ERW improvements & documentation

core/datainput.gms

@@ -290,9 +290,9 @@ fm_dataglob("inco0", "oae_ng") = fm_dataglob("inco0", "oae_ng") / (cm_33_OAE_eff
 fm_dataglob("inco0", "oae_el") = fm_dataglob("inco0", "oae_el") / (cm_33_OAE_eff / sm_c_2_co2);
 
 *** convert inco0, floorcost and omv to REMIND units by applying a factor 0.001
-***   category          energy technology   ccs technology    process-based industry 
-***   input data unit   $/kW                $/(tC/a)          $/(t/a)
-***   REMIND unit       T$/TW               T$/(GtC/a)        T$/(Gt/a)
+***   category          energy technology   ccs technology    process-based industry            weathering
+***   input data unit   $/kW                $/(tC/a)          $/(t/a)                         $/(t rock/a)
+***   REMIND unit       T$/TW               T$/(GtC/a)        T$/(Gt/a)                       T$/(Gt rock/a)
 fm_dataglob("inco0",te)        = s_DpKW_2_TDpTW   * fm_dataglob("inco0",te);
 fm_dataglob("floorcost",te)    = s_DpKW_2_TDpTW   * fm_dataglob("floorcost",te);
 fm_dataglob("omv",te)          = s_DpKWa_2_TDpTWa * fm_dataglob("omv",te);

core/equations.gms

@@ -106,7 +106,7 @@ q_costOM(t,regi)..
              vm_costTeCapital(t,regi,te) * vm_cap(t,regi,te,rlf)
             )
   )
-  + vm_omcosts_cdr(t,regi)
+  + vm_EW_transport_costs(t,regi)
 ;
 
 ***---------------------------------------------------------------------------

core/input/generisdata_tech.prn

@@ -1,7 +1,7 @@
 *** SOF ./core/input/generisdata_tech.prn
 $ontext
 tech_stat   technology status: how close a technology is to market readiness. Scale: 0-3, with 0 'I can go out and build a GW plant today' to 3 'Still some research necessary'
-inco0       Initial investment costs given in $[2015] / kW[output] capacity; for dac/prc cc: $[2015] / (tC[captured]/a); for other indutry prc: $[2015]/(t[output]/a)
+inco0       Initial investment costs given in $[2015] / kW[output] capacity; for dac/prc cc: $[2015] / (tC[captured]/a); for other industry prc: $[2015]/(t[output]/a); for weathering:  $[2015]/(t rock/a)
 floorcost   Floor investment costs, given in $[2015] / kW[output]; for dac: $[2015] / (tC[captured]/a)
 constrTme   Construction time in years, needed to calculate turn-key cost premium compared to overnight costs
 lifetime    Average lifetime of a technology, given in years. Effective maximum lifetime is longer than that.
@@ -155,14 +155,14 @@ lifetime               30        30          45          45          45
 
 *** carbon management
 +           ccsinjeon   ccsinjeoff    weathering         dac      oae_ng      oae_el
-tech_stat           0            0                         4
-inco0             350          525          0.01       18800         200         400
+tech_stat           0            0             1           4 
+inco0             350          525            43        18800        200         400
 floorcost                                               4800
 constrTme           3            5
 lifetime           40           40            20          20          25          25
 mix0             1.00         1.00
 eta              1.00         1.00          1.00        1.00        1.00        1.00
-omf              0.06         0.12          0.84       0.025        0.35        0.17
+omf              0.06         0.12          0.59       0.025        0.35        0.17
 ccap0                                                 0.0008
 learn                                                   0.15
 
@@ -303,6 +303,14 @@ Ocean Liming - oae
     Costs per tC removed is calculated in the code as it depends on the efficiency (tCO2/tCaO; exogenous):
         cost (USD/tC) = inco0 (USD/tCaO) / ( efficiency (tCO2/tCaO) / 3.66 (tCO2/tC) )
 
+Enhanced Rock Weathering - weathering
+    Parameterization based on Strefler et al (2018) doi.org/10.1088/1748-9326/aaa9c4
+    annuity factor = 0.08 for lifetime of 20 years and r = 0.05; capacity factor = 0.69
+    inco0: 5 (USD/t rock) * 0.69 / 0.08 = 43 USD/t rock/a for mining and production
+    omf: O&M cost from rock mining & production (25 USD/t rock) and spreading on fields (12 USD/t rock), i.e. 37/(43/0.69) = 0.59
+    Additional transport cost from mine to field are accounted separately in 33_carbonRemoval depending on distance grade.
+    To use the upper Capital Cost estimate from Strefler et al, 15 USD/t rock, set inco0 = 129 and omf = 0.2
+
 Gas to Liquids (GtL) Fischer-Tropsch Process - gasftrec/gasftcrec
     efficiency eta = 0.60 (0.57 with capture), estimation at higher end of efficiency spectrum
     Details in Issue 518/PR 2034

main.gms

@@ -1081,15 +1081,17 @@ parameter
 *'           5 Gt CO2/yr uptake limit corresponds roughly to CaO being distributed in the upper 2m of the entire (!) EEZ
 *'           up to the precipitation avoiding concentration limit, assuming average uptake efficiency. 
 *' 
+
 parameter
-  cm_gs_ew                  "grain size (for enhanced weathering, CDR module) [micrometre]"
-;
-  cm_gs_ew                 = 20;     !! def = 20  !! regexp = is.numeric
-*'
-parameter
-  cm_LimRock                "limit amount of rock spread each year [Gt]"
+  cm_33_EW_rockRemPot             "Maximum CO2 removal potential per ton of rock (t CO2 / t rock)."
 ;
-  cm_LimRock               = 1000;   !! def = 1000
+  cm_33_EW_rockRemPot            = 0.3;   !! def = 0.3 t CO2 / t basalt
+*' Theoretical potential is influenced by the chemical composition of the rock, in particular calcium and magnesium content. 
+*' * (0.3): 0.3 t CO2 / t basalt is the commonly used average, see e.g. Strefler et al 2018 (SI-A Table A-1)
+*' * (0.2-0.4): 0.2 and 0.4 t CO2 / t basalt are a lower and upper bound in Strefler et al 2018 (SI-A Table A-1) 
+*' The theoretical potential may not be reached due to different loss pathways (dissolution through strong acids;
+*' secondary mineral formation (esp. clays); secondary carbonate formation (where carbon retention is only temporary)) which 
+*' strongly depend on the local soil conditions. Reduction below 50% of the theoretical potential is well possible. 
 *'
 parameter
   cm_33_EW_upScalingRateLimit    "Annual growth rate limit on upscaling of mining & spreading rocks on fields"

modules/33_carbonRemoval/portfolio/bounds.gms

@@ -30,7 +30,7 @@ vm_co2emi_cdrFE_beforeCapture.fx(t,regi,te_all33)$(not te_ccs33(te_all33)) = 0;
 vm_emiCdrTeDetail.fx(t,regi,te_used33)$(t.val lt 2025) = 0.0;
 v33_FEdemand.fx(t,regi,entyFe,entyFe2,te_used33)$(fe2cdr(entyFe,entyFe2,te_used33) AND (t.val lt 2025)) = 0.0;
 vm_emiCdr.fx(t,regi,"co2")$(t.val lt 2025) = 0;
-vm_omcosts_cdr.fx(t,regi)$((t.val lt 2025)) = 0;
+vm_EW_transport_costs.fx(t,regi)$((t.val lt 2025)) = 0;
 vm_cap.fx(t,regi,"weathering",rlf)$(t.val lt 2025) = 0;
 vm_co2emi_cdrFE_beforeCapture.fx(t,regi,te_used33)$(t.val lt 2025) = 0;
 v33_co2emi_non_atm_calcination.fx(t,regi,te_oae33)$(t.val lt 2025) = 0;
@@ -61,7 +61,7 @@ if(te_used33("weathering"),
     v33_EW_onfield_tot.fx(ttot,regi,rlf_cz33,rlf)$(ttot.val lt max(2025,cm_startyear)) = 0.0; !! 
     vm_emiCdrTeDetail.up(ttot,regi,"weathering")$(ttot.val gt 2040) = - sm_eps; !! force some minimum amount of EW to help the solver see it 
 else
-    vm_omcosts_cdr.fx(t,regi) = 0;
+    vm_EW_transport_costs.fx(t,regi) = 0;
     vm_cap.fx(t,regi,"weathering",rlf) = 0;
 );
 

modules/33_carbonRemoval/portfolio/datainput.gms

@@ -18,14 +18,14 @@ p33_fedem("dac", "fehes") = 21.12; !! FE demand heat for material recovery
 *' #### EW input data
 *------------------------------------------------------------------------------------
 *' @stop
-table f33_maxProdGradeRegiWeathering(all_regi,rlf)  "regional maximum potentials for enhanced weathering in Gt of grinded stone/a for different grades"
+table f33_maxProdGradeRegiWeathering(all_regi,rlf)  "regional maximum potentials for enhanced weathering in Gt of ground rock/a for different grades"
 $ondelim
 $include "./modules/33_carbonRemoval/portfolio/input/f33_maxProdGradeRegiWeathering.cs3r"
 $offdelim
 ;
 display f33_maxProdGradeRegiWeathering;
 
-parameter p33_EW_transport_costs(all_regi,rlf,rlf)    "transport costs [T$/Gt stone]"
+parameter p33_EW_transport_costs(all_regi,rlf,rlf)    "transport costs [T$/Gt rock]"
 /
 $ondelim
 $include "./modules/33_carbonRemoval/portfolio/input/p33_transportCostsWeathering.cs4r"
@@ -34,28 +34,23 @@ $offdelim
 ;
 display p33_EW_transport_costs;
 
-s33_step = 2.5;
-
 *' @code
-*' fix costs [T$/Gt stone]. Data from strefler et al. in $/t stone: mining, crushing, grinding (5.0 investment costs, 25.1 O&M costs), spreading (12.1 O&M costs)
-s33_costs_fix = 0.0422;
-s33_co2_rem_pot = 0.3 * 12/44;       !! default for basalt, for Olivine 1.1
+s33_rockRemPot = cm_33_EW_rockRemPot / sm_c_2_co2;       !! default for basalt is 0.3 t CO2/t rock, for Olivine 1.1 t CO2/t rock. Converted to t C/t rock.
+*' Sources for loss pathways that would reduce the total removal potential per ton rock: 
+*' https://www.carbon-drawdown.de/blog/2026-7-18-where-does-the-co-removal-potential-of-enhanced-weathering-actually-go; https://cdrxiv.org/preprint/417
 
 *' rock weathering rate (i.e. fraction of rock weathering per year) at ambient temperature (25 degree C), based on 
 *' eq 2 in strefler, amann et al. (2018): 
 *' wr = grain surface area based weathering rate (10^-10.53 mol m^-2 s^-1) * molar weight of basalt/forsterite (140.7 g/mol) 
-*'      * 3.155^7 s/a * specific surface area(depending on grain size cm_gs_ew)
-s33_rock_weath_rate_ambientT = 10**(-10.53) * 125 * 3.155*10**7 * 69.18*(cm_gs_ew**(-1.24));
+*'      * 3.155^7 s/a * specific surface area(depending on grain size s33_rockGrainSize)
+s33_rock_weath_rate_ambientT = 10**(-10.53) * 125 * 3.155*10**7 * 69.18*(s33_rockGrainSize**(-1.24));
 *' rock weathering rate for different climate grades: SI Tab F-1 of strefler, amann et al. (2018)
 p33_rock_weath_rate("1") = s33_rock_weath_rate_ambientT * 0.94;
 p33_rock_weath_rate("2") = s33_rock_weath_rate_ambientT * 0.29;
 
 *' JeS FE demand fit from Thorben: SI D in strefler, amann et al. (2018)
-p33_fedem("weathering", "feels") = 6.62 * cm_gs_ew**(-1.16);
-p33_fedem("weathering", "fedie") = 0.3;
-
-*' Factor distributing the global rock limit across regions according to population
-p33_LimRock(regi) = pm_pop("2005",regi) / sum(regi2,pm_pop("2005",regi2));
+p33_fedem("weathering", "feels") = 6.62 * s33_rockGrainSize**(-1.16);    !! electricity for grinding of rocks, depends on the grain size. 
+p33_fedem("weathering", "fedie") = 0.3;                         !! diesel for spreading rocks on fields using tractors
 
 *' Annual growth rate limit on upscaling of mining & spreading rocks on fields
 p33_EW_upScalingLimit(ttot) = cm_33_EW_upScalingRateLimit;
@@ -64,7 +59,7 @@ p33_EW_upScalingLimit(ttot) = cm_33_EW_upScalingRateLimit;
 p33_EW_shortTermEW_Limit(regi) = cm_33_EW_shortTermLimit * sum(rlf, f33_maxProdGradeRegiWeathering(regi, rlf));
 
 *' Narrative switch: what share of cropland can be used for EW?
-parameter f33_EW_maxShareOfCropland(ext_regi) "Maximum share of cropland available for enhanced weathering by region" / %cm_33_EW_maxShareOfCropland% /;
+parameter f33_EW_maxShareOfCropland(ext_regi) "Maximum share of suitable cropland available for enhanced weathering by region" / %cm_33_EW_maxShareOfCropland% /;
 p33_EW_maxShareOfCropland(regi) = 1; !! if no value is assigned to GLO, the default share is set to 100%
 p33_EW_maxShareOfCropland(regi) = f33_EW_maxShareOfCropland("GLO"); !! if a value is assigned to GLO, this value is set for all regions
 loop(ext_regi$f33_EW_maxShareOfCropland(ext_regi),

modules/33_carbonRemoval/portfolio/declarations.gms

@@ -9,10 +9,10 @@ scalars
 *** Multiple options
 sm_capture_rate_cdrmodule       "CO2 capture rate for CDR energy and process emissions, i.e. fegas use in OAE and DAC and for calcination emissions in oae" / 0.9 /
 *** EW
-s33_co2_rem_pot                 "specific carbon removal potential [Gt C per Gt ground rock]"
+s33_rockGrainSize               "grain size of ground rock, influences electricity demand and weathering rate. By default 20 micrometer based on Strefler et al. (2018) [micrometre]" /20/
+s33_rockRemPot                 "specific carbon removal potential [t C / t rock]"
 s33_rock_weath_rate_ambientT    "fraction of stone weathering per year at ambient temperature (25 degree C)"
-s33_costs_fix                   "fixed costs for mining, grinding, spreading [T$/Gt stone]"
-s33_step                        "size of bins in v33_weathering_onfield [Gt stone]"
+s33_step                        "size of bins in v33_EW_onfield_tot [Gt rock]" / 2.5 /
 *JeS* GJ/tCO2 = EJ/Gt CO2 = 44/12 EJ/Gt C.
 *** OAE
 s33_OAE_efficiency          "the amount of rock required to sequester 1GtC [Gt rock / GtC]"
@@ -22,9 +22,8 @@ s33_OAE_glo_limit           "global limit for OAE [tC / a]"
 
 parameters
 *** Multiple options
-p33_fedem(all_te,all_enty)               "final energy demand of each technology [EJ/GtC] (for EW the unit is [EJ/Gt stone])"
+p33_fedem(all_te,all_enty)               "final energy demand of each technology [EJ/GtC] (for EW the unit is [EJ/Gt rock])"
 *** EW
-p33_LimRock(all_regi)                    "regional share of EW limit [fraction], calculated ex ante for a maximal annual amount of 8 Gt rock in D:\projects\CEMICS\paper_technical\supply_curve_transport_remind_regions.m"
 p33_rock_weath_rate(rlf)                 "fraction of stone weathering per year depending on climate grade (warm or temperate)"
 p33_EW_upScalingLimit(ttot)              "Annual growth rate limit on upscaling of mining & spreading rocks on fields"
 p33_EW_shortTermEW_Limit(all_regi)       "Limit on 2030 potential for enhanced weathering, defined in Gt rocks, based on % of land on which EW is applied"
@@ -42,7 +41,7 @@ p33_GDP_NetNeg_share(all_regi)                    "Upper bound on share of expen
 ;
 
 variables
-vm_omcosts_cdr(tall,all_regi)                        "O&M costs for spreading grinded rocks on fields [T$]"
+vm_EW_transport_costs(tall,all_regi)     "O&M costs for transporting ground rocks from mines to fields [T$]"
 ;
 
 positive variables
@@ -85,11 +84,10 @@ q33_DAC_FEdemand(ttot,all_regi,all_enty)  "calculates final energy demand from D
 *** EW
 q33_EW_capconst(ttot,all_regi)  "calculates amount of ground rock spread on fields"
 q33_EW_onfield_tot(ttot,all_regi,rlf,rlf)  "total amount of ground rock on fields"
-q33_EW_omcosts(ttot,all_regi)  "calculates O&M costs for spreading ground rocks on fields"
-q33_EW_FEdemand(ttot,all_regi,all_enty)  "calculates final energy demand from enhanced weathering"
+q33_EW_transportCosts(ttot,all_regi)  "calculates transport costs for transporting ground rocks from mines to fields"
+q33_EW_FEdemand(ttot,all_regi,all_enty)  "calculates final energy demand from enhanced weathering for grinding and spreading rocks on fields"
 q33_EW_potential(ttot,all_regi,rlf)  "limits the total potential of EW per region and grade"
 q33_EW_emi(ttot,all_regi)  "calculates amount of carbon captured by EW"
-q33_EW_LimEmi(ttot,all_regi)  "limits EW to a maximal annual amount of ground rock of cm_LimRock"
 q33_EW_upscaling_rate(ttot, all_regi) "limits spreading of rock to a steep but credible upscaling rate"
 q33_EW_ShortTermBound(ttot,all_regi)   "Limits short term potential for enhanced weathering"
 

modules/33_carbonRemoval/portfolio/equations.gms

@@ -154,13 +154,13 @@ q33_EW_emi(t,regi)..
     vm_emiCdrTeDetail(t,regi, "weathering")
     =e=
     sum((rlf_cz33, rlf),
-        - v33_EW_onfield_tot(t,regi,rlf_cz33,rlf) * s33_co2_rem_pot * p33_rock_weath_rate(rlf_cz33)
+        - v33_EW_onfield_tot(t,regi,rlf_cz33,rlf) * s33_rockRemPot * p33_rock_weath_rate(rlf_cz33)
         )
     ;
 
 ***---------------------------------------------------------------------------
 *'  Calculation of FE demand for enhanced weathering, i.e., electricity demand for grinding,
-*'  and the diesel demand for transportation and spreading on crop fields.
+*'  and the diesel demand for spreading rocks on crop fields.
 ***---------------------------------------------------------------------------
 q33_EW_FEdemand(t,regi,entyFe2)$sum(entyFe, fe2cdr(entyFe,entyFe2,"weathering"))..
     sum(fe2cdr(entyFe,entyFe2,"weathering"), v33_FEdemand(t,regi,entyFe,entyFe2,"weathering"))
@@ -169,13 +169,13 @@ q33_EW_FEdemand(t,regi,entyFe2)$sum(entyFe, fe2cdr(entyFe,entyFe2,"weathering"))
     ;
 
 ***---------------------------------------------------------------------------
-*'  O&M costs of EW, consisting of fix costs for mining, grinding and spreading, and transportation costs.
+*'  Transport cost for rocks from mine to field
 ***---------------------------------------------------------------------------
-q33_EW_omcosts(t,regi)..
-    vm_omcosts_cdr(t,regi)
+q33_EW_transportCosts(t,regi)..
+    vm_EW_transport_costs(t,regi)
     =e=
     sum((rlf_cz33, rlf),
-        (s33_costs_fix + p33_EW_transport_costs(regi,rlf_cz33,rlf)) * v33_EW_onfield(t,regi,rlf_cz33,rlf)
+        (p33_EW_transport_costs(regi,rlf_cz33,rlf)) * v33_EW_onfield(t,regi,rlf_cz33,rlf)
     )
     ;
 
@@ -189,16 +189,6 @@ q33_EW_potential(t,regi,rlf_cz33)..
     ;
 
 
-***---------------------------------------------------------------------------
-*'  An annual limit for the maximum global amount of rocks spread [Gt] can be set via cm_LimRock,
-*'  e.g. due to sustainability concerns.
-***---------------------------------------------------------------------------
-q33_EW_LimEmi(t,regi)..
-    sum((rlf_cz33, rlf), v33_EW_onfield(t,regi,rlf_cz33,rlf))
-    =l=
-    cm_LimRock * p33_LimRock(regi)
-    ;
-
 ***---------------------------------------------------------------------------
 *' Short term bound on spreading of rock
 ***---------------------------------------------------------------------------

modules/33_carbonRemoval/portfolio/realization.gms

@@ -15,13 +15,15 @@
 *' low-temperature heat demand. The heat can be provided via district heat, electricity, gas, or H2. If gas is used,
 *' the resulting CO2 is captured with a capture rate of 90%.
 *'
-*' (EW) Basalt is mined and ground to fine grain sizes (specified in cm_gs_ew, by default 20 µm), and then spread
+*' (EW) Basalt is mined and ground to fine grain sizes (default 20 µm), and then spread
 *' on crop fields where it weathers in reaction with water and atmospheric CO2. Electricity is needed to grind the
-*' rocks and diesel is needed for transportation and spreading on crop fields. The weathering process leads to an exponential
+*' rocks and diesel is needed for spreading on crop fields. Transport costs from mine to fields depend on distance grades.
+*' In addition, capital cost for mining and production, and O&M cost for mining and distribution on fields are added. 
+*' The amount of rock that can be spread on fields is limited by the maximum potential for enhanced weathering, 
+*' which depends on the region and climate grade. The weathering process leads to an exponential
 *' decay over time of the spread rocks. There is an upper limit on the amount of rock that can be on the fields, so that
-*' in equilibrium only the part that decays in one timestep can be replaced in the next. In addition, an arbitrary
-*' limit of the amount of rock spread each year can be set in cm_LimRock. Costs consist of costs for capital, O&M,
-*' distribution and transport (grades depend on region specific transport distance from mine to fields).
+*' in equilibrium only the part that decays in one timestep can be replaced in the next. The share of suitable fields that can be 
+*' used for spreading rocks can be adjusted via cm_33_EW_maxShareOfCropland.
 *'
 *' (OAE) Ocean alkalinity enhancement via ocean liming draws down CO2 from the atmosphere by adding (hydrated) lime
 *' to the coastal or open ocean. Calcination process, which involves heating limestone to typically around 900-1000°C,
@@ -35,6 +37,11 @@
 *' material).
 *'
 *' Equations for each option determine the capacity, emissions, energy demand, costs and limits.
+
+*' (Overarching) This module further limits the amount of final energy that can be used for CDR technologies (via cm_33_maxFeShare), 
+*' and the share of GDP that can be spent on net negative emissions (via cm_33_GDP_netNegCDR_maxShare). It also contains
+*' the biochar material value price assumption and revenue calculation.
+
 ***----------------------------------------------------
 
 *####################### R SECTION START (PHASES) ##############################