# Determination of 12 Combustion Products, Flame Temperature and Laminar Burning Velocity of Saudi LPG Using Numerical Methods Coded in a MATLAB Application

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) mixtures at different values of equivalence ratio and diluent concentration using two experimental methods: Bunsen burner and cylindrical tube [6]. In the same year, Domnina Razus, Venera Brinzea, Maria Mitu and Dumitru Oancea determined the laminar flame speeds of LPG–air and LPG–air–exhaust mixtures from pressure vs. time graphs obtained from a spherical container with central ignition, making use of a correlation based on the cubic law of the pressure increase during the initial phase of the explosion at different fuel/oxygen ratios and in different environmental conditions [7]. Later, in 2016, Ahmed Yasiry and Haroun Shahad carried out an experimental study of the laminar flame speed of Iraqi LPG using a constant volume chamber with central ignition at different initial pressures (0.1–0.3 MPa) and an initial temperature of 308 K. Likewise, a range of equivalence ratios from 0.8 to 1.3 were used [8]. Recently, in the year 2022, Bader Alfarraj, Ahmed Al-Harbi, Saud A. Binjuwair and Abdullah Alkhedhair carried out the characterization of the Saudi LPG using a Bunsen burner and a modified Bunsen burner, which allowed them to work in a range of equivalence ratios of 0.68 to 1.3 [9].

## 2. Materials and Methods

#### 2.1. Materials and Procedure

#### 2.2. Numerical Methodology for the Determination of Combustion Products and Flame Temperature

_{n}+ H

_{m}+ O

_{l}+ N

_{k}, the equivalence ratio Φ, X

_{1}→X

_{12}as the mole fractions of the products and x

_{13}as the number of moles from fuel that give 1 mol of products.

_{13}[C

_{n}+ H

_{m}+ O

_{l}+ N

_{k}+ ((n + 0.25 ∗ m − 0.5 ∗ l)/Φ) (O

_{2}+ 3.7274N

_{2}+ 0.0444Ar)] →

X

_{1}H + X

_{2}O + X

_{3}N + X

_{4}H

_{2}+ X

_{5}OH + X

_{6}CO + X

_{7}NO + X

_{8}O

_{2}+ X

_{9}H

_{2}O + X

_{10}CO

_{2}+ X

_{11}N

_{2}+ X

_{12}Ar

_{13}[nC + mH + rO

_{2}+ r′N

_{2}+ r″Ar],

_{o},

_{o},

_{o},

_{o}= (n + 0.25 ∗ m − 0.5 ∗ l)/Φ.

_{6}+ X

_{10}= n ∗ X

_{13},

_{1}+ 2X

_{4}+ X

_{5}+ 2X

_{9}= m ∗ X

_{13},

_{2}+ X

_{5}+ X

_{6}+ X

_{7}+ 2X

_{8}+ X

_{9}+ 2X

_{10}= 2r ∗ X

_{13},

_{3}+ X

_{7}+ 2X

_{11}= 2r’ ∗ X

_{13,}

_{12}= r’’ ∗ X

_{13},

_{1}+ X

_{2}+ X

_{3}+ X

_{4}+ X

_{5}+ X

_{6}+ X

_{7}+ X

_{8}+ X

_{9}+ X

_{10}+ X

_{11}+ X

_{12}= 1.

_{2}↔ H,

_{2}↔ O,

_{2}↔ N,

_{2}+ ½ O

_{2}↔ OH,

_{2}+ ½ N

_{2}↔ NO,

_{2}+ ½ O

_{2}↔ H

_{2}O,

_{2}↔ CO

_{2},

_{1}= X

_{1}∗ p

^{1/2}/X

_{4}

^{1/2},

_{2}= X

_{2}∗ p

^{1/2}/X

_{8}

^{1/2},

_{3}= X

_{3}∗ p

^{1/2}/X

_{11}

^{1/2},

_{5}= X

_{5}/(X

_{4}

^{1/2}∗ X

_{8}

^{1/2}),

_{7}= X

_{7}/(X

_{8}

^{1/2}∗ X

_{11}

^{1/2}),

_{9}= X

_{9}/(X

_{4}∗ X

_{8}

^{1/2}∗ p

^{1/2}),

_{10}= X

_{10}/(X

_{6}∗ X

_{8}

^{1/2}∗ p

^{1/2}).

_{n}) can be set for each combustion product, which will remain for every equation with X

_{4}, X

_{6}, X

_{8}and X

_{11}pressure as the only variables. In this way,

_{1}= C

_{1}∗ X

_{4}

^{1/2}, where C

_{1}= K

_{1}/p

^{1/2},

_{2}= C

_{2}∗ X

_{8}

^{1/2}, where C

_{2}= K

_{2}/p

^{1/2},

_{3}= C

_{2}∗ X

_{8}

^{1/2}, where C

_{3}= K

_{3}/p

^{1/2},

_{5}= C

_{5}∗ X

_{4}∗ X

_{8}

^{1/2}, where C

_{5}= K

_{5},

_{7}= C

_{7}∗ X

_{8}

^{1/2}∗ X

_{11}

^{1/2}, where C

_{7}= K

_{7},

_{9}= C

_{9}∗ X

_{4}∗ X

_{8}

^{1/2}, where C

_{9}= K

_{9}∗ p

^{1/2},

_{10}= C

_{10}∗ X

_{6}∗ X

_{8}

^{1/2}, where C

_{10}= K

_{10}∗ p

^{1/2},

_{12}= r″X

_{13}= r″(X

_{6}+ X

_{10})/n,

_{12}and X

_{13}from (7)–(12) and form

_{1}+ 2X

_{4}+ X

_{5}+ 2X

_{9}– m ∗ (X

_{6}+ X

_{10})/n = 0,

_{2}+ X

_{5}+ X

_{6}+ X

_{7}+ X

_{9}+ 2X

_{10}− 2r ∗ (X

_{6}+ X

_{10})/n = 0,

_{3}+ X

_{7}+ 2X

_{11}− 2r′/n (X

_{6}+ X

_{10}) = 0,

_{1}+ X

_{2}+ X

_{3}+ X

_{4}+ X

_{5}+ X

_{6}+ X

_{7}+ X

_{8}+ X

_{9}+ X

_{10}+ X

_{11}+ r″(X

_{6}+ X

_{10})/n − 1 = 0.

_{4}, X

_{6}, X

_{8}and X

_{11}). The equation system is a non-linear system with 4 variables whose general representation is

_{j}(X

_{4}, X

_{6}, X

_{8}, X

_{11}) = 0, j = 1, 2, 3, 4.

_{4}

^{(1)}, X

_{6}

^{(1)}, X

_{8}

^{(1)}, X

_{11}

^{(1)}],

_{4}*, X

_{6}*, X

_{8}*, X

_{11}*],

_{i}= X

_{i}* − X

_{i}

^{(1)}, i = 4, 6, 8, 11.

_{j}+ (∂f

_{j}/∂X

_{4}) ∆X

_{4}+ (∂f

_{j}/∂X

_{6}) ∆X

_{6}+ (∂f

_{j}/∂X

_{8}) ∆X

_{8}+ (∂f

_{j}/∂X

_{11}) ∆X

_{11}≅ 0, j = 1, 2, 3, 4,

_{4}, ∆X

_{6}, ∆X

_{8}, ∆X

_{11}that will be useful to bring the known vector closer to the solution vector by applying

_{i}

^{(2)}= X

_{i}

^{(1)}+ ∆X

_{i}, i = 4, 6, 8, 11.

_{i}

^{(2)}is the improved vector which is entered into (43) in order to obtain another improvement. This process is repeated the necessary times until the values of ∆X

_{4}, ∆X

_{6}, ∆X

_{8}, ∆X

_{11}are less than or equal to 0.0001, which is the maximum error margin considered for each molar fraction.

_{o}, F

_{o}) − h

_{r}(T

_{o}, p

_{o}, F

_{o}) = 0.

_{n + 1}= T

_{n}− (h(T

_{n}, p

_{o}, F

_{o}) − h

_{r})/(∂h/∂T)

_{n}.

_{n}is the first assumed temperature (preferably greater than the final temperature), h

_{r}is the reactant enthalpy at initial conditions of temperature (T

_{o}), pressure (p

_{o}) and equivalence ratio (F

_{o}), h(T

_{n}, p

_{o}, F

_{o}) is obtained once the combustion products are calculated at the first assumed temperature (T

_{n}) as

_{n}, p

_{o}, F

_{o}) = ∑X

_{i}h

_{i}/M,

_{i}dh

_{i}/dT + h

_{i}dX

_{i}/dT) − ∂M/∂T h(T

_{n}, p

_{o}, F

_{o})],

_{i}/dT is the specific heat at a constant pressure of each element, so

_{i}/dT = Cp

_{i,}

_{i}/dT is calculated using (27)–(33) and ∂M/∂T is the molar mass of the mixture with respect to the temperature, that is,

_{i}/dT (M

_{i}).

_{n}, p

_{o}, F

_{o}) − h

_{r})/(∂h/∂T)

_{n}≤ 1

#### 2.3. Determination of the Laminar Burning Velocity

_{L}= (e

^{−Ea/RuT})

^{1/2}

_{u}is the universal gas constant (1.987 cal/mol·K) and T is the flame temperature calculated using the method. The value for Ea for every calculation is taken from the average of two values. The first one is set according to Kenneth Kuo, who said that for most hydrocarbon reactions the energy of activation is around 120 kJ/mol [2]. The second one is from Markatou, who studied methane–air oxidation and determined an activation energy of approximately 130 kJ/mol [14], so the average is 125 kJ/mol or 29,675.7 cal/mol.

#### 2.4. Development of the MATLAB Application

#### 2.4.1. First Part: New_Code.m

_{2}). The first part of the code corresponds to the archive called New_code.m, which can be found in Code S1, having defined as inputs the equivalence ratio, percentage of diluent if applicable, name of diluent and name of fuel. The indices of each element of the selected fuel (C, H, O, N) are stored in an Excel archive called Reactants_Enthalpy.xlsx and those of the diluents in Reactants_Diluents.xlsx, and they can be found in Archives S1 and S2. In order to improve the application range of the MATLAB application, it is possible to add more fuels and diluents to Archives S1 and S2.

_{r}) is carried out, for which the initial temperature and pressure of work will always be 298 K and 1 atm, respectively. After the first steps are carried out, New_code.m enters into a loop in order to obtain the combustion products by calling the function Fractions_Derivatives.m and, after it, the first assumed temperature is adjusted with the value calculated in (51) or “DELTA” which is the name used in the code.

#### 2.4.2. Second Part: Fractions_Derivatives.m

_{4}, X

_{6}, X

_{8}and X

_{11}using the 7 chemical reactions as a starting point (Equations (13)–(19)). Additional to this, Equations (35)–(38) are set in order to obtain the equation system (39) in which the Taylor series is applied to linearize the system and the Gaussian elimination method is applied to solve the linearized system.

_{n},

#### 2.4.3. Third Part: Developing the MATLAB Application in the MATLAB App Designer Interface

_{2}) vs. equivalence ratio for the LPG with 10% CO

_{2}obtained just by two resources (MATLAB code and San Diego mechanism). The equivalence ratio knob is also set at the stoichiometric value so the flame temperature and laminar burning velocity values are shown for that ratio value in their respective gauges (H and I).

#### 2.5. Composition of Fuel and Mixtures to Be Tested

_{3}H

_{8}) and 50% butane (C

_{4}H

_{10}) and is the same used by Bader Alfarraj et al. [9]. The tested mixtures are from 0.6 to 1.7, increasing by 0.1. As was mentioned previously, the initial conditions are 298 K for temperature and 1 atm of pressure.

#### 2.6. Simulation in Ansys Chemkin

## 3. Results and Discussion

#### 3.1. Combustion Products

_{1}–X

_{6}) and Table 3 (X

_{7}–X

_{12}).

_{8}O

_{2}, X

_{9}H

_{2}O, X

_{10}CO

_{2}and X

_{11}N

_{2}. This is an expected result and it is the first proof that the MATLAB application method agrees with the general combustion theory statements (lean mixture, excess of oxygen, greater percentage of oxygen in the products). As the equivalence ratio increases, X

_{8}O

_{2}decreases and X

_{10}CO

_{2}decreases while X

_{6}CO increases, which agrees with rich mixtures, in other words, there is not enough oxygen for the combustion process. Considering Equation (19), it is not possible to transform CO to CO

_{2}. Moreover, the results obtained by carrying out the simulation in Ansys Chemkin using the San Diego mechanism are presented in Table 4 (X

_{1}–X

_{6}) and Table 5 (X

_{7}–X

_{12}). It is important to mention that there were more combustion products in the results given by Ansys Chemkin such as propane and butane that did not manage to react and this can be seen principally at higher equivalence ratios (1.2–1.7). The results using RedSD mechanism are presented in Table 6 (X

_{1}–X6) and Table 7 (X

_{7}–X12).

_{1}to X

_{6}, while Figure 6a–f show the results from X

_{7}to X

_{12}. From Figure 5d,f it can be affirmed for all cases that only hydrogen (X

_{4}H

_{2}) and carbon monoxide (X

_{6}CO) had an increase as the equivalence ratio increased. This is mainly a consequence of the increase in the amount of fuel in the mixture and the lack of oxygen in it to finish transforming these variables into hydrogen hydroxide (X

_{9}H

_{2}O) and carbon dioxide (X

_{10}CO

_{2}), respectively, which is shown by the fall in the fractions corresponding to those products at a higher equivalence ratio. On the other hand, nitrogen (X

_{11}N

_{2}) and argon (X

_{12}AR) presented a decrease for all cases as the equivalence ratio increased because of the opposite effect that this change has on the elements that compound the oxidization, in this case, air.

_{8}O

_{2}), whose value, in cases of a higher ratio, tends to practically zero. Similarly, in the case of hydroxide (X

_{5}OH), there is a tendency to zero for its values at the highest equivalence ratio and this is due to the lack of molecular oxygen to complete the whole reaction (16). Regarding the similarity and difference in the results for all cases, in general, there exists a correlation between those determined by the MATLAB application and simulation in Ansys Chemkin using the San Diego mechanism and RedSD mechanism, specifically for X

_{4}H

_{2}, X

_{5}OH, X

_{6}CO, X

_{8}O

_{2}, X

_{9}H

_{2}O, X

_{10}CO

_{2}, X

_{11}N

_{2}, X

_{12}AR, whose values presented the same evolutionary curve between all the sources as the value of the equivalence ratio varied.

_{9}, X

_{10}, X

_{11}, X

_{12}were found, being 3.05%, 5.95%, 1.15%, 2.22%, respectively.

#### 3.2. Flame Temperature

#### 3.3. Laminar Burning Velocity

_{3}H

_{8}or C

_{4}H

_{10}, NO

_{X}, among others, that appeared in the Ansys Chemkin simulations) that cause the difference to increase, as can be seen in Figure 8. This does not happen for lower ratios. A better approximation for the calculation and another improvement for this application is to define an activation energy as a function of the equivalence ratio and temperature, taking as a reference the reactions considered in the MATLAB application and adding the ones involved directly with the tested fuel.

## 4. Conclusions

- For the laminar burning velocity results, the numerical method agrees with the experimental results for ratios (0.6–1.2) used by other authors and the simulation carried out in Ansys Chemkin, while, for the highest studied equivalence ratios (1.3–1.7) the laminar burning velocity results show a greater difference between all the resources.
- The numerical method used in the MATLAB application agrees with the simulation in Ansys Chemkin for the Saudi LPG combustion products, except for N and NO, for the whole range of equivalence ratios.
- The Saudi LPG maximum laminar burning velocity determined by the modified Bunsen burner method [9] was 35 ± 0.91 while that determined by the MATLAB application was 40.3 cm/s, having a difference of 5.35 ± 0.91 and an overestimate of 15.2% in favor of the MATLAB application.
- The Saudi LPG maximum laminar burning velocity determined by the MATLAB application was 40.3 cm/s, corresponding to a ratio of 1.1, with an underestimate of 2.3% with respect to the simulated values in Ansys Chemkin using the San Diego mechanism and an underestimate of 1.4% using the RedSD mechanism.
- The maximum adiabatic flame temperature of the Saudi LPG determined using the MATLAB application was 2326.2 K, corresponding to a ratio of 1.1, with an overestimate of 2.6% and 2.5% with respect to the simulated values in Ansys Chemkin using the San Diego and RedSD mechanisms, respectively.
- The MATLAB application, compared with previous experimental studies, presents the same behavioral results as those obtained by Miao et al. [16], B. Yang [15] and B.A. Alfarraj et al. (2022) [9] for lean mixture conditions. Meanwhile, for stoichiometric and fuel-rich conditions, it presents the same plot shape as that of B. Yang (2006) [15].
- The new code in the MATLAB application determined the experimental results more accurately, for equivalence ratios from 0.7 to 1.4, compared to Ansys Chemkin, taking B. Yang (2006) [15] as the experimental result reference.
- The MATLAB application has been developed for additional fuels such as methane, propane and natural gas and has the possibility of adding extra fuels, diluents and tools to improve the analysis of the results. It could be also applied to further studies using different kinds of mixtures.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Φ | is the equivalence ratio; |

n | is the carbon coefficient value of the fuel; |

m | is the hydrogen coefficient value of the fuel; |

l | is the oxygen coefficient value of the fuel; |

k | is the nitrogen coefficient value of the fuel; |

X_{1} | is the molar fraction of hydrogen (H) in the products; |

X_{2} | is the molar fraction of oxygen (O) in the products; |

X_{3} | is the molar fraction of nitrogen (N) in the products; |

X_{4} | is the molar fraction of hydrogen (H_{2}) in the products; |

X_{5} | is the molar fraction of hydroxide (OH) in the products; |

X_{6} | is the molar fraction of carbon monoxide (CO) in the products; |

X_{7} | is the molar fraction of nitric oxide (NO) in the products; |

X_{8} | is the molar fraction of oxygen (O_{2}) in the products; |

X_{9} | is the molar fraction of dihydrogen oxide (H_{2}O) in the products; |

X_{10} | is the molar fraction of carbon dioxide (CO_{2}) in the products; |

X_{11} | is the molar fraction of nitrogen (N_{2}) in the products; |

X_{12} | is the molar fraction of argon (Ar) in the products; |

X_{13} | is the number of moles from fuel that give 1 mol of product; |

K_{i} | is the partial pressure equilibrium constant of a chemical reaction; |

p | is the pressure; |

f_{j} | is the equation system with 4 variables (X_{4}, X_{6}, X_{8} and X_{11}) |

X_{i}* | is the molar fraction real solution value used in Taylor series; |

X_{i}^{(1)} | is the molar fraction approximate value to the real one used in Taylor series; |

∆X_{i} | is the difference between the molar fraction real value and the approximate one; |

∂f_{j}/∂X_{i} | is the equation system derivative with respect to molar fraction (X_{4}, X_{6}, X_{8} and X_{11}); |

X_{i}^{(2)} | is the improved molar fraction value after the first iteration; |

h_{r} | is the reactant enthalpy; |

h | is the product enthalpy; |

p_{o} | is the initial pressure; |

F_{o} | is the initial equivalence ratio; |

T_{o} | is the initial temperature; |

T | is the adiabatic flame temperature; |

T_{n} | is the first assumed flame temperature (n = 1) or a current temperature iteration (n > 1); |

T_{n + 1} | is the improved temperature after an iteration using the Newton–Raphson method; |

(∂h/∂T)_{n} | is the enthalpy derivative with respect to temperature at n iterations; |

M | is the molar mass of the mixture; |

dh_{i}/dT | is the specific heat at constant pressure of an element (i); |

Cp_{i} | is the specific heat at constant pressure of an element (i); |

dX_{i}/dT | is the partial derivative of a molar fraction with respect to temperature; |

∂M/∂T | is the molar mass of the mixture with respect to temperature; |

S_{L} | is the laminar burning velocity; |

Ea | is the activation energy; |

Ru | is the universal gas constant. |

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**Figure 2.**Identification of tools available in the application: (A) Fuel list; (B) Molar fraction list; (C) Diluent button list; (D) Percentage bar of diluent; (E) Results button list; (F) Plot button list; (G) Equivalence ratio knob; (H) Laminar burning velocity gauge; (I) Flame temperature gauge.

**Figure 3.**Results for the molar fraction of hydrogen (X

_{4}-H

_{2}) vs. equivalence ratio for the LPG with 10% CO

_{2}determined by MATLAB code (blue circles) and San Diego mechanism (green circles).

**Figure 5.**Results for molar fractions from X

_{1}–X

_{6}: (

**a**) Molar fraction versus equivalence ratio of X

_{1}H; (

**b**) molar fraction versus equivalence ratio of X

_{2}O; (

**c**) molar fraction versus equivalence ratio of X

_{3}N; (

**d**) molar fraction versus equivalence ratio of X

_{4}H

_{2}; (

**e**) molar fraction versus equivalence ratio of X

_{5}OH; (

**f**) molar fraction versus equivalence ratio of X

_{6}CO.

**Figure 6.**Results for molar fractions from X

_{7}–X

_{12}: (

**a**) Molar fraction versus equivalence ratio of X

_{7}NO; (

**b**) molar fraction versus equivalence ratio of X

_{8}O

_{2}; (

**c**) molar fraction versus equivalence ratio of X

_{9}H

_{2}O; (

**d**) molar fraction versus equivalence ratio of X

_{10}CO

_{2}; (

**e**) molar fraction versus equivalence ratio of X

_{11}N

_{2}; (

**f**) molar fraction versus equivalence ratio of X

_{12}AR.

Position in Figure 2 | Name of Tool | Description | Type of Selection |
---|---|---|---|

A | Fuel list | List of fuels available for calculus in the application | Unique |

B | Molar fraction list | List of molar fractions available for plotting results | Unique |

C | Diluent button list | List of diluents available to use in the calculus | Unique |

D | Percentage bar of diluent | Percentage of diluent by volume to be considered in fuel | Unique |

E | Results button list | Results from resources available to be shown in the plot | Multi |

F | Plot button list | Type of plot to be shown on the screen | Unique |

G | Equivalence ratio knob | Knob that shows the value of laminar burning velocity and flame temperature in their respective gauges | Unique |

H | Laminar burning velocity gauge | Laminar burning velocity value at the knob equivalence ratio value selected | NA |

I | Flame temperature gauge | Flame temperature value at the knob equivalence ratio value selected | NA |

Equivalence Ratio (Φ) | X_{1}H | X_{2}O | X_{3}N | X_{4}H_{2} | X_{5}OH | X_{6}CO |
---|---|---|---|---|---|---|

0.6 | 9.2644 × 10^{−7} | 2.3773 × 10^{−5} | 1.6175 × 10^{−11} | 1.2640 × 10^{−5} | 0.00041207 | 3.5819 × 10^{−5} |

0.7 | 1.0249 × 10^{−5} | 0.00010408 | 3.4726 × 10^{−10} | 8.5230 × 10^{−5} | 0.0011626 | 0.00028795 |

0.8 | 6.5024 × 10^{−5} | 0.00028288 | 3.4003 × 10^{−9} | 0.00039475 | 0.00240522 | 0.0015017 |

0.9 | 0.00025914 | 0.00048031 | 1.6695 × 10^{−8} | 0.00138214 | 0.00369457 | 0.00556398 |

1 | 0.00066624 | 0.00046349 | 4.0295 × 10^{−8} | 0.00393763 | 0.00401577 | 0.0154476 |

1.1 | 0.00108218 | 0.00021577 | 4.3271 × 10^{−8} | 0.00962653 | 0.00281794 | 0.0331991 |

1.2 | 0.00116468 | 5.8248 × 10^{−5} | 2.3838 × 10^{−8} | 0.0194133 | 0.00141014 | 0.0549746 |

1.3 | 0.00099712 | 1.3753 × 10^{−5} | 9.9015 × 10^{−9} | 0.0323431 | 0.00063771 | 0.075101 |

1.4 | 0.00075851 | 3.2136 × 10^{−6} | 3.6705 × 10^{−9} | 0.047353 | 0.00028167 | 0.0922573 |

1.5 | 0.00053636 | 7.5281 × 10^{−7} | 1.2757 × 10^{−9} | 0.0636388 | 0.00012302 | 0.106798 |

1.6 | 0.00035653 | 1.7192 × 10^{−7} | 4.1393 × 10^{−10} | 0.0806081 | 5.2459 × 10^{−5} | 0.119274 |

1.7 | 0.00022589 | 3.8207 × 10^{−8} | 1.2688 × 10^{−10} | 0.097815 | 2.1858 × 10^{−5} | 0.13018 |

Equivalence Ratio (Φ) | X_{7}NO | X_{8}O_{2} | X_{9}H_{2}O | X_{10}CO_{2} | X_{11}N_{2} | X_{12}AR |
---|---|---|---|---|---|---|

0.6 | 0.00232901 | 0.0786287 | 0.0935573 | 0.0729014 | 0.743231 | 0.00886708 |

0.7 | 0.00353978 | 0.0575011 | 0.107843 | 0.084112 | 0.73656 | 0.00879482 |

0.8 | 0.00436595 | 0.0373029 | 0.121284 | 0.094098 | 0.729583 | 0.00871664 |

0.9 | 0.00425856 | 0.0196666 | 0.133438 | 0.100834 | 0.721799 | 0.00862329 |

1 | 0.00300759 | 0.0071197 | 0.143566 | 0.101098 | 0.712176 | 0.0085012 |

1.1 | 0.0013496 | 0.00141652 | 0.150092 | 0.0925431 | 0.699319 | 0.00833818 |

1.2 | 0.00044049 | 0.00019234 | 0.151587 | 0.0790268 | 0.683587 | 0.00814537 |

1.3 | 0.00013844 | 2.6966 × 10^{−5} | 0.148982 | 0.0665658 | 0.667245 | 0.0079489 |

1.4 | 4.4765 × 10^{−5} | 4.1781 × 10^{−6} | 0.143582 | 0.056652 | 0.651305 | 0.00775848 |

1.5 | 1.4838 × 10^{−5} | 6.9691 × 10^{−7} | 0.136333 | 0.0489914 | 0.635987 | 0.00757583 |

1.6 | 4.9101 × 10^{−6} | 1.1887 × 10^{−7} | 0.127913 | 0.0430682 | 0.621321 | 0.00740107 |

1.7 | 1.6125 × 10^{−6} | 2.0403 × 10^{−8} | 0.118823 | 0.0384122 | 0.607287 | 0.00723388 |

Equivalence Ratio (Φ) | X_{1}H | X_{2}O | X_{3}N | X_{4}H_{2} | X_{5}OH | X_{6}CO |
---|---|---|---|---|---|---|

0.6 | 6.6093 × 10^{−7} | 1.8192 × 10^{−5} | 3.5006 × 10^{−12} | 1.0017 × 10^{−5} | 0.00039345 | 2.7661 × 10^{−5} |

0.7 | 8.3166 × 10^{−6} | 8.693 × 10^{−5} | 1.3135 × 10^{−10} | 7.4804 × 10^{−5} | 0.00117059 | 0.00024538 |

0.8 | 4.9654 × 10^{−5} | 0.00022725 | 1.4973 × 10^{−9} | 0.00033309 | 0.00236175 | 0.00123292 |

0.9 | 0.00019441 | 0.00038015 | 7.3197 × 10^{−9} | 0.00114976 | 0.00356367 | 0.00454945 |

1 | 0.00055523 | 0.00032513 | 1.6402 × 10^{−8} | 0.00388401 | 0.00365408 | 0.0149326 |

1.1 | 0.00085203 | 0.00010131 | 8.8505 × 10^{−9} | 0.0107692 | 0.00205185 | 0.0351553 |

1.2 | 0.00083450 | 2.1024 × 10^{−5} | 2.6195 × 10^{−9} | 0.0221748 | 0.00088483 | 0.058047 |

1.3 | 0.00064603 | 3.7060 × 10^{−6} | 5.9878 × 10^{−10} | 0.0380662 | 0.00034043 | 0.0792958 |

1.4 | 0.00047560 | 8.6550 × 10^{−7} | 1.3136 × 10^{−10} | 0.0536471 | 0.00014997 | 0.0948882 |

1.5 | 0.00031061 | 1.7192 × 10^{−7} | 1.7254 × 10^{−11} | 0.0717481 | 6.0068 × 10^{−5} | 0.109207 |

1.6 | 0.00020575 | 4.1360 × 10^{−8} | 1.9497 × 10^{−12} | 0.0882793 | 2.6349 × 10^{−5} | 0.120062 |

1.7 | 0.00013802 | 1.1794 × 10^{−8} | 2.8318 × 10^{−13} | 0.101292 | 1.2937 × 10^{−5} | 0.12784 |

Equivalence Ratio (Φ) | X_{7}NO | X_{8}O_{2} | X_{9}H_{2}O | X_{10}CO_{2} | X_{11}N_{2} | X_{12}AR |
---|---|---|---|---|---|---|

0.6 | 1.2659 × 10^{−6} | 0.0778787 | 0.0957267 | 0.0734329 | 0.0743441 | 0.00906312 |

0.7 | 1.0758 × 10^{−5} | 0.0564053 | 0.111239 | 0.0849199 | 0.73685 | 0.00898358 |

0.8 | 7.4972 × 10^{−5} | 0.0364389 | 0.124853 | 0.0951511 | 0.730366 | 0.00890481 |

0.9 | 0.00028322 | 0.0190562 | 0.136546 | 0.102239 | 0.723214 | 0.00881881 |

1 | 0.00036887 | 0.00517981 | 0.147765 | 0.102416 | 0.712228 | 0.00868567 |

1.1 | 8.0115 × 10^{−5} | 0.00060559 | 0.15336 | 0.0911168 | 0.697399 | 0.00850336 |

1.2 | 1.8270 × 10^{−5} | 6.1474 × 10^{−5} | 0.153406 | 0.076219 | 0.680035 | 0.0082915 |

1.3 | 3.9921 × 10^{−6} | 6.2188 × 10^{−6} | 0.149864 | 0.0628266 | 0.660878 | 0.00805869 |

1.4 | 7.1151 × 10^{−7} | 9.9641 × 10^{−7} | 0.143506 | 0.0540122 | 0.645431 | 0.00786988 |

1.5 | 8.0017 × 10^{−8} | 1.4057 × 10^{−7} | 0.135334 | 0.0466537 | 0.628933 | 0.00766906 |

1.6 | 2.5797 × 10^{−8} | 2.5968 × 10^{−8} | 0.127036 | 0.0415919 | 0.614249 | 0.00749027 |

1.7 | 1.1576 × 10^{−8} | 6.0938 × 10^{−9} | 0.119289 | 0.0384194 | 0.602665 | 0.00734881 |

Equivalence Ratio (Φ) | X_{1}H | X_{2}O | X_{3}N | X_{4}H_{2} | X_{5}OH | X_{6}CO |
---|---|---|---|---|---|---|

0.6 | 6.9492 × 10^{−7} | 1.8833 × 10^{−5} | 3.5006 × 10^{−12} | 1.0326 × 10^{−5} | 0.00039894 | 2.8759 × 10^{−5} |

0.7 | 8.4643 × 10^{−6} | 8.8159 × 10^{−5} | 1.3135 × 10^{−10} | 7.5337 × 10^{−5} | 0.00117376 | 0.00024771 |

0.8 | 5.5236 × 10^{−5} | 0.00024429 | 1.4973 × 10^{−9} | 0.00035698 | 0.00244458 | 0.00132638 |

0.9 | 0.00022744 | 0.00041572 | 7.3197 × 10^{−9} | 0.0012917 | 0.00374339 | 0.00510691 |

1 | 0.00059085 | 0.00034823 | 1.6402 × 10^{−8} | 0.00399172 | 0.00377842 | 0.015321 |

1.1 | 0.00088504 | 0.00010743 | 8.8505 × 10^{−9} | 0.0108747 | 0.00211538 | 0.0354616 |

1.2 | 0.00084480 | 2.0644 × 10^{−5} | 2.6195 × 10^{−9} | 0.0226464 | 0.00087630 | 0.0588178 |

1.3 | 0.00066097 | 3.9565 × 10^{−6} | 5.9878 × 10^{−10} | 0.0377389 | 0.00035226 | 0.0789434 |

1.4 | 0.00047605 | 8.4477 × 10^{−7} | 1.3136 × 10^{−10} | 0.0542954 | 0.00014795 | 0.0952242 |

1.5 | 0.00032336 | 1.9393 × 10^{−7} | 1.7254 × 10^{−11} | 0.0706793 | 6.4263 × 10^{−5} | 0.108435 |

1.6 | 0.00021240 | 4.3565 × 10^{−8} | 1.9497 × 10^{−12} | 0.0887154 | 2.7351 × 10^{−5} | 0.120091 |

1.7 | 0.00014340 | 1.2649 × 10^{−8} | 2.8318 × 10^{−13} | 0.101579 | 1.3416 × 10^{−5} | 0.127924 |

Equivalence Ratio (Φ) | X_{7}NO | X_{8}O_{2} | X_{9}H_{2}O | X_{10}CO_{2} | X_{11}N_{2} | X_{12}AR |
---|---|---|---|---|---|---|

0.6 | 1.2659 × 10^{−6} | 0.0778787 | 0.0957267 | 0.0734329 | 0.0743441 | 0.00906312 |

0.7 | 1.0758 × 10^{−5} | 0.0564053 | 0.111239 | 0.0849199 | 0.73685 | 0.00898358 |

0.8 | 7.4972 × 10^{−5} | 0.0364389 | 0.124853 | 0.0951511 | 0.730366 | 0.00890481 |

0.9 | 0.00028322 | 0.0190562 | 0.136546 | 0.102239 | 0.723214 | 0.00881881 |

1 | 0.00036887 | 0.00517981 | 0.147765 | 0.102416 | 0.712228 | 0.00868567 |

1.1 | 8.0115 × 10^{−5} | 0.00060559 | 0.15336 | 0.0911168 | 0.697399 | 0.00850336 |

1.2 | 1.8270 × 10^{−5} | 6.1474 × 10^{−5} | 0.153406 | 0.076219 | 0.680035 | 0.0082915 |

1.3 | 3.9921 × 10^{−6} | 6.2188 × 10^{−6} | 0.149864 | 0.0628266 | 0.660878 | 0.00805869 |

1.4 | 7.1151 × 10^{−7} | 9.9641 × 10^{−7} | 0.143506 | 0.0540122 | 0.645431 | 0.00786988 |

1.5 | 8.0017 × 10^{−8} | 1.4057 × 10^{−7} | 0.135334 | 0.0466537 | 0.628933 | 0.00766906 |

1.6 | 2.5797 × 10^{−8} | 2.5968 × 10^{−8} | 0.127036 | 0.0415919 | 0.614249 | 0.00749027 |

1.7 | 1.1576 × 10^{−8} | 6.0938 × 10^{−9} | 0.119289 | 0.0384194 | 0.602665 | 0.00734881 |

Equivalence Ratio (Φ) | MATLAB Application T (K) | San Diego Mechanism T (K) | RedSD Mechanism T (K) |
---|---|---|---|

0.6 | 1763.1 | 1723.7 | 1721.8 |

0.7 | 1945.7 | 1914.3 | 1911.5 |

0.8 | 2108.1 | 2076.8 | 2075.6 |

0.9 | 2238.6 | 2202.8 | 2206.0 |

1 | 2318.5 | 2283.9 | 2283.3 |

1.1 | 2326.2 | 2267.3 | 2268.9 |

1.2 | 2272.7 | 2198.0 | 2196.9 |

1.3 | 2197.8 | 2109.6 | 2111.1 |

1.4 | 2118.8 | 2033.4 | 2031.4 |

1.5 | 2040.1 | 1956.1 | 1961.1 |

1.6 | 1963.1 | 1889.2 | 1889.0 |

1.7 | 1888.0 | 1831.0 | 1831.7 |

**Table 9.**Flame temperature differences between the MATLAB application and simulations in Ansys Chemkin.

Equivalence Ratio (Φ) | MATLAB Application—San Diego Mechanism | MATLAB Application—RedSD Mechanism | ||
---|---|---|---|---|

∆T (K) | % | ∆T (K) | % | |

0.6 | 39.4 | 2.2 | 41.2 | 2.4 |

0.7 | 31.3 | 1.6 | 34.1 | 1.7 |

0.8 | 31.2 | 1.5 | 32.4 | 1.5 |

0.9 | 35.8 | 1.6 | 32.6 | 1.4 |

1 | 34.5 | 1.5 | 35.1 | 1.5 |

1.1 | 58.5 | 2.6 | 57.3 | 2.5 |

1.2 | 74.7 | 3.4 | 75.8 | 3.4 |

1.3 | 88.1 | 4.1 | 86.7 | 4.1 |

1.4 | 85.4 | 4.2 | 87.4 | 4.3 |

1.5 | 84.0 | 4.3 | 79.0 | 4.0 |

1.6 | 73.8 | 3.9 | 74.0 | 3.9 |

1.7 | 57.0 | 3.1 | 56.3 | 3.0 |

Equivalence Ratio (Φ) | MATLAB Application S_{L} (cm/s) | San Diego Mechanism S_{L} (cm/s) | RedSD Mechanism S_{L} (cm/s) |
---|---|---|---|

0.6 | 14.4 | 16.7 | 17.0 |

0.7 | 21.5 | 26.3 | 26.4 |

0.8 | 28.9 | 33.8 | 33.9 |

0.9 | 35.5 | 38.6 | 39.1 |

1 | 39.9 | 41.7 | 41.6 |

1.1 | 40.3 | 41.3 | 40.9 |

1.2 | 37.4 | 37.5 | 36.4 |

1.3 | 33.4 | 29.0 | 27.3 |

1.4 | 29.4 | 19.5 | 17.1 |

1.5 | 25.7 | 12.9 | 12.2 |

1.6 | 22.2 | 9.9 | 9.5 |

1.7 | 19.1 | 8.0 | 7.7 |

**Table 11.**This is a table. Tables should be placed in the main text near to the first time they are cited.

Equivalence Ratio (Φ) | MATLAB Application—San Diego Mechanism | MATLAB Application—RedSD Mechanism | ||
---|---|---|---|---|

∆S_{L} (cm/s) | % | ∆S_{L} (cm/s) | % | |

0.6 | −2.2 | −13.3 | −2.5 | −15.1 |

0.7 | −4.7 | −18.1 | −4.9 | −18.6 |

0.8 | −4.8 | −14.4 | −5.0 | −14.8 |

0.9 | −3.0 | −7.9 | −3.5 | −9.0 |

1 | −1.8 | −4.4 | −1.7 | −4.0 |

1.1 | −0.9 | −2.3 | −0.5 | −1.4 |

1.2 | −0.1 | −0.2 | 0.9 | 2.6 |

1.3 | 4.3 | 15.0 | 6.0 | 22.1 |

1.4 | 9.9 | 50.7 | 12.3 | 72.3 |

1.5 | 12.8 | 99.0 | 13.5 | 110.6 |

1.6 | 12.3 | 123.5 | 12.7 | 134.6 |

1.7 | 11.1 | 137.7 | 11.3 | 145.9 |

Work | Type of Study | Pressure (atm) | Initial Temperature (K) | LPG Composition | |||
---|---|---|---|---|---|---|---|

Propane C _{3}H_{8} | Butane C_{4}H_{10} | Ethane C_{2}H_{6} | Pentane C_{5}H_{12} | ||||

MATLAB Application—Current Work | Numerical methodology in MATLAB | 1 | 298.15 | 50% | 50% | 0% | 0% |

San Diego Mechanism—Current Work | Numerical Simulation in Ansys Chemkin | 1 | 298.15 | 50% | 50% | 0% | 0% |

RedSD Mechanism—Current Work | Numerical Simulation in Ansys Chemkin | 1 | 298.15 | 50% | 50% | 0% | 0% |

B.A. Alfarraj et al. [9] | Experimental—Modified Bunsen Burner Method | 1 | 298.15 | 50% | 50% | 0% | 0% |

B. Yang [15] | Experimental—Constant Volume Bomb Method | 1 | 298.15 | 50% | 50% | 0% | 0% |

Huzayyin et al. [5] | Experimental—Constant Volume Chamber Method | 1 | 294 ± 3 | 26.41% | 73.54% | 0.04% | 0% |

Ahmed Sh. Yasiry et al. [8] | Experimental—Constant Volume Chamber Method | 1 | 308 | 36.3% | 62.3% | 0.9% | 0.5% |

Miao et al. [16] | Experimental—Constant Volume Chamber Method | 1 | 298.15 | 30% | 70% | 0% | 0% |

Chakraborty et al. [17] | Experimental—Flat Flame Burner Method | 1 | 298 | 30.1% | 67.7% | 1.4% | 0% |

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## Share and Cite

**MDPI and ACS Style**

Cisneros, R.F.; Rojas, F.J.
Determination of 12 Combustion Products, Flame Temperature and Laminar Burning Velocity of Saudi LPG Using Numerical Methods Coded in a MATLAB Application. *Energies* **2023**, *16*, 4688.
https://doi.org/10.3390/en16124688

**AMA Style**

Cisneros RF, Rojas FJ.
Determination of 12 Combustion Products, Flame Temperature and Laminar Burning Velocity of Saudi LPG Using Numerical Methods Coded in a MATLAB Application. *Energies*. 2023; 16(12):4688.
https://doi.org/10.3390/en16124688

**Chicago/Turabian Style**

Cisneros, Roberto Franco, and Freddy Jesús Rojas.
2023. "Determination of 12 Combustion Products, Flame Temperature and Laminar Burning Velocity of Saudi LPG Using Numerical Methods Coded in a MATLAB Application" *Energies* 16, no. 12: 4688.
https://doi.org/10.3390/en16124688