.. _example-phreeqc-manual-20:

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
---------------

.. raw:: html
   :file: study_20 - Isotope Distributiona.html

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.

.. raw:: html
   :file: study20 - Isotope Distributionb_1.html

.. raw:: html
   :file: study20 - Isotope Distributionb_2.html


The results
-----------

.. figure:: Carbon_minus_13.svg
   :alt: Carbon-13 in dissolved carbon and calcite against calcite reacted, open and closed, with NETPATH
   :align: center

   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.

.. figure:: Carbon_minus_14.svg
   :alt: Carbon-14 as percent modern carbon, the same four cases
   :align: center

   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.

.. figure:: Oxygen_minus_18.svg
   :alt: Oxygen-18 in dissolved carbon and calcite against calcite reacted
   :align: center

   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.