.. _example-phreeqc-manual-06:

06 - Reaction Path Calculations
===============================

Pure water attacking K-feldspar, and the sequence of clay minerals that
forms as it does. This is the classic reaction path of low-temperature
geochemistry, and the example computes it three different ways to show they
agree.

The chemistry is **incongruent dissolution**: K-feldspar does not simply
dissolve into its components. As it breaks down, the aluminium and silicon it
releases immediately form something else, and which something depends on how
far the reaction has gone. Only the four phases of the original treatment --
K-feldspar, gibbsite, kaolinite and K-mica -- are considered.


The activity diagram
--------------------

.. raw:: html
   :file: study_06 - Reaction Path Calculations.html

The input defines the four phases explicitly rather than relying on the
database, so that the calculation reproduces the published one exactly.

The path is drawn on axes of log[H₄SiO₄] against log([H⁺][K⁺]) -- the two
quantities the stability of these phases depends on. The phase boundaries are
straight lines on these axes, because each is a reaction with fixed
stoichiometry, and that is the whole reason this particular pair of axes is
used.


Three ways to the same path
---------------------------

.. figure:: linePlot1.svg
   :alt: Reaction path of K-feldspar dissolution on an activity diagram, three methods and the phase boundaries
   :align: center

   The path, with the phase boundaries drawn over it. It starts at the bottom
   left in pure water and climbs as feldspar dissolves, crossing from the
   gibbsite field into kaolinite and on towards K-mica.

   The corners are the interesting part. Each is where the path meets a phase
   boundary, and at that point the mineral that was precipitating begins to
   redissolve while the next one takes over. The path then runs *along* the
   boundary for a while -- both phases present, the system buffered -- before
   leaving it.

   Three methods are drawn, and they lie on top of each other:

   * **6A, intersections** -- solve directly for the composition at each
     phase boundary. Exact, and it gives the corners and nothing between
     them.
   * **6B, increments** -- dissolve a fixed amount of feldspar at a time and
     see where the water goes. Fills in the path, with a resolution set by
     the step.
   * **6C, kinetics** -- dissolve feldspar at a rate, so the path is
     parameterised by time rather than by extent.

   Three formulations of the same problem agreeing is the result. 6A says
   where the corners are, 6B says what the path looks like, and 6C says how
   long it takes -- and the first two cannot answer that last question at
   all.


What it shows
-------------

That a reaction path is a trajectory through a stability diagram, and that
the choice of how to compute it is separate from the chemistry. Choose the
formulation by what you need to know.


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 6 of that manual.
* Helgeson, H. C., Garrels, R. M. and Mackenzie, F. T. (1969). *Evaluation of
  irreversible reactions in geochemical processes involving minerals and
  aqueous solutions -- II. Applications.* Geochimica et Cosmochimica Acta 33,
  455-481. The four phases and the original treatment of this path are
  theirs.