Supplementary material file
Leakage and diffusion model of heavy gas
The molecular weight of CO2 is 44g/mol, and the molecular weight of air is 29g/mol. Thus, CO2 can be treated as a heavy gas. The SLAB program, developed by Lawrence Livermore National Laboratory in California (USA) to assess the sudden release of heavy gas pollutants,was used in this paper to simulate the dispersion of CO2. The SLAB program establishes a rectangular coordinate systemby taking the source of the release as the origin, the downwind direction as the x-axis, the crosswind direction as the y-axis, and the vertical direction as the z-axis(Ermak, 1990). The model in the SLAB program can be used to simulate the dispersion process of four types of sources, i.e.,releases from evaporating pools, releases from horizontal jets, releases from a vertical jet ora stack, and instantaneous or short-duration releases from evaporating pools (Yang et al., 2006). The diffusion models in the SLAB program can be divided into two types of diffusion modes, i.e.,the steady state plume mode and the transient puff mode. The SLAB program can be used to assess continuous, finite duration, and instantaneousreleases (Ermak, 1990).
The SLAB model considers the concentration of the CO2cloud as a time-independent function, which means the shape of the cloud will reach steady state after some time of dispersion. The concentrations of CO2at some points in the cloud depend on the distance between the calculation point and the source where the cloud was released. Assuming that the air entrainment concept is valid, the mode of the steady state plume is based on the equation for the conservation of mass, momentum, energy, and species averaged in the crosswind direction (Fig. A1). As Eq.(1) shows, the concentration at every point in the cloud can be calculated according to the average concentration and the concentration distribution function. The transient puff mode is based on the equation for the conservation of mass, momentum, energy, and species averaged in the entire volume of the cloud (Ermak, 1990). As the puff that is formed drifts along the windward direction, it mixes with surrounding air (Fig.A2),and Eq. (7) is an expression of its concentration.
Fig.A1.Heavy gas cloud dispersing in the plume dispersion mode (Ermak, 1990)
,(1)
where:
(2)
(3)
(4)
(5)
,(6)
where x, y, and z represent the downwind direction, crosswind direction, and vertical directionm, respectively; t is the release time, s; B and h are the half width and height of cross section, m, respectively; Maand Ms are the molecular weight of dry air and the releases gas, kg/mol, respectively; are parameters of the cloud’s height; b and βare parameters of the cloud’s width; u is the velocity of cloud in the downwind direction, m/s; vg is the horizontal crosswind gravity flow velocity, m/s; ve is the horizontal entrainment rate, m/s; m is the mass concentration of the cloud, kg/m3; erf is the error function; is the average concentration; and are the crosswind and the vertical profile functions, respectively.
Fig.A2.Dispersing the cloud of heavy gas in the puff dispersion mode (Ermak, 1990)
,(7)
where are the plume’s half-length parameters; and are the plume’s half-width parameters; and are the horizontal downwind and crosswind gravity flow velocities, respectively; is the average concentration of the whole plume, which is calculated by Eq.(2), in which the independent variable is changed from x to t. The crosswind and vertical profile functions are given by Eqs.(3) and (5), respectively, where ，，now are functions of t rather than x; the new function has the same form as.
REFERENCES
Ermak, D.L. (1990). User's Manual for SLAB: An Atmospheric Dispersion Model for Denser-Than-Air Releases, Lawrence Livermore National Laboratory, Livermore, CA, USA, p. 150.
Yang, D., Chen, G. and Zhang, R. (2006). Estimated Public Health Exposure to H2S Emissions from a Sour Gas Well Blowout in Kaixian County, China. Aerosol Air Qual. Res. 6: 430-443.