Process Safety and Environment Safety - Math Problem Example

Name: Course: Instructor: Date: Process Safety and Environment Safety The Pasquill-Gifford formula provides an outline of the dispersion coefficient and stability classes. It assumes that the Gaussian materials can be spread out through a normal process of distribution. The Pasquill-Gifford formula shows that the dispersion of coefficients is normal, where when the plume is swept by the wind velocity as will be shown below, it is spread in a downwind concentration (García-Díaz and Gozalvez-Zafrilla, 19). The Pasquill-Gifford Model is presented as a classic equation that determines the pollutant concentration in the air that uses air through the predefined parameters such as wind speed, stack height, emission rates and distance. The equation below is the Pasquill-Gifford formula, which describes the concentration values expressed as below: For neutral to moderately unstable atmospheric conditions and distances out to a few metres. The concentrations should be within a factor of 2 or 3 of the actual values. Usually, σz is less certain than σy especially for x>1km. To find σy and σz we use the empirical equations σy = Cxd where x= downwind distance given in km σz = axb = a,b,c,d = coefficients from the tables below. The assumption is that downwind/downstream distance = 1km where the stability is of class A Pasquill Gifford Stability Category Parameters used to calculate Pasquill-Gifford formula σy C D A 24.167 2.5334 B 18.333 1.8096 C 12.5 1.0857 D 8.333 0.72382 E 6.25 0.54287 F 4.1667 0.36191 σy = Cxd σz = axb C = 24.1670 a = 453.850 D = 2.5334 b = 2.11660 σy = Cxd = 24.1670 (1km) 2.5334 = 24.17m σx = axb = 453.850 (1km) 2.11660 = 453.9m Parameters used to calculate Pasquill Gifford formula σz Pasquill Stability Category x(km) a b A 3.11     i) The concentration of a pollutant as a function of distance is given where x-distance vary from 100m to about 500m ( at intervals of 50m) for the following conditions: Wind velocity = 1 m/s; Day time, cloudy skies. Wind velocity = 1 m/s; Night sky, clear skies. Q = 0.1 kg/s in all cases H = 30m. Y distances varies from 0m to about 200m at the height where z = 0m Q = 0.1kg U =1m/s H = 30m Y = 200m Z = 0m (which is the ground level) σy=24.17m σz = 453.9m At ground level, Pasquill- Gifford formula is reduced to the following C (x, y, 0) = Q/ Π4 σy σz [exp –H2/ 2σ2z ) exp (-y2/zo 2 y) 0.1 / Π *1 * 24.17 * 453.9 = 0.0000029014 σ ( -302 / 2 * 206025.21) = (0.0021841987) σ = 0.0593726763 σ (-200 / 2 * 584.1889) = σ (34.235501565) = 93.061741792 Product of all = 0.0001603117 = 0.0001603117kg/m3 0.0001603117 / 1000 = 0.1603117g/m3 ii) Y distances varies from 0m to about 200m at the height where z = 15m Q = 100g/m3 U = 1m/s y = 200m z = 1m σy = 24.17m σ = 453.9m H = 30 (100 / 2 * Π * 24.17 * 453.9 * 1) * σ (40000 / 2 * 584.1889) 0.0014507189 * 93.061741791 = 0.1350064276 e ( 152/ 2 * 206025.21) = 0.0014843167 e (-452 / 2 * 206025.21) = 0.0133588522 0.1350064276 * (0.0014843167) + (0.0133588522) = 0.0020039232g/m3 iii) Y distances varies from 0m to about 200m at the height where z = 40m Q = 100g/s U = 1m/s y = 200m z = 40m σ y = 24.17m σ z = 453.9m H = 30m Based on equation 2: (σ / 2Π yσµ) and the equation σ (-y2 / 2 σ y2) = 0.1350064276 [ σ (-102 / 2 * 206025.21) ] + [ σ (-702 / 2 * 206025.21) 0.0006596964 + 0.323251238 = 0.032984202 The two sums are joined together. 0.1350064276 * 0.032984202 = 0.0044531627g/m3 Horizontal and vertical stability parameters are therefore, given through the Pasquill-Gifford equation as shown above. Where the atmospheric stability conditions are given through the coefficients of the equation above. Task 2: plot the C(x,y,z) vs. the x-distance Task 3: 2D map with the horizontal axis being the x-distance, where y is the y-distance with the contour values of the plume well highlighted. The plume as presented above presents the dispersion of the plume, which represents the normal distribution through the crosswind distance axes and the vertical distances provided. The co-efficients of the dispersion functions present the atmospheric downwind distance conditions (García-Díaz and Gozalvez-Zafrilla, 17). The stability of this conditions is dependent on the wind velocity as presented above. At day time, the wind velocity leads to an increase in the stability compared to night time atmospheric stability. The pasquill-Gifford plume model presents that the dispersion co-efficient provided in the grapg is a downwind distance function with the increased tmospheric stability (Haight, 49). The plume centerline is given at the concentration level of z = 0, through the downwind function. The increased concentration presents that the maximum concentrtion occurs through the continous ground level, which is given using the pasquill-gifford formula. Thus, the plume model shows the behvior of the material in a countinous source as it is directed through the velocity of the wind Conclusion The concentrations of the pollutants change depending on the changes that the stack height undergoes. For instance, equation i), ii), and iii) above have different stack heights given in the Y-distance that varies between 0m, 15m, and 40m. The results provided above show that the concentration pollutants based on the pasquill-gifford and it is influenced by facctors such as weather conditions, wind velocity, position and time among others. The coefficient provided to solve the equations show standard concentration deiations in the downwind direction represented as x in the equation C (x,y,z), where y represents the crosswind and z represents the vertical concentration deviation. Works Cited García-Díaz, J, Carlos and J, M Gozalvez-Zafrilla. "Uncertainty and sensitive analysis of environmental model for risk assessments: An industrial case study." Reliability Engineering & System Safety (2012): 16-22. Journal. Haight, M, Joel. Handbook of Loss Prevention Engineering. 2. New York: John & Wiley Sons, 2013. Read More