A novel empirical model for predicting the carbon dioxide emission of a gas turbine power plant

Abstract

Carbon dioxide (CO₂) is a major greenhouse gas released by gas turbine power plants that is hazardous to the environment. Hence, it is vital to investigate the operational conditions that influence its emissions. Various research papers have utilized a variety of techniques to estimate CO₂ emissions from fuel combustion in various power plants without taking into account the environmental operational characteristics which in turn may have a significant effect on the obtained output values. Therefore, the purpose of this research is to assess the carbon dioxide emissions while considering both external and internal functioning characteristics. In this paper, a novel empirical model for predicting the feasible amount of carbon dioxide emitted from a gas turbine power plant was developed based on ambient temperature, ambient relative humidity, compressor pressure ratio, turbine inlet temperature and the exhaust gas mass flow rate. The predictive model developed shows that the mass flow rate of CO₂ emitted has a linear relationship with the turbine inlet temperature to ambient air temperature ratio, ambient relative humidity, compressor pressure ratio, and exhaust gas mass flow rate with a determination coefficient (R²) of 0.998. Results obtained shows that rise in ambient air temperature and air fuel ratio led to increase in CO₂ emission, while increase in ambient relative humidity and compressor pressure ratio resulted in reduction of CO₂ emission. Furthermore, the average emission of CO₂ obtained for the gas turbine power plant was 644.893kgCO₂/MWh and 634, 066, 348.44kgCO₂/yr, of which the latter is within the guaranteed values of 726, 000, 000 kgCO₂/yr. Thus, the model can be utilized to perform an optimal study for CO₂ reduction in gas turbine power plants.

Nomenclature

Abbreviation/symbol

AFR

Air Fuel Ratio

CC

Combustion chamber

CIT

Compressor Inlet Temperature (⁰C, K)

CO₂

Carbon dioxide

cp

Specific heat capacity at constant pressure (kJ/kg K)

EIA

Environmental Impact Assessment

GHG

Greenhouse gas

GT

Gas turbine unit

HR

Heat rate (kJ/kWh)

IEA

International Energy Agency

IFC

International Finance Corporation

ISO

International Standard Organization

LF

Load factor (%)

LHV

Lower heating value (kJ/kg)

LNG

Liquefied Natural Gas

M

Molar mass (kg/kmol)

ṁ

Mass flow rate (kg/s)

Molar flow rate (kmol/s)

n

Number of moles

NOx

Nitrogen oxides

OPT

Operation Time (s, h)

p

Pressure (bar)

P

Power (MW)

r_p

Compressor Pressure ratio

T

Absolute temperature (⁰C, K)

TIT

Turbine Inlet Temperature (⁰C, K)

X

Mole fraction

Greek Symbols

Carbon dioxide Emission Rate (kg/MWh)

Relative Humidity

ɳ_c

Compressor isentropic efficiency

ɳ_net

Net Thermal Efficiency

γ

Specific heat capacities ratio

λ

Fuel air ratio

ρ

Density (kg/m³)

Subscripts

a

Air

AC

Air compressor

Amb

Ambient

CC

Combustion chamber

da

Dry air

f

Fuel

g

Exhaust gas

gen

Generator

GT

Gas turbine

Mech

Mechanical

T

Turbine

V

water vapour

1. Introduction

In the past decades, the environment has been degraded due to various technological innovations. The environmental issues posed by technological advances are of concern to individuals and companies around the world. From a wider impact and policy perspective on environmental degradation, greenhouse gas (GHG) emissions are the most significant environmental issue for industries, while recognizing that other environmental impacts are potentially significant, especially at the local level [1,2]. Due to the effect of GHG on the environment, the Conference of the Parties (COP21) on Climate Change held in Paris had set an objective to maintain the average ambient air temperature below 1.5 °C. To achieve the said objective, the United Nations [3]and Abdallah & El-Shennawy [4] recommended that the determination of CO₂ emissions from power plants is crucial because the power plant and other industries that supply and consume energy are major sources of CO₂ emissions, which led to a rise in ambient air temperature. Again, carbon dioxide has been said to be the most important greenhouse gas [[5], [6], [7]]. The burning of fossil fuels is responsible for 73% of the CO₂ emitted into the atmosphere [8]. The continued utilization of fossil fuels such as coal, natural gas, petroleum products, etc. To meet most of the world's energy demand will increase the amount of CO₂ emitted into the environment and hence keep increasing the Earth's ambient temperature [9,10]. The aforementioned fact has spurred governments, private companies, and research bodies to look at energy techniques that will help lower the effect of natural gas and oil sectors' environmental impact on the total budget of carbon dioxide emissions [11]. While the request for alternative energy recourses is on, the reliance on fossil fuel for power generation will continue because of its extensive infrastructure for fuel production and distribution [12].

In the case of natural gas, relevant studies such as Yousefi et al. [13]; Ayaz et al. [14]; Kim et al. [15] have shown that natural gas combustion mainly emits carbon dioxide, nitrous oxide, and sometimes methane when unburnt. Also, it has been established that natural gas emits less carbon dioxide than coal [6,16]. Environmental researchers have categorized carbon dioxide (CO₂) as the most notable anthropogenic ozone-harming substance [[17], [18], [19]]. Memon et al. [20] stated that CO₂ emission effects from fossil fuels is the reason researchers are interested in exploring various environmental impact mitigation strategies while considering the use of fossil fuels for power generation. This provided an opportunity to investigate its emissions and suggest ways to reduce them.

Gas turbine (GT) power plants generate exhaust gases apart from electricity production. The flue gas emitted into the power plant's surroundings contains carbon dioxide and other gases which pollute the air and contribute to GHG [21]. Saravanamutto et al. [22] stated in their book that a large amount of excess air is needed in gas turbine combustible engines, which leads to considerable oxygen in the exhaust gases. The work also explains that the exhaust of any gas turbine consists mainly of CO₂, H₂O, O₂, and N₂, and the combustion products can be expressed as either gravimetric (by mass) or molar (by volume) composition. With this explanation, CO₂ is the main gas emitted by gas turbine power plants that is harmful to the environment.

In light of the aforementioned, various approaches have been used in many research works on how CO₂ emissions are estimated from the combustion of fuel in different power plants. The United States Environmental Protection Agency (USPEPA), the Intergovernmental Panel for Climate Change (IPCC), and IEA have deplored the emission factors to predict the emission of CO₂. Also, the study on CO₂ emissions by Manceralla and Chicco [23]; Kazemi et al. [24]; and Sousa et al. [25] stated that the use of the CO₂ emission factor to evaluate the power plant's emissions of CO₂ is on the increase. The emission factor has been used in previous work because it is easy to compute CO₂ emissions from power plants. However, the issue of a particular power plant location was not considered because environmental location parameters were not considered. Qader et al. [26] developed a model using Holt's, Gaussian Process Regression, and neural network methods for the estimation of CO₂ emitted from a power plant in Bahrain. This particular model was mainly based on time series, which again has a deficiency of particular environmental parameters such as ambient temperature and relative humidity. Zhao et al. [27] used the econometrical method to estimate CO₂ and Nassar et al. [28] utilized the method of life cycle assessment to estimate the emission of CO₂ from a power plant that uses diesel in Libya. In addition, many other studies, such as Wang et al. [29]; Wang & Song [30], used the aggregate carbon intensity to determine the emission of CO₂ from power plants.

Furthermore, Memon et al. [20] and Memon et al. [31] investigated the CO₂ emission for simple and regenerative gas turbine power plant configurations, deploying the combustion equation. These studies considered changes in operating parameters such as compressor inlet temperature, compressor pressure, and turbine inlet temperature with CO₂ emission. The results obtained were used to develop models using regression analysis for predicting CO₂ emissions. Their results showed that the investigated operating parameters have an important effect on the performance of the cycle and the emission of CO₂. Though these studies considered operating parameters, important parameters such as relative humidity and exhaust gas mass flow rate that critically influence gas turbine power plants performance were not considered in their predicting models. For other models developed, Ibrahim et al. [32] deployed statistical tools to develop a novel model for predicting the optimum performance of GT power plant. The model obtained was satisfactory with a coefficient of determination (R²) value of 0.985. Also, Kwasi-Effah et al. [33] developed a novel model for accumulation of heat prediction in a solar thermal application with thermal storage medium. The R² value of 0.783 was obtained for the developed model. Likewise, Oyedepo et al. [34] studied the CO₂ emissions of 11 selected GT power plants using the combustion equation. The study analyzed the variation of CO₂ emissions with turbine inlet temperature (TIT) and exergy efficiency. Findings from the work showed that an increase in the exergetic efficiency of the GTs plant resulted in a reduction in CO₂ emission. Moreso, Kanbur et al. [35] also used the combustion equation method to analyze the CO₂ emissions of a combined cycle for a small-scale LNG cold plant. The findings from the environmental analysis revealed that the combined cycle system had a lesser CO₂ emission rate than the single GT system because it produced a more energy rate while both systems emitted the same amount of CO₂ into the atmosphere. Also, Karapekmez and Dincer [36] evaluated the emission of CO₂ from various fuels and stated that wood and sawdust are rewarding alternative fuels because of their biofuel nature. Steen [37] reported that the discharge of CO₂ from fossil fuel-fired gas power plants was found to be reduced with an increase in its thermal efficiency. Also, research work on carbon dioxide emissions from fuel consumption in Iran was carried out by Lotfalipour et al. [38] and it's revealed that carbon dioxide emissions will increase by 2.1 times as of 2025. Additionally. Fofrich et al. [39] stated in their research work that to maintain global warming at a temperature below 2 °C, an ambitious way of mitigating climate change problems from power facilities needs to be studied by continuous monitoring of carbon dioxide from power plant facilities. More so, the need to reduce gas turbine CO₂ emission was emphasized by Choudhary et al. [40].

In the evaluation of CO₂ emissions, an average carbon dioxide emission intensity or rate for simple open gas turbines has been determined by EIA [41] as 557 g CO₂/kWh. Fofrich et al. [39] also mentioned in their paper that the carbon dioxide emission rate varies from 274 to 720 g CO₂/kWh depending on technology and region. Gas turbine power plants are sensitive to environmental parameters such as, ambient air pressure, ambient air temperature and ambient air relative humidity [[42], [43], [44], [45]]. These parameters were not considered in modelling and evaluation of CO₂ emission by previous studies reviewed. So, in evaluating and predicting CO₂ emissions in GT power plants, these parameters require to be included for holistic study.

Additionally, the SGT5–2000E GT model considered for this study has a good record of controlling negligible low NOx and CO emissions [46,47]. So, the major exhaust constituent that has been flared is CO₂, as mentioned by Saravanamuttoo et al. [22]. To advance the frontier of knowledge in CO₂ emission studies, this makes it necessary to develop an empirical model for predicting CO₂ emission considering both internal and external parameters of a 153 MW GT Power Plant, that has not been earlier studied. Hence, the present study intends to model and evaluate the variation of the CO₂ emissions with operating parameters (ambient air temperature, ambient relative humidity, compressor pressure ratio, turbine inlet temperature and exhaust gas mass flow rate) for the power plant. The objectives of the study are to develop and validate a gas turbine model which will be used for the study; develop an empirical model for predicting CO₂ emission based on operating parameters for a gas turbine power plant; and evaluate the effect of ambient air temperature, thermal efficiency and turbine inlet temperature on the annual CO₂ emission rate from the gas turbine power plant. Furthermore, the study will also compare the actual CO₂ emitted during this period with the CO₂ emission specified by the manufacturer and other available literature.

2. Methodology

2.1. Description and operation of the 153 MW ga turbine power plant

The gas turbine considered for this study is the SGT5-2000E GT power plant located in Benin City, Edo State, Nigeria. The natural gas use to powered the gas turbine power was supplied by Nigeria Gas Company (NGC) pipeline network in partnership with Seplat Nigeria Limited. The manufacturer-installed capacity of model SGT5-2000E was 153 MW output power at this site with a net heat rate value of 10,528 kJ/KWh at 26 °C [48].

The considered model consists of single casing design, a single shaft, two side flanges, a high capacity, two silo-type combustors, a 4 -stage turbine and a 16 – stage axial compressor. The generator is attached to the side of the compressor (cold end) which is air-cooled. One advantage of this Siemens gas turbine model is that its arrangement permits easy attachment of HRSG, unlike other models where the generator is coupled to the turbine side. The SGT5-2000E model efficiently burn a mixture of fuel and compressed air to control CO and NOx emissions because of its good combustion chamber. The combusted products, which include carbon dioxide, water vapour, and oxygen, are emitted into the power plant's surroundings through the stack. The Siemens Gas Turbine Power Plant operates on the Brayton cycle. Fig. 1, Fig. 2 represent the schematic and specific temperature-entropy (T-s) diagrams of the SGT5-2000E gas turbine power plant respectively.

Fig. 1.

A typical schematic diagram of SGT5 – 2000E gas turbine power plant.

Fig. 2.

The T-s Diagram of SGT5 – 2000E Gas Turbine Power Plant Cycle.

Part of the power mechanical power produced by turbine is utilized by the air compressor, while the rest is converted to electrical power by the 3000-rpm generator. The synchronized electrical power is fed into the public power grid [49].

2.2. Thermodynamic model equations

The thermodynamic model equations used for the modelling of carbon dioxide emissions from the gas turbine power plant are illustrated in Equations (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14). Also, the composition and properties of the fuel (natural gas) used to fire the gas turbine power plant are presented in Table 1.where ${\dot{m}}_f$ is the fuel mass flow rate and M_f is fuel molar mass

Table 1.

Composition and property of the fuel.

$$n_f=\frac{{\dot{m}}_f}{M_f}$$ (1)

S/N	Name of Constituent	Formula of Constituent	Molar fraction (Volumetric) (xf)	Molar mass of Constituent (Mi) (kg/kmol)
1	Methane	CH4	0.87721	16
2	Ethane	C2H4	0.03658	30
3	Propane	C3H8	0.03031	44
4	Normal –Butane	C4H10–N	0.003325	58
5	Iso – Butane	C4H10–I	0.003318	58
6	Normal – Pentane	C5H12–N	0.002157	72
7	Normal – Hexane	C6H14–N	0.000448	86
8	Iso – Pentane	C5H12–I	0.002352	72
9	Carbon (IV) Oxide	CO2	0.02722	44
10	Nitrogen	N2	0.01708	28

*Source [50].

Equations (1), (2), (3) were used to determine the molar flow rates of fuel and air, and fuel air ratio respectively as expressed by Egware et al. [45].

The fuel molar flow rate, n_f in kmol/s was computed using Equation (1).

The molar flow rate of air (n_a) in kmol/s was calculated as expressed in Equation (2).

$$n_a=\frac{{\dot{m}}_a}{M_a}$$ (2)

where, ${\dot{m}}_a$ is the mass flow rate of air as obtained from the 153 MW GT Power Plant.

The fuel air ratio, $\lambda$ was calculated as shown in Equation (3).

$$\lambda =\frac{n_f}{n_a}$$ (3)

In the various computations, the air chemical compositions were assumed to be carbon (IV) oxide, water vapour, and nitrogen, and all gases were assumed to be ideal gases [51], respectively. The relationship between the chemical contents of the fuel, as presented in Table 1, air, and exhaust gases, is indicated in the combustion reaction that took place in the combustor, as illustrated in Equation (4).

$$\lambda \left[\begin{array}{l}0.87721C{H}_4+\\ 0.03658C_2{H}_6+\\ 0.03031C_3{H}_8+\\ 0.003325C_4{H}_{10-N}+\\ 0.003318C_4{H}_{10-I}+\\ 0.002157C_5{H}_{12-N}+\\ 0.000448C_6{H}_{14-N}+\\ 0.002352C_5{H}_{12-I}+\\ 0.02722C{O}_2+\\ 0.01708N_2\end{array}\right]+\left[\begin{array}{l}{x}_{a{O}_2}{O}_2+\\ x_{a{N}_2}{N}_2+\\ x_{aC{O}_2}C{O}_2+\\ x_{a{H}_{2}O}{H}_{2}O\end{array}\right]\to \left(1+\lambda \right)\left[\begin{array}{l}{x}_{pC{O}_2}C{O}_2+\\ x_{p{H}_{2}O}{H}_{2}O+\\ x_{p{O}_2}{O}_2+\\ x_{p{N}_2}{N}_2\end{array}\right]$$ (4)

where x_a is the molar fraction of the air components, x_p is the molar fraction of combustion products components, and λ is the fuel-air ratio of the power plant. The combustion equation was obtained from Bejan et al. [51] where more details can be found.

Applying carbon, hydrogen, oxygen and nitrogen balance to solve the combustion reaction expressed in Equation (4). The molar fraction of carbon (IV) oxide x_pCO2, water vapour x_pH2O, oxygen x_pO2 and nitrogen x_pN2 were computed as shown in Equations (5), (6), (7), (8) respectively.

$$x_{pC{O}_2}=\frac{1.118765\lambda +x_{aC{O}_2}}{1+\lambda }$$ (5)

$$x_{p{H}_{2}O}=\frac{1.2022233\lambda +x_{a{H}_{2}O}}{1+\lambda }$$ (6)

$$x_{p{O}_2}=\frac{0.02722\lambda +x_{a{O}_2}+x_{aC{O}_2}+0.5x_{a{H}_{2}O}-x_{pC{O}_2}-0.5x_{p{H}_{2}O}}{1+\lambda }$$ (7)

$$x_{p{N}_2}=\frac{0.01708\lambda +x_{a{N}_2}}{1+\lambda }$$ (8)

The molar flow rate of the exhaust gases was evaluated by applying Equation (9).

$$n_p=n_a*\left(1+\lambda \right)$$ (9)

The mass flow rate of each constituent of the product or exhaust gases was computed by using Equation (10) [52,53].

$${\dot{m}}_{pC{O}_2}=x_{pC{O}_2}*n_p*M_{C{O}_2}$$ (10)

where n_aco2, n_aO2 and na_N2 are the molar values for carbon dioxide, oxygen and nitrogen, which are 0.0003058, 0.20988789 and 0.78980632 respectively as gotten from Kanbur et al. [53].

The compressor pressure ratio (r_p) was determined by applying Equation (11) as obtained from Refs. [49,54,55].

$$r_p=\frac{p_2}{p_1}$$ (11)

The Air fuel ratio (AFR) was evaluated by using Equation (12).

$$AFR=\frac{{\dot{m}}_a}{{\dot{m}}_f}$$ (12)

Equation (13) was used to obtain the net efficiency of the GT Power plant [54].

$${\eta }_{net}=\frac{P_{net}}{{\dot{m}}_f\times LHV}$$ (13)

The GT power plant net heat rate was evaluated applying Equation (14) [48].

$$HR=\frac{3600}{{\eta }_{net}}$$ (14)

2.3. The SGT5 – 2000E GT power plant modelling and simulation

The installed parameters of the 153 MW GT Power Plant model are given in Table 2 as obtained from Azura [50,56], which is used as the roof profile for the simulation. Fig. 3 represents the structure of the GT Power Plant executed with Ebsilon Professional. Summary of data obtained from the 153 MW Ga Turbine Power Plant between December 2017 and December 2021 as presented in Table 3 was used for off design conditions during modelling and simulation process.

Table 2.

Nominal conditions for the gas turbine power plant.

S/N	Variables	Quantities
1	Net Power Output (MW)	153
2	Net Heat Rate(kJ/kWh)	10,528
3	Ambient air temperature (0C)	26
4	Ambient air pressure (bar)	1.013
5	Turbine Exhaust Temperature (0C)	557.50
6	Exhaust mass flow (kg/s)	506
7	Compressor pressure ratio	11.44
8	Relative Humidity (%)	70
9	Lower Heating Value (MJ/kg), LHV	45.011
10	Annual CO2 Emission (kg)	726,000,000

Fig. 3.

Topology of the SGT5 – 2000E for installed condition.

Table 3.

Summary of Operating data from the power plant.

S/N	Variables	Quantities
1	Ambient Temperature (0C), T1	20–35
2	Ambient Relative Humidity (%), ɸ	41.02–92
3	Turbine Exhaust Temperature (0C), T4	531.5–549.3
4	Compressor Inlet Pressure (bar), p1	1.011–1.013
5	Compressor Outlet Pressure (bar), p2	10.898–11.071
6	Mass flow rate of air (kg/s), ${\dot{m}}_a$	480.34–514.40
7	Mass flow rate of fuel (kg/s), ${\dot{m}}_f$	10.28–11.41
8	Net Power output (MW), Pnet	140.869–159.272

The assumptions taken in modelling the power plant are.

• (i)Steady-state was assumed for the simulation as in Ref. [57], which means that the mass and other parameters within the various components and the boundary do not vary with time. Quasi steady state is assumed for compressor inlet air temperature because it depends on time which was assumed to steady at every hour.
• (ii)Transient effects of start-up and shutdown during operations were neglected because the data obtained were recorded at times when the power plant are fully in operation without fault.
• (iii)The nominal pressure drops used in the Ebsilon Professional were obtained from the power plant. This was done in order to ensure that the pressures of the various fluids were more realistic.

The turbine model for a 153 MW gas-fired power plant (SGT5 – 2000E) includes an air compressor, combustor, gas turbine, and generator, which were modelled by linking the selected various components together as shown in Fig. 3 The SGT5-2000E model installed performances were obtained using the installed parameters of the ambient temperature of 26 °C and ambient air pressure of 1.013 bar and other variables from Table 2A “general input value” was used to set the nominal flue gas mass flow rate and temperature while adjusting the pressure ratios of the gas turbine components. Compressor and turbine isentropic efficiencies from the power plant manual of 90% and 85%, respectively, were used. This was done because the mass flow rates of fuel and air were not provided, which will be obtained after the model simulation. Generator and mechanical efficiencies of 98.5% and 99%, respectively, which were obtained after a series of iteration processes, were used for the modelling. The fuel composition and LHV were entered correspondingly. Subsequently, entering all the necessary values and running the model, the fuel and air mass flow rates were obtained at nominal conditions for the gas turbine.

The simulation was repeated using the obtained mass flow rates of fuel and air without the installed exhaust mass flow rate and temperature as shown in Fig. 3. This was done so that the air mass flow rate and fuel mass flow rate entering the compressor and combustor, respectively, could determine the performance of the gas turbine under different inlet conditions and partial loads. This formed the root profile for this model, which made it possible to enter the new values of air for off-design conditions applying the “boundary value input”. The modelling of the 153 MW GT Power Plant for the installed condition using Ebsilon is presented in Fig. 3.

2.4. Ebsilon model validation

The built model is used to monitor the performance of existing gas turbine power plants. The values obtained were validated with the 153 MW Ga Turbine Power Plant installed capacity data using the power generated and heat rate. The percentage errors of the model observed were calculated using Equation (15) [[58], [59], [60], [61]].

$$\begin{gathered} \% \\ \text{ModelError}=\frac{\left(\text{AD}-\text{MD}\right)*100\%}{\text{AD}} \end{gathered}$$ (15)

where AD and MD are actual data and model data obtained.

2.5. Off-design modelling for the SGT5 – 2000E gas turbine

When a gas turbine is operating at design conditions, it is sometimes called rated condition or 100% design condition. When a power plant is operated outside its nominal specifications, this is called an “off-design condition”. Off-design conditions can occur if ambient air conditions such as temperature or humidity change, or if the power produced by the turbine falls below or above its rated power. Off-design models were run by changing the ambient temperature and relative humidity when the output power deviated from rated conditions. The Ebsilon Professional software was used to model the 153 MW gas-fired power plant output power and thermal efficiency variation with ambient air temperature, as shown in Fig. 4.

Fig. 4.

Topology of azura edo SGT5 – 2000E for off-design conditions.

Power plant performance is affected by changing environmental conditions. The deviations in performances of the power plant that occur are owing to changes in the air properties entering the air compressor, such as relative humidity and temperature. Different ambient air densities and mass flow rates were computed applying Equations (16), (17), respectively, for various ambient air temperatures as expressed by Egware et al. [48].

$${\rho }_i={\rho }_N\frac{T_N}{T_i}$$ (16)

$${\dot{m}}_i={\dot{m}}_N\frac{{\rho }_i}{{\rho }_N}$$ (17)

where T_N is the absolute temperature, ρ_N is the density and ṁ_N is air mass flow rate for the nominal condition; T_i is the absolute temperature, ρ_i is the density and ṁ_i is air mass flow rate for the off-design condition [48].

The net power output, net thermal efficiency, and mass flow rate of CO₂ emitted from the GT power plant due to change in ambient air temperature and relative humidity were obtained from Ebsilon simulated model. The carbon dioxide emission from gas turbine power plant is a function of the following parameters which include; ambient air temperature, compressor pressure inlet and outlet pressures, turbine inlet temperature, relative humidity, exhaust gas mass flow rate Saravanamuttoo et al. [22] as shown in Equation (18).

$$\dot{m}{}_{C{O}_2}{{{{{=}^{C{O}_2}}^{C{O}_2}}^{C{O}_2}}^{C{O}_2}}^{C{O}_2}f\left(r_p,t,\phi ,{\dot{m}}_g\right)$$ (18)

Where ${\dot{m}}_g={\dot{m}}_a+{\dot{m}}_f$, TIT to ambient air temperature ratio, $t=\frac{T_3}{T_1}$, and compressor pressure ratio, $r_p=\frac{p_2}{p_1}$.

The values of the mentioned independent variables obtained from the simulated Ebsilon model was used for the in the regression model.

2.6. Regression model

The regression analysis model was developed to predict the mass flow rate of CO₂ emitted from the gas turbine power plant. The ambient air temperature, compressor pressure ratio, relative humidity, turbine inlet temperature and exhaust gas mass flow rate were considered independent variables, while the mass flow rate of CO₂ emitted is the dependent variable.

Therefore, to predict the CO₂ mass flow rate emitted, the β parameters in Equation. (19) must be evaluated for minimum value of the sum of the square of the differences between the observations Yi and the actual curve [33].

$${\mathrm{Y}}_{\mathrm{i}}={\mathrm{\beta }}_{\mathrm{o}}+\mathrm{f}\left({\mathrm{X}}_{\mathrm{i}}{\mathrm{\beta }}_1\right)+{\epsilon }_{\mathrm{i}}\mathrm{i}=\mathrm{1,2,3},\dots ..\mathrm{n}$$ (19)

The coefficients β_o and ${\mathrm{\beta }}_1$ that minimize the square of the distance between the curve and the point as expressed in Equations (20), (21) respectively as expressed in Ref. [33].

$${\hat{\mathrm{\beta }}}_0\bar{y}-{\hat{\mathrm{\beta }}}_1\bar{x}$$ (20)

$${\mathrm{\beta }}_1\frac{\sum _{i=1}^n{y}_i{x}_i-\frac{\left(\sum _{i=1}^{n}yi\right)\left(\sum _{i=1}^{n}xi\right)}{n}}{\sum _{i=1}^n{x}_i^2-\frac{{\left(\sum _{i=1}^n{x}_i\right)}^2}{n}}$$ (21)

Equations (22), (23) was used to compute the coefficient of correlation and the standard error obtained [33];

$$\mathrm{r}=\frac{n\sum _{i=1}^n{y}_i{x}_i-\left(\sum _{i=1}^{n}yi\right)\left(\sum _{i=1}^{n}xi\right)}{\sqrt{\left[n\sum _{i=1}^n{x}_i^2-{\left(\sum _{i=1}^n{x}_i\right)}^2\right]}\left[n\sum _{i=1}^n{y}_i^2-{\left(\sum _{i=1}^n{y}_i\right)}^2\right]}$$ (22)

$$\mathrm{S}=\frac{\sum _{i=1}^n{y}_i^2-{\mathrm{\beta }}_0\sum _{i=1}^n{y}_i-{\mathrm{\beta }}_1\sum _{i=1}^n{y}_i{x}_i}{n}$$ (23)

The determination coefficient (R²) was computed by applying Equation (24) [33].

$${\mathrm{R}}^2=\frac{\sum _{i=1}^n{\left({\hat{y}}_i-\bar{y}\right)}^2}{\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2}$$ (24)

2.7. Evaluation of CO₂ emission rate

The mass of carbon dioxide emission rate in terms of kg/kWh and annual mass of carbon dioxide discharged was computed by applying Equations (25), (26) respectively [35,62,63].

$${\xi }_{C{O}_2}=\frac{3600*m_{pC{O}_2}}{P_{net}}$$ (25)

$${\dot{m}}_{pC{O}_2/yr}=m_{pC{O}_2}*LF*OPT$$ (26)

where LF = 0.75 and OPT = 8760 h s are load factor and operation time for the 153 MW Power Plant for one year respectively.

3. Results and Discussion

3.1. Model validation and variation of CO₂ emission with the operating parameters

In this study, Ebsilon Professional software was deployed to model and simulate the SGT5-2000E model GT power plant. Table 4 shows the validated results for the installation conditions of the SGT5 – 2000E model developed by Ebsilon. Equation (15) was used to calculate the per cent deviation or error between model and design data. This is to confirm that there is consistency between model developed and the installed design data that form the root profile of the model. Thus, the developed model was used to evaluates CO₂ emissions, net power output, net heat rate, and net thermal efficiency.

Table 4.

Model validation results for installed data.

S/N	Parameters	Design	Model	Deviation	%Error
1	Net Power Output (MW)	153	151.645	1.355	0.885621
2	Net Heat Rate(kJ/kWh)	10,528	10,858	−330	−3.1345

After the validating the model, the off-design conditions were carried out to ascertain the behaviour of CO₂ with ambient relative humidity, ambient temperature, compressor pressure ratio, exhaust gas mass flow rate, TIT, net power out and net thermal efficiency of the gas turbine power plant. The off-design condition was also validated to show how the model mimic the actual gas turbine power plant as presented in Fig. 5. The results of carbon dioxide emission variation with ambient temperature and relative humidity; air fuel ratio and compressor pressure ratio are presented in Fig. 6, Fig. 7 respectively.

Fig. 5.

Model Validation for change in Ambient Air Temperature with Net Power Output.

Fig. 6.

Variation of CO₂ with ambient air temperature and relative humidity.

Fig. 7.

Variation of CO₂ with r_p and AFR.

Fig. 5 shows that the model mimics the actual performance of the gas turbine power plant because of the negligible variation observed Also, the average percentage error between the model and the actual net output power was −0.31% for the GT unit. Again, the validation results conform with the outcomes attained by Wallentinen [58] and Miguez Da Rocha [59] who utilized very similar software for their studies. Consequently, the model validation outcomes showed the adequacy and consistency of the developed model. Therefore, the results were used for the thermodynamic evaluation of the model power plant SGT5 – 2000E GT. Therefore, its outcomes were utilized in evaluating the thermodynamic performance for the SGT5 – 2000E GT model power plant.

A sensitivity analysis was performed for the independent variable parameters to examine the output response of the carbon dioxide emission from the gas turbine power plant. Fig. 6 shows the variation of carbon dioxide emissions with ambient relative humidity and ambient air temperature. The plot shows that the relative humidity decreases as the magnitude of CO₂ increases, while the reverse is the case of the ambient temperature because it increases as the mass flow rate of carbon dioxide emission increases from the power plant. This is in agreement with results obtained by Teng and Chen [64]. The implication of this observation is that high-magnitude carbon dioxide emissions from gas turbine power have occurred at a high ambient temperature and low relative humidity of the environment. This can be minimized by introducing an air inlet cooling system to reduce the compressor's air inlet temperature and increase its relative humidity. Fig. 7 shows the variation of carbon dioxide emissions with the compressor pressure ratio and air-fuel ratio of the gas turbine power plant. The plot shows that the air-fuel ratio slightly increases and the compressor pressure ratio decreases as CO₂ emissions from the power plant increase. It agrees with the statement made by Kruk-Gotzman [65]. This revealed that the gas turbine power plant emitted more carbon dioxide at a low compressor pressure ratio, and the AFR has less effect on the CO₂ emission compared to the compressor pressure ratio. This can be improved by operating the gas turbine power plant at a high compressor pressure ratio.

3.2. Regression model

The data obtained from the off-design analysis was used to carry out a regression analysis that will be used to predict carbon dioxide emissions from gas turbine power plants. From the regression analysis, the empirical model for predicting the mass of carbon dioxide emission rate in gas turbine power plant is obtained as follows;

$${\dot{m}}_{C{O}_2}=0.000365t-0.00478\phi -5.272583r_p-0.000546{\dot{m}}_g+83.734$$ (27)

The predictive model obtained as shown in Equation (27) shows a linear relationship with the TIT to ambient temperature ratio, ambient air relative humidity, compressor pressure ratio, and exhaust gas mass flow rate with an R² value of 0.998. The coefficient of determination (R²) obtained is satisfactory as stated by Ibrahim et al. [32] and Kwasi-Effah et al. [33].

Equation (27) can be used to predict the mass flow rate of carbon dioxide emissions from any related gas turbine power plant for a given ambient air temperature, ambient relative humidity, compressor pressure ratio, and exhaust gas mass flow rate. The model is valid for gas turbines within the range of 20–35 °C in a humid environment. One major advantage of this model is that it encompasses environmental and internal operating parameters in predicting the emission of carbon dioxide from gas turbine power plants.

3.3. Carbon dioxide emission rate evaluation

The environmental variables evaluated are CO₂ emission in kg/MWh of electricity generated and the mass of CO₂ emitted annually for the GT unit. The variation of the CO₂ rate emitted in kg/MWh and the mass of CO₂ emitted per year with ambient air temperature are presented in Fig. 8, Fig. 9 respectively. Fig. 10 illustrates the variation of CO₂ in kg/MWh with net thermal efficiency for the GT unit. Also, the change in turbine inlet temperature with carbon dioxide emission from the gas turbine power plant is presented in Fig. 11. The average results of the CO₂ emission in kgCO₂/MWh and the annual mass of CO₂ emitted obtained from the environmental analysis of the 153 MW Ga Turbine Power Plant unit are presented in Fig. 12.

Fig. 8.

Variation of carbon dioxide emission rate in (kg/MWh) with ambient temperature.

Fig. 9.

Variation of carbon dioxide emitted per year with ambient temperature.

Fig. 10.

Variation of Carbon Dioxide Emission Rate in (kg/MWh) with Net Thermal Efficiency.

Fig. 11.

Variation of Carbon Dioxide Emission Rate in (kg/MWh) with Turbine Inlet Temperature.

Fig. 12.

Average amount of carbon dioxide emission rate for the gas turbine power plant.

As seen in Fig. 8, Fig. 9, the carbon dioxide emission rate in kg/MWh and annual emission increase with ambient air temperature. Thus, at high ambient air temperatures, more CO₂ was emitted, so the air intake cooling system will be required to lower the CO₂ emission from the 153 MW Ga Power Plant. Fig. 10 is a plot of the CO₂ emission rate against net thermal efficiency for the GT unit. It was observed that the CO₂ emission rate in kg/kWh decreases as the net thermal efficiency increases. This indicates that improved net thermal efficiency will reduce CO₂ emissions by kg/MWh, which agrees with the work of Memon et al. [31] and Steen [37] and. Furthermore, the CO₂ emission from the gas turbine power plant reduces as the turbine inlet temperature increases, as shown in Fig. 11. This is in agreement with what was mentioned by Oyedepo et al. [34]; Qi and Huang [66]; Pashchenko et al. [67].

The average emission of CO₂ rate for the gas turbine unit varies from 591.50 to 701.46 kg CO₂/MWh during the period of this study, as presented in Fig. 12. The power plant average of 644.893 kg CO₂/MWh, which is in the range value of 214–720 kgCO₂/MWh obtained from various studies as mentioned by Fofrich et al. [39]; Von Wald [68] and Barquín del Rosario [69]. The average value is on the high side of the mentioned range, which means CO₂ capture technology will be encouraged to reduce its emission rate. The average mass of CO₂ emitted annually as shown in Fig. 12 ranges from 618, 946, 501.58 kg to 649, 208, 301.04 kg with a station average of 634, 066, 000 kg (634.066 kton CO₂). Also, the station average is less than the guaranteed value of 726, 000, 000 kgCO₂ annually. The results obtained indicate that the 153 MW Ga Turbine Power Plant has a good carbon dioxide emission rate. However, the values obtained are still higher than the International Finance Council (IFC) performance standard recommendation of 100, 000, 000 kg CO₂/yr as stated by Azura EIA [56] and Herremans and Tyler [70]. So, there is a need to reduce the quantity of CO₂ emissions from the power plant.

This research work has shown that the 153 MW gas power plant's emission can be reduced in two ways. By enhancing the most ineffective components, such as reducing the temperature of the air flowing into the compressor and using the least sufficient flow rate of fuel to ensure its maximum burning. Also, the reduction in the net CO₂ emission rate will be achieved by improving the overall plant thermal efficiency. Additionally, the incorporation of inlet air cooling systems will help to maintain a low compressor air inlet temperature and reduce carbon dioxide emission; since low CO₂ is emitted at a low ambient air temperature.

4. Conclusion and recommendation

In this study, the carbon dioxide emission model and analysis of the 153 MW gas turbine power plant have been carried out using the data from the power plant. An empirical model for predicting the feasible amount of carbon dioxide emitted from a gas turbine power plant was developed based on ambient temperature, ambient relative humidity, compressor pressure ratio, and the exhaust mass flow rate. The summary of findings from the study are as follows.

• •The validation error values of 0.886% and −3.135% for the design and −0.31% for off – design conditions were obtained for the developed gas turbine power plant, which ascertained that the gas turbine model used for the obtained the CO2 emission data was good.
• •After validation the sensitivity analysis results obtained shows that rise in ambient air temperature and air fuel ratio led to increase in mass flow rate of CO2 emission, while increase in ambient relative humidity and compressor pressure ratio resulted in reduction of CO2 emission mass flow rate.
• •The predictive model developed shows that the mass flow rate of CO2 emitted has a linear relationship with the turbine inlet temperature to ambient air temperature ratio, ambient relative humidity, compressor pressure ratio, and exhaust gas mass flow rate with a coefficient of determination (R2) of 0.998. The value of R2 obtained revealed that the model developed is good.
• •The carbon dioxide emission rate in kg/MWh and annual emission increase with ambient air temperature. It was observed that the CO2 emission rate in kg/kWh decreases as the net thermal efficiency increases. The CO2 emission from the gas turbine power plant reduces as the turbine inlet temperature increases. The average emission of CO2 obtained for the gas turbine power plant was 644.893kgCO2/MWh and 634, 066, 348.44kgCO2/yr, of which the latter is within the guaranteed values of 726, 000, 000 kgCO2/yr.

The CO₂ emission rates obtained were within the range of the installed data but higher than the IFC standard. The study also showed that the emission of CO₂ in kgCO₂/MW annually was affected by the ambient air temperature, TIT, and net thermal efficiency. To address the adverse effects of ambient air temperature and relative humidity on carbon dioxide emission, the integration of an air intake cooling system should be encouraged. Further study on carbon capture techniques, can be considered to reduce the carbon dioxide emission from power plants to maintain IFC standards. Also, the model is valid for humid region, consequently, similar study can be recommended for arid and temperate regions. Hence, the model should be recommended in selecting parameters that affect CO₂ emission for gas turbine modelling.

Author contribution statement

Henry Okechukwu Egware: Conceived and designed the experiments; Performed the experiments; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Collins Chike Kwasi-EffahConceived designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

The data that has been used is confidential.

Declaration of interest's statement

The authors declare no conflict of interest.