The 33_CDR module calculates CO2 removed from the atmosphere by options other than BECCS or afforestation, which are calculated in the core.
| Description | Unit | A | B | C | D | |
|---|---|---|---|---|---|---|
| cm_ccapturescen | carbon capture option choice | x | ||||
| cm_gs_ew | grain size (for enhanced weathering, CDR module) | \(micrometre\) | x | x | ||
| cm_LimRock | limit amount of rock spread each year | \(Gt\) | x | x | ||
| cm_startyear | first optimized modelling time step | \(year\) | x | x | ||
| fm_dataemiglob (all_enty, all_enty, all_te, all_enty) |
read-in of emissions factors co2,cco2 | x | x | |||
| pm_eta_conv (tall, all_regi, all_te) |
Time-dependent eta for technologies that do not have explicit time-dependant etas, still eta converges until 2050 to dataglob_values. | \(efficiency (0..1)\) | x | x | ||
| pm_pop (tall, all_regi) |
population data | \(bn people\) | x | x | ||
| pm_ts (tall) |
(t_n+1 - t_n-1)/2 for a timestep t_n | x | x | |||
| sm_EJ_2_TWa | multiplicative factor to convert from EJ to TWa | x | x | x | ||
| sm_eps | small number: 1e-9 | x | ||||
| vm_cap (tall, all_regi, all_te, rlf) |
net total capacities | x | x | x | x | |
| vm_capFac (ttot, all_regi, all_te) |
capacity factor of conversion technologies | x | x | x | ||
| vm_emiCdr (ttot, all_regi, all_enty) |
total (negative) emissions due to CDR technologies of each region. | \(GtC\) | x | x | x | x |
| vm_omcosts_cdr (tall, all_regi) |
O&M costs for spreading grinded rocks on fields | x | x | x | x | |
| vm_otherFEdemand (ttot, all_regi, all_enty) |
final energy demand from no transformation technologies (e.g. enhanced weathering) | x | x | x | x | |
| vm_prodFe (ttot, all_regi, all_enty, all_enty, all_te) |
fe production. | \(TWa\) | x | x |
| Description | Unit | |
|---|---|---|
| vm_ccs_cdr (ttot, all_regi, all_enty, all_enty, all_te, rlf) |
CCS emissions from CDR | \(GtC / a\) |
In this realization, direct air capture and enhanced weathering can be used to remove CO2 from the atmosphere in addition to BECCS and afforestation. Based on Broehm et al. we assume an energy demand of 2 GJ/tCO2 electricity and 10 GJ/tCO2 heat for DAC which can be met via gas or H2. If gas is used, the resulting CO2 is captured with a capture rate of 90%. For EW, electricty is needed to grind the rocks and diesel is needed for transportation and spreading on crop fields.
Calculation of the amount of ground rock spread in timestep t.
\[\begin{multline*} \sum_{rlf2}\left(\sum\left(rlf, v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right)\right) \leq \sum_{teNoTransform2rlf\_dyn33(te,rlf2)}\left( vm\_capFac(t,regi,"rockgrind") \cdot vm\_cap(t,regi,"rockgrind",rlf2)\right) \end{multline*}\]
Calculation of the total amount of ground rock on the fields in timestep t. The first part of the equation describes the decay of the rocks added until that time, the rest describes the newly added rocks.
\[\begin{multline*} v33\_grindrock\_onfield\_tot(ttot,regi,rlf,rlf2) = v33\_grindrock\_onfield\_tot(ttot-1,regi,rlf,rlf2) \cdot exp\left(-p33\_co2\_rem\_rate(rlf) \cdot pm\_ts(ttot)\right) + v33\_grindrock\_onfield(ttot-1,regi,rlf,rlf2) \cdot \left(\sum_{tall \$ \left(\left(tall.val lt \left(ttot.val-\frac{pm\_ts(ttot)}{2}\right)\right) \$ \left(tall.val gt \left(ttot.val-pm\_ts(ttot)\right)\right)\right)}\left(exp\left(-p33\_co2\_rem\_rate(rlf) \cdot \left(ttot.val-tall.val\right)\right)\right)\right) + v33\_grindrock\_onfield(ttot,regi,rlf,rlf2) \cdot \left(\sum_{tall \$ \left(\left(tall.val le ttot.val\right) \$ \left(tall.val gt \left(ttot.val-\frac{pm\_ts(ttot)}{2}\right)\right)\right)}\left(exp\left(-p33\_co2\_rem\_rate(rlf) \cdot \left(ttot.val-tall.val\right)\right)\right)\right) \end{multline*}\]
Calculation of (negative) CO2 emissions from enhanced weathering.
\[\begin{multline*} v33\_emiEW(t,regi) = \sum_{rlf}\left( - \sum_{rlf2}v33\_grindrock\_onfield\_tot(t,regi,rlf,rlf2) \cdot s33\_co2\_rem\_pot \cdot \left(1 - exp\left(-p33\_co2\_rem\_rate(rlf)\right)\right) \right) \end{multline*}\]
Calculation of (negative) CO2 emissions from direct air capture. The first part of the equation describes emissions captured from the ambient air, the second part calculates the CO2 captured from the gas used for heat production assuming 90% capture rate.
\[\begin{multline*} v33\_emiDAC(t,regi) = -\sum_{teNoTransform2rlf\_dyn33(te,rlf2)}\left( vm\_capFac(t,regi,"dac") \cdot vm\_cap(t,regi,"dac",rlf2)\right) - \left(\frac{1 }{ pm\_eta\_conv(t,regi,"gash2c")}\right) \cdot fm\_dataemiglob("pegas","seh2","gash2c","cco2") \cdot vm\_otherFEdemand(t,regi,"fegas") \end{multline*}\]
Sum of all CDR emissions other than BECCS and afforestation, which are calculated in the core.
\[\begin{multline*} vm\_emiCdr(t,regi,"co2") = v33\_emiEW(t,regi) + v33\_emiDAC(t,regi) \end{multline*}\]
Calculation of energy demand of DAC and EW. The first part of the equation describes the electricity demand for grinding, the second part the diesel demand for transportation and spreading on crop fields. The third part is DAC electricity demand and the last part is DAC heat demand. Heat for DAC can be provided by gas or H2; vm_otherFEdemand(t,regi,“fegas”) is calculated as the total DAC energy demand for heat minus what is already covered by h2, i.e. vm_otherFEdemand(t,regi,“feh2s”) and vice versa.
\[\begin{multline*} vm\_otherFEdemand(t,regi,entyFe) = \sum_{rlf}\left( s33\_rockgrind\_fedem\$sameas(entyFe,"feels") \cdot sm\_EJ\_2\_TWa \cdot \sum_{rlf2}v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) + \sum_{rlf}\left( s33\_rockfield\_fedem\$sameas(entyFe,"fedie") \cdot sm\_EJ\_2\_TWa \cdot \sum_{rlf2}v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) - v33\_emiDAC(t,regi) \cdot sm\_EJ\_2\_TWa \cdot p33\_dac\_fedem(entyFe) - vm\_otherFEdemand(t,regi,"feh2s")\$sameas(entyFe,"fegas") - vm\_otherFEdemand(t,regi,"fegas")\$sameas(entyFe,"feh2s") \end{multline*}\]
Limit the amount of H2 from biomass to the demand without DAC.
\[\begin{multline*} vm\_prodSE(t,regi,"pebiolc","seh2",te)\$pe2se("pebiolc","seh2",te) \leq vm\_prodFe(t,regi,"seh2","feh2s","tdh2s") - vm\_otherFEdemand(t,regi,"feh2s") \end{multline*}\]
O&M costs of EW, consisting of fix costs for mining, grinding and spreading, and transportation costs.
\[\begin{multline*} vm\_omcosts\_cdr(t,regi) = \sum_{rlf\$\left(rlf.val le 2\right)}\left( \sum_{rlf2}\left( \left(s33\_costs\_fix + p33\_transport\_costs(regi,rlf,rlf2)\right) \cdot v33\_grindrock\_onfield(t,regi,rlf,rlf2) \right) \right) \end{multline*}\]
Limit total amount of ground rock on the fields to regional maximum potentials.
\[\begin{multline*} \sum_{rlf2}v33\_grindrock\_onfield\_tot(t,regi,rlf,rlf2) \leq f33\_maxProdGradeRegiWeathering(regi,rlf) \end{multline*}\]
Preparation of captured emissions to enter the CCS chain.
\[\begin{multline*} \sum_{teCCS2rlf(te,rlf)} vm\_ccs\_cdr(t,regi,enty,enty2,te,rlf) = -v33\_emiDAC(t,regi) \end{multline*}\]
An annual limit for the maximum amount of rocks spred [Gt] can be set via cm_LimRock, e.g. due to sustainability concerns.
\[\begin{multline*} \sum_{rlf}\left( \sum\left(rlf2,v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) \right) \leq cm\_LimRock \cdot p33\_LimRock(regi) \end{multline*}\]
Limitations There are no known limitations.
In this realization, direct air capture can be used to remove CO2 from the atmosphere in addition to BECCS and afforestation. Based on Broehm et al. we assume an energy demand of 2 GJ/tCO2 electricity and 10 GJ/tCO2 heat which can be met via gas or H2. If gas is used, the resulting CO2 is captured with a capture rate of 90%.
Calculation of (negative) CO2 emissions from direct air capture. The first part of the equation describes emissions captured from the ambient air, the second part calculates the CO2 captured from the gas used for heat production assuming 90% capture rate.
\[\begin{multline*} v33\_emiDAC(t,regi) = - \sum_{teNoTransform2rlf\_dyn33(te,rlf2)}\left( vm\_capFac(t,regi,"dac") \cdot vm\_cap(t,regi,"dac",rlf2)\right) - \left(\frac{1 }{ pm\_eta\_conv(t,regi,"gash2c")}\right) \cdot fm\_dataemiglob("pegas","seh2","gash2c","cco2") \cdot vm\_otherFEdemand(t,regi,"fegas") \end{multline*}\]
Sum of all CDR emissions other than BECCS and afforestation, which are calculated in the core.
\[\begin{multline*} vm\_emiCdr(t,regi,"co2") = v33\_emiDAC(t,regi) \end{multline*}\]
Calculation of energy demand of direct air capture. Heat can be provided by gas or H2; vm_otherFEdemand(t,regi,“fegas”) is calculated as the total energy demand for heat minus what is already covered by h2, i.e. vm_otherFEdemand(t,regi,“feh2s”) and vice versa.
\[\begin{multline*} vm\_otherFEdemand(t,regi,entyFe) = - vm\_emiCdr(t,regi,"co2") \cdot sm\_EJ\_2\_TWa \cdot p33\_dac\_fedem(entyFe) - vm\_otherFEdemand(t,regi,"feh2s")\$sameas(entyFe,"fegas") - vm\_otherFEdemand(t,regi,"fegas")\$sameas(entyFe,"feh2s") \end{multline*}\]
Preparation of captured emissions to enter the CCS chain.
\[\begin{multline*} \sum_{teCCS2rlf(te,rlf)} vm\_ccs\_cdr(t,regi,enty,enty2,te,rlf) = -vm\_emiCdr(t,regi,"co2") \end{multline*}\]
Limit the amount of H2 from biomass to the demand without DAC.
\[\begin{multline*} vm\_prodSE(t,regi,"pebiolc","seh2",te)\$pe2se("pebiolc","seh2",te) \leq vm\_prodFe(t,regi,"seh2","feh2s","tdh2s") - vm\_otherFEdemand(t,regi,"feh2s") \end{multline*}\]
Limitations There are no known limitations.
In this realization, no additional CDR option other than BECCS and afforestation is available.
Limitations There are no known limitations.
In this realization, enhanced weathering of rocks can be used to remove CO2 from the atmosphere in addition to BECCS and afforestation. Electricty is needed to grind the rocks and diesel is needed for transportation and spreading on crop fields.
Calculation of the energy demand of enhanced weathering. The first part of the equation describes the electricity demand for grinding, the second part the diesel demand for transportation and spreading on crop fields.
\[\begin{multline*} vm\_otherFEdemand(t,regi,entyFe)\$\left(sameas(entyFe,"feels") OR sameas(entyFe,"fedie")\right) = \sum_{rlf\$\left(rlf.val le 2\right)}\left( s33\_rockgrind\_fedem\$sameas(entyFe,"feels") \cdot sm\_EJ\_2\_TWa \cdot \sum_{rlf2}v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) + \sum_{rlf\$\left(rlf.val le 2\right)}\left( s33\_rockfield\_fedem\$sameas(entyFe,"fedie") \cdot sm\_EJ\_2\_TWa \cdot \sum_{rlf2}v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) \end{multline*}\]
Calculation of the amount of ground rock spread in timestep t.
\[\begin{multline*} \sum_{rlf2}\left(\sum_{rlf\$\left(rlf.val le 2\right)} v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) \leq \sum_{teNoTransform2rlf\_dyn33(te,rlf2)}\left( vm\_capFac(t,regi,"rockgrind") \cdot vm\_cap(t,regi,"rockgrind",rlf2)\right) \end{multline*}\]
Calculation of the total amount of ground rock on the fields in timestep t. The first part of the equation describes the decay of the rocks added until that time, the rest describes the newly added rocks.
\[\begin{multline*} v33\_grindrock\_onfield\_tot(ttot,regi,rlf,rlf2)\$\left(rlf.val le 2\right) = v33\_grindrock\_onfield\_tot(ttot-1,regi,rlf,rlf2)\$\left(rlf.val le 2\right) \cdot exp\left(-p33\_co2\_rem\_rate(rlf)\$\left(rlf.val le 2\right) \cdot pm\_ts(ttot)\right) + v33\_grindrock\_onfield(ttot-1,regi,rlf,rlf2)\$\left(rlf.val le 2\right) \cdot \left(\sum_{tall \$ \left(\left(tall.val lt \left(ttot.val-\frac{pm\_ts(ttot)}{2}\right)\right) \$ \left(tall.val gt \left(ttot.val-pm\_ts(ttot)\right)\right)\right)}\left(exp\left(-p33\_co2\_rem\_rate(rlf)\$\left(rlf.val le 2\right) \cdot \left(ttot.val-tall.val\right)\right)\right)\right) + v33\_grindrock\_onfield(ttot,regi,rlf,rlf2)\$\left(rlf.val le 2\right) \cdot \left(\sum_{tall \$ \left(\left(tall.val le ttot.val\right) \$ \left(tall.val gt \left(ttot.val-\frac{pm\_ts(ttot)}{2}\right)\right)\right)}\left(exp\left(-p33\_co2\_rem\_rate(rlf)\$\left(rlf.val le 2\right) \cdot \left(ttot.val-tall.val\right)\right)\right)\right) \end{multline*}\]
Calculation of (negative) CO2 emissions from enhanced weathering.
\[\begin{multline*} v33\_emiEW(t,regi) = \sum_{rlf\$\left(rlf.val le 2\right)}\left( - \sum_{rlf2}v33\_grindrock\_onfield\_tot(t,regi,rlf,rlf2) \cdot s33\_co2\_rem\_pot \cdot \left(1 - exp\left(-p33\_co2\_rem\_rate(rlf)\right)\right) \right) \end{multline*}\]
Sum of all CDR emissions other than BECCS and afforestation, which are calculated in the core.
\[\begin{multline*} vm\_emiCdr(t,regi,"co2") = v33\_emiEW(t,regi) \end{multline*}\]
O&M costs of EW, consisting of fix costs for mining, grinding and spreading, and transportation costs.
\[\begin{multline*} vm\_omcosts\_cdr(t,regi) = \sum_{rlf\$\left(rlf.val le 2\right)}\left( \sum_{rlf2}\left( \left(s33\_costs\_fix + p33\_transport\_costs(regi,rlf,rlf2)\right) \cdot v33\_grindrock\_onfield(t,regi,rlf,rlf2) \right) \right) \end{multline*}\]
Limit total amount of ground rock on the fields to regional maximum potentials.
\[\begin{multline*} \sum_{rlf2}\left(v33\_grindrock\_onfield\_tot(t,regi,rlf,rlf2)\$\left(rlf.val le 2\right)\right) \leq f33\_maxProdGradeRegiWeathering(regi,rlf)\$\left(rlf.val le 2\right) \end{multline*}\]
An annual limit for the maximum amount of rocks spred [Gt] can be set via cm_LimRock, e.g. due to sustainability concerns.
\[\begin{multline*} \sum_{rlf}\left( \sum\left(rlf2,v33\_grindrock\_onfield(t,regi,rlf,rlf2)\right) \right) \leq cm\_LimRock \cdot p33\_LimRock(regi) \end{multline*}\]
Limitations There are no known limitations.
| Description | |
|---|---|
| f33_maxProdGradeRegiWeathering (all_regi, rlf) |
regional maximum potentials for enhanced weathering in Gt of grinded stone/a for different grades |
| p33_co2_rem_rate (rlf) |
carbon removal rate [fraction of annual reduction of total carbon removal potential], multiplied with grade factor |
| p33_dac_fedem (all_enty) |
specific heat and electricity demand for direct air capture |
| p33_LimRock (all_regi) |
regional share of EW limit [fraction], calculated ex ante for a maximal annual amount of 8 Gt rock in D:_technical_curve_transport_remind_regions.m |
| p33_transport_costs (all_regi, rlf, rlf) |
transport costs |
| q33_capconst_dac (ttot, all_regi) |
calculates amount of carbon captured by DAC |
| q33_capconst_grindrock (ttot, all_regi) |
calculates amount of ground rock spred on fields |
| q33_ccsbal (ttot, all_regi, all_enty, all_enty, all_te) |
calculates CCS emissions from CDR technologies |
| q33_emicdrregi (ttot, all_regi) |
calculates the (negative) emissions due to CDR technologies |
| q33_emiEW (ttot, all_regi) |
calculates amount of carbon captured by EW |
| q33_grindrock_onfield_tot (ttot, all_regi, rlf, rlf) |
total amount of ground rock on fields |
| q33_H2bio_lim (ttot, all_regi, all_te) |
limits H2 from bioenergy to FE - otherFEdemand, i.e. no H2 from bioenergy for DAC |
| q33_LimEmiEW (ttot, all_regi) |
limits EW to a maximal annual amount of ground rock of cm_LimRock |
| q33_omcosts (ttot, all_regi) |
calculates O&M costs for spreading ground rocks on fields |
| q33_omcosts_onfield (ttot, all_regi) |
calculates O&M costs for spreading ground rocks on fields |
| q33_otherFEdemand (ttot, all_regi, all_enty) |
calculates final energy demand from no transformation technologies (e.g. enhanced weathering) |
| q33_potential (ttot, all_regi, rlf) |
limits the total potential of EW per region and grade |
| s33_co2_rem_pot | specific carbon removal potential |
| s33_co2_rem_rate | carbon removal rate |
| s33_costs_fix | fixed costs for mining, grinding, spreading |
| s33_rockfield_fedem | specific energy demand for spreading rocks on field |
| s33_rockgrind_fedem | specific energy demand for grinding rocks |
| s33_step | size of bins in v33_grindrock_onfield |
| v33_emiDAC (ttot, all_regi) |
carbon captured from DAC |
| v33_emiEW (ttot, all_regi) |
negative CO2 emission from EW |
| v33_grindrock_onfield (ttot, all_regi, rlf, rlf) |
amount of ground rock spread on fields in each timestep |
| v33_grindrock_onfield_tot (ttot, all_regi, rlf, rlf) |
total amount of ground rock on fields |
| Unit | A | B | C | D | |
|---|---|---|---|---|---|
| f33_maxProdGradeRegiWeathering (all_regi, rlf) |
x | x | |||
| p33_co2_rem_rate (rlf) |
x | x | |||
| p33_dac_fedem (all_enty) |
\(EJ/Gt of C captured\) | x | x | ||
| p33_LimRock (all_regi) |
x | x | |||
| p33_transport_costs (all_regi, rlf, rlf) |
\(T\$/Gt stone\) | x | x | ||
| q33_capconst_dac (ttot, all_regi) |
x | x | |||
| q33_capconst_grindrock (ttot, all_regi) |
x | x | |||
| q33_ccsbal (ttot, all_regi, all_enty, all_enty, all_te) |
x | x | |||
| q33_emicdrregi (ttot, all_regi) |
x | x | x | ||
| q33_emiEW (ttot, all_regi) |
x | x | |||
| q33_grindrock_onfield_tot (ttot, all_regi, rlf, rlf) |
x | x | |||
| q33_H2bio_lim (ttot, all_regi, all_te) |
x | x | |||
| q33_LimEmiEW (ttot, all_regi) |
x | x | |||
| q33_omcosts (ttot, all_regi) |
x | ||||
| q33_omcosts_onfield (ttot, all_regi) |
x | ||||
| q33_otherFEdemand (ttot, all_regi, all_enty) |
x | x | x | ||
| q33_potential (ttot, all_regi, rlf) |
x | x | |||
| s33_co2_rem_pot | \(Gt C/Gt ground rock\) | x | x | ||
| s33_co2_rem_rate | \(fraction of annual reduction of total carbon removal potential\) | x | x | ||
| s33_costs_fix | \(T\$/Gt stone\) | x | x | ||
| s33_rockfield_fedem | \(EJ/Gt of ground rock\) | x | x | ||
| s33_rockgrind_fedem | \(EJ/Gt of ground rock\) | x | x | ||
| s33_step | \(Gt stone\) | x | x | ||
| v33_emiDAC (ttot, all_regi) |
\(GtC / a\) | x | x | x | |
| v33_emiEW (ttot, all_regi) |
\(GtC / a\) | x | x | x | |
| v33_grindrock_onfield (ttot, all_regi, rlf, rlf) |
\(Gt\) | x | x | x | x |
| v33_grindrock_onfield_tot (ttot, all_regi, rlf, rlf) |
\(Gt\) | x | x | x | x |
| description | |
|---|---|
| adjte_dyn33(all_te) | technologies with linearly growing constraint on control variable |
| all_enty | all types of quantities |
| all_regi | all regions |
| all_te | all energy technologies, including from modules |
| ccs2te(all_enty, all_enty, all_te) | chain for ccs |
| ccsCo2(all_enty) | only cco2 (???) |
| enty(all_enty) | all types of quantities |
| entyFe(all_enty) | final energy types. Calculated in sets_calculations |
| in(all_in) | All inputs and outputs of the CES function |
| modules | all the available modules |
| pe2se(all_enty, all_enty, all_te) | map primary energy carriers to secondary |
| regi(all_regi) | all regions used in the solution process |
| rlf | cost levels of fossil fuels |
| t(ttot) | modeling time, usually starting in 2005, but later for fixed delay runs |
| tall | time index |
| te(all_te) | energy technologies |
| te_dyn33(all_te) | all technologies |
| teAdj(all_te) | technologies with adjustment costs on capacity additions |
| teCCS2rlf(all_te, rlf) | mapping for CCS technologies to grades |
| teNoTransform(all_te) | all technologies that do not transform energy but still have investment and O&M costs (like storage or grid) |
| teNoTransform_dyn33(all_te) | all technologies that do not transform energy but still have investment and O&M costs (like storage or grid) |
| teNoTransform2rlf(all_te, rlf) | mapping for no transformation technologies to grades |
| teNoTransform2rlf_dyn33(all_te, rlf) | mapping for final energy to grades |
| ttot(tall) | time index with spin up |
Jessica Strefler