Roadway Tunnel Air Quality Models - ACS Publications - American

The air quality management of roadway tunnels (or buried roadways) is an important task; that is, in roadway tunnels, either natural or mechanical ven...
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Environ. Sci. Technol. 1990, 24, 672-676

Roadway Tunnel Air Quality Models Tal Y. Chang' and Sara J. Rudy

Research Staff, Ford Motor Company, P.O. Box 2053, Dearborn, Michigan 48121 Quasi-steady-state, analytic air quality models for various types of roadway tunnels are presented. These models can be used to estimate the concentrations of pollutants in roadway tunnels and to determine vehicular emission rates. These models are used to evaluate formaldehyde concentrations resulting from the emissions of methanol-fueled vehicles. It is shown that, within the expected emission rates of methanol-fueled vehicles, formaldehyde concentrations in roadway tunnels are not likely to be a health concern for the general public. One possible exception is during heavily congested traffic conditions; during these conditions, formaldehyde concentrations may result in eye irritation for sensitive individuals.

Introduction The air quality management of roadway tunnels (or buried roadways) is an important task; that is, in roadway tunnels, either natural or mechanical ventilation is required to keep air quality within acceptable levels for pollutants such as CO and particulates (1). Furthermore, pollutant measurements in roadway tunnels are used to derive vehicular emission factors for particulates (ref 2 and references therein) and gaseous species (ref 3 and references therein). For these purposes, appropriate tunnel air quality models are needed. An extensive study of air quality management of highway tunnels has been performed by Schlaug and Carlin ( 4 ) for the U.S. Federal Highway Administration. This study identified factors affecting aerodynamic flow and air quality in highway tunnels and developed a model for calculating quasi-steady-state longitudinal air velocities and pollutant concentrations. From this study the TU" computer model was developed (5). Although the TUN" model is very useful for detailed evaluation of air quality in tunnels, it requires extensive input data. Some limited analytic tunnel air quality models have also been developed (1, 6 ) . Methanol-fueled vehicles are getting increasing attention because of the potential reduction in urban ozone levels as a result of methanol-fueled vehicle usage. However, high levels of formaldehyde in roadway tunnels resulting from a wide usage of methanol-fueled vehicles is a possible concern. Methanol-fueled vehicles emit more formaldehyde than gasoline-fueled vehicles (7, 8), and formaldehyde at high levels is an irritant and a health concern. Recent formaldehyde air quality evaluations (7, 9) in roadway tunnels have been based on a simple box model suggested by Ingalls (10). In this paper, several analytic air quality models for roadway tunnels are developed. These simplified models are useful for evaluating the main features of air quality in roadway tunnels and are sufficient for determining pollutant levels or vehicular emission rates in roadway tunnels for most practical purposes. These models are applied to possible formaldehyde levels resulting from methanol-fueled vehicle usage. Mathematical Formulation Air pollutant levels in highway tunnels are governed mainly by tunnel characteristics (tunnel dimensions and 672

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surrounding conditions), traffic volume and type, traffic direction (one way or two way), and type of ventilation. The ventilation system is usually the most important means of air quality management. The most commonly used ventilation systems, shown in Figure 1, can be grouped into the following (1,4, 10): natural (including the vehicle piston effect), longitudinal, semitransverse, and fully transverse. In most cases, the length of the tunnel determines the type of ventilation system employed. Air flows in roadway tunnels are shown to be predominantly longitudinal, with random fluctuations caused by the turbulent nature of the flow and local transient fluctuations associated with the passage of vehicles, and can be assumed to be in the quasi-steady state (1,4). Consequently, pollutant concentrations show a primarily longitudinal dependence. In the present paper, a one-dimensional form of the steady transport equation for pollutant concentrations is assumed. It is also assumed that the vehicular emission rate and mechanical ventilation rate along a tunnel (taken to be the x axis) are constant. (If a tunnel has a number of different sections with different mechanical ventilation rates, each section can be treated separately.) A tunnel with longitudinal ventilation can be treated mathematically by the same formulation as one with natural ventilation. Consider a tunnel of length L (m) with an effective cross-sectional area A (m2). Under the above assumptions, the pollutant concentration C(x) (in mg m-3) satisfies the following one-dimensional steady-state mass-balance equation: d(uC)/dx

q

+ C Y ~-CCY,C ~ - kC

(1)

where u (m min-') is the mean air flow velocity, q (mg min-l m-3) is the vehicular source strength, ai (mix') and CY, (min-') are inflow and outflow rates from the ventilation system, Ci (mg m-3) is the pollutant concentration in the inlet ventilation air, and k (min-') is the deposition rate. Chemical reactions have been neglected in eq 1. The vehicular source strength, q, is given by q = ne/A

(2)

where n (vehicle min-') is the traffic volume and e (mg m-l vehicle-') is the average per-vehicle emission rate. The traffic density, D (vehicle m-l), is related to the traffic volume, n, and average vehicular speed, u (m min-l), by

D = n/u

(3)

and the total number of vehicles, N , in a tunnel is given by N = DL = nL/u (4) The ventilation rates CY, and CY, are related to the volumetric flow rates by

Ri/AL; CY, = R,/AL (5) where Ri (m3min-') and R, (m3min-') are total volumetric flow rates of inlet and outlet ventilation to the tunnel. The deposition rate can be expressed as k = uP/A (6) LY~ =

where u (m min-') is the deposition velocity and P (m) is

00 13-936X/90/0924-0672$02.50/0

0 1990 American Chemical Society

u(x) = u, = u,

(84

Natural

(b) For inflow semitransverse ventilation, ai # 0 and a, = 0.

++

+ (c,-

C(X) = qk aici ai

-)(

1

+

z)

-(k+ai)/ai

(1lb) (c) For outflow semitransverse ventilation, ai = 0 and a, f 0,

+ (c, -

C(X) = ! k!

;)(

)I:

11 -

klao

(llc)

(d) For outflow semitransverse ventilation and k = 0, Transverse

L

dem

r

It is noted that the pollutant concentration C(x,) at the stagnation point ( x , = u,/a, uo/a,+ L / 2 < L)may be very high. Consequently, outflow semitransverse ventilation systems are rare compared to inflow systems. (e) For natural ventilation, ai = a, = 0,

Semi-Transverse

Figure 1. Schematics for types of tunnel ventilation systems: natural, longitudinal, transverse, and semitransverse. Arrows represent air Row.

the (effective) perimeter of the tunnel. The mean air flow velocity, u, is found from the equation of continuity du/dx = ai - a, (7) Since it is assumed that ai and a, are independent of x , eq 7 yields u ( x ) = u, + (ai - a,)x (8) where u, (m min-’) is the velocity at x = 0 (one end of tunnel, taken to be the entrance portal for one-way traffic). When ai = a, = 0 (natural ventilation) or ai = a, (balanced transverse ventilation), u, reduces to u, (m min-l) which is the velocity resulting from natural ventilation (including the piston effect of traffic flow). Schlaug et al. ( I , 4 ) considered general cases to derive u, and u numerically. These flow velocities are generally complex functions of traffic flow, ventilation system, and tunnel characteristics. However, u, is approximated for many situations as ( I , 4 ) u, = u, - (ai - a,)L/2 (9) It is noted that the entrance velocity, u,, can be negative for the case of ai > a,,that is, u(x) can have a stagnation point (u = 0 at x = xJ. First, cases with u, > 0 are considered. Substitution of eq 8 into eq 1 yields udC/dx = q aiCi - kC - aiC (10)

+

The solution of eq 10 is

(11) where C, (mg m-3) is the pollutant concentration at x = 0 and u is given by eq 8. The following special cases can be considered from the general solution: (a) For balanced transverse ventilation, ai= a. = a,

(f) For natural ventilation and k = 0, qx C(x) = c, + UO

Some of the above cases without the deposition have been studied by Schlaug et al. (1)and eq l l b has been derived and applied previously (6, 11). Next, cases with a negative entrance velocity (u, I0) are considered. These cases can arise only when ai- a, 2 0, including inflow semitransverse ventilation systems, and there is a stagnation point (u = 0 at x = xs). For these “overdriven” cases ( 4 ) , the solution of eq 10 with finite values of C ( x ) along the tunnel is C ( X )= ( 4 aiCi)/(k ai) (12) This can also be seen from eq 11 by choosing a new coordinate origin ( x ’ = 0 ) to be at x , and putting u, 0. Here the concentration is the same everywhere along the tunnel (independent of x ) and independent of a,,. (In real tunnels, concentrations will vary somewhat along the tunnel because the emission sources and air flow will vary somewhat along the tunnel.) These cases include the following: overdriven, inflow semitransverse ventilation systems (ai # 0 and a, = 0); balanced, transverse ventilation systems (ai= a, = a)with u, = 0 (no natural ventilation and no piston effect). For balanced two-way traffic flows, there will be essentially no piston effect, i.e., u, N 0; consequently, semitransverse and balanced transverse ventilation systems with ai = a will provide the same concentration levels. For one-way traffic flows, there are always piston effects for balanced transverse ventilation (u, > 0) and the concentration is given by eq l l a . Obviously, the concentrations given by eq l l a are always lower than those given by eq 12 with ai = a except for unusual cases of C, > ( q + a C i ) / ( k + a).

+

+

-

Application In general, natural ventilation is used in commuter tunnels under 300 m long, longitudinal ventilation for tunnels up to 600 m long, semitransverse for tunnels up Environ. Sci. Technol., Vol. 24, No. 5, 1990 673

Table I. Simulation Conditions for Roadway Tunnels (One Way, Two Lanes per Tube) natural (typicaljsevere) length, L (m) cross-sectional area, A (m2) perimeter, P (m) natural flow velocity, uo (m 9-l) inlet ventilation rate, ai( m i d ) outlet ventilation rate, a0 (min-') concentration in inlet air, Ci(pg m-3) concentration at entrance, C, (pg m-3) traffic volume, n (vehicles h-l) vehicle speed, u (km h-l) vehicle emission factor (mg kg-')

300 45 30 411

1000 45 30 411 0.310.2

2.515.0 3.717.4 200011500 6418 10140

2.515.0 3.7 17 .4 2000/1500 6418 10140

to 1500 m long, and transverse for tunnels longer than 1500 m (1, 10). In the present paper commuter tunnels with two lanes per tube are considered. Two cases of typical and congested vehicular traffic with median vehicular speeds of 64 km h-' (40 mph) and 8 km h-l (5 mph) are emphasized ( 4 ) . Input data for base computations of formaldehyde concentrations are listed in Table I for tunnels with two lanes per tube and one-way traffic. Natural air flow velocities are chosen to be 4 and l m s-l for typical and severe (congested) traffic conditions based on observed values (4, 6, 11)and modeling results (4). Maximum ventilation rates for commuter tunnels are quite variable. Ventilation rates given in Table I are chosen based on maximum ventilation rates for some roadway tunnels in the United States (10). For the typical case, an average maximum ventilation rate is used; for the severe case, a lower ventilation rate is chosen. It is noted that formaldehyde concentrations in the inlet ventilation air and the entrance portal air will be highly variable, depending upon the tunnel location and meteorological conditions. For formaldehyde, the indoor deposition velocity was derived to be 0.005 f 0.003 cm s-l based on analysis of the concentration decay rate from a gas-stove emission experiment in a test room (12). In a tunnel experiment, the deposition velocity for SO2 was estimated to be 0.07 cm s-l (6). Since tunnel walls are likely to be much wetter than indoor test rooms and formaldehyde is highly soluble in water, the deposition velocity for formaldehyde is taken to be 0.05 cm s-l. With u = 0.05 cm s-l, P = 30 m, and A = 45 m2, the deposition rate, lz, is 0.02 m i d from eq 6, which is compared to ventilation rates, 0.20-0.40 min-'. Thus, for formaldehyde, the deposition rate is likely to be nonnegligible. In order to show overall characteristics of pollutant concentrations in tunnels using various types of ventilation systems, concentrations resulting from vehicular sources in tunnels are evaluated for typical and severe one-way traffic conditions. For this purpose, it is chosen for all tunnels: length, L = 1000 m; and Ci = Co = 0. All other input variables are taken from Table I. Concentrations vs the distance from the entrance portal are shown in Figure 2a for typical conditions and in Figure 2b for severe conditions. Here five situations, natural, k = 0; natural, k # 0; inflow semitransverse; outflow semitransverse; and balanced transverse ventilation, are considered. For typical conditions all five cases reveal similar concentration levels up to 500 m from the entrance portal, but significantly different concentrations result for distances longer than 500 m. For severe conditions, there exists a stagnation point for inflow and outflow semitransverse ventilation tunnels. Equation 12 (not eq l l b ) holds for the inflow semitransverse case; consequently, concentrations along the tunnel 674

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semitransverse (typical /severe)

balanced transverse (typical/severe) 2000 45 30 41 1 0.310.2 0.310.2 2.5 j5.0 3.717.4 2OdO / 1500 6418 10140

HCHO h/fi)

" 0

200

400

600

800

1000

Distance (m) HCHO h o l m 3 )

1000800

r

Outflow

600 r

0

200

400

600

800

' 1000

Distance (m)

- -Natural

Semi-transverse

-Balanced Transverse

Figure 2. Characteristicsof formaldehyde concentrationvs distance through the tunnel by type of ventilation system. For all tunnels, L = 1000 m and C, = C, = 0. Other input values are taken from Table I. (a) typical conditions; (b) severe conditions.

are constant (in real tunnels there will be some variations of concentrations). For the outflow semitransverse case (eq llc), the maximum concentration at the stagnation point is given by q l k as shown in Figure 2b. (Although the peak at the stagnation point in Figure 2b is sharp, the peak in real tunnels will be broadened because of fluctuations of air flow velocity and turbulence due to traffic.) For distances longer than -500 m, concentration levels for balanced transverse and inflow semitransverse ventilation tunnels are much lower than natural and outflow semitransverse ventilation tunnels. I t is also noted that there are concentration differences between cases of k = 0 (deposition neglected) and k # 0. By use of input values of Table I, formaldehyde concentrations are calculated as a function of the distance from the entrance portal under typical and severe one-way traffic conditions. Results are plotted in Figure 3. Here natural, inflow semitransverse, and balanced transverse ventilation tunnels are considered including the deposition of formaldehyde on surfaces ( u = 0.05 cm s-*). Maximum

80

I Typical Case

0

200

400

600

800

1000 1200 1400 1600 1800 2000

Distance (m)

- - -Natural

-Balanced Transverse Figure 3. Formaldehyde concentration vs distance through the tunnel for natural, inflow semitransverse, and balanced transverse ventilation systems. input values in Table I are used. Semi-transverse

HCHO @elm?

-I

300 250 200 -

Severe Case

150 100 -

0

10

20

30

40

50

60

70

80

90

100

Emission Factor (mg/km)

- - Natural

Semi-transverse

-Balanced Transverse

Figure 4. Maximum formaldehyde concentrationvs vehicle emission factor for typical and severe conditions Except for emission factors, input values in Table I are used. For the severe case,inflow semitransverse and balanced transverse tunnels result in equal maximum concentrations.

concentrations for all three ventilation systems are quite comparable. As expected, much higher maximum concentrations are obtained under severe conditions. From eqs 11and 12, it is noted that concentrations are linear functions of vehicular emission factors. By use of input values of Table I, but varying emission factors, maximum concentrations under typical and severe one-way traffic conditions are calculated and the results are plotted in Figure 4. For the typical case, the balanced transverse ventilation tunnel ( L = 2000 m) has the highest maximum concentration and the inflow semitransverse ventilation tunnel ( L = 1000 m) has a lower maximum concentration compared to the balanced transverse ventilation tunnel, but a higher maximum concentration compared to the natural ventilation tunnel ( L = 300 m). Differences increase as the emission rate increases. For the severe case, balanced transverse and inflow semitransverse ventilation tunnels have equal maximum concentrations, and these tunnels have lower maximum concentrations than the natural ventilation tunnel. For the severe case, maximum concentration differences among tunnels are relatively small under the simulation conditions. So far one-way traffic tunnels have been considered. For two-way traffic tunnels, the vehicular piston effect will be reduced significantly. Particularly, the piston effect disappears under balanced two-way traffic conditions. As a result, two-way traffic tunnels will observe higher pollutant concentrations under the same tunnel conditions.

Discussion Quasi-steady-state, analytic air quality models for var-

ious types of roadway tunnels have been derived. These simplified models are useful for evaluating air quality in roadway tunnels and for determining vehicular emission rates in roadway tunnels for most operating conditions. The derived models have been applied to the evaluation of possible formaldehyde concentrations resulting from emissions of methanol-fueled vehicles. It is also shown that the tunnel wall deposition of formaldehyde is likely to be important. It is noted that the derived models can be applied to other vehicular pollutants such as methanol from methanol-fueled vehicles and CO. The effect of chemical reactions (13) has not been included in the present study since the residence time of air in tunnels is short compared to typical reaction times of many pollutants. In cases where chemical reaction times are comparable to or shorter than the residence time of air in a tunnel, e.g., the reaction of O3 NO, consequences of chemical reactions have to be considered or reactive models (13) have to be used. In the present paper, derived air quality models have been applied to estimate pollutant concentrations in roadway tunnels. These models, eqs 11-12, can be used to derive vehicular emission rates once pollutant concentrations, ventilation rates, air flow velocities, and traffic conditions are measured. Parts b, e, and f of eq 11have been used to derive vehicular emission rates previously (2, 3, 6, 11). Gold and Moulis (9) reviewed emission measurements of current-technology methanol-fueled vehicles and derived an average formaldehyde emission rate of 110 mg mi-' for in-use, current-technology methanol-fueled vehicles. Future methanol-fueled vehicles will have much lower formaldehyde emission rates than current ones as advanced emission technologies are implemented. In March 1989, the California Air Resources Board adopted a 15 mg mi-' (24 mg km-') formaldehyde emission standard for lightduty methanol-fueled vehicles to be effective for the 1993 and later model years. At this time the U.S. Environmental Protection Agency (EPA) chose not to adopt a separate formaldehyde emission standard for methanolfueled vehicles (14). The emission standard is based on the Federal Test Procedure (15). Vehicular emission rates are sensitive to driving modes, vehicular speed, and coldstart percentages. In roadway tunnels, vehicles are in cruising modes for most driving situations. Formaldehyde emission rates in Table I were chosen for possible future emission rates for methanol-fueled vehicles in roadway tunnels. The U.S. EPA proposed the level of concern for formaldehyde to be 500 pg m-3 (14). Exposure at this level may cause irritation for most individuals. There is a fraction of the population sensitive to formaldehydeconcentrations as low as 50-100 pg m-3 (9). The present evaluation shows that formaldehyde concentrations in roadway tunnels resulting from emissions of methanol-fueled vehicles are unlikely to be above 500 pg m-3, but could be high enough to be of concern to the sensitive fraction of the population under congested traffic conditions (see Figures 3 and 4). A further analysis of possible formaldehyde exposures in microscale situations such as roadway tunnels, garages, and street canyons using emissions data collected for advanced technology vehicles will be reported at a later date.

+

Registry No. Methanol, 67-56-1; formaldehyde, 50-00-0.

Literature Cited (1) Schlaug, R. N.; Teuscher, L. H.; Newmark, P. Management of Air Quality in and near Highway Tunnels. NTIS No. PB80-140007; Report No. FHWA-RD-78-184; Federal Highway Administration, Washington, DC, 1980. Environ. Sci. Technol., Vol. 24, No. 5, 1990

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Pierson, W. R.; Brachaczek, W. W. Enuiron. Sci. Technol. 1983, 17, 757-760. Gorse, R. A., Jr. Enoiron. Sci. Technol. 1984, 18, 500-507. Schlaug, R. N.; Carlin, T. J. Aerodynamicsand Air Quality Management of Highway Tunnels. NTIS No. PB80-143803; Report No. FHWA-RD-78-185;Federal Highway . Administiation, Washington, DC, 1979. Schlaug, R. N. Users Guide for the TUNVEN and DUCT Programs. NTIS No. PB80-141575;Report No. FHWARD-78-187;Federal Highway Administration,Washington, DC, 1980. Chang, T. Y.; Modzelewski,S. W.; Norbeck, J. M.; Pierson, W. R. Atmos. Enuiron. 1981, 15, 1011-1016. Regulatory Support Document Proposed Organic Emission Standards and Test Procedures for 1988 and Later Methanol Vehicle and Engine. U S . EPA Office of Mobile Sources, Ann Arbor, MI, 1986. Nichols, R. J.; Clinton, E. L.; King, E. T.; Smith, C. S.; Wineland, R. J. A View of Flexible Fuel Vehicle Aldehyde Emissions. SAE Paper 881200; Society of Automotive Engineers, Inc., 400 Commonwealth Dr., Warrendale, PA, 1988.

(9) Gold, M. D.; Moulis, C. E. Effects of Emission Standards on Methanol Vehicle-Related Ozone, Formaldehyde and Methanol Exposure. APCA Paper No. 88-41.4; Pittsburgh, PA, 1988. (10) Ingalls, M. N. Estimating Mobile Source Pollutants in

Microscale Exposure Situations. EPA-460/3-81-021;U.S. EPA, Ann Arbor, MI, 1981. Ingalls, M. N.; Garbe, R. J. Ambient Pollutant Concentrations from Mobile Sources in Microscale Situations. SAE Paper 820787; Society of Automotive Engineers, Inc., 400 Commonwealth Dr., Warrendale, PA, 1982. (11) Gorse, R. A., Jr.; Norbeck, J. M. J.Air Pollut. Control Assoc. 1981, 31, 1094-1096. (12) Traynor, G. W.; Anthon, D. W.; Hollowell, C. D. Atmos.

Environ. 1982,16, 2979-2987.

(13) Nazaroff, W. W.; Cass, G. R. Enuiron. Sci. Technol. 1986, 20, 924-934.

(14) U.S. EPA, Fed. Regist. 40 CFR Part 86, April 11, 1989. (15) US.EPA, Fed. Regist. 42 FR 32954, June 28, 1977. Received for review August 10, 1989. Accepted December 11, 1989.

Effect of Soil Moisture on the Sorption of Trichloroethene Vapor to Vadose-Zone Soil at Picatinny Arsenal, New Jerseyt James A. Smith* US. Geological Survey, 810 Bear Tavern Rd., Suite 206, West Trenton, New Jersey 08628

Cary T. Chiou, James A. Kammer, and Daniel E. Kite U S . Geological Survey, Box 25046, MS 407, Denver Federal Center, Denver, Colorado 80225

This report presents data on the sorption of trichloroethene (TCE) vapor to vadose-zone soil above a contaminated water-table aquifer at Picatinny Arsenal in Morris County, NJ. To assess the impact of moisture on TCE sorption, batch experiments on the sorption of TCE vapor by the field soil were carried out as a function of relative humidity. The TCE sorption decreases as soil moisture content increases from zero to saturation soil moisture content (the soil moisture content in equilibrium with 100% relative humidity). The moisture content of soil samples collected from the vadose zone was found to be greater than the saturation soil-moisture content, suggesting that adsorption of TCE by the mineral fraction of the vadose-zone soil should be minimal relative to the partition uptake by soil organic matter. Analyses of soil and soil-gas samples collected from the field indicate that the ratio of the concentration of TCE on the vadose-zone soil to its concentration in the soil gas is 1-3 orders of magnitude greater than the ratio predicted by using an assumption of equilibrium conditions. This apparent disequilibrium presumably results from the slow desorption of TCE from the organic matter of the vadose-zone soil relative to the dissipation of TCE vapor from the soil gas. Introduction From 1960 to 1981, wastewater from metal-plating and degreasing operations was discharged into two unlined 'The use of trade names in this report is for identification purposes only and does not constitute endorsement by the U S . Geological Survey. 676

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wastewater lagoons and an unlined overflow dry well adjacent to building 24 (Figure 1) at Picatinny Arsenal in Morris County, NJ. As a result, the unconfined sand and gravel aquifer that underlies the site has been contaminated by several chlorinated organic compounds. The plume of groundwater contamination extends from building 24 to Green Pond Brook. The major component of the organic contamination in the groundwater is trichloroethene (TCE); the approximate areal distribution of the TCE is shown by the isoconcentration lines in Figure 1, which are based on an extensive groundwater sampling program conducted in October-November 1987. Details of the groundwater contamination, as well as additional information on site hydrology, lithology, and source contamination history are reported elsewhere (1-6). This study investigates the potential effect of soil-moisture content on the sorption of TCE vapor by vadose-zone soil above the groundwater solute plume a t Picatinny Arsenal in order to gain a better understanding of the system parameters mediating the dynamics of vapor movement in the vadose zone. This study also describes the relation between the concentrations of TCE in the soil gas and underlying shallow groundwater along the main axis of the plume. Background Recent scientific evidence indicates that natural soil functions as a dual sorbent for the uptake and release of nonionic organic compounds (7-9). The mineral surfaces of the soil function as a conventional solid adsorbent and the soil organic matter functions as a partition medium. Mineral adsorption is characterized by vapor or solute condensation onto the mineral surface by physical and/or

Not subject to US. Copyright. Published 1990 by the American Chemical Society