Limits on upscaling for enhanced weathering

main.gms

@@ -903,6 +903,17 @@ parameter
 ;
   cm_LimRock               = 1000;   !! def = 1000
 *'
+
+parameter
+  cm_33_EW_upScalingRateLimit    "Annual growth rate limit on upscaling of mining & spreading rocks on fields"
+;
+  cm_33_EW_upScalingRateLimit = 0.2;  !! def = 20% 
+
+parameter 
+  cm_33_EW_shortTermLimit         "Limit on 2030 potential for enhanced weathering, defined as % of land on which EW is applied. Default 0.5% of land"
+;
+  cm_33_EW_shortTermLimit = 0.005; 
+
 parameter
   cm_expoLinear_yearStart   "time at which carbon price increases linearly instead of exponentially"
 ;

modules/33_CDR/portfolio/datainput.gms

@@ -50,6 +50,12 @@ 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));
 
+*' Annual growth rate limit on upscaling of mining & spreading rocks on fields
+p33_EW_upScalingLimit(ttot) = cm_33_EW_upScalingRateLimit;
+
+*' Calculation of short term limit on rocks spread on field in terms of Gt rocks that can be spread. 
+p33_EW_shortTermEW_Limit(regi) = cm_33_EW_shortTermLimit * sum(rlf, f33_maxProdGradeRegiWeathering(regi, rlf));
+
 *** ocean alkalinity enhancement input data (Kowalczyk et al., 2024)
 
 !! An assumption; generally the efficiency might vary between 0.9-1.4 tCO2/tCaO (1.2-1.8 molCO2/molCaO),

modules/33_CDR/portfolio/declarations.gms

@@ -23,6 +23,8 @@ parameters
 p33_fedem(all_te,all_enty)               "final energy demand of each technology [EJ/GtC] (for EW the unit is [EJ/Gt stone])"
 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_co2_rem_rate(rlf)                    "carbon removal rate [fraction of annual reduction of total carbon removal potential], multiplied with grade factor"
+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"
 ;
 
 positive variables
@@ -55,6 +57,8 @@ q33_EW_FEdemand(ttot,all_regi,all_enty)  "calculates final energy demand from en
 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"
 
 q33_OAE_FEdemand(ttot,all_regi,all_enty,all_te) "calculates final energy demand for ocean alkalinity enhancement"
 q33_OAE_co2emi_non_atm_calcination(ttot,all_regi,all_te)   "calculates the CO2 that comes from calcination (limestone decomposition)"

modules/33_CDR/portfolio/equations.gms

@@ -189,7 +189,27 @@ q33_EW_LimEmi(t,regi)..
     =l=
     cm_LimRock * p33_LimRock(regi)
     ;
-
+
+***---------------------------------------------------------------------------
+*' Short term bound on spreading of rock
+***---------------------------------------------------------------------------
+
+q33_EW_ShortTermBound(t, regi)$(t.val eq 2030)..
+    sum((rlf_cz33, rlf), v33_EW_onfield(t,regi,rlf_cz33,rlf))
+    =l=
+    p33_EW_shortTermEW_Limit(regi) 
+    ;
+
+***---------------------------------------------------------------------------
+*' Limits on the upscaling rate of mining and spreading of rocks. 
+*' Current cost parameters do not include cost of additional mining being developed, 
+*' thus adjustment cost are not effective.
+***---------------------------------------------------------------------------	
+q33_EW_upscaling_rate(ttot,regi)$(ord(ttot) lt card(ttot) AND pm_ttot_val(ttot) gt 2030)..
+   sum((rlf_cz33, rlf), v33_EW_onfield(ttot,regi,rlf_cz33,rlf))
+    =l=
+   (1+p33_EW_upScalingLimit(ttot))**pm_dt(ttot) * sum((rlf_cz33, rlf), v33_EW_onfield(ttot-1,regi,rlf_cz33,rlf))
+;
 
 ***---------------------------------------------------------------------------
 *' #### OAE equations