Investigation of the Effects of Steam Injection on Equilibrium Products and Thermodynamic Properties of Diesel and Biodiesel Fuels

The effects of steam injection on combustion products and thermodynamic properties of diesel fuel, soybean oil-based biodiesel (NBD), and waste cooking oil biodiesel (WCOB) are examined in this study by considering the chemical equilibrium. The model gives equilibrium mole fractions, specific heat of the exhaust mixtures of 10 combustion products, and adiabatic flame temperatures. The results show that the mole fractions of carbon monoxide (CO) and carbon dioxide (CO2) decrease with the steam injection ratios. Nitric oxide (NO) mole fractions decrease with the steam injections ratios for lean mixtures. The specific heat of combustion products increases with the steam injection ratios. The equilibrium combustion products obtained can be used to calculate the nonequilibrium values of NO in the exhaust gases using some existing correlations of NO kinetics.


Introduction
Fossil-based fuels derived from crude oil are the main sources of energy for internal combustion engines worldwide in general and in Cameroon in particular. However, combustion in internal combustion engines is a major source of pollutant emissions. More severe environmental restrictions have been put into effect in many countries worldwide due to the growing concern about environmental issues. In addition, the use of fossil-based fuels is still dominant in almost all internal combustion engines despite the fact that the resources of the fossil-based fuels are depleting rapidly.
us, researchers carry out studies on combustion in internal combustion engines and alternative fuels. In this regard, biodiesel could be considered as an alternative fuel to fossil diesel to meet the growing fuel demand and the severe environmental norms. Biodiesel is engine wear are also the shortcomings of biodiesel which affect the combustion characteristics [7]. e poor lowtemperature properties of biodiesel are an obstacle to its utilization in cold weather conditions [8]. e differences in chemical properties of fuels affect the combustion process development, which lead to the alteration of performance and emissions of engine [9]. Biodiesels are formed from many different classes of saturated and unsaturated fatty acids, which form their physical and chemical properties [10]. Higher viscosity results in higher spray penetration into the combustion chamber, which is very important to enhance air-fuel mixing quality especially for big and slow engines with large open combustion chambers, but there are more adverse impacts for small and fast engines such as poor fuel atomization, larger droplet size, bad mixing quality, incomplete combustion, and lower combustion efficiency, which contribute to decreasing the engine performance and increasing the exhaust emissions [11]. Biodiesel combustion is difficult to model because of the diversity of its sources and complexity in molecular structure [12][13][14][15][16]. Chemical equilibrium model is a better estimation for a combustion model assuming that the combustion products are at a chemical equilibrium in a high-temperature combustion. e combustion products react together to produce and remove each species at equal rates, and consequently, the net change in species composition remains constant at a given condition [17]. Chemical equilibrium models are used in thermodynamic simulations of internal combustion engines [18]. A simple model including only six species of the products, namely, carbon dioxide (CO 2 ), water (H 2 O), nitrogen (N 2 ), oxide (O 2 ), carbon monoxide (CO), and hydrogen (H 2 ), has been defined by Heywood [19]. Gonca [20] investigated the effects of steam injection on performance and nitric oxide (NO) emissions of a diesel engine running with ethanoldiesel blend. In his study, various ethanol-diesel blends were evaluated depending on the steam/air ratios by means of constituted solving schema based on chemical equilibrium. Ngayihi Abbe et al. [21] carried out a numerical study to compare four biodiesel surrogates using a zero-dimensional thermodynamic model involving a chemical equilibrium combustion model. A chemical equilibrium model was used by Ust and Kayadelen [22]. In their study, 10 combustion products were used to predict the equilibrium and thermodynamic properties in an H 2 O injected combustion system at various H 2 O rates. ey neglected the CO and H 2 formations in lean mixtures. ey formed their equation systems for lean and rich mixtures separately. Rakopoulos et al. [23] performed a two-zone thermodynamic model for combustion and emissions formation in a direct injection diesel engine. ey used a chemical equilibrium scheme involving 11 species of combustion products for calculating the constituents in exhaust gases. Diotallevi [24] developed a multi-zone thermodynamic model of a diesel engine for NO x formation. He created a chemical equilibrium scheme by considering 10 combustion products. e nonlinear system of equations created was solved using an iterative method developed by the author using the Matlab program. Mourya and Roy [25] performed a study on the combustion modelling of a diesel engine operating using jatropha biodiesel and diesel engine blends according to a chemical equilibrium model. e C program and Mathematica software developed by the authors were used to solve their equations. Kayadelen [26] developed a multi-featured model for estimation of the mole fractions of 14 equilibrium combustion products, thermodynamic properties and constant-pressure adiabatic flame temperature of fuels, surrogates, and fuel additives. He constituted his equation systems for lean and rich mixtures separately. CO and H 2 mole fractions were neglected in lean mixtures. e nonlinear equation systems were solved using both Newton-Raphson and Gauss-Seidel methods. Some equilibrium computer programs exist like GASEQ [27] and Chemical Equilibrium with Applications (CEA) of NASA [28]. However, GASEQ software neglects the effects of dissociations on the specific heat of the combustion products. Consequently, noticeable errors may result in engine performance calculations. On the other hand, CEA of NASA necessitates adiabatic flame temperature or enthalpy of combustion to be given. Important differences are reported between the specific heat results of GASEQ and CEA of NASA particularly at high temperatures. In literature, there is a lack of studies carried out on the effects of steam injection on equilibrium products and thermodynamic properties of diesel and biodiesel fuels. Nevertheless, the equilibrium combustion products can be used to calculate the nonequilibrium NO emissions in exhaust gases. e present model takes into account the effect of combustion products dissociations with temperature on specific heat of the gas mixture. e adiabatic flame temperature or combustion enthalpy is not needed as an input, but they can be calculated by the model. e main purpose of the present study is to investigate the effects of steam injection on equilibrium products and thermodynamic properties of diesel fuel, soybean oil-based biodiesel (NBD), and waste cooking oil biodiesel (WCOB). For this purpose, the solving schema of the combustion model based on a chemical equilibrium was developed for diesel and biodiesel fuels.
e nonlinear system of equations is solved using Newton-Raphson and Gauss-Seidel methods. e diesel and biodiesel with chemical formulae C 14 [30] were used in this study to represent diesel fuel, soybean oil-based biodiesel (NBD), and waste cooking oil biodiesel (WCOBD), respectively.

Equilibrium Combustion
Products. e combustion products are supposed to consist of ten species which are all assumed as ideal gases and they are defined by dissociation considerations as follows [31]: where the unit of pressure p is atmospheres and K 1 to K 6 are the equilibrium constants of the reactions. Olikara and Borman [32] have curve-fitted the equilibrium constants K i to tabulated JANAF thermochemical tables for the temperatures between 600 K and 4000 K and its values are calculated by using where the equilibrium constant curve-fit coefficients A i , B i , C i , D i , and E i are listed in Table 1 and presented by Ferguson [31].

Equilibrium Combustion Model
2.2.1. Low-Temperature Products. At low temperatures (T < 1000 K) and for α/c ratios less than one, the overall chemical reaction, which describes the combustion (ϕ < 3) is given, as follows: For the lean and stoichiometric combustion, it is assumed that there would be enough oxygen to oxidize all CO and H 2 and that means CO and H 2 are negligible. It can be noticed that the equilibrium composition is independent from temperature and pressure. It only depends on equivalence ratio ϕ. e product composition is determined using atom balance equations. Products of wet combustion for the low temperature are given in Table 2. For the rich case, it is assumed that there is insufficient oxygen to oxidize all CO and H 2 , which means all the oxygen is consumed.
When writing atom balances, five unknowns and four equations are found. One more equation (10) is used and it depends on the equilibrium constant for the water-gas reaction given by Ferguson [31] for the range of temperatures between 400 K and 3200 K: where t � T/1000. e equilibrium constant at constant pressure K of the water-gas reaction is expressed as follows:

High-Temperature Products.
At higher temperatures (T ≥1000 K) and for α/c ratios less than one, the overall chemical reaction, which describes the combustion (ϕ < 3), is given as follows: where ] i denotes the number of moles for each product, and α, β, c, and δ represent the atom numbers of carbon, hydrogen, oxygen, and nitrogen in the used fuel, respectively. For diesel fuel, c and δ are zeroes. When the product mole fraction composition is known at a given temperature, equivalence ratio, and pressure, the thermodynamic properties of interest such as enthalpy, entropy, specific volume, and internal energy can be computed. e atom balance for various elements in equation (11), the constraint that the mole fraction of all the products adds up to one, the unknown total product moles N, and the six dissociation equations (1)-(6) provided by the criteria of equilibrium among combustion products yield 11 equations for 11 unknowns, namely, unknown mole fractions y i and unknown total product moles N. After writing the mole fractions of the other combustion species with respect to the mole fractions of four independent variables y 3 , y 4 , y 5 , and y 6 , the following nonlinear equations are obtained: f 1 � C 6 y 1/2 4 y 5 + C 5 y 1/2 4 y 6 + y 3 + y 4 + y 5 + y 6 Journal of Combustion 3 e equivalence ratio ϕ and the molar fuel/air ratio ε are expressed as follows: By letting Y � (y 3 , y 4 , y 5 , y 6 ) T be the vector of the independent variables, δY � (δy 3 , δy 4 , δy 5 , δy 6 ) T the solution vector of the linear system, and F the vector containing the functions f 3 , f 4 , f 5 and f 6 , the system of nonlinear equations can be written in a single expression using vectors: where Y (0) is a given rough initial guess for the solution. In the neighbourhoods of Y (0) , the functions f i (Y) can be expanded in Taylor series and truncated after the first derivative. We obtain a set of linear equations for the vector δY (0) that move each value f i (Y (0) ) closer to zero simultaneously: e Jacobian matrix I is expressed as e set of linear equations equation (29) is solved for δY(0) using Gauss-Seidel iterative method.
e new approximated solution is calculated as If Y (1) does not approximate the solution to the given tolerance, successive approximations of the solution are obtained as follows: e procedure is repeated until δY (k) reaches a specified tolerance which leads to the values for Y: e other dependent unknowns are expressed after determining the mole fractions y 3 , y 4 , y 5 , and y 6 as follows: e same procedure is used to solve equation (39). e results are used in computing the specific heat of the gas mixture in equation (46). [33] proposed the expressions of molar specific heat at constant pressure c p,i enthalpy h i and entropy s 0 i values of each species that were curve-fitted to the tabulated JANAF thermochemical tables [34].

Gordon and McBride
At constant pressure, enthalpy of the gas mixture h changes due to the dissociations because the mole fractions of the species change with temperature: where M T � zM/zT � 10 i�1 M i zy i /zT and c p � (zh/zT) p .

Constant-Pressure Adiabatic Flame
Temperature. e constant-pressure adiabatic flame temperature (T ad ) is calculated iteratively using (47). An initial temperature is required to determine the total enthalpy of reactants h u : where h is the enthalpy of combustion products obtained by (44) and c p is the specific heat of the combustion products obtained by (46). For each iteration i, h and c p are reevaluated until an acceptable prescribed tolerance is reached.   Table 3.
Standard specifications for biodiesel and diesel fuels are shown in Table 4 according to ASTM D6751 and EN 14214.

Validation of the Model.
e validation of the model is done by comparing the model results with the ones of software CEA of NASA [28] and software GASEQ [27], which use element potential method and minimization of Gibbs free energy approach, respectively. e simulations of methane with steam injection are carried out. e mole fraction of chemical equilibrium products and thermodynamic properties obtained with the model compared with the ones of software CEA of NASA and GASEQ at ϕ � 0.6 with steam injection 10% are mentioned in Table 5 and at ϕ � 1.2 with steam injection 10% are listed in Table 6.

Mole Fraction of Combustion Products.
Adiabatic combustion simulation with steam has been carried out for the biodiesel and the diesel fuels in order to investigate the effects of steam injection on the equilibrium combustion products and thermodynamic properties. Before the combustion, the temperature of the air and the fuel is assumed to be equal to 300 K and the pressure of the air and the fuel mixture is equal to the combustion chamber pressure. e pressure inside the combustion chamber is 30 atm, which is supposed to be the pressure of injection steam. e temperature of injected steam is 300°C. e temperature of the unburned mixture is found by assuming a thermal equilibrium amongst the reactants. Initial temperature is obtained from the thermal equilibrium of fuel-air and steam mixture. e results have been comparatively presented for lean and rich combustion with increasing steam injection from 0% to 10%. Figures 1(a) and 1(b) show the CO 2 equilibrium mole fractions with steam injection ratios and they decrease remarkably with increasing steam injection ratios. NBD gives the highest results, while WCOBD presents the lowest results. Kayadelen [26] obtained the same behaviour in his study. Journal of Combustion H 2 O equilibrium mole fraction increases with increasing steam injection ratios. e maximum H 2 O equilibrium mole fraction is obtained with WCOBD and the minimum H 2 O equilibrium mole fraction is observed with diesel fuel. e reason is the WCOBD has the lowest α/β ratio and diesel fuel has the highest α/β ratio. e smaller the α/β ratio is, the larger the H 2 O equilibrium mole fraction is. Figures 3(a) and 3(b) illustrate the N 2 equilibrium mole fractions with steam injection ratios. It is clear that the N 2 equilibrium mole fraction decreases with increasing steam injection ratios. e maximum N 2 equilibrium mole fraction is obtained with diesel fuel and the minimum N 2 equilibrium mole fraction is observed with WCOBD. e reason is the WCOBD has the lowest α/β ratio and diesel fuel has the highest α/β ratio. Figures 4(a) and 4(b) shows the O 2 equilibrium mole fractions with steam injection ratios. It is clear that the O 2 equilibrium mole fraction decreases with increasing steam injection ratios in the case of lean combustion. e maximum O 2 equilibrium mole fraction is obtained with diesel fuel and the minimum O 2 equilibrium mole fraction is observed with WCOBD. e O 2 equilibrium mole fraction is much lower in rich combustion due to lower oxygen concentration compared to lean combustion. e maximum O 2 equilibrium mole fraction occurs with WCOBD and the minimum O 2 equilibrium mole fractions occurs with diesel e maximum CO equilibrium mole fraction is observed with diesel fuel and the minimum CO equilibrium mole fraction is observed with WCOBD in the case of rich combustion. e maximum CO equilibrium mole fraction is obtained with NBD and the minimum CO equilibrium mole fraction is observed with WCOBD in the case of lean combustion. Figures 9(a) and 9(b) demonstrate the OH equilibrium mole fractions with steam injection ratios. e OH equilibrium mole fractions increase slightly with increasing steam injection ratios in rich and lean combustion. WCOBD releases the highest OH equilibrium mole fractions while diesel fuel releases the lowest OH equilibrium mole fractions in both rich and lean combustions. Figures 10(a) and 10  fractions, while WCOBD releases the lowest NO equilibrium mole fractions in lean combustions.

ermodynamic Properties of Combustion
Products. e specific heat and the enthalpy of the mixture of the gases increase with the steam injection ratios due to the specific heat of superheated steam which is higher than the one of air at that temperature condition. Kayadelen [26] obtained the same behaviour in his study. Figures 11(a) and 11(b) show the variation of specific heats of combustion products with respect to steam injection ratios. Higher specific heats are obtained in the rich combustions compared to the lean combustions. e highest specific heats are seen with WCOBD and the lowest specific heats are obtained with diesel fuel. In both combustions, specific heats increase with increasing steam injection ratios because the specific heat of the steam is much more than the ones of the combustion products at the same temperature except the specific heat of CO 2 . Figures 12(a) and 12(b) show the variation of enthalpy of combustion products with respect to steam injection ratios. Higher enthalpies of combustion products are obtained in the lean combustions compared to the rich combustions. e highest enthalpies of combustion products are seen with diesel fuel and the lowest enthalpies of combustion products are obtained with WCOBD. In both combustions, enthalpy of combustion products decreases with increasing steam injection ratios due to the enthalpy of the steam which is much less than the ones of the combustion products at the same temperature. Figures 13(a) and 13(b) show the variation of entropy of combustion products with respect to steam injection ratios. Higher entropies of combustion products are obtained in the rich combustions compared to the lean combustions. e highest entropies of combustion products are seen with WCOBD and the lowest entropies of combustion products are obtained with diesel fuel. In both combustions, entropy of combustion products increases with increasing steam injection ratios.

Conclusion
e equilibrium combustion model is used to provide mole fractions and thermodynamic properties of combustion products in chemical equilibrium. Equilibrium mole fractions and the adiabatic flame temperature are necessary for estimating thermodynamic properties of exhaust gases and for providing key data to obtain nonequilibrium mole fractions. e precise calculation of thermodynamic properties is necessary for accurate performance estimations of internal combustion engines. e influences of steam injection on equilibrium combustion products and thermodynamic properties of diesel fuel and biodiesels have been modelled. e equilibrium mole fractions and thermodynamic properties of combustion products showed good agreement with the results obtained from CEA of NASA and GASEQ using methane. e highest CO 2 equilibrium mole fractions are seen with NBD, and the lowest ones are formed with WCOBD. e reduction rate of NO is higher for biodiesel fuels as compared with the one of diesel fuel in lean combustion conditions. us, the steam injection ratios can be used for biodiesel fuels in order to lower NO equilibrium combustion products in the lean combustion conditions. e model can be a recourse tool for researchers studying fuels, surrogates, emissions, and internal combustion modelling due to its accuracy and convenience. e equilibrium mole fractions are used in combustion engineering, for example, in chemical kinetics to look for a reference point and in parametric emission monitoring systems to estimate the emissions of power systems.  Figure 13: Variation of gas mixture entropy with steam injection ratios.