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Traditional Mass Balance

Mass balance methods are, in essence, based upon the Law of Conservation of Mass. This approach hinges upon the principle that, for a conserved tracer, if one measures the mass of a species entering the system and the mass of that species exiting the system, then the mass originating from within the system (i.e., an emissions source) can be determined as the difference (the balance) of the two measurements. With the additional knowledge of flow rate (i.e., wind speed), a flux can be calculated as a horizontal mass flow across a vertical plane (White et al., 1976). emitted massi = v • ∫nzdz • ∫Xidy 

In the atmosphere, this approach is often used for long-lived trace-gas species, such as methane or CO2. Numerous studies have demonstrated the utility of using an aircraft platform for performing mass balance measurements to determine emissions from large area sources, such as landfills, oil and gas fields, and even entire cities (e.g., Mays et al., 2009; Karion et al., 2013; Caulton et al., 2014; Cambaliza et al., 2015; Peischl et al., 2015; Peischl et al., 2016). For aircraft-based mass-balance measurements, transects are typically flown perpendicular to the wind direction both upwind (to obtain the background) and downwind of the source of interest. These transects may consist of multiple stacked legs (i.e., a curtain pattern) or a single altitude transect within the boundary layer that is sufficiently downwind of a source such that the trace-gas species is fully mixed within the boundary layer. In other situations, such as when there are no significant upwind sources of species or nearby rising terrain presents physical limitations, transects may only be flown on the downwind side. In this case, the “background” concentration of the gas can be assumed from the edges of the transect that are outside of the source plume.

Gauss’s Law

The traditional mass-balance approach is typically best suited for large area sources, such as an entire oil and gas production field, for example, or a large source that is isolated/remote from other sources. The development of the Gauss’s Theorem method grew out of the need to identify and quantify emissions from individual point sources, such as individual well pads within an extensive oil and gas production field. This approach relies on flying consecutive loops around a targeted source at multiple altitudes to create a virtual cylinder that encompasses the lowest safe-flight level (~200 ft agl) and extends up to an altitude just above the vertical extent of the measured plume. In this fashion, the plume is fully contained within the cylinder, and the volume flux of a gas out of the cylinder (downwind from the source) can be determined and corrected for the flux of that gas entering into the cylinder (upwind from the source). Gauss’s Law is used to convert the volume integral to a surface integral to calculate the horizontal mass flow of gas across the surface plane of the cylinder (Conley et al., 2017).

In practice, a full “research-grade” quantification of a point source requires ~15-20 laps (approximately 30 minutes flight time). The uncertainty of the resulting emissions estimate reduces as the number of laps is increased. Under optimal conditions, demonstrated uncertainties are quite low, often better than 10%, and limits of detection are 5 – 10 kg/hr. For applications for which high measurement accuracy is not required (e.g., do we have a small leak or a large leak?), quick-look estimates can be achieved in as little as 5 – 10 minutes to provide an order-of-magnitude level emission rate. This approach can greatly increase time efficiency and cost efficiency when assessing numerous sites.

The diameter of the loops (i.e., the measurement footprint) flown by the airplane is typically 1 – 2 km. Thus, in areas with more densely located sources, the measurement footprint may potentially contain more than one individual point source. In this case, the resulting emissions estimate will represent the total emissions from all sources located within the footprint. For smaller sources and for where near-field quantification and pinpoint-location accuracy are desired, our unmanned drone platforms are the ideal solution. Our drones operate on the same principles as our aircraft, including the capability for measuring horizontal winds, and offer a much lower limit of detection (.01 kg/hr). The ability to fly nearer to sources, combined with the winds and methane measurements, allows us to locate the source of a leak to within ~ 1 meter. 

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