Monod-type kinetics implementation

[pietromazzon]

Hi everyone,

I would like to ask your help about a monod-type kinetics.
I would like to calculate the degradation of a Master Species (Dca) through a monod term. The problem is that PHREEQC calculates an initial degradation rate and uses it as constant through the whole simulation, instead of changing it in each time step, making it a first-order kinetics.
How do I make PHREEQC change the degradation rate within the time steps considering the variation of substrate concentration?
Here below I leave my code and the simulation.

Code: [Select]

TITLE Batch biodegradation of 1,2 DCA following an easy Monod kinetics
SOLUTION_MASTER_SPECIES
    Dca           Dca              0     98.97           98.97
    Ethene         Ethene            0     28.05           28.05
SOLUTION_SPECIES
Dca=Dca
    log_k     0
Ethene=Ethene
    log_k     0

SOLUTION 1 #Standard solution containing 1000 ug/L of Dca
    temp      25
    pH        7
    pe        4
    redox     pe
    units     ug/L
    density   1
    Dca       1000
    Ethene    0
    -water    1 # kg
RATES
    Dca
-start
10 Ks = 0.000001 # mol/l
15 umax = 2.48E-08 # 1/s
20 dca=MOL("Dca") #reads the Dca moles
30 rate = umax*dca/(Ks+dca) #Monod term to calculate substrate consumption
40 moles = rate*TIME #Moles of substrated consumed
50 SAVE moles
-end

KINETICS 1
Dca
    -formula  Dca  -1 Ethene  1
-steps       43200000 in 20 steps # seconds

INCREMENTAL_REACTIONS true

USER_GRAPH 1
    -headings               _time_ Dca
    -axis_titles            "Time (days)" "Mole per kilogram water"
    -chart_title            "Dca degradation"
    -initial_solutions      true
    -connect_simulations    true
    -plot_concentration_vs  t
  -start
10 GRAPH_X TOTAL_TIME/86400
20 GRAPH_Y TOT("Dca")
  -end

END

Thank you very much for the help,

Pietro

[dlparkhurst]

Your rate is not constant; it is just very fast. umax is 2.48e-8 per second, which is 2.14e-3 per day. The Dca concentration is only 1e-5 per day, so it only takes about 0.01 days to remove all the Dca. If you set your -steps to 864 s, you will see the decrease in Dca. The following also plots the rate.

Code: [Select]

TITLE Batch biodegradation of 1,2 DCA following an easy Monod kinetics
SOLUTION_MASTER_SPECIES
    Dca           Dca              0     98.97           98.97
    Ethene         Ethene            0     28.05           28.05
SOLUTION_SPECIES
Dca=Dca
    log_k     0
Ethene=Ethene
    log_k     0

SOLUTION 1 #Standard solution containing 1000 ug/L of Dca
    temp      25
    pH        7
    pe        4
    redox     pe
    units     ug/L
    density   1
    Dca       1000
    Ethene    0
    -water    1 # kg
RATES
    Dca
-start
10 Ks = 0.000001 # mol/l
15 umax = 2.48E-08 # 1/s
20 dca=MOL("Dca") #reads the Dca moles
30 rate = umax*dca/(Ks+dca) #Monod term to calculate substrate consumption
40 moles = rate*TIME #Moles of substrated consumed
45 put(rate, 1)
50 SAVE moles
-end

KINETICS 1
Dca
    -formula  Dca  -1 Ethene  1
-steps     864 in 20 #  43200000 in 20 steps # seconds

INCREMENTAL_REACTIONS true

USER_GRAPH 1
    -headings               _time_ Dca Rate
    -axis_titles            "Time (days)" "Mole per kilogram water" "mol/s"
    -chart_title            "Dca degradation"
    -initial_solutions      true
    -connect_simulations    true
    -plot_concentration_vs  t
  -start
10 GRAPH_X TOTAL_TIME/86400
20 GRAPH_Y TOT("Dca")
30 GRAPH_SY GET(1)
  -end

END


[pietromazzon]

Thank you very much for your help!

Pietro