Bubbling point of NCGs (CO2) in geothermal wellbore

[FreakQC]

Dear community,
I am about to model the bubbling point in a geothermal wellbore. It is the pressure (or the equivalent depth in the wellbore) when due to pressure decrease the solubility w.r.t. non-condensable gases is exceeded and a gas phase is forming. I am simplifying my problem to only CO2 for the beginning. I have a measurement of the aqueous phase (simplified to main components). There is no gas phase at reservoir conditions (140 bar, 65°C), the CO2 is completely dissolved and measured as HCO3-.
I want to calculate the bubbling point as a quasi sensitivity analysis with steadily decreasing total pressure. I am very much confused about the handling of gas phases in PhreeqC, or at least I am struggling with all possibilities (fixed-pressure, fixed-volume, EQUILIBRIUM_PHASES). A fixed-pressure gas phase seems to be wrong, since I don’t want to saturate my solution with a defined gas-composition of infinite volume. A fixed-volume gas phase is to my opinion also not appropriate, since it is my target result, to observe for which pressure a gas phase (volume in gas description) is forming with decreasing total pressure. I also cannot use the EQULIBRIUM_PHASES approach easily, since I do not know the target partial pressure of CO2. For me the most plausible way is actually to determine the (virtual?) partial pressure of the (non-existing) CO2 phase in reservoir depth and equilibrate the measured solution (EQUILIBRIUM_PHASES) for steadily decreasing total pressures. Unfortunately, this does not lead to any results.
Can anyone give advice on it? Any suggestion are highly appreciated, thank you very much in advance!
My (simplified) input is as follows:

SELECTED_OUTPUT
      -file   TEST.pun
      -temperature
   -pH
   -gases   CO2(g) #Ntg(g)
   Anhydrite
   #-activities         CO2      
   USER_PUNCH
      -headings PRESSURE  PCO2
      10 PUNCH  PRESSURE
      20 PUNCH  log10(PR_P("CO2(g)"))

SOLUTION 1             LH13
   pe        4         
       redox     pe         
       units    mg/kgw         
       density   1         
       -water    1 # kg         
   -pressure 140         
            
   temp   65      
   pH   5.55      
   Na   41000      
   Ca   4650      
   Cl   72800      
   C(4)   5534      
   #Ntg   83

USE solution 1   
   GAS_PHASE 1               
   -fixed_volume
   -equilibrate with solution 1
   -pressure 140
      -temperature 65
       -volume 0.0000000001   
    CO2(g) 0
      # Ntg(g) 0
END

USE SOLUTION 1
REACTION_PRESSURE
   140 1 in 50 steps   

EQUILIBRIUM_PHASES 1
   CO2(g) -2.2557e+00

END

[dlparkhurst]

The following simulation generates a bubble when the pressure is reduced to about 5 atm. The same information could be obtained from the original calculated partial pressure (10^0.73=5.3 atm). Temperature is constant at 65 C, but is set up to have a linear decrease in temperature proportional to pressure.

Note the calculation is somewhat sensitive to carbon concentration and pH. C(4) (default gfw of HCO3 in pitzer.dat) includes CO2 and all other C(4) species, whereas, Alkalinity (definition  does not include CO2). The calculated partial pressure of CO2(g) is directly related to the in situ pH, which is probably difficult to measure.

Code: [Select]

SOLUTION 1 LH13
    temp      65
    pH        5.55
    pe        4
    redox     pe
    units     mg/kgw
    density   1
    C(4)      5534 as HCO3
    Ca        4650
    Cl        72800
    Na        41000
END
GAS_PHASE 1
    -fixed_pressure
    -pressure 140
    -volume 1
    -temperature 65
    CO2(g)    0
END
USE solution 1
USE gas_phase 1
REACTION_PRESSURE
   140 1 in 200 steps   
REACTION_TEMPERATURE
   65 65 in 200 steps
USER_GRAPH 1
    -axis_titles            "CO2(g), moles in gas phase" "Pressure, atm" ""
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_Y PRESSURE
20 GRAPH_X GAS("CO2(g)")
  -end
END


[FreakQC]

Dear David,
thank you very much for your fast reply. This helps me a lot. Insitu conditions should be fine. I adjusted in a pre-run  the conditions to calcite-carboninc acid equilibrium (by adding potentially degassed CO2 prior to sampling back to solution). For my understanding CO2/pH should be controlled by sthe presence of calcite in the reservoir. What irritates me a bit, is that their is no degassing for increasing temperatures (isobaric). Even to an extreme temperature of 300°C. I ask myself if a system in equilibrium with calcite at intermediate temperatures (around 100°C) in general does not tend to degass for increasing temperatures.

[dlparkhurst]

Your initial solution is about 10 times supersaturated with calcite, which seems inconsistent with your assumption that calcite should be in equilibrium as temperature rises.

Here is a modified script that equilibrates the initial solution with calcite by adjusting pH. A pH of 5 produces equilibrium, which seems plausible, given the uncertainties.

Heating up the solution, including calcite equilibrium, does increase the CO2 partial pressure, but not nearly enough to form a bubble. Maximum P(CO2) is about 20 atm. Instead of just heating the initial solution, you probably want to reconsider different conditions for the initial solution itself, but I think it is pretty well constrained with the data that you have.

Code: [Select]

SOLUTION 1 LH13
    temp      65
    pH        5.55 calcite 0.0
    pe        4
    redox     pe
    units     mg/kgw
    density   1
    C(4)      5534 as HCO3
    Ca        4650
    Cl        72800
    Na        41000
END
GAS_PHASE 1
    -fixed_pressure
    -pressure 140
    -volume 1
    -temperature 65
    CO2(g)    0
END
USE solution 1
USE gas_phase 1
EQUILIBRIUM_PHASES
Calcite 0 10
REACTION_TEMPERATURE
   65 300 in 50 steps
USER_GRAPH 1
    -headings               tc P(CO2) lk(CO2)
    -axis_titles            "Celsius" "CO2(g) partial pressure, atm" ""
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X TC
20 GRAPH_Y 10^SI("CO2(g)")/PR_PHI("CO2(g)")
  -end
    -active                 true
END


[FreakQC]

Thanks for your answer.
It was obviously a typing error. 534 mg/kgw HCO3- reflects calcite equilibrium. Sorry to bother you with such things.
Nevertheless it is very conclusive for me, that a system in equilibrium with calcite "caps" in a way the CO2 concentration, that
the system is not prone to degassing for increasing reservoir tempertures (application is HT-ATES)...

Thanks again!