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*Energies*
**2017**,
*10*(8),
1200;
doi:10.3390/en10081200

Article

Combustion and Heat Release Characteristics of Biogas under Hydrogen- and Oxygen-Enriched Condition

^{1}

Department of Chemical Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan

^{2}

Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, China

^{3}

Faculty of Mechanical Engineering, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan

^{*}

Authors to whom correspondence should be addressed.

Received: 10 May 2017 / Accepted: 20 July 2017 / Published: 13 August 2017

## Abstract

**:**

Combustion and heat release characteristics of biogas non-premixed flames under various hydrogen-enriched and oxygen-enriched conditions were investigated through chemical kinetics simulation using detailed chemical mechanisms. The heat release rates, chemical reaction rates, and molar fraction of all species of biogas at various methane contents (35.3–58.7%, mass fraction), hydrogen addition ratios (10–50%), and oxygen enrichment levels (21–35%) were calculated considering the GRI 3.0 mechanism and P1 radiation model. Results showed that the net reaction rate of biogas increases with increasing hydrogen addition ratio and oxygen levels, leading to a higher net heat release rate of biogas flame. Meanwhile, flame length was shortened with the increase in hydrogen addition ratio and oxygen levels. The formation of free radicals, such as H, O, and OH, are enhanced with increase in hydrogen addition ratio and oxygen levels. Higher reaction rates of exothermic elementary reactions, especially those with OH free radical are increased, are beneficial to the improvement in combustion and heat release characteristics of biogas in practical applications.

Keywords:

biogas; heat release; methane content; hydrogen addition; oxygen enriched## 1. Introduction

With continuous depletion of fossil fuels and worsening pollution, research and development of renewable energy sources have attracted considerable interest [1,2,3,4,5,6,7]. Biogas can be produced using an anaerobic digester of biomass or biodegradable organic wastes. Compositions of biogas vary with the feedstock and the fermentation process [1,2,3]. The main compositions of biogas are methane (CH

_{4}) and carbon dioxide (CO_{2}), as well as a small amount of water (H_{2}O), nitrogen (N_{2}), and hydrogen (H_{2}) [3,4,5].As an advantageous energy source, biogas is widely considered as a suitable fuel for heating facilities, power generation, and vehicles [8,9,10,11,12,13,14,15]. However, biogas possesses a relatively lower heating value (about 3000–6000 kcal·m

^{−3}) and lower heat release rate than conventional fuels, which limits the application of biogas in combustion devices. Somehsaraei et al. [16] developed a steady state thermodynamic model for biogas application in 100 kW micro gas turbines. They found that mass flow and pressure ratio in the micro gas turbines are lower than those of the natural gas–fueled turbines. Furthermore, the total electrical efficiency decreases with decreasing CH_{4}content in biogas fuel, and the use of biogas negatively affects heat recovery. A three-dimensional computational fluid dynamic study on biogas flameless mode was developed by Hosseini et al. [17]. Although increasing preheated temperature positively affects the reduction of fuel consumption, a fuel with high calorific value is necessary to preheat the furnace prior to the application of biogas combustion in the combustion furnace. The flameless combustion temperature of a biogas furnace is lower than traditional combustion throughout a combustion chamber. Several experimental and numerical studies have explored the fuel characteristics of biogas. In such studies, high-quality fuel such as H_{2}[18, 19, 20, 21, 22] is blended with biogas to improve the relatively poor combustion characteristics of biogas. Zhen et al. [18] experimentally investigated the effect of H_{2}addition on the characteristics of a biogas diffusion flame. They found that H_{2}addition significantly improved the stability of the biogas flame. The flame temperature increased and visible flame length reduced with increasing H_{2}addition ratios. Wei et al. [19] numerically investigated the effects of equivalence ratio, H_{2}, and CO_{2}on the heat release characteristics of the premixed laminar biogas-hydrogen flames. The results showed that OH + H_{2}⇔ H + H_{2}O was major endothermic reaction for biogas-hydrogen premixed flames. The total heat release was enhanced evidently with H_{2}addition. Non-premixed are widely applied in the industrial process, while the heat release rate of biogas flame is low, which obstructs the application of biogas in practical application. Therefore, the improvement of heat release characteristics of biogas flame at various condition are necessary.The above results show that numerous studies have investigated the combustion characteristics of biogas premixed flame. Nevertheless, understanding the non-premixed combustion of a fuel in practical application is necessary. To utilize biogas in internal combustion engines, the unburnt composition CO

_{2}or N_{2}is expected to be excluded from biogas. Therefore, mechanical biological treatment is needed to upgrade raw biogas and increase CH_{4}content in biogas. The high cost of such treatment process is unfavorable to the application of biogas as a fuel. Therefore, the direct application of raw biogas is more economic for engines or heat supply. The current research proposes biogas combustion under hydrogen-enriched and oxygen-enriched conditions as potential methods to improve biogas combustion. The non-premixed flames of biogas under various hydrogen-enriched and oxygen-enriched conditions are studied, and the combustion and heat release characteristics of biogas non-premixed flames are numerically investigated. A non-premixed combustion model of biogas is established. The GRI 3.0 mechanism with 53 species and 325 elementary chemical reactions is employed, and the P1 radiation model is considered. All elementary chemical reaction rates and heat release rates are programmed. To enhance the combustion and heat release characteristics, hydrogen addition and oxygen enriched combustion are selected for biogas combustion in future practical application. The mass contents of CH_{4}in biogas, hydrogen addition ratios, and oxygen enrichment levels are ranged from 35.3% to 58.7%, 0% to 50%, and 21% to 35%, respectively.## 2. Numerical Simulations

A typical gaseous combustion cylindrical chamber with a diameter of 200 mm (r) and 600 mm length (z) is employed in this research, as shown in Figure 1. The fuel inlet is located at a central nozzle with a radius of 6.8 mm, and air inlet is surrounded with a fuel inlet with a radius of 100 mm. Three kinds of biogas fuel are applied in this research. The H
where ${V}_{{\mathrm{CH}}_{4}}$, ${V}_{{\mathrm{H}}_{2}}$, ${V}_{{\mathrm{O}}_{2}}$, and ${V}_{{\mathrm{N}}_{2}}$ are the flow rates of CH

_{2}addition ratio to fuel (${X}_{{\mathrm{H}}_{2}}$, based on low heat value) and O_{2}-enriched level (${\Omega}_{{\mathrm{O}}_{2}}$) are defined as following equations:
$${X}_{{\mathrm{H}}_{2}}\text{}=\text{}\frac{{V}_{{\mathrm{H}}_{2}}\text{}\times \text{}LH{V}_{{\mathrm{H}}_{2}}}{{V}_{{\mathrm{CH}}_{4}}\text{}\times \text{}LH{V}_{{\mathrm{CH}}_{4}}\text{}+\text{}{V}_{{\mathrm{H}}_{2}\times LH{V}_{{\mathrm{H}}_{2}}}}$$

$${\Omega}_{{\mathrm{O}}_{2}}\text{}=\text{}\frac{{V}_{{\mathrm{O}}_{2}}}{{V}_{{\mathrm{O}}_{2}}\text{}+\text{}{V}_{{\mathrm{N}}_{2}}}$$

_{4}, H_{2}, O_{2}, and N_{2}respectively; $LH{V}_{{\mathrm{H}}_{2}}$ and $LH{V}_{{\mathrm{CH}}_{4}}$ are the low heat values of H_{2}and CH_{4}. The inlet fuel and oxidizer conditions at various H_{2}-enriched condition and O_{2}-enriched condition are shown in Table 1. The inlet power is kept constant under all calculation conditions. The mass contents of CH_{4}in biogas are 35.3%, 45.9%, and 58.7%, namely BG-1, BG-2, and BG-3, respectively. H_{2}addition ratio to biogas is arranged from 10% to 50%, and O_{2}in the oxidizer is from 21% to 35%.The flow mass, chemical species, momentum, and energy equation based on Navier–Stokes equations is expressed in Equation (3):
where $\rho $, $Y$, $\overrightarrow{V}$, ${\mathsf{\Gamma}}_{Y}$, and ${S}_{Y}$ are density, general dependent variable, velocity vector, associated transport coefficient of Y, and the source term. Thermal radiation is programmed to the source term of the mixture enthalpy. In this research, P1 radiation developed by Grosshandler of National Institute of Standards and Technology (NIST) [23] was selected. The gas radiation was considered by the determination of Planck mean absorption coefficient. Gas radiation contributed to the gases of CH

$$\frac{\delta \left(\rho Y\right)}{\delta t}\text{}+\text{}div(\rho \overrightarrow{V}Y)\text{}=\text{}div\left({\mathsf{\Gamma}}_{\mathrm{Y}}gradY\right)\text{}+\text{}{S}_{Y}$$

_{4}, CO_{2}, CO, and H_{2}O. The mean absorption coefficient of these gases (${\alpha}_{i}$) can be fitted as functions of temperature, which are summarized as Equations (4)–(6):Mean absorption coefficient of CH

_{4}:
$${\alpha}_{i}\text{}=\text{}{a}_{0}\text{}+{a}_{1}T+\text{}{a}_{2}{T}^{2}\text{}+\text{}{a}_{3}{T}^{3}\text{}+\text{}{a}_{4}{T}^{4}\text{}+{a}_{5}{T}^{5}$$

Mean absorption coefficient of CO

_{2}and H_{2}O:
$${\alpha}_{i}={a}_{0}\text{}+\text{}{a}_{1}\left(\frac{1000}{T}\right)\text{}+\text{}{a}_{2}{\left(\frac{1000}{T}\right)}^{2}\text{}+\text{}{a}_{3}{\left(\frac{1000}{T}\right)}^{3}\text{}+\text{}{a}_{4}{\left(\frac{1000}{T}\right)}^{4}\text{}+\text{}{a}_{5}{\left(\frac{1000}{T}\right)}^{5}$$

Mean absorption coefficient of CO:

$${\alpha}_{i}\text{}=\text{}{a}_{0}\text{}+\text{}T\left\{{a}_{1}\text{}+\text{}T[{a}_{2}\text{}+\text{}T\left({a}_{3\text{}}+\text{}{a}_{4}T\right)]\right\}$$

The values of constants ${a}_{0}$ to ${a}_{5}$ for CH
where ${h}_{j}$ is formation enthalpy of specie $j$ (J·mol

_{4}, CO_{2}, CO, and H_{2}O are shown in Table 2. The boundary wall is treated as a gray heat sink with emissivity of 0.8, and the wall temperature is maintained at 300 K through water cooling. The total absorption coefficient of radiating gas mixture is calculated as the sum of the absorption coefficients of CH_{4}, CO_{2}, CO, and H_{2}O in the flame. All transport equations with radiation are solved by CFD software PHOENICS 2014 (Cham-Japan, Tokyo, Japan) [24]. The velocity and pressure coupling are treated by a SIMPLE method algorithm [25]. The GRI 3.0 mechanism with 53 species and 325 reactions [26] is applied to this research. The transport and thermal properties of all species are calculated by GRI 3.0 database and CHEMKIN codes. As a key parameter in fuel combustion, the heat release rates of all elementary reactions are defined and programed. Taking reaction R52 as example, we can calculate the heat release rate by following equations:
$$\mathrm{R}52:\mathrm{H}\text{}+{\text{}\mathrm{CH}}_{3}\left(+\mathrm{M}\right)\text{}\iff {\text{}\mathrm{CH}}_{4}\left(+\mathrm{M}\right)$$

$$\Delta {h}_{i=52}\text{}=\text{}\left({h}_{\mathrm{H}}+{h}_{{\mathrm{CH}}_{3}}\right)\text{}-\text{}{h}_{{\mathrm{CH}}_{4}},\text{}\mathrm{J}\xb7{\mathrm{mol}}^{-1}$$

$${q}_{i=52}\text{}=\text{}\Delta {h}_{i=52}\text{}\times \text{}{k}_{i=52}$$

$${q}_{\mathrm{net}}\text{}=\text{}{\displaystyle \sum}_{i=1}^{325}{q}_{i}$$

^{−1}); $\Delta {h}_{i}$, ${k}_{i}$, and ${q}_{i}$ are enthalpy change of reaction $i$ (J·mol^{−1}), the reaction rate of reaction $i$ (mol·cm^{−3}·s^{−1}), and heat release of reaction $i$ (J·cm^{−3}·s^{−1}), respectively. Furthermore, ${q}_{\mathrm{net}}$ indicates the total heat release rate of all reactions (mol·cm^{−3}·s^{−1}).## 3. Discussion

Figure 2 shows several typical measured outlet temperatures of BG-2/air flames with various H

_{2}addition ratios and O_{2}-enriched levels at the same input power of 1.0 kW and equivalence ratio of 0.95; the simulation results are shown for comparison. The outlet temperature was measured by a K-type thermocouple on a same combustion chamber and burner size with simulation, which was described in our previous study [27]. The error of experimental temperature at all H_{2}addition ratios and O_{2}-eneriched levels are less than 15%. Furthermore, the deviation of simulation and experimental results are below 11%. Therefore, the simulation results show good agreement with experimental data at all H_{2}addition ratios and O_{2}-enriched levels, thereby confirming that the GRI 3.0 mechanism provides an acceptable and repeatable result for biogas combustion under H_{2}-enriched and O_{2}-enriched conditions.The effect of CH

_{4}content in biogas fuel on the combustion temperature distribution is shown in Figure 3. The maximum combustion temperature increases with increasing CH_{4}content in biogas fuel. Furthermore, the flame length through the z-direction decreases at a higher CH_{4}content condition, and flame width through the r-direction also shrinks with increasing CH_{4}content in biogas fuel. These findings are attributed to the following explanations: (a) the reaction rate of elementary reactions in biogas fuel flames increases with increasing CH_{4}content in biogas fuel as shown in Figure 4, and is usually related to the flame structure; (b) the heat loss to heat up unburnt CO_{2}in biogas fuel gas decreases with higher CH_{4}content in biogas fuel; and (c) the total volume of combustion gas (including fuel gas and air) decreases when CH_{4}content in biogas fuel increases, leading to higher temperature and heat release rate under higher CH_{4}content condition. The maximum heat release rate increased by about 19.3% (from 362 to 432 J·cm^{−3}·s^{−1}) with increasing CH_{4}content in biogas from BG-1 to BG-3, leading to a stronger heat release rate flame with shorter flame lengths at higher CH_{4}content in biogas fuel.The effects of H

_{2}addition ratios and O_{2}enrichment levels in BG-2/air flame on combustion temperature distributions are shown in Figure 5. The maximum combustion temperature in flames increased by approximately 10.8% from 1803 to 1998 K as H_{2}addition ratio varied from 0% to 50%, and was slightly higher by about 11.2% from 1803 to 2005 K as O_{2}enrichment levels increased from 21% to 35%. Conversely, the maximum heat release rate in flames increased by 3.69 times from 362 to 1336 J·cm^{−3}·s^{−1}at H_{2}addition conditions and only 2.29 times from 362 to 829 J·cm^{−3}·s^{−1}under O_{2}addition conditions, as shown in Figure 6. This difference is also related to the shape and structure of biogas flames, which is important in the direct application of biogas for heating. Specifically, the position of maximum heat release rate varying with H_{2}addition and O_{2}enrichment is different. At the H_{2}addition condition, the fuel composition at fuel inlet varies with H_{2}addition rate, the fuel combustion velocity enhances because of high reactivity (more OH and H radicals with higher formation rate because of high burning velocity [28,29,30] and combustion temperature of H_{2}) and high mobility of H_{2}[28,29,30]. Therefore, the maximum heat release rate at the H_{2}addition conditions is located at center of the flame. At the O_{2}enrichment condition, the fuel composition keeps constant, and the air composition at outside of fuel inlet varies with O_{2}enrichment. The fuel combustion velocity also improves because of the higher collision rate of oxidizer with fuel near flame edges. Therefore, the maximum heat release rate locates near the flame edges at O_{2}enriched condition.To obtain an in-depth understanding of heat release characteristics of biogas flames under H

_{2}-enriched and O_{2}-enriched conditions, the net heat release rate distribution at centerline along the z-direction is shown in Figure 7. The maximum net heat release rate at centerline is enhanced by approximately two orders of magnitude (from 0.155 to 120.0 J·cm^{−3}·s^{−1}) when H_{2}addition ratio increases from 0% to 50%; and the maximum net heat release rate at centerline is enhanced by about one order of magnitude (from 0.155 to 3.66 J·cm^{−3}·s^{−1}) when the O_{2}addition ratio increases from 21% to 35%. The enhancement of the heat release rate can lead to a change in flame structure and heat release characteristics in the flame reaction zone. Therefore, average temperature T_{a}was defined to explore the effect of H_{2}-enriched and O_{2}-enriched conditions on flame kernel. T_{a}is based on the barycenter of heat release rate as follows:
$${T}_{a}=\frac{{{\displaystyle \int}}_{0}^{z}qT\mathrm{d}z}{{{\displaystyle \int}}_{0}^{z}q\mathrm{d}z}$$

Figure 8 shows the average temperature T
where ${T}_{max}$ and ${T}_{0}$ are the maximum temperature and unburned temperature respectively, ${\left(dT/dz\right)}_{max}$ is the peak gradient in temperature profile along the centerline. As shown in Figure 11, the flame thickness decreases with the increasing H

_{a}together with flame height of peak heat release rate at various H_{2}addition ratios and O_{2}enrichment levels. As shown in Figure 8, the average temperature T_{a}shows a gradual decrease with the increasing H_{2}addition ratio and O_{2}enrichment levels. For the biogas flame at same input power of 1 kW and equivalence ratio of 0.95, the value of average temperature T_{a}increases from 1215 to 1864 K, nearly yielding an enhancement of 53.4%, when H_{2}addition ratio varied from 0% to 50%. In contrast, the flame height of peak heat release rate decreases by approximately 54.5% from 19.8 to 9.0 cm when the H_{2}addition ratio increases from 0% to 50%. The enhancement of average temperature T_{a}and reduction of flame height of maximum heat release rate resulted from the high mobility and high reactivity of H_{2}, leading to a higher reaction rate of biogas flame under H_{2}-enriched condition as shown in Figure 9a. By contrast, the value of average temperature T_{a}increased from 1215 to 1428 K (~17.5% increase) and the flame height of peak heat release rate decreases from 19.8 to 10.9 cm (~44.9% decrease) when O_{2}enrichment levels increased from 21% to 35%. With the enrichment of O_{2}in combustion air, the reaction rate can be improved as shown in Figure 9b. Furthermore, unnecessary sensible heat to heat up the unburnt N_{2}gas also decreases with increasing O_{2}enrichment levels. As shown in Figure 9, the net reaction rate of biogas flames under the H_{2}-enriched condition markedly increases as H_{2}addition ratio increases from 0% to 50% and lower increase is observed under O_{2}-enriched condition when O_{2}levels increases from 21% to 35%. To clarify the main elementary reaction in biogas flame, we compared the typical elementary exothermic reaction rate of biogas flame along the centerline at H_{2}addition ratio of 0% and 50% in Figure 10. The formation of free radicals, such as H, O, and OH, are enhanced with the increase in hydrogen addition ratios; in particular, R83: OH + H_{2}⇔ H + H_{2}O markedly increases as H_{2}is added to biogas flame, similar results have been reported for the heat release rate of premixed laminar biogas-H_{2}flame by Wei et al. [19] and CH_{4}/air premixed flames with H_{2}addition by Hu et al. [31]. Furthermore, the typical elementary exothermic reaction rates of R83: OH + H_{2}⇔ H + H_{2}O; R37: H + O_{2}⇔ O + OH are important to enhance biogas combustion. The elementary reaction of R83 (H_{2}as reactant) is higher than R37 (O_{2}as reactant). Therefore, H_{2}addition has a drastic effect on heat release rate (and reaction rate) enhancement than O_{2}enrichment as shown in Figure 6 and Figure 7. The enhancement reaction rate can lead to structure and shape changes in biogas flame. The flame thickness along centerline under H_{2}-enriched conditions and O_{2}-enriched conditions are shown in Figure 11. The definition of flame thickness can be expressed as follows:
$${D}_{F}=\frac{{T}_{max}-{T}_{0}}{{\left(dT/dz\right)}_{max}}$$

_{2}addition ratio and O_{2}enrichment levels. This decrease can be attributed to the burning velocity enhancement of biogas flames under H_{2}-enriched and O_{2}-enriched conditions. Therefore, a flame with enhanced heat release rate is formed under H_{2}-enriched and O_{2}-enriched conditions, which are beneficial to the practical application of biogas as a fuel.## 4. Conclusions

The combustion and heat release characteristics of biogas non-premixed flames under various hydrogen-enriched and oxygen-enriched conditions were investigated utilizing chemical kinetics simulation and the detailed chemical mechanism. The results are summarized as follows.

- (1)
- The net reaction rate of biogas increases with increasing hydrogen addition ratio and oxygen levels, leading to a higher net heat release rate of biogas flame;
- (2)
- The formation of free radicals, such as H, O, and particularly OH, are enhanced with the increase in hydrogen addition ratio and oxygen levels;
- (3)
- Flames with enhanced heat release rates are formed under H
_{2}-enriched and O_{2}-enriched conditions. Therefore, H_{2}-enriched and O_{2}-enriched combustion is beneficial to the improvement of combustion and heat release characteristics of biogas in practical application.

## Acknowledgments

This research is partially supported by the “Knowledge Hub Aichi” Priority Research Project from Aichi Prefectural Government, Japan.

## Author Contributions

Jun Li contributed to the experiment and simulation, data analysis and paper writing; Hongyu Huang, Huhetaoli, Yu Bai, and Yong Chen contributed to experimental design, and Yugo Osaka and Noriyuki Kobayashi contributed to modeling selection and programing instruction.

## Conflicts of Interest

The authors declare no conflict of interest.

## Nomenclature

${X}_{{\mathrm{H}}_{2}}$ | H_{2} addition ratio to fuel (based on low heat value) |

${V}_{{\mathrm{H}}_{2}}$ | Flow rate of H_{2} (m·s^{−1}) |

${V}_{{\mathrm{CH}}_{4}}$ | Flow rate of CH_{4} (m·s^{−1}) |

$LH{V}_{{\mathrm{H}}_{2}}$ | Low heat value of H_{2} (kJ·mol^{−1}) |

$LH{V}_{{\mathrm{CH}}_{4}}$ | Low heat value of CH_{4} (kJ·mol^{−1}) |

${\Omega}_{{\mathrm{O}}_{2}}$ | O_{2}-enriched level (-) |

${V}_{{\mathrm{O}}_{2}}$ | Flow rate of O_{2} (m·s^{−1}) |

${V}_{{\mathrm{N}}_{2}}$ | Flow rate of N_{2} (m·s^{−1}) |

$\rho $ | Density (kg·m^{−3}) |

$Y$ | General dependent variable (-) |

$Y$ | Velocity vector (m·s^{−1}) |

${\mathsf{\Gamma}}_{Y}$ | associated transport coefficient of Y (-) |

${S}_{Y}$ | The source term (-) |

${\alpha}_{i}$ | Mean absorption coefficient of species i (-) |

${h}_{j}$ | Formation enthalpy of specie j (J·mol^{−1}) |

$\Delta {h}_{i}$ | Enthalpy change of reaction i (J·mol^{−1}) |

${k}_{i}$ | The reaction rate of reaction i (mol·cm^{−3}·s^{−1}) |

${q}_{i}$ | Heat release rate of reaction i (J·cm^{−3}·s^{−1}) |

${q}_{\mathrm{net}}$ | Total heat release rate of all reaction (J·cm^{−3}·s^{−1}) |

${D}_{F}$ | Flame thickness (cm) |

${T}_{max}$ | The maximum temperature (K) |

${T}_{0}$ | The unburned temperature (K) |

${\left(dT/dz\right)}_{max}$ | The peak gradient in temperature (K·cm^{−1}) |

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**Figure 2.**Comparison of predication temperature (line) and measurement temperature (plot) at the outlet of BG-2/air flames with various H

_{2}addition ratios (

**black line**) and O

_{2}enrichment levels (

**red line**).

**Figure 5.**Effects of H

_{2}addition ratio (

**a**) and O

_{2}enrichment levels (

**b**) in BG-2/air flame on the distribution of combustion temperature.

**Figure 6.**Effects of H

_{2}addition ratio (

**a**) and O

_{2}enrichment levels (

**b**) in BG-2/air flame on the distribution of the heat release rate.

**Figure 7.**Heat release rate of biogas flames under H

_{2}-enriched (

**a**) and O

_{2}-enriched (

**b**) conditions along the centerline.

**Figure 8.**Effects of H

_{2}addition ratio (

**a**) and O

_{2}enrichment levels (

**b**) in BG-2/air flame on the peak heat release height and average temperature T

_{a}.

**Figure 9.**Net reaction rate of biogas flame along centerline at various H

_{2}addition ratios (

**a**) and O

_{2}enrichment levels (

**b**).

**Figure 10.**Comparison of typical elementary reaction exothermic reaction rates of biogas flame along the centerline at H

_{2}addition ratio of 0% (

**a**) and 50% (

**b**).

**Figure 11.**Flame thickness along the centerline at various H

_{2}addition ratios (

**black line**) and O

_{2}enrichment levels (

**red line**).

Items | CH_{4}/L·min^{−1} | CO_{2}/L·min^{−1} | H_{2}/L·min^{−1} | O_{2}/L·min^{−1} | Air/L·min^{−1} | Power/kW |
---|---|---|---|---|---|---|

BG-1 | 1.829 | 1.220 | - | - | 18.340 | 1 |

BG-2 | 1.829 | 0.784 | - | - | 18.340 | 1 |

BG-3 | 1.829 | 0.457 | - | - | 18.340 | 1 |

H_{2} 10% | 1.647 | 1.098 | 0.602 | - | 18.014 | 1 |

H_{2} 30% | 1.281 | 0.854 | 1.805 | - | 17.361 | 1 |

H_{2} 50% | 0.915 | 0.610 | 3.008 | - | 16.709 | 1 |

O_{2} 25% | 1.829 | 1.220 | - | 0.780 | 14.626 | 1 |

O_{2} 30% | 1.829 | 1.220 | - | 1.463 | 11.376 | 1 |

O_{2} 35% | 1.829 | 1.220 | - | 1.950 | 9.054 | 1 |

Coefficient | CO_{2} | H_{2}O | CH_{4} | CO (T < 750 K) | CO (T > 750 K) |
---|---|---|---|---|---|

a_{0} | 18.741 | −0.23093 | 6.6334 | 4.7869 | 10.09 |

a_{1} | −121.31 | −1.1239 | −3.5686 × 10^{−3} | −0.06953 | −0.01183 |

a_{2} | 273.5 | 9.4153 | 1.6682 × 10^{−8} | 2.95775 × 10^{−4} | 4.7753 × 10^{−6} |

a_{3} | −194.05 | −2.9988 | 2.5611 × 10^{−10} | −4.25732 × 10^{−7} | −5.87209 × 10^{−10} |

a_{4} | 56.31 | 0.51382 | −2.6558 × 10^{−14} | 2.02894× 10^{−10} | −2.5334 × 10^{−14} |

a_{5} | −5.8169 | −1.884 × 10^{−5} | 0 | - | - |

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