Computer Science School
Technical University of Madrid
Most of the Air Quality Standards from different countries focus the attention on several primary pollutants. Secondary pollutants such as ozone are also very important for the quality of the air. Typical concentrations ranges in the atmosphere of these pollutants, frequently called "criteria pollutants", are listed in the next table.
Criteria Pollutant Typical Range of Concentration
CO 0.2-50 ppm
SO2 1 ppb-2 ppm
O3 0.01-0.05 ppmm
N2 1 ppb- 0.5 ppm
NMHC 65 ppbC- 1.5 ppmC
Because ozone is one of the most hazardous species, we will focus on the simulation of this pollutant in this study. Ozone is produced by photochemical reactions of many compounds, which can be initially divided into carbon and non-carbon compounds. Volatile organic compounds are formed from thousands of reactions, which can be simplified into lumped chemical networks. The non-carbon chemistry for the ozone is based on nitrogen and the oxyly radical. NOx is primary emitted by the transportation system and by industry. VOC's are also emitted by these two sources types. Additionally, important VOC's (such as isoprene, monoterpenes and alfa-pinene) are active and important for atmospheric chemistry and particularly for ozone production, these are also produced (mainly in some cases) by trees (caduceus, perennial and mixed) that can be found surrounding urban areas.
The following reactions are a reduced set of primary chemical equations that involve the ozone production and removal cycle:
O(3P) + O2 + M -> O3 + M
O3 + hv -> O(3P) + O2
O3 + hv -> O(1D) + O2
NO + O3 -> NO2 + O2
O3 + OH -> HO2 + O2
O3 + NO2 -> NO3 + O2
O3 + HO2 -> OH + 2O2
The first reaction shows that the formation of ozone cannot be separated from that of atomic oxygen. On the other hand, destruction of ozone results from several processes (photodissociation, recombination with NO2, HO2... etc). The equilibrium is governed by each rate constant in the previous reactions.
Because simulations based on reaction schemes for an "oxygen only" atmosphere have not been successful in reproducing the observed ozone profiles, hydrogen species and nitrogen oxides must be included. Ozone concentration is also strongly affected by the presence of nitrogen oxides NOx and HNOx.
Special attention is required for VOC's in the study of polluted air. First, VOC's have proven health effects by themselves. In addition, reactions of VOC's with NOx result in intermediate reactants (e.g. OH, O(3P),... etc.) that participate in the ozone cycle. Alkanes and aromatics are three major VOC components.
The complex mechanism begins when free radicals attack atmospheric VOC's, which is for the most part activated by sunlight during the early morning sunrise period. Hydroxyl radical reaction is the dominant mechanism by which hydrocarbons are consumed in the atmosphere. The resulting effects are the conversion of NO to NO2 and an increment of the ozone maxima about one-third.
A list of all reactions of individual primary and secondary pollutants, as well as the resulting intermediate reactants, including their kinetics and products, is known as an explicit chemical mechanism.
The numerical integrations involved in the rate equations require a great deal of computer power for the hundreds of individual hydrocarbons found in the ambient air. This becomes a serious limitation for the simulations. Two main techniques of grouping are used in chemical mechanisms. The first consists on the simplification of the chemical reactions by elimination of intermediate products from an explicit chemical mechanism of chain-reactions. This simplification can be corrected by using adjusted rate constants. In addition, we have to choose the most representative species of each group of hydrocarbons. The second technique, called "lumping" , consists on grouping together a number of reactions and/or chemical species. There is a large variety of lumping techniques.
We use the CBM-IV mechanism, which has 33 species and 81 reactions. This mechanism is a condensed form of the CBM-EX , which represents a full description of carbon mechanisms. Because some species and reactions are not included in the CBM-IV scheme (because it is the carbon based mechanism), we have included a list of new species and reactions which described in the more recent SMVGEAR scheme.
Because photochemical reactions are primary reactions, their rates are first order rates with units of s-1. Our knowledge about kinetic rates in environmental processes is limited, which is one of the strongest limitations in photochemical models. Reactions rates depend on the temperature and pressure, noticeable from one source to another.
Considering the simple set of two chemical reactions.
Asuming that all the pollutants remain in the gaseous state, we have to solve the following set of simultaneous differential equations:
where rate constants k1, k2 are determined either from separate experiments or empirically.
We use the SMVGEAR -Sparse Matrix Vectorized Gear- to solve our set of equations. This code is based on a classic code of Gear. It solves the set of ODE's in the form of
To solve these equations, a prediction matrix P is used:
where I is the identity matrix, h is the timestep (dependent on the stiffness of the equation) and is the scalar multiplier. This can be put in format shown below,
where x is a vector used to correct y and its derivates and B is a continuously changing vector found from evaluating the differential equation, with corrected values of y.
The code is vectorized around the grid-cell dimension. In addition, it has a vectorized sparse-matrix package that reduces the number of matrix calculation in several ways.
This solver has advantages over other not vectorized solver codes, particularly in terms of computer time requirements.