Slow gas expansion in saturated natural porous media by gas injection and partitioning with nonaqueous

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1 MMaster University From the SeletedWorks of Sarah E Dikson 2008 Slow gas expansion in saturated natural porous media by gas injetion and partitioning with nonaqueous phase liquids Kevin G Mumford, Queen's University - Kingston, Ontario Sarah E Dikson, MMaster University James E Smith, MMaster University Available at:

2 Advanes in Water Resoures 32 (2009) Contents lists available at SieneDiret Advanes in Water Resoures journal homepage: Slow gas expansion in saturated natural porous media by gas injetion and partitioning with non-aqueous phase liquids Kevin G. Mumford a, Sarah E. Dikson a, James E. Smith a,b, * a Department of Civil Engineering, MMaster University, Hamilton, ON, Canada L8S 4L7 b Shool of Geography and Earth Sienes, MMaster University, 1280 Main Street West, Hamilton, ON, Canada L8S 4L7 artile info abstrat Artile history: Reeived 9 May 2008 Reeived in revised form 11 September 2008 Aepted 18 September 2008 Available online 10 Otober 2008 Keywords: NAPL dissolution Spontaneous gas expansion Unstable gas flow Buoyany fores Capillary fores Gas injetion The partitioning of volatile non-aqueous phase liquid (NAPL) ompounds to a disontinuous gas phase an result in the expansion of that gas phase, and the resulting gas flow an signifiantly affet the mass transfer from NAPL soure zones. This reently reported gas flow generated by the spontaneous expansion of a disontinuous gas phase has not been extensively haraterized in the literature. This study measured the expansion rate of a single gas luster in a 1.1 mm sand above a pool of trans-1,2-dihloroethene (tdce) in small-sale flow ell experiments. To haraterize the gas flow, gas injetion experiments in three sizes of sand were onduted at very slow injetion rates typial of gas flow rates produed by gas expansion due to NAPL partitioning. Gas luster spontaneous expansion rates above a tdce pool were found to be 0.34 ± 0.02 and 0.29 ± 0.01 ml/day in dupliate experiments, whih is suffiiently slow to result in disontinuous gas flow in porous media with a grain size diameter greater than 0.02 mm. Measured apillary pressures during gas injetion showed patterns onsistent with disontinuous gas flow, and identified multiple fragmentation events and expansion by oalesene with trapped lusters. The ombination of pressure data and light transmission images were used to identify fragmentation and obtain diret measurements of the ritial luster length (i.e. the length at whih withdrawal of the gas phase from a pore spae ours) in quasi-two-dimensional porous media for the first time. The measured ritial luster lengths were , and m in 1.1, 0.7 and 0.5 mm sands, respetively. These values agreed well with estimates of the ritial luster length made using previously reported equations, and parameters derived from the medium s apillary pressure-saturation relationship. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introdution * Corresponding author. Address: Shool of Geography and Earth Sienes, MMaster University, 1280 Main Street West, Hamilton, ON, Canada L8S 4L7. Tel: x24534; fax: addresses: mumforkg@mmaster.a (K.G. Mumford), sdikso@mmaster.a (S.E. Dikson), smithja@mmaster.a (J.E. Smith). Reent studies have shown that gas flow following the spontaneous expansion of a disontinuous gas phase an signifiantly affet the mass transfer from non-aqueous phase liquid (NAPL) pools [1]. These pools are typially responsible for the persistene of NAPL soure zones [2] and the ontinued ontamination of the surrounding groundwater at NAPL-ontaminated sites over periods of deades to enturies. This reently reported mehanism of spontaneous gas expansion results in signifiant vertial gas flow away from the NAPL pool [3], potentially inreasing the mass transfer rate and hanging the spatial distribution of dissolved NAPL. This ould affet efforts to loate NAPL soure zones using aqueous onentration data, as well as the predition of risks and lifetimes assoiated with NAPL soure zones. Spontaneous gas expansion has been observed in the presene of a variety of NAPLs, inluding tetrahloroethene (PCE), trihloroethene (TCE), 1,1,1-trihloroethane (1,1,1-TCA), and trans-1,2-dihloroethene (tdce), whih have vapor pressures between and Pa [1,3,4]. Beause spontaneous gas expansion is a funtion of the hydrostati pressure, apillary pressure, and the onentrations of other dissolved gases in the groundwater, in addition to the vapor pressure of the NAPL, it is more likely to be ative at NAPL-ontaminated sites with higher volatility NAPL in shallow soure zones and oarse media [3]. However, where additional dissolved gases an be generated in the viinity of NAPL, suh as by mirobial ativity, the additional partial pressure ould result in expansion in deeper, finer systems. This mehanism has not been haraterized extensively in the literature. In partiular, little is known onerning the nature of the resulting gas flow. Roy and Smith [1] observed repeated fragmentation and mobilization of an expanding disontinuous gas /$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi: /j.advwatres

3 30 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) phase above pools of PCE, TCE and a mixture of benzene and PCE in 1- and 3-mm glass bead paks. In addition to repeated fragmentation and mobilization, Mumford et al. [3] observed extensive trapping and oalesene of a mobilized gas phase above a pool of 1,1,1-TCA in a 1.1-mm uniform sand. The gas-phase data presented in these previous studies are limited to qualitative observations of pore-sale proesses, and measurements of the maximum vertial extent of the gas phase. No quantitative information is presented in these studies, or elsewhere in the literature, onerning the rate of generated gas flow or the transient distribution of the resulting disonneted gas lusters produed via this mehanism in porous media. Measurements of gas flow rate and distribution are important first steps toward better understanding the total mass transfer away from the pool and the dissolution of the volatized NAPL into the groundwater above the pool, respetively. The urrent literature onerning gas flow in porous media does not adequately address this mehanism, whih is expeted to produe very low gas flow rates. This expetation is based on experiments onduted under diffusion-limited onditions, in the absene of porous media, where single gas bubbles were observed to expand at rates of and ml/day in the presene of tdce and PCE, respetively [4]. Although these rates were not measured in porous media, they suggest that gas flow generated by spontaneous expansion will be substantially slower than the injetion rates used in other studies of gas flow in porous media, inluding ml/min [5], ml/min [6], ml/min [7], and ml/min [8]. Gas was injeted as a point soure during these studies, using either porous stones (1 2 m diameter) [5,8], or small-diameter injetion points (2 5 mm diameter) [6,7]. Very few studies have reported results for the slow injetion of gas in water-saturated porous media [6]. Glass et al. [9] injeted CO 2 at 1.2 ml/min into uniform sand saturated with water. In an analogous study of unstable, non-wetting fluid injetion, Frette et al. [10] injeted a surose-water solution at 0.03 ml/min into a m 3 ontainer paked with 2-mm long 2-mm diameter plexiglass ylinders, saturated with dibutylphthalate. Their study used the surose-water solution as the injeted, non-wetting fluid, and dibutyl-phthalate as the wetting fluid in plae of gas and water, respetively. Our study investigated gas flow for injetion rates of and 0.01 ml/min, injeted through a 2-mm diameter tube, whih is apable of produing disontinuous flow [6] in media finer than 1 2 mm. A grain size of 1 2 mm is typially onsidered to be the transition point for ontinuous to disontinuous gas flow reported in the air sparging literature [5]. The purpose of this study is to haraterize the gas flow in natural porous media resulting from the spontaneous expansion of a disontinuous gas phase at the surfae of a NAPL pool. Two sets of benh-sale experiments were onduted in natural sand to (1) quantify the expansion rate of a disontinuous gas phase at the surfae of a NAPL pool, and (2) measure the transient gas pressures and ritial luster lengths produed by the very slow injetion of gas in three different sands. This study is the first to quantify the rate of spontaneous gas expansion above a NAPL pool in porous media, and represents the first data for the injetion of gas at these very slow flow rates. In addition, this study provides the first diret measurement of disontinuous gas-luster lengths in a porous medium with a thikness greater than one grain diameter, made possible by using a ombination of imaging tehniques and pressure measurements, in ontrast to previous studies that measured gas-luster lengths [11,12] in monolayer pakings of glass beads. The results of this study ontribute to the refinement of the oneptual model for the spontaneous expansion of a gas phase in the presene of NAPL [1], and provide key quantitative data that will failitate the inorporation of this mehanism into future numerial models. 2. Bakground 2.1. Expansion of multi-omponent disontinuous gas phases The partitioning of multiple dissolved gases to a disontinuous gas phase is well desribed by Cirpka and Kitanidis [13] and has been used for numerous appliations inluding the dissolution [14,15] and expansion [1,4,16] of disontinuous gas phases. Cirpka and Kitanidis [13] show that the dissolution or expansion of a multi-omponent gas phase results from the onstraint P g ¼ P w þ P ¼ X i P g i where P g is the gas pressure, P w is the bulk liquid pressure, P is the apillary pressure, and P g i is the partial pressure of ompound i in the gas phase. The apillary pressure is desribed by the Laplae equation of apillarity P ¼ r 1 þ 1 ð2þ r 1 r 2 where r is the gas liquid interfaial tension, and r 1 and r 2 are the prinipal radii of urvature of the gas liquid interfae. The partial pressure is desribed by Henry s law, assuming loal thermodynami equilibrium at the gas liquid interfae P g i ¼ K Hi C i ð3þ where K Hi is the Henry s law oeffiient for ompound i, and C i is the loal aqueous phase onentration of ompound i. The onstraint given by Eq. (1) an result in loal aqueous onentrations different from those in the bulk solution, whih drives mass transfer between the bulk solution and the disontinuous gas phase. The resulting hanges in the pressure and volume of the gas phase over time under isothermal onditions follows from the ideal gas law dn t dt ¼ 1 dðp g V g Þ ð4þ RT dt where n t is the total number of moles in the gas phase, t is time, R is the gas onstant, T is the temperature, and V g is the volume of the gas phase. For mass transfer into a disontinuous gas phase (i.e. dn t /dt > 0) in porous media, the hanges to pressure and volume our in a series of pore-filling (approximately onstant pressure) and pressurization (approximately onstant volume) steps [17] Gas flow in water-saturated porous media Two different flow patterns have been observed for the upwards flow of gas in otherwise water-saturated porous media: ontinuous (also alled hannel or oherent) flow and disontinuous (also alled bubbly, slug, or inoherent) flow [5 7]. Continuous flow is haraterized by a olletion of ontinuous hannels whih transport gas along a gas-phase pressure gradient. Disontinuous flow is haraterized by the presene of multiple, disrete gas lusters, whih may be either trapped or mobile, depending on the magnitude of loal apillary and buoyany fores. The differene between these two gas-phase distributions has a ontrolling effet on the mass transfer between the gas and aqueous phases [5]. For spontaneous gas expansion in partiular, the ourrene of disontinuous gas flow allows the expansion of some gas lusters and the dissolution of others, as the mass transfer is ontrolled by the loal aqueous onentrations at eah individual gas liquid interfae [3]. The threshold between ontinuous and disontinuous flow has been based solely on the onsideration of the Bond number [5,8] Bo ¼ Dqgr2 p r ð1þ ð5þ

4 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) where Bo is the Bond number, Dq is the density differene between the resident and invading fluids, g is the aeleration due to gravity, and r p is a harateristi pore radius. In a review of the literature, Selker et al. [8] found that ontinuous flow dominated for Bo < Based on the ratio of pore neks to pore bodies used by Brooks et al. [5], this is onsistent with the grain size threshold of approximately 1 2 mm for the injetion of air in water-saturated porous media referred to in the air sparging literature. Reent researh, however, shows that the onsideration of the Bond number alone is insuffiient for the haraterization of gas flow. Geistlinger et al. [6] and Stöhr and Khalili [7] report similar expressions for a ritial flow rate, at whih the frition fores resulting from the flow of gas in a hannel stabilize the flow a b Q rit ¼ pdqgr4 8l g ð6þ where Q rit is the ritial gas flow rate above whih gas flow is stable and ontinuous, r is the gas hannel radius, and l g is the gas dynami visosity. A value of Q rit apable of stabilizing the gas flow is only attainable in media where apillary fores dominate over gravity fores at the sale of a single pore [7]. Eq. (6) shows that disontinuous flow is not limited to media of greater than 1 2 mm in diameter; it will our in muh finer media when the gas flow rate is suffiiently small. to d to e 2.3. Fragmentation and mobilization The flow of disontinuous gas lusters in porous media is ontrolled by both apillary and buoyany fores, as desribed by studies that model gas flow using modified invasion perolation (MIP) in a gradient with fragmentation and mobilization [18 20]. For an immobile disontinuous gas phase (Fig. 1a) to expand, whether due to the injetion of additional gas or the partitioning of additional volatile ompounds, the gas pressure in the luster must overome the sum of the hydrostati and entry pressures in one of the adjaent pore throats P g P P w þ P e where P e is the throat entry pressure. The entry pressure an be expressed as P e ¼ 2r r t ð7þ ð8þ where r t is an effetive pore throat radius, whih impliitly inludes ontat angle onsiderations. Thus, the apillary pressure inreases with the gas pressure until the throat entry pressure is reahed. One this loal gas-phase entry pressure is ahieved the gas phase expands into the adjaent pore body (Fig. 1b) and the apillary pressure drops. This apillary pressure may be greater or less than the apillary pressure in the previous pore body, depending on the geometry of the new gas liquid interfae. This alternating sequene of pressurization and pore-entry [17] results in a dynami flutuating gas pressure. As expansion ontinues it is biased towards growth in the upwards vertial diretion (Fig. 1) sine the hydrostati pressure dereases with height making the entry into pore throats above the luster generally more favorable [21]. Therefore, although the gas pressure flutuates, due to loal pressurization and pore-entry events, the mean pressure dereases with inreasing luster height, due to the derease in hydrostati pressure as the luster expands upward. As the length of the luster extends vertially, the loal urvature of the gas liquid interfae adjusts to maintain a uniform gas pressure throughout the luster despite a derease in hydrostati pressure with height. This results in greater radii of urvature (lower apillary pressure) towards the bottom of the luster and lesser radii of urvature (high apillary pressure) towards the top. One the length of the luster reahes a ritial value, the apillary pressure towards the bottom of the luster drops to a value where the reinvasion of water into previously gas-oupied pore spae is possible. This pressure is referred to as the withdrawal threshold [12,20] and is analogous to the terminal pressure (P t ) used to desribe the formation of NAPL residual, whih has been previously defined on the marosopi sale using apillary pressure-saturation urves [22]. This re-invasion results in either the mobilization (Fig. 1d) or the fragmentation (Fig. 1e) of the luster, depending on the loation of the pore where re-invasion ours. Following fragmentation, the lower gas luster is at a lower apillary pressure than what is required for the entry into any of its adjaent pore throats. Therefore, pressurization of the entire luster must our again before repeated growth of that luster is possible. Expressions for estimating the ritial luster length have been reported based on a balane of pressure at the upper and lower tips of the luster, and onsideration of the hydrostati pressure drop [6,9] h rit ¼ Ptop d Fig. 1. Stages of growth for a gas luster in porous media showing (a) initial gas luster, (b) expansion to adjaent pore spae, () vertially-dominated expansion, (d) mobilization, and (e) fragmentation, where the blak arrows indiate the diretion of interfae movement between the different stages of growth. P bottom Dqg where h rit is the ritial luster length, P top is the apillary pressure at the top of the luster and P bottom is the apillary pressure at the bottom e ð9þ

5 32 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) of the luster, when fragmentation ours. When it is reasonable to assume that P top P bottom, the ritial length will be proportional to Bo 1 r p [21]. Geistlinger et al. [6] estimated the ritial length to be on the order of the grain size for the injetion of air into water-saturated uniform glass beads greater than 3 mm in diameter, and Glass et al. [9] estimated the ritial length to be 4.2 m for the injetion of CO 2 into water-saturated uniform sand with a median grain size of 1.1 mm. Glass et al. [9] reported that their estimated value was onsistent with their experiments, as multiple fragmentation events were observed over a distane of approximately 20 m, and Geistlinger et al. [6] reported that their estimated value was onsistent with previously reported observations of disontinuous gas flow in media with grain sizes greater than 3 mm. This suggests that Eq. (9) an provide appropriate estimates of the ritial luster length. However, a diret omparison of experimental and predited ritial luster lengths was not possible beause the ritial luster lengths were not measured during the experiments. 3. Materials and methods 3.1. Flow ell Both the NAPL pool and gas injetion experiments were onduted using a small-sale (100 mm 80 mm 8 mm) glass flow ell (Fig. 2). The flow ell was onstruted of retangular glass tubing, heated at the bottom to reate a sealed base and then ut to length. 10-mm diameter glass tubing was installed on either side of the flow ell to serve as influent and effluent ports. The top of the flow ell was sealed by the ompression of a rubber gasket along the top surfae. Constrution of the flow ell in this manner eliminated any seals near the bottom of the flow ell that ould be inompatible with NAPL and allowed visualization of the entire domain Porous media One of three size frations of natural sand (Ausand, Unimin Corporation) were used in all experiments: 12/20, 20/30, and 30/40, referred to here as 1.1, 0.7, and 0.5 mm sand, with seleted properties listed in Table 1. Bond numbers and ritial flow rates were alulated using Eq. (5) and Eq. (6), respetively, for the displaement of water by air. These sands have been used extensively in benh-sale experiments of two-phase and three-phase flow proesses due to the high degree of bath-to-bath reproduibility available from the manufaturer [23] and their ability to transmit suffiient light to allow visualization of flow proesses in transparent, two-dimensional models [8,9,24 27]. To effluent sampling 1.1 mm sand 4 mm glass beads mm glass beads Emplaed air NAPL injetion point NAPL Stand From influent reservoir Balane 1.1 mm, 0.7 mm, or 0.5 mm sand 2 mm ID air injetion tube Syringe Pump Stand Pressure Sensor Fig. 2. Experimental set-up for (a) gas expansion above a NAPL pool and (b) gas injetion.

6 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) Table 1 Porous media properties. All sands were used as reeived from the manufaturer with no further proessing exept a thorough rinsing with distilled water to remove any fines that may have aumulated during shipping. Mirosopi and marosopi air entrapment in the sand were minimized by plaing the sand in water under vauum prior to paking, and ontinuously pouring the wet sand into the waterfilled flow ell. The ontinuous pouring, together with the tapping of the flow ell walls with a small rubber mallet following the pour, ahieved a reasonably homogeneous pak. The porosity of the sand pak in eah experiment (Table 2 and Table 3) was determined based on the known volume of the flow ell and the mass of sand used in the paking Gas expansion above a NAPL pool 1.1 mm sand 0.7 mm sand 0.5 mm sand Size fration 12/20 20/30 30/40 Median grain size (mm) a Uniformity oeffiient a Air-entry pressure (m of H 2 O) a,b Bond number Critial flow rate (ml/min) d a Shroth et al. [23]. b Based on Brooks Corey fitting parameters. Calulated using Eq. (5) with r = 72 mn/m and Dq = 1000 kg/m 3. d Calulated using Eq. (6) with Dq = 1000 kg/m 3, l g = 0.02 mn s/m 2, and taking r equal to half the median grain size. Table 2 Conditions and observations for gas expansion above a NAPL pool. Experiment no mm sand mm sand Paking Porosity Aqueous flow rate (ml/min) ± ± 0.01 Average gas expansion rate (ml/day) Table 3 Conditions and observations for gas injetion. Experiment no. Air injetion rate (ll/min) Porosity Critial luster length (m) Capillary pressure during flutuation phase (m) Min. (P t ) Max. (P e ) P t /P e 1.1 mm sand mm sand mm sand To measure the expansion of a disontinuous gas phase above the surfae of a NAPL pool in experiments #1 and #2, the flow ell was paked as shown in Fig. 2a. The enter of the ell was paked with 1.1 mm sand, the bottom orners were paked with finer glass beads ( mm diameter, Potters Industries) to ontain the NAPL pool, and the influent and effluent walls were paked with 4 mm glass beads (Propper Manufaturing Co. In.) to distribute the flow along the height of the flow ell. Midway through the paking proedure 0.6 ml of trans-1,2- dihloroethene (tdce, Alfa Aesar, 98%) dyed with 100 mg/l of Sudan 4 (Aros Organis) was emplaed at the bottom of the ell to reate a pool with a length of 4.3 m. The tdce was emplaed using a gastight syringe and a stainless steel needle, inserted into the paking from the top and subsequently withdrawn. tdce was seleted for this experiment due to its relatively high vapor pressure of Pa at 25 C [28], whih was expeted to result in relatively rapid expansion of the gas phase [4]. Following emplaement of the NAPL pool, a 4 ll bubble of laboratory air was emplaed 4 mm above the pool surfae near the enter of the front wall of the flow ell using the same tehnique as for the NAPL emplaement. Both the tdce and the air were emplaed midway through the paking to allow easier insertion and withdrawal of the injetion needle, and limit the reation of a preferential gas flow path due to rearrangement of the sand grains during needle withdrawal. By emplaing the tdce and air midway through the paking, this potential preferential pathway was limited to a height of 2 m above the pool surfae. Distilled water saturated with laboratory air was pumped through the flow ell using a peristalti pump (Cole-Parmer, model No ). The effluent exited the flow ell through a port loated near the bottom of the ell, and was disharged through tubing at a fixed elevation loated 1.5 m below the top of the flow ell. The influent ontained 200 mg/l of sodium azide to at as a bioide [29 31]. The flow rate was measured periodially by weighing the effluent (Table 2), whih was olleted in a flask overed to minimize evaporative losses. To quantify the expansion of the gas phase the paked flow ell was plaed on a laboratory balane (Mettler Toledo, model No. PG5002-SDR) throughout the experiment to measure the water mass lost from the flow ell due to displaement by the expanding gas. The water-mass loss was orreted for mass lost due to NAPL dissolution using a dissolution rate alulated from periodi sampling of the effluent and subsequent analysis of dissolved tdce in experiment #2. The effluent from experiment #1 was not sampled, but the tdce pools in eah experiment were visually observed to dissolve at similar rates. Analysis of dissolved tdce was onduted by gas hromatography mass spetrosopy (Agilent 6890 GC, Agilent 5973 MS mass seletive detetor, Restek Rtx m, 0.32 mm ID, 1.8 lm film thikness olumn) equipped with a headspae autosampler (Agilent 7694E). The temperature program for the GC oven was 40 C hold for 6 min, ramp at 10 C/min to 120 C, and ramp at 25 C/min to 220 C. The total effluent mass of 0.72 ± 0.03 g, determined by integration of the breakthrough urve, was not signifiantly different from the injeted mass of 0.76 ± 0.03 g, whih indiates a satisfatory mass balane. Based on the breakthrough data, tdce was lost at a linear rate of ± g/day, with no distintion between mass lost diretly from the pool to the aqueous phase and mass lost from the pool to the aqueous phase through the gas phase. Assuming that all of the dissolved tdce was replaed by water, the dissolution of the pool resulted in a hange in mass of the flow ell of ± g/day, whih was used to orret the mass data. This rate represents 4% of the total mass hange due to dissolution of the pool, and the displaement of water by the expanding gas phase.

7 34 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) Gas injetion To assess the flow of a slowly injeted gas phase in experiments #3 #17, the flow ell was paked as shown in Fig. 2b. The flow ell was paked with 1.1, 0.7, or 0.5 mm sand. A 2-mm ID glass tube was inserted into a port and onneted to a gastight syringe (Hamilton, 2.5 ml, model No. 1002) on a syringe pump (KD Sientifi, model No. 230). The syringe pump was used to injet 1000 ll of laboratory air at rates of 1 ll/min or 10 ll/min (Table 3), whih are well below the alulated Q rit values. A relatively large-diameter injetion tube was used to avoid the reation of an artifiial fragmentation point, as would be reated by using a tube with a diameter signifiantly less than that of the surrounding pore spaes, and promote fragmentation within the sand pak. The seond port was onneted to a 9.7-m diameter water reservoir. As a result of this wide diameter, the displaement of water by the injeted air resulted in an inrease in water level of only 0.1 mm by the end of the injetion, effetively maintaining a onstant water pressure on the flow ell throughout the experiment. The water reservoir was open to the atmosphere via a small hole in a Parafilm Ò over. The water in the reservoir and the flow ell was saturated with laboratory air prior to beginning the experiment to minimize any hanges in volume due to dissolution of the gas phase. The pressure of the injeted gas phase was measured using a differential pressure sensor (Honeywell, model No. DC005NDC4) attahed to the tubing from the syringe and the water reservoir. The differential pressure was measured one per 0.5 ll of gas injeted and was reorded using a datalogger (Campbell Sientifi, model No. CR23X) Visualization Digital images of experiments #2 #17 were olleted using a CCD amera (Canon A640) onneted to a personal omputer equipped with software from the amera manufaturer. Images were olleted at a resolution of (0.05 mm) 2 /pixel. The flow ell was loated between the amera and a light soure, whih onsisted of light from three 50 W halogen bulbs (Liteline Corporation, model No. CF-130-B) refleted off a white bakground. This allowed visualization of the depth-averaged gas saturation by light transmission [25,32,33]. The digital images for experiments #3 #17 were proessed by aligning the images to orret for shifts between the amera and the flow ell, onverting the olleted RGB image to a graysale intensity image, and then subtrating the bakground image by alulating the differene in optial density [3] using [34] DOD ¼ OD t OD 0 ¼ log I 0I ref t I t I ref 0! ð10þ where DOD is the differene in optial density, OD is the optial density, I is the transmitted light intensity and I ref is the average transmitted light intensity over the referene region. The subsripts 0 and t refer to images olleted initially and at time t, respetively. The intensity of the referene region was used to orret for temporal hanges in lighting, and the referene region onsisted of a 2.4 m 1 m setion of the sand that was unaffeted by the injeted gas phase. Following bakground subtration, noise was redued by proessing using a median filter on a 3 3 pixel 2 ( mm 2 ) area. Alignment of the images and measurement of ritial luster lengths were onduted using ImageJ ( rsb.info.nih.gov/ij/), and all other proessing was done using MatLab (Release 13, MathWorks, In.). 4. Results and disussion 4.1. Gas expansion above a NAPL pool During experiments #1 and #2, repeated expansion, fragmentation, and mobilization of the gas phase was observed. The disontinuous gas phase expanded aross the surfae of the NAPL pool, was vertially mobilized, and aumulated at the top boundary of the flow ell and in the oarse bead paks along the influent and effluent walls. Mobilized gas entered the oarse bead paks by migrating along the top boundary of the ell and by penetrating the right-hand oarse bead pak near the NAPL injetion point. Fig. 3 shows the approximate distribution of the gas phase at three times for experiment #2, whih were similar to those observed in experiment #1. The general behavior of the gas phase is onsistent with previous experiments onduted in the 1.1 mm sand [3]. The aumulation of gas in the flow ell over time is shown in Fig. 4 for eah of the dupliate experiments. The initial 4 ll air bubble expanded to 4.2 ml of gas after 13.1 days in experiment #1, and 4.5 ml of gas after 13.7 days in experiment #2. Treating the entire volume of the sand pak as a representative elementary volume, this represents a hange in the marosopi gas-phase saturation of 3 orders of magnitude, from to The a b 2 m Fig. 3. Approximate loation of gas in the flow ell (indiated by the shaded areas) during experiment #2 (a) following initial emplaement of a 4 ll air bubble above the tdce pool at 0 days, and after (b) 2 days and () 13.7 days.

8 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) Gas Volume (ml) Exp #1 Exp # Time (days) average expansion rate over the duration of the experiment is given by the slope of the regression line, and was found to be 0.34 ± 0.02 and 0.29 ± 0.01 ml/day for experiments #1 and #2, respetively (Table 2). These results demonstrate good reproduibility of the expansion rate between the two experiments. The approximately linear inrease of gas volume with time in Fig. 4 implies the ahievement of an effetively steady expansion rate, whih requires the effetively steady mass transfer of tdce and other dissolved gases to the gas phase. Evidene of effetively steady mass transfer is onsistent with previous studies on the expansion of disontinuous gas above NAPL pools [4]. Based on Eq. (6) the ritial gas flow rate for the 1.1 mm sand is expeted to be ml/min, whih is well above the observed gas expansion rate. Therefore, the flow here is expeted to be disontinuous, whih is onsistent with the observations of repeated fragmentation and mobilization events. The expansion rates observed in experiments #1 and #2 are onsidered upper limits for the expeted expansion rate of a single gas luster loated above the surfae of a NAPL pool. The tdce used in these experiments has a relatively high vapor pressure ompared to other NAPLs where this mehanism may play a signifiant role [1], whih produes faster expansion rates [4]. Furthermore, early in the experiments the gas phase ontated the surfae of the NAPL pool, whih allowed rapid partitioning of the NAPL ompound to the gas phase and a faster expansion rate [4]. Although the ritial gas flow rate dereases with the grain size, the expansion rates observed here are below the ritial gas flow rate for grain diameters greater than 0.02 mm, based on Eq. (6). Therefore, disontinuous gas flow is expeted for the spontaneous expansion of a disontinuous gas phase driven by the partitioning of volatile NAPL ompounds in fine to oarse sand Gas injetion: visualization 0.34 ml/day 0.29 ml/day Fig. 4. Volume of gas aumulated due to the expansion of an initially 4 ll air bubble above a tdce pool during experiments #1 and #2, where the symbols represent the data and the lines represent the best-fit showing the average expansion rate over the total duration of eah experiment. The standard deviation of eah data point was estimated to be ml, whih is less than the size of the symbols used in this plot. The transient distribution of the injeted gas phase is illustrated in Fig. 5 for experiments #8, #12, and #16, onduted in the 1.1, 0.7, and 0.5 mm sand, respetively. Fig. 5 shows that the expansion of the injeted gas is dominated by growth in the vertial diretion, as expeted for systems where gravitational fores play a signifiant role [21]. Growth was seen to our as a series of short duration marosopi events, referred to as bursts [18], separated by longer periods of no movement. These bursts were attributed to both the alternating pore-sale mehanisms of pressurization and pore-filling assoiated with the growth of a non-wetting fluid luster [17] and the fragmentation and mobilization assoiated with the growth of a non-wetting fluid luster subjeted to a gravity field [18]. Evidene of burst growth is given in Fig. 6, whih shows two pairs of suessive images from experiment #8 as the differene in optial density from the bakground image. The time between eah image in a pair is 30 s. Fig. 6 also shows the differene between eah of the images in a pair. The two burst events shown in Fig. 6 are the result of fragmentation and migration of the disontinuous gas luster. Upon reahing the ritial luster length, the drop in the gas-phase pressure resulted in a orresponding drop in the loal apillary pressure near the gas injetion point. This resulted in the re-invasion of pores with water, fragmentation of the luster, and the signifiant mobilization of gas from lower parts of the luster to new pore spaes near the top of the luster. The disontinuous nature of the gas lusters is highlighted by the results in Fig. 6f, whih show the mobilization of gas from the right-hand side of the gas distribution but not from the left-hand side Gas Injetion: pressure measurements Transient pressure measurements for experiments #8, #12, and #16 are shown in Fig. 7, onduted in the 1.1, 0.7, and 0.5 sands, respetively. These results are representative of the general patterns observed in all other gas injetion experiments. Fig. 7 shows three phases in the evolution of the apillary pressure: (1) initial pressurization, (2) drainage, and (3) pressure flutuation, whih have also been reported for air injetion into glass beads [6]. During the initial pressurization phase the apillary pressure rises as gas is injeted into the pore spae immediately adjaent to the injetion tube. Sine the gas phase is ontinuous throughout the injetion syringe, injetion tube, and pressure sensor tubing, this pressurization requires a greater gas volume than what is expeted for the pressurization of a gas luster in a single pore. The total gas injetion and pressure measurement system had a volume of 9 ml, whih affeted the volume required to pressurize the gas phase during the initial pressurization and the pressure flutuation phases. The initial pressurization phase ends when the first pore spae adjaent to the injetion tube is invaded and the gas luster begins to expand within the porous medium. Entry pressures at the end of the initial pressurization stage were measured to be 7 ± 1, 11 ± 2, and 19 ± 5 m in the 1.1, 0.7, and 0.5 mm sand, respetively. As expeted, this entry pressure inreased with dereasing grain size, and did not vary substantially between experiments at the same grain size due to the uniformity of these sands. However, it is not equal to the value of the air-entry pressure reported for the sands (Table 1) sine not all pore spaes are available for entry. Therefore, the displaement values observed here represent the lowest loal apillary pressure of the available adjaent pore spaes. During the drainage phase the apillary pressure generally dereased with additional gas injetion due to vertial growth of the gas luster, whih resulted in dereased hydrostati pressure at the upper gas liquid interfae and lower gas pressures. The short-term periods of inreasing apillary pressure during this phase are aused by the invasion of pores with greater loal apillary pressure during gas expansion. The drainage phase ends when the gas luster reahes the ritial luster length for the first time, and fragmentation ours. During the pressure flutuation phase the apillary pressure undergoes yles of inreasing and dereasing pressure due to the repeated fragmentation of the gas luster attahed to the

9 36 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) Fig. 5. Distribution of gas in the 1.1 mm sand for experiment #8 after the injetion of (a) 150 ll, (b) 400 ll, and () 800 ll of gas 15, 40, and 80 min after the start of injetion, respetively; in the 0.7 mm sand for experiment #12 after the injetion of (d) 150 ll, (e) 400 ll, and (f) 800 ll of gas 15, 40, and 80 min after the start of injetion, respetively; and in the 0.5 mm sand for experiment #16 after the injetion of (g) 150 ll, (h) 400 ll, and (i) 800 ll of gas 150, 400, and 800 min after the start of injetion, respetively, displayed as the differene in optial density between the initial (bakground) image and suessive images. injetion tube, whih indiates disontinuous gas flow [6]. These yles are bounded by maximum and minimum pressures (Table 3), whih represent the pore-sale entry (P e ) and terminal (P t ) pressures, respetively, at the fragmentation point. As disussed for the initial pressurization phase, the entry pressures are not neessarily equal to the air-entry pressures reported for these sands due to the limited pore spaes sampled by the gas phase. However, as expeted, they follow the same trend as the reported air-entry pressures and inrease with dereasing grain size. The ratio P t /P e had an average value of 0.60 and was not signifiantly different between the different sands. This is onsistent with values of P t /P e between 0.44 and 0.71 reported by Gerhard and Kueper [22] based on their analysis of data from apillary pressure-saturation urves in several multi-fluid porous media systems in the literature and their own NAPL infiltration experiments. The transition from the minimum to maximum apillary pressures is due to pressurization of the gas luster, and appears as a onstant, positive-slope pressure inrease at the beginning of eah flutuation yle in Fig. 7. The slope of this line is an artifat of the experimental set-up aused by the volume of the injetion syringe and pressure sensor tubing, as disussed for the initial pressurization phase. In the absene of equipment and instrumentation, this volume required for pressurization would be signifiantly less. The effet of the injetion syringe and pressure sensor tubing volume

10 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) Fig. 6. Gas distributions for experiment #8 after the injetion of (a) 249 ll, (b) 254 ll, (d) 529 ll, and (e) 534 ll of gas displayed as the differene in optial density between the initial (bakground) image and suessive images; and the differene in gas distributions between () 249 and 254 ml, and (e) 529 and 534 ll of gas injeted, where a brighter image represents a dereased gas saturation (dereased optial density) and a darker image represents an inreased gas saturation (inreased optial density). The image in (a) was olleted at the end of the drainage phase, and the transition to (b) is the result of the first fragmentation of the gas luster. The ritial luster length is given by the length of the gas luster in (a). was verified in a separate experiment where the volume of the measurement system was hanged, and a orresponding hange in the pressurization slope was observed (data not shown). The transition from maximum to minimum apillary pressure is due to expansion of the gas luster, whih ours in a manner unlike during the initial drainage phase due to the presene of trapped gas lusters along the pathway of expansion. These trapped lusters form portions of a disonneted pipeline [18] that provides aess to gas-oupied pore spaes at greater elevations. Where larger trapped lusters are loated lose together, minimal volume is required to reonnet a luster of ritial length, and the derease in apillary pressure followed by fragmentation is very rapid. This is the ase for most of the yles in experiments #12 and #16. In the remaining yles, and the yles observed in experiment #8, the trapped lusters are smaller and more separated, resulting in several oalesene events prior to the reahievement of the ritial luster length. These oalesene events result in rapid hanges in the apillary pressure with no fragmentation, and produe the seondary flutuations prevalent in the data from experiment #8. The pattern of flutuating pressure in eah experiment is very onsistent between yles. The onsistent maximum and minimum pressures indiate that fragmentation is ourring in the same pore spae and returning to a lower apillary pressure ditated by the ritial luster length following fragmentation. The onsistent pattern of seondary flutuation during the derease from maximum to minimum pressure indiates that the same pathway is being followed during expansion. Changes in this pattern of seondary flutuation represent a hange in the expansion pathway. The differenes observed in experiment #16 following the injetion of 0.7 and 0.9 ml of gas were due to a differene in the distribution of trapped lusters aused by fragmentation and mobilization events at greater elevations. This resulted in seondary flutuations in apillary pressure prior to ahieving the ritial luster length in two of the eight yles. The hange in the seondary flutuation observed in experiment #8 after 0.33 ml of gas injeted was due to branhing of the injeted gas luster, whih produed an additional drainage event between 0.33 and 0.46 ml injeted. Branhing here refers to the seletion of different flow paths by mobilized gas lusters between subsequent mobilization events. Branhing of the lusters was observed in 7 of the 12 experiments onduted in the 1.1 and 0.7 mm sands, despite the very slow flow rates and nearly invisid non-wetting phase. This type of branhing in natural porous media under the onditions used

11 38 K.G. Mumford et al. / Advanes in Water Resoures 32 (2009) Capillary pressure at injetion point (m) Initial pressurization Drainage # Gas injeted (ml) in this study is unexpeted, sine branhing is typially attributed to visous effets [7,10,35,36]. However, the onset of branhing was observed to our during mobilization events, whih suggests that the veloity of a mobilized gas luster may be a more appropriate indiation of the potential for branhing than the mean veloity of the injetion front. This veloity is expeted to be high. For example, a rise veloity of m/s has been reported for single bubbles in 4-mm diameter glass beads [37]. The possibility of pipeline growth as the dominant gas-phase mass transport mehanism is an important onsideration for the mass transfer of volatile NAPLs from the surfae of NAPL pools. An expanding gas luster will reah greater heights at a muh faster rate if trapped gas is available for pipeline growth. Due to the narrow onentration boundary layers above NAPL pools [38,39] most of the trapped gas above a NAPL pool will be under onditions that favor dissolution due to hydrostati and apillary pressures. Only the gas lusters near the pool surfae will be apable of expansion due to NAPL ompound partitioning [3]. If a gas luster near the pool surfae is apable of expanding to the ritial luster length faster than the dissolution of the trapped gas lusters well above the pool, then the presene of the trapped gas lusters will be sustained due to repeated fragmentation and migration of lower lusters, and their oalesene with upper lusters. Evidene of this maro-sale gas transport by repeated oalesene events has been shown for the spontaneous expansion of a disontinuous gas phase above a NAPL pool [3]. If dissolution of the trapped gas lusters well above the pool happens faster than expansion of the lower luster to the ritial length, then the pipeline will not be sustained and the effet of the mass transport via spontaneous expansion of the disontinuous gas phase will be limited to a height above the pool less than or equal to the ritial luster length Gas injetion: ritial luster length #8 #16 Pressure flutuation Exp. #16 (0.5 mm sand) Exp. #12 (0.7 mm sand) Exp. #8 (1.1 mm sand) Fig. 7. Capillary pressure measured at the gas injetion point for experiments #8, #12, and #16. The 1 ml of gas was injeted at 10 ll/min for 100 min in experiments #8 and #12, and at 1 ll/min for 1000 min in experiment #16. The end of the drainage phase, and the ourrene of the first fragmentation event, is indiated by the white arrows for eah experiment. Diret measurement of the ritial luster length requires a lear indiation of when fragmentation of a gas luster ours. Visually identifying losely spaed, but separated lusters in a quasi-two-dimensional porous medium using light transmission is not possible due to the point-wise errors assoiated with the light transmission tehnique [25], and the additional blurring of the image assoiated with sharp transitions between phases and gas lusters that do not oupy the entire width of the pak [9]. This prevents the aurate differentiation between two lusters separated by a few pores and two sub-lusters onneted by a single gas-filled pore. To overome this limitation, the time of fragmentation was identified using the transient pressure measurements, rather than the image data. At the end of a drainage phase (Fig. 7) the minimum pressure is ahieved and the gas luster undergoes fragmentation for the first time. Until that fragmentation ours, the gas exists as a single, onneted phase that extends from the injetion point to the top of the luster. The height of this onneted luster is equal to the ritial luster length. Therefore, the image olleted immediately prior to fragmentation at the end of the drainage phase an be used to measure the ritial luster length. An example is shown in Fig. 6, where the fragmentation that ourred between 249 and 254 ll was the fragmentation at the end of the drainage phase (Fig. 7), and the length of the luster in Fig. 6a is equal to the ritial luster length. Measurements of the ritial luster length are listed in Table 3 for eah of the gas injetion experiments. Critial luster lengths range from , and m in the 1.1, 0.7 and 0.5 mm sands, respetively. For omparison, theoretial values of the ritial luster lengths were alulated using (9), where P top and P bottom were estimated aording to the method proposed by Glass et al. [9]. P top was taken to be the apillary pressure at an effetive non-wetting saturation of S enw = 0.3, alulated here using the Brooks-Corey apillary pressure-saturation relationship and parameters reported for main drainage [23], and P bottom was taken to be 1=2P top. Estimates of the ritial luster length from eah of the three sands were fit to a power-law relationship, whih is shown as the solid line in Fig. 8. A value of S enw = 0.3 was seleted by Glass et al. [9] based on the approximate perolation threshold in an unorrelated ubi lattie. However, they found that their estimates were not sensitive to the hoie of S enw, whih was also found here. To illustrate the sensitivity of the theoretial ritial luster length estimates to the hoie of S enw, power-law relationships were also fit to estimates based on S enw = 0.2 and S enw = 0.4 (Fig. 8), and only minor differenes exist. This is expeted for these sands, whih have little variation in pore sizes, and show little hange in apillary pressure with saturation at intermediate saturations. However, the sensitivity is expeted to be greater in less uniform media, and additional investigation is warranted. Critial luster length (m) Measured Theoretial (Senw=0.3) Theoretial (Senw=0.2) Theoretial (Senw=0.4) Median partile diameter (mm) Fig. 8. Measured ritial luster lengths (symbols) for the 1.1, 0.7, and 0.5 mm sand ompared to theoretial estimates (lines) based on Eq. (9), alulated using apillary pressure values at effetive non-wetting saturations of 0.2, 0.3, and 0.4.