Supporting Information for. Measuring Emissions from Oil and Natural Gas. Well Pads Using the Mobile Flux Plane Technique

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1 Supporting Information for Measuring Emissions from Oil and Natural Gas Well Pads Using the Mobile Flux Plane Technique Chris W. Rella*, Tracy R. Tsai, Connor G. Botkin, Eric R. Crosson, David Steele This document contains 28 pages, 13 figures, and 1 Table. S1

2 Individual Plume Measurements using the 6 inlet AirCore system The time series of a typical plume measurement is shown in Fig. S1. The plume is detected at the monitoring inlet (gray dashed line, mirrored about the y = 2 ppm line for clarity), and the valves are triggered to initiate the replay or the sequential routing of the gas stored in the tubes through the optical cavity for analysis. In this instance, the plume was low to the ground, with the largest peak at the lowest level, and the smallest peak at the highest level. Dispersion of the concentration profile due to gas diffusion occurs within the system of six AirCores as the samples are collected and then analyzed. Since the flow through the AirCores is in the laminar regime, the spatial scale of dispersion may be estimated by considering both molecular and Taylor components of the diffusion (Karion et al. 1 ). For the system parameters given above and considering only the dispersion that results from running the AirCore samples through the analyzer, we estimate the RMS scale of dispersion to range from 8 cm (for the first AirCore in the sequence to be analyzed) to 25 cm (for the last AirCore to be analyzed), or about seconds. At a typical vehicle speed of 10 m/s, these values correspond to a horizontal distance along the path of the vehicle of 2 m and 8 m, respectively. S2

3 Figure S1. Time series of a plume capture. The gray dashed line is the direct measurement of the plume from the monitoring inlet (mirrored in reverse for clarity). The colored data display the measured plume shape as a function of inlet port on the 3.7m mast (A is at the bottom of the mast, and F is at the top). The signal drops considerably with height, indicating that the main plume is centered at or near the ground. This distance is comparable to the lateral extent of the plume, but it is small compared to the typical horizontal extent of ~300 m for a typical plume capture. As long as the car speed and lateral wind speed remain constant during the interval of time over which the sample is collected, the effect of dispersion can be thought of as introducing a spatial convolution term to the integrand of the flux plane integral. Since both the concentration profile and convolution term are integrable, it follows from Fubini s theorem that the integral of their convolution is equivalent to the product of their integrals. Furthermore, since the integral of the convolution term is unity, it may be ignored S3

4 entirely as long as the distance scale of dispersion is small compared to the length of the AirCore so that a sufficiently-long portion of the signal can be used to determine the background concentration, C0. Vertical Wind Speed Profile The flux through the plane is calculated from the flux plane equation: q = k(c(y, z) C o ) u(z) dy dz A (S1) where q = measured flux rate of methane passing through the plane A = the surface over which the measurement is made k = factor for unit conversion from a volume of methane to kg hr -1. C(y,z) = methane concentration as a function of horizontal position, y (along the axis of the vehicle s motion) and height above the ground, z. Co = background methane concentration u(z) = component of wind speed normal to the surface A as a function of height above the ground. We model the wind gradient as having a form corresponding to simple shear 3, or u(z) u 0 = ( z z o ) α (S2) with u 0 representing the wind speed observed as the plume was sampled, and z o corresponding to the height above the ground where the wind speed was measured (2.8 m) in the mobile measurements. The power was empirically determined to be 0.17 through a series of measurements made under Pasquill-Gifford 2 C-class conditions with two anemometers, one of which was mounted in the typical survey position at 2.8 m, and the other mounted on a telescoping pole such that its height above the ground could be adjusted. S4

5 Figure S2. Measured wind ratios (u/u0) as a function of height ratios (z/z0) (blue circles), with z0 = 2.8 meters, collected on flat terrain with packed earth and low grasses < 0.25 m tall, along with the power law least squares fit to the data. The results of the measurements are shown in Fig. S2, along with a fit to the data with The data were collected on flat terrain with packed earth and low grasses < 0.25 m tall. Wind conditions during the test were 6 ± 1 m/s. The uncertainty in the vertical wind ratio is derived from the manufacturer supplied accuracy of the anemometer (0.5 m/s, assumed to be 2-sigma) and the average wind speed during the test. Given this error, we determined the uncertainty in the exponent using a simple Monte Carlo analysis to be ±. Using this wind profile, the flux can be calculated using the flux plane equation. We note that in an instantaneous measurement the vertical wind gradient may not follow the above equation, due to turbulent eddies. The simple equation above is valid only for an ensemble average of wind field realizations. This variability from plume to plume affects the precision of our measurements, an effect which is captured in our validation experiments. Validation Experiments: Methods S5

6 Validation experiments were performed on an MFP system with four inlets located on a mast at the front of a vehicle at heights of 0.5 m, 1.7 m, 2.9 m, and 4.2 m off the ground. In these experiments, methane was released at a controlled rate using a mass flow controller (Sierra Instruments, Model C50L-AL-DD-2-PV2-V0-FG, Monterey, CA, USA). Measurements were made during the day with different advective wind speeds, at different flow rates, at different distances and emission heights. The measurements were made during the day on packed earth with low grasses (<0.25 m) in Colorado (March 2013), and with high grasses (~1 meter) and pavement in North Carolina (May 2013). Table S1 summarizes the release conditions for the validation measurements: Table S1. Release conditions for the MFP validation experiments in Colorado and North Carolina. Parameter Conditions min max (mean ±std. dev.) Comments Distance to source 5 81 m (34 ± 15 m) Release Height m (2.2 ± 0.9 m) Measurements above 3 meters were made on top of a ~2 m tall trailer to simulate a tank leak Methane Flow Rate kg / hr (1.07 ± 0.69 kg / hr) Wind Speed m / s (3.6 ± 2.95 m/s) A total of 120 measurements were made, with 30 measurements under Pasquill-Gifford atmospheric stability class C and D, and 90 under stability class A and B. The median wind speed for all the measurements was 2.6 m/s, and the mean was 3.6 m/s. The validation measurements were performed with the angle between the advective wind and the normal to the surface being S6

7 within about ± 60 degrees. No significant angular bias were observed in the resulting flux measurements. The four measurements of the concentration at different heights provides quantitative information about the vertical plume distribution. For each plume transect, we calculate the centroid z cent and width σ of the plume by fitting the vertical profile to a simple Gaussian plume (using least squares optimization), including reflection at the ground surface z = 0, where integration in the transverse horizontal plane has been performed: f(z) = f 0 (e (z z cent )2 2σ 2 + e (z+z cent )2 2σ 2 ) (S3) It is important to note that the Gaussian width is not the width of the time-averaged plume, but a narrower width that captures the concentrated nature of the instantaneous plume. In addition we note that although we are modeling the vertical distribution according to this simple Gaussian plume model, single transects of individual plumes can deviate substantially from this model due to the filamentary and turbulent nature of the instantaneous plume. The Gaussian model cannot fully capture this more complex structure. These errors are contained in the validation experiments described below, and contribute in part to the observed precision and accuracy. In the fits, the centroid was limited to 8 meters, above which there is insufficient data to properly constrain the fit. In the experiments, only 6 out of the 120 measurements (5 %) were observed to exceed this limit. The centroid and width are plotted vs. the ratio of the highest inlet to the total (r top ) in Fig. S3, for all 120 measurements. Not surprisingly, there is a correlation between z cent and r top (ratio of the top inlet flux to the total measured flux). In addition, the width of the plume increases with r top. S7

8 Figure S3, top panel: measured plume centroid (vertically) as a function of the ratio of the top inlet signal to the total measured flux. The dashed gray lines indicate the location of the four inlets. Bottom panel: measured plume width. In both panels, the blue and red symbols are for Pasquill- Gifford stability classes A and B, and C and D, respectively. See text for details of the fitting method. S8

9 Figure S4. Mean of the measured plume centroid as a function of release height. The labels next to the symbols indicate the number of measurements contributing to each data point, and the error bars indicate the variability (standard deviation) of the measurements at each height. The blue data points obtained by release on tripods that do not significantly obstruct the wind. The red data point was released on a physical structure of approximately 2.5 m height. The 1:1 line is indicated in gray. Figure S4 displays the measured average centroid z cent as a function of release height. For releases below 3 meters (blue points), the gas was released at the top of a tripod, without a physical structure below the release point. For the highest release point above 3 meters (red point), the gas S9

10 was released from a point above an approximately 2.5 m tall structure (in this case, a mobile trailer), with the intention of simulating a leak from the top of a condensate or produced water tank. For the tripod releases, the measurements of the centroid track the actual release height within the uncertainty of the measurement. For the releases from on top of the trailer, the effective plume centroid is approximately 1.3 m below the actual release height. This difference is likely due to the downdraft in the wind resulting from the aerodynamics of the release structure.. If true, this downwash effect allows the 4.2-m tall sampling pole to be used to quantify leaks on comparably tall or even somewhat taller structures. Figure S5. Vertical Gaussian plume width plotted as a function of the plume propagation time. Plume which are transported quickly to the measurement plane are smaller than plumes which have longer transport times. The gray points show individual plume measurements, and the green points and error bars are the mean and standard deviation within each distance bin, spaced S10

11 geometrically. The blue line is a fit to the expression σ = 2Dτ, with a diffusion constant of 0.11 m 2 / s. In Figure S5, we plot the width of the plume vs propagation time from source to measurement plane, defined as the distance divided by the advective wind speed. A more careful analysis of the data would consider not only the propagation time, but the turbulent mixing driven by solar heat flux and surface roughness, but for simplicity, we consider only the propagation time. There is a clear dependence on the measured instantaneous plume width on propagation time, as expected: plumes that have less time to propagate are smaller than those which take longer to propagate. The blue line in the figure is a fit to the expression σ = 2Dτ, resulting in a diffusion constant of 0.11 m 2 / s. For Pasquill Gifford stability classes A through D, the time averaged plume width vertically ranges from about 3 15 m at 100 m distance downwind (or about seconds propagation time). The observed plume widths are somewhat narrower than these values, for two reasons. First, these validation experiments were performed over a range of 5 81 m from the source, so we should expect the time averaged plume width to be somewhat smaller than 3 15 meters. In addition, the meandering of the plume vertically is a significant if not dominant contribution to the overall ensemble plume width, so the time-averaged value should represent a maximum value. Plume Integration Methods S11

12 Figure S6. An example plume measured with the four-inlet mast. Black circles: relative horizontally integrated concentrations observed during the plume transect. Blue line: Fit of the black circles to a simple Gaussian plume including ground reflection, as described in the text. Purple hatched area: trapezoidal integration of the flux contained in the area bounded by the lowest and highest inlet points. Cyan area: total integration of the Gaussian fit from ground level to +. Gray dashed line: vertical wind profile used to quantify the flux through the surface. The four vertical measurements together with the vertical advective wind profile can also be used to quantify the emissions. Consider an example vertical plume profile, shown in Fig. S6. The black circles in the figure are the horizontally integrated concentrations observed during the S12

13 plume transect. The blue line is a fit to the data to a simple Gaussian plume including ground reflection (Eq. S2). We will consider two different integration methods. The first method is a conservative trapezoidal integration of the flux contained in the area bounded by the lowest and highest inlet points (which we will call TRAP ). Second, we perform a total integration of the Gaussian fit (which we will call GF ) from ground level to + (cyan area). Both methods use the same wind profile as described above, with a power law of To investigate the relative performance of the fit method and the two integration schemes, we have constructed a Monte Carlo plume simulation. In this simulation, we have generated N = 10,000 plume realizations of the form described by Eq. (S3), in which the effective emission source height z cent and the Gaussian width σ were each varied evenly, in an uncorrelated fashion, over a range of 0 6 and meters, respectively. From this simulated plume function, the measurements at each of the four measurement heights are determined to simulate the measurement by the four inlets. A moderate amount of random noise was added to each of these four measurements equal to 1% of the total of the four measurements. 1% corresponds to the observed noise of approximately 10 ppb on a plume peak of 1 ppm. These data were then fit to the same plume function described by Eq. (S3) for each plume realization. Because of the noise added to the measurements, the fit returns somewhat different values for the centroid and width. Two selection criteria were applied to the simulation: a) realizations where the top inlet was less than 40% of the total for all four inlets and b) where the plume centroid from the fit was below the top inlet height. 81% of the realizations met these two criteria. We show the recovered centroid and plume width for these realizations in Fig. S7. The plume width from the fit follows the actual model width up to about 2.5 m, above which it tends to underestimate the width and the noise increases. The centroid obtained from the fit also follows S13

14 the model centroid, although the fit has trouble properly locating the centroid when it is near the ground. This result is expected, since it is clear from the model function that it is difficult to distinguish the two Gaussian terms when z cent < σ. Further, the model has difficulty properly recovering plumes with centroids above the highest inlets. Figure S7, left panel: recovered plume width as a function of model function plume width for the Monte Carlo simulation. Purple points represent all the realizations that met the criteria described in the text, and black circles with error bars represent the mean and standard deviation within each bin (0.2 m wide). The green dashed line is the 1:1 line. Right panel: recovered plume centroid as a function of the model function centroid. The blue points are the individual plume realizations, and the black circles are the mean and standard deviation within each bin (0.2 m wide). The green dashed line is the 1:1 line. See text for more information. Figure S8 shows the results of the two integration methods, TRAP and GF. The TRAP method (left panel of Fig S8) recovers about 80% of the total for plume widths smaller than about 1 m, S14

15 and about 60% for plume widths of about 3 meters. The precision is about ± 20% of the measured ratio. The fact that the method underestimates the plume is not surprising, for two reasons: 1) the plume below the lowest inlet at 0.5 m is ignored, as is the tail of the plume above the highest inlet of 4.1 m, and 2) the trapezoidal integration method tends to underestimate integrals of functions that are concave down, like the central portion of a Gaussian. The first effect is by far the dominant effect. The right panel of Fig (S8) shows the emission ratio using the integral of the Gaussian fit from the data. The accuracy is much better, equally about 1.0 for all plumes except very narrow plumes (below 1 m), where the method overestimates by about 20%. However, the noise is somewhat larger, with a standard deviation of ±30%. Limiting the integral of the Gaussian fit to the extent of the vertical mast largely reproduces the trapezoidal integral, within the noise of the data. Figure S8, left panel. Ratio of emissions recovered from trapezoidal integration (of the four inlet locations) to total emissions in the Monte Carlo simulation. The measurements recover about 80% of the total for plume widths smaller than about 1 m, and about 60% for plume widths of about 3 S15

16 meters. The precision is about ± 20% of the measured ratio. Right panel, same ratio using the integral of the Gaussian fit from the data. The accuracy is much better, equally about 1.0 for all plumes except very narrow plumes (below 1 m), where the method overestimates by about 20%. In Fig S9, we see the same integration results, only now using the recovered fit width to parameterize the emission ratio. The TRAP method has a similar shape, with the exception that the emissions are not well represented with the fit width is less than about 0.5 m. The emissions ratio using the GF method is well behaved throughout the range, with the exception of a large overestimate below 0.5 m, and a ~10% underestimate between 1.5 and 2.5m plume width. Figure S9. Same as Figure 12, except that the results of the Monte Carlo simulation are plotted against width as reported by the fit to the Gaussian plume. The dip in the ratio for a measured plume width of 2 m in both figures is due to the tendency of the Gaussian fit to underestimate the plume width for large plumes. Validation Experiments: Results S16

17 With the results of the Monte Carlo simulation to provide context, we return to the results of the controlled release experiments. Figure S10 displays the emission ratio statistics, in which the emission ratio was calculated via the two integration methods, TRAP (purple triangles) and GF (blue triangles), and where we have restricted the data set to a) plumes with a centroid below the top inlet, b) advective wind speeds greater than 1.0 m/s, and c) a measured Gaussian width parameter less than 5 m. N = 101 out of 120 measurements, or 84%, satisfied these three criteria. Error bars are the standard deviations of the data in each bin, and the circles in each figure are the results of the Monte Carlo simulation for comparison. Figure S10. Results of controlled release experiments, in which the measured mean emission ratio was calculated via the two integration methods, TRAP (purple triangles) and GF (blue triangles). Error bars are the standard deviations of the data in each bin, and the circles in each figure are the S17

18 results of the Monte Carlo simulation for comparison. The numbers by each symbol indicate how many plumes contributed to the average. We see general agreement between the validation measurements and the Monte Carlo simulations for both integration methods. In particular, given these results, we make the following observations: 1. The TRAP method tends to underestimate the true emission rate by anywhere from 10 50%, depending on the vertical extent of the plume (with larger plumes leading to larger degrees of underestimation). The mean and standard deviation of the distribution is 70% ± 44%. The large standard deviation of 44% indicates that there is a non-zero probability of measuring a negative emission ratio. Given this non-physical result, we expect that a log-normal distribution is a better representation. 2. The GF method reproduces the flux without substantial bias, the effect of different plume shapes has not been quantified. The mean and standard deviation of the distribution is 97% ± 59%. In Figure S11, we show the measured width of the plume (top panel) and the recovered emission ratio (bottom panel) for the two integration methods. The fact that the plume width is inversely dependent on lateral wind speed is another way of looking at the results in Fig. S5. This highlights the fact that the advective wind is more than just a simple multiplier in the flux plane equation, since the physical extent of the plume is affected by the advective wind speed. The bottom panel shows a relatively strong dependence of the recovered emission ratio on the advective wind speed. At least in part, this is due to the increasing plume size at lower wind speeds, leading to underestimates in the emissions for the TRAP integration method, but this is not enough to account for all of the variation. S18

19 Figure S11, top panel: measured plume width as a function of lateral wind speed relative to the vehicle. As expected, higher wind speeds correspond to narrower plumes. Numbers by each symbol indicate the number of measurements in each bin. Bottom panel: ratio of measured emission rate to actual emission rate for two integration methods, TRAP (purple) and GF (blue), S19

20 for the same bins. Both methods underestimate the emission ratio at low wind speeds. See text for further discussion. Other potential sources of bias are listed below: 1. Anemometer errors: The stated accuracy of the anemometers used in this study is 0.5 m / s. A bias at zero, or a span error, will lead to uncertainty in the recovered emission rate. Given the mean wind speed of 3.1 m/s, this 0.5 m / s uncertainty corresponds to a 16% error (95% coverage) 2. Horizontal analysis errors: To reconstruct the horizontal axis of the concentration map on the flux plane surface, it is necessary to know the velocity of the vehicle (derived from GPS), the flow rate into the storage tubes during the recording phase, and the flow rate from the storage tubes during the playback phase. Errors in any of these quantities would lead to errors in the recovered measurement. We estimate this error to be 15% (95% coverage). 3. Vertical wind gradient errors: Any error in the actual wind gradient can lead to uncertainty in the reconstructed plumes, and a bias depending on the measured plume centroid. With a power law exponent of 0.17, the lowest inlet has a wind speed that is 69% of the top inlet. The next lowest inlet is 86% of the top inlet. If the power law exponent is 0.1 (a significant difference), the lowest inlet wind speed is 81% of the top inlet, for a 12% difference, and the next lowest inlet is 92% (or 6% different). Given these results, we estimate the statistical error due to the wind gradient at less than 10% (95% coverage). 4. Atmospheric effects: It is important to remember that the time-averaged emission rate through the flux plane is equal to the time-averaged emission rate from the source, even S20

21 if the source emission rate is constant. At any given point in time, the instantaneous flux through the plane can be higher or lower than the source emission rate, depending on the turbulent dynamics of the atmosphere. More work is needed to investigate these effects. Of these potential uncertainties, the fourth is well sampled in the validation experiments, and should be captured by the variability in the measurements. The first, second, and third uncertainties are not captured during the measurements, and therefore represent a potential overall uncertainty, which we estimate to be 24% (95% coverage) by adding the individual uncertainties in quadrature (because they are uncorrelated errors). Figure S12. Histogram of normalized emissions rate measurements from controlled releases on a log scale using the TRAP (left panel) and GF (right panel) integration methods (bars), along with a log-normal fit to the data (red lines). For the TRAP method, the center is and the width is 0.65; for the GF method, the center is and the width is The dashed line in both panels shows the log-normal distribution of the alternate distribution for reference. S21

22 In Fig. S12 we display the histograms of the N = 101 measurements shown in Fig. S10, for the two integration methods TRAP (left panel) and GF (right panel), along with fits of the data to lognormal distributions. In a log-normal distribution, the probability density function (pdf) of the natural log of the emission ratio is modelled with a Gaussian of center μ log (which is simply the mean of the natural logs of the measured emission ratios, or ln ( E meas E act ) ), and width σ log (which is just the standard deviation of the natural log of the emission ratios). The widths of the two distributions are the same (0.65 for TRAP and GF), indicating that the precision of the two methods are the same, but the centers of the two distributions are different (-0.60 and for TRAP and GF, respectively); this is a consequence of the fact that the TRAP method tends to underestimate the emission rate relative to the GF method. Note that the actual distribution of both integration methods seems to be skewed toward negative values on the log-axis; in other words, negative outliers are more likely than positive outliers. Unlike the normal distribution, where the mean, median, and mode are all the same, the lognormal distribution has different values for each of these three quantities. The arithmetic mean of a log-normal distribution is given by e μ log+ 1 2 σ 2 log, the median by e μ log, and the mode by e μ 2 log σ log. Another way of characterizing log-normal distribution is with the geometric mean and geometric standard deviation. The geometric mean is the same as the median; i.e., e μ log; the geometric standard deviation is e σ log. The population can be interpreted as with a normal distribution, except that the geometric standard deviation is multiplicative rather than additive. For example, for a distribution with a geometric mean of 0.75 and a geometric std. dev. of 2.5, 95% of the distribution is contained between 0.75/(2.5) 2 and 0.75*(2.5) 2, or between 0.12 and The arithmetic mean, geometric mean, and geometric std. dev. of the TRAP method is 0.77 ± 0.04, 0.64 ± 0.04, and 1.92 S22

23 ± 0.12 respectively, and for the GF method these statistical values are 1.07 ± 0.06, 0.86 ± 0.06, and 1.91 ± 0.12, where the uncertainty (one sigma) in the parameters have been determined using bootstrap resampling (Mooney and Duval 4 ) with a Monte Carlo simulation with 10,000 realizations. In conclusion, 1. The MFP method is a viable method of measuring emissions: Using a conservative trapezoidal integration (TRAP) method, which quantifies the emissions that traverses the flux plane surface, the method recovers on average 70% of the emissions over a wide range of lateral wind speeds and captured plume shapes. Restricting the measurements to strong lateral winds (> 2.5 m/s) and small plumes (<3 m), the TRAP method recovers 88% of the emissions. Using the Gaussian fit (GF) integration method, 107% of the released flux is recovered using the MFP method, over a broad range of conditions: lateral wind > 0.5 m / s, centroid below the top inlet, and a width parameter less than 5 m, corresponding to 83% of all measurements in Pasquill Gifford classes A through D. 2. The precision of the MFP method is -70 % / + 63% for the TRAP and GF integration methods. 67% of measurements of a given leak will be within 1 standard deviation of the mean (in natural log space), or For Pasquill-Gifford classes A and B (N = 73), the lognormal width is about 0.73 for the TRAP and GF methods, and for classes C and D (N = 30), the lognormal width is about 0.32 for both integration methods, indicating the detrimental effect of the higher levels of turbulence given smaller advective winds. While this level of precision is not ideal, it is more than adequate for quantifying leaks from well pads, which have a much larger and more skewed distribution than the measurement distribution, as will be seen below. S23

24 3. Statistical analysis of the validation experiments by bootstrap resampling imply that the TRAP method recovers 70% ± 9% of the total emissions (95% confidence), and the GF method recovers 107 ± 11% (95% confidence). We note that this uncertainty is the order of the uncertainty due to anemometer error, horizontal reconstruction error, and vertical gradient error (24%). Further work is necessary to improve the measurement accuracy. Detection Limit of the MFP method The MFP method relies on the detection of the plume with a single sampling inlet downwind of the source. The triggering of the analysis is done on the basis of the peak concentration observed in the plume; for this study, we have employed a trigger threshold of about 50 ppb above the local methane background. For a given leak rate, there is a distribution of single-inlet peak concentrations depending on a variety of factors, including but not limited to wind speed, plume centroid height, plume width, and distance to the source. Therefore, the converse also holds true: a given peak concentration measured in the plume corresponds to a distribution of leak rates at the source, depending on the same various factors. This means that the MFP method does not have a simple detection threshold, but rather has a detection threshold that may be described as a probability that varies as a function of emission rate. The detection limit Q 0 as calculated from a given event is given by the following simple expression: Q 0 = C trigger C measured Q release (S4) In this equation, C trigger is the trigger level used at the monitor inlet, typically 0.03 ppm in these experiments; and C measured is the actual peak level measured at the monitor inlet for a given event. The right panel of Fig. S13 shows the distribution of Q 0 obtained for the controlled release S24

25 experiments. The arithmetic mean of the distribution is kg / hr, with a geometric mean of kg / hr and a geometric standard deviation of 2.6. In other words, the detection probability would be 50% for a kg / hr leak under similar conditions; further, there is a 97.5% probability of detecting a leak that is twice the geometric standard deviation above the geometric mean, or x 2.6 x 2.6 = 0.14 kg / hr. Figure S13, left panel: the distribution of detection thresholds for leaks for the controlled release experiments. The arithmetic mean of the distribution is kg / hr, with a geometric mean of kg / hr and a geometric standard deviation of 2.6. Right panel: the distribution for the scaled leak threshold q 0 for the same distribution. The arithmetic mean of q 0 is kg / hr m -1 s -1/2, with a geometric mean of and a geometric standard deviation of 2.2. This scaled leak threshold distribution will be used to determine the sensitivity of the MFP measurements in the Barnett Shale. To extrapolate this detection limit to the MFP measurements made in the Barnett Shale, we search for a scaling law to remove some of the variability in the detection due to different S25

26 conditions: in particular, wind speed and source distance. The peak of a Gaussian plume is given by the following simple expression: C peak = Q 2πu x σ y σ z (S5) We can construct a scaling law relating the peak concentration to the leak rate. As is evident in Fig. S5, the vertical width scales with the square root of propagation time. We expect that the horizontal width has a similar scaling, but because the width of the plume horizontally is smaller than the response function of the instrument for the plume sizes and driving speeds in this work, this variability can be ignored. We thus arrive at a scaling law relating the leak rate to the peak concentration: C measured C trigger = Q q 0 u x τ = Q q 0 u x d (S6) Where we have used C measured, the peak concentration measured at the monitor inlet, as a proxy for the peak concentration. By comparing this equation to the equation for Q 0, we find the following simple expression for the scaled detection limit q 0 : q 0 = Q 0 u x d (S7) The right panel of Fig. S13 shows the distribution of q 0 for the controlled release tests. The arithmetic mean of q 0 is (kg / hr m -1 s -1/2 ), with a geometric mean of and a geometric standard deviation of 2.2. The log-normal distribution is narrower than the Q 0 distribution, indicating that the scaling has removed some of the variability in Q 0, but that the bulk of the variability (85%) remains. Note as well that at larger source distances (greater than about 150 m), the size of the plume in both directions and the variability of the plume centroid will limit the ability of the MFP instrument S26

27 to detect and capture the plume. For these practical reasons, we limit the practical detection distance to 150 meters, outside of which our validation work (up to 80 m) no longer applies. Measured Emissions in the Barnett Shale Table S2 lists the 115 well-pad measurements performed in the Barnett Shale. Table S2. Measurements of emission rate (in kg / hr) on 115 individual well-pads in the Barnett Shale using the MFP technique, in order of increasing emission rate S27

28 References 1. Karion, A., Sweeney, C., Tans, P., & Newberger, T. (2010). AirCore: An innovative atmospheric sampling system. Journal of Atmospheric and Oceanic Technology, 27(11), De Nevers, N. (2010). Air pollution control engineering. Waveland Press. 3. Heier, S. (2006): Wind Energy Conversion Systems, 2nd ed., John Wiley & Sons. 4. Mooney, C. Z., & Duval, R. D. (Eds.). (1993). Bootstrapping: A nonparametric approach to statistical inference (No ). Sage. S28