.. _example-phreeqc-manual-09:

09 - Kinetic Oxidation
======================

Dissolved ferrous iron meeting oxygen. Thermodynamically the answer is
immediate -- Fe(II) is not stable in oxygenated water -- so an equilibrium
calculation says all the iron is Fe(III) and stops there.

The useful question is *how long*, and that needs a rate.


A rate law in the input
-----------------------

.. raw:: html
   :file: study_09 - Kinetic Oxidation.html

The oxidation rate of ferrous iron is strongly dependent on pH -- it goes as
the square of the hydroxide activity, so a unit of pH is a hundredfold in
rate -- and on the oxygen partial pressure. That law is written into a
``RATES`` block as BASIC, and a ``KINETICS`` block integrates it over time.

This is the general shape of a kinetic model in PHREEQC: the equilibrium
calculation gives the speciation at each instant, and the rate law says how
fast the irreversible step proceeds. The two are solved together at every
step, so the rate sees the current pH and the current speciation rather than
the starting ones.


The result
----------

.. figure:: OxidationofFerrousIron.svg
   :alt: Fe(2) falling and Fe(3) rising over days, with pH on the same axes
   :align: center

   Fe(II) falling and Fe(III) rising over several days, with pH on the same
   axes.

   The pH curve is the one to watch, and it is why the two species are not
   simple mirror images. Oxidising ferrous iron and precipitating the ferric
   product releases acid, so the pH falls as the reaction proceeds -- and
   since the rate depends on the square of the hydroxide activity, the
   reaction slows itself down. The system is self-limiting through its own
   product.

   An equilibrium model gives none of this. It gives the endpoint, which was
   never in doubt.


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

That kinetics is required whenever the rate is comparable with the timescale
of interest, and that a rate law coupled to a speciation calculation can show
feedback that neither would show alone.

The practical case is iron removal from groundwater: the time to oxidise the
iron, and therefore the size of the plant, depends on a pH that the reaction
itself is changing.


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 9 of that manual.
* Singer, P. C. and Stumm, W. (1970). *Acidic mine drainage: the rate-
  determining step.* Science 167, 1121-1123, for the rate law's form.