gas mass transfer coefficient estimation

Journal of Contaminant Hydrology xxx (xxxx) xxx–xxx

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Modelling mass transfer during venting/soil vapour extraction: Non-aqueous phase liquid/gas mass transfer coefficient estimation D. Esraela, M. Kacemb,⁎, B. Benaddaa a b

Déchets Eaux Environnement Pollutions DEEP, INSA -Lyon 20, Avenue A. Einstein, Bât S. Carnot, 69621 Villeurbanne, France Univ Lyon, Ecole Nationale d'Ingénieurs de Saint-Etienne, Laboratoire de Tribologie et Dynamique des Systèmes LTDS UMR 5513 CNRS, F-42023 Saint-Etienne, France

A R T I C L E I N F O

A B S T R A C T

Keywords: Porous media NAPL/gas mass transfer coefficient Longitudinal dispersivity SVE

We investigate how the simulation of the venting/soil vapour extraction (SVE) process is affected by the mass transfer coefficient, using a model comprising five partial differential equations describing gas flow and mass conservation of phases and including an expression accounting for soil saturation conditions. In doing so, we test five previously reported quations for estimating the non-aqueous phase liquid (NAPL)/gas initial mass transfer coefficient and evaluate an expression that uses a reference NAPL saturation. Four venting/SVE experiments utilizing a sand column are performed with dry and non-saturated sand at low and high flow rates, and the obtained experimental results are subsequently simulated, revealing that hydrodynamic dispersion cannot be neglected in the estimation of the mass transfer coefficient, particularly in the case of low velocities. Among the tested models, only the analytical solution of a convection-dispersion equation and the equation proposed herein are suitable for correctly modelling the experimental results, with the developed model representing the best choice for correctly simulating the experimental results and the tailing part of the extracted gas concentration curve.

1. Introduction Decontamination of the unsaturated zone of soil by evaporation of non-aqueous phase liquids (NAPLs) trapped at residual soil saturation is influenced by the soil vapour extraction (SVE)/venting process. Pollutant evaporation is promoted by the pressure gradient in the pores that induces the circulation of air in contact with NAPL. In the above zone, pollutants are present in several states: dissolved in residual saturation water, adsorbed on the organic matter and/or clay fraction of soil, and evaporated in the gas and/or water phase, with NAPL and aqueous phases considered to be non-mobile at residual saturation, in contrast to the gas phase experiencing a pressure gradient. The model used to simulate NAPL–gas phase transfer is based on mass conservation and convection diffusion (Eq. (1)):

ϕ Sg

∂Cg, β ∂t

+ ∇[qg Cg, β ] − ∇[ϕ Sg Dg, β ∇Cg, β ] = ϕ Sg λo − g, β (Cgsat , β − Cg, β ) (1)

where φ denotes porosity [−], Sg is the gas-phase saturation [−], qg is the Darcy velocity in the gas phase [L T− 1], Dg, β is the hydrodynamic dispersion coefficient of compound β in the gas phase [L2 T− 1], λo − g , β is the coefficient of mass transfer between NAPL and the gas

⁎

phase for compound β [T− 1], and Cg , β and Cg , βsat are the actual and saturation concentrations of compound β in the gas phase [M L− 3]. In this case, the physical parameters most important for studying transport/transfer are the NAPL–gas phase mass transfer coefficient (λ) and the longitudinal dispersion coefficient (αL [L]). The αL is included in the cinematic dispersion term which forms with diffusion term, the dispersion coefficient, whereas λ significantly influences the results obtained using the above model (Zhao, 2007). Indeed, the most difficult part of real-scale process simulation is finding a mathematical relationship for estimating this coefficient based on flow, porous media type, and pollutant characteristics/content. Duggal and Zytner (2009)simulated the experimental results obtained for two soils (Ottawa sand and Elora silt) at different extraction flow rates using a one-dimensional (1D) column (diameter = 6.8 cm, height = 20 cm) and a three-dimensional (3D) radial pilot (diameter = 40.5 cm, height = 51 cm, extraction well diameter = 3.2 cm). In the 1D column case for sand, the mass transfer coefficient was observed to be very high (944–250,000 h− 1 for flow rates of 1.5–21.8 L·min− 1, respectively), being markedly lower for the pilot (4.5–43 h− 1 at the same flow rates). The same behaviour was observed in our previous works (Boudouch et al., 2016), where we compared the results of model parameter identification for experiments performed using 3D pilots and 1D columns, considering the mass

Corresponding author. E-mail address: [email protected] (M. Kacem).

http://dx.doi.org/10.1016/j.jconhyd.2017.05.003 Received 2 June 2016; Received in revised form 5 April 2017; Accepted 16 May 2017 0169-7722/ © 2017 Elsevier B.V. All rights reserved.

Please cite this article as: Esrael, D., Journal of Contaminant Hydrology (2017), http://dx.doi.org/10.1016/j.jconhyd.2017.05.003

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where Dα , βo is the effective molecular diffusion coefficient of compound β in phase α [L2 T− 1], δij is the Kronecker symbol (equalling 1 if i = j, zero otherwise), αL and αT are the longitudinal and transversal dispersivities, respectively, Uαis the pore velocity of phase α [L T− 1], Uai and Uaj are the pore velocities of phase α in directions i and j, respectively [L T− 1], and τα is the tortuosity factor calculated using the Milington model (Milington, 1959). The volatilization or mass transfer between NAPL and gaseous phases was simulated using a first-order kinetic model (Eq. (5)):

transfer to be constant in all subfields. This consideration was acceptable for a 1D approach, when pore velocity is homogeneous, whereas this velocity varied with distance from extraction wells at the radial pilot or field scale. Previously, the mass transfer coefficient was estimated based on empirical models (van Genuchten and Alves, 1982; Wilkins et al., 1995; Yoon et al., 2002), with the most frequently used ones neglecting the longitudinal dispersion coefficient and not correctly estimating porous media saturation. The coefficients of longitudinal dispersion and molecular diffusion determine the dispersion coefficient in the mass conservation equation (Eq. (1)), representing mechanical dispersion due to the heterogeneity of the fluid flow velocity in porous media. Dispersivity is an important pollutant transport property that is difficult to measure experimentally. However, it can be estimated from tracer breakthrough curves using analytical or numerical solutions of the mass conservation equation. To evaluate the effect of saturation on the mass transfer coefficient, a typical extracted gas concentration curve given by the United States Environmental Protection Agency USEPA (1994) can be divided into three parts:

sat

Eo − g, β = ϕ Sg λo − g, β (Cg, β − Cg, β )

(5)

where Eo − g , βis the term describing NAPL–gas phase mass transfer for compound β [M L− 3 T− 1], λo − g , βis the corresponding coefficient of Sat mass transfer [T− 1], and Cg , β and Cg, β are the equilibrium and saturation equilibrium concentrations of compound β in a mixture of gas phase [M L− 3]. Sat The (Cg, β ) was defined by Eq. (6): Sat

Cg, β = ωg, β CgSat ,β

(6)

• the flushing phase, where the gas concentration is constant; • the evaporation phase, corresponding to pollutant evaporation

where Cg , β is the concentration of compound β in the gas phase at equilibrium and saturation [M L− 3], and ωg , β is the molar fraction of compound β in the gas phase [−]. Mass transfer between NAPL and aqueous phases was described by Eq. (7):

•

Eo − w, β = ϕ Sw λo − w, β (Sweff, β − Cw, β )

Sat

caused by contact between air and NAPL, where the concentration of extracted gas rapidly decreases; the diffusion phase, where the decrease of the mass transfer coefficient is attributed to the decreasing contact surface between phases.

the effective solubility of compound β in the aqueous where phase [M L ]. The NAPL/aqueous phase mass transfer coefficient can be calculated using the empirical correlation of the modified Sherwood number (Eq. (8)) (Miller et al., 1990):

This study aimed to propose a model for simulating the SVE/venting process, focusing on the effect of mass transfer coefficient evaluation on the simulation of experimental results, with four experimental SVE/ venting tests performed. The developed model integrated the equation for calculating the mass transfer coefficient and was compared with five previously proposed mass transfer coefficient models to simulate experimental results. Finally, an additional expression taking saturation into account was proposed and tested.

Sho − w, β m =

2.1. SVE/venting model The SVE/venting model comprises five partial differential equations PDE, with the first being the continuity equation for gas flow simulation (Eq. (2)):

∂t

+ ∇[ρg qg ] = Qgs +

compounds β to the gas phase [M L− 3 T− 1]. The remaining four equations simulate the mass conservation of gas, NAPL, aqueous, and immobile solid phases (Eq. (3)):

(3)

α

(9)

⎛ Cs, β ⎞ ⎟ E w − s, β = ϕ Sw λ w − g, β ⎜Cw, β − K ⎝ d,β ⎠

where Cα , β is the concentration of compound β in phase α, Sα is the saturation of phase α, qα is the Darcy velocity in phase α, and ∑ Eα, β is

⎛ Cs, β ⎞ ⎟ = ϕ Sw Exp (0.301 − 0.668 log(Kd , β )) ⎜Cwβ − Kd , β ⎠ ⎝

α

the sum representing the transfers of compound β to phase α [M L− 3 T− 1]. Dα, β [L2 T− 1] is defined in Eq. (4) as:

⎡ Uαi Uαj ⎤ → o Dαβ = τα Dαβ δij + ⎢αT |Uα | δij + (αL − αT ) → ⎥ ⎢⎣ |Uα | ⎥⎦

(8)

where λw − g , β is the aqueous/gas-phase mass transfer coefficient of compound β [T− 1], Cw , β is the concentration of compound β in the aqueous phase [M L− 3], Ugis the pore velocity of the gas phase [L T− 1], and Hβis the Henry constant of compound β [−]. To simulate mass transfer between aqueous and solid phases (sorption), the corresponding mass transfer coefficient was estimated using the empirical model of Brusseau and Rao (1989) (Eq. (10)):

β

∑ Eα,β + Qαs

0.6 0.5 = 12 (ϕ − θo ) Re 0.75 w, β θo Scw, β

⎛ Cg, β ⎞ 0,55 −0.61 ⎟ ⎜C w , β − = ϕ Sw 10−2.49Dgo, β 0.16Ug 0.84 d50 Hβ Hβ ⎠ ⎝

(2)

where Sg is the saturation of the gas phase, ρg is the bulk density of the gas phase, qg is the Darcy velocity, Qgsis the gas phase supply term [M L− 3 T− 1], and ∑ Eg, β is the sum representing the transfer of all

∂ [ϕ Sα Cα, β ] + ∇[qα Cα, β ] − ∇[ϕ Sα Dα, β ∇Cα, β ] = ∂t

Dwo, β

⎛ Cgβ ⎞ ⎟ E w − g, β = ϕ Sw λ w − g, β ⎜Cwβ − Hβ ⎠ ⎝

∑ Eg,β β

2 λo − w, β d50

where λo − w , β is the NAPL/aqueous phase mass transfer coefficient of compound β [T− 1], d50 is the mean diameter of soil grains [L], Dw , βo is the molecular diffusion coefficient of compound β in the aqueous phase [L2 T− 1], θo is the volumetric content of the NAPL phase [L3L− 3], Rew , β is the Reynolds number of compound β in the aqueous phase, and Scw , βis the Schmidt number of compound β in the aqueous phase. To simulate mass transfer between aqueous and gas phases (stripping), the corresponding mass transfer coefficient was estimated from the empirical model of Chao et al. (1998) (Eq. (9)):

2. Model

∂(ϕ Sg ρg )

(7)

Sw , βeff is −3

(10)

where Cs , β is the concentration of compound β in the solid phase [M L− 3], and Kd , β is the sorption coefficient of compound β in soil [L3 M− 1]. In this work the sorption on solid phase is produced only by the

(4) 2

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2.2. Mass transfer coefficient evaluation

aqueous phase (Kaluarachchi and Parker, 1992), the gas phase and NAPL sorption are neglected. The biodegradation is also neglected. To resolve the continuity equation, we employed an equation system relating the relative permeability of a given phase to its saturation and subsequently to the used pressure, utilizing the model of Parker et al. (1987). The saturation of each phase was calculated as follows (Eqs. (11–13)):

Sl (Pcgo ) =

Six models were considered to evaluate the mass transfer coefficient, with the first one relying on the hypothesis of a local equilibrium assumption (LEA) between phases. In this case, the mobile phase is represented by Eq. (21), with the proportionality between concentrations in aqueous and gas phases deduced from the calculated concentration of compound β in the gas phase:

⎡ (1 + (γgo αvg Pcgo )nvg )−mvg ; Pcgo > 0 ⎤ Sw + So − Swr − Sor ⎥ = ⎢ ; Pcgo ≤ 0 1 − Swr ⎣1 ⎦

⎛ ρ Sw K d , β ⎞ ∂ S ⎟ Cg, β + ∇[qg Cg, β ] − ∇[ϕ Sg Dg, β ∇Cg, β ] ϕ ⎜Sg + w + b H ϕ Hβ ⎠ ∂t ⎝ β ∂ = −ϕ ρo (ωo, β So ) + Qgs + Rg, β ∂t

(11)

⎡ (1 + (γgo αvg Pcow )n vg )−mvg ; Pcow > 0 ⎤ Sw − Swr ⎥ = ⎢ 1 − Swr ; Pcow ≤ 0 ⎣1 ⎦

Sw (Pcow ) =

Sg = 1 − So − Sw

(12)

where ρb is the apparent density of soil [M L ], ρo is the bulk density of NAPL [M L− 3], and ωo , β is the molar fraction of compound β in NAPL [−]. The second method is based on the analytical solution of the pollutant mass conservation equation, where gas phase and NAPL/gas phase transfers are expressed for 1D geometry (Eq. (1)), as proposed by van Genuchten and Alves (1982) for a stationary state (Eq. 22):

(13)

where Pg and Pw are pressures of gas and aqueous phase respectively, Sw is the effective residual saturation in the aqueous phase, αvg, nvg and mvg are the van Genuchten parameter, Sor is the effective residual saturation S in the NAPL phase: Sor = 1 −orS , and Pcgo = Pg − Po and Pcow = Po − Pw wr are the capillary pressures for gas/NAPL and NAPL/aqueous phases, respectively. γgo and γow are scaling coefficients of transition from twophase system to three-phase one, which can be estimated using Eqs. (14) and (15) (Lenhard and Parker, 1987).

γgo =

γow =

λo − g, β =

(14)

σgo + σow (15)

σow

λ∗o − g, β = −

whereσgo, andσow are the interfacial tensions between gas/NAPL, and NAPL/aqueous phases, respectively. Lenhard et al. (2004) applied the above model to experimental results to determine the effective residual NAPL saturation, expressed by Eq. (16): max

Sor = Sor

max

(S t

− Sw )0,5 (1 − Sw )1,5

0,5 [(1

− (Sw + Sor )1 mvg )

− (1 − St1 mvg )

λ∗o − g, β = 10−0.5842 Dgo, β 0.32 Ug 0.68

krg (St ) = (1 − St )

1 − (1 − St

1 mvg

)

mvg ] 2

mvg ] 2

(19)

Kaluarachchi and Parker (1992) proposed defining a node as a three-phase system by imposing a condition on the inlet pressure of the NAPL phase (So > 0 ) (Eq. (20)).

⎡ βgw Pg + βow Pw Po ≥ ⎢⎢ βgw + βow ⎣ Pw

⎤ ; Pg > Pw ⎥ ⎥ ; Pg ≤ Pw ⎦

d500.44

(24)

d500.34

(25)

The above equations relate the mass transfer coefficient to the interstitial pore velocity and the mean diameter of soil particles, with the corresponding empirical models introducing gas phase content in the estimation of the mass transfer coefficient and neglecting hydrodynamic dispersion. The reduction of the mass transfer coefficient with decreasing NAPL saturation due to evaporation has been extensively documented, being attributed to an interfacial area decrease (Harper, 1999; Yoon et al., 2002; Yoon et al., 2003; Zhao, 2007; Nguyen et al., 2013). An improved model, linking the mass transfer coefficient to NAPL saturation and extraction time in the transient state was put forward by van der Ham and Brouwers (1998) (Eq. (26)), who showed that this empirical parameter was related to aqueous phase saturation and soil homogeneity. Using this relationship, Yoon et al. (2002) determined mass transfer coefficients between 0.5 and 1.2 for aqueous phase saturation values between 0.13 and 0.35. For sandy soil, these values corresponded to 1.2–4.6 for saturations of 0.48–0.61.

(18) 0,5 [

(23)

For the same experimental conditions, Yoon et al. (2002) proposed another empirical relationship to calculate the mass transfer coefficient (Eq. (25)):

(17) 1 mvg

Lc

⎛ Cg, β ⎞ ⎟⎟ ln ⎜⎜1 − Cgsat ⎝ ,β ⎠

λ∗o − g, β = 10−0.4221 Dgo, β 0.38 Ug 0.62

is the maximal effective residual saturation in NAPL [−], the maximal effective saturation in the total liquid phase [−]. Where Sw the apparent water saturation which is the sum of effective water saturation and the effective entrapped air saturation, and krw, kro, and krg are the relative permeabilities of aqueous, NAPL, and gas phases, respectively. The van Genuchten-Mualem model (van Genuchten, 1980) was used for all phases, the relative permeabilities of which were calculated using Eqs. (17)–(19):

kro (Sw , St ) = (St − Sw )

qg

where o − g, β = ϕ Sg λo − g, β . Wilkins et al. (1995) used a column 5 cm in diameter and 10 cm in height for testing several soils and pollutants in the stationary state, proposing the following empirical relationship:

(16)

mvg ] 2

(22)

λ∗

max where Sor max and St is

krw (Sw ) = Sw 0,5 [ 1 − (1 − Sw1 mvg )

2 ⎡⎛ ⎤ 2 Dg ⎛ Cg, β ⎞ ⎞ 1 ⎢⎜ 2⎥ ⎟ ⎜ ⎟ − ln 1 − − U U g g ⎜ ⎟⎟ ⎜ ⎥ Lc Cgsat 4 Dg ⎢⎣ ⎝ ⎝ ,β ⎠ ⎠ ⎦

where Lc denotes column height [L]. The third method features an analytical solution developed by Wilkins et al. (1995), which neglects hydrodynamic dispersionDg, β (Eq. (23)):

σgo + σow σgo

(21)

−3

(20)

⎛ So ⎞ε λo − g, β = λoinit − g, β ⎜, init ⎟ ⎝ So ⎠

To avoid numerical oscillations associated with the conversion of a two-phase system into a three-phase one, three-phase nodes were not allowed to revert to a two-phase system. COMSOL was used as a numerical method to resolve the twodimensional axisymmetric model (2Dxy).

(26) λo − g , βinitis

whereεis an empirical parameter, and the initial NAPL/gas mass transfer coefficient deduced from the expression for λ∗o − g, β . 3

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•Dirichlet conditions, Pg = 1 atm at outlet orifice for venting and at inlet orifice for SVE; •Neumann conditions (Eq. (31)) at inlet orifice for venting and outlet orifice for SVE, with Eq. (32) at the column wall:

A correction is necessary to account for the tailing effect in the SVE/ venting simulation, where the concentration of gas extracted in the diffusion step unexpectedly decreases. This phenomenon was observed by numerous researchers at pilot and field scales (Campagnolo, 1995; Harper, 1999; Yoon et al., 2003; Zhao, 2007; Nguyen et al., 2013) and ascribed to the extraction of pollutants dissolved in the aqueous phase, adsorbed on the solid phase, and trapped in the small pores not readily accessible to the gas flow. A typical extracted gas concentration curve can be divided into three parts described in the introduction (Anderson, 1994). In Eq. 26, decreasing ε (ε < 0.6), makes the evacuation step progressively more important. Under these conditions, all free pollutants are available to the air flow, with the mass transfer coefficient remaining important and having a value close to the initial one, corresponding to a system in a state close to LEA. In the above case, the concentration in the diffusion phase is ~0, being increasingly important at high ε (ε > 1), since a part of the free pollutant becomes inaccessible to the air flow. This case was observed by Yoon et al. (2002), who reported that increasing water saturation reduces NAPL accessibility. On the other hand, certain values of ε (ε > 1.5) result in a fast reduction of the mass transfer coefficient in the first step followed by a fast decrease of concentration. The cited models were developed to estimate the mass transfer coefficient in the unsaturated zone, where the water content is limited to the immobile residual saturation. In order to extend these models to both saturated and unsaturated zones, we proposed the use of reference NAPL saturation and estimated the mass transfer coefficient under conditions mentioned in Eq. (26). The expression given below (Eq. (27)) can be used in the case of variable-saturation media, i.e., for a multiphase extraction process, where the pollutant and water contents are not limited. This method was applied to the capillary fringe and the saturated zone drained by SVE dewatering, with the temporal and spatial variation of NAPL and water saturation given by:

λo − g, β

⎡ λ init ;So > Soref ⎤ ⎢ o − g, β ⎥ = ⎢ init ⎛ So ⎞ε ref ⎥ ⎜ ⎟ ⎢⎣ λo − g, β ⎝, S ref ⎠ ; So ≤ So ⎥⎦ o

qg =

(33)

Dg ∇Cg = 0

(34)

- Local equilibrium model (LEA, Eq. (21); - Analytical solution of the 1D dispersion-convection van Genuchten equation (Eq. (22)). In this model, two mass transfer coefficients C ,β were estimated for an outlet concentration of gSat : the average Cg, β

experimental value for the evacuation/evaporation phase and an overestimated one (0.98 for venting and 0.8 for SVE) to test the influence of this concentration. - Analytical solution of Wilkins et al. (1995) for the 1D convection model (Eq. (23)); - Empirical model of Wilkins et al. (1995) (Eq. (24)); - Empirical model of Yoon et al. (2002) (Eq. (25)). The proposed NAPL reference saturation model (Eq. (27)) was used with λo − ginit deduced from Eq. (22) taking dispersion into account, with NAPL reference saturation Soref estimated as 0.01 for all tests by fitting. Although this value provided good results, it must be verified for other soils and pollutants. Finally, the value of ε for all tested models was estimated by fitting. 2.5. Estimation of the hydrodynamic dispersion coefficient Longitudinal dispersivity (and thus the hydrodynamic dispersion coefficient) was estimated by performing a tracer experiment on the soil column, with the tracer corresponding to continuously injected oxygen and purging performed using nitrogen. By parametric identification from model (2D axisymmetric), the dispersion coefficient was estimated. Fig. 2 shows the initial and boundary conditions used. The molecular diffusion coefficient of oxygen in nitrogen was taken from literature as Dg , βo = 0.219 cm2 s− 1 at 20 °C (Welty et al., 1984).

Pgo, β Mβ (28)

(30)

qg Cg − Dg ∇Cg = 0

The results of simulated laboratory tests were compared with experimental ones. In the case of dry soil, Eqs. (9) and (10) were not applicable. Eq. (26) was used in numerous simulations to estimate the NAPL/gas phase mass transfer coefficient λo − g, and different models were used to estimate the NAPL/gas phase initial mass transfer coefficient λo − ginit:

Model geometry and boundary conditions for SVE and venting cases are provided in Fig. 1. To properly describe experimental conditions, the above model was hardwired in two axisymmetric dimensions, with the experimental cell being a cylinder 10 cm in diameter and 14 cm in height. A sand bed was placed between two 2-cm-thick gravel layers, with the inlet having a diameter of only 0.5 cm. Therefore, the flux did not exhibit a homogeneous distribution in the radial and axial column directions, especially for the gravel part. The model implies that local equilibrium can be reached after two days, which corresponds to the rest time of samples prior to extraction, with initial concentration conditions given by Eqs. (28)–(30):

Cs (r , z, 0) = Kd , β Sw, β

(32)

2.4. Modelling methodology

2.3. Model boundary conditions

(29)

(31)

For other transport equations, Neumann conditions were applied at the wall, inlet, and outlet. 2848 triangular meshes with Lagrange-quadratic element type were used, with refinement performed in the column inlet and outlet and in the sand gravel contact zone.

(27)

Cw (r , z, 0) = Sw, β

(∇Pg + ρg g∇z )

For gas transport, Dirichlet boundary conditions with Cg = 0 were valid at the inlet orifice, with Neumann conditions applied at the wall (Eq. (33)) and outlet orifice (Eq. (34)):

the reference NAPL saturation. where This model separates the steps of evaporation and diffusion under the additionally imposed conditions, thus not always being dependent on initial saturation.

Rgp T

μg

(∇Pg + ρg g∇z ) = 0

Sorefis

Cg (r , z, 0) =

K krg

The initial gas pressure Pg(r, z, 0) equalled 1 atm, with the initial NAPL saturation defined asSo(r, z, 0) = Soinit. During venting, the column inlet was linked to a nitrogen bottle, with the exit pipe kept at atmospheric pressure. Thus, the boundary conditions for flow were as follows:

2.6. Simulation evaluation Simulated and experimental results were compared using concor4

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Inlet =0.5 cm

Outlet =0.5 cm

Gravel

2 cm

=0

Sand HN0.4/0.8 Wall

=

Wall Axisymmetric axis

14 cm

Sand HN0.4/0.8 Axisymmetric axis

14 cm

2 cm

Gravel

=

Gravel Gravel =0 =0

r

r

Inlet =0.5 cm

Inlet =0.5 cm

SVE

Venting

Fig. 1. Geometries and boundary conditions for SVE/venting models.

Outlet

N

=0.5 [cm]

∑ [yi −exp − yi −mod ]2 RMSE =

i =1

(38)

N

2cm

Gravel NRMSE =

RMSE max(yi −exp ) − min(yi −exp )

(39)

Sand

Axisymmetric axis

14 cm

N

∑ [yi −exp − yi −mod ]2

Wall

R=

1−

i =1 N

∑ [yi −exp − yi −exp ]2

(40)

i =1

where N is the number of points, yi − expis the experimental value, yi − modis the model value, yi−exp is the mean experimental value, and max(yi − exp) , min(yi − exp)are the maximal and minimal experimental values, respectively. A good fit is indicated by RMSE and NRMSE values close to zero and an R value close to unity. The above parameters were helpful in comparing the global model with experimental results, where the low concentrations in the diffusional phase have no effect. To quantify the obtained results on a logarithmic scale and evaluate low concentrations in the diffusional phase, the previously proposed normalized sum of the squared relative deviations (NSSRD) parameter was used (Eq. (41)) (Gidda, 2003; Zhao, 2007; Nguyen et al., 2013). The above approach was good for evaluating the effect of low concentrations observable on a logarithmic scale and for studying the effect of tailing.

Gravel

r Inlet

=0.5 [cm]

Fig. 2. Column geometry and boundary conditions for estimating the dispersion coefficient.

dance indicators, namely root mean square error (RMSE), normalized root mean square error (NRMSE), and the correlation coefficient (R) (Eqs. (38–40)):

NSSRD =

1 N

N

⎧ log(Cgi exp ) − log(Cgi mod ) ⎫2 ⎬ log(Cgi exp ) ⎩ ⎭ ⎪

⎪

⎪

⎪

∑i =1 ⎨,

(41)

here, Cg_expiandCg_modi are experimental and calculated concentrations in the extracted gas [M L− 3], respectively. 5

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Table 1 Characteristics of the used sand. Parameters

Value

Method

d50 [mm] Cu [−] Cc [−] Classification

0.61 1.46 1.09 55% medium sand 45% coarse sand 1.53 ± 0,06 2.65 3.21 ± 0.08 10− 10 3.53 ± 0.06 10− 10 0.40 ± 0.03 0.057 7.74 4.27 13 4.7 0.05

Particles size distribution curve

ρb [g·cm− 3] ρs [g·cm− 3]

K [m2] θS [−] θwr [−] αvg [m− 1] nvg αvg [m− 1] nvg θgt [−]

Mean of 5 tests Supplier Constant head permeameter Air permeameter Büchner funnel

Drainage Imbibition

Fig. 3. Experimental and simulated results for test 1/venting.

function of time deduced from the BTC, as shown below:

Drainage: using drainage with Buchner funnel method. Imbibition: using imbibition with Buchner funnel method.

αL =

Dg, β Ug

=

Ug (t0.84 − t0.16 ) 8 t0.5

= 2.8 [cm]

(42)

where t0.84, t0.5, and t0.16 are times corresponding to relative tracer concentrations of 84, 50, and 16% at the column outlet [T], respectively. For the same value of αL, the 1D model approach afforded NRMSE = 14.8% and R = 0.932 as the best result. Transversal dispersivity αT was assumed to equal 0.1 αL,as described in several previous works (Agence de l'Environnement et de la Maîtrise de l'Energie ADEME (2007); Dridi, 2006; Daian, 2013; Nguyen et al., 2013).

3. Materials and methods Toluene was used as a model pollutant, and medium-grain HN 0.4/ 0.8 Hostun sand (SIBELCO) was used as a soil substitute, with the experimentally determined properties summarized in Table 1. Apparent sand density ρb was measured for sand compacted in a column, and the corresponding particle size distribution was determined using the French norm X 11-507 (Normalisation Francaise (1970)). Permeability was determined by using a constant head permeameter and an air permeameter using Darcy's law. The water retention curve was recorded using a Buchner funnel. The obtained experimental data were simulated using RETC software (RETention Curve software for unsaturated soils) (van Genuchten et al., 1991) to identify van Genuchten curve parameters αvgand nvg. The experimental apparatus featured a steel column (inner diameter = 10 cm, height = 15 cm) as the main part. Depending on the employed technique, i.e., soil vapour extraction or venting, the column was connected to a vacuum pump (KNF Neuberger U.K., N840 FT-18) or to a nitrogen bottle, respectively. Four tests were conducted under different experimental conditions (Table 2). Water saturations were selected to be inferior to the residual saturation. They allow simulation of the unsaturated zone with ensuring that NAPL and water phases were immobile. Venting/extraction flow rates were selected to be conforming to the reference pore velocity in the SVE process. Longitudinal dispersivity was estimated using the tracer breakthrough curve (BTC), and the best αL value was identified as 2.75 cm with NRMSE = 1% and R = 0.9997 using 2Daxy approaches. A similar value was estimated using the analytical solution cited by Benremita (2002) (Eq. (42)), which expresses the dispersion coefficient as a

4. Results and discussion Several model parameters were tested, and the best results were noted. Fig. 3 shows experimental and six model concentrations results for test 1, presenting three phases of extracted gas concentration change: flushing, evaporation, and diffusion (USEPA, 1994). The local equilibrium model simulated the first step of extraction with significant errors (NRMSE > 15%), with three other models affording better solutions with lower errors (Table 3): the model proposed herein, the dispersion-convection model assuming an overestimated outlet concentration of 0.98 (λo − ginit = 947 h− 1 , ε = 1.18), and the dispersion-convection model assuming the outlet concentration to equal 0.913 (λo − ginit = 472 h− 1 , ε = 0.93). Models proposed by Wilkins et al. (1995) and Yoon et al. (2002), based on analytical solutions of the convection equation, and the analytical convection model underestimated λo − ginit, affording respective initial relative concentrations of extracted gas as 81, 79, and 84% of the equilibrium concentration, compared to the experimental value of 91.3% (Table 3). This underestimation is due to the negligence of hydrodynamic dispersion in the calculation of the mass transfer coefficient. On the other hand, the model based on the analytical

Table 2 Experimental conditions used for testing. Conditions

Sand mass Porosity φ Toluene mass Toluene saturation Water mass Water saturation Gas flow Soil temperature Concentration at saturation

Unity

[g] [−] [mg] [−] [mg] [−] [mL·min− 1] [°C] [mg·L− 1]

Venting

SVE

Test 1

Test 2

Test 3

Test 4

1216 0.415 8397.7 0.0297 0 – 591 20.8 ± 0.6 114.5

1223 0.412 8339.5 0.0297 24,424 0.0755 604 20.3 ± 0.6 111.7

1218 0.415 8301.1 0.0294 0 – 3183 19.8 ± 0.6 108.9

1225 0.411 8413 0.0300 24,535 0.076 3203 19.3 ± 0.6 106.2

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Table 3 Different model parameters of test 1 with error evaluation. Model

λo − ginit [h− 1] (pore velocity1D 0.313 cm·s− 1)

Cg, β CgSat ,β

Local equilibrium LEA Analy-disp-conv (1D)

Wilkins et al. (1995)

1 Model 0.99 Estimated 1D 0.98 Model 0.924 Estimated 1D 0.913 Model 0.84 Estimated 1D 0.913 Model 0.812

Yoon et al. (2002)

Estimated 1D 0.889 Model 0.79

Proposed model Soref = 0.01

Estimated 1D 0.871 Model 0.924 Estimated 1D 0.913

Analy-conv (1D)

ε

RMSE [mg·L1]

NRMSE [%]

R [−]

NSSRD [−]

∬ dr dz

Tailing

0 1.18

16.02 3.24

15.17 3.07

0.924 0.997

– 0.092

Bad Very good

Bad Very good

472.5

0.93

6.27

6

0.989

1.52

Good

Bad

275

0.5

11.23

10.64

0.96

11.4

Bad

Bad

Max 271 Min 238.3 Mean 243.3a 247,9 Max 254.9 Min 220.8 Mean 225.9a 230.5 472.5

0.5

13.24

12.5

0.949

10.25

Bad

Bad

0.5

14.44

13.68

0.939

11.83

Bad

Bad

1.37

3.23

3.07

0.997

0.035

Very good

Very good

∬ λoinit − g, β (r , z ) dr dz r,z

Global ∞ 947.5

Good: good fitting. Very good: very good fitting. The NRMSE, R and NSSRD give information of the fitting of global curves. Here we give information about the global and the tailing part. a :The mean of the coefficient on the column is calculated by: − moy λoinit = − g, β

Fitting

.

r,z

(a) Test 1/ Venting

(b) Test 2/Venting

(c) Test 3/SVE

(d) Test 4/SVE

Fig. 4. Mass transfer coefficients obtained by modelling the results of four tests: (a) test1, (b) test 2, (c) test 3 and (d) test4.

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D. Esrael et al.

(a) Test 1/ Venting

(b) Test 2/Venting

(c) Test 3/SVE

(d) Test 4/SVE

Fig. 5. Experimental and simulated results displayed using a semi-logarithmic scale: (a) test1, (b) test 2, (c) test 3 and (d) test4.

extracted gas concentrations continuously decreased in a similar way for all tests (Figs. 4 and 5). The abovementioned three parts (separated by two inflexion points), namely flushing, evaporation, and diffusion, could be observed for all tests. At the end of the first part, ~ 90% of pollutant had been extracted, with the residual amount becoming progressively less accessible to the airflow due to being trapped in smalls boreholes (tests 1 and 3 (dry soils)) or dissolved in water/ adsorbed on soil grains (tests 2 and 4). The second inflexion point marks the disappearance of free NAPL, with the gas concentration after this point being determined by the diffusion part, where a new equilibrium between phases is established: adsorbed NAPL, dissolved NAPL, no accessible NAPL and airflow. For dry soil, Eq. (9) (dissolution) and Eq. (10) (adsorption) were not activated. Models assuming an initially low λo − g could not describe the new equilibrium state: the mass transfer coefficient decreased to values close or equal to zero. Subsequently, the concentration decreased to zero, not being able to model this point. Conversely, the above point and the curve beyond it could be estimated by the proposed model and the dispersion convection model (with overestimated λo − g). The presence of water in soil (tests 2 and 4) activated Eqs. (9) and (10), and a new equilibrium was established for all models, which could simulate this second inflexion point but not the subsequent curve evolution. Fig. 5b and Table 4 show the extracted gas concentrations of test 2 simulated by different models, together with the corresponding estimation errors at a logarithmic scale. Fig. 4b displays the dependence of the mass transfer coefficient on time for different models, with its initial values being similar to those obtained for test 1. The observed difference was due to the small flow rate difference and the saturation

solution of the dispersion-convection equation slightly overestimated the initial mass transfer coefficient, with a sharp drop of gas concentration and the mass transfer coefficient subsequently observed in the first stage (Fig. 4a), which was related to the values of ε and the initial mass transfer coefficient. Yoon et al. (2002) applied an analytical solution for convection dispersion first-order decay to simulate experimental venting results for dry soil, considering ε = 0. Under this condition, the interfacial area available for volatilization does not change with time, allowing one to neglect the simulation of the tailing part. In our work, we assumed ε = 0.5 for numerical consideration only, since the null value afforded the LEA model results. Fig. 5a shows the model results on a logarithmic scale, allowing the tailing effect at lower concentration to be better observed and highlighting that only the model proposed in this study and the analytical solution of the dispersion-convection equation (with overestimated λo − ginit) could simulate the above effect. The tailing part was better estimated by models with ε > 1, which indicated the importance of diffusion step concentration and the fraction of free pollutant not accessible to the air flow, as observed by Yoon et al. (2002) and Nguyen et al. (2013). The small difference of mean mass transfer coefficients estimated by Wilkins et al. (1995) and Yoon et al. (2002) models with 2Daxy and 1D geometries indicated homogeneous velocity repartition in the column. In conclusion, the above two models were able to estimate the initial mass transfer coefficient for high velocities. An adjustment accounting for dispersion, which is helpful to simulate lower velocities, should be based on experimental results obtained for several soils, pollutants, and velocities. The NAPL/gas phase mass transfer coefficient (λo − g) and then the 8

Journal of Contaminant Hydrology xxx (xxxx) xxx–xxx

D. Esrael et al.

Table 4 Results of test 2 simulation with error values. Model

Cg, β CgSat ,β

Local equilibrium LEA Analy disp- conv- (1D)

1

Wilkins et al. (1995)

Model 0.991 Estimated 1D 0.98 Model 0.92 Estimated 1D 0.905 Model 0.815

Proposed model Soref = 0.01

Estimated 1D 0.88 Model 0.92 Estimated 0.905

λo − ginit [h− 1] (pore velocity 1D 0.348 cm·s− 1)

∞

ε

RMSE [mg·L− 1]

NRMSE [%]

0

R [−]

NSSRD [−]

Fitting Global

Tailing

14.1

0.933

–

Bad

Bad

3.83

0.995

0.097

Very good

Very good

1044

1.26

140.5 3.93

511.5

0.93

6.75

6.57

0.986

0.24

Good

Bad

max 286.8 min 254 mean 259.2 273.9 (1D) 511.5

0.5

12.93

12.59

0.947

0.59

Bad

Bad

1.44

3.2

3.12

0.997

0.036

Very good

Very good

Good: good fitting. Very good: very good fitting. The NRMSE, R and NSSRD give information of the fitting of global curves. Here we give information about the global and the tailing part.

5. Conclusion

effect at 0.0755. The above saturation decreased the gas phase content and subsequently increased pore velocity. Previous reports explain the relationship between saturation and the mass transfer coefficient by the contact surface decrease accompanying decreased saturation (Yoon et al., 2003; Zhao, 2007; Nguyen et al., 2013). Tortuosity and hydrodynamic dispersion were also reduced, and the concentration did not drop to zero, as in test 1. In this situation, the presence of water activated interphase mass transfer (aqueous/gas, NAPL/aqueous, and aqueous/solid), allowing exchange between phases and increasing the extracted gas concentration in the diffusion step, with similar observations made by Yoon et al. (2003) and Nguyen et al. (2013). The results of tests 3 and 4 are presented in Figs. 4c, d and 5c, d, as well as in Tables 5 and 6, with the observations made for tests 1 and 2 remaining valid for tests 3 and 4. In each test, the proposed model afforded the best simulation of experimental data. Additionally, the analytical solution of the convection-dispersion equation (with overestimated λo − ginit) offered a good simulation of results obtained in tests 1 and 2. The model of Wilkins et al. (1995) was more successful in estimating mass transfer coefficients for tests 3 and 4 than for tests 1 and 2 due to the effect of the relative increase of hydrodynamic dispersion with the growth of pore velocity. As found by Nguyen et al. (2013), no regular relationships exist between flow rates and the resulting empirical mass transfer parameters.

A model of transport/mass transfer between NAPL and gas phases was developed and verified by simulating the results of four column tests utilizing the SVE/venting technique. The above tests were performed at different flow rates (tests 1 and 2: low, tests 3 and 4: high) and water saturations (tests 1 and 3: dry sand, tests 2 and 4: small saturation). The developed model comprises five PDE equations, with the first one being the continuity equation simulating gas flow, and the other four modelling the mass conservation of gas, NAPL, aqueous, and immobile solid phases. The model includes an expression accounting for the soil NAPL saturation conditions. Five previously reported equations for estimating the mass transfer coefficient were tested, together with an expression accounting for NAPL reference saturation. The first five expressions were used to simulate experimental results, showing that hydrodynamic dispersion cannot be neglected in the estimation of the mass transfer coefficient, particularly at low velocities. The simulation of experimental results underestimated the initial mass transfer coefficient due to neglecting the dispersion coefficient. Three models showed better solutions with low errors for two SVE tests and a venting test: the model proposed herein, the dispersion-convection model considering an overestimation of concentration, and the

Table 5 Results of test 3 simulation with error values. Model

Cg, β CgSat ,β

Local equilibrium LEA Analy disp-conv (1D)

Wilkins et al. (1995)

1 Model 0.81 Estimated 0.8 Model 0.72 Estimated 0.705 Model 0.63

Proposed model Soref = 0.01

Estimated 0.686 Model 0.72 Estimated 0.705

λo − gi [h− 1] Pore velocity 1D 1.689 cm·s− 1

ε

RMSE [mg.L− 1]

NRMSE [%]

R [−]

NSSRD [−]

Fitting Global

Tailing

∞ 1417

0 1.18

13.73 2.8

17.7 3.61

0.764 0.991

– 0.18

Bad Very good

Bad Good

994.5

0.74

3.45

4.45

0.987

6.35

Good

Bad

max 772.5 min 677.9 mean 692.3 705 (1D) 994.5

0.5

5.81

7.5

0.962

6.49

Bad

Bad

1.54

1.79

2.3

0.996

0.06

Very good

Very good

Good: good fitting. Very good: very good fitting. The NRMSE, R and NSSRD give information of the fitting of global curves. Here we give information about the global and the tailing part.

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Table 6 Results of test 4 simulation with error values. Model

Cg, β CgSat ,β

Local equilibrium LEA Analy disp-conv (1D)

Wilkins et al. (1995)

1 Model 0.82 Estimated 0.8 Model 0.73 Estimated 0.695 Model 0.64

Proposed model Soref = 0.01

Estimated 0.674 Model 0.73 Estimated 0.695

λo − gi [h− 1] (Pore velocity 1D 1.85 cm·s− 1)

ε

RMSE [mg·L− 1]

NRMSE [%]

R [−]

NSSRD [−]

Fitting Global

Tailing

∞ 1550

0 1.18

14.84 2.42

19.9 2.24

0.7 0.993

– 0.356

Bad Very good

Bad Good

1051.8

0.74

3.34

4.5

0.986

0.324

Good

Bad

max 807 min715.4 mean 729 746.3 (1D) 1051.8

0.5

4.65

6.23

0.973

0.424

Good

Bad

1.54

2.41

3.23

0.993

0.063

Very good

Very good

Good: good fitting. Very good: very good fitting. The NRMSE, R and NSSRD give information of the fitting of global curves. Here we give information about the global and the tailing part.

Unsaturated Soils. University of Guelph, Canada. Harper, B., 1999. An Experimental and Numerical Modelling Investigation of Soil Vapour Extraction in a Silt Loam Soil. University of Guelph, Canada. Kaluarachchi, J.J., Parker, J.C., 1992. Multiphase flow with a simplified model for oil entrapment. Transp. Porous Med. 7 (1), 1–14. Lenhard, R.J., Parker, J.C., 1987. Measurement and prediction of saturation-pressure relationships in three-phase porous media systems. J. Contam. Hydrol. 1 (4), 407–424. Lenhard, R.J., Oostrom, M., Dane, J.H., 2004. A constitutive model for air-NAPL-water flow in the vadose zone accounting for immobile, non-occluded (residual) NAPL in strongly water-wet porous media. J. Contam. Hydrol. 71 (1–4), 283–304. Miller, C.T., Poirier-McNeil, M.M., Mayer, A.S., 1990. Dissolution of trapped nonaqueous phase liquids: mass transfer characteristics. Water Resour. Res. 26 (11), 2783–2796. Millington, R.J., 1959. Gas diffusion in porous media. Science 130 (3367), 100–102. Nguyen, V.T., Zhao, L., Zytner, R.G., 2013. Three-dimensional numerical model for soil vapor extraction. J. Contam. Hydrol. 147, 82–95. Normalisation Françasie, 1970. Analyses granulometrique: tamisage de contrôle, NF X 11507, 60-75, second ed. AFNOR, Paris. Parker, J.C., Lenhard, R.J., Kuppusamy, T., 1987. A parametric model for constitutive properties governing multiphase flow in porous media. Water Resour. Res. 23 (4), 618–624. U.S.Environmental Protection Agency, 1994. Innovative site remediation technology. In: Vacuum Vapor Extraction. vol. 8. https://nepis.epa.gov/Exe/ZyPDF.cgi/2000ITX8. PDF?Dockey=2000ITX8.PDF (accessed 05.04.2017). van der Ham, A.J.G., Brouwers, H.J.H., 1998. Modelling and experimental investigation of transient, nonequilibrium mass transfer during steam stripping of a nonaqueous phase liquid in unsaturated porous media. Water Resour. Res. 34 (1), 47–54. van Genuchten, M.T., 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44 (5), 892–898. van Genuchten, M.T., Alves, W.J., 1982. Analytical Solutions of the One-dimensional Convective-dispersive Solute Transport Equation. (Washington, USA). van Genuchten, M.T., Leij, F.J., Yates, S.R., 1991. The RETC code for quantifying the hydraulic functions of unsaturated soils, version 1.0. (Riverside, California, USA). Welty, J.R., Wicks, C.E., Wilson, R.E., 1984. Fundamentals of momentum, heat, and mass transfer. 3rd ed. New York, USA: John Wiley & Sons. (807 p). Wilkins, M.D., Abriola, L.M., Pennell, K.D., 1995. An experimental investigation of ratelimited nonaqueous phase liquid volatilization in unsaturated porous media: steady state mass transfer. Water Resour. Res. 31 (9), 2159–2172. Yoon, H., Kim, J.H., Liljestrand, H.M., Khim, J., 2002. Effect of water content on transient nonequilibrium NAPL-gas mass transfer during soil vapor extraction. J. Contam. Hydrol. 54 (1–2), 1–18. Yoon, H., Valocchi, A.J., Werth, C.J., 2003. Modeling the influence of water content on soil vapor extraction. Vadose Zone J. 2 (3), 368–381. Zhao, L., 2007. Three-dimensional Soil Vapour Extraction Modeling. University of Guelph, Guelph, Canada.

dispersion-convection model assuming the outlet concentration to equal 0.913. The empirical models of Wilkins et al. (1995) and Yoon et al. (2002) could estimate the initial mass transfer coefficient for high velocities, with an adjustment accounting for dispersion being helpful to simulate lower velocities. The Wilkins model could correctly simulate the concentration curves for test 4, with only the model proposed herein being able to properly simulate the experimental results of all four tests, including the tailing part. The advantage of this model is the use of a constant concentration in the first stage (similarly to Wilkins and Yoon models) and the ability to describe the tailing part (similarly to the convection-dispersion model). In fact, our model separates the first stage from other stages. Our experimental results indicate that the pollutant is not available to the airflow at NAPL saturations below 0.01. References ADEME, 2007. Atténuation naturelle des composés organo-chlorés aliphatiques dans les aquifères. ADEME, France 228 p. Available on. www.ademe.fr/publications. Benremita, H., 2002. Approche Expérimentale et Simulation Numerique du Transfert de Solvants chlorés en Aquifère Alluvial Contrôlé. Université Louis Pasteur de Strasbourg (281p). Anderson, C.W., 1994. Innovative site remediation technology. In: Vacuum vapor extraction B. US EPA (224 p). Brusseau, M.L., Rao, P.S.C., 1989. Sorption nonideality during organic contaminant transport in porous media. Crit. Rev. Env. Contr. 19 (1), 33–99. Boudouch, O., Esrael, D., Kacem, M., Benadda, B., Gourdon, R., 2016. Validity of the use of the mass transfer parameters obtained with 1Dcolumnin 3D systems during soil vapor extraction. J. Environ. Eng. 142 (6), 04016018 1-9. Chao, K.P., Say Kee, O., Angelos, P., 1998. Water-to-air mass transfer of VOCs: laboratoryscale air sparging system. J. Environ. Eng. 124 (11), 1054–1060. Campagnolo, J.F., 1995. Soil Vapor Extraction (SVE) Systems, Modeling and Experiments. Texas A & M University, USA. Daian, J.F., 2013. Equilibre et Transferts en Milieux Poreux. Université Joseph Fourier (PhD thesis). Dridi, L., 2006. Transport d'un Mélange de Solvants Chlorés en Aquifère Poreux Hétérogène: Expérimentations sur Site Contrôlé et Simulations Numériques. Université Louis Pasteur de Strasbourg, France. Duggal, A., Zytner, R.G., 2009. Comparison of one- and three-dimensional soil vapour extraction experiments. Environ. Technol. 30 (4), 407–426. Gidda, T.S., 2003. Mass Transfer Processes in the Soil Vapour Extraction of Gasoline from

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