John J. Mahoney, Ph.DJohn J. Mahoney, Ph.D..

Mahoney Geochemical Consulting LLCMahoney Geochemical Consulting LLCLakewood, COLakewood, CO

jmahoney@mahoneygeochem.comjmahoney@mahoneygeochem.com

Coprecipitation Reactions Coprecipitation Reactions --

Verification of Computational MethodsVerification of Computational Methods

in Geochemical Modelsin Geochemical Models

Updated and Expanded Version for Website Viewing

Original Presentation was given in EPA/525/C-00/004,

January 2001 Mining Impacted Pit Lakes 2000

Workshop Proceedings: A Multimedia CD Presentation

Additional slides in italics have been added to the presentation

to clarify certain items

Fate of Metals in Ground-Water Systems

1. Precipitation

2. Adsorption

3. Coprecipitation or Solid Solution Reactions

Coprecipitation Reactions ControlCoprecipitation Reactions ControlConcentrations in Ground WaterConcentrations in Ground Water

Ra in BaSO4 (Barite)

Sr in CaCO3 (Calcite)

Cd in CaCO3 (Calcite)

Sr in CaSO4 2H2O (Gypsum)

AsO4 in Ca5(PO4)3OH (Apatite)

Al in FeOOH (Goethite)

MoO4 in Ca6Al2(SO4)3(OH)12 24H2O (Ettringite)

Cr(III) in Fe(OH)3 (Ferrihydrite)

Cr(VI) in BaSO4 (Barite)

Clay Minerals

Coprecipitation Reactions UnderCoprecipitation Reactions Under--UtilizedUtilized

in Applied Modelsin Applied Models

1. Emphasis on Precipitation and Adsorption Reactions

2. Belief that Standard Models (MINTEQA2, PHREEQE and

PHREEQC) Cannot Perform Coprecipitation Calculations

3. Data Bases for Coprecipitation Reactions Not Provided

in Standard Models

4. Belief That Data Describing Solid Solution Reactions is Too

Limited or Lacking for User’s Problem

Coprecipitation of Cadmium in CalciteCoprecipitation of Cadmium in Calcite

1. Well Documented Process

2. Several Referenced Articles and Numerous

Textbooks Discuss Process

3. Values for Distribution Coefficients (D) Are Large

4. D Values Range from 70 to 1,500

5. Ideal Solution - D Values of 680 or Greater Than

4,000 Reported

Requirements of CalculationRequirements of Calculation

1. Initial Concentration of Cd (Before Coprecipritation

Reactions)

2. Amount of Calcite That Will Precipitate During Each

Step of Model (Initial and Final Calcium Concentration)

3. Value for Distribution Coefficient

4. Appropriate Equation

Doerner and Hoskins EquationDoerner and Hoskins EquationFor coprecipitation in a calciumFor coprecipitation in a calcium--bearing mineralbearing mineral

== loglogloglog λλ

Where

Mei = initial quantity of trace metal in solution,

Mef = final quantity of metal,

Cai = initial quantity of calcium in solution,

Caf = final quantity of calcium in solution, and

λ = distribution coefficient (D).

MeMeii

MeMeff

CaCaii

CaCaff

Doerner and Hoskins EquationDoerner and Hoskins Equation

1. Typically Described in Textbooks

2. Heterogeneous System

3. Limited to Small Values of D

Riehl EquationRiehl Equation

Where

C 0Tr = Concentration of Trace Component (Cd) in

Boundary Layer,

C iTr = Initial Concentration of Trace Component

in Solution,

C iCr = Initial Concentrations of Carrier (Calcium)

in Solution, and

C 0Cr = Concentration of Carrier in Boundary Layer.

C 0Tr = C iTr C 0Cr

λ ( C iCr - C 0Cr ) + C iCr

Riehl EquationRiehl Equation

1. Assumes1. Assumes

WhereWhere

C C llCrCr = Concentration of the Carrier in Bulk Solution, and= Concentration of the Carrier in Bulk Solution, and

SS = 1.0 when Precipitation Stops.= 1.0 when Precipitation Stops.

2. Homogeneous System

3. Works for a Wide Range of D Values

S =S =C lCr

C 0Cr

Properties of EquationsProperties of Equations

1. Both Equations Calculate Same Concentrations

for D = 1

2. For Small Amounts of Precipitate and Low D

Values - Similar Results for Both Equations

3. At D > 1, Riehl Equation Produces More

Reasonable Concentrations

4. Homogeneous Model (Riehl Equation) also Produces

More Reasonable Concentrations at Different

Masses of Precipitate

Application of MethodApplication of Method

1. Use PHREEQC to Estimate Mass of Calcite that

will Precipitate

2. Comparison of Concentrations from Step 2 to

Step 3 of Model

3. Estimate Concentrations of Cd in Solution

4. Cd Sorbed onto Hydrous Ferric Oxide Before

Coprecipitation Reactions

5. Solve Equation for Cd Concentrations Using

Spreadsheet Program or Calculator

6. Repeat Process for Step 4 (Evapoconcentration)

Introduction to Thermodynamic ModelIntroduction to Thermodynamic Model

1. Above method, the Bulk Kd Approach, can be applied using

output from various geochemical models (MINTEQA2, PHREEQE,

and PHREEQC) see Mahoney (1998) for more details

using Bulk Kd approach

Calculations could be performed using a spreadsheet

or even a programmable calculator if amount of

precipitated phase was known

2. After completion of work summarized in Mahoney (1998)

the USGS released version 2.0 of PHREEQC

(Parkhurst and Appelo, 1999) with a thermodynamic

approach to modeling solid solution reactions

The rest of the presentation evaluated the thermodynamic

approach used in PHREEQC (version 2)

Thermodynamic ModelThermodynamic Model

Ca 2 + + CO32 - CaCO3

(Ca 2 +)(CO32 -) = Kcc (CaCO3 )

Cd 2 + + CO32 - CdCO 3

(Cd 2 +)(CO32 -) = Kota (CdCO3 )

Where

(CdCO3 ) and (CaCO3 ) represent the activities of

the solids (no solid solution),

Kcc = solubility product constant for calcite,

Kota = solubility product constant for otavite, and

(Ca 2 +), (Cd 2 +) and (CO32-) represent activities in solution.

Exchange ReactionExchange Reaction

Cd 2 + + CaCO3(s) CdCO3(s) + Ca 2 +

(CdCO 3 )s

(CaCO3 )s

= Kx(Cd 2 +)

(Ca 2 +)

Where

(CdCO3 )S and (CaCO3 )S = the activities of the components

in the solid solution, and

Kx = Kcc / Kota

Distribution CoefficientDistribution Coefficient

XCdCO3= D

XCaCO3[Ca 2 + ]

[Cd 2 + ]

Where

XCdCO3= mole fraction of cadmium in

solid solution

XCaCO3= mole fraction of calcium in

solid solution

[Cd 2 +] and [Ca 2 +] = molalities of cadmium and calcium

in solution, and

D = the Distribution Coefficient

Activity Coefficient in SolidActivity Coefficient in Solid

λCdCO3XCdCO3

= (CdCO3 )S

λCaCO3XCaCO3

= (CaCO3 )S

Where

λCaCO3and λCdCO3

represent the rational

activity coefficients in the solid

Ideal Solid SolutionIdeal Solid Solution

λCdCO3= 1

and

λCdCO3D = Kx

Non Ideal Solid SolutionsNon Ideal Solid Solutions

1nλCdCO3= X

2CaCO3

[a0 - a1 (3XCdCO3- XCaCO3

) + …]

1nλCaCO3= X

2CdCO3

[a0 - a1 (3XCaCO3- XCdCO3

) + …]

Wherea0 and a1 are the Guggenheim Nondimensional Parameters

Regular Solid SolutionRegular Solid Solution

HM = XCdCO3XCaCO3

W

Where

HM = enthalpy of mixing

W = the ion interaction parameter

D = Kxexp[ - (1 - (2XCdCO3) W /(2.303RT)], and

W /(2.303RT) = a0

Additional Issues Additional Issues -- Calculation of Calculation of

aa00

Mole fraction term (XCdCO3) in following equation needs

to be kept in mind when calculating a0

D = Kxexp[ - (1 - (2XCdCO3) W /(2.303RT)],

In general the value for XCdCO3will be small because the amount of trace

metal in the initial solution will be a small fraction of amount of carrier that willprecipitate.

112µg/L of cadmium in solution and a net removal of 40 mg/L of calcium by calcite precipitation results inXCdCO3

of 0.001 for the solid solution if all cadmium is removed from solution

Additional Issues Additional Issues -- Solubility Solubility

Products and Distribution Products and Distribution

CoefficientsCoefficients

Various values for the Kota have been presented in the literature and these values have found their way into different databases

Users should assure that the values for Kota or any other Ksp value for the trace element phase produce an internally consistent value for D and hence a0

Comparison of Riehl Equation with PHREEQC Solid SolutionCalculations

Method DistributionCoefficient

a0 Cain

Moles/L

Cafinal

Moles/L

Cdin

Moles/L

Cdfinal

Moles/L

Riehl 0.1 0.01 9.30E-05 2.00E-06 1.77E-07

PHREEQC 0.1 8.85 0.01 9.63E-05 2.00E-06 1.66E-07

Riehl 1 0.01 9.63E-05 2.00E-06 1.93E-08

PHREEQC 1 6.54 0.01 9.63E-05 2.00E-06 2.26E-08

Riehl 2 0.01 9.63E-05 2.00E-06 9.68E-09

PHREEQC 2 5.84 0.01 9.63E-05 2.00E-06 1.10E-08

Riehl 5 0.01 9.63E-05 2.00E-06 3.88E-09

PHREEQC 5 4.92 0.01 9.63E-05 2.00E-06 3.30E-09

Riehl 10 0.01 9.63E-05 2.00E-06 1.94E-09

PHREEQC 10 4.23 0.01 9.63E-05 2.00E-06 2.27E-09

Riehl 70 0.01 9.63E-05 2.00E-06 2.78E-10

PHREEQC 70 2.28 0.01 9.63E-05 2.00E-06 3.24E-10

Riehl 680 0.01 9.63E-05 2.00E-06 2.86E-11

PHREEQC 680 0 0.01 9.63E-05 2.00E-06 3.32E-11

Riehl 1510 0.01 9.63E-05 2.00E-06 1.29E-11

PHREEQC 1510 -0.8 0.01 9.63E-05 2.00E-06 1.49E-11

Riehl 1510 0.1 9.60E-05 2.00E-06 1.27E-12

PHREEQC 1510 -0.8 0.1 9.60E-05 2.00E-06 1.49E-12

Comparison of Solid Solution ModelsComparison of Solid Solution Models

1.00E-12

1.00E-09

1.00E-06

1.00E-03

1.00E+00

0.1 1 10 100 1000 10000

Distribution Coefficient (D)

Cadm

ium

Concentr

ation (

ppm

)

Doerner and Hoskins Equation

Riehl Equation

PHREEQC

Model

(Red dashes)

ConclusionsConclusionsCoprecipitation ReactionsCoprecipitation Reactions

1. Important Process to Control Metals in Aqueous

Systems

2. Numerous Methods Available to Estimate Effect

3. Results in Significant Decreases in Concentrations

4. Failure to Consider Can Produce Concentrations

That are Unrealistically High and May Cause

Regulatory Scrutiny

ConclusionsConclusionsBulk MethodsBulk Methods

1. Bulk Methods Easy to Apply

2. Textbook Examples

3. Iterative Approach Requires Shifting Between

Model Concentrations and Spreadsheet

4. Distribution Coefficients Available for Many Systems

5. Riehl Equation Most Appropriate for Predicting

Concentrations for Systems with Large

Distribution Coefficients

ConclusionsConclusionsThermodynamic ApproachThermodynamic Approach

1. Uses Single Program - Does Not Require Calculations

Outside of Program

2. Usually Requires Detailed Evaluation and Understanding

of System to Estimate Value for a0

3. PHREEQC (v2) Method Produces Final Concentrations

Comparable to Riehl Equation Values

SEE ALSOSEE ALSO

1. Mahoney, J.J., 1998, Incorporation of coprecipitation reactions in

predictive geochemical models: in Proceedings of Tailings and Mine

Waste '98, Fort Collins, Colorado, p. 689-697. A.A. Balkema pubs.

2. Mahoney, J.J., 2001, Coprecipitation reactions – verification of

computational methods in geochemical models: in Mining Impacted

Pit Lakes 2000 Workshop Proceedings: a Multimedia CD Presentation.

(Workshop held April 4–6, 2000 Reno, NV) United States

Environmental Protection Agency Office of Research and

Development. EPA/625/C-00/004. Session 4.

Example Input File for Kd = 70Example Input File for Kd = 70

TITLE Example 10.--Solid solution of otavite and calcite.

PHASES # Fix-H+ not included because of space limits

Otavite

CdCO3 = CO3-2 + Cd+2

log_k -11.31

Calcite

CaCO3 = CO3-2 + Ca+2

log_k -8.48

SOLUTION 1

-units mmol/kgw

pH 8.0

Ca 3.45

Cd 0.002

END

USE SOLUTION 1

EQUILIBRIUM_PHASES 1

CO2(g) -2.0 10

Calcite 0.0 0.0

Fix_H+ -8.0 Na(OH) 20.0

SOLID_SOLUTIONS 1

Ca(x)Cd(1-x)CO3

-comp Calcite 0.00

-comp Otavite 0.00

-Gugg_nondim 2.28

REACTION 2

Ca 0.01

END

Example Output File for Kd = 70Example Output File for Kd = 70(portion)(portion)

-------------------------------Phase assemblage--------------------------------

Moles in assemblage

Phase SI log IAP log KT Initial Final Delta

Calcite 0.00 -8.48 -8.48 0.000e+00 0.000e+00

CO2(g) -2.00 -20.15 -18.15 1.000e+01 9.988e+00 -1.250e-02

Fix_H+ -8.00 -8.00 0.00

Na(OH) is reactant 2.000e+01 2.000e+01 -9.843e-07

--------------------------------Solid solutions--------------------------------

Solid solution Component Moles Delta moles Mole fract

Ca(x)Cd(1-x)CO3 1.00e-02

Calcite 1.00e-02 1.00e-02 1.00e+00

Otavite 2.00e-06 2.00e-06 2.00e-04

For Further Information ContactFor Further Information Contact

John Mahoney, Ph.D.John Mahoney, Ph.D.

Principal Principal GeochemistGeochemist

Mahoney Geochemical Consulting LLCMahoney Geochemical Consulting LLC

Lakewood, COLakewood, CO

jmahoney@mahoneygeochem.comjmahoney@mahoneygeochem.com

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