- Email: [email protected]
Integration of sorption kinetics in carbon conversion modeling for the description of oxyfuel combustion processes
Available online at www.sciencedirect.com
ScienceDirect
Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy Procedia 142 Energy Procedia 00(2017) (2017)1361–1366 000–000 www.elsevier.com/locate/procedia
9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
Integration of sorption kinetics in carbon conversion modeling for The 15th International Symposium on District Heating and Cooling the description of oxyfuel combustion processes Assessing Carsten the feasibility of using the Roland heat demand-outdoor Wedler*, Markus Richter, Span temperature function for a long-term district heat demand forecast Thermodynamics, Ruhr-Universität Bochum, D-44780 Bochum, Germany Abstract a
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
Recherche Innovation, 291 Avenue DreyfousinDaniel, 78520 Limay, France A novel approach for thebVeolia integration of &mass transport phenomena carbon conversion modeling is reported. To c Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France consider mass transport, effective diffusion-coefficients are commonly estimated by the parallel-pore model. For this, the tortuosity of the solid fuel is required, which cannot be provided by experimental work and has to be assumed. However, by conducting sorption kinetics measurements in a magnetic suspension balance, effective diffusioncoefficients Abstract can be determined without knowing the tortuosity. This resulting mass transport coefficient can be used directly in carbon conversion models.
District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the ©greenhouse 2017 The Authors. Published Ltd. gas emissions frombytheElsevier building sector. These systems require high investments which are returned through the heat Peer-review of theconditions scientific committee of the 9th International on Applied Energy.could decrease, sales. Due under to theresponsibility changed climate and building renovation policies,Conference heat demand in the future prolonging the investment return period.
Keywords: solid fuels,the mass transfer, sorption The maincarbon scopeburnout of this modeling, paper is to assess feasibility of usingkinetics, the heatoxyfuel demand – outdoor temperature function for heat demand
forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Nomenclature renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were with results fromofa dynamic heat demand model, previously developed validated by the authors. Ccompared Concentration i at the surface r Reactionand rate i,S resultsBulk showed that when only weather change is considered, the margin of error could be acceptable for some applications DThe diffusion coefficient T Temperature B error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation D(the Effective diffusion coefficient t Time eff scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). DKn Knudsen diffusion coefficient The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the dp Particle diameter ηi Effectiveness factor decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and dpore Pore diameter θ Porosity renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Fcoupled scenarios). FractionalThe uptake factorfor the scenarios considered, and values suggested could be used to νmodify the Stoichiometric function parameters improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding author. Tel.: +49-234-3222832; fax: +49-234-3214163. Cooling. E-mail address: [email protected]
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy. 10.1016/j.egypro.2017.12.520
Carsten Wedler et al. / Energy Procedia 142 (2017) 1361–1366 Author name / Energy Procedia 00 (2017) 000–000
1362 2
Fo* ki Mi ni pi R
ξ ρ σ τ Φ Ω
Non-dimensional time Reaction rate constant Molar mass Reaction order Partial pressure Gas constant
Eigenvalue Solid density Collision diameter Tortuosity Thiele module Temperature function
1. Introduction Sorption processes are of utmost relevance for the combustion of carbon materials. Gas-solid reactions are influenced by the adsorption of gas molecules (e.g. O2, CO2 and H2O) on the solid surface. Reaction products desorb back to the combustion atmosphere. For the oxyfuel combustion of solid fuels, the mass transport of the gaseous molecules has a larger influence than for combustion in conventional oxygen/nitrogen atmosphere. High concentrations of non-inert CO2 and H2O affect the mass transport of oxygen. There are two different measurable factors used to describe these mass transport phenomena. First, the selectivity of sorption from gas mixtures leads to different compositions between gas phase and sorbed phase on the surface of the fuel. This altered composition can be determined via sorption-equilibria measurements with gas mixtures or via modeling of the multicomponent gas-sorption based on experimental data from the corresponding adsorption isotherms of the pure gas components [1–6]. Second, mass transfer is related to sorption kinetics, which are limited by diffusion in the pore structure of the fuel. Effective diffusion coefficients express these sorption kinetics and integrally combine different diffusion processes: Knudsen diffusion, surface diffusion and bulk diffusion. [1, 7–11] In carbon conversion models, effective diffusion coefficients are used to take mass transport of gas molecules into account. However, adjustable parameters of those models are usually determined using the parallel pore model, which implies different assumptions for pore and surface behavior as discussed in section 2. This article shows a new approach based on a combination of methods from sorption and combustion science. It focusses on the integration of effective diffusion-coefficients from experimental sorption data in carbon-conversion models. 2. Carbon conversion modeling Despite the fact that sorption and mass transport of gaseous molecules are discussed in literature on carbon conversion modeling, the integration of sorption and diffusion kinetics from experimental data has not been addressed yet. Conversion models consider those transport phenomena on different levels of accuracy. For example, in the simple Langmuir-Hinshelwood (two-step) kinetic for the conversion of carbon with a partial pressure of carbon dioxide PCO2, the reaction rate r is expressed as follows [12]: 𝑟𝑟𝐶𝐶𝑂𝑂2 =
𝑘𝑘1 𝑘𝑘2 𝑝𝑝𝐶𝐶𝑂𝑂2 𝑘𝑘1 𝑝𝑝𝐶𝐶𝐶𝐶2 + 𝑘𝑘2
(1)
The reaction rate constants k1 and k2 are generally referred to as adsorption and desorption controlled parameters, but they are not determined by any sorption measurements. It is questionable whether these kinetic parameters are really (and only) affected by mass transport. Based on measurements of the reaction rate rCO2 in combustion experiments with a known carbon-dioxide partial pressure, these constants can simply be fitted. Liu and Niksa [13] developed a more detailed model, the so called carbon-burnout kinetics (CBK). In this model, sorption processes are considered as effective diffusion coefficients in the Thiele moduli ΦCO2 (Eq.(2)) to express the effectiveness factor ηCO2 (Eq. (3)), which is necessary to describe the reaction rate rCO2:
𝜙𝜙𝐶𝐶𝐶𝐶2
0.5
𝑛𝑛𝐶𝐶𝐶𝐶2 + 1 𝑟𝑟𝐶𝐶𝐶𝐶2 ,𝑆𝑆 𝑑𝑑𝑝𝑝 = ∙ (𝜌𝜌𝜐𝜐𝐶𝐶−𝐶𝐶𝐶𝐶2 ∙ ) 2 2𝐷𝐷𝑒𝑒𝑒𝑒𝑒𝑒,𝐶𝐶𝐶𝐶2 𝐶𝐶𝐶𝐶𝐶𝐶2 ,𝑆𝑆
(2)
Carsten Wedler et al.Procedia / Energy 00 Procedia (2017) 1361–1366 Author name / Energy (2017) 142 000–000
𝜂𝜂𝐶𝐶𝐶𝐶2 =
𝑟𝑟𝐶𝐶𝐶𝐶2 = 𝜂𝜂𝐶𝐶𝐶𝐶2
1 1 1 [ − ] 𝜙𝜙𝐶𝐶𝐶𝐶2 tanh(𝜙𝜙𝐶𝐶𝐶𝐶2 ) 𝜙𝜙𝐶𝐶𝐶𝐶2
𝑘𝑘7 𝑘𝑘4 𝑝𝑝𝐶𝐶𝑂𝑂2 𝑘𝑘7 𝑘𝑘7 𝑘𝑘7 + 𝑘𝑘4 𝑝𝑝𝐶𝐶𝑂𝑂2 + 𝑘𝑘′4 𝑝𝑝𝐶𝐶𝐶𝐶 + 𝑘𝑘6 𝑝𝑝𝐻𝐻2𝑂𝑂 + 𝑘𝑘′6 𝑝𝑝𝐻𝐻2 𝑘𝑘5 𝑘𝑘5
1363 3
(3) (4)
dp is the particle diameter, ρ the particle density, ν the stoichiometric factor, n the reaction order, RCO2,S the reaction rate at the surface of the particle and CCO2,S the molar concentration at the surface. Due to a more complex reaction mechanism, the determination of the reaction rate also requires the partial pressures and kinetic constants of different gasification agents in the combustion atmosphere [13]. For more complex conversion models, like the CBK, effective diffusion-coefficients are commonly estimated by a combination of the parallel-pore model and the Bosanquet equation [14–17]: 𝐷𝐷𝑒𝑒𝑒𝑒𝑒𝑒 =
𝜃𝜃 1 1 −1 ( + ) 𝜏𝜏 𝐷𝐷𝐾𝐾𝐾𝐾 𝐷𝐷𝐵𝐵
(5)
This reciprocal addition shows that effective diffusivity is the combination of Knudsen Diffusion DKn and Bulk Diffusion DB in the pore structure of the fuel, which can be expressed according to Knudsen’s theory [18] and to kinetic gas theory [19]. Knudsen diffusion describes diffusion in micropores, where the molecule collides more often with the walls of the pores than with other molecules. This effect occurs when the free mean path of the molecules is smaller than the diameter of the micropores. Bulk diffusion describes the mass transport in macropores and outside of the pore structure, where molecules mainly collide with other molecules. The tortuosity τ is defined as the ratio length of the real path to the minimum distance in the pore and cannot be provided by experimental work; values for tortuosity have to be assumed [17]. The porosity θ is generally assumed to be a constant value for different chars [20]. During pyrolysis and oxidation, however, the char structure underlies changes [21,22] and so the assumptions for tortuosity and porosity can be seen as a disadvantage of the conventional estimation of the effective diffusion coefficient. 3. Determination of effective diffusion coefficients from sorption data Another possibility to determine the effective diffusion coefficient is an analysis of sorption kinetics data; this approach has the advantage that the unknown tortuosity is not required. On condition of a constant diffusion flux across the particle, Fick’s second law of diffusion introduces the effective diffusion coefficient as a function of particle radius rp, diffusion time t and non-dimensional transfer time Fo* [23]: 𝐹𝐹𝐹𝐹 ∗ 𝐷𝐷𝑒𝑒𝑒𝑒𝑒𝑒 = 2 𝑡𝑡 𝑟𝑟𝑝𝑝
(6)
During sorption kinetics measurements in a magnetic suspension balance, the amount of gas molecules adsorbed at the surface of the solid fuel is measured over sorption time (equal to diffusion time t). Because there is no convective flux in the measuring cell of the balance, sorption kinetics are only limited by the different diffusion processes. From mass increase over sorption time, the fractional uptake F can be obtained over sorption time as a measure for sorption kinetics, describing the ratio between actual loading and maximal loading of the gas on the solid. This fractional uptake F is related to Fick’s second law by the non-dimensional transfer time Fo* and is given for spherical (Eq. (7)) [24] and cylindrical particles (Eq. (8)) [25] as follows: 𝐹𝐹𝑠𝑠𝑠𝑠 = 1 −
∞
6 1 ∗ ∑ 𝑒𝑒 −𝑖𝑖²𝜋𝜋²𝐹𝐹𝐹𝐹𝑠𝑠𝑠𝑠 𝜋𝜋² 𝑖𝑖² 𝑖𝑖=1
(7)
41364
Carsten Wedler et al.Procedia / Energy 00 Procedia (2017) 1361–1366 Author name / Energy (2017)142 000–000 ∞
𝐹𝐹𝑐𝑐𝑐𝑐 = 1 − 4 ∑ 𝑖𝑖=1
1 −𝜉𝜉 ²𝐹𝐹𝐹𝐹∗ 𝑒𝑒 𝑖𝑖 𝑐𝑐𝑐𝑐 𝜉𝜉𝑖𝑖 ²
(8)
For the determination of effective diffusion coefficients in pulverized coal particles, Eq. (7) is used due to their spherical shape. However, biomass particles often have a cylindrical shape, so Eq. (8) can be relevant as well. The eigenvalue ξi is obtained from the Bessel function or from appropriate tables [26]. Fig. 1 shows the measured fractional uptake of CO2 on a pulverized Rhinish lignite over time and the relation of the uptake to the non-dimensional time at a given temperature and pressure. This measurement was conducted in the apparatus and with the method described by Seibel et al. [1]. Each measuring time, t, can be assigned to a nondimensional time, Fo*, as can be seen in Fig. 2. With the resulting linearity used in Eq. (6) an effective diffusion coefficient of CO2 on pulverized Rhinish lignite can be obtained for a certain temperature and pressure.
Figure 1: Relation between fraction uptake F, time t and non-dimensional time Fo*
Figure 2: Resulting relation between t and Fo*
Measurement conditions are limited by the onset of reactions between fuel and gas molecule. Reactive conversion of carbon material causes a mass change, so sorption and reaction influence cannot be separated properly [1]. Thus, for temperatures above reaction temperature the effective diffusion coefficients have to be extrapolated. For that purpose, the temperature dependency of Knudsen and bulk diffusion have to be considered separately [23]: 𝐷𝐷𝐾𝐾𝐾𝐾,𝑖𝑖 =
𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 8 ∙ 𝑅𝑅 ∙ 𝑇𝑇 ∙√ 3 𝜋𝜋 ∙ 𝑀𝑀𝑖𝑖
1 1 1 𝐷𝐷𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = 0.0018583 ∙ √𝑇𝑇 3 ( + ) 2 𝑀𝑀1 𝑀𝑀2 𝑝𝑝 ∙ 𝜎𝜎12 ∙ Ω𝐷𝐷,12
(9) (10)
Knudsen diffusion depends on T0.5 and bulk diffusion on T1.5. With respect to the reciprocal addition of the diffusion processes from Eq. (5), the temperature behavior shows that at high temperature the Knudsen diffusion is dominating. At high temperature, the effective diffusion coefficient will increase with T0.5.
4. Outlook A new method for the determination of effective diffusion coefficients for use in carbon burnout modeling was presented. This method is based on an analysis of sorption kinetics measurements. In further work, sorption kinetics of different gases common for combustion atmospheres on fossil and bio fuels will be determined. The knowledge
Carsten Wedler et al. / Energy Procedia 142 (2017) 1361–1366 Author name / Energy Procedia 00 (2017) 000–000
1365 5
gained will be important especially for oxyfuel combustion. The high concentrations of non-inert CO2 and H2O and their gasification products have a strong influence on mass transport inside of the particle and cannot be neglected. Acknowledgements The authors gratefully acknowledge the sponsorship of the German Research Foundation (DFG) within the framework of the SFB/Transregio 129 “Oxyflame”. References [1] Seibel C, Wedler C, Vorobiev N, Schiemann M, Scherer V, Span R, Fieback TM. Sorption measurements for determining surface effects and structure of solid fuels. Fuel Processing Technology 2016;153:81–6, doi:10.1016/j.fuproc.2016.08.004. [2] Wedler C, Seibel C, Richter M, Fieback TM, Span R. Oxyfuel Combustion – Experimental Investigation of Sorption Effects on Coal Char. Energy Procedia 2017;105C:1847–51. [3] Busch A, Gensterblum Y, Krooss BM. Methane and CO2 sorption and desorption measurements on dry Argonne premium coals: Pure components and mixtures. International Journal of Coal Geology 2003;55:205–24, doi:10.1016/S01665162(03)00113-7. [4] Busch A, Gensterblum Y, Krooss BM, Siemons N. Investigation of high-pressure selective adsorption/desorption behaviour of CO2 and CH4 on coals: An experimental study. International Journal of Coal Geology 2006;66:53–68, doi:10.1016/j.coal.2005.07.003. [5] Clarkson CR, Bustin RM. Binary gas adsorption/desorption isotherms: effect of moisture and composition upon carbon dioxide selectivity over methane. International Journal of Coal Geology 2000;42:241–71. [6] Lee H-H, Kim H-J, Shi Y, Keffer D, Lee C-H. Competitive adsorption of CO2/CH4 mixture on dry and wet coal from subcritical to supercritical conditions. Chemical Engineering Journal 2013;230:93–101, doi:10.1016/j.cej.2013.06.036. [7] Marecka A, Mianowski A. Kinetics of CO2 and CH4 sorption on high rank coal at ambient temperatures. Fuel 1998;77:1691–6, doi:10.1016/S0016-2361(98)00071-4. [8] Siemons N, Busch A, Bruining H, Krooss B, Gensterblum Y. Assessing the Kinetics and Capacity of Gas Adsorption in Coals by a Combined Adsorption/ Diffusion Method. Proceedings of SPE Annual Technical Conference and Exhibition 2003, doi:10.2118/84340-MS. [9] Tang X, Li Z, Ripepi N, Louk AK, Wang Z, Song D. Temperature-dependent diffusion process of methane through dry crushed coal. Journal of Natural Gas Science and Engineering 2015;22:609–17, doi:10.1016/j.jngse.2014.12.022. [10] Charrière D, Pokryszka Z, Behra P. Effect of pressure and temperature on diffusion of CO2 and CH4 into coal from the Lorraine basin (France). International Journal of Coal Geology 2010;81:373–80, doi:10.1016/j.coal.2009.03.007. [11] Pillalamarry M, Harpalani S, Liu S. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs. International Journal of Coal Geology 2011;86:342–8, doi:10.1016/j.coal.2011.03.007. [12] Hurt RH, Calo JM. Semi-Global Intrinsic Kinetics for Char Combustion Modeling. Combustion and Flame 2001;125:1139– 49. [13] Liu G-S, Niksa S. Coal conversion submodels for design applications at elevated pressures. Part II. Char gasification. Progress in Energy and Combustion Science 2004;30:679–717, doi:10.1016/j.pecs.2004.08.001. [14] Zalc JM, Reyes SC, Iglesia E. The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures. Chemical Engineering Science 2004;59:2947–60, doi:10.1016/j.ces.2004.04.028. [15] Kajitani S, Suzuki N, Ashizawa M, Hara S. CO2 gasification rate analysis of coal char in entrained flow coal gasifier. Fuel 2006;85:163–9, doi:10.1016/j.fuel.2005.07.024. [16] Umemoto S, Kajitani S, Hara S. Modeling of coal char gasification in coexistence of CO2 and H2O considering sharing of active sites. Fuel 2013;103:14–21, doi:10.1016/j.fuel.2011.11.030. [17] Jeong HJ, Seo DK, Hwang J. CFD modeling for coal size effect on coal gasification in a two-stage commercial entrainedbed gasifier with an improved char gasification model. Applied Energy 2014;123:29–36, doi:10.1016/j.apenergy.2014.02.026. [18] Knudsen M. Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren. Annalen der Physik 1909;333:75–130, doi:10.1002/andp.19093330106. [19] Kennard EH. Kinetic theory of gases: With an introduction to statistical mechanics: McGraw-Hill; 1938. [20] Hong J. Modeling char oxidation as a function of pressure using an intrinsic Langmuir rate equation. Phd Thesis, Brigham
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Young University. Provo; 2000. [21] Senneca O, Vorobiev N, Wütscher A, Cerciello F, Heuer S, Wedler C, Span R, Schiemann M, Muhler M, Scherer V. Assessment of combustion rates of coal chars for oxy-combustion applications. Combustion and Flame submitted. [22] Wütscher A, Wedler C, Seibel C, Hiltrop D, Fieback TM, Muhler M, Span R. On the alternating physicochemical characteristics of Colombian coal during pyrolysis. Journal of Analytical and Applied Pyrolysis 2017;123:12–9, doi:10.1016/j.jaap.2017.01.007. [23] Do DD. Adsorption analysis: Equilibria and kinetics. London, Singapore: Imperial College Press; 1998. [24] Boyd GE, Adamson AW, Myers LS. The Exchange Adsorption of Ions from Aqueous Solutions by Organic Zeolites. II. Kinetics 1. J. Am. Chem. Soc. 1947;69:2836–48, doi:10.1021/ja01203a066. [25] Skelland AHP. Diffusional mass transfer. New York: Wiley; 1974. [26] Crank J. The mathematics of diffusion. 2nd ed. Oxford: Clarendon Press; 1976.
ScienceDirect
Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy Procedia 142 Energy Procedia 00(2017) (2017)1361–1366 000–000 www.elsevier.com/locate/procedia
9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
Integration of sorption kinetics in carbon conversion modeling for The 15th International Symposium on District Heating and Cooling the description of oxyfuel combustion processes Assessing Carsten the feasibility of using the Roland heat demand-outdoor Wedler*, Markus Richter, Span temperature function for a long-term district heat demand forecast Thermodynamics, Ruhr-Universität Bochum, D-44780 Bochum, Germany Abstract a
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
Recherche Innovation, 291 Avenue DreyfousinDaniel, 78520 Limay, France A novel approach for thebVeolia integration of &mass transport phenomena carbon conversion modeling is reported. To c Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France consider mass transport, effective diffusion-coefficients are commonly estimated by the parallel-pore model. For this, the tortuosity of the solid fuel is required, which cannot be provided by experimental work and has to be assumed. However, by conducting sorption kinetics measurements in a magnetic suspension balance, effective diffusioncoefficients Abstract can be determined without knowing the tortuosity. This resulting mass transport coefficient can be used directly in carbon conversion models.
District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the ©greenhouse 2017 The Authors. Published Ltd. gas emissions frombytheElsevier building sector. These systems require high investments which are returned through the heat Peer-review of theconditions scientific committee of the 9th International on Applied Energy.could decrease, sales. Due under to theresponsibility changed climate and building renovation policies,Conference heat demand in the future prolonging the investment return period.
Keywords: solid fuels,the mass transfer, sorption The maincarbon scopeburnout of this modeling, paper is to assess feasibility of usingkinetics, the heatoxyfuel demand – outdoor temperature function for heat demand
forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Nomenclature renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were with results fromofa dynamic heat demand model, previously developed validated by the authors. Ccompared Concentration i at the surface r Reactionand rate i,S resultsBulk showed that when only weather change is considered, the margin of error could be acceptable for some applications DThe diffusion coefficient T Temperature B error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation D(the Effective diffusion coefficient t Time eff scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). DKn Knudsen diffusion coefficient The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the dp Particle diameter ηi Effectiveness factor decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and dpore Pore diameter θ Porosity renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Fcoupled scenarios). FractionalThe uptake factorfor the scenarios considered, and values suggested could be used to νmodify the Stoichiometric function parameters improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding author. Tel.: +49-234-3222832; fax: +49-234-3214163. Cooling. E-mail address: [email protected]
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy. 10.1016/j.egypro.2017.12.520
Carsten Wedler et al. / Energy Procedia 142 (2017) 1361–1366 Author name / Energy Procedia 00 (2017) 000–000
1362 2
Fo* ki Mi ni pi R
ξ ρ σ τ Φ Ω
Non-dimensional time Reaction rate constant Molar mass Reaction order Partial pressure Gas constant
Eigenvalue Solid density Collision diameter Tortuosity Thiele module Temperature function
1. Introduction Sorption processes are of utmost relevance for the combustion of carbon materials. Gas-solid reactions are influenced by the adsorption of gas molecules (e.g. O2, CO2 and H2O) on the solid surface. Reaction products desorb back to the combustion atmosphere. For the oxyfuel combustion of solid fuels, the mass transport of the gaseous molecules has a larger influence than for combustion in conventional oxygen/nitrogen atmosphere. High concentrations of non-inert CO2 and H2O affect the mass transport of oxygen. There are two different measurable factors used to describe these mass transport phenomena. First, the selectivity of sorption from gas mixtures leads to different compositions between gas phase and sorbed phase on the surface of the fuel. This altered composition can be determined via sorption-equilibria measurements with gas mixtures or via modeling of the multicomponent gas-sorption based on experimental data from the corresponding adsorption isotherms of the pure gas components [1–6]. Second, mass transfer is related to sorption kinetics, which are limited by diffusion in the pore structure of the fuel. Effective diffusion coefficients express these sorption kinetics and integrally combine different diffusion processes: Knudsen diffusion, surface diffusion and bulk diffusion. [1, 7–11] In carbon conversion models, effective diffusion coefficients are used to take mass transport of gas molecules into account. However, adjustable parameters of those models are usually determined using the parallel pore model, which implies different assumptions for pore and surface behavior as discussed in section 2. This article shows a new approach based on a combination of methods from sorption and combustion science. It focusses on the integration of effective diffusion-coefficients from experimental sorption data in carbon-conversion models. 2. Carbon conversion modeling Despite the fact that sorption and mass transport of gaseous molecules are discussed in literature on carbon conversion modeling, the integration of sorption and diffusion kinetics from experimental data has not been addressed yet. Conversion models consider those transport phenomena on different levels of accuracy. For example, in the simple Langmuir-Hinshelwood (two-step) kinetic for the conversion of carbon with a partial pressure of carbon dioxide PCO2, the reaction rate r is expressed as follows [12]: 𝑟𝑟𝐶𝐶𝑂𝑂2 =
𝑘𝑘1 𝑘𝑘2 𝑝𝑝𝐶𝐶𝑂𝑂2 𝑘𝑘1 𝑝𝑝𝐶𝐶𝐶𝐶2 + 𝑘𝑘2
(1)
The reaction rate constants k1 and k2 are generally referred to as adsorption and desorption controlled parameters, but they are not determined by any sorption measurements. It is questionable whether these kinetic parameters are really (and only) affected by mass transport. Based on measurements of the reaction rate rCO2 in combustion experiments with a known carbon-dioxide partial pressure, these constants can simply be fitted. Liu and Niksa [13] developed a more detailed model, the so called carbon-burnout kinetics (CBK). In this model, sorption processes are considered as effective diffusion coefficients in the Thiele moduli ΦCO2 (Eq.(2)) to express the effectiveness factor ηCO2 (Eq. (3)), which is necessary to describe the reaction rate rCO2:
𝜙𝜙𝐶𝐶𝐶𝐶2
0.5
𝑛𝑛𝐶𝐶𝐶𝐶2 + 1 𝑟𝑟𝐶𝐶𝐶𝐶2 ,𝑆𝑆 𝑑𝑑𝑝𝑝 = ∙ (𝜌𝜌𝜐𝜐𝐶𝐶−𝐶𝐶𝐶𝐶2 ∙ ) 2 2𝐷𝐷𝑒𝑒𝑒𝑒𝑒𝑒,𝐶𝐶𝐶𝐶2 𝐶𝐶𝐶𝐶𝐶𝐶2 ,𝑆𝑆
(2)
Carsten Wedler et al.Procedia / Energy 00 Procedia (2017) 1361–1366 Author name / Energy (2017) 142 000–000
𝜂𝜂𝐶𝐶𝐶𝐶2 =
𝑟𝑟𝐶𝐶𝐶𝐶2 = 𝜂𝜂𝐶𝐶𝐶𝐶2
1 1 1 [ − ] 𝜙𝜙𝐶𝐶𝐶𝐶2 tanh(𝜙𝜙𝐶𝐶𝐶𝐶2 ) 𝜙𝜙𝐶𝐶𝐶𝐶2
𝑘𝑘7 𝑘𝑘4 𝑝𝑝𝐶𝐶𝑂𝑂2 𝑘𝑘7 𝑘𝑘7 𝑘𝑘7 + 𝑘𝑘4 𝑝𝑝𝐶𝐶𝑂𝑂2 + 𝑘𝑘′4 𝑝𝑝𝐶𝐶𝐶𝐶 + 𝑘𝑘6 𝑝𝑝𝐻𝐻2𝑂𝑂 + 𝑘𝑘′6 𝑝𝑝𝐻𝐻2 𝑘𝑘5 𝑘𝑘5
1363 3
(3) (4)
dp is the particle diameter, ρ the particle density, ν the stoichiometric factor, n the reaction order, RCO2,S the reaction rate at the surface of the particle and CCO2,S the molar concentration at the surface. Due to a more complex reaction mechanism, the determination of the reaction rate also requires the partial pressures and kinetic constants of different gasification agents in the combustion atmosphere [13]. For more complex conversion models, like the CBK, effective diffusion-coefficients are commonly estimated by a combination of the parallel-pore model and the Bosanquet equation [14–17]: 𝐷𝐷𝑒𝑒𝑒𝑒𝑒𝑒 =
𝜃𝜃 1 1 −1 ( + ) 𝜏𝜏 𝐷𝐷𝐾𝐾𝐾𝐾 𝐷𝐷𝐵𝐵
(5)
This reciprocal addition shows that effective diffusivity is the combination of Knudsen Diffusion DKn and Bulk Diffusion DB in the pore structure of the fuel, which can be expressed according to Knudsen’s theory [18] and to kinetic gas theory [19]. Knudsen diffusion describes diffusion in micropores, where the molecule collides more often with the walls of the pores than with other molecules. This effect occurs when the free mean path of the molecules is smaller than the diameter of the micropores. Bulk diffusion describes the mass transport in macropores and outside of the pore structure, where molecules mainly collide with other molecules. The tortuosity τ is defined as the ratio length of the real path to the minimum distance in the pore and cannot be provided by experimental work; values for tortuosity have to be assumed [17]. The porosity θ is generally assumed to be a constant value for different chars [20]. During pyrolysis and oxidation, however, the char structure underlies changes [21,22] and so the assumptions for tortuosity and porosity can be seen as a disadvantage of the conventional estimation of the effective diffusion coefficient. 3. Determination of effective diffusion coefficients from sorption data Another possibility to determine the effective diffusion coefficient is an analysis of sorption kinetics data; this approach has the advantage that the unknown tortuosity is not required. On condition of a constant diffusion flux across the particle, Fick’s second law of diffusion introduces the effective diffusion coefficient as a function of particle radius rp, diffusion time t and non-dimensional transfer time Fo* [23]: 𝐹𝐹𝐹𝐹 ∗ 𝐷𝐷𝑒𝑒𝑒𝑒𝑒𝑒 = 2 𝑡𝑡 𝑟𝑟𝑝𝑝
(6)
During sorption kinetics measurements in a magnetic suspension balance, the amount of gas molecules adsorbed at the surface of the solid fuel is measured over sorption time (equal to diffusion time t). Because there is no convective flux in the measuring cell of the balance, sorption kinetics are only limited by the different diffusion processes. From mass increase over sorption time, the fractional uptake F can be obtained over sorption time as a measure for sorption kinetics, describing the ratio between actual loading and maximal loading of the gas on the solid. This fractional uptake F is related to Fick’s second law by the non-dimensional transfer time Fo* and is given for spherical (Eq. (7)) [24] and cylindrical particles (Eq. (8)) [25] as follows: 𝐹𝐹𝑠𝑠𝑠𝑠 = 1 −
∞
6 1 ∗ ∑ 𝑒𝑒 −𝑖𝑖²𝜋𝜋²𝐹𝐹𝐹𝐹𝑠𝑠𝑠𝑠 𝜋𝜋² 𝑖𝑖² 𝑖𝑖=1
(7)
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Carsten Wedler et al.Procedia / Energy 00 Procedia (2017) 1361–1366 Author name / Energy (2017)142 000–000 ∞
𝐹𝐹𝑐𝑐𝑐𝑐 = 1 − 4 ∑ 𝑖𝑖=1
1 −𝜉𝜉 ²𝐹𝐹𝐹𝐹∗ 𝑒𝑒 𝑖𝑖 𝑐𝑐𝑐𝑐 𝜉𝜉𝑖𝑖 ²
(8)
For the determination of effective diffusion coefficients in pulverized coal particles, Eq. (7) is used due to their spherical shape. However, biomass particles often have a cylindrical shape, so Eq. (8) can be relevant as well. The eigenvalue ξi is obtained from the Bessel function or from appropriate tables [26]. Fig. 1 shows the measured fractional uptake of CO2 on a pulverized Rhinish lignite over time and the relation of the uptake to the non-dimensional time at a given temperature and pressure. This measurement was conducted in the apparatus and with the method described by Seibel et al. [1]. Each measuring time, t, can be assigned to a nondimensional time, Fo*, as can be seen in Fig. 2. With the resulting linearity used in Eq. (6) an effective diffusion coefficient of CO2 on pulverized Rhinish lignite can be obtained for a certain temperature and pressure.
Figure 1: Relation between fraction uptake F, time t and non-dimensional time Fo*
Figure 2: Resulting relation between t and Fo*
Measurement conditions are limited by the onset of reactions between fuel and gas molecule. Reactive conversion of carbon material causes a mass change, so sorption and reaction influence cannot be separated properly [1]. Thus, for temperatures above reaction temperature the effective diffusion coefficients have to be extrapolated. For that purpose, the temperature dependency of Knudsen and bulk diffusion have to be considered separately [23]: 𝐷𝐷𝐾𝐾𝐾𝐾,𝑖𝑖 =
𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 8 ∙ 𝑅𝑅 ∙ 𝑇𝑇 ∙√ 3 𝜋𝜋 ∙ 𝑀𝑀𝑖𝑖
1 1 1 𝐷𝐷𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = 0.0018583 ∙ √𝑇𝑇 3 ( + ) 2 𝑀𝑀1 𝑀𝑀2 𝑝𝑝 ∙ 𝜎𝜎12 ∙ Ω𝐷𝐷,12
(9) (10)
Knudsen diffusion depends on T0.5 and bulk diffusion on T1.5. With respect to the reciprocal addition of the diffusion processes from Eq. (5), the temperature behavior shows that at high temperature the Knudsen diffusion is dominating. At high temperature, the effective diffusion coefficient will increase with T0.5.
4. Outlook A new method for the determination of effective diffusion coefficients for use in carbon burnout modeling was presented. This method is based on an analysis of sorption kinetics measurements. In further work, sorption kinetics of different gases common for combustion atmospheres on fossil and bio fuels will be determined. The knowledge
Carsten Wedler et al. / Energy Procedia 142 (2017) 1361–1366 Author name / Energy Procedia 00 (2017) 000–000
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gained will be important especially for oxyfuel combustion. The high concentrations of non-inert CO2 and H2O and their gasification products have a strong influence on mass transport inside of the particle and cannot be neglected. Acknowledgements The authors gratefully acknowledge the sponsorship of the German Research Foundation (DFG) within the framework of the SFB/Transregio 129 “Oxyflame”. References [1] Seibel C, Wedler C, Vorobiev N, Schiemann M, Scherer V, Span R, Fieback TM. Sorption measurements for determining surface effects and structure of solid fuels. Fuel Processing Technology 2016;153:81–6, doi:10.1016/j.fuproc.2016.08.004. [2] Wedler C, Seibel C, Richter M, Fieback TM, Span R. Oxyfuel Combustion – Experimental Investigation of Sorption Effects on Coal Char. Energy Procedia 2017;105C:1847–51. [3] Busch A, Gensterblum Y, Krooss BM. Methane and CO2 sorption and desorption measurements on dry Argonne premium coals: Pure components and mixtures. International Journal of Coal Geology 2003;55:205–24, doi:10.1016/S01665162(03)00113-7. [4] Busch A, Gensterblum Y, Krooss BM, Siemons N. Investigation of high-pressure selective adsorption/desorption behaviour of CO2 and CH4 on coals: An experimental study. International Journal of Coal Geology 2006;66:53–68, doi:10.1016/j.coal.2005.07.003. [5] Clarkson CR, Bustin RM. Binary gas adsorption/desorption isotherms: effect of moisture and composition upon carbon dioxide selectivity over methane. International Journal of Coal Geology 2000;42:241–71. [6] Lee H-H, Kim H-J, Shi Y, Keffer D, Lee C-H. Competitive adsorption of CO2/CH4 mixture on dry and wet coal from subcritical to supercritical conditions. Chemical Engineering Journal 2013;230:93–101, doi:10.1016/j.cej.2013.06.036. [7] Marecka A, Mianowski A. Kinetics of CO2 and CH4 sorption on high rank coal at ambient temperatures. Fuel 1998;77:1691–6, doi:10.1016/S0016-2361(98)00071-4. [8] Siemons N, Busch A, Bruining H, Krooss B, Gensterblum Y. Assessing the Kinetics and Capacity of Gas Adsorption in Coals by a Combined Adsorption/ Diffusion Method. Proceedings of SPE Annual Technical Conference and Exhibition 2003, doi:10.2118/84340-MS. [9] Tang X, Li Z, Ripepi N, Louk AK, Wang Z, Song D. Temperature-dependent diffusion process of methane through dry crushed coal. Journal of Natural Gas Science and Engineering 2015;22:609–17, doi:10.1016/j.jngse.2014.12.022. [10] Charrière D, Pokryszka Z, Behra P. Effect of pressure and temperature on diffusion of CO2 and CH4 into coal from the Lorraine basin (France). International Journal of Coal Geology 2010;81:373–80, doi:10.1016/j.coal.2009.03.007. [11] Pillalamarry M, Harpalani S, Liu S. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs. International Journal of Coal Geology 2011;86:342–8, doi:10.1016/j.coal.2011.03.007. [12] Hurt RH, Calo JM. Semi-Global Intrinsic Kinetics for Char Combustion Modeling. Combustion and Flame 2001;125:1139– 49. [13] Liu G-S, Niksa S. Coal conversion submodels for design applications at elevated pressures. Part II. Char gasification. Progress in Energy and Combustion Science 2004;30:679–717, doi:10.1016/j.pecs.2004.08.001. [14] Zalc JM, Reyes SC, Iglesia E. The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures. Chemical Engineering Science 2004;59:2947–60, doi:10.1016/j.ces.2004.04.028. [15] Kajitani S, Suzuki N, Ashizawa M, Hara S. CO2 gasification rate analysis of coal char in entrained flow coal gasifier. Fuel 2006;85:163–9, doi:10.1016/j.fuel.2005.07.024. [16] Umemoto S, Kajitani S, Hara S. Modeling of coal char gasification in coexistence of CO2 and H2O considering sharing of active sites. Fuel 2013;103:14–21, doi:10.1016/j.fuel.2011.11.030. [17] Jeong HJ, Seo DK, Hwang J. CFD modeling for coal size effect on coal gasification in a two-stage commercial entrainedbed gasifier with an improved char gasification model. Applied Energy 2014;123:29–36, doi:10.1016/j.apenergy.2014.02.026. [18] Knudsen M. Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren. Annalen der Physik 1909;333:75–130, doi:10.1002/andp.19093330106. [19] Kennard EH. Kinetic theory of gases: With an introduction to statistical mechanics: McGraw-Hill; 1938. [20] Hong J. Modeling char oxidation as a function of pressure using an intrinsic Langmuir rate equation. Phd Thesis, Brigham
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