Study of Flow Transitions during Air Sparging Using the Geotechnical Centrifuge

Hu, Liming; Meegoda, Jay N.; Li, Hengzhen; Du, Jianting; Gao, Shengyan

doi:10.1061/(ASCE)EE.1943-7870.0000877

Open access

Technical Papers

Aug 1, 2014

Study of Flow Transitions during Air Sparging Using the Geotechnical Centrifuge

Authors: Liming Hu, A.M.ASCE [email protected], Jay N. Meegoda, F.ASCE [email protected], Hengzhen Li, Jianting Du, and Shengyan GaoAuthor Affiliations

Publication: Journal of Environmental Engineering

Volume 141, Issue 1

https://doi.org/10.1061/(ASCE)EE.1943-7870.0000877

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Abstract

Air sparging (AS) is an in-situ groundwater remediation technique for volatile organic compounds (VOCs) in contaminated sites. Knowledge of effect of the injected air on air flow patterns and extent of the zone known as zone of influence (ZOI) is crucial for design of in situ air sparging. The two main objectives of this research are to study transition of air flow patterns and characteristics of ZOI under different air injection pressures during centrifugal tests and to find the scaling factors for centrifugal tests under different gravitational levels (

N

times gravitational force). In this research, the modeling of models test was first performed to validate centrifugal technique for simulating air sparging. Then, a set of two-dimensional (2D) centrifugal modeling tests were performed under various gravitational levels to study the transition of air flow patterns and characteristics of ZOI during air sparging. The centrifugal model tests showed that the observed 2D ZOI was truncated-cone under various gravitational levels. It was also observed that flow pattern for the same soil transits from channel flow under lower gravitational levels to bubble flow under higher gravitational level. If there are same air flow regimes during air sparging tests under varied gravitational levels, then the scaling factor for air sparging is

N

, and a formula was proposed to check the flow regime. In this research, a formula was proposed to explain the transition of air flow patterns during air sparging and determine the boundary of flow regime transition based on grain size and unit-sparging rate.

Introduction

Contaminated soils and groundwater is currently one of the major environmental problems facing the earth. There are many technologies to remediate contaminants in soil and groundwater (U.S. EPA 1995). Air sparging is an in-situ remediation technology where air is injected under pressure into a well installed in the saturated zone beneath the contaminated zone. Air injected below the water table during air sparging volatilizes contaminants dissolved in groundwater. Volatilized contaminants removed during air sparging migrate upward into the vadose zone and are removed using a soil vapor extraction technique. In addition to air stripping, air sparging also promotes biodegradation of organic contaminants by increasing oxygen concentrations in the subsurface. Air sparging systems must be designed with adequate air flow rates and pressures for the effective removal of contaminants from the sites.

The nature and extent of the air pathways determine the zone of influence (ZOI) during air sparging. Two-phase flow in porous media is one of the theoretical models for describing the air sparging process. McCray and Falta (1997) used a multiphase flow model (T2VOC) based on the integrated finite difference method to simulate the air sparging process. McCray (2000) presented a comprehensive review on numerical modeling of air sparging. Several numerical models were employed for air sparging modeling and compared with the experiments data (Mei and Cheng 2002; Jang and Aral 2009; Wang and Hu 2012). Gao et al. (2011, 2012, 2013a, b) proposed a microscopic model to describe air migration behavior during air sparging.

Several laboratory investigations have been conducted to determine the contributing factors and efficiency of air sparging (Ji et al. 1993; Nyer and Suthersan 1993; Johnson et al. 1993; Elder and Benson 1999; Reddy and Adams 2001; Adams and Reddy 2003; Hu and Liu 2008). The efficiency of an in-situ sparging system is controlled by the extent of contact between injected air and contaminated soil or pore fluid. However, most of the experiments were conducted under

1 g

using scaled models, and the in-situ stress state was not simulated. Also only small injection pressure can be applied with

1 g

models to avoid soil failure. The geotechnical centrifugal modeling can be used to simulate the movement and remediation of contaminants under in-situ stress state in both soil mass and interstitial fluid of porous media (Culligan-Hensley and Savvidou 1995). The scaled model is typically constructed in the laboratory and then loaded onto the end of the centrifuge. The purpose of spinning the models on the geotechnical centrifuge is to increase the centrifugal force on the model so that stresses in the model are made equal to stresses in the prototype. A

1 / N

scale model tested at

N

times the gravity because of centrifugal acceleration experiences stress conditions identical to that in the prototype. Soils are compressible, and the hydrogeological properties are affected by in-situ stress. Hence the behavior of a prototype subjected to the earth’s gravity

g

, can be reproduced in the scaled model subjected to a centrifugal force. The centrifuge models provide the unique advantage of testing field soils under exact in-situ stresses and fluid pressures, and can simulate the in-situ pore fluid flow as well as contaminant transport, which one-dimensional (1D) laboratory scale models are incapable of (Culligan-Hensley and Savvidou 1995). Arulanandan et al. (1988) developed scaling laws to be used with the centrifuge in simulating geoenvironmental problems. With the use of scaling laws, the phenomena being observed in the centrifuge can be correlated to the prototype, and centrifuge modeling can be applied in environmental engineering, including contaminants transport, multiphase flow, site remediation, and so on (Soga et al. 2003; Lo and Hu 2004a, b; Lo et al. 2005; Hu et al. 2006a, b; Meegoda and Hu 2011). Some of the scaling factors used during centrifugal tests are listed in Table 1. Recently the centrifuge technique was employed to investigate the mechanism of air sparging (Marulanda et al. 2000; Hu et al. 2010, 2011).

Table 1. Basic Scaling Laws Used in Centrifuge Modeling

Parameter	Scaling law
Gravity ( ${LT}^{- 2}$ )	$N$
Length (L)	$1 / N$
Mass (M)	$1 / N^{3}$
Density ( ${ML}^{- 3}$ )	1
Pressure ( ${MLT}^{- 2}$ )	1
Intrinsic permeability ( $L^{2}$ )	1
Permeability ( ${LT}^{- 1}$ )	$N$
Viscosity ( ${ML}^{- 1} T^{- 1}$ )	1
Time (T)	$1 / N^{2}$

With centrifugal tests, in-situ stress state is always maintained while applying a wide range of air pressures during air sparging. Marulanda et al. (2000) investigated the air flow characteristics through pure fluid and saturated porous media by means of centrifugal tests under a wide range of gravitational accelerations, and the effect of injector geometry on the breakthrough velocity and air plume shape was studied under a specific injection pressure. Hu et al. (2010) investigated the effect of particle size and air injection pressure on size and shape of ZOI using a point sparger, and showed that ZOI can be expressed by two components: the horizontal expansion from preferential intrusion around the injection point and the angle of ZOI, which is the angle between the vertical direction and the boundary of ZOI. The centrifuge investigation by Hu et al. (2011) showed that air mass flow rate increases linearly with the effective sparging pressure ratio, which is the difference between sparging pressure and hydrostatic pressure normalized with respect to the effective overburden pressure at the sparging point. With increasing sparging pressure, the zone of influence will increase in both lateral intrusion and the cone angle until a limited ZOI, which will not expand further.

During all the above centrifugal studies (Marulanda et al. 2000; Hu et al. 2010, 2011), as the flow regimes under different

g

levels changed, however, the scaling factors for the ZOI was not defined. Hence, it is not clear if the test results under different

g

levels are comparable. In order to develop a scaling factor for ZOI, the applicability of centrifugal models to simulate the field air sparging should be carefully checked. The best way to very this would be to simulate actual field test in the centrifuge. This is rather difficult to accomplish unless air sparging test data are available from rather uniform field test sites. The modeling of models technique is an alternative technique to validate centrifuge test results. Arulanandan et al. (1988) showed that if several centrifugal model tests simulating the same prototype can predict similar prototype behavior, then centrifugal tests can be used to simulate that prototype geoenvironmental problem. In addition, during all these centrifugal studies mentioned above, point spargers, which simulate three-dimensional (3D) profiles, were employed; however, while performing result analysis, only two-dimensional (2D) images were captured and analyzed in using narrow or thin centrifugal models. The use of point spargers to observe 2D images introduces errors. Hence 2D spargers should be used to observe 2D images in order to obtain air migration mechanisms during air sparging.

There are two main research objectives of this research: one is to investigate the flow pattern transition during centrifugal tests under different

g

levels, and the other is to study the scaling factor for ZOI during centrifugal tests by considering flow pattern transition both using a 2D or line sparger. To obtain the scaling factor for ZOI and to validate the applicability of using the centrifuge to model air sparging, the modeling of models technique was employed in this research.

Experimental Procedure

Experimental Setup

A centrifuge strongbox was used as a soil container for the centrifugal experiments. The internal dimensions of the strongbox were

600 mm (length) \times 800 mm (height) \times 43 mm (width)

. The strong box was fabricated using Plexiglas to view airflow patterns in soil during testing. A linear air sparger with a length of 43 mm, which was the same as the width of the centrifugal model, was installed at the middle of the strongbox to simulate 2D prototype tests. The 43-mm long line sparger had an aperture width of the sparger that was either 2.0 mm or 1.5 mm depending on the acceleration of the centrifugal test. The sparger was connected to a compressed air supply, which included a compressor, a regulator, a pressure gauge, a flow meter, and a valve. The regulator can alter the air pressure, and a constant air flow rate can be measured using the flow meter. The mass flow rate was computed using the known volume flow rate and the corresponding pressure. Three pore-water pressure transducers (PPTs) were installed at the bottom of the strongbox to monitor water pressure during air sparging. A schematic diagraph for centrifugal testing setup is shown in Fig. 1.

Fig. 1. Testing setup for centrifugal modeling of air sparging

Centrifugal tests were performed at the Tsinghua University geotechnical centrifugal facility. This centrifuge has a radius of 2.5 m and is capable of spinning a maximum payload of 250 kg (model mass). The maximum acceleration that can be applied is 200 times gravitational acceleration. 2D digital images were collected during centrifuge flight by a high resolution charge coupled device (CCD) camera. The data collecting system was mounted in the centrifuge and was transferred to the control room via slip rings.

Testing Materials

The opacity of natural soil prevents the direct observation of air flow patterns during air sparging. Hence in this study, transparent fused silica glass beads, having almost the similar physical properties as sand, were used as a replacement for sand. Water was used as pore fluid. Hu et al. (2010, 2011) showed that air movement in glass beads saturated with water could be adequately captured in flight by a video recorder.

Two types of glass beads, named coarse beads and fine beads, were used for the centrifugal models. The physical properties of the coarse glass beads are as follows: particle size 5.0–6.0 mm; effective size (

d_{10}

) 5.1 mm; coefficient of uniformity (

C u

) 1.10; and coefficient curvature (

C c

) 0.98. The physical properties of the fine glass beads are as follows: particle size 0.8–1.0 mm; effective size (

d_{10}

) 0.82 mm; coefficient of uniformity (

C u

) 1.12; and coefficient curvature (

C c

) 0.98.

Centrifugal Models

The dry pluviation method was adopted to obtain uniform samples (Hu et al. 2010). Then the sample was connected to a water tank allowing the water level to gradually rise and saturate the soil by soaking in water for 12 h before the centrifugal testing. During saturation, the water level was kept at 2 cm above the surface of the soil sample to simulate the constant groundwater level. The height of the glass beads model was 45 cm with a porosity of 0.34 for coarse glass beads and 0.41 for fine glass beads, and test samples were subjected to 5, 10, 15, 20, 30, 40, and 50 gravitational levels.

Additional two centrifugal tests were conducted (20 and 40 gravitational levels) with coarse glass beads to simulate the same prototype obtained from 15 to 30 gravitational levels tests with 45-cm high coarse glass beads models. For those two tests, the aperture width of linear air sparger and sample height were reduced to 1.5 mm and 33.7 cm respectively to produce the same prototype dimensions as the 15 and 30 gravitational level tests of the first test series.

Experiment Procedure

Centrifugal tests were performed under a wide range of sparging pressures and centrifugal gravitational levels for two soil types. The soil model was spun at a desired gravitational level for 30 min for further compaction and homogenization before air sparging tests. The water table was maintained at a constant level during all tests, and pore water pressures were measured using a miniature transducer near the sparger. Then the air pressure was gradually increased in small 5 kPa steps until air was able to be injected into the soil sample. This threshold air pressure was referred to as the minimum sparging pressure. Beyond this pressure level, the sparging pressure increased in 10 kPa steps. For each step, the pressure level was maintained for at least 10 min to stabilize the air flow and to facilitate full development of ZOI. The air flow rate was measured, and the full development of ZOI using a video camera was monitored. The centrifugal tests were terminated when there was no further expansion of the ZOI. The rise of the water level was observed in the centrifugal model during air sparging, which is from the air movement within ZOI. Typical image of the zone of influence in centrifugal model was shown in Fig. 2.

Fig. 2. Typical image of the zone of influence during air sparging in centrifugal model

Experimental Results

Modeling of Model Tests

The modeling of model tests was first performed to validate the applicability of a centrifugal testing technique for air sparging. Arulanandan et al. (1988) provided the scaling laws to be used in predicting prototype behavior. For example depth has a scaling factor of

N

. Hence, a 45-cm high model at a 15 gravitational level would produce a 6.75-m high prototype (

15 \times 45 cm = 6.75 m

). In this research, two prototypes were modeled using centrifugal tests at various gravitational levels.

1.

The first prototype was a 6.75-m high coarse glass beads layer with a 30-mm wide sparger. Two different centrifuge models were run to simulate the same prototype: one was a 45-cm high model with 2-mm wide sparger aperture at a 15 gravitational level, and the other was a 33.7-cm high model with 1.5-mm wide sparger at a 20 gravitational level.

2.

The second prototype was a 13.5-m high coarse glass beads layer with a 60-mm wide linear sparger, which was simulated using two centrifuge models: one is a 45-cm high model with 2-mm wide sparger at a gravitational level of 30 and the other a 33.7-cm high model with 1.5-mm wide sparger with a gravitational level of 40.

As per the test results shown in Table 2, both modeling of model tests produced prototypes with similar sized ZOI and bubble flow, confirming that air sparging tests could be reproduced in a centrifuge with a scaling law of

N

for a centrifugal model simulated at

N

gravitational level.

Table 2. Zone of Influence for Modeling of Model Tests

Model test number	Centrifugal model			Prototype		Effective sparging pressure (kPa)	Cone angle from sparging point (°)	Cone angle (°)	Prototype lateral intrusion (cm)
Model test number	Sparger width (mm)	Sample height (cm)	$g$ level	Sparger width (mm)	Soil mass depth (m)	Effective sparging pressure (kPa)	Cone angle from sparging point (°)	Cone angle (°)	Prototype lateral intrusion (cm)
Test 1	2.0	45	15	30	6.75	160	7.25	7.0	22.5
Test 2	1.5	33.7	20	30	6.75	160	7.25	7.0	28.0
Test 3	2.0	45	30	60	13.5	200	5.75	5.5	30.0
Test 4	1.5	33.7	40	60	13.5	200	6.05	5.8	36.0

The effective sparging pressure, which is defined as the air injection pressure subtracting the corresponding hydrostatic pressure, is used to study the correlation between air flow rate and air injection pressure under different gravitational levels. Table 3 lists the minimum effective entry air pressures. Although the entry pressure increased with the increase in centrifugal gravitational level, the minimum effective entry air pressure did not change with the centrifugal gravitational level. Hence it can be stated that minimum effective entry air pressure only depends on soil properties, such as the grain size distribution and the pore network structure. The relationship between air mass flow rate per unit width and effective sparging pressure for four modeling of model tests is shown in Fig. 3. From Fig. 3 one can observe that for the same prototype, the variation of air mass flow rate per unit width with effective sparging pressure for different model tests are similar. In the following sections, the air flow rate, characteristics of ZOI, and air flow patterns and air flow pattern transition are further investigated and discussed.

Table 3. Minimum Injection Pressure and Zone of Influence for Air Sparging with Various

g

Levels

Particle size	$g$ level	Sample height (cm)	Minimum effective AS pressure $P_{min}$ (kPa)	Cone angle (°)	Length of lateral intrusion (cm)	Cone angle from sparging point (°)
Coarse	1	45	0.1	12.0	2.0	14.4
Coarse	5	45	6.3	8.5	1.9	10.9
Coarse	10	45	7.3	7.5	1.5	9.4
Coarse	15	45	6.0	7.0	1.5	8.9
Coarse	20	45	6.4	6.5	1.2	8.0
Coarse	30	45	8.5	5.5	1.0	6.8
Coarse	40	45	7.6	5.0	0.5	5.6
Coarse	50	45	10.5	5.0	0.3	5.4
Fine	1	45	0.9	17.0	4.4	22.0
Fine	5	45	7.5	16.5	2.5	19.4
Fine	10	45	7.6	10.0	2.1	12.6
Fine	15	45	6.8	9.5	1.5	11.3
Fine	20	45	7.0	8.0	1.4	9.7
Fine	30	45	8.2	6.0	1.3	7.6
Fine	40	45	9.0	5.5	0.7	6.4
Fine	50	45	10.8	4.0	0.7	4.9

Fig. 3. Relationship between air mass flow rate per unit width and effective sparging pressure for modeling of model tests

Air Flow Rate during Centrifugal Tests

The stable air sparging was obtained when a constant air flow rate occurred under a given sparging pressure. The effective sparging pressure and corresponding air mass flow rate

Q

were monitored during stable air sparging, and the relationship was shown in Fig. 4. The air mass flow rate

Q

increased with the increase in injection pressure for all tests. Initially with the increase of air pressure, increase of flow rate was due to the pressure gradient and the apparent expansion of ZOI. Then the ZOI reached its maximum size, and the pressure gradient became the only contributing factor for air flow rate. Therefore, the slope of air mass flow rate to effective sparging pressure was larger at the early stage during the increase of injection pressure and leveled off after full development of the ZOI.

Fig. 4. Relationship between air mass flow rate and effective sparging pressure for coarse glass beads

Development of the ZOI with Increase of Sparging Pressure

The captured camera images show that the observed shape of 2D ZOI was a truncated cone. However, the camera images obtained during this 2D test are much sharper than those reported by Hu et al. (2010, 2011) using a point sparger. Fig. 5 shows a selected stable ZOI boundary for different gravitational levels under similar normalized effective sparging pressure. For the data shown in Fig. 5, the normalized effective sparging pressure was chosen as 0.5 for all gravitational level tests. The test results showed that for the same normalized effective sparging pressure, the shapes of ZOI are quite similar for different gravitational levels. Fig. 6 shows that the cone angle increased with the increase of air sparging pressure and reached a stable value of around 7° for the model with coarse glass beads. The ZOI expanded with the increase in injection air pressure when the sparging pressure was low. Hu et al. (2010) reported that ZOI contains two components: the lateral expansion due to pneumatic fracturing or preferential intrusion around the injection port and the cone angle between the vertical direction and boundary of ZOI, and this conclusion was confirmed by results from this research. The increase in air pressure produced well-developed air pathways. However, with the increase of the sparging pressure, the cone angle rapidly reached a limiting value, and thereafter the lateral expansion was the main contributor to the expansion of the ZOI.

Fig. 5. Selected stable ZOI boundary under normalized effective sparging pressure of 0.5 for different gravitational levels tests

Fig. 6. Variation of ZOI angle with increase of effective sparging pressure ratio for different gravitational levels for coarse beads model

Table 3 summarizes the ultimate boundaries of ZOI under various gravitational levels of centrifuge tests for the fine glass beads for both coarse beads and fine beads. According to Table 3, the ZOI decreased as the centrifugal gravitational levels increased. It can be further observed that for 1 and 5 gravitational levels tests for fine glass beads, the cone angle values were similar but much higher than that for

10 g

tests because of different air flow patterns. This observation will be discussed later in this manuscript. Please note that previous researchers have defined the ZOI as a cone, and the slope of the sparging angle as the slope of the line connecting the sparging point to the edge of the ZOI based on

1 g

tests (Reddy and Adams 2008). Hence the reported angles of the ZOI values in Table 3 are much smaller than previously reported values for similar soil types.

Air Flow Pattern Transition

Bubble flow patterns were observed in all centrifugal tests with coarse glass beads. In centrifugal tests with fine glass beads, both channel and bubble flows were observed. Air flowed through microchannels in 5 gravitational level centrifugal tests with fine glass beads, whereas those for 10 and higher gravitational levels tests bubble flow was observed. In the following part, the air flow pattern transition is discussed.

When the air sparging is initiated, the air bubbles are formed at the sparging point, and they enter the soil matrix. The minimum sparging or injection pressure

P_{min}

is calculated by the balancing force from injection pressure by that due to surface tension as given below (Marulanda et al. 2000)

P_{\min} = P_{hyd} + P_{cap} = ρ g h_{w} + \frac{4 σ \cos θ}{D}

(1)

Where

P_{hyd}

is hydrostatic pressure at the sparging point,

P_{cap}

is the capillary pressure for the soil,

σ

is the interfacial tension between air and the pore water that is

0.074 N / m

at 20°C,

ρ

is the density of the pore water,

h_{w}

is the height of the water table above the sparge point,

θ

is the contact angle that was assumed equal to zero for complete wetting, and

D

is the average pore size diameter assumed as

d_{10} / 5

. Once an air bubble is formed, it is moved into the path of least resistance from the pressure gradient created by the sparging pressure. Hence, depending on the inclination of injection port and the hydraulic conductivity tensor of the pore structure, air bubbles can move both vertically as well as laterally due to anisotropy (Meegoda et al. 1989).

Selker et al. (2007) proposed that during air sparging tests, the zone of influence can be separated into two regions: one is around the air sparger called near source region whereas the other one is far from the air sparger called far source region. The main characteristic of air driven mode in the near source region distinguishes from that in far source region is the driving force of air flow. Within near source region, air is primarily driven by gradients of air pressure whereas in far source region, the buoyant force is the main driving force for the air phase. In the far source region, the bubble movement is governed by the following three forces, including the surface tension force (

π D σ \cos θ

), buoyant force [

π D^{3} g (ρ - ρ_{a}) / 6

], and frictional or Stokes force (

3 π D μ v

), where

ρ_{a}

is the air density, which is approximately zero,

μ

is absolute viscosity which in

0.001 Pa \cdot s

, and

v

is the bubble velocity that varied from 30 to

200 cm / s

for all tests. Please note that the two pore diameters (

D_{10} / 5

) for fine and coarse glass beads are 0.164 mm and 1.02 mm, respectively. When the numerical values of three forces are calcuated for fine glass beads, it was found that buoyant force was at least two orders of magnitude smaller than other two forces for 1 gravitational level test. However, with higer gravitational levels, magnitude of buoyant force becomes comparable with the other two forces. Under such situations, bubble flow occurs. Under low gravitational levels, bubbles collapse into the channel flow, so that a buoyant force of combined tube shape bubbles in the channel becomes comparable with the other two forces that cause the tube shape bubbles to rise. The low cone angles observed in this research for high gravitational levels suggest that there was bubble flow in both fine and coarse glass bead samples. This observation also suggests that in order to apply the scaling law of

N

, particle size should also be modeled. However, this requirement could be avoided if flow regimes of both prototype and the model are similar. This can be achieved by equating the buoyant force to surface tension force and computing a test diameter

[D_{test} = {(6 σ / ρ N g)}^{0.5}]

. All the test diameter values in all tests conducted in this research are listed in Table 4.

Table 4. Test Diameters of All Tests

Particle size	$g$ level	$D_{test} = {(6 σ / ρ N g)}^{0.5}$ (mm)	Pore diameter ( $d_{10} / 5$ ) (mm)	Ratio of test diameter to pore diameter
Coarse	1	6.73	1.02	7
Coarse	5	3.01	1.02	3
Coarse	10	2.13	1.02	2
Coarse	15	1.74	1.02	2
Coarse	20	1.51	1.02	1
Coarse	30	1.23	1.02	1
Coarse	40	1.06	1.02	1
Coarse	50	0.95	1.02	1
Fine	1	6.73	0.16	42
Fine	5	3.01	0.16	19
Fine	10	2.13	0.16	13
Fine	15	1.74	0.16	11
Fine	20	1.51	0.16	9
Fine	30	1.23	0.16	8
Fine	40	1.06	0.16	7
Fine	50	0.95	0.16	6

The relationship between the ratio of test diameter and the pore diameter and cone angle is drawn in Fig. 7. From Fig. 7 and Table 4, it can be observed that for the fine glass beads, the ratio of test diameter to pore diameter sharply changed from 19 (for

5 g

centrifugal test) to 13 (

10 g

centrifugal test), which indicates an air pattern transition from bubble flow under higher gravitation levels to channel flow of the ZOI under lower gravitational level. Hence, one could estimate the critical value of the ratio of test diameter to pore diameter (

D_{test} / D

) where a transition from bubble to channel flow occurs. Based on Fig. 7, it can be concluded that if the

D_{test} / D

value is greater than about 19, channel flow would occur. Also a

D_{test} / D

value less than 4 would gurarantee stable bubble flow pattern irrespective of the soil particle size. Hence, with the above information, centrifuge modeling can be used as a design tool for remediating contaminated soils used in-situ sparging eliminating the need for expensive pilot tests. However, the soil heterogeneity plays a significant role in ZOI dimensions, so the pilot tests are still recommended for air sparging system design sites with heterogeneous soil deposits. Based on the above discussion, the observation from Fig. 7 and Table 3 is consisent with the conclusion that the cone angle of the ZOI is much higher for channel flow than that for bubble flow.

Fig. 7. Relationship between ratio of test diameter to pore diameter and cone angle

In this research, the centrifugal tests under different gravitational levels were performed to investigate air flow pattern transition during centrifugal tests. It was found that in the centrifugal tests, air migrates in the form of discrete bubble instead of air channel at high gravitational levels. A test diameter

[D_{test} = {(6 σ / ρ N g)}^{0.5}]

was computed by equating the buoyant force to surface tension force. The ratio of test diameter to pore diameter can help inferring the flow regimes.

Similarly, Geistlinger et al. (2006) proposed a flow rate and grain-size dependent stability criterion based on constricted capillary tube model. They used carefully conducted experimental data from Brooks et al. (1999) with a wide range of grain sizes and air flow rates. The air flow rate depends on the size of the sparger. Hence, the variation of air flow rate per unit area values with grain-size from this research as well as from Brooks et al. (1999) were plotted in Fig. 8. For the centrifugal test data, the grain size is multiplied by the gravitational level to theoretically account for the increased gravity in the centrifuge. Please note that only confirmed bubble and channel flow data from the centrifugal tests were included in Fig. 8. Fig. 8 shows there is a clear boundary from bubble flow to channel flow and that boundary is a straight line, which can be described as

q = 0.2 \cdot D^{4}

(2)

where

q

= air flow rate per unit area in

{ml / \min / mm}^{2}

, and

D

= grain size in mm.

Fig. 8. Classification of channel flow and bubble flow

Based on the reported results shown in Fig. 8, if the Poiseuille equation is used to back calculate the air flow rate assuming an average air channel diameter of around

D / 4

, one would obtain Eq. (2). Hence, based on Fig. 8 and Eq. (2), it can be concluded that the initiation of channel flow in a soil mass subjected to air sparging may be described using Poiseuille equation. The above finding is very preliminary and should be confirmed by carefully conducted micro mechanics research program (Gao et al. 2011, 2012, 2013a, b). Also, previous researchers were not able to obtain channel flow patterns for grain diameters larger than 4 mm. However, based on Fig. 8 with centrifugal tests, there should not be such limitation. Channel flow requires higher pressure-gradients than that for bubble flows for any grain size. Based on results from Brooks et al. (1999), the maximum gradient that could be applied to soil is around 3.0 without causing soil liquefaction. Based on Eq. (2), this would occur around grain diameter of 4 mm, making it impossible to have channeled flows for grain diameters larger than 4 mm for small-scale laboratory tests conducted under regular gravitational levels. However, with the centrifugal tests, there is no such limitation, and Eq. (2) is valid for all grain sizes.

Summary and Conclusions

The modeling of model tests was first performed to validate the applicability of centrifugal tests to model air migration through saturated soils during air sparging, and confirmed that air sparging tests could be simulated using the centrifuge. Then a series of 2D centrifugal model tests were performed under various gravitational levels to study air flow patterns transition under prototype stresses and with a wide range of air injection pressures. The following conclusions can be drawn from this research:

•

The observed 2D ZOI was a truncated cone under various gravitational levels, and ZOI under low gravitational level is always larger than that under high gravitational level. In addition, the observed cone angle of the ZOI is much higher for channel flow, when compared with that for bubble flow.

•

For the same normalized effective air sparging pressure at the injection port, sizes of the 2D ZOI under different gravitational levels are quite similar.

•

The research confirmed that the scaling factor for air mass flow during air sparging is

N

, if there are similar air flow regimes during air sparging tests under varied gravitational levels.

•

It was observed that flow pattern for the same soil changed from channel flow under lower gravitational levels to bubble flow under higher gravitational levels. In order to make the centrifugal tests results under varied gravitational levels comparable, soil should be selected such that its size is scaled by

N

. This requirement of scaling of particles could be avoided by ensuring similar air flow regimes during air sparging modeling tests under varied gravitational levels. A test diameter [

D_{test} = {(6 σ / ρ N g)}^{0.5}

] was computed by equating the buoyant force to surface tension force. The ratio of test diameter to pore diameter can help inferring the flow regimes. Based on the test results, if the ratio of test diameter to pore diameter was greater than about 15, one would expect channel flow. Stable bubble flow patterns would occur irrespective of the soil particle size if the ratio of test diameter to pore diameter (

D_{test} / D

) is less than 4.

•

The flow rate per unit area versus grain size data were plotted using centrifugal test results from this research as well as those from

1 g

test with either clear bubble flow or channel flows. There is a clear demarcation between bubble flow and channel flow. The air flow pattern transition can be predicted using Poiseuille equation.

Acknowledgments

The financial support from State Key Laboratory of Hydro Science and Engineering (SKLHSE-2012-KY-01, SKLHSE-2013-D-01), National Key Basic Research Program (2012CB719804), and National Natural Science Foundation of China (Project No. 51323014, 41372352, 50879038) are gratefully acknowledged.

References

Adams, J. A., and Reddy, K. R. (2003). “Extent of benzene biodegradation in saturated soil columns during air sparging.” Ground Water Monit. Rem., 23(3), 85–94.

Abstract

Introduction

Experimental Procedure

Experimental Setup

Testing Materials

Centrifugal Models

Experiment Procedure

Experimental Results

Modeling of Model Tests

Air Flow Rate during Centrifugal Tests

Development of the ZOI with Increase of Sparging Pressure

Air Flow Pattern Transition

Summary and Conclusions

Acknowledgments

References

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