Thermodynamic and Environmental Assessment of Gas Flaring in the Niger Delta Region of Nigeria

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1. Introduction

Throughout human evolution and history, significant advancement in human development has been accomplished with increase in energy consumption, especially electricity, and this has a tie with population explosion. Energy consumption correlates with industrialization and standard of living of any society [1]. It is indeed irrefutable that oil and gas exploration and production activities play a central role and have economic gains for countries that have such natural resource. It provides wealth creation as well as building a sustained economy all over the world especially if well managed [2]. However, it is worthwhile to state that there are negative consequences of crude oil extraction. Crude oil is a combination of oil, gas, water and other impurities. This gas associated with the crude oil is known as associated natural gas. Ideally this associated gas would have been harnessed and sold to consumers or for electricity generation. This however requires costly investment in pipelines, gas gathering facilities, power plants and others related infrastructure. In practice therefore, oil multinationals opt to sell the oil and flare the gas, which is known as gas flaring. In Nigeria, crude oil was discovered in commercial quantity in 1956 in Oloibiri, present day Bayelsa State, and ever since, gas has continually been flared. This is because at the time, the gas was seen as a nuisance by-product and much was not known about the potential of natural gas and its processing facilities were non-existent, therefore flaring was the only option. Another reason why there is continuous flare of gas is complacence of multi-national companies. On a global scale, Nigeria is currently the seventh largest gas-flaring country as against the second largest over the last 10 years [3], indicating there are tremendous efforts to cut down gas flaring. In Nigeria, access to reliable and sustained supply of electricity is a major challenge for both the urban and rural dwellers. Several analyses of Nigeria’s electricity supply problems and prospects posit that electricity demand far outstrips the supply [4]. Nigeria generates barely 4000 MW of electricity, which is grossly inadequate for her population, but tremendously wastes a recognized source of energy for more than five decades now. It is against this back drop that this research is conceived to thermo-mechanically and environmentally assess issues of gas flaring, which if harnessed can be used to fire gas turbines, heat to generate steam for steam turbines, gas-to-liquid conversion using the Fischer-Tropsch process, collection, compression and reinjection into oil wells for enhanced oil recovery, and Liquefied Natural Gas and other perceived uses.

In most of the literatures reviewed, it was observed that the effects of gas flares is mostly thermal related as a result of the exit temperatures of the flares, with a huge consequence on the natural environment. Reference [5] developed a model for an accurate prediction of heat flux at any point within the vicinity of gas flares through numerical methods. Reference [6] looked at the effects of gas flaring on the basis of the amount of carbon dioxide released using four villages in the Niger Delta region as a case study, their studies showed that the volume of CO_{2} produced is greater than the critical threshold limit (about 30,000 ppm). Reference [7] however used a system of differential equations in their model analysis to get the amount of flared gas. The report by [8] showed that gas flaring, especially thermal impacts affects soil temperature, soil moisture content, soil PH, soil microbes. There is a general opinion by [6], [8] and [9] that flaring also contaminates water bodies thereby having a direct impact on water aquifers and aquatic community. Reference [9], did an extensive work on the impacts of gas flaring as it concerns environmental contaminants, health consequences, socio-economic problems and degradation of host communities. Their studies revealed that incomplete combustion produces a variety of volatile organic compounds (VOCs), polycyclic aromatic hydrocarbons (PAHs) and inorganic contaminants. Reference [10] also added that acid rain and soot deposited on roofs is another factor that environmentally degrades soil, water, and roof erosion. Thus, the concentration of acid in rain water appears to be higher in the Niger Delta region and decreases further away from the region. Reference [11] investigated lengths and widths of crops leaves, height of crop plant and Cassava yields were measured at specific distances from a case study flare point. The results suggest that spatial gradients exist in crop development. Their results further showed that Cassava yields were higher in areas further away from the flare points. This is a consequence of thermal pollution within the flare perimeter.

From exergy point of view, [12] in their paper worked on extended exergy accounting method within which they quantified environmental externality linked to the chemical pollutants released by an elevated flare stack. The work provided both the exergy flux released into the environment by the flare stack and the cost in primary resource equivalents. Reference [13] on their part used exergy analysis to evaluate the environmental impact potential of systems and improved the performance of the systems through reduction of waste emissions. The asserted that exergy is released by a system that is not in thermodynamic equilibrium with the environment. They further posited that the release of emissions by our systems is tantamount to the release of exergy into the environment, which not only limit the efficiency of the system and waste our resources, but also contribute to the global warming of our planet. Again, there is similarity between the works of [12], [13], and [14], but it was observed that [14], on their part did extensive work on exergy analysis on waste emission from gas flares to have a model through which impact of gas flaring can be measured, they went further to develop exergy calculator. Although in their analyses, the gas stream was modelled as a perfect gas, and perfect gas relations and equations were used, which at this level of study should not suffice. Reference [15] Used exergy accounting and rules of thumb, Aspen plus, Dynamic Network analysis, and Aspen HYSYS to evaluate and assess the thermodynamic performance of an oil and gas platform. They attributed 62% - 65% of total exergy destruction of the offshore platform to the power generation and waste heat recovery system, and 35% - 38% to the oil and gas processing. They affirmed that the rejection of high-temperature gases from utility and flaring systems is a major contributor to the exergy losses. Some of the drawbacks this paper identifies and in most of the literatures reviewed, carbon capture technology was not incorporated with thermal and environmental analysis in most papers. Furthermore, heat fluxes were exhaustively calculated in this work, which x-rayed the effects of heat on soil PH, soil microbes, low yield of vegetation amongst others. Another monumental achievement of this paper is the aggregated fuel composition shown in Table 2.

2. Material and Method

2.1. Overview of Gas Flaring

Gas flaring has been a contentious issue and still a contemporary issue being discussed around the globe, especially in oil and gas producing countries where flaring activities are predominant. It occurs in the process of crude oil production and processing. Reference [16] and [17] in their separate papers stated that gas flaring is the process of controlled burning of natural gas from oil wells, gas wells, hydrocarbon processing plants, coal industries either as a means of disposal or as a safety measure. The idea of flaring is because it is perceived as the financially cheapest possible means of disposal of natural gas in the short term [17]. Reference [18] also posited that the process of flaring is carried out using flare stack which may be vertical or horizontal.

Gas flaring is a significant source of greenhouse gases such as methane (CH_{4}), carbon dioxide (CO_{2}), water vapour and other emissions with a consequence of noise generation, increased ambient temperature and provides large area inhabitable. Furthermore, it is a known fact that there are two options for gas utilization instead of outright flaring: the first option is gas utilization for domestic and commercial purposes, which inevitably involves equipment acquisition for liquefaction and transportation. The second option is reinjection for enhanced oil recovery. In lots of countries, Nigeria inclusive, the law prohibits gas flaring because it is harmful to natural ecological systems and constitutes huge loss of revenue.

2.2. Data Collection

The data required for this investigation was obtained for a period of Nine (9) Years. The data was sourced for on volume of gas flared in an oil field designated as the Alpha field in the Niger Delta region of Nigeria within. It has two oil fields, but the research effort is concentrated on one of the fields. The field data such as well pressures, mass flow rate, oil-to-gas ratio, discharge velocity, flame height, ambient temperature, well outlet temperature, operating stack temperature, gas composition, stack height, were retrieved from the company’s log sheets, interviewing of key personnel, email correspondences and field visitations.

2.3. Combustion Analyses

Combustion by definition is a process of rapid oxidation of combustible elements of a fuel resulting in the release of energy and products of combustion. Several combustion equations were encountered. However, the equation model by [19] was used, that when 1 kmol of a stream of gas with volumetric compositions: CH_{4}―a%, C_{2}H_{6}―b%, C_{3}H_{8}―c%, C_{4}H_{10}―d%, N_{2}―e%, the combustion equation is given as:

$\begin{array}{l}\left(\frac{a}{100}\right){\text{CH}}_{4}+\left(\frac{b}{100}\right){\text{C}}_{2}{\text{H}}_{6}+\left(\frac{c}{100}\right){\text{C}}_{3}{\text{H}}_{8}+\left(\frac{d}{100}\right){\text{C}}_{4}{\text{H}}_{10}+\left(\frac{e}{100}\right){\text{N}}_{2}\\ +\text{}\frac{\left[a+2b+3c+4d+\left(2a+3b+4c+5d\right)/2\right]}{100}\left({\text{O}}_{2}+3.76{\text{N}}_{2}\right)\\ \to \frac{a+2b+3c+4d}{100}{\text{CO}}_{2}+\frac{2a+3b+4c+5d}{100}{\text{H}}_{\text{2}}\text{O}\\ +\text{}\left[3.37\left(\frac{\left[a+2b+3c+4d+\left(2a+3b+4c+5d\right)/2\right]}{100}\right)+\frac{e}{100}\right]{\text{N}}_{2}\end{array}$ (1)

From Equation (1), if we know the composition of the natural gas, the aggregated carbon to hydrogen ratio in the gas can be evaluated.

Estimation of Carbon (IV) Oxide

To estimate the amount of Carbon (IV) Oxide and water vapour the equation by [20], is used, and is expressed as:

(2)

where,
$MAS{S}_{{\text{CO}}_{\text{2}}}$ is mass of carbon (IV) oxide,
${M}_{\text{flaredgas}}$ ―mass of flared gas (kg),
$M{M}_{{\text{CO}}_{\text{2}}}$ ―molecular mass of CO_{2};
$M{M}_{\text{fuel}}$ ―molecular mass of the fuel (gas stream). Equation (2) used is an attempt to check the percentage correlation by this research and that proposed by [20].

2.4. Adiabatic Flame Temperature (AFT)

Adiabatic flame temperature is a parameter in combustion that describes the maximum theoretical temperature attained by the combustion products (flue gases), if no exergy is lost to the outside environment [21]. It is evaluated using the equations:

$Q=\Delta {H}^{c}={H}_{P}-{H}_{R}$ (3)

when the process is adiabatic,

${H}_{P}={H}_{R}$ (4)

where:

${H}_{P}={\displaystyle {\sum}_{e}^{P}{n}_{e}{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+\stackrel{\xaf}{h}-{\stackrel{\xaf}{h}}_{o}\right)}_{e}}$ (5)

Also

${H}_{R}={\displaystyle {\sum}_{e}^{R}{n}_{i}{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+\stackrel{\xaf}{h}-{\stackrel{\xaf}{h}}_{o}\right)}_{i}}$ (6)

where, Q is the heat transfer, ${\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}$ is the enthalpy of formation ${n}_{e}$ and ${n}_{i}$ are number of moles of products and reactants respectively. P & R are parameters for products and reactants respectively.

Also, $\stackrel{\xaf}{h}-{\stackrel{\xaf}{h}}_{o}={\stackrel{\xaf}{\Delta}}_{h}$ , is the difference in enthalpy for a particular temperature and that of the reference temperature usually 298 k (25˚C), and values are gotten from Jadranski naftovod (JANAF) thermodynamic data Tables.

2.5. The Concept of Exergy

Exergy ( ${E}_{X}$ ) of a system also known as availability is the maximum theoretical work obtainable between the system and a specified reference environment when they interact [1]. It is based on the first and second laws of thermodynamics.

Two types of exergies exist. These are thermo-mechanical exergy or physical exergy and Chemical exergy.

2.5.1. Thermo-Mechanical or Physical Exergy

The thermo-mechanical (physical) exergy depicts the deviation in temperature and pressure between the flowing matter and that in the reference environment [21].

The thermo-mechanical exergy is expressed as:

${e}_{x,TM}={E}_{x,\text{nonflow}}+{E}_{x,\text{flow}}$ (7)

${e}_{x,TM}=\left(U-{U}_{o}\right)+{P}_{o}\left(V-{V}_{o}\right)-{T}_{o}\left(S-{S}_{o}\right)+\frac{1}{2}m{c}^{2}+mgz+\left(P-{P}_{o}\right)V$ (8)

where, ${E}_{x,\text{nonflow}}$ is non-flow exergy; ${E}_{x,\text{flow}}$ is flow exergy; ${P}_{o}$ ―surroundings pressure (kpa).

Dividing Equation (8) by mass, all properties becomes specific and will therefore transform to:

${e}_{x,TM}=\left(u+Pv\right)-\left({u}_{o}+{P}_{o}{v}_{o}\right)-{T}_{o}\left(s-{s}_{o}\right)+\frac{1}{2}{c}^{2}+gz$

${e}_{x,TM}=\left(h-{h}_{o}\right)-{T}_{o}\left(s-{s}_{o}\right)+\frac{1}{2}{c}^{2}+gh\text{\hspace{0.17em}}\left(\text{kJ}/\text{kg}\right)$ (9)

But the kinetic and potential exergy terms are negligibly small as compared to the enthalpy and entropy terms, and are therefore neglected.

${e}_{x,TM}=\left(h-{h}_{o}\right)-{T}_{o}\left(s-{s}_{o}\right)$ (10)

h―specific enthalpy of the system (kJ/kg); s―specific entropy of the system (kJ/kg K); ${h}_{o}$ ―surroundings specific enthalpy (kJ/kg); ${s}_{o}$ ―surroundings specific entropy (kJ/kg K); ${T}_{o}$ ―surroundings reference temp. (K). Equation (10) will be expanded in Chapter 3.

2.5.2. Chemical Exergy

The chemical exergy of a substance is the maximum work obtainable from a system by taken it to chemical equilibrium with a reference environment at constant temperature and pressure. It is evaluated using:

$\begin{array}{c}{e}_{x,ch}=\left[{\stackrel{\xaf}{g}}_{F}+\left(a+\frac{b}{4}\right){\stackrel{\xaf}{g}}_{{\text{O}}_{\text{2}}}-a{\stackrel{\xaf}{g}}_{{\text{CO}}_{\text{2}}}-\frac{b}{2}{\stackrel{\xaf}{g}}_{{\text{H}}_{\text{2}}\text{O}}\right]\left({T}_{o},{P}_{o}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+R{T}_{o}\mathrm{ln}\left[\frac{{\left({y}_{{\text{O}}_{\text{2}}}^{e}\right)}^{a+b/4}}{{\left({y}_{{\text{CO}}_{\text{2}}}^{e}\right)}^{a}{\left({y}_{{\text{H}}_{\text{2}}\text{O}}^{e}\right)}^{b/2}}\right]\end{array}$ (11)

where, R―universal gas constant (kJ/kmolK); ${y}^{e}$ ―mole fractions of environmental composition; $\stackrel{\xaf}{g}$ ―molar Gibbs function component obtained from standard thermo-mechanical properties tables [21].

2.6. Total Specific Exergy Computation

The total specific exergy is the combination of the specific thermo-mechanical exergy and the specific chemical exergy given as:

${e}_{x,T}={e}_{x,TM}+{e}_{x,ch}$ (13)

$\begin{array}{c}{e}_{x,T}=\left(h-{h}_{o}\right)-{T}_{o}\left(S-{S}_{o}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left[{\stackrel{\xaf}{g}}_{F}+\left(a+\frac{b}{4}\right){\stackrel{\xaf}{g}}_{{\text{O}}_{\text{2}}}-a{\stackrel{\xaf}{g}}_{{\text{CO}}_{\text{2}}}-\frac{b}{2}{\stackrel{\xaf}{g}}_{{\text{H}}_{\text{2}}\text{O}}\right]\left({T}_{o},{P}_{o}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+R{T}_{o}\mathrm{ln}\left[\frac{{\left({y}_{{\text{O}}_{\text{2}}}^{e}\right)}^{a+b/4}}{{\left({y}_{{\text{CO}}_{\text{2}}}^{e}\right)}^{a}{\left({y}_{{\text{H}}_{\text{2}}\text{O}}^{e}\right)}^{b/2}}\right]\end{array}$ (14)

2.7. The Absolute Exergy (E_{X}_{,T})

The total or absolute exergy is computed as follows:

$\begin{array}{c}{E}_{X,T}=\text{mass}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{gas}\text{\hspace{0.17em}}\text{stream}\left(m\right)\times {e}_{x,T}\\ =m[\left(h-{h}_{o}\right)-{T}_{o}\left(S-{S}_{o}\right)+[{\stackrel{\xaf}{g}}_{F}+\left(a+\frac{b}{4}\right){\stackrel{\xaf}{g}}_{{\text{O}}_{\text{2}}}-a{\stackrel{\xaf}{g}}_{{\text{CO}}_{\text{2}}}\underset{}{\overset{}{\begin{array}{l}\\ \end{array}}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-\frac{b}{2}{\stackrel{\xaf}{g}}_{{\text{H}}_{\text{2}}\text{O}}]\left({T}_{o},{P}_{o}\right)+\left[\frac{{\left({y}_{{\text{O}}_{\text{2}}}^{e}\right)}^{a+b/4}}{{\left({y}_{{\text{CO}}_{\text{2}}}^{e}\right)}^{a}{\left({y}_{{\text{H}}_{\text{2}}\text{O}}^{e}\right)}^{b/2}}\right]]\left(\text{kJ}\right)\end{array}$ (15)

Heat flux density by Radiation

Heat flux is referred to as the flow of heat energy per unit area per unit time. The Stefan-Boltzmann equation describes the rate of transfer by radiant energy as:

Heat flux, $Q=\sigma \u03f5{T}^{4}$ (16)

where, Q―heat flux (W/m^{2});
$\u03f5$ ―emissivity of the surface/source (which is one in this case); T―temperature in kelvin (K);
$\sigma $ ―Stefan-Boltzmann constant (
$5.67\times {10}^{-8}\text{\hspace{0.17em}}\text{W}/{\text{m}}^{\text{2}}$ ).

3. Results and Discussion

The data shown in Table 1 correlates with average gas compositions for each year.

3.1. Combustion Analysis

The following are useful assumptions:

1) The fuel entered the flare stack at 25˚C and 1 atm while the air at 27˚C.

2) Flow is steady.

3) Water at the product side is vapour.

Using Equation (1), and substituting values, for 1 kmol of the fuel we have:

With a = 93.9; b = 3.6; c = 1.3; d = 1.2; e = 0 [for the first year, 2008]

$\begin{array}{l}\left(\frac{a}{100}\right){\text{CH}}_{4}+\left(\frac{b}{100}\right){\text{C}}_{2}{\text{H}}_{6}+\left(\frac{c}{100}\right){\text{C}}_{3}{\text{H}}_{\text{8}}+\left(\frac{d}{100}\right){\text{C}}_{4}{\text{H}}_{\text{10}}+\left(\frac{e}{100}\right){\text{N}}_{2}\\ +\frac{\left[a+2b+3c+4d+\frac{2a+3b+4c+5d}{2}\right]}{100}\left({\text{O}}_{2}+3.76{\text{N}}_{2}\right)\\ \to \frac{a+2b+3c+4d}{100}{\text{CO}}_{\text{2}}+\frac{2a+3b+4c+5d}{100}{\text{H}}_{\text{2}}\text{O}\\ +\text{}\left[3.37\left(\frac{\left[a+2b+3c+4d+\left(2a+3b+4c+5d\right)/2\right]}{100}\right)+\frac{e}{100}\right]{\text{N}}_{2}\end{array}$

$\begin{array}{l}0.939{\text{CH}}_{4}+0.036{\text{C}}_{2}{\text{H}}_{6}+0.013{\text{C}}_{3}{\text{H}}_{\text{8}}+0.012{\text{C}}_{4}{\text{H}}_{\text{10}}+2.147\left({\text{O}}_{2}+3.76{\text{N}}_{2}\right)\\ \to 1.098{\text{CO}}_{2}+2.098{\text{H}}_{\text{2}}\text{O}+\text{8}.0{\text{7272N}}_{2}\end{array}$ (17)

Table 1. Variation of Percentage by volume of hydrocarbons (natural gas) flared in the oil field (Alpha-Field) under investigation.

Source: Alpha field data log sheet (2016).

From the above, it is evident that the number of carbon atoms is the coefficient of CO_{2} at the product side of the combustion equation = 1.098, while the number of hydrogen atoms is coefficient of H_{2}O ×2 = 2.089 × 2 = 4.196

Thus, the simple aggregated fuel for this gas composition is: C_{1.098}H_{4.196}

This will give rise to the following stoichiometric equation:

${\text{C}}_{\text{1}\text{.098}}{\text{H}}_{\text{4}\text{.196}}+2.147\left({\text{O}}_{2}+3.7676{\text{N}}_{2}\right)\to 1.098{\text{CO}}_{2}+2.098{\text{H}}_{\text{2}}\text{O}+\text{8}.0{\text{7272N}}_{2}$ (18)

A MATLAB program was developed to evaluate other gas samples as displayed on Table 2.

Table 2 depicts the combustion characteristics of the natural gas. Column one is the natural gas sample for each year while column two is the aggregated fuel content. It is evident that as the year progresses, lighter components decreased while the heavier alkanes become predominant. Furthermore, the other columns show the number of moles of the stoichiometric air, CO_{2}, H_{2}O, and nitrogen.

3.2. Analysis of Amount of CO_{2} and Water Vapour (H_{2}O) Produced for the First Year (2008)

Analysis showed that for the fuel with composition, C_{1.098}H_{4.196}, for 1 m^{3} of the fuel that burns in air, 1.098 m^{3} of CO_{2} and 2.098 m^{3} of water vapour were respectively produced. Proportionately to get the quantities of flue gases, flare volume values are obtained from Table 3 as depicted below:

Flare volume for the year (2008) = 75,399,656.65 m^{3}

Amount of CO_{2} produced per year = 1.098 × 75,399,656.65 = 82,788,823.0017 m^{3}

Amount of H_{2}O produced per year = 2.098 × 75,399,656.65 = 158,188,479.6517 m^{3}

With the above analysis and with the help of MATLAB program codes, the following values are obtained in Table 3.

Table 2. Table of gas samples, fuel aggregates, amount of air and amount of flue gases after combustion.

Table 3. Amount (volume) of Flue Gases for the period under investigation.

3.3. Estimation of Carbon (IV) Oxide for Comparison

Using the relation , in the validation of the amount of CO_{2} as asserted by [20].

${M}_{\text{flaredgas}}=\text{59791927}.\text{7266}\text{\hspace{0.17em}}\text{kg}/\text{year}$ ; $M{M}_{{\text{CO}}_{\text{2}}}=44\text{\hspace{0.17em}}\text{g}/\text{mol}$ ; $M{M}_{\text{fuel}}=\text{17}.\text{372}$

Substituting values, we have:

$MAS{S}_{{\text{CO}}_{\text{2}}}=\frac{59791927.7266\text{\hspace{0.17em}}\text{kg}/\text{year}\times 44\text{\hspace{0.17em}}\text{g}/\text{kmol}}{17.372\text{}}=\text{151441677}.\text{41}\text{\hspace{0.17em}}\text{kg}$

But density of CO_{2} = 1.98 kg/m^{3}

Using the relation: $\text{Density}\left(\rho \right)=\frac{\text{mass}}{\text{volume}}=\frac{m}{V}$

$\text{Volume}=151441677.41/1.98=76485695.661\text{\hspace{0.17em}}{\text{m}}^{\text{3}}/\text{year}$

The percentage correlation of this research work and that done by [20] is:

$\%\text{correlation}=\text{76485695}.\text{661}/\text{82788823}.00\text{17}=0.\text{923864}=\text{92}.\text{28}\%$

Table 3 depicts the yearly natural gas production volumes, flared volumes, the percentage of gas flared for each year, the quantity of carbon (IV) oxide and water vapour produced. Analyses showed that total natural gas production over the nine-year period was estimated to be 1,870,070,117.41 standard cubic meters from which 541,023,993.9 standard cubic meters was flared. This generated 582,319,618.2 (≈1.046 MMt) cubic meter of CO_{2} and about 1,077,510,054.31 (≈2.05 MMt) cubic meters of water vapour. Another analysis indicates that about 14,960,560.91 standard cubic meters of methane was also discharged to the atmosphere through transient loses.

From Figure 1 and the results obtained showed that there is a linear variation (i.e. the quantity of CO_{2} increases with flared volumes.), same is applicable for

Figure 1. Plot of flared volume and variation in CO_{2} and H_{2}O.

water vapour. It is also evident that by the steepness of the lines, the amount of water vapour effluent is about twice that of carbon (IV) oxide. Also approximately 27% - 40% of gas produced in the field was flared.

3.4. Analysis of Adiabatic Flame Temperature AFT for the First Year (2008)

From Equation (2):

$\begin{array}{c}{H}_{R}={\displaystyle {\sum}_{R}{n}_{i}{\left({\stackrel{\xaf}{h}}_{f}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{i}}\\ =0.939{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{CH}}_{\text{4}}}+0.036{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}}+0.013{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{C}}_{\text{3}}{\text{H}}_{\text{8}}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.012{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{C}}_{\text{4}}{\text{H}}_{\text{10}}}+2.147{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{O}}_{\text{2}}}+8.07272{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{N}}_{\text{2}}}\end{array}$

Since ${\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}$ for diatomic gases are zero, and ${\stackrel{\xaf}{\Delta}}_{h}$ for the fuel is also zero (reference temperature 25˚C) and also ${\stackrel{\xaf}{\Delta}}_{h}=300\text{\hspace{0.17em}}\text{K}$

$\begin{array}{c}{H}_{R}=0.939{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}\right)}_{{\text{CH}}_{\text{4}}}+0.036{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}\right)}_{{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}}+0.013{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}\right)}_{{\text{C}}_{\text{3}}{\text{H}}_{\text{8}}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.012{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}\right)}_{{\text{C}}_{\text{4}}{\text{H}}_{\text{10}}}+2.147{\left({\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{O}}_{\text{2}}}+8.07272{\left({\stackrel{\xaf}{\Delta}}_{h}\right)}_{{\text{N}}_{\text{2}}}\end{array}$

Substituting values from established standard thermodynamic tables from [21] we have:

$\begin{array}{c}{H}_{R}=0.939\left(-74873\right)+0.036\left(-84667\right)+0.013\left(-103874\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.012\left(-126148\right)+2.147\left(54\right)+8.07272(54)\end{array}$

${H}_{R}=-75666.03212\text{\hspace{0.17em}}\text{kJ}/\text{kmol}$ (19)

Similarly, for the products, we have:

$\begin{array}{c}{H}_{P}={\displaystyle {\sum}_{P}{n}_{e}{\left({\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right)}_{e}}\\ =1.098{\left[{\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right]}_{{\text{CO}}_{\text{2}}}+2.098{\left[{\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right]}_{{\text{H}}_{\text{2}}\text{O}}+8.07272{\left[{\stackrel{\xaf}{h}}_{\begin{array}{l}o\\ f\end{array}}+{\stackrel{\xaf}{\Delta}}_{h}\right]}_{{\text{N}}_{\text{2}}}\end{array}$

$\begin{array}{c}{H}_{P}=1.098\left(-393522\right)+1.098{\left[\stackrel{\xaf}{\Delta}h\right]}_{{\text{CO}}_{\text{2}}}+2.098\left(-241827\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+2.098{\left(\stackrel{\xaf}{\Delta}h\right)}_{{\text{H}}_{\text{2}}\text{O}}+8.07272{\left[\stackrel{\xaf}{\Delta}h\right]}_{{\text{N}}_{\text{2}}}\\ =-938440.202+1.098{\left[\stackrel{\xaf}{\Delta}h\right]}_{{\text{CO}}_{\text{2}}}+2.098{\left(\stackrel{\xaf}{\Delta}h\right)}_{{\text{H}}_{\text{2}}\text{O}}+8.07272{\left[\stackrel{\xaf}{\Delta}h\right]}_{{\text{N}}_{\text{2}}}\end{array}$ (20)

Equating (19) & (20), and solving the resulting equations, we have:

$\Rightarrow 1.098{\left[\stackrel{\xaf}{\Delta}h\right]}_{{\text{CO}}_{\text{2}}}+2.098{\left(\stackrel{\xaf}{\Delta}h\right)}_{{\text{H}}_{\text{2}}\text{O}}+8.07272{\left[\stackrel{\xaf}{\Delta}h\right]}_{{\text{N}}_{\text{2}}}=863774.16988$ (21)

By iterative thermodynamics and from standard tables of thermo-mechanical properties of selected substances [21], we have Table 4.

By linear interpolation

$\frac{X-2300}{2400-2300}=\frac{863774.16988-846590.42}{893862.094-846590.42}$

$X=AFT=2336.351\text{\hspace{0.17em}}\text{K}\text{\hspace{0.17em}}\left(2063.351\u02da\text{C}\right)$

The value so calculated is the adiabatic flame temperature, and other values are calculated using MATLAB codes and are depicted in Figure 2.

The plot of Figure 2 indicates that from 2008 to 2016 the natural gas quality reduces, with a consequence of decrease of adiabatic flame temperature as shown by the profile of the graph. Apart from 2009 and 2010, the adiabatic flame temperatures decreased progressively.

3.5. Estimation of Heat Flux (Thermal Pollution Rate)

From the evaluated adiabatic flame temperature, the thermal pollution rate can be calculated as follows:

$\begin{array}{c}Q=\sigma \u03f5{T}^{4}\\ =5.67\times {10}^{-8}\text{W}/{\text{m}}^{\text{2}}\cdot {\text{K}}^{\text{4}}\times 1\times \left({2336.351}^{4}\right){\text{K}}^{\text{4}}\\ =1.6380\times {10}^{6}\text{W}/{\text{m}}^{\text{2}}\end{array}$

Again MATLAB program was used to evaluate other values of the heat fluxes and values are depicted in Figure 3.

Table 4. Iterated values of the maximum temperature at the discharge of the flare stack, with given gas composition.

Figure 2. Plot of AFT and fuel content.

Figure 3. Plot of heat flux and fuel content.

From Figure 3, again there is a progressive decrease of heat flux density as the fuel constituent becomes heavier. Meaning that when the lighter components are predominant, the flame tends to be hotter, which is in tandem with the adiabatic flame temperatures. This enormous amount of heat is the reason why there is deficiency in crop yield production, decrease in microbes, and soil PH, erosion of corrugated sheets in flare areas.

3.6. Chemical Exergy Computation

The molar analysis from the reference environmental model is:

${y}_{{\text{N}}_{\text{2}}}^{e}=0.7567$ ; ${y}_{{\text{O}}_{\text{2}}}^{e}=0.\text{2}0\text{35}$ ; ${y}_{{\text{H}}_{\text{2}}\text{O}}^{e}=0.0\text{3}0\text{3}$ ; ${y}_{{\text{CO}}_{\text{2}}}^{e}=0.000\text{3}$

The balanced combustion equation is:

${\text{C}}_{\text{1}\text{.098}}{\text{H}}_{\text{4}\text{.196}}+2.147\left({\text{O}}_{2}+3.76{\text{N}}_{2}\right)\to 1.098{\text{CO}}_{\text{2}}+2.098{\text{H}}_{\text{2}}\text{O}+\text{8}.0{\text{7272N}}_{2}$

${e}_{x,ch}=\left[{\stackrel{\xaf}{g}}_{F}+\left(a+\frac{b}{4}\right){\stackrel{\xaf}{g}}_{{\text{O}}_{\text{2}}}-a{\stackrel{\xaf}{g}}_{{\text{CO}}_{\text{2}}}-\frac{b}{2}{\stackrel{\xaf}{g}}_{{\text{H}}_{\text{2}}\text{O}}\right]\left({T}_{o},{P}_{o}\right)+R{T}_{o}\mathrm{ln}\left[\frac{{\left({y}_{{\text{O}}_{\text{2}}}^{e}\right)}^{a+b/4}}{{\left({y}_{{\text{CO}}_{\text{2}}}^{e}\right)}^{a}{\left({y}_{{\text{H}}_{\text{2}}\text{O}}^{e}\right)}^{b/2}}\right]$

Applying to the products of combustion and with the given composition of the environment and data from tables of thermochemical properties of selected substances at 298 K and 1 atm [21] the above equation yields:

$\begin{array}{c}{e}_{x,ch}=\left[-49026.89+\left(2.147\right)\left(0\right)-1.098\left(-394380\right)-2.098\left(-228590\right)\right]\left({T}_{o},{P}_{o}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left(8.3144\right)\left(298\right)\mathrm{ln}\left[\frac{{\left(0.2035\right)}^{2.147}}{{\left(0.0003\right)}^{1.098}{\left(0.0303\right)}^{2.098}}\right]\end{array}$

$\begin{array}{c}{e}_{x,ch}=\left[-49026.89+433029.24+479581.82\right]+\left[31814.8984\right]\\ =863584.17+31814.8984\\ =\text{895399}.\text{1}\left(\text{kJ}/\text{kmol}\right)\end{array}$

Dividing through by the molecular weight of the fuel (17.379 kg/kmol), we have

${e}_{x,ch}=\frac{895399.1}{17.379}=51521.8999\left(\text{kJ}/\text{kg}\right)$ Of the fuel

3.7. Thermo-Mechanical Exergy Computation, e_{x}_{,TM}

Applying ideal gas models, the thermo-mechanical contribution of the flue gases per kmol of fuel with, $T=AFT=2336.351\text{\hspace{0.17em}}\text{K}\left(2063.351\u02da\text{C}\right)$ . We have:

$\begin{array}{l}\stackrel{\xaf}{h}-\stackrel{\xaf}{{h}_{o}}-{T}_{O}\left(\stackrel{\xaf}{s}\u2013\stackrel{\xaf}{{s}_{o}}\right)\\ =1.098\left[\stackrel{\xaf}{h}\left(T\right)-\stackrel{\xaf}{h}\left({T}_{O}\right)-{T}_{O}\left({\stackrel{\xaf}{s}}^{O}\left(T\right)\u2013{\stackrel{\xaf}{{s}_{o}}}^{O}\left({T}_{O}\right)\right)-R\mathrm{ln}\left(\frac{{y}_{{\text{CO}}_{2},P}}{{y}_{{\text{CO}}_{2},{P}_{O}}^{e}}\right)\right]{\text{CO}}_{2}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+2.098\left[\stackrel{\xaf}{h}\left(T\right)-\stackrel{\xaf}{h}\left({T}_{O}\right)-{T}_{O}\left({\stackrel{\xaf}{s}}^{O}\left(T\right)\u2013{\stackrel{\xaf}{{s}_{o}}}^{O}\left({T}_{O}\right)\right)-{R}_{O}\mathrm{ln}\left(\frac{{y}_{{\text{H}}_{\text{2}}\text{O},P}}{{y}_{{\text{H}}_{\text{2}}\text{O},{P}_{O}}^{e}}\right)\right]{\text{H}}_{\text{2}}\text{O}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+8.07272\left[\stackrel{\xaf}{h}\left(T\right)-\stackrel{\xaf}{h}\left({T}_{O}\right)-{T}_{O}\left({\stackrel{\xaf}{s}}^{O}\left(T\right)\u2013{\stackrel{\xaf}{{s}_{o}}}^{O}\left({T}_{O}\right)\right)-{R}_{O}\mathrm{ln}\left(\frac{{y}_{{\text{N}}_{2},P}}{{y}_{{\text{N}}_{2},{P}_{O}}^{e}}\right)\right]{\text{N}}_{2}\end{array}$

Since $P={P}_{O}$ , each of the logarithmic terms drop out, also T is the adiabatic flame temperature, and $\stackrel{\xaf}{{h}_{o}}$ and ${\stackrel{\xaf}{{s}_{o}}}^{O}$ are data at ${T}_{O}$ from standard tables for ideal gas properties of selected gases [21], the thermo-mechanical contribution is:

$\begin{array}{l}\stackrel{\xaf}{h}-\stackrel{\xaf}{{h}_{o}}-{T}_{O}\left(\stackrel{\xaf}{s}\u2013\stackrel{\xaf}{{s}_{o}}\right)\\ =1.098\left[\stackrel{\xaf}{h}\left(T\right)-\stackrel{\xaf}{h}\left({T}_{O}\right)-{T}_{O}\left({\stackrel{\xaf}{s}}^{O}\left(T\right)\u2013{\stackrel{\xaf}{{s}_{o}}}^{O}\left({T}_{O}\right)\right)\right]{\text{CO}}_{2}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+2.098\left[\stackrel{\xaf}{h}\left(T\right)-\stackrel{\xaf}{h}\left({T}_{O}\right)-{T}_{O}\left({\stackrel{\xaf}{s}}^{O}\left(T\right)\u2013{\stackrel{\xaf}{{s}_{o}}}^{O}\left({T}_{O}\right)\right)\right]{\text{H}}_{\text{2}}\text{O}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+8.07272\left[\stackrel{\xaf}{h}\left(T\right)-\stackrel{\xaf}{h}\left({T}_{O}\right)-{T}_{O}\left({\stackrel{\xaf}{s}}^{O}\left(T\right)\u2013{\stackrel{\xaf}{{s}_{o}}}^{O}\left({T}_{O}\right)\right)\right]{\text{N}}_{2}\end{array}$

$\begin{array}{l}\stackrel{\xaf}{h}-\stackrel{\xaf}{{h}_{o}}-{T}_{O}\left(\stackrel{\xaf}{s}\u2013\stackrel{\xaf}{{s}_{o}}\right)\\ =1.098\left[121235.32-9364-298\left(318.642-213.685\right)\right]{\text{CO}}_{2}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+2.098\left[\left(100104.84-9904\right)-298\left(272.659-188.720\right)\right]{\text{H}}_{\text{2}}\text{O}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+8.07272\left[\left(76986.4-8669\right)-298\left(257.59-191.502\right)\right]{\text{N}}_{2}\end{array}$

$\stackrel{\xaf}{h}-\stackrel{\xaf}{{h}_{o}}-{T}_{O}\left(\stackrel{\xaf}{s}\u2013\stackrel{\xaf}{{s}_{o}}\right)=87889.4391+136762.364+392521.2854=617183.1\left(\text{kJ}/\text{kmol}\right)$

of the fuel.

Dividing through by the molecular weight of the fuel, we have the value in kJ/kg as:

$\stackrel{\xaf}{h}-\stackrel{\xaf}{{h}_{o}}-{T}_{O}\left(\stackrel{\xaf}{s}\u2013\stackrel{\xaf}{{s}_{o}}\right)=\frac{617183.1\left(\text{kJ}/\text{kmol}\right)}{17.379\left(\text{kg}/\text{kmol}\right)}=\text{35513}.\text{153}\text{\hspace{0.17em}}\left(\text{kJ}/\text{kg}\right)$ of the fuel.

3.8. Total Specific Exergy Computation

The total exergy from Equation (13) is:

$\begin{array}{c}{e}_{x,T}={e}_{x,TM}+{e}_{x,ch}\\ =\text{35513}.\text{153}\text{\hspace{0.17em}}\left(\text{kJ}/\text{kg}\right)+51521.8999\left(\text{kJ}/\text{kg}\right)\\ =87035.0529\text{\hspace{0.17em}}\left(\text{kJ}/\text{kg}\right)\end{array}$

which is the exergy per unit mass.

3.9. Total Exergy Computation for the Period under Review

From Table 3 the total flare volume for the first year 2008 is:

${V}_{f}=75399656.65\text{\hspace{0.17em}}{\text{m}}^{\text{3}}/\text{year}$

${\rho}_{ga}=0.713\text{\hspace{0.17em}}\text{kg}/{\text{m}}^{3}$

$\begin{array}{l}\therefore \text{The mass of flared gas}=\text{density}\times \text{flared volume}\left({V}_{f}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=0.713\text{\hspace{0.17em}}\text{kg}/{\text{m}}^{3}\times 75399656.65\text{\hspace{0.17em}}{\text{m}}^{3}/\text{year}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{53759955}.\text{19}\text{\hspace{0.17em}}\text{kg}/\text{year}\end{array}$

Hence, total exergy, ${E}_{X,T}$ :

$\begin{array}{c}{E}_{X,{T}_{1}}={e}_{x,T}\times 59791927.7266\text{\hspace{0.17em}}\text{kg}/\text{year}\\ =87035.0529\left(\text{kJ}/\text{kg}\right)\times 59791927.7266\text{\hspace{0.17em}}\text{kg}/\text{year}\\ =4.6789\times {10}^{12}\text{\hspace{0.17em}}\text{kJ}/\text{peryear}\end{array}$

3.10. The Electrical Equivalent of the Total Exergy

The electrical equivalent of the total exergy so calculated is $=5.204\times {10}^{12}\times 0.000\text{2778}\text{\hspace{0.17em}}\text{kWh}=1300761.361\text{\hspace{0.17em}}\text{kWh}$ of electricity for that year.

Thus, with the different density values of the gas compositions and with the help of MATLAB program, results are shown in Table 5.

From Table 5 flared volume and total exergy showed that the more gas flared in the field the more the exergy (work potential). Correspondently, the exergy is dependent on the amount of gas flared, with the highest exergy corresponding to 2010 and the least exergy to 2016. The total exergy over the period from Table 5 is estimated to be 3.6099 × 10^{13} kJ (36.099 TJ) this exergy value would have translated to 1.0189 × 10^{1}^{0} kWh of electrical energy.

4. Conclusions

This research discussed the thermo-mechanical and environmental assessment

Table 5. Specific, total and electric energy values.

of flared gases in an oil field. The study proffered solution to the objectives of this research work, which are:

1) Combustion analysis carried out with the aid of fundamental thermodynamic combustion equations and with the help of the equation by [19] and the flared volumes, densities, molar masses, the amounts of carbon (IV) oxide, water vapour, and methane are estimated at 582,319,618.1825 m^{3} (≈1.046 million tons), 1,077,510,054.31 m^{3} (≈2.0 million tons) and 14,960,560.91 m^{3} respectively, which are all greenhouse gases and therefore very pernicious to the natural environment. The research also showed that the equation by [20] for quantifying the amount of carbon (IV) oxide has a 92.3 % correlation with this research.

2) In fulfilling further objectives, the adiabatic flame temperatures were precisely evaluated using thermodynamic equations, correctly written combustion equations, different gas compositions, iterative thermodynamics, interpolations and with the help of MATLAB program. The adiabatic flame temperatures as evaluated in this work for natural gas also averagely correlated with those quoted in other literatures and are approximately 1965˚C, this is also in line with the inlet temperatures of gas turbines. The concept of exergy and related equations were also applied, this encompassed thermo-mechanical and chemical exergies to evaluate the total exergy which was found to be 3.6099 × 10^{13} kJ (36.099 TJ) translating to 1.0189 × 10^{10} kWh amount of electrical energy. The report also reveals that about 27% - 40% of gas produced in the field for the period under investigation was flared.

In conclusion therefore, if only one oil Field gave such astronomical amount of exergy, it then means that enormous amount of energy loss have been incurred in flaring gas from all the oil fields in the Niger Delta region of Nigeria which otherwise would have been utilized to generate electricity or for other useful purposes.

Acknowledgements

The researchers sincerely thank the Operator of the Alpha-Field for the opportunity to use their company as a case study. Data retrieved, interview with relevant personnel, Field visitations were very instrumental to the success of this research work.

Nomenclature

P_{o} = Ambient pressure [kpa]

T_{o} = Ambient temperature [K]

a = No of moles of carbon [kmol]

b = No of moles of hydrogen [kmol]

AFT = Adiabatic flame temperature [K]

ΔH^{C} = Enthalpy of combustion [kJ/kg]

IT = Iterative thermodynamic

e_{x} = Specific Exergy [kJ/kg]

E_{x} = Total Exergy [kJ]

R = Universal gas constant [kJ/kmolk]

IOCs = International Oil Companies

${\stackrel{\xaf}{g}}_{F}$ = Gibb’s function of formation [kJ/kmol]

E_{p} = Electrical Power generated [kWh]

${\stackrel{\xaf}{h}}_{f}^{\text{o}}$ = Molar enthalpy of formation [kJ/kmol]

y = Mole fraction

V_{f} = flared volume [m^{3}]

TJ = Terajoules^{ }

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