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

TITLE Example 3, part A.--Calcite equilibrium at log Pco2 = -2.0 and 25C.        

SOLUTION 1  Pure water

        pH      7.0

        temp    25.0

EQUILIBRIUM_PHASES

        CO2(g)          -2.0    

        Calcite         0.0

SAVE solution 1

END

TITLE Example 3, part B.--Definition of seawater.

SOLUTION 2  Seawater

        units   ppm

        pH      8.22

        pe      8.451

        density 1.023

        temp    25.0

        Ca              412.3

        Mg              1291.8

        Na              10768.0

        K               399.1

        Si              4.28

        Cl              19353.0

        Alkalinity      141.682 as HCO3

        S(6)            2712.0

END

TITLE Example 3, part C.--Mix 70% groundwater, 30% seawater.

MIX 1

        1      0.7

        2      0.3

SAVE solution   3

END

TITLE Example 3, part D.--Equilibrate mixture with calcite and dolomite.

EQUILIBRIUM_PHASES 1

        Calcite         0.0

        Dolomite        0.0

USE solution 3

END

TITLE Example 3, part E.--Equilibrate mixture with calcite only.

EQUILIBRIUM_PHASES 2

        Calcite         0.0

USE solution 3

END

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

table_ex3

pH	log p_CO2	SI Calcite	SI Dolomite	CO2 milimole transfer	Calcite milimole transfer	Dolomite milimole transfer
7	-999.999	-999.999	-999.999	0	0	0
7.295318639023	-2.000024043554	0	-999.999	-1.953262864854	-1.622676894661	0
8.22	-3.371868992362	0.7839927124289	2.444158894627	0	0	0
7.325417025437	-2.213669504545	-0.1226975338546	0.4642824161498	0	0	0
7.049933482764	-1.97611724146	0	0	0	-15.21235469332	7.684049538494
7.43220905893	-2.30892764763	0	0.7050862396872	0	-0.04598673110756	0

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.