Dissolution of CO2 Gas

[Mgill9460]

Hello,

I have been working on creating a model which looks at CO2 flux into solution based on an experimentally determined reaction rate

Code: [Select]

R = k[OH]^n
Where, R is reaction rate in mol/m2min, k is the rate constant (8x10^-4), and n is the reaction order (0.45).

This rate equation I determined experimentally using an equation for gas flux

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Flux = V(dP)/RTA(dt)
where, V is volume in m^3, dP is change in gas partial pressure, R is the ideal gas constant, T is temp in kelvin, A is surface area in m^2, and dt is time in minutes

When I run my code my goal is to graph the increase in CO2 over time. However, I am not getting the result I want on my user graph. Is there something wrong with the RATES block or the USER_GRAPH block?

Code: [Select]

TITLE - CO2 Sequestration Model
SOLUTION 1
pH 11.5
units mol/L
RATES
CO2_Sequestration
-start
1 REM Parm(1) is radius of pool area in meters
2 REM surface area and volume are scaled based on (PARM(1)) radius of pool
3 iR = 8.314  #REM Ideal gas constant in m??Pa/(kmol?K)
4 SA = 0.31416 * (PARM(1) / 0.1) ^ 2  # Scaled surface Area calculation
5 V = 7.548e-3 * (PARM(1) / 0.1) ^ 3  # Scaled volume calculation
6 k1 = 8e-4 #rate constant
7 n1 = 0.45 #reaction order
10 R = k1* (TOT("OH-")) ^ n1  # Reaction rate calculation
20 dP = (R * TIME * iR * TK * SA) / V  # Change in pressure
30 ppm = (dP / 101325) * (1e6)  # Convert pressure change to ppm
40 molC = (ppm * V) / 12.01  # Calculate moles of carbon
50 moles = molC
60 save moles
-end

KINETICS 1
CO2_Sequestration
-formula CO2 1
-parm   0.1          #radius of pool in m
-time   1800 in 10 #seconds in 30 minutes

USER_GRAPH 1
-axis_titles    "Time (seconds)"   "[CO2] (moles)"
-connect_simulations true
-start
10 GRAPH_X TOTAL_TIME
20 GRAPH_Y CO2

-end


Cheers :-)

[dlparkhurst]

You need to check out the Basic functions that you need to use in RATES and in USER_GRAPH.

You need MOL("OH-") in your rate expression, and MOL("CO2") in USER_GRAPH.

It seems you have a gas phase in contact with the solution, that is changing pressure as the CO2 dissolves. You may want to consider a GAS_PHASE calculation, which would account for the changing pressure automatically. However, nothing is as easy as it seems. There is not a direct way to account for the kinetic dissolution of the gas; the gas phase is always in equilibrium with the solution.

Here is an option to produce kinetic dissolution. I have defined a new element and gas, Carbon_dioxide that is insoluble. The reaction converts Carbon_dioxide to CO2, which then partitions between the solution and the gas phase. Ultimately all the Carbon_dioxide converts to CO2, which produces equilibrium between gas and solution. I leave it to you to figure out whether it is suitable for your purposes and how to get the right units and gas-phase definitions.

Code: [Select]

SOLUTION_MASTER_SPECIES
    Carbon_dioxide Carbon_dioxide    0     CO2             28
SOLUTION_SPECIES
Carbon_dioxide = Carbon_dioxide

PHASES
Carbon_dioxide(g)
Carbon_dioxide = Carbon_dioxide
      log_k -100
-T_c 304.2 # critical T, K
-P_c 72.86 # critical P, atm
-Omega 0.225 # acentric factor
RATES
CO2_Sequestration
-start
10 k = 1/60 # 1/min
20 rate = k * GAS("Carbon_dioxide(g)") * GAS("Carbon_dioxide(g)") / (1e-8 + GAS("Carbon_dioxide(g)"))
30 moles = rate * TIME
40 SAVE moles
50 END
-end
END

TITLE - CO2 Sequestration Model
SOLUTION 1
pH 11.5
Na 1 charge
units mol/L

KINETICS 1
CO2_Sequestration
-formula Carbon_dioxide -1 CO2 1
-parm   0.1          #radius of pool in m
-time   500 in 100 #seconds in 30 minutes
-cvode
INCREMENTAL_REACTIONS
GAS_PHASE
-fixed_volume
Carbon_dioxide(g) 1
CO2(g) 0

USER_GRAPH 1
    -headings               time CO2 Pressure
    -axis_titles            "Time, seconds)" "MOL(CO2)" "Pressure, atm"
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X TOTAL_TIME
20 GRAPH_Y MOL("CO2")
30 GRAPH_SY GAS_P
  -end
    -active                 true