Document OEm0YeE6BzNMwR3BVdLz93MZw

AR226-2240 Vapor Scavenging Coefficient Estimation Vapor scavenging coefficients are used to estimate the rate of removal of a soluble species that exists below the cloud line based on rain event characteristics, such as intensity and droplet size. This section explains the technical basis for the estimation of the scavenging coefficient of C-8 out of the vapor phase. Th e basis for this estimation is provided in "Atmospheric Chemistry and Physics" by J.H. Seinfeld and S.M. Pandis (1998, W iley & Sons). Two key assumptions have been made for the purposes of this estimation. First, we have assumed C -8 is irreversibly absorbed into the rain droplet. This is a reasonable assumption in this case, since the C-8 concentration in the droplet would be low and the C-8 would almost certainly be dissociated and therefore non-volatile. Second, while Seinfeld steps through a derivation for scavenging coefficients for a specified droplet size, it is much more accurate a determination to include a more representative spectrum of droplet sizes. This assumption will be discussed in more detail below. The scavenging coefficient for an irreversibly soluble gas by definition is A = ( x * D zp * K c *n)dDp where Dp is the diameter of the raindrop (cm), Kc is the mass transfer coefficient of a gaseous molecule to a sphere and n represents some raindrop size distribution relationship. The mass transfer coefficient, Kc, can be calculated by empirical correlations (Bird, R.B., Steward, W .E., and Lightfoot, E.N., "Transport Phenomena", W iley & Sons (i9 6 0 )), such as K, = 2 + 0.6 * Pair * U t * D Dn VL/2 \l/3 M-air Pair * D,9 J where Dgis the gas phase diffusivity of the species (cm2/sec), Ut is the droplet velocity (cm/sec), pair is the density of air (g/cm3) and p.air is the viscosity of air (g/cm-sec). The gas phase diffusivity of the C-8 molecule was estimated to be 0 0423 cm2/sec by the method of Fuller et al (Fuller E.N., Giddings J.C., J. Gas Chromatogr. Vol.3, 222 (1965); Fuller E.N., Schettler P.D., Giddings J.C., lnd.Eng.Chem. Vol.58(5), 18 (1966); Fuller E.N., Ensiey K,, Giddings J.C., J.Phys.Chem. Vol.73., 3679(1969).). Droplet velocity is a function of raindrop particle diameter, Dp, and for the purposes of this estimation, was estimated by a curve-fit of data from Table 20.1 (page 1006) of Seinfeld's book, and expressed as EDD0079359 Ut = 1041.7 * J d ~p The raindrop size distribution, n, as described by Marshall and Palmer (Marshall, J.S., and Palmer, M .W .M ., J. MeteoroL, V 5, pg 165-166 (1948)) is commonly used in estimating scavenging coefficients. According to the authors, this relationship may overestimate by as much as 50% the number of small droplets in the 0.02 to 0.12 cm size range, thus causing a conservative estimate of the scavenging coefficient. The relationship is expressed as n - 0.08 * exp{- 4.1 * D p * p ^ '21} where p,, is the rain intensity (mm/hr). (There is a typographical error in Seinfeld's book on page 1007. Above relationship comes from page 831) Substitution of the expressions for Kc, Ut, and n into the scavenging coefficient equation yields an integral expression that is difficult to integrate explicitly. For the purposes of this estimation, the final expression was numerically integrated between raindrop particle sizes of 0 and 1 cm. An upper limit of 1 cm was chosen because it represents a reasonable maximum raindrop size, as can be seen from extrapolation of the raindrop spectra data presented in Seinfeld's book, page 832. The number distribution at drop diameter equal to 1 cm is approximately 1.0E-09 and integration beyond that point adds no value to the final scavenging coefficient. Results of the numerical integration are shown below in tabular and graphical form. The maximum intensity value used was 30 mm/hr, which exceeded the maximum observed intensity of 27.9 mm/hr recorded at the Washington Works site during 1996. (This is the year of on-site meteorological data that has been processed for use in the ISC model.) EDD0079360 ieiiiBrS^5sssaHiszii SHSscasaavsaeggniiggsiBnaggi;g-! M11.B;/-mWmp/nBPB^BBB 0 4.408E-05 1 2.311E-02 2 3.106E-02 4 4.067E-02 6 4.705E-02 8 5.190E-02 10 5.583E-02 12 5.915E-02 14 6.203E-02 16 6.457E-02 18 6.685E-02 20 6.892E-02 22 7.082E-02 24 7.256E-02 26 7.418E-02 28 7.570E-02 30 7.711E-02 Scavenging Coefficients for C-8 EDD0079361