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Homework Assignment - 4

Air Pollution Engineering (MCHE 4400/6400), Spring 2024

Due on: Friday, March 29 at 11:59 pm

Submit to eLC (follow instructions that Anita posted oneLC)

Problem statement:

You are tasked with building a box model that simulates some key processes of smog formation over a small city during a subsidence inversion episode for the period between 8:00AM and 6:00PM. The city has dimensions of 10 km by 10 km, and the mixing height can be considered to be 200 m. The wind speed is 1.5 m/s. The temperature is 20 °C and the relative humidity is 60%. Your model should account for the following chemical reactions:

i)          O3   photolysis leading to OH production. Use the same rate constants for the relevant reactions as those given in class (assume that the photolysis rate of O3  does not change overtime).

ii)         Reaction of OH with volatile organic compounds (VOCs) according to: VOCs + OH à Products (k = 2 x 10-12  (cm3/molec.s)

The emission rates and background concentrations (which you can also assume to be initial concentrations in the box at 8:00AM) are:

*Note: This is a simplification. As you know, O3 is a secondary pollutant that is not emitted directly, but forms in the atmosphere. You can think of the emission rate here as a ‘formation rate.’

1.   Present the governing box model differential equations and chemical reactions. (30 pts)

2.   Implement the resulting system of equations numerically in MATLAB in order to calculate the evolution of the concentrations of each of the pollutants between 8:00AM and 6:00PM. Use a time step of 0.1 seconds. Generate plots of (i) O3 and VOCs mixing ratios versus time on the same plot, and (ii) OH molecular concentration versus time on a separate plot. (70 pts)