Modeling CO, CO 2 and NO x Evolution from Small and Medium Size Electric Gensets

The Carbon monoxide, Carbon dioxide and Nitrogen oxides emission data from 100 small and medium generator sets with capacity ranging from 10 to 20 kVA are obtained from portable combustion gas analyzer using KAN90PLUS model. The resolutions for measurement for the gasses are 1 ppm, 0.1ppm and 1ppm respectively. The emission of the gasses together with the temperature of the exhaust and generator set capacities are studied. The models used for the study are calibrated using some polynomial interpolation methods and the results obtained compare with the emission benchmark value of the environmental management (Air Quality Standard) of 2007. It is found that the sets emits excessive carbon monoxide far above the standard value 175mg/nm2. The nitrogen oxide produces high temperature in the combustion system. Moreover, using asymptotic analysis, for large generator capacities, nitrogen oxides emission tends to be decreasing compared to the small and medium generators. The nitrogen oxides emission tends to converge to 20.189T, T is the temperature of the exhaust in Kelvin. Polynomial interpolation method used for prediction of CO, CO2, and nitrogen oxides (NOx) with respect to generator capacity and then simulation for the emission of the gasses at various scenarios carried. We Proposed emission and spread functions and simulate the functions to obtain the random emission and random spread of the gases into the environment from the available emission data for the gases. From our finding large quantity of CO, CO2 & NOX, are being emitted by the generators sets and this will have serious effect on the air quality in the remote environment where small and medium size generator sets are being used for generating electricity. The agricultural productive of the community will also be affected because of possible acid rain in that environment couple with allergic and respiratory diseases because of emission of the poisonous gases to the remote environment. As a policy, only generator sets with low emission should be allowed into the developing countries.


Introduction
The use of fossil fuels in stationary and mobile engines is the single most important contributor to anthropogenic greenhouse gases. For instance, it is estimated that transport alone is responsible up to a quarter of the global greenhouse gases [1] whereas the industry and other anthropogenic activities are responsible for the remaining three quarter global emission of the greenhouse gases. It is now widely accepted that the accumulation of the greenhouse gases that result in climate change is negatively influencing public health and welfare [2,3]. In the Tanzania context, energy sector is second most important sector, after agriculture (94.98%), as it emits 4.41% of total CO 2 emissions [4]. In Nigeria combustion of fossil oil is the major contributor of CO 2 and other greenhouse gases into the Nigeria airspace [5].
The main source of CO 2 emissions from the energy sector is from thermal power plants that utilize fossil fuels to generate electricity. Isolated off-grid areas are the major user of fossil fuel for electricity generation, and hence the major contributor of fossil CO 2 , and more emissions are produced during power cuts that forces all standby generator sets to be engaged. Thus for the purpose of mitigating these emissions, it is important to understand their evolution characteristics and the influencing features.
The temperature of the earth is found to be increasing because of the greenhouse gases. The combustion of fuel in the generator sets produces Carbon Monoxide (CO), Carbon Dioxide (CO 2 ), Nitrogen Oxides (NO, NO x ) and Sulphur dioxides (SO 2 ). The incomplete combustion of gasoline supplies much of the volatile organic compound which, in turn, combines with sunlight to produce unhealthy levels of ozone [5]. Under high temperature nitrogen will combine with oxygen to form a class of nitrogen oxides .Nitrogen oxides and sulphur dioxide with water give rise to acid rain which is dangerous to human health and biodiversity [6].
Modeling toxic fumes in form of greenhouse gases, Volatile Organic Compounds (VOCs) and Respirable Suspended Particulates(RSPs) have been subject of many researches in the recent times [7,8]. The reason d'état are that pollutants have been established to have negative effect on human health, ecosystem imbalance and global warming. One of such models is the EMFAC_HK model developed for estimating vehicular tailpipe emission of CO, CO 2 , NO x , VOCs and RSPs emission from petrol vehicles (EPA).
The model for studying aerodynamic behavior of particulates that diffused into the airways in the human lower respiratory track and the attendant medical implication has been considered [6]. Ezaina and Saheed modeled the global emission of pollutants emanating from flaring of natural gases from industries and released of greenhouse gases into the environment. Krzywaski and Norwalk [9] calculated CO 2 , CO, SO 2 , O 2 and NOemission from coal combustion in air and oxygen enriched circulating fluidized bed boiler.
The CO 2 emission auditing in the Nigeria airspace have been done using greenhouse training equation, artificial neural network model, polynomial fitting method by Oyelami and Buba [5]. The researchers predicted CO 2 emission and CO 2 emission per capita of Nigeria from 2013 to 2030.
This paper aims at developing models that describes the evolution characteristics of carbon monoxide (CO), carbon dioxide (CO 2 ) and nitrogen oxides (NO x ) emitted from small and medium generator sets. In the energy sector under consideration, the emissions of CO, CO 2 , and NO x generated during fossil fuels combustion are of paramount importance when designing generator sets that would conform to standard air quality requirements. Therefore, the evolution of the individual emission being governed by specific phenomena needs to be understood. The best mitigation plan must, therefore, take into consideration of their evolution characteristics.
We intend to use polynomial interpolation method to obtain prediction of CO, CO 2, nitrogen oxides (NO x ) and then carried simulation for the emission of the gasses at various scenarios. In order to understand the random emission of pollutant gases into atmosphere, we proposed emission and spread functions. We will simulate the emission and spread functions to obtain information on the emission and spread of the gases into the environment using the available emission data.

Carbon Dioxide Emissions
As described in equation (1) all combustion processes result in the production of carbon dioxide and water. Thus the carbonaceous materials are oxidized with oxygen to produce carbon dioxide and water and thereby releasing heat. 2

Carbon Monoxide Emissions
In the event the combustion is not complete, the carbon monoxide becomes more evident in the generator engine's exhaust. Thus poorly maintained generator sets and those which are not well-tuned they usually exhibit excessive carbon monoxide since the carbon does not get sufficient oxygen for producing CO 2 (equation 2). The production of CO is at the carbon surface where the carbon can either be attacked by oxygen (O 2 ), carbon monoxide (CO 2 ) or water (H 2 O). Carbon monoxide is not a greenhouse gas. However it is poisonous when inhaled.

Nitrogen Oxides Emissions
The existing stringent environmental regulations on the greenhouse effect of the oxides of nitrogen, commonly known as NO x , require understanding their formation mechanisms for designing effective interventions. A detailed count of NO x formation mechanism is detailed in Gardiner Jr. [10] and Glassman [11] where the authors gave comprehensive reviews on nitrogen oxide (NO) which is known to be formed in a variety of ways: (1) "Thermal NO" is primarily a consequence of high flame temperatures; (2) "Prompt NO" is generated in fuel-rich parts of flames; (3) the "N 2 O mechanism" is common in high-pressure flames; (4) "Fuel nitrogen NO" results from converting the nitrogen constituents of the fuel (petroleum, coal and biomass) into NO; and (5) the "NNH mechanism" is pronounced in flame fronts with high atom concentrations appear. Thus, with the exceptions of "fuel nitrogen" mechanism, all the remaining mechanisms convert atmospheric (from combustion air) nitrogen into NO.
The principal reactions in the thermal NO formations are: Due to the high activation (320 kJ/mol) of equation (3), the thermal mechanism is predominant in high temperature combustion zones.
In Figure 1 we consider, the emission of , & x CO CO NO NO to the environment in a network fashion.

Methods and Materials
This paper bases on in environmental auditing of a combustion system in which one of the requirements is to assess environmental performance of existing combustion systems like generator sets. A databank of emissions from 100 previously assessed generator sets was utilized for the modeling purpose. As detailed in Table 1, the generator sets were 100 different small to medium size kVA generator sets with capacities ranging from 10 to 20 kVA. The portable combustion gas analyzed model KANE900 PLUS was utilized for emissions assessment. Its resolution for measurement of CO, CO 2 and NO is 1 ppm, 0.1 ppm, and 1 ppm.

Emission and Spread of Gases Functions
The distribution of the gases into the atmosphere ( ) D x can provide important information about emission of gases. We define the emission distribution function as Where ( ) f v is the estimate of the emission of the gases from the emission data from the generator set with capacity , x x being it's mean and σ is the standard deviation of the gases .with the dummy variable v for the generator capacity. For purpose of randomising the generator set capacity, we assume that N that is the total number of generator in the whole community is very large, hence by law of large numbers, x has normal distribution.
The Spread of the emitted gases into the environment can determine using

Results and Discussion
Summarized findings of the emission from generator sets are presented in Table 2.

Carbon Dioxide Emissions
The overall average carbon dioxide emission averaged was 3.29% with a median value of 3.29% whereas the maximum and minimum values were 3.64 and 3.06%, respectively. The graphical presentations of the CO 2 emissions presented in Figure 2 was highly correlated regression polynomial functions and are represented in the following of order 2 and order 3 respectively: Where,

Carbon Monoxide Emissions
Details presented in Figure 4 below shows that the average carbon monoxide emission from the studied generator engines averaged 408.64 mg/nm 3 . The median, maximum, and minimum CO emission values were 409.74, 493.17, and 341.69 mg/nm 3 , respectively. With comparison with the carbon monoxide threshold standard values for Tanzania Air Quality Standard (2007), all the generator engines are emitting excessive CO emission. The standard has set 175 mg/nm 3 as the maximum attainable CO emission.
The CO emission evolution from the studied engines was fitted to a logarithmic function, Equation (10). However, the emissions were equally well-fitting to a polynomial function presented in equation (9) Where, (2) (3) , , CO CO CO y y y are the CO emissions (mg/nm 3 ) and x is the engine capacity (kVA).   and x is the engine capacity (kVA). Where, y is the NO x emissions (mg/nm 3 ) and x is the engine capacity (kVA).

Exhaust Gas Temperature
As shown in Figure 8, the generator engines' exhaust gas temperature ranged between 188.81 and 146.81°C with an average temperature of 167.57°C. Lower and higher engines capacity had relatively higher exhaust gas temperatures. This fact was also applicable to the NOx evolution where it was observed that lower and higher engine capacities emitted more emissions (Figure 8 and Figure 9). This is because thermal NOx is more pronounced in high temperature combustion systems. Figure 9 is on Nitrogen oxide emission and Exhaust temperature. The exhaust gas temperature, Nitrogen oxides emissions are best described by a polynomial function, Equation 12.
Where, y is the NO x emissions (mg/nm 3 ) and x is the engine capacity (kVA).     In the Figure 11, dual axis plot is made for carbon dioxide in red colour against temperature in in blue colour. In the Figure 12, dual axis plot is made for carbon monoxide in blue colour against temperature in in red colour.
We obtain asymptotic expansion of ratio of carbon dioxide and Nitrogen oxide (NO x ) against temperature of the exhaust as follows: We propose two models for emission CO 2 as function temperature of the exhaust T and generator set capacity x as follows:       Nitrogen oxide emission is very high for large capacity generator set. This is because the temperature of the exhaust is extremely high which leads to nitrogen in the air combining with oxygen to produce nitrogen oxide gases and the nitrogen in the hydrocarbon fuel together with impurities in it produces NO x at the high temperature zone of the exhaust. The surround of the exhaust is often brownish in colour. This brownish colour is characteristic high temperature emission of NO x when rocket and missiles are fired.

Conclusion
The Carbon monoxide, Carbon dioxide and Nitrogen oxides emission data from 100 small and medium generator sets with capacity ranging from 10 to 20 kVA are obtained from portable combustion gas analyzer using KAN90PLUS model. Two models are proposed to study the emission of gases from the exhaust of the generator sets. We also proposed emission and spread function to analysis pollution of the environment from burning fossil fuel by the generator sets. From our finding large quantity of CO, CO 2 , NO x are being emitted by the generators sets and this will have serious effect on the air quality in the remote environment where small and medium size generator sets are being used for generating electricity. The agricultural productive of the community will also be affected because of acid rain in that environment couple with allergic and respiratory diseases because of emission of the poisonous gases to the remote environment.
As a policy, generator sets with low emission such as those whose exhausts have monocatalytic beds should be allowed into the developing country.