Ecotoxicology and Environmental Safety 278 (2024) 116440

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Ecotoxicology and Environmental Safety
journal homepage: www.elsevier.com/locate/ecoenv

Simulation and parameter determination of the net sorption ofphenanthrene by sediment particles
Donglin Yu a, b, Xinyu Guo c, Aobo Wang d, Zhaosen Wu a, b, Jie Shi a, b, *a

Key Laboratory of Marine Environment and Ecology, Ocean University of China, Ministry of Education, 238 Songling Road, Qingdao 266100, China
Laboratory for Marine Ecology and Environmental Sciences, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, ChinacCenter for Marine Environmental Studies, Ehime University2-5 Bunkyo-cho, Matsuyama 790-8577,JapandSchool of Hydraulic Engineering, Ludong University, Yantai, Shandong 264025, Chinab

A R T I C L E I N F O

A B S T R A C T

Edited by Dr Yong Liang

The distribution of polycyclic aromatic hydrocarbons (PAHs) in the ocean is affected by the sorption-desorption
process of sediment particles. This process is determined by the concentration of PAHs in seawater, watertemperature, and organic matter content of sediment particles. Quantitative relationships between the net
sorption rates (=the difference of sorption and desorption rates) and these factors have not been established yet
and used in PAH transport models. In this study, phenanthrene was chosen as the representative of PAHs. Threegroups of experimental data were collected to address the dependence of the net sorption processes on the initialconcentration, water temperature, and organic carbon content representing organic matter content. One-site andtwo-compartment mass-transfer models were tested to represent the experimental data using various parameters.
The results showed that the two-compartment mass-transfer model performed better than the one-site masstransfer model. The parameters of the two-compartment mass-transfer model include the sorption rate co­

Keywords:
Polycyclic aromatic hydrocarbons
Sorption-desorption model
Particles
Temperature
Organic carbon content

efficients kfa and ksa (L g− 1 min− 1), and the desorption rate coefficients kd and ksd (min− 1). The parameters at
different temperatures and organic carbon contents were obtained by numerical simulations. Linear relationshipsffwere obtained between the parameters and water temperature, as well as organic carbon content. kfa , ksa and kd

decreased linearly, while ksd

increased linearly with temperature. kfa , ksa
2f
and kdincreased linearly, while ksd

decreased linearly with organic carbon content. The r values between the simulation results based on the re­lationships and the experimental results reached 0.96–0.99, which supports the application of the model tosimulate sorption-desorption processes at different water temperatures and organic carbon contents in a realistic
ocean.

1. Introduction
Polycyclic aromatic hydrocarbons (PAHs) are biotoxic and exert
carcinogenic, teratogenic, and mutagenic effects on organisms (Chenand Liao, 2006; Hao et al., 2016; Goswami et al., 2018; Alaekwe andAbba, 2022). PAHs are semivolatile and difficult to degrade in the nat­ural environment (Goswami et al., 2017; 2019). They persist in theenvironment and migrate over long distances (Jones and Voogt, 1999;
Wang et al., 2011; Xu et al., 2022). Thus, PAHs are widespread andpotentially harmful to the environment. The United States Environ­mental Protection Agency listed 16 types of PAHs as priority pollutants(USEPA, 1992; IARC, 2007; Zheng and Li, 2017).

The ocean is regarded as a sink of pollutants (Lara-Martin et al.,2020; Wang et al., 2020), and PAHs also exist in it. Concentrations of
PAHs in the ocean have been previously reported (Al-Farawati et al.,2009; Zhang et al., 2013; El-Naggar et al., 2021; Shi et al., 2022). PAHs
exist not only in aqueous phase (seawater) but also in solid phase (sus­pended sediment particles) (Neroda et al., 2020; Sakellari et al., 2021;
Sun et al., 2021; Wang et al., 2022). PAHs can migrate between aqueousand solid phases through the sorption-desorption process. PAHs in theparticles can be transported from the sea surface to the sea bottom by thesinking of particles. Consequently, the sediments are enriched in PAHs
(Hu et al., 2010, 2011; Zafarani et al., 2022).
PAHs inside the sediment can return to the water column through the* Corresponding author at: Key Laboratory of Marine Environment and Ecology, Ocean University of China, Ministry of Education, 238 Songling Road, Qingdao
266100, China.
E-mail address: shijie@ouc.edu.cn (J. Shi).
https://doi.org/10.1016/j.ecoenv.2024.116440
Received 25 January 2024; Received in revised form 16 April 2024; Accepted 3 May 2024
Available online 10 May 2024
0147-6513/© 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).

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Ecotoxicology and Environmental Safety 278 (2024) 116440

resuspension of particles and the diffusion of interstitial water. PAHs in
the particles can be released back into seawater through sorptiondesorption. The sorption-desorption processes occur in both the watercolumn and the sediment, and their difference results in net sorption
amount, which play an important role in the distribution of PAHs in theocean. Therefore, it is necessary to quantify the net sorption of PAHs
between seawater and sediment particles.
Previous studies have used different types of sorption kinetic models
to explore the net sorption process, such as first-, second-, pseudo-firstand pseudo-second-order models, to fit data from laboratory experi­ments (Ho and Mckay, 1999; Oh et al., 2013; Wu et al., 2009; Yang andZheng, 2010). In the laboratory experiment, the net sorption rate wasdetermined by the amount of sorbed pollutant in the particles until theequilibrium state was reached, which cannot be directly observed inrealistic oceans. Therefore, these models are not suitable for simulating
the net sorption processes in realistic oceans. Nzengung et al. (1997)
applied a one-site mass-transfer model to calculate the net sorption rateof naphthalene using organic clay. This model was later used to describe
the net sorption of hydrophobic organic pollutants (Oh et al., 2011,2013). Ding et al. (2008) divided the net sorption into fast and slow
processes, established a two-compartment mass-transfer model, andachieved good agreement in simulating the net sorption process ofhexachlorobenzene. In the one-site mass-transfer model andtwo-compartment mass-transfer model, the net sorption rate can becalculated as the difference between the concentrations of pollutants inthe aqueous and solid phases, which can be observed in realistic oceans.
Thus, these two models are suitable for simulating the net sorption
processes in realistic oceans. However, these models have not been used
to simulate the transport of pollutants in the ocean (Wang et al., 2019).
The addition of a sorption-desorption module to the pollutant transportmodel is preferred. Before this, we need to quantify the impact of thefactors on the sorption-desorption process.
In laboratory experiments, certain conditions such as the initialconcentration of the pollutant or water temperature can be fixed. Bychanging only one condition, the parameters related to this condition in
the model can be determined by fitting the model results to the exper­
imental data. Different experimental conditions were expected to affectthe net sorption results. Experiments have shown that net sorption
processes vary with the initial concentration of pollutant (Shi et al.,2015), water temperature (Zhu et al., 2006), and organic carbon content(representing organic matter content) of the sediment particles (Wanget al., 2008). Because these conditions are always changing in therealistic ocean, it is necessary to establish quantitative relationships
between the parameters of the sorption-desorption models and these
conditions, including the initial concentration of PAHs, water temper­
ature, and organic carbon content. This supports the embedding of the
net sorption model into pollutant transport models in the ocean.
This study aimed to accurately simulate the net sorption processes ofphenanthrene, a representative PAH, in marine environments. To ach­
ieve this goal, tuning the parameters to make the model results approachto the experimental data, and then the optimal parameters of the onesite and two-compartment mass-transfer models were obtained. Quan­
titative relationships were then established between the model param­
eters and the initial concentration of phenanthrene, water temperature,
as well as organic carbon content of the sediment particles. The con­tributions of fast and slow processes in the two-compartment masstransfer model were analyzed. The differences between the net sorption
models of sediment particles and phytoplankton were discussed. Finally,
we explored the temperature dependence of the two-compartment masstransfer model in a realistic coastal ocean simulation. This study lays thefoundation for embedding the sorption-desorption model into pollutant
transport models.

2. Methods
2.1. Model descriptions
2.1.1. One-site mass-transfer model
In the one-site mass-transfer model (Nzengung et al., 1997), the net
sorption rate was set as a first-order function of the concentration dif­ference between the aqueous and solid phases. The net sorption rate isexpressed as follows:dCp= kas • (Kp • Cd − Cp )
dt
Kp =

(1)

Cpe
Cde

(2)

where Cp (mg g− 1) and Cd (mg L− 1) are the concentrations of the solidand aqueous phases, respectively. In Eq. (1), Cd is converted to thecorresponding concentration of the solid phase in the theoretical sorp­
tion equilibrium state by multiplying with the partition equilibriumcoefficient (Kp , L g− 1). Cpe (mg g− 1) and Cde (mg L− 1) are the concen­
trations in the solid and aqueous phases, respectively, when sorptiondesorption reaches equilibrium. kas (min− 1) is the mass transfer coeffi­
cient, which represents the linear relationship between the net sorption
rate and concentration difference.
2.1.2. Two-compartment mass-transfer model
In the two-compartment mass-transfer model, the net sorption pro­
cess is divided into fast and slow processes (Ding et al., 2008). Conse­
quently, the pollutant concentration in the solid phase (Cp ) also have

two components: the concentrations of fast (Cfp , mg g− 1) and slow pro­

cesses (Csp , mg g− 1). The net sorption rates of the fast and slow processes
can be expressed as
dCfp= kfa • Cd − kfd •Cfp
dt

(3)

dCsp
= ksa •Cd − ksd •Csp
dt

(4)

where kfa and ksa (L g− 1 min− 1) are the sorption rate coefficients, andf

kd and ksd (min− 1) are the desorption rate coefficients, kfa • Cd and ksa •Cdfare sorption rates for the fast and slow processes, and kd •Cfp and ksd •Csp
are desorption rates for the fast and slow processes. The net sorption rateis the sum of the two processes and can be expressed asf
dCp dCp
=
dt
dt

+

dCsp
= (kfa • Cd − kfd •Cfp ) + (ksa •Cd − ksd •Csp )dt(5)2.2. Experimental data
The experimental data to test the simulation results were obtained
from the measured net sorption processes of phenanthrene between
sediment particles and seawater reported by the other studies (Yang andZheng, 2010; Zheng, 2010; Xu and Huang, 2011).
Different phenanthrene concentrations in seawater will result indifferent net sorption capacity. The experimental data of Yang andZheng (2010) were used to conduct numerical simulations to explore theresponses of model parameters to different phenanthrene concentra­
tions. The experimental data were the phenanthrene concentrations in
sediment particles measured at 11 time points through the net sorption
using three different initial concentrations of phenanthrene in seawater.
The data of each time point was obtained through 3 measurements.
In addition, numerical simulations were carried out using theexperimental data of net sorption kinetics given by Zheng (2010) to
discuss the parameters of the sorption-desorption models at different
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Ecotoxicology and Environmental Safety 278 (2024) 116440

temperatures. This experimental data were the phenanthrene concen­
trations in sediment particles measured at 11 time points through the net
sorption at three different water temperatures. The data of each time
point was obtained through 3 measurements.
Similarly, the experimental data of net sorption kinetics given by Xu
and Huang (2011) showed the concentrations of phenanthrene in waterat 9 time points through the net sorption process at four different organiccarbon contents of sediment particles. The results were obtained byconducting 2 parallel experiments. In this study, based on the massconservation of total phenanthrene in the water and sediment particles,
the concentration of phenanthrene in the sediment particles at each time
point was obtained. The relationship between parameters of the twomodels given in Section 2.1 and organic carbon content was determinedby numerical simulations.
The above experimental data were arranged into three groups, andused to determine model parameters under different phenanthrene
concentrations in seawater (Group I), water temperatures (Group II),and organic carbon contents of the sediment particles (Group III). It
must be noted that these experimental data were the results of previous
studies and the specific experimental methods are given in the corre­
sponding papers (Yang and Zheng, 2010; Zheng, 2010; Xu and Huang,2011). A brief description on each group is provided in Text S1 in the
Supplementary Materials.
2.3. Numerical simulations
In MATLAB (R2022b), the numerical solution of Eq. (1) and (5) wereapproached to each group of experimental data by tuning parameters,
and the optimal parameters of the models were determined from thesolution that has the minimum difference from the experiment data.
Based on these determined optimal parameters, the dependences of theparameters in Eq. (1) and (5) on the initial phenanthrene concentrationin seawater, water temperature, and organic carbon content of thesediment particles were examined. After knowing the dependences, themodel simulation can be carried out for any initial phenanthrene con­centration in seawater, any water temperature, and any organic carbon
content of the sediment particles, which exist in the realistic ocean. The
determination coefficient (r2 ) and sums of squares of error (SSE) be­
tween the model results and the experimental data were calculated toevaluate the performance of the simulations.
Fig. 1. Simulation curves of the two sorption kinetics models for phenanthrene
at different initial concentrations with the same set of parameters. a: One-site
mass-transfer model. b: Two-compartment mass-transfer model.

3. Results
3.1. Influence of the initial concentration in seawater on net sorption
valuesmigration rates of phenanthrene from seawater to sediment particles
fand kd and ksd represent the migration rates from sediment particles to

The net sorption experimental data for Group I were obtained forthree different initial pollutant concentrations. The parameters deter­
mination and simulation results of the one-site and two-compartment
mass-transfer models in Group I are given in Text S2 of the Supple­
mentary Materials. The simulation results showed that the twocompartment mass-transfer model performed better than the one-site
mass-transfer model.
In the one-site mass-transfer model, kas represents the exchange rateof phenanthrene between seawater and sediment particles, and Kp rep­resents the transporting trend of phenanthrene from seawater to sedi­ment particles. kas and Kp did not differ significantly among the threeexperiments (Table S1). When one set of parameters was used to simu­
late all three experiments, the value of r2 reached 0.9710, indicatingthat a fixed set of parameters can accurately reproduce the three ex­periments. In other words, the initial concentration of phenanthrene inseawater had little impact on the kas and Kp values (Fig. 1). By tuning theparameters, the optimal kas and Kp were determined to be 0.342 min− 1
and 0.1197 L g− 1, which achieved the highest r2 of 0.9738 (Table S2).

fseawater. kfa and kd determine the net sorption rate of the fast process,and ksa and ksd determine the net sorption rate of the slow process. kfa , ksa ,f

kd , and ksd showed little change at the three different initial concentra­
tions (Table S1). Thus, similar to the one-site mass-transfer model, a
fixed set of parameters was used in all three experiments (Fig. 1). kfa , ksa ,f

kd , and ksd were tuned to obtain a set of optimal values to reduce the bias
between the model results and the experimental data, which were0.0395 L g− 1 min− 1, 0.00391 L g− 1 min− 1, 0.482 min− 1, and
0.0815 min− 1, respectively (Table S2), obtaining an r2 of up to 0.9931.
The results show that each model can reproduce the experimental
data using a set of parameters for different initial concentrations.
Therefore, it is feasible to use a set of parameters for ocean simulations
with variable PAH concentrations.
3.2. Influence of the water temperature on net sorption values

In the two-compartment mass-transfer model, kfa and ksa represent the

The experiments in Group II tested the dependence of the net sorp
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Ecotoxicology and Environmental Safety 278 (2024) 116440

tion curves on the water temperature. The parameters determinationand simulation results of the two models are provided in Text S3. Basedon the parameters determination results of these three experiments(Table S3), quantitative relationships between the parameters in the
one-site mass-transfer model and the water temperature were estab­lished, which are expressed as follows:
kas = 0.0071 • T + 0.1333(6)

Kp = − 0.0045 • T + 0.2467(7)

established and expressed as follows:
kfa = − 0.000445 • T + 0.0504(8)ksa = − 0.000181 • T + 0.0085(9)kfd = − 0.0008 • T + 0.4943(10)

ksd = 0.0022 • T + 0.0333(11)

when the linear relationships between the parameters and the watertemperature in Eqs. (8)–(11) were considered, the mean r2 reached up to
0.9963, with an SSE of 6.06×10− 6 (Table S4), which indicated a better
performance of the model (Fig. 2).
The accuracy of the simulations was improved by considering thedependence of the model parameters on water temperature. Moreover, it
has become more reasonable and feasible to apply these models to
realistic oceans with spatially and temporally changes in the watertemperature.

where T is the water temperature (℃).
When considering the dependence of the parameters on water tem­
perature in the one-site mass-transfer model (Fig. 2), the r2 was high, at
up to 0.9504, and SSE was 9.24×10− 5 for the three water temperatureexperiments (Table S4). However, when using fixed values of the pa­
rameters from one experiment under a given water temperature, themaximum r2 was only 0.8606, indicating a weaker accuracy of thesimulations.
In the two-compartment mass-transfer model, the linear relation­
ships between the four parameters and the water temperature were

3.3. Influence of the organic carbon content of sediment particles on net
sorption values
The experiments in Group III showed the net sorption curves of thesediment particles with four different organic carbon contents. The pa­
rameters determination and simulation results of the two models areprovided in Text S4 of the Supplementary Materials. The parameters
were assumed to be linear functions of the organic carbon content. In the
one-site mass-transfer model, the linear relationships between kas and Kp
and the organic carbon content are expressed as follows:
kas = − 0.2579 • foc + 0.0148(12)

Kp = 29.0077 • foc − 0.0527(13)

where foc is the organic carbon content (%).
When using Eqs. (12) and (13) in the one-site mass-transfer model(Fig. 3), the mean values of r2 and SSE were 0.9411 and 1.98×10− 4,
respectively (Table S6). When fixed values of kas and Kp , the optimal r2
was only 0.7139, indicating the importance of considering the depen­
dence of the model parameters on the organic carbon content.
The linear relationships between the parameters in the twocompartment mass-transfer model and the organic carbon content
were obtained as follows:
kfa = 0.3321 • foc + 0.00036108(14)

ksa = 0.0495 • foc − 0.00017075(15)

kfd = 0.2554 • foc + 0.0271(16)

ksd = − 0.0258 • foc + 0.0033(17)

When considering the dependence of the parameters on the organiccarbon content of the sediment particles (Fig. 3), the results showed thatr2 was up to 0.9612 and SSE was 1.35×10− 4 (Table S6). However, if thedependences of the parameters on organic carbon content is ignored, theoptimal r2 was only 0.7600. The results showed that the simulation
accuracy significantly improved by changing the model parameters fordifferent organic carbon contents.
4. Discussion
4.1. Two processes of the two-compartment mass-transfer model
As indicated by the higher values of determination coefficient withthe experimental data in the simulations, the two-compartment masstransfer model performed much better than the one-site mass-transfer

Fig. 2. Simulation curves of the two sorption kinetics models considering thedependence of the parameters on the water temperature. a: One-site masstransfer model. b: Two-compartment mass-transfer model.
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Ecotoxicology and Environmental Safety 278 (2024) 116440

Fig. 4. Variations of the sorption rates of fast and slow processes in the twocompartment mass-transfer model.

consists of the amorphous organic matter (Xing and Pignatello, 1997;
Fan et al., 2010), the unconsolidated structure of which guarantees thefast net sorption of phenanthrene in seawater. The concentration of thephenanthrene at the surface of the amorphous organic matter increased
rapidly, whereas that in seawater decreased. When the concentration in
the solid phase exceeded that in seawater, phenanthrene desorbed fromthe sediment particles into the seawater, which induced a negative net
sorption rate of the fast process. Finally, the fast net sorption reached its
equilibrium state when the difference in concentrations disappeared.
Therefore, the sorption rate remained zero.
The inner parts of the sediment particles are occupied by condensed
organic matter, which has no opportunity to directly reach the phen­anthrene (Fan et al., 2010; Werner et al., 2012). Phenanthrene is sorbed
only when it diffuses through the pores in sediment particles and reaches
the inner part. Therefore, the net sorption rate of the slow process wascomparably low but lasted a longer time.
The two-compartment mass-transfer model expresses the twosimultaneous net sorption processes caused by different components of
sediment particles. Therefore, this model achieved better agreementwith the results of experiment. And the results of the two-compartment
mass-transfer model are used in the following discussion.

Fig. 3. Simulation curves of the two sorption kinetics models considering thedependence of the parameters on the organic carbon contents. a: One-site masstransfer model. b: Two-compartment mass-transfer model.

model in all experiments for the three groups. To evaluate the contri­
butions of fast and slow processes in the two-compartment mass-transfer
model, a new simulation was carried out under the initial concentrationof 0.8 mg L− 1, organic carbon content of sediment of 0.75 %, and watertemperature of 25 ℃.
The net sorption rates of the fast and slow processes were calculated
and compared (Fig. 4). The net sorption rate of the fast process increased
sharply at the beginning and reached its peak value of 0.0314 mg g− 1
s− 1 at 1 min. Subsequently, it rapidly decreased to below zero at
2.5 min. It then gradually increased to zero and remained almost con­stant until the end of the experiment. The net sorption rate of the slow
process was significantly lower than that of the fast process. It also
increased at the beginning and peaked at 0.0027 mg g− 1 s− 1 at 1 min,which was only about 10 % of that of the fast process. It then gradually
decreased to approximately zero at 120 min but had no negative value
during the entire experiment.
The fast and slow net sorption processes were attributed to thestructures of the sediment particles. The composition of sediment par­ticles includes inorganic surfaces, amorphous and condensed organic
matter (Walter et al., 1996), which plays a dominant role in the net
sorption (Zhang et al., 2016). The surface of sediment particles usually

4.2. Comparisons of the net sorption processes of sediment particles andphytoplankton
PAHs have been detected not only in sediment particles but also in
phytoplankton (Tao et al., 2017; Duarte et al., 2021; Castro-Jimenez
et al., 2021), indicating that PAHs in the ocean can also be sorbed byphytoplankton (Cerezo et al., 2017). Unlike sediment particles, phyto­plankton are living organisms. Therefore, their net sorption process is
expected to differ from that of the sediment.
Previous studies have also divided the net sorption processes ofphytoplankton into two parts: net sorption of the surface and net sorp­
tion of the internal matrix (Dachs et al., 1999). The net sorption rates ofpollutants on the surface of phytoplankton are faster than those in theinternal matrix (Vento and Dachs, 2002), similar to the fast and slow
processes of sediment particles described in the two-compartment
mass-transfer model in this study. The structure of the net sorption
model for phytoplankton was similar to that of the two-compartment
mass-transfer model, which was determined using four parameters:
surface sorption rate coefficient kad (L g− 1OC min− 1), desorption rate
coefficient kdes (L g− 1OC min− 1), matrix sorption rate coefficient ku(min− 1), and desorption rate coefficient kd′ (min− 1) (Dachs et al., 1999).

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D. Yu et al.

For phenanthrene, the values of kad , kdes , ku , and kd′ were 2.80 L g− 1OC
min− 1, 0.117 min− 1, 0.00440 L g− 1OC min− 1, and 0.000285 min− 1,
respectively (Table 1). In the net sorption model of phytoplankton, theorganic matter in phytoplankton is thought to be fully responsible forthe net sorption of phenanthrene. If the organic matter in sedimentparticles is thought to be fully responsible for the net sorption ofphenanthrene, the governing equation of the two-compartment mas­s-transfer model is as follow:
f′

dCsp′
′
′
′
= (kfa • Cd − kfd • Cfp ) + (ksa′•Cd − ksd′ • Csp′)
dt

dCp′ dCp
=
+
dt
dt

(18)

than those between the seawater and phytoplankton. The value of ksa /ksd′

(19)

Therefore, Eq. (18) can be expressed as(20)Comparing with Eq. (5), kfa , ksa , kfd , and ksd can be expressed as′(21)

ksa = foc • ksa′(22)

kfd = kfd

′

(23)
(24)

ksd = ksd′f′f′where ka , ksa , kd , and ksd are the parameters similar to those in the net
sorption model of phytoplankton. The relationship between the pa­
rameters of the two-compartment mass-transfer model and the organiccarbon content of sediment particles in Section 3.3 (Eqs. (14)–(17))′′

4.3. Influence of the water temperature on simulation of net sorption
process in the Bohai Sea

indicate that kfa and ksa are dominated by terms related to foc , while kfd andksd are dominated by terms unrelated to foc , which is consistent with Eqs.
(21)–(24). Therefore, it is reasonable to assume that organic matter insediment particles is fully responsible for the net sorption ofphenanthrene.
The net sorption processes of phenanthrene in the sediment particles
and phytoplankton were evaluated by comparing the parameters of thetwo net sorption models. The parameters in the two-compartment mass-

In Section 3.2, linear relationships between the parameters in themodel and water temperatures were established, which made it practical
to apply the net sorption model in a realistic ocean with changing
temperatures. The Bohai Sea is a semi-enclosed sea located in north­eastern China (Fig. S4, 37–41◦ N, 117–122◦ E) with an average depth of
18 m. The water temperature of the Bohai Sea exhibited apparent sea­sonal variations (Fig. S5) (Ding et al., 2021). The influences of the watertemperature on the net sorption process of phenanthrene were studied
by comparing the simulation under the seasonal variations of tempera­ture and the result of the net sorption at an average temperature of 15℃.
The observed concentration of phenanthrene in surface sedimentwas 34.4 ng g− 1 in the Bohai Sea (Hu et al., 2011). At the average bot­
tom water temperature of 15℃, the concentration of phenanthrene in
the seawater was calculated to be 193.7 ng L− 1 when reaching theequilibrium state (the blue horizontal line in Fig. 5). The organic carbon
content was set to 0.75%. If the parameters were fixed to the values at
15℃ in the two-compartment mass-transfer model, the concentration ofphenanthrene in the sediment particles remained 34.4 ng g− 1 all year
round, although considering the seasonal variations of the watertemperature.
Considering the dependence of the model parameters on watertemperature, the two-compartment mass-transfer model was used toftransfer model derived in Group I were used as examples. kfa , ksa , kd , and
f′

s′

f′

ksd were converted to ka , ka , kd , and kd by Eqs. (21)–(24) and werecompared with those of the net phytoplankton sorption model (Table 1).

s′

Table 1
Parameters of the net sorption models of phenanthrene by sediment particles
and phytoplankton.
Parameters of the net sorption
By sediment particles′

kfa (L g− 1OC min− 1) = 5.27

By phytoplankton (Vento and Dachs, 2002)
kad (L g− 1OC min− 1) = 2.80′

ku (L g− 1OC min− 1) = 0.00440

f′kdes (min− 1) = 0.117

ksa (L g− 1OC min− 1) = 0.521
kd (min− 1) = 0.482

ksd (min− 1) = 0.0815′′

was 6.39 L g− 1, which was much smaller than ku /kd′ (15.44 L g− 1),suggesting that the accumulation capacity of phytoplankton was alsostronger than that of sediment particles in the slow process.
In addition, the net sorption kinetics models of different types ofpollutants are also different. For inorganic pollutants, the net sorption
processes of inorganic phosphorus (Li et al., 2018) and divalent mercury(Tuzen et al., 2009; Sahu et al., 2022) are often simulated bypseudo-first-order and pseudo-second-order kinetic models. The
pseudo-second-order kinetic model is more suitable for the net sorptionof hexavalent chromium onto activated carbon than thepseudo-first-order kinetic model (Malwade et al., 2016). The above twomodels describe the net sorption rate as a first- and second- orderfunction of the difference between the final equilibrium sorption amountin the experiment and the current sorption amount in the experiment,
respectively. These two models can reproduce the corresponding
experimental data. Since the initial concentration of pollutants in me­
dium of each experiment is determined, the final equilibrium sorption
amount is unique. In the actual environment, the concentration of pol­lutants in the medium is changing, and the net sorption is difficult toreach the equilibrium, and the final equilibrium sorption amount cannot
be observed. Therefore, it is difficult to apply these models to simulate
the net sorption process in a realistic ocean environment. The descrip­tion of the net sorption rate by the models in this study took into accountthe change of pollutant concentration in the environmental medium
such as the concentration of phenanthrene in seawater.

respectively. The relationship between Cp and Cp′ is as follows:

kfa = foc • kfa′

larger than ku and kd′, suggesting that the exchange rates of phenan­
threne between the seawater and sediment particles were much faster′fs
dCp dCp dCp′′=+= (foc • kfa • Cd − kfd •Cfp ) + (foc • ksa′•Cd − ksd′•Csp )
dt
dt
dt

f′

′

′

Cp
foc

′

During the slow process, ksa and ksd were two orders of magnituderespectively, and kfd and ksd (min− 1) are the desorption rate coefficientsof organic matter in the sediment particles of the fast and slow processes,

Cp′ =

f′

kfa /kd was 10.93 L g− 1, which was only half of the value of kad /kdes(23.93 L g− 1), indicating the accumulation capacity of phytoplankton
was stronger than that of sediment particles in the fast process.

OC). kfa and ksa (L g− 1OC min− 1) are the sorption rate coefficients oforganic matter in the sediment particles of the fast and slow processes,′′

kfa /kd and kad /kdes represent the accumulation capacity of phenanthrene
in sediment particles and phytoplankton in the fast process, respectively.

where Cp′ is phenanthrene concentration in organic matter (mg g− 1
′

f′

′

kfa and kad were of the same order of magnitude, as were the kd andkdes . It suggested that the net sorption rates of phenanthrene by sedimentparticles and by phytoplankton in the fast process were comparable.

kd′(min− 1) = 0.000285

6

D. Yu et al.

Ecotoxicology and Environmental Safety 278 (2024) 116440

temperatures.
Further improvements are required in this study. Estimations of theparameters of the two-compartment mass-transfer model largely
depended on the three selected laboratory experiments. Thus, additional
sorption kinetics experiments must be conducted to verify the accuracyof the parameters in the model.
In future studies, similar methods can be used to determine thesorption-desorption parameters of other PAHs and POPs. In addition, theresults of this study make it possible to simulate the distribution and fateof PAHs in both seawater and sediment by embedding a net sorption
module into the transport model of PAHs, which improves the accuracyof the simulation. Moreover, the parameters can be adjusted according
to the comparison between the simulated results and the observations,and the sorption-desorption parameters suitable for other PAHs andPOPs can be determined.
CRediT authorship contribution statement
Xinyu Guo: Writing – review & editing, Supervision, Resources,
Methodology, Funding acquisition, Conceptualization. Donglin Yu:
Writing – review & editing, Writing – original draft, Visualization,
Validation, Methodology, Investigation, Data curation. Aobo Wang:
Visualization, Supervision, Methodology. Jie Shi: Writing – review &editing, Supervision, Resources, Methodology, Funding acquisition.
Zhaosen Wu: Visualization, Methodology.

Fig. 5. Simulated seasonal variations of the phenanthrene concentrations in thesediment particles in the Bohai Sea.

simulate the annual cycle of the phenanthrene concentrations in thesediment particles under seasonal variations in the bottom water tem­
perature. The model was integrated for 3 years, and the results in thethird year were used for analysis. The model results (the red horizontal
line in Fig. 5) showed that the concentration of phenanthrene in thesediment particles increased to the maximum of 66.1 ng g− 1 in February(day 43) and then gradually decreased to its minimum value of
27.1 ng g− 1 in September (day 271). In winter, it gradually increased as
the water temperature decreased. Regardless of the dependence of the
net sorption-related parameters on water temperature, the maximum
underestimation and overestimation reached 48.0% and 26.9%,
respectively. The average bias of the concentration was 10.9 ng g− 1,
accounting for approximately 24.1% of average concentration(45.3 ng g− 1).
There are still some limitations in this study. Compared with thelaboratory experiment, the pollutants sorbed by sediment particles in
the ocean are not only phenanthrene, but also other PAHs and evenother persistent organic pollutants (POPs). Due to different spatial
scales, the molecular dynamics in the actual ocean are probably
different from those in laboratory experiments. In similar oceanographic
studies, parametric schemes are also derived from experiments and havebeen applied with good results, such as simulation of phytoplankton
growth and fate of POPs in the ocean (Gao et al., 2020; Wang et al.,2019). With such previous research experience, we believe that thisstudy, which also use the laboratory experimental data to finish theparameterization of sorption-desorption process, really lay a foundation
for further research in the simulations in the realistic ocean.

Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data Availability
The authors do not have permission to share data.
Acknowledgments
This study was supported by the National Natural Science Founda­tion of China (NSFC) (41976013). X. Guo was supported by a Grant-inAid for Scientific Research (MEXT KAKENHI, grant number: 20KK0239).
D. Yu was supported by the Ministry of Education, Culture, Sports,
Science and Technology, Japan (MEXT) to a project on JointUsage/
Research Center–Leading Academia in Marine and Environment Pollu­
tion Research (LaMer).
Appendix A. Supporting information
Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.ecoenv.2024.116440.

5. Conclusions
Based on the published experimental results on the net sorption ofphenanthrene by sediment particles, one-site and two-compartment
mass-transfer models were used to simulate the net sorption processes.
The two-compartment mass-transfer model performed much better thanthe one-site mass-transfer model in the simulations. By quantifying thedependence of the model parameters on various factors, the influencesof the initial concentration, water temperature, and organic carbon
content of the sediment particles on the net sorption of phenanthrene
were analyzed. This supports the simulation of the two-compartment
mass-transfer model in a realistic ocean with variable factors. The us­ability of the model was proven by analyzing the mechanism of the twocompartment mass-transfer model, comparing it with the phytoplankton
model, and simulating the net sorption process in the ocean at different

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