Conceptual Models > Kinetics and rate controlling factors

Acetogenesis reaction

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stfmtu:
Hello,

I am trying to extend the duration of the reaction, but even after increasing the gas phase or the volume of the solution, the reaction still stops relatively quickly. When I increase the amount of H₂ or CO₂ present, the reaction produces more acetate daily, but it doesn't prolong the overall reaction time. More acetate is produced each day, yet the reaction still stops in the same number of days. Why is the reaction stopping so quickly?

Thank you!


--- Code: ---SOLUTION_MASTER_SPECIES
    Acetate       HAcetate         0     Acetate         59
SOLUTION_SPECIES
HAcetate =  HAcetate
-gamma 3.0000
log_k 0
HAcetate =  Acetate- + H+
         -gamma         4.5         
         log_k        -4.7572
         -analytic    -0.96597E+02   -0.34535E-01    0.19753E+04    0.38593E+02    0.30850E+02

RATES
    Acetate_formation
-start
10 qm = 1.0093E-5                                   #specific maximum growth rate
15 Y = 0.079                                     #Yield coefficient
20 rate = qm/Y * TOT("C(4)")/(1.155E-4 + TOT("C(4)"))  * TOT("Hdg")/(2.5E-6 + TOT("Hdg")) * kin("Biomass") #Acetate Formation using Dual Monod Rate
30 moles = rate * TIME                              #positive value decreases Hdg
40 put(rate,1)
50 SAVE moles
-end

Biomass
-start
   1 Y = 0.079
   2 b = 1.0093E-7
   10 rate = get(1)
   20 rate = -Y*rate + b*M  # negative rate increases M (biomass)
                              # positive rate (d*B) decreases M (biomass)
   30 moles = rate * time
   40 save moles
-end
END

SOLUTION 1
    temp      90
    pH        7 charge
    pe        4
    redox     pe
    -water    1 # kg
END

GAS_PHASE 1
    -fixed_volume
    -pressure 300
    -volume 1
    -temperature 90
    CO2(g)    100
    Hdg(g)    200
END

INCREMENTAL_REACTIONS true

KINETICS 1
Acetate_formation
    -formula  CO2  -2 H2O  2 HAcetate  1 Hdg  -4
    -m0       6.552e+00
    -tol      1e-08

Biomass
   -formula       CH1.8O0.5N0.2 0.0
   -m0             1e-5

-steps       1728000 in 100 steps  #20 Tage
-cvode
END

USE solution 1
USE kinetics 1
USE gas_phase 1

USER_GRAPH 1
    -chart_title      "Gaseous components during acetogenesis"
    -headings               CO2(g) Acetate Hdg(g)
    -axis_titles            "Days"  "Pressure gas phase [atm]"
    -axis_scale y_axis      auto auto auto
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 PLOT_XY TOTAL_TIME/86400, GAS("CO2(g)"), color=Black,symbol=Square,symbol_size=0,y_axis=1,line_width=3
20 PLOT_XY TOTAL_TIME/86400, GAS("Acetate"),color=Orange,symbol=Triangle,symbol_size=0,y_axis=1,line_width=3
30 PLOT_XY TOTAL_TIME/86400, GAS("Hdg(g)"), color=Blue,symbol=Diamond,symbol_size=0,y_axis=1,line_width=3
  -end
    -active                 true
USER_GRAPH 2
    -chart_title      "Aqueous species during methanogenesis"
    -headings               CO2(aq) Acetate Hdg(aq)  Biomass(aq)
    -axis_titles            "Days" "Mole concentration of aqu. species" "Moles of Biomass in aqu. phase"
    -axis_scale y_axis      auto auto auto auto
    -axis_scale sy_axis      auto auto
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 PLOT_XY TOTAL_TIME/86400, TOT("C(4)"), color=Black,symbol=Square,symbol_size=0,y_axis=1,line_width=3
20 PLOT_XY TOTAL_TIME/86400, TOT("Acetate"),color=Orange,symbol=Triangle,symbol_size=0,y_axis=1,line_width=3
30 PLOT_XY TOTAL_TIME/86400, TOT("Hdg"), color=Blue,symbol=Diamond,symbol_size=0,y_axis=1,line_width=3
40 PLOT_XY TOTAL_TIME/86400, KIN("Biomass"), color=Green,symbol=Circle,symbol_size=6,y_axis=2,line_width=1
  -end
    -active                 true

USER_GRAPH 3
    -chart_title      "Total Moles in the System"
    -headings               CO2 Hdg Acetate
    -axis_titles            "Days" "Moles" "Moles Acetate"
    -axis_scale y_axis      auto auto
    -axis_scale sy_axis      auto auto
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 PLOT_XY TOTAL_TIME/86400, TOTMOLE("C(4)")+GAS("CO2(g)"), color=Black,symbol=Square,symbol_size=0,y_axis=1,line_width=3
20 PLOT_XY TOTAL_TIME/86400, TOT("Hdg")+GAS("Hdg(g)"), color=Blue,symbol=Diamond,symbol_size=0,y_axis=1,line_width=3
30 PLOT_XY TOTAL_TIME/86400, TOT("Acetate")+GAS("Acetate"),color=Orange,symbol=Triangle,symbol_size=0,y_axis=2,line_width=3
  -end
    -active                 true
--- End code ---

dlparkhurst:
Your simulation stops because you run out of CO2 and Hdg. If you increase the volume of the gas phase to 10, the simulation runs to completion, but then the reaction stops at about 12 days because KIN("Acetate_formation") (or M for the reaction) goes to zero. If the moles of a kinetic reactant is zero, the reaction stops.

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