Modeling the Impacts from Nonlinear Sorption on PRCs and Target Compounds Quantification through Passive Sampling 

Xiaolong Shen, Magdalena Rakowska, Songjing Yan, and Danny Reible(Texas Tech University, Lubbock, TX, USA)

Passive Sampling

PE PDM

Passive sampling

(Lu et al., 2011)

CAt Equilibrium 

K : Partitioning Coefficient between Polymer and Water

C C K f

PRC Correction

FSS 1 C /C ,

FSS C /C ,

1-D Diffusion Model

Sediment layer r L : R D

Polymer layer 0 r L : D

Rectangular Coordinate 2‐layer Model (PE, POM)

Sediment Layer Resistance Dominant Solution

FSS 1 expRDt

K Lerfc

RDtK L

log RD ~ log K

(Lampert et al., 2015)

Cylindrical Coordinate Model

Cylindrical Coordinate Model (PDMS fiber)

ξ - ratio of sorption on polymer to “displaced sediment”

1 1 e erfc 1 ω 1 e erfc 1 ω

Where ξ 1 δ , ω 1 ξ

Sediment layer r L : R D r

Polymer layer L r L : D r

Sediment Layer Resistance Dominant Solution

log R ~ log K

Impact from Cylindrical Geometry

Cylindrical geometry more rapid approach to equilibrium

Typical ξ for HOCs ~ 50

ξ for various PDMS fibers 17 μm 50 μm 100 μm

PCB28 47.6 31.4 26.6PCB52 48.6 32.2 27.2PCB10

1 52.2 34.5 29.2PCB13

8 55.4 36.6 30.9PCB18

0 59.4 39.3 33.2

Passive Sampling Calibration Tool

Available at: https://www.depts.ttu.edu/ceweb/groups/reiblesgroup/downloads.html

PRC_Model_v_1.4• Analytical model for predicting 

targets’ FSS based on PRCs

• Include all existing kinetic models

• Excel spreadsheet with VBA

Asymmetric Behaviors of PRCs

Choi et al., 2016

PRC release rate > Target uptake rate

Sampler: PE

Target: 4 PCBs

PRCs: 5 PCBs not existed in sediment

Activated carbon amended sediment from Hunter’s Point

Sorption in Activated Carbon

(Azhar, 2015)

Sorption in AC – Nonlinear

logK NPCB 18 7.3 0.51PCB 52 6.9 0.42PCB 77 7.8 0.67

PCB 101 6.9 0.48PCB 118 7.3 0.54

q K C

Freundlich Isotherm 

Non-linear Sorption Model

C : Concentration in polymer

D : Diffusivity in polymer

D: Water diffusivity

C : Concentration in porewater

q : Solid concentration in AC

ρ : Bulk density of AC

ε: Porosity

1‐D Diffusion Model

Non‐linear Sorption Model – Freundlich Isotherm

Non‐Competitive:

Competitive:

q K C

q , q , K C , C ,

q , /q , C , /C ,

Numerical Simulation

CapSim 3 ‐ A numerical model solves the one-dimensional transient non-linear advection-diffusion-reaction-sorption equation using finite difference method.

Problematic PRC CasesInitial porewater concentration (μg/L)

Scenarios Plot FSS Polymer (C /K ) Sediment+AC (C)1 PRC 0.01 02 Target 0 0.013 Target 0 0.0001

PRC FSS < Target

PRC FSS > Target

Non‐competitive CaseFreundlich Isotherm

q K C

N 0.7

Initial porewater concentration (μg/L) Scenarios Plot FSS Polymer (C /K ) Sediment+AC (C)

1 PRC 0.01 04 Target 0 0.0015 PRC 0.1 0

Problematic PRC Cases

PRC FSS > Target

PRC FSS < TargetNon‐competitive CaseFreundlich Isotherm

q K C

N 0.7

General FSS Behavior from PRCs

Non‐competitive CaseFreundlich Isotherm

q K C

Competitive Sorption Initial porewater concentration (μg/L)

Scenarios Plot FSS Polymer (C /K ) Sediment+AC (C)1 PRC 0.01 0.12 Target 0.01 0.1

q , q , K C C

q , /q , C /C

Competitive Case

N 0.7

Nonlinear Model Results

𝟓𝐰𝐭 % 𝐀𝐂𝐍𝐀𝐂 𝟎. 𝟕𝐥𝐨𝐠𝐊𝐀𝐂 𝟎. 𝟖𝟑 ∗ 𝐥𝐨𝐠𝐊𝐎𝐖𝟎. 𝟓

Nonlinear(NL) model predicts the difference of FSS between PRCs and target compounds with appropriate parameters

AC Amendment in Hunter’s Point

AquaGate + PAC

Sedimite

Aquagate + PAC Sedimite

Apparent Increase in FSS with ACThe green dots are apparent FSS from post‐AC placement and the blue/purple/cyan dots are FSS correcting for nonlinear sorption.

The FSS from baseline (orange) is a good approximation to the actual FSS both pre and post placement

SummaryPRC calibration modeling tool

‐ Analytical model for predicting targets’ FSS based on PRCs

‐ Include existing PRC kinetic models (cylindrical)‐ Spreadsheet model

Passive sampling with nonlinear sorption ‐ 1‐D diffusion model with nonlinear sorption terms‐ Concentration/nonlinearity of the sorbent sorption 

Application of the modeling tool‐ Analyzing porewater concentration of PCBs at HP ‐ FSS from baseline is a good approximation for post 

placement of AC

ReferencesAzhar, W. (2015). Evaluation of sorbing amendments for in-situ remediation of contaminated sediments

(Doctoral dissertation).

Bao, L. J., X. Wu, F. Jia, E. Y. Zeng and J. Gan (2015). "Isotopic exchange on SPME fiber in sediment under stagnant conditions: Implications for field application of PRC calibration." Environmental Toxicology and Chemistry.

Choi, Y., Y. Wu, R. G. Luthy and S. Kang (2016). "Non-equilibrium passive sampling of hydrophobic organic contaminants in sediment pore-water: PCB exchange kinetics." Journal of Hazardous Materials 318: 579-586.

Kupryianchyk, D., M. Rakowska, J. Grotenhuis and A. Koelmans (2012). "In situ sorption of hydrophobic organic compounds to sediment amended with activated carbon." Environmental pollution 161: 23-29.

Lampert, D., C. Thomas and D. Reible (2015). "Internal and external transport significance for predicting contaminant uptake rates in passive samplers." Chemosphere 119: 910-916.

Lu, X., A. Skwarski, B. Drake and D. D. Reible (2011). "Predicting bioavailability of PAHs and PCBs with porewater concentrations measured by solid‐phase microextraction fibers." Environmental Toxicology and Chemistry 30(5): 1109-1116.