Journal of Contaminant Hydrology 196 (2017) 43–51

Contents lists available at ScienceDirect

Journal of Contaminant Hydrology
journal homepage: www.elsevier.com/locate/jconhyd

Dissolution kinetics of volatile organic compound vapors in water: An
integrated experimental and computational study
Mojtaba G. Mahmoodlu a,b,⁎, Elizabeth M. Pontedeiro a,c, Jesús S. Pérez Guerrero d, Amir Raoof a,S. Majid Hassanizadeh a, Martinus Th. van Genuchten a,ea

Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands
Department of Watershed and Rangeland Management, Gonbad Kavous University, Iran
Department of Nuclear Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, BrazildRadioactive Waste Division, Brazilian Nuclear Energy Commission, CNEN, Rio de Janeiro, Brazile
NIDES Interdisciplinary Centr for Social Development, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, Brazilbca r t i c l e

i n f oArticle history:
Received 2 April 2016
Received in revised form 28 November 2016
Accepted 7 December 2016
Available online 10 December 2016
Keywords:
Volatile organic compounds
Dissolution
Kinetics
Molecular diffusion
Salinitya b s t r a c t
In this study we performed batch experiments to investigate the dissolution kinetics of trichloroethylene (TCE)and toluene vapors in water at room temperature and atmospheric pressure. The batch systems consisted of awater reservoir and a connected headspace, the latter containing a small glass cylinder ﬁlled with pure volatileorganic compound (VOC). Results showed that air phase concentrations of both TCE and toluene increased relatively quickly to their maximum values and then became constant. We considered subsequent dissolution into
both stirred and unstirred water reservoirs. Results of the stirred experiments showed a quick increase in the
VOC concentrations with time up to their solubility limit in water. VOC vapor dissolution was found to be independent of pH. In contrast, salinity had a signiﬁcant effect on the solubility of TCE and toluene vapors. VOC evaporation and vapor dissolution in the stirred water reservoirs followed ﬁrst-order rate processes. Observed data
could be described well using both simpliﬁed analytical solutions, which decoupled the VOC dynamics in the
air and water phases, as well as using more complete coupled solutions. However, the estimated evaporation(ke) and dissolution (kd) rate constants differed by up to 70% between the coupled and uncoupled formulations.
We also numerically investigated the effects of ﬂuid withdrawal from the small water reservoir due to sampling.
While decoupling the VOC air and water phase mass transfer processes produced unreliable estimates of kd, theeffects of ﬂuid withdrawal on the estimated rate constants were found to be less important. The unstirred experiments showed a much slower increase in the dissolved VOC concentrations versus time. Molecular diffusion of
the VOCs within the aqueous phase became then the limiting factor for mass transfer from air to water. Fluid
withdrawal during sampling likely caused some minor convection within the reservoir, which was simulated
by increasing the apparent liquid diffusion coefﬁcient.
© 2016 Elsevier B.V. All rights reserved.

1. Introduction
Possible contamination of soil and groundwater by volatile organic
compounds (VOCs) is a major environmental concern at many sites currently or formerly occupied by large-scale chemical industries or smallscale users such as dry cleaners or gasoline stations (Han et al., 2016;
Rivett et al., 2011; Schubert et al., 2011). VOCs frequently contaminate
soil and groundwater and pose a potential threat to human healthwhen migrating upward through the unsaturated soil to indoor air⁎ Corresponding author at: Department of Earth Sciences, Utrecht University, Utrecht,
The Netherlands.
E-mail addresses: m.gharehmahmoodlu@uu.nl, m.g.mahmnoodlu@gmail.com(M.G. Mahmoodlu).

http://dx.doi.org/10.1016/j.jconhyd.2016.12.004
0169-7722/© 2016 Elsevier B.V. All rights reserved.

(Berscheid et al., 2010; Han et al., 2016; Mahmoodlu et al., 2013;
Rivett et al., 2011).
Mass transfer of VOCs across air-water interfaces is a key process affecting the fate of VOCs in the environment, including their volatilization and partitioning into atmospheric water (Aumont et al., 2000;
Boris et al., 2014; Ervens and Volkamer, 2010), as well as VOC removalfrom the unsaturated zone using various remediation techniques(Mahmoodlu et al., 2015; Schwarzenbach et al., 2003; Yap et al.,2012). Understanding the main factors affecting the dissolution of
VOC into the water phase during their migration through the unsaturated zone is critical to optimizing subsurface remediation practices, aswell as for developing predictive models of VOC reactive transport.
VOCs are generally hydrophobic and only slightly soluble in water(Görgényi et al., 2005; Peng et al., 2003). This can be a major hindrance
to successful implementation of soil treatment technologies, which

44

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

often target the dissolved mass of VOCs in the water phase. Low VOC
dissolution rates lead to low conversion rates and hence longer
treatment times and higher remediation costs (Chawla et al., 2001).
Having accurate data about VOC dissolution processes into water
under different conditions is for these reasons essential to foresee thepotential of enhanced soil and groundwater remediation techniques(Yap et al., 2012).
The effects of selected chemical properties of the water phase, mostnotably salinity, on mass transfer of residual VOCs in the subsurface
have been widely studied. Several studies have shown that salinity
can decrease the solubility of VOC in water (Endo et al., 2012;
Falabella and Teja, 2008; Görgényi et al., 2005; Schwarzenbach et al.,
2003; USEPA, 1991). The presence of dissolved electrolytes, in particularsmall ions, increases the structuring of aqueous phases and thus the cohesive energy in the water phase (Bowen and Yousef, 2003; Endo et al.,2012). Salinity can also cause a shift in the equilibrium partitioning of
neutral organic solutes toward non-aqueous phases. This effect is sometimes referred to as the salting-out effect (Endo et al., 2012). The literature shows that all gasoline components are salted out by sodium
chloride such that they become less soluble in saline solutions than inpure water (e.g., Falabella and Teja, 2008). This can lower the removal
efﬁciency of remediation methods. Furthermore, as a result of saltingout effects, Henry's constants of VOCs in saline water decrease. Several
soil and groundwater remediation methods for removing VOC vapors,such as air stripping and soil vapor extraction, depend on having reliable
estimates of Henry's constant (Falabella and Teja, 2008; Vane andGiroux, 2000). This requires knowledge of the partitioning behavior of
VOCs between the air and water phases.
Current literature lacks information about the dissolution kinetics of
VOC vapors into water and the different factors that may affect VOC
partitioning between the air and water phases. Moreover, many or
most reactive transport models assume that mass transfer across airwater interfaces is an equilibrium process governed by Henry's law.
This assumption does not always hold. For example, Sleep and Sykes(1989) reported that at many sites where VOC vapors were present as
an immiscible phase, VOC concentrations in the water phase were notconsistent with equilibrium concentrations. Hence, it remains unclear
how kinetic processes and other factors such as molecular diffusion of
VOCs do affect the mass transfer of VOC vapors across air-waterinterfaces. To address this problem, we performed a series of batch experiments to more closely investigate VOC vapor dissolution and subsequent diffusion into the liquid phase. Speciﬁc objectives of our study
were to (1) estimate the kinetics of VOC vapor dissolution (TCE and toluene in this study) into a stirred water reservoir, (2) investigate the effect of chemical properties of the water phase such as pH and especiallysalinity on VOC vapor dissolution in water, (3) evaluate the effect of molecular diffusion in water on VOC mass transfer across the air-water interface, and (4) numerically simulate VOC vapor dissolution andtransport within the aqueous phase.
2. Materials and methods
2.1. Experimental setup and procedure
The chemicals used in this study were pure TCE and toluene (obtained from Sigma-Aldrich and Merck, respectively), and mercury chloride(HgCl2) of 99.5% purity (Sigma-Aldrich). Fig. 1 shows a schematic of
our experimental setup. The system consisted of a glass cylinder (column) of 5.0 cm length and 4.0 cm internal diameter, together with avery small glass cylinder hanging in the middle of the larger container.
The larger cylinder had three ports capped by stainless steel lids. We
ﬁrst introduced 24.5 ml deionized (DI) water into the column via thelower water sampling port which was located 0.8 cm from the bottomof the column. Next, 0.5 ml mercury chloride of 10 mg l−1 was added
to the water pool to suppress any microorganism activity within the
setup, thus eliminating possible biodegradation processes during the

Fig. 1. Schematic view of the experimental setup. LH is the height of headspace, LW theheight of water reservoir, and D is the inner diameter of container.

experiments. Water inside the column was subsequently mixed thoroughly using a magnetic stirring bar (SCILOGEX PTFE, with pivot ring,
25 × 7.9 mm) and a magnetic stirrer (IKA, Germany) to obtain a homogenous solution of DI water and the mercury chloride. We next introduced 2.0 ml of pure phase VOC into the small hanging glass cylinder
in the headspace (Fig. 1), after which the top of the column was capped
immediately with a vapor-tight stainless steel lid.
Several batch experiments were conducted to determine the evaporation rate constants (ke) of TCE and toluene from the small hanging
VOC container into the headspace, and the dissolution rate constant(kd) describing subsequent dissolution kinetics of the VOC vapors
from the headspace into the water phase. For the stirred experiments
we used the magnetic stirrer to eliminate any VOC diffusion gradients
within the water phase, thus ensuring uniform concentrations within
the water reservoir. Precautions were taken not to disturb the airwater interface. We also performed batch experiments without stirring
the water phase to evaluate the effect of VOC diffusion within the waterphase on mass transfer, and hence the dissolution rate. To investigate
the effects of salinity on VOC dissolution, an experiment was conducted(while again stirring) using seawater with a salinity of 0.6 M. Additional
experiments for each compound were performed with a pH buffer todetermine the effect of pH on the dissolution kinetics of the two VOC vapors in water. The buffer solution was prepared using HCl and NaOH of
1 M. We assumed that the temperature and pressure inside the batches
were constant and remained at room temperature (21 ± 1 °C) and atmospheric pressure, respectively. In all experiments, the volume of
VOC liquid was large enough so that it did not deplete during the full duration of the experiments. All experiments were carried out in duplicate(Exp. 1 and 2 in this study represent the two replicates of the VOC
experiments).
2.2. Sampling and measurements
We measured VOC concentrations of both the gas and water phases
during the stirred and unstirred experiments. Gas samples of 1.5 ml
were periodically taken from the headspace of the column using a
2.5 ml gas-tight syringe (SGE Analytical Science, Australia). To avoid adrop in air pressure due to sampling, the same volume of air (1.5 ml)M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

45

governing equations for the experiments with the stirred and unstirred
water reservoirs, as well as provide several exact and approximate
analytical and numerical solutions that were for optimal analysis of
the data.
3.1. Governing equations for the stirred experiments
The governing equations for the VOC concentrations in the headspace and the water reservoir (Mahmoodlu et al., 2014, 2015;
Schwarzenbach et al., 2003; Yoshii et al., 2012) can be written as:
Fig. 2. Observed concentrations of TCE and toluene in the air phase.

was simultaneously injected into the upper part of the column througha separate port (Fig. 1). The VOC gas samples were injected into 10-ml
transparent glass vials, which were sealed with a magnetic cap andhard septum (Magnetic Bitemall; Grace Alltech). We periodically also
took aqueous samples of 1.5 ml each via the water sampling port
using a 2.5 ml gas-tight syringe. We then injected simultaneously thesame volume of air (1.5 ml) into the headspace through the separate injection port, again to avoid any air pressure changes. The aqueous samples were inserted into 10-ml transparent glass vials and sealed with amagnetic cap and hard septum.
Sampling vials were immediately placed into the tray of a gas chromatograph (GC). Gas samples of 2.0 ml were taken from each vial with
an autosampler using the headspace syringe of the GC. Samples werenext injected into the GC. The GC (Agilent 6850) we used was equippedwith a ﬂame ionization detector. Separation was done on an Agilent HP1 capillary column (stationery phase: 100% dimethylpolysiloxane,
length: 30 m, ID: 0.32 mm, ﬁlm thickness: 0.25 μm). A temperature programmed run was used to analyze the samples. VOC concentrations
were determined using a headspace method as employed in previous
studies (e.g. Almeida and Boas, 2004; Przyjazny and Kokosa, 2002;
Sieg et al., 2008; Snow, 2002). The limits of quantiﬁcation were calculated by using a signal-to-noise ratio of 10:1 (Kubinec et al., 2005).
3. Processes and governing mass transfer equations
As shown in Fig. 1, our experimental setup contained three domains.
The ﬁrst domain consisted of a water pool (reservoir) at the bottom of
the column. The second domain comprised the air space above thewater reservoir. The third domain was a pool of the particular VOC inside a small hanging glass container in the middle of air space. Fromthe moment the pure VOC was placed in the hanging glass container,
the following processes took place in the column: (1) evaporation of
the VOC from the small liquid pool into the closed air space, (2) diffusion of VOC vapor within the air space, and (3) dissolution of VOCvapor into the water reservoir. We assumed that the air pressure andtemperature did not change during the experiments. Our analysis also
assumed that diffusion in air was fast enough so that a uniform concentration in the headspace could be assumed. We describe separately the

Va

 a

a

dC
e
d C
¼ Aap k C amax −C a −Aaw k
−C w
dt
Hc

ð1Þ

Vw

 a

w
dC
d C
¼ Aaw k
−C w
dt
Hc

ð2Þ

where Ca and Cw are the VOC concentrations of the head air space andthe water reservoir, respectively [ML−3], t is time [T], C amax is the maximum headspace concentration, corresponding to the VOC vapor pressure [MT−1], Va and Vw are the volumes of the headspace and stirred
water reservoir, respectively [L3], ke denotes the apparent rate coefﬁcient for evaporation from the VOC pool into the headspace [LT− 1],
Aap is the surface area of the pure VOC reservoir in the internal cylinderof the headspace [L2], Aaw is the surface area of the air-water interface
between the headspace and the water reservoir [L2], and kd is rate coefﬁcient for VOC dissolution into the stirred water phase [LT−1].
As mentioned above, we assumed that the headspace is a wellmixed reservoir throughout which the evaporated VOCs are distributed
instantaneously and uniformly. This assumption can be made in view of
the relatively large diffusion coefﬁcients of VOCs in free air (about
5 × 10−4 cm2 min− 1) and the small volume of the headspace (lessthan 40 cm3). Since diffusion within the water phase was eliminatedby stirring, VOC concentrations can be assumed to be uniform also
within the water reservoir. Eqs. (1) and (2) further assume thatboth VOC evaporation into the headspace and subsequent dissolution
into the water reservoir can be modeled as linear kinetic processes(Schwarzenbach et al., 2003; Yoshii et al., 2012). They were solved
subject to zero initial concentrations in both the headspace and water
reservoir. Below we present both approximate and exact solutions of
the model for a stirred reservoir, as well as a more comprehensive formulation and numerical solution for an unstirred reservoir, in whichcase diffusive transport is considered from the air-water interface into
the liquid phase. We further provide an analysis of the possible effectsof ﬂuid withdraw during sampling on the results.
3.2. Approximate solution for the stirred experiments
Our experimental results (Fig. 2) showed that VOC concentrations in
the headspace reached their maximum values (C amax ) relatively quickly(mostly within 50 min), whereas mass transfer across the air-water interface took place over much longer time periods before equilibrium

Fig. 3. Observed and predicted concentrations of TCE and toluene in unstirred water. Experimental (symbols) and simulation (lines) results for TCE and toluene evaluated at the sampling
location x = L(t) − 0.8. Exp. 1 and 2 represent two replications of the VOC experiments. Mod. 1 and 2 represent numerical results for VOC dissolution in water. Mod. 1 used known values of
the VOC molecular diffusion coefﬁcient in water (Table 1), whereas Mod. 2 used diffusion coefﬁcients that were increased by a factor of three.

46

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

was reached within the water reservoir. One can take advantage of thisby decoupling Eq. (2) from Eq. (1) to produce a separate independentequation for Cw of the form (Mahmoodlu et al., 2014, 2015;
Schwarzenbach et al., 2003; Yoshii et al., 2012)dC
dw
¼ Aaw k C w
max −C
dt
w

Vw

ð3Þ

where
w
a
Cw
max ¼ S ¼ C max =H c

ð4Þ

Eq. (3) can be solved readily to givedC w ðt Þ
Aaw k t
¼ 1− exp −
Vw
Sw

!
ð5aÞ

or equivalently
 wdS −C w ðt Þ
Aaw k t
ln
¼−
w
w
V
S

ð5bÞ

Eq. (5b) shows that the dissolution rate coefﬁcient (kd) can be
estimated immediately from the slope of a straight line betweenln[(Sw − Cw)/Sw] versus t.

Table 1
Experimental conditions and input parameters for the VOC simulations.
Parameters

VOC

Value

Reference

Length of column (cm)Internal diameter of column (cm)
Initial volume of water in column, Vw(cm3)
Initial volume of air in column, Va (cm3)Air-water surface area, Aaw (cm2)
Length of VOC container (cm)Internal diameter of VOC container (cm)
Initial volume of VOC pool in container,
Vp (cm3)
Air-VOC pool surface, Aap (cm2)Henry's Law constant for water at 20 °C,
Hc (–)
Henry's Law constant for sea water at
20 °C (–)
VOC solubility in seawater

–
–
–

5.0
4.0
25.0

–
–
–

–
–
–
–
–

37.8
12.56
2.0
1.5
2.0

–
–
–
–
–

–
TCE
TolueneTCE
TolueneTCE
TolueneTCE
TolueneTCE
Toluene
TCE

1.767
0.42
0.358
0.28
0.19
8.5 × 10−4
3.4 × 10−4
4.93 × 10−4
1.71 × 10−4
1.15 × 10−3
4.79 × 10−4
4.74

–
–
–
–
–
–
–
–
–
–
–
Estivill et al.
(2007)
Hers et al.
(2000)
Lewis et al.
(2009)
Hers et al.
(2000)

Maximum VOC concentration in air, C amax
(g cm−3)
Maximum VOC concentration in water,−3)
Cw
max (g cm
Molecular diffusion coefﬁcient in air, Da(cm2 min−1)

Toluene 5.22
Molecular diffusion coefﬁcient in water,
Dw (cm2 min−1)

5.4 × 10−4

Toluene 5.1 × 10−4

3.3. Exact solution for the stirred experiments
While approximate, the above solution should provide a useful description of the VOC dissolution process. More precise solutions are possible by directly solving Eqs. (1) and (2) simultaneously subject to zero
initial concentrations for Ca and Cw. We obtained the following exact solutions for the coupled set of equations:C ðt Þ
ða2 þ a3 Þ
ða1 −a3 Þ
ða3 −a2 Þ
ða1 þ a3 Þ
¼ 1−
exp −
t −
exp −
t
a
2a3
2a4
2a3
2a4
C max
a

ð6Þ




C w ðt Þ
ða1 þ a3 Þ
ða1 −a3 Þ
ða3 −a1 Þ
ða1 þ a3 Þ
¼
1−
exp
−
t
−
exp
−
t
2a3
2a4
2a3
2a4
Cw
max
ð7Þ
where

 d
e
a1 ¼ Aaw H c V a þ V w k þ Aap Hc V w k

ð8aÞ


 d
e
a2 ¼ Aaw H c V a þ V w k −Aap Hc V w k

ð8bÞrﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃh d i2ee d
Aap Hc V w k þ Aaw H c V a þ V w k −4Aap Aaw H 2c V a V w k k ð8cÞ
a3 ¼
a4 ¼ Hc V a V w

TCE

ð8dÞ

example, in several experiments 1.5-ml sampling ﬂuid was withdrawn
at various times, leading to following expression for Vw(t)
8
25:0
>
>
>
> 23:5>>>>< 22:0V w ðt Þ ¼ 20:5
>
>
19:0
>
>
>
>
>
17:5
>
:
16:0

0≤t ≤55bt ≤1010bt ≤20
20bt ≤40
40bt ≤60
60bt ≤90
tN90

ð9Þ

where Vw(t) is given in ml and t in mins. Fluid sampling hence took
place at times t = 5, 10, 20, 40, 60 and 90 mins from the water sampling
port located 0.8 cm from the bottom of cylinder. As a ﬁrst approximation we hence simply employed Eq. (5a) again but now accounting for
ﬂuid phase sampling by considering Vw as functions of time as given
by Eq. (9), consistent with the invoked sampling protocols, i.e.,dC w ðt Þ
Aaw k tw ¼ 1− exp −V w ðt ÞS!
ð10Þ

The accuracy of the decoupled Eqs. (5a), (5b) and (10) for estimating
kd was tested by comparing results with complete coupled exact andEqs. (6) to (7) will be used to verify the appropriateness of
decoupling Eqs. (1) and (2) and using the independent Eq. (5b) for estimating the rate coefﬁcient kd from semi-logarithmic plots of the VOC
ﬂuid concentration versus time.
3.4. Effects of ﬂuid withdrawal during sampling
Repeated sampling from the relatively small volume of the water
reservoir caused the water level to decrease slowly but appreciably during the experiments. We investigated the signiﬁcance of these ﬂuid
withdrawals by adjusting the above solutions for the withdrawals. An
approximate way would be to simply adjust the values of Vw as a function of time in Eqs. (5a) and (5b) to correct for the sampling. For

Fig. 4. Effect of stirring speed (rpm) on the dissolution rate of TCE into water (rpmindicates the number of revolutions per minute).

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

47

Fig. 5. Salinity effects on the dissolution and solubility of TCE and toluene in stirred water.

numerical solutions of Eqs. (1) and (2) subject to constant and timevarying values of Va and Vw values. We note that the removed sampling
ﬂuid always contained some dissolved VOCs, which hence constituted asmall sink in the governing mass balance equation. This removal of VOCis actually accounted for automatically in the governing equation for theVOC ﬂuid reservoir, given by Eq. (2), by keeping Vw(t) outside of thetime derivative.

Eq. (13) may be used to account for increased air phase VOC concentrations during the early part of the experiments. For the fully decoupledscenario without considering mass transfer across the air-water interface, the value of μ then follows from the exact solution of Eq. (1), without the last (third) term, to give μ = Apke / Va.
At the lower boundary L(t) of the ﬁnite experimental setup we further have a no-ﬂux boundary condition given by

3.5. Governing equations for the unstirred experiments∂C w ðx ¼ Lðt Þ; t Þ¼0∂x

The rate of VOC diffusion into the water reservoir was followed bytaking small samples from the sampling port located 0.8 cm above thebottom of the water reservoir. The resulting problem can be approximated as one-dimensional diffusion problem. Similarly to the stirred
experiments, the water level (L) of the liquid reservoir during theunstirred experiments decreased signiﬁcantly: from about 2.0 cm at
t = 0 to about 1.5 cm at t = 4000 min. To account for the ﬂuid withdrawal, the resulting diffusion problem was modeled as a moving
boundary value problem using the equation
2∂C w ðx; t Þ∂ C ðx; t Þ
¼ Dw
∂t
∂x2

0 ≤x≤Lðt Þ

ð11Þ

where x is distance from the water level downwards, Dw
A is the molecular diffusion coefﬁcient of the VOC in water, and L(t) is the length(height) of the liquid reservoir, being initially at L0 = L(0), but slowly
decreasing as a function of time. The height of the reservoir could be described in the same form as Eq. (9), except for different sampling times(up to about 4500 min as shown in Fig. 3).
Eq. (11) was solved subject to a zero initial concentration, i.e.,w

C ðx; t ¼ 0Þ ¼ 0 0≤x ≤Lðt Þ

ð12Þ

ð14Þ

Since solute is withdrawn at the same time as the value of L(t) ischanged, the local concentration in the reservoir at the sampling pointshould change little or not at all, provided convective mixing due to
ﬂuid withdrawal is minimized during sampling. Since sampling took
place from inside the water reservoir (roughly from the middle of thereservoir), the local concentrations immediately above and below thesampling point would become brieﬂy discontinuous after ﬂuid withdrawal. If the sampling had been conducted at the very bottom of theliquid reservoir, no such discontinuity would have occurred. Our modeling approach hence assumes that the slow withdrawal of ﬂuid due tosampling will not affect the concentration distribution within thewater reservoir, with the lower boundary slowly moving upward.
The resulting diffusion problem with a moving boundary condition
is described by Eqs. (11) through (14), with L(t) given by Eq. (9) or asimilar discontinuous equation versus time. The problem can be
redeﬁned into an equivalent set of equations with a ﬁxed boundary condition using a change of variable as follows:
ξ¼

x
Lðt Þ

ð15Þ

leading to the set of equations
Since the VOC concentration in the air phase reached its equilibrium
value relatively quickly, the simplest boundary condition at the airwater surface (x = 0) is a Dirichlet type condition of the formμt
C w ðx ¼ 0; t Þ ¼ C w
max 1−eð13Þ

which relates the boundary ﬂuid concentration to the air phase VOC
concentration using Henry's law (Eq. (4)). The exponential term in

2∂C w ðξ; t Þ
Dw ∂ C w ðx; t Þξ dLðt Þ ∂C w ðx; t Þþ
¼ 2A
2
Lðt Þ dt∂t∂ξL ðt Þ
∂ξ

ð16Þ

C w ðξ; t ¼ 0Þ ¼ 0

ð17Þ



μt
C w ðξ ¼ 0; t Þ ¼ C w
0 1−e

ð18Þ

Fig. 6. Plots of Vw/Aaw ln[(Sw −Cw)/Sw] vs. time corresponding to Eqs. (5a) and (5b) assuming constant values of Va and Vw.

48

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

Table 2Estimated dissolution rate coefﬁcients (kd) for the stirred experiments without (AD) andwith (AD-W) accounting for ﬂuid withdrawal during sampling, and estimated evaporation (ke) and dissolution (kd) rate coefﬁcients for the coupled models for the unstirred experiments without (EC) and with (NC-W) ﬂuid withdrawal.
Model Description

VOC

kd
ke
(cm min−1) (cm min−1)

AD

TCE
TolueneTCE
TolueneTCE
TolueneTCE
Toluene

–
–
–
–
5.7
5.2
6.0
5.5

AD-W
EC
NC-W

Approximate decoupled solution,
Eqs. (5a) and (5b)
Approximate decoupled solution
with ﬂuid withdrawal; Eq. (10)Exact coupled solution, Eqs. (6)and (7)
Numerical coupled solution withﬂuid withdrawal; Section 3.3∂C w
0 ðξ ¼ 1; t Þ
¼0
∂ξ

0.074
0.060
0.055
0.044
0.121
0.086
0.069
0.055

stirrer eliminate VOC diffusion within the water phase. Fig. 4 depicts
normalized concentrations of TCE as a function of time for different stirring speeds. The results show that stirring the water reservoir caused aquick increase in the TCE concentrations. The data in Fig. 4 show that anincrease in the stirring speed from 100 to 300 rmp had minimal effecton the TCE concentration distributions in the water reservoir.
4.2. Salinity and pH effects on the dissolution of VOC vapors in water

ð19Þ

No exact analytical solutions exist for the resulting moving boundary
diffusion problem given by Eqs. (16) through (19), sometimes referred
to as a Stefan problem (Stefan, 1889) in the heat transfer and diffusion literature (Ockendon and Hodgkings, 1975; Crank, 1984; Tarzia, 2000). We
solved the moving boundary problem numerically using the NDSolvesubroutine from the Mathematica Software (Wolfram, 2009).
4. Results and discussion
4.1. VOC concentration in the air phase and water phases
Fig. 2 depicts the normalized concentration (Ca/C amax ) of the two
VOCs as a function of time, where Ca denotes the observed concentration of the target compound in air at a given time and C amax is the maximum concentration of the target compound in air (corresponding to its
vapor pressure). Results show that the air phase concentrations of both
TCE and toluene increased relatively quickly to their maximum values
and then remained constant. The evaporation rates of TCE and toluene
were very similar, leading to almost identical concentration distributions versus time. This is because both the vapor pressures and diffusion
coefﬁcients of TCE and toluene in air are very similar (Table 1).
Fig. 3 shows normalized concentrations (Cw/C w
max ) of TCE and toluene in the unstirred water as a function of time, where Cw denotes theobserved VOC concentration in the water phase and C w
max is the maximum concentration of the VOC in water (=Sw: solubility). The data indicate that the dissolution rate of TCE vapor into water is slightly fasteras compared to toluene vapor. The results in Fig. 3 for the unstirred experiments show a signiﬁcant difference between the dissolution rate inwater as compared to the evaporation rates into air (Fig. 2). Molecular
diffusion within the water reservoir away from the air-water interface
clearly acted as a barrier for effective mass transfer from the air phase
into the water phase. To investigate this effect, we used a magnetic

Dissolved salts in the water phase can have an important effect on
the partitioning behavior of VOCs between the air and water phases.
Fig. 5 shows normalized concentrations of TCE and toluene as a functionof time for both DI water and seawater. The normalized concentrationsin Fig. 5 were plotted relative to the solubility VOC concentrations of DI
water. Results indicate that salinity has a signiﬁcant effect on especiallythe solubility (Sw) of TCE, which decreased by about 30% for seawater ascompared to DI water. This is in line with previous studies (e.g.,
Schwarzenbach et al., 2003) showing that at moderate salt concentrations typical for seawater (~0.5 M), salinity will affect the aqueous solubility by a factor of between less than 1.5 for small and/or polar
compounds to about 3 for large, nonpolar compounds. Our experiments
further showed relatively small effects on the rates of mass transfer of
TCE and toluene across the air-water interfaces (see also Supplemental
Fig. 1s). The rate of mass transfer into seawater for TCE was slightly
higher than for Toluene. Our ﬁndings are consistent with a previous
study by Ramus et al. (2012) showing that moderate salinities (≤1 M)
will have relatively small effects on the mass transfer of VOCs across
air-water interfaces. We further estimated Henry's constants of TCE
and toluene dissolving in seawater. Henry's constants of both TCE andtoluene decreased to 69% and 70%, respectively, of the values for DI
water.
Fig. 2s (Supplementary Material) depicts normalized concentrations(Cw/Sw) of TCE and toluene as a function of time for various pH values (2,7, and 12) of the water reservoir. Results show that dissolution of VOCvapors into water is essentially independent of pH. Hence, pH cannot
be a limiting factor for the dissolution kinetics of these two VOCs. However, we note that the literature shows that the solubility of the chlorinated solvents (e.g., TCE) is considerably increased by biosurfactants at
pH values less than 7 (Albino and Nambi, 2009).
4.3. Approximate kinetic analysis of the stirred experiments
We ﬁrst analyzed the data using the approximate decoupled analytical solution (referred to as AD) given by Eqs. (5a) and (5b) to estimate
the dissolution (kd) rate coefﬁcient of the two VOCs. Fig. 6 shows plots ofw
w
ln[(C w
max − C )/C max ] vs. time for both TCE and toluene dissolution into
water, consistent with Eq. (5b). Results conﬁrm that dissolution followed a ﬁrst-order rate process. Values of the coefﬁcient of determination(R2) of the semi-log regressions obtained for TCE and toluene were in
most or all cases equal to 0.98 or higher. The corresponding dissolution
rate constants (kd) are given in Table 2. Results indicate that theFig. 7. Plots of Vw(t)/Aaw ln[(Sw −Cw)/Sw] vs. time corresponding to Eqs. (5a) and (5b) assuming time-variable values of Va(t) and Vw(t).

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

49

Fig. 8. Observed and calculated normalized air (Ca) and water phase (Cw) concentrations of TEC and toluene as obtained with the exact coupled solution (ECS) given by Eqs. (6) and (7).

dissolution rate constant (kd) for TCE was slightly larger as compared to
the value for toluene.
The results in Fig. 6 were obtained using the approximate decoupledanalytical solutions neglecting the effect of withdrawal of ﬂuid due tosampling. Fig. 7 gives similar results when ﬂuid withdrawal is taken
into account (AD-W). The regressions in Fig. 7 are very similar to
those in Fig. 6, except that the ﬁtted kd values are about 25% smaller.
These small differences in the rate constants were expected since thevolume of the water reservoir (Vw) slowly decreased, thus requiring aslightly slower rate of dissolution to reach similar concentrations in
the water reservoir. We will show in the following section that the differences are actually relatively small and probably can be neglected inexperiments where the reductions in liquid volume are less thanabout 20 to 40% of the original volume (in our stirred experiments thevolume of the water reservoir decreased from 25 ml to 16 ml).

4.4. Full analytic solution of the stirred experiments
The results in Figs. 6 and 7 were obtained assuming the fully
decoupled analytical solution (AD and AD-W) for the VOC concentrations of the water phases as given by Eqs. (5a) and (10), respectively.
Fig. 8 shows the ﬁtted solutions using the exact analytical solution(EC) assuming coupled air and water phases, i.e., using Eqs. (6) and(7) for Ca(t) and Cw(t), respectively. A sequential iterative ﬁtting process
was used in which ke was ﬁtted ﬁrst to the Ca data, followed by ﬁtting kd
to the Cw data using the ﬁtted value of ke as a known parameter. The ke
ﬁtting processes continued by using the ﬁtted value of kd, etc., until convergence was reached where the optimized ke and kd values did notchange anymore. R2 values of the separate Ca(t) and Cw(t) optimizations
where 0.999 and 0.997, respectively for TCE, and 0.999 and 0.998 fortoluene, thus reﬂecting very close matches with the data as shown
also by the close ﬁts of the TCE and toluene data in Fig. 8.
Fitted values of the rate coefﬁcients using the complete coupled
exact solution are listed in Table 2. Values of kd for the coupled solutions
for TCE and toluene were about 60% higher than those estimated withthe decoupled solutions. These results are important in that they indicate that decoupling the air- and water-phase solutions can lead to signiﬁcantly different (lower) values of the dissolution rate coefﬁcients.
Accounting for the effects of ﬂuid withdrawal also affected the estimatesof kd, but they were less dramatic then those caused by decoupling the
air and water phase VOC solutions (Table 2).
The differences between the various formulations are further demonstrated in Fig. 9, which shows results obtained with the different models
using the ke and kd values estimated with the coupled exact solution.
The plots include the approximate decoupled analytical solutions without(AD) and with (AD-W) sampling ﬂuid withdrawal, the exact coupled analytical solution (EC) without ﬂuid withdrawal, and the numericalcoupled solution with ﬂuid withdrawal (NC-W). The plots indicate that
decoupling the air phase and ﬂuid phase solutions (e.g., AD versus EC)
leads to inaccurate results, while the effects of ﬂuid withdrawal are farless signiﬁcant (e.g., AD versus AD-W). Still, the withdrawal of ﬂuid
from the water reservoir does have a noticeable effect on the calculated
VOC distributions in the water reservoir. Our results hence suggest thatsample withdrawal should be limited as much as possible relative to theavailable total amount of water in the experimental setup.
Also, one interesting result of the modeling analysis is that the calculated decoupled (AD-W) distributions with ﬂuid withdrawal are notcontinuous versus time due to discontinuity in the water volumes versus time as given by Eqs. (9) and (10). These discontinuities, however,are relatively small and barely visible on the AD-W plots in Fig. 9, andas such probably can be ignored in the analyses of many or mostFig. 9. Plots of calculated normalized VOC air phase (Ca) and water phase (Cw) distributions versus time using different models for the stirred TCE and toluene experiments. The models
used were the approximate decoupled analytical solutions without (AD) and with (AD-W) ﬂuid withdrawal, the exact coupled analytical solution (EC) without ﬂuid withdrawal, and thenumerical coupled solution (NC-W) with ﬂuid withdrawal.

50

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51

experiments. Please note, however, that no discontinuities occur in the
coupled numerical solutions for the case with ﬂuid withdrawal (NC-W).
4.5. Analysis of the unstirred experiments
Finally, Fig. 3 gave results for the unstirred VOC dissolution/diffusion
experiments. Included in the ﬁgure are predictions obtained with themoving boundary numerical solution in Section 3.4. The numerical results were obtained assuming that VOC concentrations in the headspaceremained constant in time at their maximum values corresponding totheir vapor pressures (i.e., Camax). This approach restricts the analysis
to only the water reservoir, and thus allowed us to ﬁx the coefﬁcient μ
in Eq. (13) at zero. Values of the various parameters used in the calculations are given in Table 1.
The plots in Fig. 3 show observed and calculated TCE and toluene
concentration values at the sampling point 0.8 cm from the bottom,
i.e., at x = L(t) − 0.8. As indicated by the plots, simulation results
using known values of the VOC molecular diffusion coefﬁcients (Dw)
in water showed signiﬁcant discrepancies with the experimental data
(Mod. 1 in Fig. 3). However, when we used in our simulations effective
VOC molecular diffusion coefﬁcients that were three times the known
values (3 × Dw), relatively good agreement resulted with the observed
data (Mod. 2). We believe that the withdrawal of water during sampling, even if done very carefully, may have caused some minor convection of the ﬂuid within the reservoir. Even if extremely small, theseeffects macroscopically will quickly overshadow pure liquid diffusion
within the water reservoir. Rather than using a reservoir ﬁlled withwater, perhaps experiments with a saturated porous medium in the reservoir (e.g., with very coarse sand or glass beads) could have minimized
these type of ﬂuid convection processes due to sampling.

Results for the undisturbed (unstirred) water reservoir showed avery slow rise of the VOC concentrations in the water phase withtime. A signiﬁcant difference existed between the dissolution rate of
VOC vapors into the undisturbed water and the VOC evaporation rates
in air above the reservoir. Simulations of VOC transport in undisturbed
water using a moving boundary value model that accounted for ﬂuid
withdrawal showed a signiﬁcant discrepancy between experimental
data and simulation results when know values for the VOC molecular
diffusion coefﬁcients (Dw) were used. An artiﬁcial increase in the VOC
molecular diffusion (3 × Dw) could satisfactorily simulate the experimental data, presumably because of some convection in the water reservoir caused by the sampling process

Acknowledgements
This work was supported in part by Veni Research Program Project
no. 016.151.047, which is ﬁnanced by the Netherlands Organisationfor Scientiﬁc Research (NWO). S. Majid Hassanizadeh received funding
from the European Research Council under the European Union's
Seventh Framework Programme (FP/2007-566 2013)/ERC Grant
Agreement no. 341225. The comments by anonymous reviewers further
helped to improve the manuscript.
Appendix A. Supplementary data
Supplementary data to this article can be found online at http://dx.
doi.org/10.1016/j.jconhyd.2016.12.004.

References
5. Conclusions
In this study we performed a series of batch experiments to investigate the kinetics of TCE and toluene vapors into both stirred andunstirred water reservoirs at room temperature (21 ± 1 °C). The effectsof pH and especially salinity on the dissolution of TCE and toluene vapors in water were investigated. We also evaluated the effects of molecular diffusion on mass transfer across the air-water interfaces using
stirred and unstirred water reservoir experiments. We further evaluated the evaporation kinetics of the two VOC compounds in the headspace
above the water reservoir.
VOC vapor dissolution in the water phase was found to be independent of pH. However, salinity was found to have an important effect on
dissolution, mass transfer rates as well as the solubility of TCE and toluene into water. The maximum concentrations of two compounds, corresponding to their solubilities, decreased by about 30% in seawater ascompared to DI water. Henry's law constants of both TCE and toluene
hence were also about 30% less in seawater. This shows that salinity
can be a limiting factor for VOC mass transfer across air-water interfaces.
Results of the stirred water experiments revealed a quick increase in
the VOC concentrations with time since molecular diffusion was eliminated as a possible barrier for VOC transfer ways from the air-water interface. Stirring speed had only a small effect on the VOC concentrationsin the water phase. Dissolution of the VOC vapors from the headspace
into the water reservoir was found to follow ﬁrst-order kinetics.
Several models were used to analyze the water phase VOC concentrations. The data could be described equally well using approximate
analytical solutions that decoupled the VOC concentration dynamics inthe water phases from those in the air phase, as well more complete
coupled solutions. However, the estimated dissolution rate constants(kd) were quite different for the various formulations, including formodels that accounted for ﬂuid withdrawal from the water reservoir
during sampling. Decoupling VOC air and water phase mass transfer
processes produced especially unreliable estimate of kd, whereas the effects of ﬂuid withdrawal on the rate coefﬁcients were far less dramatic.

Albino, J.D., Nambi, I.M., 2009. Effect of biosurfactants on the aqueous solubility of PCE and
TCE. J. Environ. Sci. Health, Part A. Toxic Hazard. Subst. Environ. Eng. 44 (14),1565–1573.
Almeida, C.M.M., Boas, L.V., 2004. Analysis of BTEX and other substituted benzenes inwater using headspace SPME-GC-FID: method validation. J. Environ. Monit. 6, 80–88.
Aumont, B., Madronich, S., Bey, I., Tyndall, G.S., 2000. Contribution of secondary VOC tothe composition of aqueous atmospheric particles: a modeling approach. J. Atmos.
Chem. 35, 59–75.
Berscheid, M., Burger, K., Hutchison, N., Muniz-Ghazi, H., Renzi, B., Ruttan, P., Sterling, S.,
2010. Proven Technologies and Remedies Guidance. Remediation of ChlorinatedVolatile Organic Compounds in Vadose Zone Soil. California Department of Toxic
Substances Control (154 pp).
Boris, A.J., Desyaterik, Y., Collett Jr., J.L., 2014. How do components of real cloudwater affect aqueous pyruvate oxidation? Atmos. Res. 143, 95–106.
Bowen, W.R., Yousef, H.N.S., 2003. Effect of salts on water viscosity in narrow membranepores. J. Colloid Interface Sci. 264 (2), 452–457.
Chawla, R.C., Doura, K.F., McKay, D., 2001. Effect of alcohol cosolvents on the aqueous solubility of trichloroethylene. Proc. 2001 Conf. on Environmental Research; New Approaches to Managing Environmental Quality in the Heartland. May 21–24, Kansas
State Univ., Manhattan, KS . https://www.engg.ksu.edu/HSRC/01Proceed/docs/52.pdf.
Crank, J., 1984. Free and Moving Boundary Problems. Clarendon Press, Oxford.
Endo, S., Pfennigsdorff, A., Goss, K.U., 2012. Salting-out effect in aqueous NaCl solutions:trends with size and polarity of solute molecules. Environ. Sci. Technol. 46,
1496–1503.
Ervens, B., Volkamer, R., 2010. Glyoxal processing by aerosol multiphase chemistry:
towards a kinetic modeling framework of secondary organic aerosol formation
in aqueous particles. Atmos. Chem. Phys. 10, 8219–8244.
Estivill, I.S., Hargreaves, D.M., Puma, G.L., 2007. Evaluation of the intrinsic photocatalyticoxidation kinetics of indoor air pollutants. Environ. Sci. Technol. 41 (6), 2028–2035.
Falabella, J.B., Teja, A.S., 2008. Air–water partitioning of gasoline components in thepresence of sodium chloride. Energy & Fuels 22 (1), 398–401.
Görgényi, M., Dewulf, J., Van Langenhove, H., Király, Z., 2005. Solubility of volatile organic
compounds in aqueous ammonia solution. Chemosphere 59 (8), 1083–1090.
Han, L., Qian, L., Yan, J., Liu, R., Du, Y., Chen, M., 2016. A comparison of risk modeling tools
and a case study for human health risk assessment of volatile organic compounds incontaminated groundwater. Environ. Sci. Pollut. R. 23 (2), 1234–1245.
Hers, I., Atwater, J., Li, L., Gilje, R.Z., 2000. Evaluation of vadose zone biodegradation of BTX
vapours. J. Contam. Hydrol. 46, 233–264.
Kubinec, R., Adamuscin, J., Jurdakova, H., Foltin, M., Ostrovsky, I., Kraus, A., Sojak, L., 2005.
Gas chromatographic determination of benzene, toluene, ethylbenzene and xylenes
using ﬂame ionization detector in water samples with direct aqueous injection up
to 250 µl. J. Chromatogr. A 1084, 90–94.
Lewis, S., Lynch, A., Bachas, L., Hampson, S., Ormsbee, L., Bhattacharyya, D., 2009. Chelatemodiﬁed Fenton reaction for the degradation of trichloroethylene in aqueous andtwo-phase systems. Environ. Eng. Sci. 26 (4), 849–859.

M.G. Mahmoodlu et al. / Journal of Contaminant Hydrology 196 (2017) 43–51
Mahmoodlu, M.G., Hartog, N., Hassanizadeh, S.M., Raoof, A., 2013. Oxidation of volatile organic vapours in air by solid potassium permanganate. Chemosphere 91 (11),1534–1538.
Mahmoodlu, M.G., Hassanizadeh, S.M., Hartog, N., Raoof, A., 2014. Oxidation of trichloroethylene, toluene, and ethanol vapors by a partially saturated permeable reactive
barrier. J. Contam. Hydrol. 164, 193–208.
Mahmoodlu, M.G., Hassanizadeh, S.M., Hartog, N., Raoof, A., van Genuchten, M.T., 2015.
Evaluation of a horizontal permeable reactive barrier for preventing upward diffusionof volatile organic compounds through the unsaturated zone. J. Environ. Manag. 163,
204–213.
Ockendon, J.R., Hodgkings, W.R (Eds.), 1975. Moving boundary problems in heat ﬂow anddiffusion. Proc. Oxford Conf., March 1974. Clarendon Press.
Peng, M., Vane, L.M., Liu, S.X., 2003. Recent advances in VOCs removal from water bypervaporation. J. Hazard. Mater. 98 (1), 69–90.
Przyjazny, A., Kokosa, J.M., 2002. Analytical characteristics of the determination of benzene, toluene, ethylbenzene and xylenes in water by headspace solvent
microextraction. J. Chromatogr. A 977 (2), 143–153.
Ramus, K., Kopinke, F.D., Georgi, A., 2012. Inﬂuence of dissolved humic substances on themass transfer of organic compounds across the air-water interface. Chemosphere 86,
138–143.
Rivett, M.O., Wealthall, G.P., Dearden, R.A., McAlary, T.A., 2011. Review of unsaturatedzone transport and attenuation of volatile organic compound (VOC) plumes leachedfrom shallow source zones. J. Contam. Hydrol. 123, 130–156.
Schubert, M., Schmidt, A., Müller, K., Weiss, H., 2011. Using radon-222 as indicator for theevaluation of the efﬁciency of groundwater remediation by in-situ air sparging. Environ. Radioact. 102, 193–199.
Schwarzenbach, R.P., Gschwend, P.M., Imboden, D.M., 2003. Environmental Geochemistry. John Wiley & Sons, Inc.

51

Sieg, K., Fries, E., Püttmann, W., 2008. Analysis of benzene, toluene, ethylbenzene, xylenes
and n-aldehydes in melted snow water via solid-phase dynamic extraction combinedwith gas chromatography/mass spectrometry. J. Chromatogr. A 1178 (1-2), 178–186.
Sleep, B.E., Sykes, J.F., 1989. Modeling the transport of volatile organics in variably saturated
media. Water Resour. Res. 25 (1), 81–92.
Snow, N.H., 2002. Head-space analysis in modern gas chromatography. Trace-Trend Anal.
Chem. 21, 608–617.
Stefan, J., 1889. Über einige Probleme der Theory der Wärmeleitung. S.-B. Wien. Akad.
Mat. Natur. 98, 473–484.
Tarzia, D.A., 2000. A bibliography on moving–free boundary problems or the heat–diffusion equation. The Stefan and related problems. MAT Ser. A, No. 2. Austral
Univ., Rosario, Argentina.
USEPA (U.S. Environmental Protection Agency), 1991. Dense non-aqueous phase liquid.
Ground Water Issue. EPA/540/4-91-002. www.epa.gov/superfund/remedytech/tsp/
downl-oad/issue8.pdf.
Vane, L.M., Giroux, E.L., 2000. Henry's law constants and micellar partitioning of volatileorganic compounds in surfactant solutions. J. Chem. Eng. Data 45 (1), 38–47.
Wolfram Research, Inc., 2009. Mathematica, Version 7.0, Champaign, IL.
Yap, C.L., Gan, S., Ng, H.K., 2012. Evaluation of solubility of polycyclic aromatic hydrocarbons in ethyl lactate/water versus ethanol/water mixtures for contaminated soil
remediation applications. J. Environ. Sci. 24 (6), 1064–1075.
Yoshii, T., Niibori, Y., Mimura, H., 2012. Some fundamental experiments on apparent dissolution rate of gas phase in the groundwater recovery processes of the geologicaldisposal system. WM2012 Conf., Feb. 26–March 1, Phoenix, AZ, USA.