20 - Isotope Distribution

Marine calcite dissolving into groundwater, and what it does to the carbon and oxygen isotopes.

The reason to model isotopes is that they record where atoms came from. But reading that record requires knowing how the isotopes redistribute as the reaction proceeds – and that depends on whether the system can exchange with anything outside itself.

Open and closed

TITLE Example 20A.--Calculate carbonate solid solution
PRINT
	-censor_species        1e-006
SOLUTION 1 # water to find composition of marine carbonate
	pH      8.2
	Na	1       charge
	Ca	10      Calcite        0
	C	2	
	[13C]	0       # permil
	[14C]	0       # pmc
	D	0       # permil
	[18O]	0       # permil
END
SOLID_SOLUTION 1 No [14C]
Calcite 
	-comp	Calcite                 0
	-comp	CaCO2[18O](s)           0
	-comp	CaCO[18O]2(s)           0
	-comp	CaC[18O]3(s)            0
	-comp 	Ca[13C]O3(s)            0
	-comp	Ca[13C]O2[18O](s)       0
	-comp	Ca[13C]O[18O]2(s)       0
	-comp	Ca[13C][18O]3(s)        0
END 	
RUN_CELLS
	-cells 1
USER_PRINT
-start
	10 PRINT pad("Component", 20), "Mole fraction"
	20 t = LIST_S_S("Calcite", count, name$, moles)
	30 for i = 1 to count
	40   PRINT pad(name$(i),20), moles(i)/t
	50 next i
-end
END

The same dissolution is computed under two conditions:

  • Open – the water stays in contact with a CO₂ reservoir, typically soil gas. Carbon entering from the calcite is diluted by an effectively unlimited supply with its own isotopic signature.

  • Closed – no exchange after the start. The isotopes present are all there is, so every atom from the calcite shifts the composition.

The two give different answers from the same amount of calcite dissolved, and real systems are usually somewhere between – a recharge area being open and a confined aquifer closed. Which assumption is made is the main source of uncertainty in carbon-14 groundwater dating, and it is a judgement about hydrogeology, not chemistry.

TITLE Example 20B.--Isotope evolution.
PRINT
	-censor_species        1e-006
KNOBS
	-diagonal_scale
	-step 10
	-pe   5
#
# Open system calculation 
# 	
SOLID_SOLUTION 1 With [14C]
Calcite 
	-comp	Calcite                 0
	-comp	CaCO2[18O](s)           0
	-comp	CaCO[18O]2(s)           0
	-comp	CaC[18O]3(s)            0
	-comp 	Ca[13C]O3(s)            0
	-comp	Ca[13C]O2[18O](s)       0
	-comp	Ca[13C]O[18O]2(s)       0
	-comp	Ca[13C][18O]3(s)        0
	-comp 	Ca[14C]O3(s)            0
	-comp	Ca[14C]O2[18O](s)       0
	-comp	Ca[14C]O[18O]2(s)       0
	-comp	Ca[14C][18O]3(s)        0
END
REACTION 1
	Calcite               9.8283e-001 
	Ca[13C]O3(s)          1.1011e-002 
	CaCO2[18O](s)         6.0825e-003 
	Ca[13C]O2[18O](s)     6.8147e-005 
	CaCO[18O]2(s)         1.2548e-005 
	Ca[13C]O[18O]2(s)     1.4058e-007 
	CaC[18O]3(s)          8.6284e-009 
	Ca[13C][18O]3(s)      9.6671e-011 
	0.0005 mole
END
SOLUTION 1
	pH	5  	charge
	pe      10
	C	2	CO2(g)  -1.0	
	[13C]	-25	# permil
	[14C]	100	# pmc
	[18O]	-5	# permil
END
USE solution 1
USE solid_solution 1
USE reaction 1
SAVE solution 1
END
USE solution 1
USE solid_solution 1
USE reaction 1
SAVE solution 1
END
USE solution 1
USE solid_solution 1
USE reaction 1
SAVE solution 1
END
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USE reaction 1
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END
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END
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END
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END
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END
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END
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END
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END
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END
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END
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END
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END
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END
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END

TITLE Example 20B.--Isotope evolution.
PRINT
	-censor_species        1e-006
KNOBS
	-diagonal_scale
	-step 10
	-pe   5
#
# Open system calculation 
# 	
SOLID_SOLUTION 1 With [14C]
Calcite 
	-comp	Calcite                 0
	-comp	CaCO2[18O](s)           0
	-comp	CaCO[18O]2(s)           0
	-comp	CaC[18O]3(s)            0
	-comp 	Ca[13C]O3(s)            0
	-comp	Ca[13C]O2[18O](s)       0
	-comp	Ca[13C]O[18O]2(s)       0
	-comp	Ca[13C][18O]3(s)        0
	-comp 	Ca[14C]O3(s)            0
	-comp	Ca[14C]O2[18O](s)       0
	-comp	Ca[14C]O[18O]2(s)       0
	-comp	Ca[14C][18O]3(s)        0
END
SOLUTION 1
	pH	5  	charge
	pe      10
	C	2	CO2(g)  -1.0	
	[13C]	-25	# permil
	[14C]	100	# pmc
	[18O]	-5	# permil
END	
INCREMENTAL_REACTIONS true
# Alternative to redefinition of REACTION 1
#REACTION_MODIFY 1
#	-steps
#		0.05
#	-equal_increments	1
#	-count_steps		100
REACTION 1
	Calcite               9.8283e-001 
	Ca[13C]O3(s)          1.1011e-002 
	CaCO2[18O](s)         6.0825e-003 
	Ca[13C]O2[18O](s)     6.8147e-005 
	CaCO[18O]2(s)         1.2548e-005 
	Ca[13C]O[18O]2(s)     1.4058e-007 
	CaC[18O]3(s)          8.6284e-009 
	Ca[13C][18O]3(s)      9.6671e-011 
	0.05 mole in 100 steps
RUN_CELLS
	-cells 1
END

The results

Carbon-13 in dissolved carbon and calcite against calcite reacted, open and closed, with NETPATH

δ¹³C in the dissolved carbon and in the calcite, against calcite reacted, for both systems. ¹³C is stable: it changes only by mixing and fractionation, so these curves are the mixing of two carbon sources – the marine calcite and the soil CO₂ – and the separation between the open and closed curves is exactly the dilution the open system allows.

Carbon-14 as percent modern carbon, the same four cases

¹⁴C, in percent modern carbon. This is the one that matters for dating, and the problem it shows is the central one of the method: the marine calcite is dead, radiocarbon-free, so dissolving it dilutes the ¹⁴C and makes the water look older than it is. The correction for that is the difference between these curves, and it depends on the open-or-closed choice above.

The Netpath series on both carbon figures is an independent calculation of the same quantity by a different program. Two codes agreeing is worth more than either one on its own, and this is the kind of check worth making before trusting an isotope correction.

Oxygen-18 in dissolved carbon and calcite against calcite reacted

δ¹⁸O. Oxygen behaves differently from carbon here because the water itself is an enormous oxygen reservoir – the dissolving calcite contributes a negligible fraction of it, so the dissolved oxygen isotopes barely move. The calcite’s own composition is the part that responds.

This asymmetry is worth noticing: the same reaction shifts one element’s isotopes substantially and another’s hardly at all, purely because of the relative size of the pools involved.

Source

  • Parkhurst, D. L. and Appelo, C. A. J. (2013). Description of input and examples for PHREEQC version 3. U.S. Geological Survey Techniques and Methods, book 6, chapter A43. This is Example 20 of that manual.

  • Plummer, L. N., Prestemon, E. C. and Parkhurst, D. L. (1994). An interactive code (NETPATH) for modeling net geochemical reactions along a flow path, version 2.0. U.S. Geological Survey Water-Resources Investigations Report 94-4169. The comparison series are from NETPATH.