Comment on Nonlinear and 

Nonequilibrium Sorption 

and Sorbed-Phase 

Degradation in PRZM5

Dirk F. Young

Office of Pesticide Programs

US Environmental Protection Agency

Washington, DC

1
Background

• Requests by registrants to incorporate 

nonlinear & nonequilibrium sorption into 

modeling (primarily groundwater)

• Submitted modeling studies incorporating 

nonlinearity and nonequilibrium always 

show a decrease in aquifer concentrations

2
NAFTA Groundwater Conceptual Model

3
Nonlinearity, Equilibrium, & 

Nonequilibrium Definitions

( ) N k S f KFC

t

S (1 ) 2 2

2

= − − ∂

∂

S2

At equilibrium: S1 = fKFCN

At Equilibrium: S2 = (1-f)KFCN

S1

Nonequilibrium:

4
FOCUS Degradation Conceptualization

S2

S1

Degradation Occurs in Aqueous

and Equilibrium Sorbed Phase (S1)

Degradation Does Not Occur in 

Nonequilibrium Region (S2)

5
EPA does not distinguish between sorbedand aqueous-phase degradation

• Submitted studies are typically inadequate to 

make such a determination 

• Sorption properties are not measured for 

soil used in degradation study

• EPA models total system degradation to 

correspond to available laboratory

6
Literature Heavily Weighted To 

Aqueous-Phase Only Degradation

Ainsworth et al. (1993); Basagaoglu et al. (2002); 

Bengtsson & Carlsson (2001); 

Bertelkamp et al. (2014); Bosma et al (1997); 

Brusseau et al., (1999); Chen et al. (2011); 

Fry and Istok (1994); Gou et al. (2000); 

Heitkamp et al. (1984); Haws et al. (2006); 

Hu and Brusseau, (1998); Huixian et al (1992); 

Johnsen et al., (2005); Kim et al. (2003); 

Karapanagioti et al. (2001); Manilal & Alexander (1991); 

Mihelcic and Luthy (1991); 

Ogram et al. (1985); Pignatello et al. (1990); 

Ramaswami and Luthy (1997); Rao et al. (1993); 

Rijnaarts et al. (1990); Sabbah et al. (2004); 

Scow (1993); Scow & Alexander (1992); 

Smith et al. (1992); Steen et al. (1980)

Volkering et al. (1992); Scow et al. (1995); 

Weber and Colbe (1968); Stevens, et al. (1990); 

Weissenfels et al. (1992); Wodzinski and Bertolini (1972); 

Wszolek and Alexander (1979); 

Zhang et al. (1998); Zhao et al. (2000)

Feng et al. (2000); Woo et al. (2001); 

Poeton et al. (1999); Tang et al. (1998); 

Guerin & Boyd (1992, 1997) 

Remberger et al. (1986)

7
Residence Time and Degradation

Two Concepts:

Aqueous-Phase Residence

Aqueous /S1 Residence Time

FLOW IN

FLOW OUT 8
Low concentration 

would result in higher 

retardation.

Aq/S1 residence time 

increases

Aqueous-phase 

residence is the same

Current Standard Nonlinear Isotherm Nonlinear & Nonequilibrium

Simple conceptualization. 

Implied sorbed-phase 

degradation. 

Aq/S1 Residence time is 

constant with conc

Aqueous-phase residence 

is the same

Nonequilibrium sites 

further lower the 

concentration.

Aq/S1 residence time 

increases even more

Aqueous-phase 

residence is the same9
Impact of Nonequilibrium & Nonlinearity

Aqueous-Phase Only Degradation:

Nonlinearity: No Effect

Nonequilibrium: No Effect

Nonequilibrium & Nonlinearity: No Effect

Aqueous- & Sorbed-Phase Degradation:

Nonequilibrium: No Effect

Nonlinearity: More Degradation

Nonequilibrium & Nonlinearity: Even More Degradation

10
Incorporation of Nonlinearity into 

SWCC &PRZM5

• Added GW to SWCC

• Added Freundlich Isotherm Option

• Solved with predictor-corrector procedure

• Included sub-daily time step option for testing

• Included option for Aqueous-Phase Only 

degradation

11
SWCC Nonlinear Isotherm Inputs

12
Test effect of Nonlinearity with SWCC 

and NAFTA Groundwater Scenario

Hypothetical Example: Isotherm Half Life Aquifer Conc.

Total System Degradation:

Linear Isotherm Koc = 50 ml/g 60 day 68 ppb

Nonlinear Isotherm KFoc = 50; N = 0.88 60 day 3.5 ppb

Aqueous Only Degradation:

Linear Isotherm Koc = 50 ml/g 26 day 66 ppb

Nonlinear Isotherm KFoc = 50; N = 0.88 26 day 69 ppb

13
Final Points

• Although EPA’s current conceptualization implies 

sorbed-phase degradation, it should not be construed 

as mechanistic.

• Sorbed-phase degradation implies degradation is not 

retarded by increased sorption, which seems to be 

contrary to the bulk literature.

• Use of nonlinearity should be explored. However, a 

sensible and transparent conceptual model regarding 

degradation would be needed prior to its use.

14