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RATESCO2_dissolution20 k = parm(2) / 8640030 eq_CO2 = 10^PARM(1)*10^LK_PHASE("CO2(g)")40 act_CO2 = ACT("CO2")50 moles = k * (eq_CO2 - act_CO2) * TIME 60 SAVE molesENDSOLUTIONKINETICSCO2_dissolution-formula CO2 1-parm 0 1 # target log PCO2(g), rate constant 1/day-time 500000 in 10USER_GRAPH 1 -axis_titles "Time, in days" "LOG P(CO2(g))" "" -initial_solutions false -connect_simulations true -plot_concentration_vs x -start10 GRAPH_X TOTAL_TIME/8640020 GRAPH_Y SI("CO2(g)") -end

logK(CO2(g)) = a(CO2(aq)) / f(CO2(g))ora(CO2(aq)) = logK(CO2(g))*f(CO2(g))andf(CO2(g)) is approximately P(CO2(g))

CO2 + H2O -> H2CO3 -> H+ + HCO3-

CO2 + OH- -> HCO3-

SOLUTION_MASTER_SPECIES [CO2] [CO2] 0 CO2 44SOLUTION_SPECIES[CO2] = [CO2]log_k 0CO3-2 + 2 H+ = H2CO3 -log_k 16.681 -delta_h -5.738 kcal -analytic 464.1965 0.09344813 -26986.16 -165.75951 2248628.9 -dw 1.92e-9 -Vm 7.29 0.92 2.07 -1.23 -1.60 # ref. 1 + McBride et al. 2015, JCED 60, 1712H2CO3 = (CO2)2 + 2H2O # activity correction for CO2 solubility at high P, T -log_k -1.8 -analytical_expression 8.68 -0.0103 -2190 -Vm 14.58 1.84 4.14 -2.46 -3.20PHASESCO2(g) CO2 + H2O = H2CO3 -log_k -1.468 -delta_h -4.776 kcal -analytic 10.5624 -2.3547e-2 -3972.8 0 5.8746e5 1.9194e-5 -T_c 304.2 # critical T, K -P_c 72.86 # critical P, atm -Omega 0.225 # acentric factorRATESCO2_hydration-start# CO2 + H2O -> H2CO310 kf = 3e-2 # 1/s20 kb = 12 # 1/s30 rf = kf*ACT("[CO2]")*ACT("H2O")^240 rb = kb*ACT("H2CO3")50 rate = (rf - rb)60 moles = rate * TIME70 SAVE moles-endCO2_hydroxylation-start# CO2 + OH- = HCO3-10 kf = 8.5e-3 # mol-1 s-120 kb = 2e-4 # 1/s30 rf = kf*ACT("[CO2]")*ACT("OH-")40 rb = kb*ACT("HCO3-")50 rate = (rf - rb)60 moles = rate * TIME70 SAVE moles-endENDSOLUTION-pH 9[CO2] 1KINETICSCO2_hydration-formula [CO2] -1 CO2 +1CO2_hydroxylation-formula [CO2] -1 CO2 +1-step 2 in 10USER_GRAPH 1 -headings time [CO2] H2CO3 HCO3- pH -axis_titles "Seconds" "log molality" "" -initial_solutions false -connect_simulations true -plot_concentration_vs x -start10 GRAPH_X TOTAL_TIME20 GRAPH_Y LOG10[TOT("[CO2]")], LM("H2CO3"), LM("HCO3-")30 GRAPH_SY -LA("H+") -end -active trueEND

SOLUTION_MASTER_SPECIES [CO2] [CO2] 0 CO2 44SOLUTION_SPECIES[CO2] = [CO2]log_k 0CO3-2 + 2 H+ = H2CO3 -log_k 16.681 -delta_h -5.738 kcal -analytic 464.1965 0.09344813 -26986.16 -165.75951 2248628.9 -dw 1.92e-9 -Vm 7.29 0.92 2.07 -1.23 -1.60 # ref. 1 + McBride et al. 2015, JCED 60, 1712H2CO3 = (CO2)2 + 2H2O # activity correction for CO2 solubility at high P, T -log_k -1.8 -analytical_expression 8.68 -0.0103 -2190 -Vm 14.58 1.84 4.14 -2.46 -3.20PHASESCO2(g) CO2 + H2O = H2CO3 -log_k -1.468 -delta_h -4.776 kcal -analytic 10.5624 -2.3547e-2 -3972.8 0 5.8746e5 1.9194e-5 -T_c 304.2 # critical T, K -P_c 72.86 # critical P, atm -Omega 0.225 # acentric factorRATESCO2_hydration-start# CO2 + H2O -> H2CO310 kf = 3e-2 # 1/s20 kb = 12 # 1/s30 rf = kf*ACT("[CO2]")*ACT("H2O")40 rb = kb*ACT("H2CO3")50 rate = (rf - rb)60 moles = rate * TIME70 SAVE moles-endCO2_hydroxylation-start# CO2 + OH- = HCO3-10 kf = 8.5e-3 # mol-1 s-120 kb = 2e-4 # 1/s30 rf = kf*ACT("[CO2]")*ACT("H2O")40 rb = kb*ACT("HCO3-")*ACT("H+")50 rate = (rf - rb)60 moles = rate * TIME70 SAVE moles-endENDSOLUTION-pH 9[CO2] 1KINETICSCO2_hydration-formula [CO2] -1 CO2 +1CO2_hydroxylation-formula [CO2] -1 CO2 +1-step 2 in 10USER_GRAPH 1 -headings time [CO2] H2CO3 HCO3- pH -axis_titles "Seconds" "log molality" "" -initial_solutions false -connect_simulations true -plot_concentration_vs x -start10 GRAPH_X TOTAL_TIME20 GRAPH_Y LOG10[TOT("[CO2]")], LM("H2CO3"), LM("HCO3-")30 GRAPH_SY -LA("H+") -end -active trueEND

SOLUTION_SPECIESCO3-2 + 2 H+ = CO2 + H2Olog_k -1002H2CO3 = (CO2)2 + 2H2O # activity correction for CO2 solubility at high P, Tlog_k -100

At equilibrium,kf[CO2][H2O] = kb[H2CO3]kf/kb = [H2CO3]/([CO2][H2O]) = Keq = 2.5e-3CO2 + H2O = H2CO3log_k -2.6

CO2 + H2O = H2CO3log_k -2.6CO3-2 + 2 H+ = H2CO3* ~ CO2(aq) (from phreeqc.dat) -log_k 16.681 CO3-2 + 2H+ = H2CO3log_k = 16.681 + (-2.6) = 14.081

CO2 + H2O = HCO3- + H+kf[CO2][H2O] = kr[HCO3-][H+]kf/kr = 8.5e-3/2e-4 = [HCO3-][H+]/([CO2][H2O]) = Keq = 42.5CO2 + H2O = HCO3- + H+log_k 1.63

CO3-2 + H+ = HCO3- -log_k 10.329CO3-2 + 2 H+ = CO2 + H2O -log_k 16.681CO2 + H2O = HCO3- + H+log_k = 10.329 - 16.681 = -6.352

KNOBS-conv 1e-13SOLUTION_MASTER_SPECIES [CO2] [CO2] 0 CO2 44SOLUTION_SPECIES[CO2] = [CO2]log_k 0CO3-2 + 2 H+ = CO2 + H2Olog_k -1002H2CO3 = (CO2)2 + 2H2O # activity correction for CO2 solubility at high P, Tlog_k -100CO3-2 + 2 H+ = H2CO3 -log_k 14.081# -log_k 16.681# -delta_h -5.738 kcal# -analytic 464.1965 0.09344813 -26986.16 -165.75951 2248628.9 -dw 1.92e-9 -Vm 7.29 0.92 2.07 -1.23 -1.60 # ref. 1 + McBride et al. 2015, JCED 60, 171PHASES[CO2](g) [CO2] = [CO2] -log_k -1.468 -delta_h -4.776 kcal -analytic 10.5624 -2.3547e-2 -3972.8 0 5.8746e5 1.9194e-5 -T_c 304.2 # critical T, K -P_c 72.86 # critical P, atm -Omega 0.225 # acentric factorRATESCO2_hydration-start# CO2 + H2O -> H2CO310 kf = 3e-2 # 1/s20 kb = 12 # 1/s30 rf = kf*ACT("[CO2]")*ACT("H2O")40 rb = kb*ACT("H2CO3")50 rate = (rf - rb)60 moles = rate * TIME70 SAVE moles-endCO2_hydroxylation-start# CO2 + H2O = HCO3- + H+10 kf = 8.5e-3 # mol-1 s-120 kb = 2e-4 # 1/s30 rf = kf*ACT("[CO2]")*ACT("H2O")40 rb = kb*ACT("HCO3-")*ACT("H+")50 rate = (rf - rb)60 moles = rate * TIME70 SAVE moles-endENDSOLUTION-pH 9Na 1 charge#[CO2] 1KINETICSCO2_hydration-formula [CO2] -1 CO2 +1-tol 1e-12#CO2_hydroxylation#-formula [CO2] -1 CO2 +1-step 40 in 10EQUILIBRIUM_PHASES[CO2](g) -3.4 10USER_GRAPH 1 -headings time [CO2] H2CO3 HCO3- pH -axis_titles "Seconds" "log molality" "" -initial_solutions false -connect_simulations true -plot_concentration_vs x -start10 GRAPH_X TOTAL_TIME20 GRAPH_Y LOG10[TOT("[CO2]")], LM("H2CO3"), LM("HCO3-")30 GRAPH_SY -LA("H+") -end -active trueEND