text{em} {\text{calc},i} + \sum {j=1}^{m} \text{em} {\text{meas},j} + \sum {k=1}^{l} \text{em} {\text{other},k} where em inst ➡️ the (direct) emissions of the installation expressed in tonnes co₂e em calc,i ➡️ the emissions from source stream i determined using a calculation based methodology expressed in tonnes co₂e em meas,j ➡️ the emissions from emission source j determined using a measurement based methodology expressed in tonnes co₂e em other,k ➡️ the emissions determined by another method, index k expressed in tonnes co₂e ⛽🧱🪨 fuel and materials only the equations for the calculation based approach are presented, as this is the only approach currently used by our platform reminder the measurement based approach is mandatory only for monitoring nitrous oxide ( n₂o ) emissions and requires a continuous emission measurement system ( cems ) installed at an appropriate measurement point in the factory standard method combustion emissions \text{equation 5 } \quad em i = ad i \cdot ef i \cdot of i where em i ➡️ the emissions \[tco2] caused by fuel i ad i ➡️ the activity data \[tj] of fuel i ef i ➡️ the emission factor \[tco2/tj] of fuel i of i ➡️ the oxidation factor (dimensionless) of fuel i ad i is calculated as \text{equation 6 } \quad ad i = fq i \cdot ncv i where fq i ➡️ the fuel quantity consumed \[t or m3] of fuel i ncv i ➡️ the net calorific value (lower heating value) \[tj/t or tj/m3] of fuel i ef i can be calculated as if the emission factor ( ef ) of a fuel i is to be calculated from the analyses of carbon content and ncv , the following equation shall be used \text{equation 8 } \quad ef i = cc i \cdot \frac{f}{ncv i} where cc i ➡️ the carbon content of fuel i f ➡️ the ratio of the molar masses of co2 and c ➡️ f = 3,664 tco2/t c ncv i ➡️ the net calorific value (lower heating value) \[tj/t or tj/m3] of fuel i if the emission factor ( ef ) of a material or fuel i expressed in tco2/t is to be calculated from an analysed carbon content, the following equation is used \text{equation 9 } \quad ef i = cc i \cdot f where cc i ➡️ the carbon content of fuel or material i f ➡️ the ratio of the molar masses of co2 and c ➡️ f = 3,664 tco2/t c as the emission factor of biomass shall be zero provided that the "zero rated" criteria are met (view them eu cbam q\&a docid\ d2zsuoqnhqioqfue5yqpu ), this fact may be taken into account for mixed fuels (i e fuels which contain both fossil and biomass components) as follows \text{equation 10 } \quad ef i = ef {\text{pre},i} \cdot (1 bf i) where ef pre,i ➡️ the preliminary emission factor of fuel i (i e emission factor assuming the total fuel is fossil) bf i ➡️ the biomass fraction (dimensionless) of fuel i for fossil fuels and where the biomass fraction is not known, bf i shall be set to the conservative value zero of i is calculated as \text{equation 7 } \quad of = 1 \frac{c {\text{cash}}}{c {\text{total}}} where c ash ➡️ the carbon contained in ash and flue gas cleaning dust c total ➡️ the total carbon contained in the fuel combusted the conservative assumption that of = 1 may always be used in order to reduce monitoring efforts process emissions \text{equation 11 } \quad em j = ad j \cdot ef j \cdot cf j where ad j ➡️ the activity data \[t of material] of material j ef j ➡️ the emission factor \[t co2/t] of material j cf j ➡️ the conversion factor (dimension less) of material j the conservative assumption that cf j = 1 may always be used in order to reduce monitoring efforts mass balance method \text{equation 12 } \quad em k = f \cdot ad k \cdot cc k where f ➡️ the ratio of the molar masses of co2 and c ➡️ f = 3,664 tco2/tc ad k ➡️ the activity data \[t] of material k ➡️ for outputs, ad k is negative cc k ➡️ the carbon content of material k (dimensionless and positive) cc k can be calculated as if the carbon content of a fuel k is calculated from an emission factor expressed in tco2/tj, the following equation shall be used \text{equation 13 } \quad cc k = ef k \cdot \frac{ncv k}{f} where ef k ➡️ the emission factor \[tco2/tj] of fuel k ncv k ➡️ the net calorific value \[tj/t or tj/m3] of fuel k f ➡️ the ratio of the molar masses of co2 and c ➡️ f = 3,664 tco2/t c if the carbon content of a material or fuel k is calculated from an emission factor expressed in tco2/t, the following equation shall be used \text{equation 14 } \quad cc k = \frac{ef k}{f} where ef k ➡️ the emission factor \[t co2/t] of material or fuel k f ➡️ the ratio of the molar masses of co2 and c ➡️ f = 3,664 tco2/t c for mixed fuels, meaning fuels which contain both fossil and biomass components or mixed materials, the biomass fraction may be taken into account, provided that the "zero rated" criteria are met (view them eu cbam q\&a docid\ d2zsuoqnhqioqfue5yqpu ), as follows \text{equation 15 } \quad cc k = cc {\text{pre},k} \cdot (1 bf k) where cc pre,k ➡️ the preliminary carbon content of fuel k (i e emission factor assuming the total fuel is fossil) bf k ➡️ the biomass fraction of fuel k (dimensionless) for fossil fuels or materials and where the biomass fraction is not known, bf shall be set to the conservative value zero 🔌 electricity external \text{equation 44 } \quad em {el} = e {el} \cdot ef {el} where em el ➡️ the emissions related to electricity produced or consumed, expressed in tco2 e el ➡️ the electricity produced or consumed expressed in mwh or tj ef el ➡️ the emission factor for electricity applied, expressed in tco2/mwh or tco2/tj self generated \text{equation 47 } \quad ef {el} = \frac{\sum ad i \cdot ncv i \cdot ef i + em {fgc}}{el {prod}} where ef el ➡️ the emission factor of electricity ad i ➡️ the annual activity data (i e quantities consumed) of the fuels i used for the electricity production expressed in tonnes or nm3 ncv i ➡️ the net calorific values of the fuels i expressed in tj/t or tj/nm3 ef i ➡️ the emission factors of the fuels i expressed in tco2/tj em fgc ➡️ the process emissions from flue gas cleaning expressed in tco2 el prod ➡️ the net amount of electricity produced expressed in mwh it may include quantities of electricity produced from sources other than combustion of fuels 🌡️ heat net amounts of measurable heat one of the following methods shall be applied if a production process consumes measurable heat generated within the installation these methods are designed to determine the net quantity of measurable heat produced calculate the emissions associated with the consumption of that heat method 1 is regarded as the most accurate, followed by methods 2 and 3 in terms of quality method 1 using measurements our platform does not support this method yet under this method, all relevant parameters shall be measured, in particular temperature, pressure, state of the transmitted as well as the returned heat medium the mass flow rate of the medium shall be calculated as \text{equation 30 } \quad \dot{m} = \frac{\dot{v}}{v} where ṁ ➡️ the mass flow rate in kg/s v̇ ➡️ the volumetric flow rate in m3/s v ➡️ the specific volume in m3/kg as the mass flow rate is considered the same for transmitted and returned medium, the heat flow rate shall be calculated using the difference in enthalpy between the transmitted flow and the return, as follows \text{equation 31 } \quad \dot{q} = (h {\text{flow}} h {\text{return}}) \cdot \dot{m} where q̇ ➡️ the heat flow rate in kj/s h flow ➡️ the enthalpy of the transmitted flow in kj/kg h return ➡️ the enthalpy of the return flow in kj/kg ṁ ➡️ the mass flow rate in kg/s in the case of steam or hot water used as heat transfer medium, where the condensate is not returned, or where it is not feasible to estimate the enthalpy of the returned condensate, h return shall be determined based on a temperature of 90°c method 2 calculation of a proxy based on measured efficiency our platform currently employs this method the amounts of net measurable heat shall be determined based on the fuel input and the measured efficiency related to the heat production, as follows \text{equation 32 } \quad q = \eta h \cdot e {in} where q ➡️ the amount of heat expressed in tj ηh ➡️ the measured efficiency of heat production e in ➡️ the energy input from fuels e in is calculated as \text{equation 33 } \quad e {in} = \sum {i} ad i \cdot ncv i where ad i ➡️ the annual activity data (i e , quantities consumed) of the fuels i ncv i ➡️ the net calorific values of the fuels i ηh is measured either over a reasonably long period, which sufficiently takes into account different load states of the installation taken from the boiler's manufacturer's documentation in this case, the specific part load curve must be taken into account by using an annual load factor, as follows \text{equation 34 } \quad l f = \frac{e {in}}{e {max}} where lf ➡️ the load factor e in ➡️ the energy input as determined using equation 33 over the reporting period e max ➡️ the maximum fuel input if the heat producing unit had been running at 100% nominal load for the full calendar year in the case of a steam raising boiler, the efficiency shall be based on a situation in which all condensate is returned a temperature of 90 °c shall be assumed for the returned condensate method 3 calculating a proxy based on the reference efficiency our platform uses the reference efficiency of 70%, unless a specific ηh value is provided by the user this method is identical to method 2 , but uses a reference efficiency of 70% (ηref,h = 0,7) as a conservative assumption hence \text{equation 32 } \quad q = \eta h \cdot e {in} where q ➡️ the amount of heat expressed in tj ηh ➡️ the measured efficiency of heat production ➡️ ηref,h = 0,7 e in ➡️ the energy input from fuels fuel mix emission factor of measurable heat for measurable heat produced from the combustion of fuels within the installation except heat produced by cogeneration, the emission factor of the relevant fuel mix shall be determined and the emissions attributable to the production process shall be calculated as \text{equation 35 } \quad em {heat} = ef {mix} \cdot \frac{q {consumed}}{\eta} where emheat ➡️ the heat related emissions of the production process in tco2 efmix ➡️ the emission factor of the respective fuel mix expressed in tco2/tj including emissions from flue gas cleaning, where applicable qconsumed ➡️ the amount of measurable heat consumed in the production process expressed in tj η ➡️ the efficiency of the heat production process efmix shall be calculated as \text{equation 36 } \quad ef {mix} = \frac{\sum ad i \cdot ncv i \cdot ef i + em {fgc}}{\sum ad i \cdot ncv i} ad i ➡️ the annual activity data (i e quantities consumed) of the fuels i used for the measurable heat production expressed in tonnes or nm3 ncv i ➡️ the net calorific values of the fuels i expressed in tj/t or tj/nm3 ef i ➡️ the emission factors of the fuels i expressed in tco2/tj emfgc ➡️ the process emissions from flue gas cleaning expressed in tco2 🌡️+🔌 combined heat and power (chp) \text{equation 37 } \quad em {chp} = \sum {i} ad i \cdot ncv i \cdot ef i + em {fgc} where emchp ➡️ the emissions of the cogeneration unit during the reporting period expressed in tco2 ad i ➡️ the annual activity data (i e quantities consumed) of the fuels i used for the chp unit expressed in tonnes or nm3 ncv i ➡️ the net calorific values of the fuels i expressed in tj/t or tj/nm3 ef i ➡️ the emission factors of the fuels i expressed in tco2/tj emfgc ➡️ the process emissions from flue gas cleaning expressed in tco2 the energy input to the chp unit shall be calculated in accordance with equation 33 the respective average efficiencies over the reporting period of heat production and electricity (or mechanical energy, if applicable) production shall be calculated as follows \text{equation 38 } \quad \eta {heat} = \frac{q {net}}{e {in}} where ηheat ➡️ the average efficiency of heat production during the reporting period (dimensionless) qnet ➡️ the net amount of heat produced during the reporting period by the cogeneration unit expressed in tj e in ➡️ the energy input as determined using equation 33 expressed in tj \text{equation 39 } \quad \eta {el} = \frac{e {el}}{e {in}} where ηel ➡️ the average efficiency of electricity production during the reporting period (dimensionless) eel ➡️ the net electricity production of the cogeneration unit during the reporting period, expressed in tj e in ➡️ the energy input as determined using equation 33 expressed in tj where the determination of the efficiencies ηheat and ηel is technically not feasible or would incur unreasonable costs, values based on technical documentation (design values) of the installation shall be used if no such values are available, the following conservative standard values shall be used (used in our platform) ηheat = 0,55 ηel = 0,25 the attribution factors for heat and electricity from chp shall be calculated as follows \text{equation 40 } \quad f {chp,heat} = \frac{\frac{\eta {heat}}{\eta {ref,heat}}}{\frac{\eta {heat}}{\eta {ref,heat}} + \frac{\eta {el}}{\eta {ref,el}}} where f chp,heat ➡️ the attribution factor for heat (dimensionless) ηheat ➡️ the average efficiency of heat production during the reporting period (dimensionless) ηref, heat ➡️ the reference efficiency for heat production in a stand alone boiler (dimensionless) ηel ➡️ the average efficiency of electricity production during the reporting period (dimensionless) ηref, el ➡️ the reference efficiency of electricity production without cogeneration (dimensionless) \text{equation 41 } \quad f {chp,el} = \frac{\frac{\eta {el}}{\eta {ref,el}}}{\frac{\eta {heat}}{\eta {ref,heat}} + \frac{\eta {el}}{\eta {ref,el}}} where f chp,el ➡️ the attribution factor for electricity (or mechanical energy, if applicable) (dimensionless) ηel ➡️ the average efficiency of electricity production during the reporting period (dimensionless) ηref, el ➡️ the reference efficiency of electricity production without cogeneration (dimensionless) ηheat ➡️ the average efficiency of heat production during the reporting period (dimensionless) ηref, heat ➡️ the reference efficiency for heat production in a stand alone boiler (dimensionless) the specific emission factor of the chp related measurable heat to be used for the attribution of heat related emissions to production processes shall be calculated as \text{equation 42 } \quad ef {chp,heat} = \frac{em {chp} \cdot f {chp,heat}}{q {net}} where ef chp, heat ➡️ the emission factor for the production of measurable heat in the cogeneration (chp) unit expressed in tco2/tj emchp ➡️ the emissions of the cogeneration unit during the reporting period expressed in tco2 f chp,heat ➡️ the attribution factor for heat (dimensionless) qnet ➡️ the net heat produced by the cogeneration unit expressed in tj the specific emission factor of the chp related electricity to be used for the attribution of electricity related emissions to production processes shall be calculated as \text{equation 43 } \quad ef {chp,el} = \frac{em {chp} \cdot f {chp,el}}{e {el,prod}} where ef chp, el ➡️ the emission factor for the production of electricity in the cogeneration (chp) unit expressed in tco2/tj emchp ➡️ the emissions of the cogeneration unit during the reporting period expressed in tco2 f chp,el ➡️ the attribution factor for electricity (or mechanical energy, if applicable) (dimensionless) e el,prod ➡️ the electricity produced by the chp unit pfc emissions the emissions of cf4 and c2f6 emitted through a duct or stack shall be calculated by using one of the following methods calculation method a – slope method \text{equation 21 } \quad \text{cf} 4 \text{ emissions } (t) = \text{aem} \times \left( \frac{\text{sef} {\text{cf} 4}}{1000} \right) \times \text{pr} {\text{al}} where aem ➡️ the anode effect minutes/cell day sef cf4 ➡️ the slope emission factor expressed in \[(kg cf4/t al produced)/(anode effect minutes/cell day)] where different cell types are used, different sef may be applied as appropriate pr al ➡️ the production of primary aluminium \[t] during the reporting period aem is calculated as \text{equation 23 } \quad \text{aem} = \textit{frequency} \times \textit{average duration} \text{equation 22 } \quad \text{c} 2\text{f} 6 \text{ emissions } (t) = \text{cf} 4 \text{ emissions} \times f {\text{c} 2\text{f} 6} where f c2f6 ➡️ the weight fraction of c2f6 \[tc2f6/tcf4] calculation method b – overvoltage method \text{equation 24 } \quad cf 4 \\, emissions\[t] = ovc \times \left(\frac{aeo}{ce}\right) \times pr {al} \times 0 001 where ovc ➡️ the overvoltage coefficient (emission factor) expressed in kg cf4 per tonne of aluminium produced per mv overvoltage aeo ➡️ the anode effect overvoltage per cell \[mv] determined as the integral of (time × voltage above the target voltage) divided by the time (duration) of data collection ce ➡️ the average current efficiency of aluminium production \[%] pr ai ➡️ the annual production of primary aluminium \[t] \text{equation 25 } \quad c 2f 6 \\, emissions\[t] = cf 4 \\, emissions \times f {c 2f 6} where fc2f6 ➡️ the weight fraction of c2f6 \[tc2f6/tcf4] pfc emissions are calculated as \text{equation 26 } \quad pfc \\, emissions\[t \\, co 2e] = cf 4 \\, emissions\[t] \times gwp {cf 4} \\\\ \quad + c 2f 6 \\, emissions\[t] \times gwp {c 2f 6} where gwp cf4 ➡️ eu cbam q\&a gwp c2f6 ➡️ eu cbam q\&a ↪️ attributed emissions direct attributed emissions \text{equation 48 } \quad \textbf{attrem} {dir} = \textbf{direm}^{ } + em {h,imp} \textbf{em} {h,exp} \\\\ \+ wg {corr,imp} wg {corr,exp} \textbf{em} {el,prod} where attrem dir ➡️ the attributed direct emission of the production process over the whole reporting period, expressed in tco2e direm ➡️ the directly attributable emissions from the production process, determined for the reporting period em h,imp ➡️ the emissions equivalent to the quantity of measurable heat imported to the production process, determined for the reporting period em h,exp ➡️ the emissions equivalent to the quantity of measurable heat exported from the production process, determined for the reporting periop wg corr,imp ➡️ the attributed direct emissions of a production process consuming waste gases imported from other production processes, corrected for the reporting period wg corr,exp ➡️ the emissions equivalent to the quantity of waste gases exported from the production process, determined for the reporting period em el,pro ➡️ the emissions equivalent to the quantity of electricity produced within the boundaries of the production process, determined for the reporting period where attrem dir is calculated to have a negative value, it shall be set to zero em h,imp is calculated as \text{equation 52 } \quad em {h,imp} = q {imp} \cdot ef {heat} where q imp ➡️ the net heat imported to and consumed in the production process expressed in tj ef heat ➡️ the emission factor for the production of measurable heat expressed in tco2/tj wg corr,imp is calculated as \text{equation 53 } \quad wg {corr,imp} = v {wg} \cdot ncv {wg} \cdot ef {ng} where v wg ➡️ the volume of the waste gas imported ncv wg ➡️ the net calorific value of the waste gas imported ef ng ➡️ the standard emission factor of natural gas ➡️ 56,1 tco2/tj wg corr,exp is calculated as \text{equation 54 } \quad wg {corr,exp} = v {wg,exp} \cdot ncv {wg} \cdot ef {ng} \cdot corr {\eta} where v wg,exp ➡️ the volume of waste gas exported from the production process ncv wg ➡️ the net calorific value of the waste gas ef ng ➡️ the standard emission factor of natural gas ➡️ 56,1 tco2/tj corr η ➡️ the factor that accounts for the difference in efficiencies between the use of waste gas and the use of the reference fuel natural gas the standard value is corr η = 0,667 indirect attributed emissions \text{equation 49 } \quad attrem {indir} = em {el,cons} where em el,cons ➡️ the emissions equivalent to the quantity of electricity consumed within the boundaries of the production process, determined for the reporting period ➕ embedded emissions if a production process consumed relevant precursors, the embedded emissions of these goods need to be added direct embedded emissions ee {proc,dir} = attrem {proc,dir} + \sum {i=1}^{n} m i \cdot see {i,dir} where ee proc,dir ➡️ the direct embedded emissions at the level of the production process over the reporting period attrem proc,dir ➡️ the attributed direct emissions of the production process as determined in equation 48 m i ➡️ the mass of precursor i consumed in the production process during the reporting period see i,dir ➡️ the specific direct embedded emissions of precursor i indirect embedded emissions ee {proc,indir} = attrem {proc,indir} + \sum {i=1}^{n} m i \cdot see {i,indir} where ee proc,indir ➡️ the indirect embedded emissions at the level of the production process over the reporting period attrem proc,indir ➡️ the attributed indirect emissions of the production process as determined in equation 49 m i ➡️ the mass of precursor i consumed in the production process during the reporting period see i,indir ➡️ the specific indirect embedded emissions of precursor i ➗ specific embedded emissions (see) direct see see {g,dir} = \frac{ee {proc,dir}}{al g} where see g,dir ➡️ the direct specific embedded emissions of the goods under the aggregated goods category g ee proc,dir ➡️ the direct embedded emissions at the level of the production process over the reporting period al g ➡️ the eu cbam q\&a of the production process producing goods of the aggregated goods category g , i e the mass of all goods of that category produced during the reporting period indirect see see {g,indir} = \frac{ee {proc,indir}}{al g} where see g,indir ➡️ the indirect specific embedded emissions of the goods under the aggregated goods category g ee proc,indir ➡️ the indirect embedded emissions at the level of the production process over the reporting period al g ➡️ the eu cbam q\&a of the production process producing goods of the aggregated goods category g , i e the mass of all goods of that category produced during the reporting period