.. _example-phreeqc-manual-13:

13 - 1D Dual Porosity Transport
===============================

Real porous media do not have one porosity. Fractured rock, aggregated soil
and layered sediment all have water that flows and water that does not, with
exchange between the two by diffusion -- and a model with a single porosity
cannot reproduce what that does to a breakthrough curve.

This example runs the same dual-porosity column three ways, and the three
appear on one figure so they can be compared.


Mobile and immobile water
-------------------------

The column is divided into **mobile** pores, where advection happens, and
**immobile** pores, which exchange with them only by diffusion.

The consequence is a breakthrough curve with a long tail. Solute entering the
column diffuses into the stagnant water and is held there; when the flush
arrives it diffuses back out slowly, so the concentration decays over a far
longer time than the flow alone would suggest. Tailing of this kind is
routinely mistaken for sorption, and the two have quite different
implications for how long a contaminated site takes to clean up.


Three approximations
--------------------

.. figure:: D_pnt_P_comma_F_pnt_O_pnt_andF_pnt_D_pnt_Approximations.svg
   :alt: Sodium and chloride profiles from three dual-porosity formulations
   :align: center

   Sodium and chloride along the column from three formulations, labelled
   ``a``, ``b`` and ``c``:

   * **First-order exchange** (``FO``), cases a and b. The exchange between
     mobile and immobile water is a single rate constant times the
     concentration difference. Cheap, and it collapses the whole geometry of
     the stagnant zone into one number.
   * **Finite differences** (``FD``), case c. Diffusion inside the immobile
     zone is resolved explicitly, so the concentration gradient within it is
     computed rather than assumed.

   The finite-difference result is the reference. Where the first-order
   approximation follows it, the one-rate simplification is adequate; where
   it parts from it, the internal gradient matters and the rate constant
   cannot stand in for it.

   The two chloride curves and the two sodium curves also separate the two
   effects: chloride is affected by the dual porosity alone, while sodium has
   exchange chemistry on top of it.

The three inputs are included below, one per formulation.

.. raw:: html
   :file: study_13 - 1D Dual Porosity Transporta.html

.. raw:: html
   :file: study_13 - 1D Dual Porosity Transportb.html

.. raw:: html
   :file: study_13 - 1D Dual Porosity Transportc.html


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

That tailing can come from physical heterogeneity rather than from chemistry,
and that the choice of how to represent the immobile zone is a modelling
decision to be checked rather than assumed. The cheap approximation is often
right, and this is how you find out whether it is right for your case.


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 13 of that manual.
* Appelo, C. A. J. and Postma, D. (2005). *Geochemistry, Groundwater and
  Pollution*, 2nd edition. Balkema, Leiden.