WO1998046376A1

WO1998046376A1 - Method and system to locate leaks in subsurface containment structures using tracer gases

Info

Publication number: WO1998046376A1
Application number: PCT/US1998/007687
Authority: WO
Inventors: William E. Lowry; Sandra Dalvit Dunn; Robert Walsh; Daniel Merewether; Desario V. Rao
Original assignee: Science & Engineering Associates, Inc.
Priority date: 1997-04-15
Filing date: 1998-04-15
Publication date: 1998-10-22
Also published as: AU7125998A

Abstract

The present invention integrates an inverse modelling technique and a field measurement system. The system uses inexpensive and non-hazardous gaseous tracers injected inside the contained volume of a subsurface barrier or geomembrane to quantify the location and size of any leaks in the barrier. The vapor sampling point installation, which allows the collection of soil gas samples from multiple points (#1 - #12) around the outside surface of barrier installation, can be accomplished with conventional rotational drilling, direct push or sonic emplacement technologies. The system uses a field-proven soil gas analyzer for evaluating composition of such collected vapor samples and indicating penetration of tracer gas past the barrier, incorporated in a sampling system capable of monitoring many sample points with relatively high time resolution. A rigorous numerical inverse modelling technology, as used with or without non-linear global optimization and simulated annealing, is integrated with the data system for real time analysis.

Description

METHOD AND SYSTEM TO LOCATE LEAKS IN SUBSURFACE CONTAINMENT STRUCTURES USING TRACER GASES

Field of the Invention

This invention relates to quantitative subsurface barrier assessment systems

using gaseous tracers to pinpoint leak sources and sizes in real time. The invention

is applicable to impermeable barrier emplacements above the water table to provide

a conservative assessment of barrier integrity as well as long term integrity

monitoring.

Background of the Invention

The Department of Energy is currently developing in-situ barrier emplacement

techniques and materials for the containment of high-risk contaminants in soils.

Injected grouts, waxes, polymers, slurries and freezing of soil moisture are barrier

techniques currently under development and/or being demonstrated. Because of

their relatively high cost, the barriers are intended to be used in cases where the risk

is too great to remove the contaminants, the contaminants are too difficult to remove

with current technologies, or the potential movement of the contaminants to the

water table is so high that immediate action needs to be taken to reduce health risks. Consequently, barriers are primarily intended for use in high-risk sites where few

viable alternatives exist to stop the movement of contaminants in the near term. The

intent of these designs is to prevent the movement of contaminants in either the

liquid or vapor essentially buying time until remediation can be implemented or until

the contaminant depletes naturally. Assessing the integrity of the barrier once it is

emplaced, and during its anticipated life, is a very difficult but necessary

requirement.

Surface based geophysical techniques, such as ground penetrating radar,

electromagnetic, or seismic surveys, can only detect the presence of barrier

materials in the soil. They are incapable of resolving imperfections on the scale of

fractions of an inch, which is required to assess the integrity of these subsurface

structures. Borehole geophysical techniques (neutron, gamma, EM and acoustic

tomograph) are potentially capable of the required resolution, but because of the

measurement depth (fractions of meters) necessary to attain the desired resolution,

many closely spaced access holes are needed to perform the integrity validation

function. Because of the limitations in geophysical techniques (and limited hope that

their resolution can be practically improved) gaseous tracers have been suggested.

See "Subsurface Barrier Verification Technologies," J. H. Jeiser, BNL-61127,

Brookhaven National Laboratory, June 1994.

Tracers have been used previously for landfill liner and underground storage

tank leak detection. A typical usage is to inject small amounts of perfluorocarbon

tracer gas and monitor for its appearance on the other side of an impermeable layer

(such as landfill liner or UST wall). Several different tracers can be used to distinguish leak locations. Gas analysis is usually done with GC-MS or similar

sophisticated analytic device, and inference of leakage characteristics accomplished

by post test analysis of the soil gas data. This is a time consuming, artful process.

The challenge with the use of tracers is to develop a system which automatically

assesses barrier integrity in real time, to avoid time consuming and expensive

numerical back-calculations.

The present invention is a turn-key, autonomous monitoring system to provide

leakage characteristics in real time. This will significantly reduce the labor required

for assessment of barrier integrity. The conservative vapor testing methodology,

combined with the real time assessment, introduces the possibility that breaches in a

barrier can be repaired before liquid contaminant is released from the contained

volume.

The present invention has the following benefits:

Reducing public and occupational health risks by assuring that the integrity of

barriers intended to contain high risk contaminants. As such, it will quantify

leaks so that remedial actions (repairs) can be accomplished to minimize risk

to the public. The method of sampling system installation (direct push or

ResonantSonic™) minimizes occupational risk by reduction of secondary

waste generation.

• Improving cleanup operations by assuming that barriers are constructed as

desired.

• Cost reduction.

Ability to meet regulatory requirement. The present invention is applicable to the assessment of any impermeable

barrier constructed above the water table. Furthermore, the system is equally

capable of performing as the long term monitoring system of the barrier's integrity.

Summary of the Invention

The present invention integrates an inverse modeling technique and a field

measurement system. The system uses inexpensive and non-hazardous gaseous

tracers injected inside the contained volume of a barrier to quantify the location and

size of any leaks in the barrier. The vapor sampling point installation, which allows

the collection of soil gas samples from multiple points around the barrier installation,

can be accomplished with conventional drilling or direct push techniques. The

system uses a field-proven soil gas analyzer, incorporated in a sampling system

capable of monitoring many sample points with relatively high time resolution. A

rigorous inverse modeling technology is integrated with the data system for real time

analysis.

The invention is applicable to impermeable barrier installations above the

water table. The system requires that multiple vapor sampling points be installed

around the perimeter of the barrier, and one or several tracer injection points be

emplaced inside the contained volume. Vapor point installation can be

accomplished in virtually any geologic media, using a variety of techniques. Grout

wall, cryogenic, viscous, and sheet barriers are all viable applications for the

disclosed monitoring system. To date, potential Department of Energy ("DOE")

installations exist at Hanford, Oak Ridge, Savannah River, and Portsmouth. The present invention uses gaseous tracer injection, in-field real-time

monitoring, and real time data analysis to evaluate barrier integrity in the

unsaturated zone. The design has the following features:

• It measures vapor leaks in a containment system whose greatest risk is

posed by liquid leaks;

• It is applicable to any impermeable barrier emplacement technology in the

unsaturated zone;

It qualifies both the leak location and size;

• It uses readily available, non-toxic, inexpensive, nonhazardous gaseous

tracers;

• The vapor injection and sampling points can be emplaced by direct push

techniques (such as Geoprobes) or the rapid ResonantSonic™ technique,

avoiding excessive drilling costs and secondary waste generation;

• It provides continuous and unattended contaminant plume measurements for

remote site operation;

In incorporates the methodology for unfolding the soil gas analysis data in

real time using a rigorous inverse modeling technique which accommodates

uncertainties in field data; and

• In addition to assessing initial barrier integrity, the system can also provide

long term monitoring of contaminant soil gases for surveillance of the

containment system's performance over time.

The barrier monitoring system of the present invention is predicated on the

very simple and predictable transport process of binary gaseous diffusion in porous media. A hole or similar imperfection in a barrier will allow tracer gas to diffuse

through at a rate orders of magnitude greater than through the solid barrier material.

If the hole is small relative to the surface area of the barrier, the tracer gas will

diffuse away from the source in a spherical fashion.

Spherical diffusion is utilized for leak detection because the tracer

concentration histories measured at locations distant from the source are highly

sensitive to both the size of the leak and the radial distance from the leak source.

This sensitivity allows an effective inverse modeling methodology to be applied to

recorded concentration histories at several points around the barrier. The technique,

known as simulated annealing, iterates to a leak site and location by minimizing

errors in the transport calculations. It is a rigorous generalized methodology which

can accommodate real world uncertainties.

Brief Description of the Drawings

Figure 1 is a schematic view of the barrier test configuration;

Figure 2(a) is schematic view of the leak process model;

Figure 2(b) is a graph illustrating the tracer diffusion model;

Figure 3 is a graph illustrating the tracer concentration profile at various times

(10 cm² leak);

Figure 4 is a graph illustrating tracer concentration model at 3 radial distances

from source (10 cm² leak);

Figure 5 is a graph illustrating tracer concentration at 5 meters from source for

two different leak sizes; Figure 6 is perspective schematic illustrating the sample configuration for

inverse model assessment;

Figures 7(a)-(e) illustrate potential barrier installations and monitoring

configurations;

Figure 8 is a schematic view of the multipoint tracer gas monitoring system of

the present invention;

Figure 9 is a schematic illustrating the barrier integrity monitoring system

operational flow; and

Figures 10(a)-(b) illustrate the end and side views of a test configuration.

Description of the Preferred Embodiment

The basic approach to using gaseous tracers for barrier integrity assessment

is to inject a tracer gas into the barrier-contained volume, then monitor outside of the

contained volume for indications of leaks. The dominant transport process in this

case is molecular diffusion, driven by concentration gradients of the tracer gas in the

soil. This is depicted schematically in Figure 1.

To understand the suitability of this approach, consider the configuration

shown in Figure 2(a). A tracer has been injected into a contained volume. An

imperfection (e.g. hole) exists in the container, with a cross sectional area A_leak. If

the tracer concentration inside the container is high, it will serve as an infinitely large

reservoir of tracer gas at a fixed concentration c₀. The tracer gas will diffuse from

the leak in roughly a spherical flow geometry, especially if A,_θak is small compared to

the size of the container, and the wall of the container forms a flat no-flow boundary.

Tracer transport is modeled, at least to the first order, as one-dimensional spherical diffusion from a source with the radius r₀ This is represented in Figure 2(b)

schematically. The partial differential equation describing this transient spherical

process is the diffusion equation:

where c is the concentration at radial position r and time t. The controlling

parameter in this process is D, the diffusivity of the tracer in soil gas, which includes

the effects of soil tortuosity and porosity. To solve this equation we set the left

boundary condition as: c(r_o, = c_o t > 0

and solve for a semi-infinite medium. whose initial tracer concentration is zero. This

results in a straightforward expression of the tracer concentration:

To illustrate the potential for delineating leak location and size, consider

several simulations. The modeled source is a constant concentration of 10 percent

(10⁵ ppm) SF₆ (sulfur hexafluoride) in soil gas (air). The diffusivity is 10^"5 m^{2 s}, a

typical value in soils for heavier compounds such as sulfur hexafluoride. The leak is

represented by a constant source concentration with a source radius, r₀, chosen to

represent A_lβak (i.e., A_|eak=πr₀ ²). using the foregoing parameters, two simulations

were conducted: one with a leak area of 10cm², and the other 1cm². The significant

results are: 1. The process is relatively fast for the modeled leak sizes. As seen in

Figure 3 the progression of the tracer concentration profile out in the soil is plotted

for the 10cm² leak. In roughly a one-week period, the fringe of the tracer "plume" has

extended to 5 meters. Consequently, this allows a tradeoff between test duration

and probe spacing.

2. The concentration histories are very sensitive to distance from the

source. The sensitivity of the measurement to distance from the source is shown in

Figure 4. At early times the concentration predicted at 2m is more than two decades

higher than that measured at 5m. As the transport reaches steady state, the

concentrations will be inversely proportional to radial distance from the source (r in

Equation 2).

3. Different leak sizes can be distinguished. The concentration histories

at 5m from the two different size sources are shown as Figure 5. The smaller leak

results in lower amplitude response (although the arrival time of the front is similar in

both cases). The amplitude is directly proportional to the leak radius, or the square

root of the leak area.

The above described monitoring approach allows for quantitative location of the leak

by triangulation of concentration histories from three sample points (using probes

placed 5 to 10 m apart, for example) and determination of the leak size by

evaluating the magnitude of the concentration response. The simplicity of the

transport equation allows an easy test of a rigorous inverse modeling technique to

automatically determine leak location and size given soil gas analysis records. Inverse modeling is used to reverse calculate flow and transport processes in

an effort to understand unknown properties and flow conditions. This can be

accomplished with numerical or analytical techniques, depending upon the

complexity of the process and the detail required in the final result.

For the present invention a numerical method was chosen which would allow

near real time assessment of recorded gas data. Consequently, the solution method

chosen is readily programmed for use on a portable personal computer, which also

performs the role of controlling data acquisition, archiving data, and

reporting/transmitting the results.

The estimation of the size and location of a leak from measured concentration

histories is an inverse problem of multiphase flow in porous media. From measured

tracer concentrations C_ik taken at locations, Xj = (x., y_if z,) and times tj_k one seeks

estimates for a set of parameters p. that characterize the leak.

The inverse problem requires a leakage model

c(p_; x, t) that solves the forward problem; that is, it maps each point j> from a multiparameter

space into a set of predicted concentration histories. For example, an idealized

leakage model for a vertical barrier surface described by y=a+bx is

where

r ' (x-x₀)² + (y-y₀)² + (_z-₂ )², V a + bX_Q, (x₀, y₀, z₀) is the location of the leak, t₀ is the time that the leak began, r₀ is the

constant radius of the leak after time t₀, c₀ is the uniform tracer concentration within

the hemisphere of radius r₀ after time t₀, D is the uniform diffusivity of the medium,

and erfc(x) is the complement of the error function. In the idealized case at least the

first four parameters are unknown. In a realistic application the model may be more

complex, perhaps a finite element model, and there may be many unknown

parameters.

The inverse problem is cast in the form of a nonlinear global optimization

problem. The objective function to be minimized is taken as the sum of the squares

of the differences between predicted and measured tracer concentrations:

The problem is made difficult by the fact that there may be more than one set of

parameter values for which E achieves the minimum.

No algorithm can solve a general, smooth global optimization problem in finite

time. This fact has lead to the use of stochastic methods, some of which are called

"Simulated Annealing" ("SA").

The simplest stochastic method for global optimization is to repeatedly select

points in the parameter space at random, using a uniform probability distribution

(i.e., Pure Random Research). The objective function is evaluated at each point; the

minimum value and the point with the minimum value are remembered, all other

information is discarded. Even with a large sample of points, the Pure Random Search method may not find the global minimum, but it probably will come close. As

the sample increases, the probability of success converges to 1.

SA methods are similar to Pure Random Search. Points are selected at

random and the best point is remembered. The difference is that an SA method

does not use a uniform distribution to select points in the parameter space. Instead,

the probability distribution depends in a complex way on the objective function of

previous points.

In an SA method the probability distribution for the next point is centered

around a particular point in parameter space, which we call the base point, by

analogy to a base camp. As discussed below, the base point need not be the best

point found so far. One way in which various SA methods differ from each other is in

the exact form of the probability distribution.

The rule for determining the base point is responsible for the name Simulated

Annealing. If the objective function is smaller at the next point than it was at the

base point, then the base point is moved to the new point. If the objective function is

larger, we take a chance on moving the base point; we "roll the dice". If the objective

function is much larger at the next point, the probability of moving the base point is

less, because that probability is given by the following expression:

_c-ΔE/T [Eq. 5]

This is analogous to the physical annealing process, where ΔE is the difference in

energy states and T is proportional to the temperature. When T is relatively large,

there is a good possibility that the base point will climb out of a local minimum to

look for other minima. If T is small, the base point is more likely to avoid "uphill" steps. In an SA method, the temperature is reduced as the process proceeds, just

as in physical annealing.

SA methods not only differ in the form of the probability distribution used to

select the new point, they also differ in the cooling schedule.

To select the next set of parameter values to be tested, each parameter is

selected independently, using a probability distribution proportional to

_c-w|p_rqj|/( _rmj) [Eq. 6]

where jo and g; are the new point and the base point, respectively, [mj.Mj] is the

interval of allowed values of p_r and W is a shape constant. This is a relatively simple

probability distribution that satisfies the requirements that the probability density be

positive over all possible parameters values and that the density be a maximum at

the base point.

In order to assure that T converges to zero even when Eo is underestimated,

the present algorithm uses

where n is the number of points for which E has been evaluated and V is a constant.

The value for E₀ is based on the fractional measurement errors ei at the various

monitors; that is,

For the calculations reported here, V was set to 100. With this choice, the

probability of accepting a point that would "double" the error is about 98.6 percent for

n=1 and about 86 percent for n=2000.

An SA algorithm needs a stopping rule, which tends to be

problem-dependent. The present algorithm stops a search when E(p_)<E₀ or after a

fixed number of evaluations N.

In order to estimate the uncertainty in the result, several sequences are run,

each starting from the same initial p_ but using a different sequence of random

numbers. Because of this repetition, it is reasonable to use a relatively small value of

N for each search.

This iterative methodology was incorporated into a C++ code developed to

run on a standard personal computer. Tests with simulated soil gas concentration

histories from a one-dimensional spherical diffusion model were conducted to

demonstrate the methodology. Results are described below.

Testing of the code was performed by generating concentration histories for

monitoring points in a typical barrier monitoring/verification configuration. The

sample configuration, illustrated in Figure 6, included a vertical barrier 100 ft deep

and 200 ft wide. Four multipoint monitoring wells were located in a plane 20 ft from

the outside surface of the barrier. The 40 ft spacing of the points within each well

was equal to the spacing of the wells from one another. This spacing allowed for all

points on the surface of the barrier except those near the top and side edges to be

within 30 ft of a monitoring point. The location of the leak was arbitrarily chosen. The

distance from the leak center to each monitoring point was calculated, and a one-dimensional radial analytic solution for molecular diffusion was used to generate

concentration histories at each of the monitoring points. The total number of times

(i.e., 30) calculated for each point was chosen assuming a soil gas sample would be

collected once a day with data downloaded from the MultiScan™ system once every

30 days. In calculating the concentrations, it was assumed that the barrier did not

begin to leak until the beginning of the 8th day after the last collection time. Two

different leak radii, 10 cm and 1 m, were used in the calculations. Once

concentrations were calculated from the analytical solution, random errors were

incorporated in the values. It was assumed that under field conditions the gas

analyzer could measure the tracer gas to within ±5 percent accuracy for values

under 500 ppm, and within ±10 percent for values over 500 ppm. These

inaccuracies are greater than what should actually be measured, but were used in

an effort to be conservative. Even though the gas analyzer can measure SF₆ to 50

ppb in laboratory analysis, a 1 ppm lower detection was assumed for the field

conditions. The source concentration of the tracer used in calculations was 70,000

ppm, the upper calibrated detection limit of the gas with the proposed gas analyzer.

The effective diffusion constant of the tracer in the soil gas was assumed to be

1.0(10⁵) m²/s. This value was measured in the vadose zone at the Chemical Waste

Landfill at Sandia National Laboratory, Albuquerque, New Mexico, and accounts for

soil porosity and tortuosity.

The code allows for a range of values to be input for all of the pertinent

variables. Ranges for the x and z location of the leak on the barrier were chosen

based on the monitor information (the barrier was vertical and coordinates chosen such that y=0). The monitors closest to the leak will detect the tracer earliest and will

measure the highest concentrations with time. Thus a cursory overview of the

collected data will allow the user to determine a very general location of the leak.

Figure 6 shows the coordinate system used to generate the input file and lists the

monitoring points which are close enough to the leak to detect the tracer gas. For

the baseline case, the area of the barrier searched to find the leak was

24.38<x<48.77 and -21.34<z<-9.14 meters. The range of the tracer source

concentration was ±10 percent of the "known" source concentration of 70,000 ppm

for the baseline case (this value would be measured in the field). Comparison runs

were performed where the range was increased to ±30 percent (50,000<source

concentration<90,000 ppm). The effective diffusivity of the medium was entered as a

constant of 1.0 (10⁵) m²/s in the baseline case, with comparison runs changing the

range to 5.0 (10^~6) to 1.5 (10⁵) m²/s. Additionally, changes to the base runs were

made to determine the effect of other potential errors from field conditions. The input

locations of the monitoring points were altered in one run so that they were one to

2.25 meters off from their true location.

Table 1 shows several examples of the input parameters for the analytic

calculations and the codes. The code was consistently able to accurately determine

the location of the leak. For most of the cases, the calculated X, Z locations were

within 0.5 m of the actual values. Calculation of the leak radius also showed good

agreement with the actual values, within 20 percent. In most cases, the best fit was

very close to the real value, and in all cases, the calculated range of values did

encompass the true value. The code was also able to determine the time the leak began to accuracies of less than ±2 days. As expected, as more unknowns were

introduced into the code (as larger ranges) or as the accumulation of errors

increased in calculating the analytic histories, the accuracy of the code diminished.

However, even under the worst case simulated conditions, results were still good.

Under true field conditions where additional data and monitor points would be

included in the calculations with time, the results would continue to become more

accurate.

These simulations were completed on a 133 MHz Pentium PC, requiring four

hours for the case with the greatest number of iterations. No effort was made to

optimize the runs.

To apply this approach to an existing emplaced barrier, one or several tracer

gas injection points would be placed inside the contained volume. Monitoring points

would be installed outside the contained volume at prescribed locations. The range

of potential barrier installation configurations and proposed monitoring system

configurations are shown in Figures 7(a)-(e). A multipoint soil gas sampling and

analysis system would automatically sense tracer concentrations at the monitoring

points ("M"). Tracer gas ("Inject") would be injected into the soil gas contained within

the barrier, at a prescribed concentration, to diffuse uniformly into the contained

volume.

One of the benefits of using SF₆ is its relatively high molecular weight (146)

which results in it tending to stay inside a contained volume (at least in high

concentrations) and it is a reasonable surrogate for some of the heavier

contaminants of interest (such as TCE and CCI₄). It is a relatively inexpensive tracer

material: a 1000 m+³ volume of soil (30 percent porosity) would require 185 kg of

SF6 to achieve a 10 percent concentration, costing $3000. SF₆ has been used as a

hydrologic tracer, attesting to its non-toxic and stable nature. See "The Use of

Sulphur Hexafluoride as a Conservative Tracer in Saturated Sandy Media."

Implementation issues are related to vapor point emplacement and soil gas

monitoring techniques, each described below.

Vapor and injection point emplacement may be accomplished by a direct

push emplacement tool. If the barrier is shallow (i.e., 10 to 20 ft deep), a manually

operated system would suffice, such as the KVA vapor point system. As the

emplacement depth increases or the geology becomes more resistive to vapor point

emplacements, a Geoprobe truck-mounted system would be required. For more

difficult emplacements, cone penetrometer or ResonantSonic™ emplacements

would be suitable. The latter technologies have been demonstrated to depths of

150 to 200 ft in Hanford, Washington soils.

The spacing and configuration of the vapor point installations are critical to

the effectiveness and cost of the monitoring system. By arranging the vapor points

carefully it is possible to capitalize upon the distance sensitivity of the monitoring

system.

The tracer gas monitoring system must be capable of sampling multiple soil

gas vapor lines and providing compositional analysis in real time. The Brϋel & Kjasr

model 1302 photoacoustic gas analyzer is well-suited for unattended operation in

field environments. It s automated to provide multipoint scanning system to map SF₆

tracer gas, chlorinated hydrocarbon, and C0₂ movement in the unsaturated zone.

This system can automatically monitored up to 64 vapor sampling lines for several

weeks, allowing measurement of gas diffusivity and monitoring of contaminant

movement due to barometric pressure oscillations. The system is schematically

shown in Figure 8. The system is capable of unattended operation for long periods (weeks to several months). Sampling frequency is dictated by the number of vapor

points monitored. In one application 45 vapor lines were sampled every 3 hours.

The Bruel & Kjasr photoacoustic analyzer is well suited to SF₆ and C0₂

concentration measurements. It maintains a dynamic range of 3 to 5 orders of

magnitude, and is capable of also measuring four other analytes in one sample

(such as organic compounds). Less than half a liter of soil gas is required for each

sample.

The scanning system is well-developed and its software tested in long

duration field applications. The inverse modeling leak determination software runs

on a standard personal computer. The data acquisition and leakage determination

software have been designed for future integration into a common software

application. The general flow of this operation is depicted in Figure 9, showing the

interaction between the software units.

Several design features need to be evaluated to substantiate this system's

capability of both locating and determining the relative size of leaks in in-situ

barriers. These issues include the characteristics of the tracer, the geologic medium

in which the battier has been placed and through which the tracer diffuses, and the

sampling system geometry.

The choice of tracer gas is dictated by the tracer's ability to delineate leaks in

the barrier at reasonable cost and with relative ease of monitoring. The tracer must

be non-hazardous, conservative, non-reactive, relatively inexpensive, readily

available, and easily diagnosed with a field-rugged, stand-alone gas analysis

system. Sulfur hexafluoride (SF₆) is a non-toxic conservative tracer gas commonly used in building ventilation testing as well as hydrologic measurements.

Atmospheric background concentrations are on the order of I to 2 parts per trillion.

SF₆ costs approximately $10/m³ at standard conditions. This compound has a

molecular weight of 146, which is comparable to the molecular weight of the heavier

chlorinated hydrocarbons frequently encountered at contaminated sites. This is a

useful characteristic of the gas in that the test conducted using this tracer will be

relevant to leaks of similar molecular weight vapors. The diffusion rates of gases in

air are well-characterized as a function of their respective molecular weights. See

"Fundamentals of Physical Chemistry," S.H. Maron and J.B. Lando, Case Western

Reserve University, MacMillan Publishing Co., Inc., 1974. The diffusion constant of

SF₆ is very close to that of trichlorethylene in air.

Another tracer gas which may satisfy the criteria for this test program is

carbon dioxide, primarily due to its low cost ($1.75/m³) and ease of measurement.

An attractive feature of C0₂ is that, because of its lower molecular weight, its

diffusion rate will be almost twice that of SF₆. Carbon dioxide, while it exists

naturally in air at concentrations of 300 to 500 parts per million (ppm), may be

applicable to sites where very little organic contaminant is present in the soil, such

as buried nuclear waste. This gas is only suitable under conditions where there is

little or no microbial degradation of organic contaminants in the soil, (which would

result in C0₂ generation).

Several parameters will impact the rate of tracer gas transport through the

soil. One is the thermodynamic state of the soil gas (temperature and pressure). In

most barrier applications these will not deviate enough from standard conditions to impact the diffusion constant. Cryogenically-cooled barriers, however, will result in

soil gas temperature as low as -30 °C. According to a model based on kinetic theory

and corresponding-states arguments, the diffusion constant is proportional to the

absolute temperature raised to the power of 1.8 for a given binary gas mixture. See

"Transport Phenomena," R.B. Bird, W.E. Stewart, and E.N. Lightfoot, University of

Wisconsin, John Wiley & Sons, 1960. Consequently, cooling a binary mixture from

+20°C to -30°C will reduce the diffusion constant to (243/293)^{1 8} = 0.71 of its value at

standard conditions. Temperature-induced density gradients will induce advective

flow, which requires modeling to discern its impact on the overall transport.

A more variable influence is that of tortuosity, or the effective increase in the

transport path in porous media caused by complicated pore structure. In the

transport model, the (binary gas in air) diffusion constant is multiplied by the

tortuosity to yield an effective diffusion constant. Tortuosity has been found to

empirically follow the relation:

t (tortuosity) = (soil porosity)¹'³ (soil gas saturation) ^{7 3} [Eq. 9]

where soil porosity represents the dry state and soil gas saturation is that fraction of

the soil pores occupied by gas. With a typical range of porosities (0.2 to 0.5) and

gas saturation (0.95 to 0.50) in typical and sites, this results in a range of tortuosity

of 0.1 to 0.7. Knowing this we can bound the range of effective diffusion constants

to be anticipated in the field. In any case, the diffusive transport characteristics of

the soil should be measured in the site media prior to application of the above

described assessment methodology. The number and geometry of the vapor sampling points must be optimized for

the particular barrier installation. Increasing the number of sampling points will

increase the precision of the leak location capability, but will also increase the costs

of the overall emplacement. A test configuration is depicted in Figure 10. It consists

of trench excavated and lined with polyethylene geomembrane material. Holes have

been formed, in various sizes and at various locations, in the geomembrane.

Sampling tubing ("S") would be placed at various locations throughout the volume,

and samples drawn from this array and analyzed with a photoacoustic gas analyzer

over time. Prior to each test, an effective diffusion test is performed by injecting a

known concentration of SF₆ into the volume and observing its diffusion.

A monitoring installation is designed for a specific barrier application. The first

step is to design the vapor point installation to optimize vapor point spacing with

respect to anticipated initial concentrations and anticipated response under given

conditions. The second step is the installation of the vapor sampling points and

monitoring system. This task is completed with a background survey to verify the

monitoring system's installation and the integrity of the vapor sample point

installation. The monitoring system is then operated for a one week period to verify

that reasonable samples are being taken based on the in-situ gas composition.

Once this verification is complete, leak testing begins. This starts with baseline data

accumulation for a period of approximately a week, then initiation of the tracer gas

injection, and subsequent monitoring by the multipoint scanning system described

above. This testing would require one to three weeks. A second tracer injection

could be used, using an alternate tracer such as carbon dioxide if the site conditions permit. This allows checking the initial results with a tracer whose diffusion constant

is known to be higher than that of the initial tracer.

A test installation is depicted in Figure 10. A geomembrane is installed, with

fabricated holes of various sizes at various locations on its surface, in a trench which

is then filled with soil. Vapor sampling and injection points are installed as shown.

The integrated monitoring and data analysis system developed is connected to the

sampling lines. The procedures for each test are basically identical:

1. Conduct baseline measurements of soil gas concentration for at

least two days before injecting the tracer gas.

2. Review the baseline data for consistency to assure the

monitoring system is operating correctly

3. Inject tracer gas (SF₆ or C0₂) into the contained volume to

achieve the desired initial concentration.

4. Start the monitoring system operation, including the leak

detection software module. At this point the system operates

autonomously, calculating leak sizes and locations in real time

as soil gas analysis is completed.

5. Run the test until the tracer gas concentrations in the soil drop

to background levels.

6. Repeat the test at other initial tracer gas concentrations (e.g.,

sulfur hexafluoride: Initial concentration (C₀) = 5000, 25000,

50000 ppm; and carbon dioxide: Initial concentration (C₀) =

5000, 25000, 50000 ppm). Testing requires, approximately, a week total duration, including two days of

background measurements and the balance of the week to run the injection and

monitoring test. Some of the tests, however, may run for two weeks. The multipoint

gas analysis system will collect and store all of the data required for these tests.

This system records ambient temperature, barometric pressure, soil gas pressure at

all of the sample points, and soil gas composition at all of the sample points in the

soil. Several soil gas points will also draw gas from the soil inside the contained

volume to measure C₀. This information will be collected a number (at least four) of

times a day. The software module which determines the leak characteristics

operates after soil gas analysis shows the presence of tracer gas at the vapor

sampling points outside of the contained volume. This is done automatically, and

the code outputs the leak sizes, locations, and uncertainties in these determinations.

Data is transmitted or printed, then archived after each sampling and analysis

sequence.

Whereas the drawings and accompanying description have shown and

described the preferred embodiment of the present invention, it should be apparent

to those skilled in the art that various changes may be made in the form of the

invention without affecting the scope thereof.

Claims

We claim:

1. A method of determining the size and location of leaks in a barrier in real

time, said method comprising the steps of:

(a) injecting at least one gas inside said barrier;

(b) providing a plurality of vapor sampling points outside of said

barrier;

(c) collecting vapor samples from said vapor sampling points;

(d) analyzing said vapor samples with a gas analyzer to determine

soil gas composition data; and

(e) calculating the size and location of said leaks in real time.

2. The method of claim 1 wherein said barrier is a subsurface barrier.

3. The method of claim 1 wherein injecting said gas and providing said sampling

points is accomplished using manually-operated direct push emplacement.

4. The method of claim 1 wherein injecting said gas and providing said sampling

points is accomplished using standard rotational drilling techniques.

5. The method of claim 1 wherein injecting said gas and providing said sampling

points is accomplished using a mounted mechanically-operated push

emplacement.

6. The method of claim 1 wherein injecting said gas and providing said sampling

points is accomplished using sonic emplacement.

7. The method of claim 1 wherein collecting said vapor samples is done using

sample tubing.

8. The method of claim 1 wherein analyzing said samples is done using a

photoacoustic gas analyzer.

9. The method of claim 1 wherein calculating the size and location of said leaks

utilizes numerical inverse modeling.

10. The method of claim 9 wherein said numerical inverse modeling is achieved

using nonlinear global optimization which is solved using simulated annealing

techniques.

11. The method of claim 1 wherein said gas is selected from the group consisting

of SF₆ and CO₂.

12. The method of claim 1 which further comprises

(a) repeating steps a - e with a further gas chemically

distinguishable from the gas or gases of step a.

13. A multipoint tracer gas monitoring system, said system comprising:

(a) means for injecting at least one gas inside a barrier;

(b) means, outside said barrier, for collecting gas samples;

(c) a gas analyzer for analyzing said samples, coupled to said

means for collecting, to determine gas composition data; and

(d) a computer for calculating the size and location of leaks in said

barrier in real time.

14. The system of claim 12 wherein said barrier is a subsurface barrier.

15. The system of claim 12 wherein said means for injecting said gas is

accomplished using manually-operated direct push emplacement.

16. The system of claim 12 wherein said means for injecting said gas is

accomplished using standard rotational drilling techniques.

17. The system of claim 12 wherein said means for injecting said gas is

accomplished using a mounted mechanically-operated push emplacement.

18. The system of claim 12 wherein said means for injecting said gas is

accomplished using sonic emplacement.

19. The system of claim 12 wherein said means for collecting said samples is

sample tubing.

20. The system of claim 12 wherein said gas analyzer is a photoacoustic gas

analyzer.

21. The system of claim 12 wherein said computer calculates the size and

location of said leaks utilizing numerical inverse modeling.

22. The system of claim 21 wherein said numerical inverse modeling is achieved

using nonlinear global optimization which is solved using simulated annealing

techniques.

23. The system of claim 12 wherein said gas is selected from the group

consisting of SF₆ and CO₂.

24. The system of claim 12 which further comprises

a. means for repeating steps a - d with a further gas chemically

distinguishable from the gas or gases of step a.