.. _example-phreeqc-basics-02:

02 - Parametric Mixing
======================

A sensitivity analysis: two waters mixed in every proportion, at a range of
temperatures, and what that does to the saturation of calcite and dolomite.

:ref:`example-phreeqc-manual-03` runs one mixing calculation. This one turns
the mixing fraction into a parameter and sweeps it, which is the step from
*a* model to *a study of* a model.


Parameterising the input
------------------------

.. raw:: html
   :file: study_ex2.html

The ``MIX`` block's proportion is written as a parameter rather than a
number, and so is the temperature. The input stays an ordinary PHREEQC input
-- the parameters are substituted before it is run -- so it can still be
checked by running it once with its parameters at their own values.

A *Parametric Study* then sweeps the two: the mixing factor from 0 to 1, and
temperature over a range. Chaining the two sweeps gives the grid, exactly as
in the first Core example.


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

.. figure:: SaturationIndices_op_T=10_cp_.svg
   :alt: Calcite and dolomite saturation index against mixing factor at 10 degrees
   :align: center

   Calcite and dolomite saturation index against mixing factor at 10 °C --
   one slice through the grid.

   Both curves dip below the straight line that would join their endpoints.
   That is mixing corrosion again: the two end-member waters are each at or
   near saturation, and intermediate mixtures are undersaturated and would
   dissolve carbonate. Dolomite responds more strongly than calcite, as it
   generally does, because its saturation index carries the product of two
   cation activities rather than one.

.. figure:: SaturationIndexSurface.svg
   :alt: Saturation index surfaces of calcite and dolomite over mixing factor and temperature
   :align: center

   The whole grid: saturation index over mixing factor *and* temperature,
   as two surfaces. The slice above is one line across them.

   Plotly draws no legend for surface traces, so read them by their relief:
   dolomite spans about twice the range calcite does -- it reaches higher
   where the water is saturated and falls further where it is not, and the
   two cross. That is the same two-cation effect the slice shows, seen over
   the whole plane.

   A surface is the right form for a sensitivity analysis because it answers
   the question the analysis is for -- which input matters more. Here the
   gradient along the mixing axis is much the steeper of the two over this
   range, so the mixing proportion dominates and temperature is a second-
   order effect. That conclusion is visible at a glance and would take
   several slices to establish otherwise.


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

That a parameterised input plus a parametric study turns a single calculation
into a map, and that the map answers questions about *sensitivity* that no
single run can.


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.