.. _example-phreeqc-manual-03:

03 - Mixing
===========

Two waters, each in equilibrium with calcite, mixed together. The mixture is
*not* in equilibrium with calcite -- and that is the point.

Where seawater meets carbonate groundwater, each water on its own is stable
against the limestone it sits in, and the mixture dissolves it. The
phenomenon has a name, mixing corrosion, and it is one reason coastal
carbonate aquifers develop caves and high porosity at the freshwater-seawater
interface. It falls straight out of a model that does nothing but mix.


Why mixing is not interpolation
-------------------------------

Mix two waters and the totals do interpolate: half of one and half of the
other gives the average of each element. The *saturation index* does not,
because it depends on ion activities, and activities depend non-linearly on
ionic strength and on how the ions pair up.

So a mixture of two calcite-saturated waters can be undersaturated. Nothing
in the arithmetic of the analysis predicts it; it takes a speciation of the
mixture.


Simulations that build on each other
------------------------------------

.. raw:: html
   :file: study_03 - Mixing.html

This is the first example in the set where simulations depend on earlier
ones within the same run. The input equilibrates each water with calcite and
dolomite, saves the result, mixes the saved solutions in a series of
proportions, and then reacts the mixtures further.

``SAVE`` and ``USE`` are what make that possible: a solution computed in one
simulation is kept under a number and picked up by the next. It is the
mechanism behind every multi-step PHREEQC model, and it is why a single input
file can express a sequence of processes rather than one state.


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

.. csv-table:: table_ex3
   :file: table_ex3.csv
   :header-rows: 1
   :delim: ;

The table gives the mixtures and their saturation state. The saturation index
of calcite falls below zero at intermediate mixing fractions and returns
towards zero at the ends, where the mixture is mostly one water or the
other -- so the dissolution is strongest where the two waters are most evenly
mixed, which is where the interface actually sits.


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 3 of that manual.
* The effect it demonstrates was described by Wigley, T. M. L. and Plummer,
  L. N. (1976), *Mixing of carbonate waters*, Geochimica et Cosmochimica Acta
  40, 989-995.