Laser absorption spectroscopy (LAS) has been used over the last several decades for the measurement of trace gasses in the atmosphere. For over a decade, LAS measurements from multiple sources and tens of retroreflectors have been combined with sparse-sample tomography methods to estimate the 2-D distribution of trace gas concentrations and underlying fluxes from point-like sources. In this work, we consider the ability of such a system to detect and estimate the position and rate of a single point leak which may arise as a failure mode for carbon dioxide storage. The leak is assumed to be at a constant rate giving rise to a plume with a concentration and distribution that depend on the wind velocity. We demonstrate the ability of our approach to detect a leak using numerical simulation and also present a preliminary measurement.

Carbon capture and geological storage

One obvious objection to geological repositories is that the CO

Remote sensing of atmospheric gasses, frequently for pollution control goes
back several decades

Long-baseline DOAS has been used to measure trace gasses in the atmosphere
tomographically. Whereas in medical tomography, the number of individual
projections can be in the millions, the practice in tomographic DOAS has been
to make tens of measurements in two dimensions

In the case of the verification of the integrity of structures dedicated to
the sequestration of carbon dioxide, we may suspect a single point leak in
the presence of a reasonably steady wind. The sequestration region might be
on the order of 1 km square, so using roughly 36 measurements as
considered by

Typically, it is assumed that the measurement is taken quickly enough so that
the plume does not vary due to changing winds. Here, we consider a different
constraint: if we assume that the leak rate

If we assume that the concentration of gas is due to a single steady leak,
the strong constraints of a plume model can be imposed. If the speed and
direction of the wind are known throughout the measurement then a given leak
strength will give rise to a characteristic plume. We adopt coordinates in
which

If the emission is continuous at a constant rate, making the standard
approximation of the advection–diffusion equation, i.e., ignoring diffusion
parallel to the wind direction

The plume basis function is normalized such that

The actual concentration is given by

At a given distance downwind, the total concentration in a line of
observation orthogonal to both the wind direction and the direction of
gravity is given by

Another property of interest is the peak observed value of the concentration
for a given value of

In Ermak's formulation, the transverse diffusion is independent of the wind
speed when considered as a function of time. The proportionality constant
between time and downwind position is simply the wind speed. If downwind
distances which are comparable to the length scale for pressure and density
differences in the atmosphere are considered, this approximation will break
down. However, for distances up to 500 m, it is a reasonable approximation

The famous filtered back-projection method of tomography requires regular
sampling. In Bayesian tomography

Assuming the measurements, denoted

Below, each

Putting Eq. (

The projections are related to the concentration

The posterior distribution

In performing the maximization, the most time-consuming step is the
calculation of the projections in Eq. (

While we have formulated Eq. (

Field measurements from the Greenhouse gas Laser Imaging Tomography
Experiment or GreenLITE

Parameters used in the calculation. Units are omitted for dimensionless quantities.

The lines of observation in both the experiment and the simulation are shown here, with up being north and right being east. Each of the two light sources starts 27 line segments which end on each of the 27 reflectors. The pale blue ellipse represents the region in which carbon dioxide sources were simulated. The red dot represents the position of the leak found in the experiment as calculated by maximizing the likelihood using the Ermak plume model.

The GreenLITE system was deployed at a farm outside of Fort Wayne, IN, in
February of 2015 in the configuration shown in Fig.

Because no source of CO

Number of optical observations for each wind measurement, with the
value for the first six wind measurements given in the first row, the value for the second six wind measurements in the second row, etc. The
maximum possible entry is 54

The measured wind velocity during the experiment at 20 min intervals. The first and last measurements are labeled “1” and “24”, respectively, which represent 5 February 2015 from 13:00 to 21:00 EST (local time). The average velocity is also given.

First, we simulate measurements assuming that the true leak position is
exactly at the estimated position from the experimental data. Simulated
measurements suggest that the signal can be recovered well at both the
measurement height of

We simulated 389 cases of a gas leak with strength

We were able to find the maximum of the log likelihood in 380 of 389 cases with the higher leak strength and 103 of 109 cases with the lower leak strength using the algorithm described in Sect. 3. Cases for which the reported maximum was less than the log likelihood of the known true value were discarded. However, the known true value was not otherwise used in the analysis.

Contour plot of log likelihood for a source at (

A typical example of the log likelihood and its maximum is given in
Fig.

Typical contour plot of the log likelihood when

Maximum log-likelihood values were acquired from

Positions of 380 simulations with

Our simulated measurements are created from the projection of the CO

Results of calculations. Units of

Similar to Fig.

Contour plot of the log likelihood of a source at a given position
(in meters, with

The ability to predict the position of the leak is shown in
Figs.

The data were reconstructed with the model given above. Before
reconstruction, we subtracted a background of 390

We find, as shown in Figs.

A close-up of the plot shown in Fig.

We find that with a measurement height of

The challenge of carbon sequestration required the development of a technology to ensure that sequestration sites are not leaking substantial amounts of gas into the atmosphere. The required measurements have certain undesirable characteristics, namely the detection of a small signal against a much larger background and the variability of that background.

Laser absorption spectroscopy, combined with the Ermak plume model, can be
used to observe relatively small isolated sources of CO

Contour plot of the log likelihood with detectors at

We have made a preliminary measurement of a gas source, giving both its position and strength. While we did not independently verify the nature and strength of the source, we did show that the strength of the detection was consistent with what would be expected given the correctness of the model and the experimental signal-to-noise value. Using actual wind data and a physically realized experimental protocol, we have found through simulation that the ability to localize both the strength and the spatial position of the leak is quite good.

Experimental observations and simulated observations used in this paper are available in the Supplement as text files which are described in the file README.txt.

The authors thank James Whetstone for suggesting this line of research and
Kuldeep Prasad for discussions about the plume model. The experimental
portion of this work was supported by grant number DE-FE00012574 from the US
Department of Energy (DOE), a collaborative agreement between Exelis, AER,
and the DOE's National Energy Technology Laboratory.