A New Mathematical Model Study on CO2 Gasification Reaction of

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A New Mathematical Model Study on CO2 Gasification Reaction of Typical Agricultural Residues Hua Fei,*,† Song Hu,‡ Faen Shi,† Yuanlin Li,† Dahua Jiang,† and Jun Xiang‡ †

School of Architectural and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganhzhou 34100, Jiangxi Province, China ‡ State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China ABSTRACT: In this context, the differential mass conservation equations were used to describe typical noncatalytic gas−solid reactions, such as biomass chars gasification, and an approximate method was applied to solve these equations. The methodology developed in this work was based on an approximate method for decoupling the gas conservation equation. With this strategy, the calculation of gas concentration and solid conversion at any time and position during reaction could be converted to the solution of two coupled algebraic equations. Thereby, a new mathematical model, modified quantize model (MQM), was constructed to describe the gasification rates of biomass chars according to a nonlinear relationship between the porosity and reaction surface of biomass chars when pore diffusion effect is considered. Carbon conversion rates predicted by the MQM were in closer agreement with the experimental data than those predicted by the Rafsanjani model (QM) and discrete random pore model (DRPM). Using the MQM, the gasification process of biomass chars in CO2 at different temperatures was analyzed.

1. INTRODUCTION With the excessive use of fossil fuels and the concerns over environmental protection, the utilization of biomass resources has attracted increasing worldwide interest. Biomass including agricultural residues is one of the main renewable energy resources available especially in an agricultural country such as China. There has been considerable focus on agricultural residues as a source of renewable energy to reduce the potential environmental impact of fossil fuels. Agricultural residues belong to natural high-molecular organic substances of lignocellulosic structure.1,2 Being available in abundance, agricultural residues are recognized as one of the main renewable energy sources used for thermal power, electrical energy, and syngas. Moreover, the agricultural biomass fuels can be considered CO2-neutral fuels and give lower emissions of NOx, SOx, and heavy metals with respect to coals. In China, the agricultural biomass residues are becoming an issue of increasing importance, not only for economical reasons but also for environmental impact and energy security. At present, rice straw, rice husk, and maize stalk are the major agricultural residues produced in large quantities in developing countries. Direct combustion of biomass results in fuel-bound nitrogen and sulfur being converted to NOx and SOx. Gasification offers the opportunity to control the level of gaseous and particulate emissions, leading to lower concentrations of soot particles, aerosols, NOx, SOx, and the production of fuel gas (H2, CO, or CH4).3,4 However, biomass gasification or combustion, which is influenced by many factors (such as atmosphere, heating rate, temperature),5−8 is a complex thermochemical process. There are also a limited number of studies that have focused on the mathematical model of the structural evolution during char gasification. The structural-type models explicitly considered the structural solid changes during reaction. This was done by modeling the variation of either the internal solid or the internal pore structure.9−12 Lee et al.13 depicted © 2012 American Chemical Society

reaction rates of chars by using the simple particle model (SPM). Brem and Brouwers14 presented analytical depiction for the case of general order with respect to gas concentration. The model accounting for the changes in reaction surface area and effective pore diffusivity during reaction shows satisfactory agreement between experiment and theory, and extensive literature about the computational aspects of these differential models can also be found.15−17 To take advantage of this solution, it is first required to overcome the coupling between the two equations of model, that is, to reduce them to a set of linear equations. To achieve this, an approximate solution for such coupled differential equations is possible for simplified cases when either the diffusion or the kinetic regime is present.18,19 These authors illustrated the quantize method potential by applying it to several mathematical models, including half-order model, nucleation model, the grain model, and modified grain model.20−23 Rafsanjani et al.18 applied this approach to give a new mathematical model (QM) for predicting char reaction, but the linear relationship of the porosity and reaction surface during reaction was assumed in this model. Moreover, this method also was applied to the random pore model, and the results showed good agreement of this solution with the experimental data.24 In this work, the modified quantize model was applied to describe the reaction rates of biomass chars when pore diffusion effect is considered. Carbon conversion rates predicted by the MQM were in closer agreement with the experimental data than those predicted by the Rafsanjani model (QM) and discrete random pore model (DRPM)25 developed by Bhatia and Vartak, which accounting for the changes in pore structure with carbon Received: Revised: Accepted: Published: 13619

June 6, 2012 September 29, 2012 October 1, 2012 October 1, 2012 dx.doi.org/10.1021/ie301488z | Ind. Eng. Chem. Res. 2012, 51, 13619−13626

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Table 1. Proximate and Ultimate Analysis of Biomass Samplesa proximate analysis (wt %, air-dried basis)

a

ultimate analysis (wt %, air-dried basis)

sample

moisture

volatile

ash

fixed carbon

carbon

hydrogen

nitrogen

sulfur

oxygen

RS RH MS

8.13 9.02 5.70

64.67 61.79 76.15

14.57 13.36 5.70

12.62 15.83 12.45

37.27 40.93 43.68

5.68 5.92 5.80

0.71 0.47 1.38

0.12 0.11 0.15

33.51 30.20 37.62

RS, rice straw; RH, rice husk; MS, maize stalk.

where η is dimensionless radius, x is local carbon conversion, X is overall carbon conversion, ε0 is the initial porosity of the solid, τ is dimensionless time, C′ is dimensionless concentration in the QM (C′ = sinh(λ′η)/η sinh(λ′)), and λ′ is a modified Thiele modulus in the QM. A number of sets of experimental data from the literature were used to validate the QM developed by the Rafsanjani.18 The char conversion−time behavior predicted by the QM was consistent with the experimental data, up to a carbon conversion of about 0.7, but it was in poor agreement with the experimental data in carbon conversion of >0.7 because the linear relationship between the surface area and porosity of the char was assumed in this model, as shown in the literature.18 Thus, the QM can be modified according to the nonlinear relationship between the surface area and porosity of the char. 3.2. Modified Quantize Model. According to the QM and simple particle model (SPM), the differential mass conservation equations describing the reactant gas and the carbon materials within a spherical char particle are13

conversion was supported as being appropriate for application under chemical reaction control.

2. EXPERIMENTAL SECTION Rice straw (RS), rice husk (RH), and maize stalk (MS) were used in the present study as the representatives of agricultural residues. The samples were meshed to small particles with the size range of 900 °C. Figure 5 shows the experimental data from the literature35 versus the predictions by MQM and QM. At the carbon conversion range beyond 0.7, the predictions of MQM agree better with the experimental data for wheat straw gasification under CO2 environment than that of QM, despite the fact that experimental data from the literature were obtained at various conditions and with different particle sizes. 4.3. Error Analysis. The QM has good ability to describe the gasification reaction of char particles at the beginning stage, but it shows limitations in one aspect especially at the carbon conversion of X > 0.7. The fitting effects of the models can be judged by using error percentages δi, which are defined as i i δi = (X pred − Xexp ) × 100%

Xipred

5. CONCLUSIONS The agricultural biomass chars gasification under CO2 atmosphere is investigated with the help of the modified quantize model (MQM). The main conclusions obtained are summarized as follows: (1) A general and simple method for obtaining the solution of biomass chars gasification is presented. The method is based on an approximate method for decoupling the solid and gas equations. The application of this simplified solution can be a valuable tool for providing estimations

(27)

Xiexp

in which is the predicted data point, and is the experimental data point. It can be seen from Table 2 that predictions of the MQM are more accurate than those of QM and DRPM at carbon conversion beyond 0.8 for RS char gasification at different temperatures. Similarly, MQM have the most satisfying results with 13624

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with reasonable accuracy in the case where rapid calculation is necessary. (2) The modified quantize model (MQM), which is constructed to describe the gasification rates of biomass chars according to a nonlinear relationship between the porosity and reaction surface of biomass chars, is presented. As compared to the QM and DRPM, carbon conversion rates predicted by the MQM are in closer agreement with the experimental data. On the other hand, the discrete random pore model is not appropriate to describe biomass chars gasification in CO2 at high temperature. (3) The MQM is recommended as a convenient submodel for predicting the reaction rates of biomass chars when both chemical reaction and diffusion through the porous char are considered.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-797-8161560. Fax: 86-797-8312551. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful for financial support for this research from the National Science Foundation of China (NSFC) (no. 51176062). NOMENCLATURE C = concentration of gaseous reactant: CA/CA0 D = molecular diffusivity De = effective diffusivity Dash = ash component h = Thiele modulus: r0(k0ρtS0/D)1/2 k0 = reaction rate constant r = radius R = gas constant r0 = particle radius rA = reaction rate of gas reactant rB = reaction rate of the solid S0 = initial surface area of the solid S = surface area of the solid t = time T = temperature x = local carbon conversion X = overall carbon conversion η = dimensionless radius: r/r0 ε = the porosity of char ε0 = the initial porosity of char ρt = true density of the solid ρb = bulk density of the solid τM = tortuosity: 1/ε ψ = structural parameter τ = dimensionless time: τ = cA0k0ρtS0t/cB0 = kst

Indices

0 = initial stage A = gas component B = solid component

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