Practical Relationships fromTheoretical Lead Solubility Modeling

David G. Wahman, Matthew D. Pinelli,Michael R. Schock, and Darren A. Lytle

Center for Environmental Solutions & Emergency ResponseU.S. Environmental Protection Agency

Cincinnati, Ohio, United States2020 EPA Drinking Water Workshop

September 3, 2020

After this presentation, you will

09/03/2020 22020 EPA Drinking Water Workshop

1. Know of lead solubility simulation code

LimitationsCapabilities

2. Understand practical relationships from theory

Dissolved inorganic carbon (DIC) & pHDIC, pH, & orthophosphateSulfateChloride

Notes on Models – George Box

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British statistician

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1740-9713.2010.00442.x

The most that can be expected from any model is that it can supply a useful approximation to reality:

All models are incomplete; some models are useful.

Notes on Models – Ongoing Process

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Real System

ExperimentalData

ConceptualModel

Conceptual ModelEvaluation

ComputerizedModel

Model Implementationand Verification

ModelAnalysis

Simulation

ModelValidation

Adapted from Augusiak et al. (2014): https://doi.org/10.1016/j.ecolmodel.2013.11.009

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Lead Solubility Model – LEADSOL

Written by Mike Schock (1978 with subsequent updates)Theoretical equilibrium assumed (where you are going)No kinetic considerations (how fast you get there)Fortran older language, difficult to maintain/share/update

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Lead Solubility Model Code – R “Fixed” optionsWater!Pro, Tetra Tech (RTW) Model

“Custom” options Excel, PHREEQC, MINEQL+, Python, etc.R open source, freeware https://cran.r-project.org/

Code on GitHub eventually Reproducible Update/expansion by others

Graphical user interface Shiny package User–selectable inputs Select “simulation type” Select solids to consider Select equilibrium constants to use

Verified against LEADSOL & Excel version

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Lead Solubility Models – Limitations Equilibrium assumption (no kinetic limitations)

Single, controlling solid (i.e., homogeneous scale) Discrepancy with field scale (e.g., Tully et al., 2019) Unknown/multiple solubility constants for solids (e.g., calcium substituted) Amorphous versus crystalline solids

Pb(II) only (i.e., no Pb(IV) no redox, disinfectants/O2)Total lead (TOTPb) = soluble only (no particulate)No mass transfer limitations (e.g., Ma et al., 2018)Only 25°C temperatureNo biotic (e.g., biofilm) or organic matter (i.e., NOM) interactionsPhosphate

Scavenging ignored (e.g., calcium solids) Orthophosphate only (i.e., polyphosphates ignored)

Limitation – Heterogeneous Scale

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Multiple solids & thicknesses (controlling? eq. constant?)

Figure 4 from Tully et al. (2019): https://doi.org/10.1002/aws2.1127

Limitations – Multiple Constants (Uncertainty)

pH6.5 7.0 7.5 8.0 8.5

Lead

, mg/

L

0.001

0.01

0.1

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Hydroxypyromorphite (Pb5(PO4)3OH(s)) example 1 mg phosphate/L; DIC as noted

log K-62.83 (Nriagu 1972), 10 mg C/L-66.77 (Zhu et al. 2015), 10 mg C/L-62.83 (Nriagu 1972), 50 mg C/L-66.77 (Zhu et al. 2015), 50 mg C/L Action Level

Nriagu (1972): https://doi.org/10.1021/ic50116a041Zhu et al. (2015): https://doi.org/10.1155/2015/269387

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Limitations – Mass Transfer (Diffusion)

pH ~ 7 (Bulk)

pH ~ 4 (Surface)

Bulk,What we measure

Surface,What scale sees

Hydraulics matter Flow velocity Stagnation

Figure 3 (a) from Ma et al. (2018): https://doi.org/10.1021/acs.est.7b05526

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Lead Solubility Models – Useful? Historically used Schock (1980, 1981)

Applicable for simple Pb carbonate or phosphate scales (Tully et al., 2019)Tool in the toolbox

Pipe rigs, scale analyses, coupon studies, premise sampling, biostability, cleaning

Show trends with water chemistry Alkalinity, DIC, pH, phosphate, chloride, sulfate

Potential impact of operational changesGuide research questions

Evaluate/interpret experimental/field results Propose solids georgeite (Lytle et al., 2019) Estimate unknown solubilities Indicate other mechanisms controlling?

Schock (1980): https://doi.org/10.1002/j.1551-8833.1980.tb04616.xSchock (1981): https://doi.org/10.1002/j.1551-8833.1980.tb04615.xLytle et al. (2019): https://doi.org/10.1016/j.cej.2018.08.106Tully et al. (2019): https://doi.org/10.1002/aws2.1127

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Lead Solubility Model Code BasicsTheoretical Equilibrium Lead Solubility Simulator (TELLS)

Future GitHub download instructions to run locallyNine solids included individual & multipleMajor complexes included

Hydroxide, carbonate, phosphate, chloride, and sulfate TOTPb = Pb(II) + Pb(II) complexes

Evaluate change in a selected parameter pH, DIC, phosphate, chloride, sulfate, or ionic strength

Generate solubility plotsExport data (.csv)

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TELLS – Sidebar & General Info Tab

Solubility Plots

User Selections

General Info

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TELLS – Equilibrium Constants

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TELLS – Simulation Type Example

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TELLS – Solids to Consider & Buttons

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TELLS – Individual Solid (Log C vs. pH)L)

g/m

or ar

olm

ion

(atr

ent

onc

Log

c

User selected simulation type (pH, DIC, IS, Cl–, TOTSO4, TOTPO4)

T

Pb(II

) Com

plex

es

Pb(II)

OTPbAL

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TELLS – Multiple Solids Considered

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LEADSOL Verification

pH6 7 8 9 10 11

Lead

, mg/

L

0.01

0.1

1

105 mg C/L DIC (Digitized)50 mg C/L DIC (Digitized)100 mg C/L DIC (Digitized)5 mg C/L DIC (Simulation)50 mg C/L DIC (Simulation)100 mg C/L DIC (Simulation)

Digitized from Schock (2017):https://www.researchgate.net/publication/315761502_Lead_Corrosion_Control_101_A_Journey_in_Rediscovery

After this presentation, you will

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1. Know of lead solubility simulation code Limitations Capabilities

2. Understand practical relationships from theory DIC & pH DIC, pH, & orthophosphate Sulfate Chloride

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DIC & pH – Pb Solubility

At lower pH,↑ DIC = ↓ TOTPb

At higher pH,↑ DIC = ↑ TOTPb

Around pH 8,minor DIC impact

As ↑ pH, controllinglead solid changes from

cerussite hydrocerussite

Cerussite Hydrocerussite

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DIC & pH – Important Species Simulator provides all individual lead species’ concentrationsLead and lead complex concentrations

Allows understanding of some trends

Carbonate solids example: ↑ DIC = ↑ Pb(CO3)22– importance at high pH

L/g m

ad,

eL

0.01

0.1

1

10

6 7 8 9 10 11

DIC = 5 mg C/L

Pb 2+ Total Pb

PbCO3

Pb(OH)2 2-

H)3PbOH + 4

(O

)H

b (OPPbHCO3 + bP

TOTPb

PbCO3

Pb2+

Pb(

6 7 8 9 10 11

L/g m

ad,

eL

0.01

0.1

1

10

TOTPb

pH

OH)2

DIC = 100 mg C/L

Total Pb

PbCO3

Pb 2+

Pb(CO3)2 2-

PbHCO (OH) H)3

Pb 2 (O3 +

Pb

PbCO3Pb2+

Pb(CO3)2–

Pb(OH)2

pH

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DIC, pH, & Orthophosphate #1

6.5 7.0 7.5 8.0 8.5 9.0 9.50.01

0.1

With orthophosphate, minimum lead solubility near pH 7.5 ↑ orthophosphate = ↓ TOTPb

Lead

, mg/

L

0.016.5 7.0 7.5 8.0 8.5 9.0 9.5

0.1

DIC = 10 mg C/L

pH pH6.5 7.0 7.5 8.0 8.5 9.0 9.5

Lea

d, m

g/L

0.01

0.1

0 mg PO4/L .5 mg PO4/L 1 mg PO4/L 3 mg PO4/L 5 mg PO4/L

Lead

, mg/

L

0.01

0.1

6.5 7.0 7.5 8.0 8.5 9.0 9.5

0.0 mg TOTPO4/L0.5 mg TOTPO4/L1.0 mg TOTPO4/L3.0 mg TOTPO4/L5.0 mg TOTPO4/L

DIC = 50 mg C/L

pH

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DIC, pH, & Orthophosphate #2 For given orthophosphate,↓ DIC = ↓ TOTPb

For same target Pb,↑ DIC = ↑ orthophosphate

0 1 2 3 4 5

Lead

, mg/

L

0.01

0.1

1

pH 7.0 (48 mg C/L DIC)pH 7.5 (48 mg C/L DIC) pH 8.0 (48 mg C/L DIC)pH 8.5 (48 mg C/L DIC)

pH 7.0 (4.8 mg C/L DIC)pH 7.5 (4.8 mg C/L DIC)pH 8.0 (4.8 mg C/L DIC)pH 8.5 (4.8 mg C/L DIC)

48 mg C/L DIC

4.8 mg C/L DIC

Orthophosphate, mg PO 3–4 /L

pH3.0 3.5 4.0 4.5 5.0 5.5 6.0

Lead

, (m

g/L)

1

10

100

1000 mg SO4/L (CSMR=0.1)200 mg SO4/L (CSMR=0.5)100 mg SO4/L (CSMR=1)

50 mg SO4/L (CSMR=2)20 mg SO4/L (CSMR=5) 10 mg SO4/L (CSMR=10)

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Sulfate (100 mg chloride/L)

Minimal impact pH 7–11

Under acidic pH Anglesite (PbSO4) controls pH impact is minimal ↑ sulfate = ↓ TOTPb

3 4 5 6 7 8 9

)Lg/

(mad

,eL

0.01

0.1

1

10

100

pH

DIC = 5 mg C/L

1,000 mg TOTSO4/L (CSMR = 0.1)200 mg TOTSO4/L (CSMR = 0.5)100 mg TOTSO4/L (CSMR = 1.0)

50 mg TOTSO4/L (CSMR = 2)20 mg TOTSO4/L (CSMR = 5)10 mg TOTSO4/L (CSMR = 10)

CSMR = chloride to sulfate mass ratio

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Chloride (100 mg sulfate/L)

Minimal impact pH 7–11

Under acidic pH

Anglesite (PbSO4) controls

1,000 mg Cl–/L (CSMR = 10)500 mg Cl–/L (CSMR = 5)200 mg Cl–/L (CSMR = 2)100 mg Cl–/L (CSMR = 1.0)50 mg Cl–/L (CSMR = 0.5)10 mg Cl–/L (CSMR = 0.1)

pH impact is minimal ↑ chloride = ↑ TOTPb

• ↑ chloride is less impactfulthan ↑ sulfate

• Chloride impact fromPbCl+ complex

CSMR = chloride to sulfate mass ratio pH3 4 5 6 7 8 9

)Lg/

(mad

,eL

0.01

0.1

1

10

100

DIC = 5 mg C/L

After this presentation, you will

09/03/2020 272020 EPA Drinking Water Workshop

1. Know of lead solubility simulation code Limitations Capabilities

2. Understand practical relationships from theory DIC & pH DIC, pH, & orthophosphate Sulfate Chloride

Summary R source code simulate theoretical lead solubility Verified against LEADSOL & Excel implementation Tool in the toolbox Highlighted limitations & capabilities Trends versus actual concentrations

Practical relationships from theory No orthophosphate

• ↑ DIC reduces or increases solubility (pH dependent)• Controlling carbonate solid switches (pH dependent) With orthophosphate, solubility depends on pH & DIC

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Sulfate & chloride• Minimal impact pH 7–11• Acidic pH anglesite controls• Sulfate more impactful

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Questions?AcknowledgementsCasey Formal

Contact InformationDavid G. Wahman

wahman.david@epa.gov

DisclaimerThe information in this presentation has been reviewed and approved for public dissemination in accordance with U.S. Environmental Protection Agency (EPA) policy. The views expressed in this presentation are those of the author and do not necessarily represent the views or policies of the EPA. Any mention of trade names or commercial products does not constitute EPA endorsement or recommendation for use.