The dissolution of benzene, toluene, m-xylene and naphthalene from a residually trapped non-aqueous...

Ž .Journal of Contaminant Hydrology 36 1999 313–331

The dissolution of benzene, toluene, m-xylene andnaphthalene from a residually trapped non-aqueousphase liquid under mass transfer limited conditions

Sanjay Garg, William G. Rixey )

Department of CiÕil and EnÕironmental Engineering, Cullen Engineering Building, Rm. N117, 4800 Calhoun,UniÕersity of Houston, Houston, TX 77204-4791, USA

Received 3 December 1997; revised 13 July 1998; accepted 9 October 1998

Abstract

The results of dissolution experiments for benzene, toluene, m-xylene and naphthaleneŽ . Ž .BTXN from a relatively insoluble oil phase tridecane , residually trapped in a non-sorbingporous medium, are described. This mixture was chosen to simulate dissolution of solublearomatic compounds from a petroleum hydrocarbon mixture, e.g., crude oil, for which a largefraction of the mixture is relatively insoluble. The experiments were carried out at a small source

Ž .length to interstitial velocity ratio, LrÕ, so that dissolution would be mass transfer limited MTL .When fitted to data for toluene, a multiregion mass transfer model was found to predict theexperimental data satisfactorily for the other components without adjustment of the mass transferrate parameters. These results indicate that the dissolution process can be generalized for various

Ž .hydrophobic organic compounds present in a multicomponent non-aqueous phase liquid NAPLwhen mass transfer limitations are present. This also suggests that dissolution data obtained forone compound can be useful for predicting the dissolution histories for other compounds frompetroleum hydrocarbon mixtures. q 1999 Elsevier Science B.V. All rights reserved.

Keywords: Dissolution; Mass transfer; Non-aqueous phase liquid; Petroleum hydrocarbons

1. Introduction

At many field sites contaminated with petroleum hydrocarbons, soils contain aresidually trapped hydrocarbon phase. For these soils, the release of contaminant to the

) Corresponding author. Tel.: q1-713-743-4279; fax: q1-713-743-4260; e-mail: [email protected]

0169-7722r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-7722 98 00149-1

( )S. Garg, W.G. RixeyrJournal of Contaminant Hydrology 36 1999 313–331314

aqueous environment occurs by dissolution of contaminant from the residually trappedhydrocarbon phase in addition to desorption from the soil. In this paper, the dissolution

Ž .characteristics of components from the non-aqueous phase liquid NAPL itself, notdesorption from soil, are presented. The results are used to compare the dissolutioncharacteristics of several aromatic compounds present in multicomponent NAPLs, e.g.,petroleum hydrocarbon mixtures, under MTL conditions.

1.1. PreÕious studies

Research on the dissolution of single-component NAPLs residually trapped in porousmedia has demonstrated that mass transfer limitations become important at low sourcelength to aquifer velocity ratios, LrÕ, or when NAPL-aqueous interfacial areas are

Ž .significantly reduced Imhoff et al., 1994; Powers et al., 1994 . The latter case isencountered when pure phase dissolution occurs. As the pure phase NAPL dissolves, thetotal interfacial area is reduced, and at sufficiently reduced NAPL saturations the masstransfer can become rate limited. Mass transfer correlations have emerged from thisresearch that can be used to predict solute mass transfer rates from the NAPL to theaqueous phase.

In addition to the research with pure NAPLs, there have been studies with multicom-Žponent hydrocarbon mixtures designed to simulate petroleum fuel dissolution Borden

.and Kao, 1992; Geller and Hunt, 1993; Rixey, 1996 . Two of these studies investigatedŽthe complete aqueous dissolution history i.e., from the solubility of a compound to its

.detection level in water . However, interpretation of the results was complicated bypotential contributions from slow desorption from the soil, especially at the loweraqueous concentrations.

In this paper, the dissolution of BTXN from a relatively non-dissolving hydrocarbonŽ .phase tridecane is assessed. The initial concentrations of BTXN in the NAPL were

such that the corresponding aqueous equilibrium concentrations were several orders ofmagnitude higher than their detection limits, so that leachate concentrations could bemeasured over a wide range. This model mixture was chosen to simulate the dissolutionof aromatic compounds from petroleum hydrocarbon mixtures, e.g., crude oil, diesel,gasoline, and various oily residuals, for which the majority of the NAPL components arerelatively insoluble. These experiments were designed to characterize only those contri-butions that arise from the dissolution of NAPL itself.

The experimental data were characterized with a multicomponent dissolution modelŽdeveloped previously which takes into consideration mass transfer limitations Rixey,

.1996 .

2. Experimental apparatus and procedures

A simplified diagram of the apparatus used for this study is shown in Fig. 1. Twoexperiments were conducted at a source length to velocity ratio of 0.0036 day. Anaqueous solution was pumped through a porous region containing residually trappedNAPL. The aqueous leachate from the source then passed through a glass column

( )S. Garg, W.G. RixeyrJournal of Contaminant Hydrology 36 1999 313–331 315

Fig. 1. Simplified diagram of the experimental apparatus for dissolution of BTXN from a residually trappedtridecane source.

containing glass beads. The experiments were set up in this way, so that a directŽ .comparison could be made with parallel experiments not reported here in which the

columns were packed with different soils coupled to similar NAPL sources in order toinvestigate the dissolutionrdesorption characteristics of NAPLs residually trapped insoil. Both the source and the column for the experiments reported here are describedfurther below.

2.1. Source

Ž .The source zone was comprised of a porous glass frit Kontes with pores with amean diameter of 17 mm determined by mercury porosimetry. This glass frit had the

Žfollowing dimensions: 1.0 in. in diameter=3 mm with a porosity of 0.4 determined.from separate displacement experiments with tridecane for a total pore volume of 0.6

cm3. The glass frit was fused in the center of a glass cell which was tapered at the inletand outlet to evenly distribute flow across the frit. A thin source was used to produce the

Ž .low LrÕ ratio 0.0036 day , so that dissolution would be MTL at a representativegroundwater velocity.

A model NAPL mixture was prepared to simulate the dissolution of organic com-pounds from an otherwise insoluble hydrocarbon matrix. Four organic compounds of


varying solubility were used in this study. Benzene, toluene, m-xylene and naphthalenewere dissolved in tridecane to provide a model NAPL with the following weightfractions: benzene, 0.05; toluene, 0.05; m-xylene, 0.10; and naphthalene, 0.05. BenzeneŽ . Ž .99q% purity was obtained from Fisher Scientific, m-xylene 99q% and tridecaneŽ . Ž .99% from Aldrich Chemical, toluene 99q% from Scientific Products, and naphtha-

Ž .lene 99q% from Sigma.

2.2. Source preparation

Prior to its use, the glass frit was sequentially rinsed with deionized water, methanol,and again deionized water before being heated in an oven at 4508C for 4 h. The glass frit

Ž .and glass cell were then autoclaved 30 min at 1258C . The model NAPL mixture wasthen applied in small increments to 20–30 locations on the autoclaved glass frit. Theglass frit was dry prior to the application of the NAPL. The NAPL source was preparedin this way rather than by displacement by water to obtain NAPL at residual saturation

Žbecause of the small amount of NAPL used for the experiments. A total of 0.025 g 31.ml of the model mixture was added to the frit based on integration of effluent

concentrations for each of BTXN compounds for an entire dissolution experiment.Consistent masses were determined from integrations of effluent concentrations for allfour compounds. Naphthalene is approximately 10 times less volatile than BTX overaqueous solution, therefore, if any significant losses due to volatilization occurred, lessBTX relative to naphthalene would have been recovered. The source zone was extractedwith methanol at the end of the experiments—benzene, toluene, m-xylene, and naphtha-lene were not detected, indicating that essentially all of the BTXN initially in thetridecane was removed during the aqueous leaching process. Precautions to minimizelosses due to volatilization and biodegradation are discussed in detail below.

2.3. Column

Ž .A glass column, 30 cm length=37 mm internal diameter I.D. was presentdownstream of the NAPL source. The ends of the columns were tapered to 1r2-in.

Ž . woutside diameter O.D. and connected to Swagelok compression fittings with Teflonferrules. The compression fittings limited the exposure of the aqueous solution to

Ž .polymeric seals e.g., o-rings, etc. , thereby minimizing potential sorption of organiccompounds which could seriously impact the interpretation of long-term, column

Ž .leaching behavior at low concentrations -10 mgrl . During the course of theexperiments the fittings were changed to confirm that there was no influence on thedissolution behavior.

Ž .Glass beads made of borosilicate glass 30–50 mm in diameter obtained fromPolysciences were used as the porous media. The beads were heated in an oven for 4 hat 4508C to pyrolyze any organic that may be present before packing into the column.

2.4. Column preparation

All glassware, columns, and fittings were first washed with Sparkleen soap and tapwater. This glassware was then sequentially rinsed with deionized Nanopurew water,


methanol and again deionized Nanopurew water. The glassware and columns werefurther heated in an oven at 4508C for 4 h. All stainless steel fittings were cleanedsimilarly.

An aqueous solution containing 0.005 M CaCl was prepared in deionized Nano-2

purew water and autoclaved in 1-L bottles for 45 min. The column was packed byadding the 0.005 M CaCl solution and glass beads in small increments. A glass wool2

plug and a 30-mm stainless steel screen were placed in the Swagelokw fittings toprevent any loss of the porous media. Once the column was packed and the end fittingsattached, the column was placed in a water bath of 0.005 M CaCl and autoclaved on2

slow exhaust for 90 min. The autoclaving was repeated twice more, each after a 24-hinterval of the preceding autoclaving.

2.5. Operation and sampling

The prepared source and the packed column were coupled through Swagelokw

fittings such that the effluent from the source was the influent to the column. Theapparatus was set up such that during the course of the experiment, the source and thecolumn could be decoupled and monitored independently. The experiment was con-ducted in the upward flow mode. The mobile phase was autoclaved 0.005 M CaCl2

solution prepared in deionized Nanopurew water. This water was delivered to theŽbottom of the source, through a 0.2-mm filter to prevent introduction of microorgan-

. Žisms , using a cassette peristaltic pump Cole Parmer, Pump Drive Model 7521-50,.Pump Head Model 7519-25 . All tubing on the influent and effluent end was 1r16-in.

Ž .O.D. 1r32-in. I.D. stainless steel tubing except for a 1-ft long section of Viton tubingwhich was required for the peristaltic pump. The water flow rate was initially set at 160

Ž .mlrday corresponds to an interstitial velocity of 83 cmrday but was adjusted at a latertime to confirm mass transfer limitations. The effluent from the column was bifurcated

Ž .between a 50-ml borosilicate glass syringe Hypo Surgical Supply and 1r16-in.stainless steel tubing leading to a waste collection system; the narrow bore of the tubingensured that the sample preferentially flowed to the syringe until the syringe was full. Toobtain measurements in the mgrl range, sample volumes of 5 ml and greater wererequired, for which the time for sample accumulation in the syringe varied from 2 to 18h depending on the flow rate through the column. The samples were collected every 2 hduring the initial phase of the experiment. The sampling interval was increased as theexperiment progressed. Once the syringe was full, the sample was transferred using a

Ž . Ž .three-way valve Aldrich Chemicals to 40-ml VOA vials Fisher Scientific . Thissampling technique ensured zero head space during sample accumulation. Separatestudies indicated that the loss of volatile compounds from the syringe over a 24-h periodwas approximately 5%. This loss did not increase when the holding time of the samplein the syringe was increased to 72 h, suggesting that the loss was probably during thestep when the sample from the syringe was transferred to the vials.

The apparatus was initially set up as shown in Fig. 1 and samples were collected atŽtwo locations: immediately downstream of the source and at the column containing

.glass beads effluent. The samples collected were diluted or analyzed as is, dependingon the concentration, using purge and traprgas chromatography. Samples at the source


were drawn through a valve using a 500-ml syringe. As the concentrations at the sourcedecreased to approximately 200 mgrl, collecting samples at the source was not feasible

Ž .because of the large volume 40 ml of sample required for purge and trap analysis atlow concentrations. Therefore, samples were then collected only at the column effluent.A comparison of the source and column effluent curves, for the time samples could be

Ž .collected at both the source and the column 5 days , indicated that there was littledispersion in the column—the column effluent concentrations were the same as thesource concentrations following a travel time corresponding to one column pore volume.To assess potential impact of sorption from the column, the column and the source weredecoupled after 48 days, and the 0.005 M CaCl solution then flowed through the source2

and the column separately. The effluent concentrations were monitored for the effluentfrom both source and the column. After decoupling, the column effluent concentrationsfor all compounds rapidly reduced to nondetectable levels after approximately onecolumn pore volume. This indicated that sorption and dispersion in the column contain-ing glass beads could be neglected and that effluent column concentrations could beused to represent source dissolution.

2.6. Analytical equipment and procedures

Ž .A LSC-2 model liquid sample concentrator Tekmar coupled with an Aquatek 50Ž .Tekmar autosampler was used for the pre-concentration of dilute aqueous samples. Forthe analysis of aqueous leachates by purge and traprgas chromatography, three internalstandards were used: trichloroethylene, chlorobenzene and 1,2,4-trichlorobenzene. Theinternal standards were selected to cover the same range of boiling points for benzene,

Žtoluene, m-xylene, and naphthalene. An HP-5890 series II chromatograph Hewlett. Ž . Ž .Packard equipped with a photo-ionization detector PID Finnigan and an HP-5

Ž .capillary column 30 m=0.54 mm=5 mm was used for the analysis. The GC programŽ . Ž .sequence was as follows: 1 408C for 1 min, 2 an increase in temperature at

Ž . Ž .208Crmin to 1008C, 3 constant temperature of 1008C for 6 min, 4 an increase inŽ .temperature at 258Crmin to 1508C, and 5 constant temperature at 1508C for 15 min.

Quantitative detection down to 0.1 mgrl for benzene, toluene, m-xylene, and naphtha-lene was achieved for 5 ml aqueous samples.

2.7. Batch equilibrium experiment

To obtain partition coefficients, dissolution of BTXN from tridecane was also carriedout in a batch apparatus, and the equilibrium aqueous concentrations were measured.Glass vials with Mini-Inerte valves were used as batch extractors. Three vials wereprepared with a waterroil ratio of 39 cm3rg. All glassware and apparatuses wereautoclaved before use. The batch experiments were conducted with autoclaved 0.005 MCaCl to be consistent with the fixed-bed experiments. The vials were tumbled2

end-over-end for 48 h. At the end of the equilibration time, the vials were centrifugedŽ .2000 rpm, 30 min to separate any dispersed oil, and aqueous samples were drawnusing a glass syringe and analyzed by HPLC.


3. Mathematical modeling

The experimental results were analyzed with a multicomponent, multiregion dissolu-tion model; two and five regions were used to describe the data. This approach is similarto previous approaches used to describe dissolution behavior from residually trapped

Ž .NAPLs Borden and Kao, 1992; Rixey, 1996; Reynolds et al., 1996 .ŽA one-dimensional leaching process with vertical flow the column experiments were

.conducted with upward vertical flow can be described with the following equationŽ .Rixey, 1996 :

w N j o , j s , j 2 w wE S C E S C E q E C E CŽ . Ž .w i o i i i ijf q F f qr sD yu 1Ž .Ý b y y2ž /E t E t E t E yE yjs1

Ž .In Eq. 1 , it has been assumed that the NAPL is divided into several regions ofprogressively lower mass transfer rate constants denoted by F j. It has also been assumedfor the purposes of this model that all of the aqueous phase in the source region ismobile.

Ž . Ž .Eq. 1 includes the effects of a finite amount of dispersion characterized by D iny

the source zone. The impact of dispersion on effluent concentrations will depend on thePeclet number, PesÕ LrD , which becomes small as the length decreases. Since they y

Ž .length of the source zone in this experiment was short 3 mm , the source wasŽ .approximated as a completely-mixed region, i.e., Pe™0 Ruthven and Stapleton, 1993 .

Ž .For a completely-mixed system, Eq. 1 becomes:

w N j o , j s , jd S C d S C r dq uŽ . Ž .w i o i b i yj wq F q sy C 2Ž .Ý iž /dt dt f dt fLjs1

In this study, contributions due to sorption and desorption from the solid phase can beŽ .neglected as discussed earlier. Eq. 2 then simplifies to:

w N j o , jd S C d S C uŽ . Ž .w i o i yj wq F sy C 3Ž .Ý idt dt fLjs1

For MTL dissolution, one can write the following expression for the rate of masstransfer between the aqueous phase and the NAPL phases within each MTL region:

d S jCo , jŽ .o i j w o , j o – w , jska C yC rK 4Ž .Ž .i i idt

The quantity ka j is the mass transfer rate constant for a given region. It is a lumpedparameter which includes a mass transfer coefficient, k, and a specific interfacial area,a, for mass transfer. If the dissolution process is controlled by an aqueous filmresistance, then the mass transfer rate constant would be expected to be independent ofcontaminant, neglecting small differences due to different aqueous phase moleculardiffusivities. Therefore, for constant values of ka, the time it takes to reduce the


contaminant concentration in the trapped NAPL will be proportional to the value of thepartition coefficient.

Mass-balance equations are also required to describe the variation in NAPL saturationwith time. The rate of change of NAPL saturation in any region was determined fromthe sum of the change in the individual concentrations of the n components in the NAPLmixture as:

j n j o , jdS 1 d S CŽ .o o is 5Ž .Ý

dt r dtiis1

The NAPL–water partition coefficient also changes with dissolution because ofchanges in the average molecular weight of the NAPL, average density of the NAPL andthe activity coefficients of the individual components in the NAPL. The NAPL–waterpartition coefficient at any time t was determined from:

MW r j g oo0 o i0o – w , j o – wK sK 6Ž .i i0 j j o , jMW r go o0 i

where,

1jMW s 7Ž .no

o , jw rMWÝ i iis1

1jr s 8Ž .no

o , jw rrÝ i iis1

The initial NAPL–water partition coefficient, K o – w, was determined by independenti0

batch experiments. The activity coefficients in the NAPL at any time were calculatedŽusing Scatchard–Hildebrand equations based on regular solution theory Prausnitz,

.1969 .

3.1. Non-dimensionalized equations

It is convenient to non-dimensionalize equations when considering the behavior ofŽ . Ž .several contaminants. Eqs. 3 and 4 when non-dimensionalized yield, respectively:

) w ) N j) o , j)1 d S C R y1 d S CŽ . Ž .w i i0 o ij w )q F syC 9Ž .Ý i) )R dt R dti0 i0 js1

d S j) Co , j) R Co , j)Ž .o i i0 ij w )sDD aa C y 10Ž .i) o – w , j)ž /dt R y1 Ki0 i


where

C w ) sC wrC w , Co , j) sCo , jrCo , ji i i0 i i i0

Co , j sK o – wC w , DD aaj ska jLfrui0 i0 i0 y

Õ su rfS , t ) s tÕ rLRy y w 0 y i0

K o – w , j) sK o – w , jrK o – w, R s1q S rS K o – wŽ .i i i0 i0 o0 w 0 i0

S j) sS jrS , S) sS rSo o o0 w w w 0

Ž . Ž . w ) )Eqs. 9 and 10 indicate that plots of C vs. t for different components shouldi

coincide for large values of R and for constant values of S j) and K o – w, j). For largei0 o iŽ . Ž .values of R , the quantity R y1 r R ™1 and the first term on the left-hand sidei0 i0 i0

Ž . Ž . Ž Ž ) w ) . Ž ) .of Eq. 9 , 1rR d S C r dt , becomes small relative to the second. For thesei0 w i

experiments S j) and K o – w, j) did change during dissolution. This effect was accountedo i

for in the model calculations. Despite changes in S j) and K o – w, j) , it is shown in theo i

discussion of results that dimensionless curves for the various compounds in thisexperiment also tend to coincide. The non-dimensionalized time, t ) , is equal to thenumber of relative pore volumes of leachate divided by the retardation coefficient,N rR , of leachate which has passed through the source zone. The parameterPV i0

N rR is a convenient one for comparing the dissolution behavior of variousPV i0

contaminants.The model presented above was coupled to a simple advection–dispersion model to

simulate the transport of the leachate through the glass-beads column. A Peclet numberof 100 was used to characterize the dispersion in the column. Results of calculationswith both two-region and five-region MTL models are presented below.

4. Presentation and discussion of results

4.1. Batch experiment

Partition coefficients obtained from the batch experiments are presented in Table 1.The experimental partitioning coefficients were determined as the ratio of the massconcentrations in the oil and aqueous phases at equilibrium, i.e.,

Co Co Vie i0 wo – wK s s y 11Ž .i w wC C Vie ie o

In Table 1, the actual partition coefficients are compared with those assuming that theNAPL–water partitioning phase follows Raoult’s law. The theoretical partition coeffi-cients were determined with the following equation which follows from equating

Ž .component fugacities Prausnitz, 1969 between the NAPL and aqueous phase:

g w r MWi o wo – wK s 12Ž .i og r MWi w o


Table 1NAPL–water partition coefficients and NAPL activity coefficients for benzene, toluene, m-xylene, andnaphthalene

o – w o – w 0 0K K g gi i i i

Experimental Raoult’s law Observed Regular solutionog s1.0 theoryi

Benzene 220"5 235 1.08 1.14Toluene 810"20 959 1.19 1.11m-Xylene 3230"70 3514 1.09 1.11Naphthalene 3600"60 6785 1.89 1.80

Experimental K o – w values indicate "1 standard deviation.i

o w Ž .For the activity coefficients, g and g , in Eq. 12 the reference fugacities are thei i

same and equal to that for the solute as a liquid in pure form at the system temperature.The activity coefficients for the solutes in water were determined from the solubilities ofthe pure compounds in water at 258C. For naphthalene, a solid at 258C, the aqueousactivity coefficient was calculated from a combination of the pure compound’s aqueoussolubility, melting point, heat of fusion, and solid and liquid heat capacities according to

Ž .equations described elsewhere Prausnitz, 1969; Mukherji et al., 1997 .For Raoult’s law, the component activity coefficients in the NAPL g o, are assumedi

to be equal to 1.0 at all concentrations. From the ratio of the Raoult’s law and themeasured partition coefficients, actual activity coefficients for BTXN in the NAPL werecalculated and are also shown in Table 1. These observed activity coefficients are allgreater than unity indicating positive deviations from Raoult’s law. The activity coeffi-

Ž .cient for benzene 1.08 is not significantly greater than 1.0, however the activityŽ .coefficient for naphthalene 1.89 was found to be significantly greater than 1.0. Given

Ž .that the aromatic compounds are in a nonpolar solution tridecane , it would be expectedthat the solution be regular, i.e., intermolecular forces are principally due to Londondispersion forces. Thus, the observed activity coefficients were also compared withthose predicted using Scatchard–Hildebrand equations based on regular solution theoryŽ .Prausnitz, 1969 using known solubility parameters for the various components. For thepredicted values, the solubility parameters and molar volumes for all componentsŽ .subcooled liquid in the case of naphthalene at 258C were obtained from Hansen and

Ž .Beerbower 1963 . The experimentally observed activity coefficients are in goodŽ .agreement with the calculated values Table 1 , indicating that the measured partition

coefficients are consistent with those expected for BTXN in this tridecane mixture.The measured and calculated values of g o listed in Table 1 correspond to the initiali

composition of the NAPL prior to dissolution with water. As the more solublecomponents dissolve from the NAPL, the activity coefficients would be expected toincrease. These changes were incorporated into the NAPL source dissolution calcula-

Ž Ž .. otions see Eq. 6 . The activity coefficient, g , for naphthalene was calculated toi

increase from 1.8 to 2.16 as the soluble NAPL constituents are depleted from tridecane.The calculated increase was smaller for the other constituents. A maximum increase of5% in g o was calculated for benzene, toluene and m-xylene during dissolution.i


4.2. Dissolution experiment

Two experiments were conducted at a source length to velocity ratio, LrÕ, of 0.0036day. Effluent concentrations were measured for BTXN and are shown for one of theexperiments in Figs. 2–6. Data for the second experiment are compared with those ofthe first experiment in Fig. 4.

Fig. 2 shows the dissolution data for BTXN for the first experiment. Since theconcentrations were measured at the column effluent, there was a sharp initial break-through of BTXN as the pore fluid in the column was displaced. These initialbreakthrough data are not shown—the effluent data shown are for concentrationsbeginning with the peak concentration that was observed. This enables a more directcomparison of the rate-limited dissolution data with the model calculations. The dotted

Ž . Ž .lines in Fig. 2 are curves calculated from Eqs. 3 – 8 assuming no mass transferŽ j .limitations ka ™` . In Fig. 2, aqueous concentrations qualitatively follow equilibrium

dissolution for approximately two orders of magnitude reduction in concentration, evenŽ .for the low LrÕ ratio 0.0036 day used for this experiment. However, for longer times

a significant departure from equilibrium dissolution is observed for all contaminants.Fig. 2 indicates that mass transfer limitations become significant at the later stages ofdissolution for this LrÕ ratio.

ŽAs a first step in modeling the data of Fig. 2, a two-region model was used Eqs.Ž . Ž ..3 – 8 . Curves were fitted to the data for toluene by adjusting the following parame-

Fig. 2. Effluent concentrations for BTXN dissolving from a residually trapped tridecane source. Solid curveswere determined from a two-region, MTL model fitted to data for toluene.


Fig. 3. Effluent concentrations for BTXN dissolving from a residually trapped tridecane source. Solid curveswere determined from a five-region, MTL model fitted to data for toluene.

ters: the fractions of volume in the mass transfer regions, F j, and the rate constants, ka j,where j is either region 1 or 2. The initial portion of the dissolution data was used toobtain F and ka for region 1, and the dissolution data at longer times were used toobtain these parameters for region 2. Values for these parameters are shown in Table 2.The additional curves in Fig. 2 for benzene, m-xylene, and naphthalene were thencalculated using the measured partition coefficients with the mass parameters in Table 2adjusted only for differences in aqueous diffusion coefficients relative to that for

Ž .toluene, using the Wilke and Chang 1955 correlation. The rate constants were adjustedŽ .0.6by the quantity MV rMV , where MV is the molar volume at the boiling point for aT i i

given compound and MV is the molar volume for toluene.TŽThe inability of the two-region model to describe the entire dissolution history Fig.

.2 suggests that multiple regions with progressively lower mass transfer rate constantsare necessary to describe the entire dissolution history at the LrÕ conditions of thisexperiment. Additional regions were added to the model calculations, and it was foundthat five-regions provided a good description of the data as shown in Fig. 3. The use ofmultiple regions reflects a distribution of rate constants and initial mass for each MTL

Žregion. Alternatively, a continuous distribution function could have been used to.describe this distribution. Again, parameters were fit only to the data for toluene. The

curves for benzene, naphthalene, and m-xylene are calculated curves based on the rateparameters determined for toluene, adjusted only by the aqueous diffusion coefficient.Good agreement between observed and predicted dissolution was observed for benzene,


Fig. 4. Non-dimensionalized effluent concentrations for BTXN dissolving from a residually trapped tridecanesource. Aqueous concentrations listed in the legend are calculated aqueous concentrations in equilibrium withthe NAPL source given the initial NAPL composition. Results for a second experiment using similar

Ž .dissolution conditions are also shown open symbols .

m-xylene, and naphthalene with the exception that the observed naphthalene concentra-tions at longer times were greater than those predicted from the model.

The mass transfer rate constants in Table 2 were assumed not to change during thecourse of the dissolution. The NAPL was assumed to have a fixed distribution of masstransfer zones with a fixed distribution of mass transfer rate constants which isestablished once the flow of water is initiated and the dissolution process begins. Therange of mass transfer rate constants interpreted from the dissolution of toluene may be

Ž . Ž . Ž .due to 1 a distribution of NAPL ganglia Chatzis et al., 1983 or 2 maldistributions inŽ .the flow flow bypassing within the residually trapped source. It is more likely that

significant bypassing of flow occurs around certain regions of the trapped NAPL giventhe extremely low mass transfer constants observed for a portion of the trapped NAPL.The smallest mass transfer rate constant interpreted from modeling the data, kas0.83dayy1, was nearly three orders of magnitude smaller than the largest inferred masstransfer rate constant, kas735 dayy1.

At the early stages of dissolution, the effluent concentrations are controlled by masstransfer from NAPL regions through which the flow directly passes. As these regions

Žbecome depleted in solute not NAPL, because the tridecane does not dissolve in this.experiment , the effluent concentrations are dominated by the slower mass transfer from

regions of trapped NAPL that are bypassed by the aqueous flow. The mass transfer fromthese flow bypassed regions is likely the result of slow diffusion through the aqueous-


Fig. 5. Effect of flow perturbations on the effluent concentrations for BTXN dissolving from a residuallytrapped tridecane source.

filled interstitial pores within the aqueous stagnant regions. In Figs. 2–6, this processhas been modeled as an aqueous film controlled mass transfer process. Although themechanism for dissolution at longer times should perhaps be better characterized astransient diffusion through a stagnant layer of trapped NAPL, this transient diffusionprocess, at long times, can still be approximated with a rate constant based on a linear

Ž .driving force assumption like that given by Eq. 4 . If stagnant diffusion layers arepresent, then the rate constants do not truly reflect film coefficients—instead, the rateconstants should be considered as effective mass transfer rate constants describing theinternal mass transfer limitations within bypassed, stagnant regions.

4.2.1. Non-dimensionalization of NAPL dissolution dataThe data of Fig. 3 have been plotted in non-dimensionalized form in Fig. 4. A

non-dimensionalized curve for toluene based on model calculations using the modelparameters in Table 2 for the five mass transfer regions is also shown. An equilibriumdissolution curve for toluene is shown for comparison. The non-dimensionalized data forall four compounds coincide indicating a generalization of the dissolution process forvarious compounds when mass transfer limitations are present. This suggests thatdissolution data obtained for one component may be useful for predicting the dissolutionhistories for other compounds.

It was shown in the mathematical development that when plotted in dimensionlessform, the dissolution curves for various compounds would coincide for large values ofR and for constant values of S j) and K o – w, j). However, in this experiment, despitei0 o i


Fig. 6. Effect of the length of the source to leachate velocity ratio, Lr Õ , on non-dimensionalized effluenty

concentrations for BTXN dissolving from a residually trapped tridecane source.

changes in S j) and K o – w, j) during dissolution, the curves tend to coincide. This can beo i

explained by comparing the relative dissolution behavior of naphthalene vs. benzene.For this experiment, the NAPL saturation decreased by a maximum of 25% and thepartition coefficient for naphthalene was predicted to decrease by a maximum of 31%during dissolution. Thus, it may have been anticipated that on a non-dimensionalizedtime basis, naphthalene would have depleted faster than benzene which should have

Table 2Mass transfer parameters for the multiregion MTL model fitted to the dissolution data for toluene dissolvingfrom residually trapped tridecane

y1Ž .F, Fraction of initial NAPL volume ka day

2-region modelregion 1 0.93 717region 2 0.07 2.9

5-region model:region 1 0.68 735region 2 0.17 54region 3 0.07 17region 4 0.07 3.6region 5 0.01 0.83

Parameters are shown assuming two-regions and five-regions of MTL dissolution.


depleted without a significant change in saturation or partition coefficient during itsdissolution. However, the multicomponent, MTL model calculations show that the effectof lower saturation and decreased partition coefficient on the relative aqueous concentra-tions for naphthalene is compensated by transfer of some of the naphthalene from thefast mass transfer regions to adjacent slower mass transfer regions during dissolution.This occurs because as the more soluble compounds are depleted from a relatively fastermass transfer region, there is a time period when the naphthalene concentration isgreater in a faster vs. a slower, adjacent region.

Ž .Also shown in Fig. 4 are data from a second dissolution experiment open symbols .For this second experiment, the source was prepared using the same procedure as thatfor the first experiment. Dissolution conditions were also the same. Despite thedifference in the dissolution data for the two experiments, the significant aspect of the

Žsecond set of data is that it also shows the same generalized dissolution trend under a.MTL condition for BTXN as that observed for the first experiment. The difference

observed in concentrations for the dissolution data for the two experiments most likelyreflects a somewhat different distribution of flow andror NAPL distribution in thesource region. Despite the same procedure for preparing the source, small variations inthe application of the NAPL during source preparation may have resulted in the differentdistribution of NAPL within the porous frit.

4.2.2. Effect of flow perturbations on NAPL dissolutionFlow perturbations have been frequently used to confirm the presence of mass

Ž .transfer limitations Brusseau et al., 1989; Pennel et al., 1993 . As a confirmation ofmass transfer limitations in this experiment, the flow rate was reduced from 160cm3rday to 12 cm3rday after 55 days, held constant at 12 cm3rday for an additional 47days, then increased again to 130 cm3rday. The data of Fig. 5 are the same datapresented in Fig. 3 but are shown for a longer time period which included the flowperturbation period. The changes in flow rate resulted in corresponding changes ineffluent concentrations. The observed changes in the effluent concentrations are qualita-tively consistent with those predicted from the calculated curves using the five-region,MTL model. The calculated curves are shown only to indicate that a step increase inconcentrations is expected if mass transfer limitations exist. The mass transfer rateconstants used in the model calculations were not adjusted for changes in the flow rate—to simulate the effect of the a perturbations in flow rate, the five-region model wasused with the same model parameters used to model the data of Fig. 3.

4.2.3. Comparison with literature correlationsTo model the initial portion of the dissolution curves in Fig. 3, a value of kas735

dayy1 applied to 68% of the initial NAPL volume was used. If this value were based onthe total volume of media rather than on only 68% of the volume, then a value of 500dayy1 would be obtained which compares favorably with an estimated value of 530

y1 Ž .day using the correlation of Powers et al. 1994 for the conditions of the experimentŽ . y1 y1reported here S s0.052 . For comparison, values of 410 day and 710 day wereo

Ž . Ž .calculated using the correlations by Imhoff et al. 1994 and Miller et al. 1990 ,Ž . Ž .respectively. The correlations from Powers et al. 1994 and Imhoff et al. 1994 were


Ž .multiplied by the term 1rf and the correlation from Miller et al. 1990 was multipliedby the term S to be consistent with the definition of ka in this paper.w

For the more MTL regions observed for the dissolution of BTXN from tridecane, it isdifficult to make a direct comparison with the mass transfer correlations in the literature,since the correlations were developed from the dissolution of a pure organic phase forwhich the NAPL volume and interfacial area decrease as the pure component dissolves.In the experiments with tridecane however, the NAPL dissolves by at most 25% for eachof the mass transfer regions, so that NAPL interfacial area would not change assignificantly during dissolution. Flow bypassing in these experiments may have beenexacerbated relative to previously reported experiments with unconsolidated media, if

Žsome of the pores are poorly connected resulting in resulting in stagnant or dead-end.pores than those for unconsolidated media. In addition, the initial wetting conditions

were different in the previously reported experiments which can also affect the NAPLdistribution and interfacial areas, thereby impacting mass transfer rates.

4.2.4. Dissolution at higher LrÕ ratiosŽ .The experiments reported here were conducted at a low LrÕ ratio 0.0036 day to

induce MTL dissolution. For higher LrÕ ratios, the mass transfer limitations would beless pronounced. The results of model calculations for various LrÕ values are shown inFig. 6. The curves for LrÕs0.1 and 1.0 day were calculated assuming the same valuesof F j and ka j given in Table 2 and a velocity of 83 cmrday. Calculations were carriedout for increasing values of L—it was assumed that the length is scaled and not thevelocity. For these calculations it was also assumed that the source zone was completelymixed, i.e., Pe™0—the Peclet number would also increase as L increases. The mainpurpose of Fig. 6 is to illustrate that if these laboratory experiments were conducted at aLrÕ ratio of greater than 1 day, then one would not expect to see the effects of masstransfer limitations even for the most severely MTL regions. Fig. 6 is not intended torepresent the effect of mass transfer limitations that may be encountered at the fieldscale. At the field scale, larger-scale heterogeneities in flow andror NAPL distributionfrequently occur, so that the characteristic diameter for mass transfer may also increasewith scale. Fig. 6 does illustrate the trend, however, that mass transfer limitationsbecome less significant as the LrÕ ratio is increased.

5. Summary

When fitted to data for toluene, a multiregion, MTL model was found to predictexperimental data satisfactorily for the dissolution of benzene, m-xylene, and naphtha-lene from tridecane without adjustment of the mass transfer rate parameters. Forthis hydrocarbon mixture, a generalized plot of dimensionless effluent concentrations,C w ) sC wrC w, vs. dimensionless time, t ) sN rR , was anticipated from thei i i0 PV i0

multicomponent model and was observed experimentally for BTXN. These resultsindicate that the NAPL dissolution process can be generalized for various compoundseven when mass transfer limitations are present and that dissolution data obtained forone component can be useful for predicting the dissolution histories for other com-


pounds. Generalized plots similar to the one presented here could be applied to thecharacterization of MTL dissolution of compounds with aqueous solubilities in the sameranges as those for BTXN dissolving from various petroleum hydrocarbon mixtures forwhich a large fraction of the NAPL is relatively insoluble, e.g., crude oil, diesel,gasoline and various oily residuals.

6. Nomenclature

SymbolsŽ 2 3a specific interfacial area between NAPL and aqueous phase cm rcm

.interstitial volumeŽ 3 .C concentration g rcm phasei

Ž 2 .D dispersion coefficient in source zone cm rdayy

F fraction of initial NAPL volumewŽ 3K partition coefficient between NAPL and water phases g rcmi

. Ž 3 .xNAPL r g rcm wateri

k mass transfer coefficient characterizing mass transfer limitations betweenŽ .NAPL and aqueous phases cmrday

ka mass transfer rate constant characterizing mass transfer limitations betweenŽ y1 .NAPL and aqueous phases day

Ž .L length of the source zone cmŽ .MW molecular weight grmole

Ž 3 .MV molar volume cm rmolen number of components in the NAPLN number of mass transfer regionsN number of pore volumesPV

s Ž .q soil phase concentration g rg soiliŽ 3 3 .S saturation cm phasercm pores

Ž .u Darcy flux of leachate through source zone cmrdayyŽ .Õ interstitial velocity of leachate through source zone, u rfS , cmrdayy y w

Ž 3.V volume of phase in a batch extraction system cmw weight fraction

Ž 3 3 .f porosity of the source region cm poresrcm mediag activity coefficient

Ž 3.r average density grcmŽ 3 .r bulk density of media g mediarcm mediab

Subscriptso of NAPLw of aqueous phasei of component i0 initiale at equilibrium


Superscriptsj in region jw in aqueous phaseo in NAPL

Acknowledgements

This research was supported in part from grants from the American PetroleumInstitute under contract 08200-0400-SS9369 and from the Gulf Coast Hazardous Sub-stance Research Center. The views and conclusions in this document are those of theauthors and should not be interpreted as necessarily representing official policies, eitherexpressed or implied of the sponsors.

References

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The dissolution of benzene, toluene, m-xylene and naphthalene from a residually trapped non-aqueous...

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