Effects of temperature on fractionation of carbon isotopes during precipitation

[RPM]

Hello everyone,

I’m a beginner at modeling with PHREEQC and I’m looking for some help.

As part of a general model for my thesis, I’m trying to understand the effects of temperature on the 13C isotope composition of a fluid during CO2 degassing and calcite precipitation. To do this, I thought it would be a good idea to start by using PHREEQC and code from https://www.hydrochemistry.eu/exmpls/istp.html (example 2), and to simply adjust solution temperature to see how d13c varies. Sadly, after mulling it over for some weeks and several gallons of coffee, I’m afraid I don’t understand the code well enough.

Putting aside cases B and C for a minute, in case A, parameters are set so that degassing and calcite precipitation rates approach equilibrium at the same pace. As I increase the temperature of my solution (up to ~140 °C), the final d13c values of sol_tot become more negative. The higher the temperature of the system, the more negative the solution will be once equilibrium is achieved.

However, I’m not sure I completely understand WHY this is the case. At first I thought the d13C depletion of the fluid with increasing temperature was simply due to the temperature dependency of the isotope fractionation equilibrium constants, but now I’m not so sure. Degassing rate of CO2(g) is  a function of sr("CO2(g)"), which I assume is affected by the temperature of the system, and calcite precipitation rate is also a function of system temperature (‘tc’ is right there in the code). Does this mean that if I modify the temperature in SOLUTION, parameters in KINETICS also have to be adjusted to maintain rates of precipitation/degassing the same relative to one another? If so, how can I find out what the new parameters should be? And between the degassing, precipitation, and solute C species distribution, what is the ‘dominating’ effect on the final fluid isotope composition at increased temperatures? Is there a more efficient way to approach this problem using PHREEQC?

If anybody could help me understand what exactly is happening here, or at least point me to any references that could help me understand, I’d be truly, deeply grateful. I’m a bit hardheaded and normally would never ask for help with things like this, but I’ve already spent a lot of time thinking about this problem and unlike calcite precipitation, my thesis deadline is approaching at a steady, unchanging rate.

Best regards,
RPM

[dlparkhurst]

So you want to take a water composition, degas CO2, and allow calcite to precipitate; then you want to do that at multiple temperatures? Is the degassing into air or some other fixed composition gas phase?

Anyway, perhaps you should start with equilibrium. Here is the evolution of a fixed volume gas phase and aqueous solution in equilibrium with an essentially fixed composition zero permil calcite using iso.dat.

Code: [Select]

SOLUTION
pH 7.0
C    1 CO2(g) -1.0
[13C]  -25 permil
END
USE solution 1
SOLID_SOLUTION 1
Calcite
-comp Calcite   1000
-comp Ca[13C]O3(s) 11.1802
GAS_PHASE 1
-fixed_volume
CO2(g)  0
[13C]O2(g) 0
REACTION_TEMPERATURE
25 150 in 26 steps
USER_GRAPH 1
    -headings               TC 13C(aq) 13C(CO2(g)) 13C(Calcite)
    -axis_titles            "Temperature, Celsius" "PERMIL" ""
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X TC
20 GRAPH_Y ISO("[13C]"), ISO("R(13C)_CO2(g)"), ISO("R(13C)_Calcite")
  -end
    -active                 true
END


[RPM]

Dear David,

Thank you very much for your reply!

While the code you provided was quite useful to me for understanding the similar case of equilibrium, I think it doesn’t quite fit the problem I have currently. Perhaps I was a bit too ambiguous in my original description.

I have a data set consisting of water samples from springs in my study area, which I’ve classified based on discharge temperature as either thermal (30° to 90°C) or non-thermal (discharging at ambient T, about ~12°C). So far I’ve noticed two trends in my data: 1) hot springs have consistently lower TDIC concentrations and higher d13C values than cold springs 2) hot springs are saturated in calcite, while cold springs are subsaturated.

My hypothesis is that the relatively low TDIC values and high d13C values of hot springs are due to degassing and calcite precipitation during ascent, but I’d like to test numerically if this is plausible. What you ask is correct, my intention was to take an initial, deep reservoir water composition (which I have more or less constrained), then progressively degas CO2 and allow calcite to precipitate to see the effects on d13c values (assuming rayleigh fractionation - removing both phases from contact with the fluid to simulate the conditions of an ascending fluid, and a target partial pressure of CO2 equal to air). Then, my idea was to repeat this process at multiple temperatures, to account for the range of conditions in the study area.

Was the idea from my initial post incorrect? If so, what would be the best way to approach this problem using Phreeqc? 

Thank you again so much in advance.

[dlparkhurst]

I'm sure Tony knows how to do it with kinetics. Here I use iso.dat and equilibrium to sequentially remove CO2 from a solution while precipitating calcite, all at a given temperature. Both 12C and 13C partition into the gas phase and calcite. Repeat the final simulation (cut and paste) many times to degas more and more CO2 (and precipitate more calcite) while removing them from the system at each step. You can also adjust the volume of the gas phase to degas more or less CO2 at each step.

You can add REACTION_TEMPERATURE blocks at each step if you want to adjust the temperature, although that gets tedious.

You can replace the solution with your estimate of a deep water sample composition. Iso.dat has a limited set of elements, but it should be sufficient for the basic processes. It is a little clunky, but hopefully it is sufficient to determine the basic response of the isotopes as a function of degassing and temperature. You could also use it to check a KINETICS calculation it you pursue that route.

The graph is a bit funky in that reaction progress goes from right to left as carbon is removed from the system, but it was easy to implement.

Code: [Select]

SOLUTION
temp 140
pH 5. charge
C    1 CO2(g) 1.0
Ca   1 Calcite 0
[13C]  0 permil
END
GAS_PHASE 1
-fixed_volume
-vol 0.01
CO2(g)  0
[13C]O2(g) 0
SOLID_SOLUTION 1
Calcite
-comp Calcite 0 0
-comp Ca[13C]O3(s) 0 0
END
USER_GRAPH 1
    -headings               TC 13C(aq) 13C(CO2(g)) 13C(Calcite)
    -axis_titles            "TDIC, moles" "PERMIL" "pH"
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X TOT("C")
20 GRAPH_Y ISO("[13C]"), ISO("R(13C)_CO2(g)"), ISO("R(13C)_Calcite")
30 GRAPH_SY -LA("H3O+")
  -end
    -active                 true
END
USE solution 1
USE gas_phase 1
USE solid_solution 1
SAVE solution 1
END