energies

Article Entrained-Flow Coal Gasification Process Simulation with the Emphasis on Empirical Char Conversion Models Optimization Procedure

Jakub Mularski * and Norbert Modli ´nski

Department of Energy Conversion Engineering, Wrocław University of Science and Technology, Wybrzeze˙ Wyspia´nskiego27, 50-370 Wrocław, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-71-320-21-81

Abstract: Computational fluid dynamics (CFD) modeling of an entrained-flow reactor is demon- strated and compared with experimental data. The study is focused on char conversion modeling and its impact on gasification simulation results. An innovative procedure of optimizing input data to empirical char conversion kinetic-diffusion model is investigated, based on the complex carbon burnout kinetic model for oxidation (CBK/E) and gasification (CBK/G). The kinetics of the CBK/G model is determined using the data from char gasification experiments in a drop tube reactor. CFD simulations are performed for the laboratory-scale entrained-flow reactor at Brigham Young Univer- sity for the bituminous coal. A substantial impact of applied kinetic parameters on the in-reactor gas composition and char conversion factor was observed. The effect was most considerable for the reduction zone, where gasification reactions dominate, although a non-negligible impact could also



be observed in the flame zone. Based on the quantitative assessment of the incorporated optimization
 procedure, its application allowed to obtain one of the lowest errors of CO, H2, CO2, and H2O axial

Citation: Mularski, J.; Modli´nski,N. distribution with respect to the experimental data. The maximum errors for these species were equal Entrained-Flow Coal Gasification to 18.48, 7.95, 10.15, and 20.22%, respectively, whereas the average errors were equal to 4.82, 5.47, Process Simulation with the 4.72, and 9.58%, respectively. Emphasis on Empirical Char Conversion Models Optimization Keywords: CFD; coal gasification; char conversion; entrained-flow reactor Procedure. Energies 2021, 14, 1729. https://doi.org/10.3390/en14061729

Academic Editor: Bjørn H. Hjertager 1. Introduction More than 80% of the world’s energy comes from fossil fuels [1]. Coal is one of the Received: 19 February 2021 main sources of fossil fuel energy as it generates nearly 40% of the world’s electricity [2]. Accepted: 17 March 2021 Coal-fired power plants were the single largest contributor to the growth in emissions Published: 20 March 2021 observed in 2018 [3]. As a result, coal-fired electricity generation made up 30% of global CO emissions [3]. Unfortunately, this ongoing trend tremendously impacts the natural en- Publisher’s Note: MDPI stays neutral 2 with regard to jurisdictional claims in vironment, climate, and human health. As a result, specific measures are taken to promote published maps and institutional affil- and develop efficient technologies which can mitigate the negative impact on our planet. iations. Coal, despite its gradually decreasing consumption in many countries, will continue to be a meaningful energy source for many years to come. This results in continuous research into environmentally benign coal-based technologies. Gasification is one of the most promising technologies for solid fuels since it allows the conversion of solid materials to gas consisting of H2, CO, CO2, CH4, and smaller amounts of different hydrocarbons [4,5]. Production Copyright: © 2021 by the authors. of such gas enables effective implementation of alternative ways of electricity generation Licensee MDPI, Basel, Switzerland. This article is an open access article (e.g., internal combustion engines, fuel cells, gas turbines) as well as a synthesis of different distributed under the terms and products (e.g., Fischer-Tropsch process, production of H2). Therefore, gasification is a conditions of the Creative Commons beneficial coal technology, offering high efficiency, low environmental impact, and new Attribution (CC BY) license (https:// possibilities regarding the synthesis of chemicals [6]. However, gasification is still not fully creativecommons.org/licenses/by/ understood on a fundamental level, and although CFD has been proven to be an efficient 4.0/).

Energies 2021, 14, 1729. https://doi.org/10.3390/en14061729 https://www.mdpi.com/journal/energies Energies 2021, 14, 1729 2 of 20

modeling tool [7–12], many models that describe specific gasification sub-phenomena still lack extreme accuracy. The main gasification sub-phenomena are moisture evaporation, devolatilization, partial oxidation, and gasification/reduction. In [13], where a well-stirred reactor was investigated with a first-of-its-kind model which considered detailed gas-phase chemistry, drying, devolatilization kinetics, particle-phase reactions, boundary layer diffusion, pore evolution and coupling between the phases, the effect of moisture mainly inhibited the overall gasification rate because of the temperature drop. Its impact on the char-H2O reaction was very small. Therefore, the increase in the moisture content generally increased the coal conversion time. The rate of drying/devolatilization was found to have little effect on the final syngas composition. The same result was obtained by [14,15] under the CFD studies for a 2D reactor. On the other hand, the final volatile yield from devolatilization turned out to have a substantial impact on the final carbon conversion [15]. The CFD study by Mularski and Modli´nski[14] confirmed the huge importance of devolatilization in the accurate estimation of the flame properties and its stabilization and structure, which can directly impact such issues as, e.g., flame lift-off. Kinetic parameters were found to have a huge influence on the rate of production of the main syngas components in the flame region. A recent study by Mularski and Modli´nski[16], which investigated a plug-flow reactor, a perfectly-stirred reactor, and a CFD analysis of three different operating reactors, confirmed a substantial effect of gas-phase modeling on the production rate of syngas components (CO, H2, CO2,H2O) in coal gasification conditions, which ultimately resulted in different final gas composition and in-reactor temperature distribution. While each gasification stage is of crucial importance, the char conversion process is the coal gasification rate-limiting step, which determines the residence time in the gasifier. Based on the literature review by Mularski et al. [17], most of the attention was paid to this particular phase. Syngas yield was found to be most sensitive to char-CO2 and char-H2O reactions. A variety of models have been developed. The most basic ones, such as surface-based kinetic-diffusion approaches where bulk diffusion was perceived by the competition between chemical kinetics and film diffusion [18,19] or more complex ones [20,21], which are accounted for in pore diffusion phenomena with internal surface area evolution, regime-dependent particle diameter, and density evolution, ash inhibition, thermal annealing, or even pore closing [22]. However, in order to limit the computational requirements which especially concern 3-D cases with a large eddy simulation (LES) or direct numerical simulation methods (DNS), CFD simulations of coal gasification generally consider simplified models. The surface-based kinetic-diffusion model was found to be the most widely applied in the literature. Unfortunately, the literature review indicated that in most of the cases the kinetic parameters were not optimized prior to a numerical simulation. For instance, for the char-H2O and char-CO2 reactions, the following pre-exponential factors and activation 7 7 energies (AH2O = 0.0782, EH2O = 1.15 × 10 , ACO2 = 0.0732, ECO2 = 1.125 × 10 ) were used by [23–35] for five different reactors. Each reactor has specific operating conditions. This should result in unique kinetic parameters for each condition. Unfortunately, the use of experimental techniques for the determination of kinetic parameters can be very challenging or even inviable, especially in the case of large-scale reactors. The direct use of complex models such as the carbon burnout kinetic (CBK) approach can significantly impact the computational effort. Therefore, following the strategy presented by Mularski and Modli´nskifor the optimization of kinetic parameters for devolatilization in [14], in the present study kinetic parameters for the empirical char conversion kinetic-diffusion model are optimized, based on the independent results of the complex CBK/E and CBK/G models. The optimization is performed through the minimization of the objective function, which was found to be the most efficient approximation method amongst the investigated ones [14]. The analysis is carried out for the laboratory-scale, one-stage reactor at Brigham Young University in the U.S. in the city of Provo, Utah [36]. Energies 2021, 14, 1729 3 of 20

2. Numerical Models 2.1. CFD Modeling of Entrained-Flow Gasification The entrained-flow coal gasification process is investigated by means of the commer- cial CFD software: (2020R2, ANSYS Fluent, Canonsburg, PA, USA) [37]. The finite-volume discretization approach is used to solve the Reynolds averaged Navier–Stokes (RANS) equations. The semi-implicit method for the pressure-linked equation (SIMPLE) [38] algorithm is used for pressure-velocity coupling. Second-order schemes are used for spatial discretization. The gas phase is modeled with the Eulerian approach. The discrete-phase trajectories are calculated with the Lagrangian formulation, whereas the coupling between the phases is determined through the particle sources of the Eulerian gas-phase equations [39]. The following processes are accounted for in the gasifier: turbulent flow, moisture release, devolatilization, gas-phase reactions, char conversion, particle transport, and radiative transport. A summary of applied models is presented in Table1. Turbulence is modeled with the realizable k-ε approach [40]. Turbulent particle dispersion is modeled with the discrete random walk model [41]. The time scale constant in the discrete random walk model-Cτ was set to 0.6, based on the study by Kumar and Ghoniem [42] in order to improve the prediction of turbulent diffusion of particles. Radiation is simulated with the discrete ordinate method [37]. The weighted-sum of gray gas (WSGG) model [37] is used to calculate the gas absorption coefficient. For the gas phase, the specific global reaction mechanism is used which was found to have the closest agreement with regard to the detailed GRI-Mech mechanism [16].

Table 1. Summary of applied modeling approaches.

Models Devolatilization: Competing two-step reaction mechanism (C2SM) [43] Gas phase: Global reaction approach with finite-rate/eddy dissipation model [44] Char conversion: Kinetic-diffusion model [19] Turbulence: Realizable k-ε model [40] Radiation: Discrete ordinate method [37], weighted sum of gray gas model [37] Particle tracking: Discrete phase model, Discrete random walk model [41] Spherical particle drag law [45], Rosin-Rammler particle size distribution, Wet Particle models: combustion [37], Particle radiation interaction [37] Pressure-velocity coupling Semi-implicit method for pressure linked equations (SIMPLE) [38]

2.1.1. Devolatilization Modeling Devolatilization is modeled with the competing two-step reaction mechanism (C2SM) [43] through the optimization procedure presented in [14]. The main benefit of this approach is that it accounts for the effect of operating conditions (fuel properties, heating rate) on the volatile matter release [46]. The optimization process yields kinetic parameters (the activation energy and pre-exponential factor) for C2SM, based on the results from the complex functional-group, depolymerization, vaporization, and cross-linking (FG-DVC) model. FG-DVC is utilized independently of CFD, as a stand-alone model. The volatile matter evolved during the process is assumed to consist of tar, light gases, H2O, CO, and CO2. The tar molecule was assumed to be a CxHyOz molecule with C7 as the main component [47,48]. Light gases are considered as an CmHn molecule. The volatile evolves as a single compound that instantaneously breaks up into products. The final volatile composition has the following form:

Vol → a1CxHyOz + a2CmHn + a3CO + a4H2O + a5CO2 (1)

where ai, x, y, z coefficients are calculated from the FG-DVC results and the fundamental atom conservation equations. Energies 2021, 14, 1729 4 of 20

2.1.2. Char Conversion Modeling Char conversion is modeled with the empirical kinetic-diffusion approach [19,49]. It can be perceived as a resistance network comprised of diffusion and kinetic resistances. Reaction rate per unit surface area (g/cm2-s) is defined as: p R = s,i (2) s,i 1 + 1 D0,i Rkin,i

where ps,i is the bulk partial pressure of the gas phase species i, D0,i is the diffusion rate coefficient for species i and Rkin,i is the kinetic rate of species i. The diffusion rate coefficient is defined as:

0.75  Tp+Tg  2 D0,i = Ci (3) dp

where Tp is the particle temperature, dp is the particle diameter, Tg is the gas temperature, −12 −0.75 Ci is the mass diffusion constant and is equal to 5 × 10 sK . The kinetic rate for species i is expressed as follows:   βi Ei Rkin,i = AiTp exp − (4) RTp

where A is the pre-exponential factor, β is the temperature exponent, E is the activation energy and R is the universal gas constant. The carbon burnout kinetic model (CBK) [50–53] is recognized as one of the most ad- vanced combustion models available. The original version was developed by Robert Hurt’s research group at Sandia National Laboratories and Brown University. The key feature of CBK is the ability to model the low reaction rates in late burnout. The latest known modifi- cations of the model are the carbon burnout kinetic model for oxidation (CBK/E) [20] and gasification (CBK/G) [21]. The models incorporate an eight-step Langmuir-Hinshelwood (LH) kinetics, random pore model surface area evolution of intrinsic particle surface, single film diffusion, pore diffusion, ash inhibition, and thermal annealing. These approaches provide accurate results for a wide range of operating conditions. However, their di- rect implementation into CFD would considerably raise the computational effort. Hence, following the strategy for devolatilization optimization [14], the current study allows obtaining adjusted kinetic parameters for the kinetic-diffusion model on the basis of the results from CBK/E and CBK/G. CBK/E and CBK/G are used independently of CFD as stand-alone models.

3. Optimization Procedure The main idea of the optimization procedure is presented in Figure1. At first, a CFD simulation is carried out with literature-taken kinetic parameters for the global kinetic-diffusion model. In the next step, CFD results provide specific input data for CBK, such as O2% volume distribution, gas temperature, wall temperature, and particle residence time. Additionally, operating pressure, fuel properties from proximate and ultimate analyses and particle size are provided. It must be mentioned that CBK can handle only monodisperse particles. Therefore only the mean particle size was investigated. The main results of interest are the reaction rate of char-O2 (obtained from CBK/E), one reaction rate as the sum of char-CO2, char-H2O, and char-H2 reactions (obtained from CBK/G), and char conversion factor due to the oxidation reaction and overall gasification reaction. Afterwards, an optimization of kinetic parameters (activation energy, pre-exponential factor, temperature exponent) is performed through the minimization of the objective function (Equation (5)). Newly obtained pre-exponential factor, activation energy, and temperature exponents are further applied into CFD. The second step of the procedure considered the Energies 2021, 14, x FOR PEER REVIEW 5 of 21 Energies 2021, 14, 1729 5 of 20

the comparison of the results with optimized kinetic parameters and non-optimized (lit- comparisonerature-taken) of the parameters results with base optimizedd on the experimental kinetic parameters data. and non-optimized (literature- taken) parameters based on the experimental data. 2 Nt,j net emp ∑ Ri,j − Ri,j xk2 Nt,jj=1 net emp  (5) OFxk ∑= j=1 Ri,j − Ri,j (xk) OF(x ) = Nt,i (5) k N net t,i where: R is the reaction rate from the complex models (CBK/E and CBK/G), xk are the net where:model Rparametersis the reaction (the pre-exponential rate from the complexfactor, activation models (CBK/E energy, andtemperature CBK/G), exponent),xk are the modelNt,j is parametersthe number (the of discrete pre-exponential time steps. factor, The activation solution energy,is obtained temperature based on exponent), the Levenberg-Nt,j is theMarquardt number offitting discrete routine. time steps. Remp The is the solution reaction is obtained rate from based the on empirical the Levenberg-Marquardt model (Equation fitting(2)). routine. Remp is the reaction rate from the empirical model (Equation (2)).

FigureFigure 1.1. OptimizationOptimization procedureprocedure ofof empiricalempirical charchar conversionconversion model. model.

ItIt isis importantimportant toto mentionmention thatthat thethe objective objective function function is is calculated calculated twice. twice. OneOne casecase considersconsiders oxidation, oxidation, whereas whereas the the second second case, case, gasification. gasification. The The reaction reaction rate rate from from CBK/E CBK/E is 2 givenis given in g/cmin g/cm-s.2-s. The The reaction reaction rate rate from from CBK/G CBK/G is is given given in in 1/s. 1/s. Therefore,Therefore, itit isis necessarynecessary 2 toto convertconvert thethe raterate intointo g/cmg/cm2-s.-s. The The following following relationship relationship has has been been applied applied [21,54]: [21,54]:   h g i ρ dp 1 Rnet = c Rnet (6) cm2s 6(1 − X) s Energies 2021, 14, x FOR PEER REVIEW 6 of 21

g ρ dp 1 Rnet = c Rnet (6) cm2s 61 - X s

where ρc is the particle density, X is the conversion degree factor. Particle density and char conversion are also obtained from the CBK/G model. The reason why this is a two-step process lies in the fact that the char-O2 reaction completely dominates the gasification pro- cess as long as the O2 concentration is greater than approximately 500 ppm [20,21]. There- fore char combustion and char gasification are considered to occur consecutively.

4. Reactor. Computational Domain The Brigham Young University (BYU) reactor is a one-stage entrained-flow reactor operated with oxygen under 1 atm (Figure 2). It is 1.8 m long and has a diameter of 0.2 m. Energies 2021, 14, 1729 6 of 20 Pulverized bituminous Utah coal was used in the investigations. The ultimate and proxi- mate analyses are presented in Table 2.

Tablewhere 2.ρ Proximatec is the particle and ultimate density, analyses X is the of conversion Utah coal [36]. degree factor. Particle density and char conversion are also obtained from the CBK/G model. The reason why this is a two-step Proximate Analysis, % as Received process lies in the fact that the char-O reaction completely dominates the gasification Volatile matter2 45.6 process as long as the O2 concentrationFixed carbon is greater than approximately 500 ppm 43.7 [20,21]. Therefore char combustion and charAsh gasification are considered to occur consecutively.8.3 Moisture 2.4 4. Reactor. Computational Domain Ultimate Analysis, % Dry-Ash-Free The Brigham Young UniversityC (BYU) reactor is a one-stage entrained-flow77.6 reactor operated with oxygen under 1 atmH (Figure2). It is 1.8 m long and has a diameter6.56 of 0.2 m. Pulverized bituminous UtahN coal was used in the investigations. The ultimate1.42 and proximate analyses are presented inS Table2. 0.55

FigureFigure 2. 2. BYUBYU reactor reactor [36]. [36].

TableCoal 2. Proximate was supplied and ultimate in the analyses primary of stream Utah coal with [36 ].a gas composed of O2, Ar, and H2O. The secondary stream contained only H2O. The mass flow rates with molar fractions of the gas components are presentedProximate in Analysis, Table 3. % The as Received particle size followed the Rosin- Rammler distributionVolatile where matter the mass fraction of particles of diameter 45.6 greater than d is given by: Fixed carbon 43.7 Ash 8.3 n Moistured 2.4 (7) Yd = e d Ultimate Analysis, % Dry-Ash-Free where d is the mean diameter, n is the spread parameter. C 77.6 H 6.56 N 1.42 S 0.55

Coal was supplied in the primary stream with a gas composed of O2, Ar, and H2O. The secondary stream contained only H2O. The mass flow rates with molar fractions of the gas components are presented in Table3. The particle size followed the Rosin-Rammler distribution where the mass fraction of particles of diameter greater than d is given by:

n d −( d ) Y = e d (7)

where d is the mean diameter, n is the spread parameter.

Table 3. Mass flow rates of coal and gas with molar composition for BYU reactor.

1st Stream, kg/h 26.24

O2 0.85 Ar 0.126 H2O 0.024 2nd Stream, kg/h 6.62

H2O 1 Utah Bituminous Coal, kg/h 23.88 Energies 2021, 14, 1729 7 of 20

The parameters applied in this study are presented in Table4. The kinetic parameters of devolatilization and homogeneous reactions are presented in Table5. The reactor geometry was discretized applying a 2-D axisymmetric grid consisting of approximately 100,000 rectan- gular cells. A grid independence study was carried out. For further information regarding the model please refer to the supplementary data. The numerical simulation was validated against the experimental data of Smith et al. [36] who measured gas-phase concentrations of CO, H2, and CO2 at different axial and radial locations using isokinetic probes. H2O concentration was calculated on the basis of the hydrogen elemental balance. This calculation, however, leads to an ±14% uncertainty owing to the reported uncertainty in the char ash analysis [36], especially in the flame region. Therefore, the model quality estimation with regard to the experimental data should only be performed for CO, H2, and CO2.

Table 4. Parameters used for Rosin Rammler distribution.

Min. Diameter Max. Diameter Mean Diameter Spread Parameter

dmin, µm dmax, µm d, µm n 1 85 36 1.033

Table 5. Kinetic parameters for devolatilization and gas-phase reactions (global reaction approach).

Kinetic Parameters: A—kg/s Pa, Reactions: E—J/kmol, α—No Unit Devolatilization:

A1= 42, 690 7 Vol → 0.218C7H10.61O0.87 + 0.322CH6.33 + E1= 3.71×10 0.309H2O + 0.127CO + 0.024CO2 α1= 0.246 6 x = 7, y = 10.61, z = 0.87 A2= 9.785×10 7 m = 1, n = 6.33 E2= 8.993×10 α2= 0.931 Gas-Phase Reactions: A = 4.4×1011 C H O + x−z O → xCO+ y H x y z 2 2 2 2 E = 1.25×108 [42] A = 3×108 C H O + (x − z)H O → xCO+ y +x − z
H x y z 2 2 2 E = 1.25×108 [42] A = 4.4 × 1011 C H + m O → mCO+ n H m n 2 2 2 2 E = 1.25 × 108 [42] A = 3 × 108 C H + H O → mCO+ n +1
H m n 2 2 2 E = 1.25 × 108 [42] A = 2.75 [46] CO + H O → CO + H 2 2 2 E = 8.38×107 [55] A = 2.24×1012 CO + 0.5O → CO 2 2 E = 1.67×108 [56] A = 6.8×1015 8 H2+0.5O2 → H2O E = 1.67×10 [42] β = −1

The reaction kinetics of CxHyOz and CmHn with O2 and H2O were assumed to be identical to those of light hydrocarbon molecules, such as CH4 [42]. The choice is justified because these reaction rates do not vary greatly [55,56]. Table6 presents four sets of widely applied literature-taken kinetic parameters and one set of parameters, which was obtained through the optimization procedure. Energies 2021, 14, x FOR PEER REVIEW 8 of 21

Energies 2021, 14, 1729 The reaction kinetics of CxHyOz and CmHn with O2 and H2O were assumed to be iden-8 of 20 tical to those of light hydrocarbon molecules, such as CH4 [42]. The choice is justified be- cause these reaction rates do not vary greatly [55,56]. Table 6 presents four sets of widely applied literature-taken kinetic parameters and one set of parameters, which was obtained throughTable the optimization 6. Kinetic parameters procedure. for surface reactions. Kinetic Optimized Parameters TableLiterature 6. Kinetic parametersParameters for surface reactions.Literature Literature Literature Reactions A—kg/s Pa Parameters No. 1 Based on CBK/E Parameters No. 2 Parameters No. 3 Parameters No. 4 Kinetic Parameters E—J/kmol [30] Optimizedand CBK/G Parameters [42] [15] [15] A–kg/s Pa Literature Param- Literature Param- Literature Param- Literature Param- Reactions β—No Unit BasedModels on CBK/E and E–J/kmol eters No. 1 [30] eters No. 2 [42] eters No. 3 [15] eters No. 4 [15] CBK/G Models−3 β–NoA Unit 0.052 1.298 × 10 2.3 0.005 0.005 7 8 7 7 7 C + 0.5O → CO × × 3 × × × 2 E A 6.1 0.05210 1.3241.29810 × 10 9.23 102.3 7.40.00510 0.0057.4 10 β 07 1.2338 17 07 07 C + 0.5O2 → CO E 6.1 × 10 1.324 × 10 9.23 × 10 7.4 × 10 7.4 × 10 Aβ 0.07320 0.0661.233 4.41 0.34930 0 0.0635 8 8 8 8 8 C + CO2 → 2CO E A 1.125 ×0.073210 1.385 ×0.06610 1.62 × 104.4 2.360.3493× 10 0.06351.62 × 10 8 8 8 8 8 C + CO2 → 2CO β E 1.1250 × 10 −0.2631.385 × 10 11.62 × 10 2.36 0 × 10 1.62 × 10 0 Aβ 0.07820 1.877 ×- 100.263−3 1.331 61.4840 0 0.0019 8 8 -3 8 8 8 C + H2O → CO + H2 E A 1.5 ×0.078210 1.5881.877× 10 × 10 1.47 × 101.33 3.1661.484× 10 0.00191.47 × 10 8 8 8 C + H2O → CO + H2 β E 01.5 × 10 −0.1241.588 × 10 1.47 1 × 10 3.16 0 × 10 1.47 × 10 0 β 0 - 0.124 1 0 0 5. Results 5. Results The results are divided into two parts. The first part considers the results from the The results are divided into two parts. The first part considers the results from the optimizationoptimization procedure. The The second second part part regards regards the the CFD CFD results. results. 5.1. Optimization Procedure Results 5.1. Optimization Procedure Results The results consider the optimization of kinetic parameters for the kinetic-diffusion The results consider the optimization of kinetic parameters for the kinetic-diffusion modelmodel basedbased onon thethe reaction rates obtained from from the the CBK/E CBK/E and and CBK/G CBK/G models. models. FigureFigure 3a 3a presentspresents thethe reactionreaction rates from from CBK/E CBK/E and and the the kinetic-diffusion kinetic-diffusion model model with with literature- literature- taken kinetic parameters 1 [30]. One can notice that the O consumption rate is strongly taken kinetic parameters 1 [30]. One can notice that the O2 consumption2 rate is strongly overpredictedoverpredicted by the kinetic-diffusion mode modell with with literature-taken literature-taken kinetic kinetic parameters parameters withwith respectrespect toto thethe detaileddetailed CBK/E approach, approach, especially especially up up to to2.2 2.2 ms. ms. Figure Figure 3b 3depictsb depicts optimizedoptimized reactionreaction rates of the the kinetic-diff kinetic-diffusionusion model model based based on on CBK/E CBK/E results. results. One One can can observeobserve aa relativelyrelatively reasonable agreement. agreement. The The final final coefficient coefficient of ofdetermination determination is equal is equal toto 96.1%.96.1%. In comparison with, with, e.g., e.g., intrinsi intrinsic-basedc-based char char conversion conversion models, models, the thekinetic- kinetic- diffusiondiffusion approachapproach is a a relatively relatively simple simple mode model,l, and and therefore therefore extremely extremely high high coefficients coefficients ofof determinationdetermination for this approach approach were were not not possible. possible.

(a) (b)

Figure 3. (a) Reaction rates of CBK/E and kinetic-diffusion models with literature parameters no. 1 from Table6.( b) reaction rates of CBK/E and kinetic-diffusion models with optimized kinetic parameters.

As regards the optimization of the gasification step, the first phase in the optimization process required proper estimation of the frequency factor for surface oxide desorption in the CBK/G model [21]. The CBK/G version implemented into NEA’s PC Coal lab accounts Energies 2021, 14, x FOR PEER REVIEW 9 of 21

Figure 3. (a) Reaction rates of CBK/E and kinetic-diffusion models with literature parameters no. 1 from Table 6. (b) reac- Energies 2021tion, rates14, 1729 of CBK/E and kinetic-diffusion models with optimized kinetic parameters. 9 of 20

As regards the optimization of the gasification step, the first phase in the optimiza- tion process required proper estimation of the frequency factor for surface oxide desorp- fortion an in empiricalthe CBK/G correlation, model [21]. linkingThe CBK/G the kineticversion parametersimplemented in into the NEA’s model PC with Coal the lab daf carbon contentaccounts offor the an empirical parent coal correlation, [57]: linking the kinetic parameters in the model with the daf carbon content of the parent coal [57]: 0.1Cdaf−0.64 A70 = 10 (8) A = 100.1Cdaf 0.64 (8) where A70 is the frequency factor, C70daf is coal carbon content in dry-ash-free (daf) wt.%. whereHowever, A70 is the frequency while analyzing factor, C thedaf is performance coal carbon content of CBK/G in dry-ash-free for a dataset (daf) of wt.%. 228 coals with charHowever, conversion while in analyzing the range the from performance 0% to 100%, of CBK/G a significant for a dataset scatter of 228 with coals respect with to the experimentschar conversion was in the observed. range from It concerned 0% to 100%, especially a significant low scatter and highwith respect conversion to the levels. It wasexperiments concluded was observed. that the aboveIt concerned empirical especial relationly low and only high depicted conversion the levels. overall It was tendency in theconcluded gasification that the reactivity above empirical with the relation coal rank.only depicted Therefore, the overall it was tendency suggested in the to adjustgas- all the kineticification ratesreactivity proportionally with the coal to rank. the Therefor rate of thee, it COwas desorptionsuggested to (Cadjust (O) all→ theCO) kinetic to obtain the rates proportionally to the rate of the CO desorption (C (O) → CO) to obtain the most most accurate match with experiments. As a result, instead of applying Equation (8), the accurate match with experiments. As a result, instead of applying Equation (8), the fre- frequency factor was scaled on the basis of the char conversion experiment of the Illinois quency factor was scaled on the basis of the char conversion experiment of the Illinois coal coal[58], which [58], which is close is to close that toanalyzed that analyzed in the present in the study present of Utah study coal, of was Utah based coal, on was the based on theVan VanKrevelen Krevelen diagram diagram (Figure (Figure 4). 4).

Figure 4. 4. LocationLocation of ofcoals coals in the in thevan vanKrevelen Krevelen diagram. diagram. Plot also Plot reports also reportscoal database coal databasefor CBK/G for CBK/G validation [21]. [21 ].

FigureFigure 55 presents presents the the results results of the of theCBK/G CBK/G model model with the with frequency the frequency factor obtained factor obtained from Equation (8), and with the adjusted frequency factor on the basis of the experimental Energies 2021, 14, x FOR PEER REVIEWfrom Equation (8), and with the adjusted frequency factor on the basis of the10 of experimental 21 data [58]. Judging by the results, the modified frequency factor will be further incorpo- data [58]. Judging by the results, the modified frequency factor will be further incorporated rated in the calculations. in the calculations.

Figure 5. Char conversion of the Illinois coal in a drop tube furnace. Gas temp.–1727 K, composition: Figure 5. Char conversion of the Illinois coal in a drop tube furnace. Gas temp.–1727 K, composi- tion:21% 21% CO CO2, 79%2, 79% N N2.2. Results Results ofof CBK/GCBK/G with with freq. freq. factor factor from from Equation Equation (8) (8)and and with with modified modified freq. factor. freq. factor. Figure6a presents the gasification reaction rate of CBK/G and the reaction rate of theFigure kinetic-diffusion 6a presents the model gasifica withtion literature-taken reaction rate of CBK/G parameters and the no. reaction 1 [30 ].rate Owing of the to the fact kinetic-diffusionthat the reaction model rate with from literature-taken CBK/G is actually parameters the sum no. 1 of [30]. char-CO Owing2, to char-H the fact2O, that and char-H2 therates, reaction the rate overall from gasification CBK/G is actually rate for the the sum empirical of char-CO kinetic-diffusion2, char-H2O, and char-H model2 wasrates, formulated the overall gasification rate for the empirical kinetic-diffusion model was formulated as the sum of char-CO2 and char-H2O rates. Based on the literature, the char-H2 reaction rate is generally very low compared to the other gasification reactions. Therefore its impact was neglected in the empirical model. The final gasification reaction rate for the empirical kinetic-diffusion model is therefore defined as follows:

RCO2 + H2O + H2 = RCO2 + RH2O (9)

(a) (b) Figure 6. (a) reaction rates of CBK/G and kinetic-diffusion models with literature parameters no. 1 from Table 6. (b) reac- tion rates of CBK/G and kinetic-diffusion models with optimized kinetic parameters.

The choice is relevant because at atmospheric pressures separated active sites for CO2 and H2O can be assumed and consequently, the total reaction rate can be the sum of the individual rates [59–61]. Based on Figure 6, one can notice a strong overprediction by the kinetic-diffusion model with literature-taken kinetic parameters no. 1. In such a case, the char conversion factor would be strongly overpredicted. The figure clearly indicates that applying literature kinetic parameters can lead to substantial errors. Figure 6b depicts the Energies 2021, 14, x FOR PEER REVIEW 10 of 21

Figure 5. Char conversion of the Illinois coal in a drop tube furnace. Gas temp.–1727 K, composi- tion: 21% CO2, 79% N2. Results of CBK/G with freq. factor from Equation (8) and with modified Energies 2021, 14, 1729 freq. factor. 10 of 20 Figure 6a presents the gasification reaction rate of CBK/G and the reaction rate of the kinetic-diffusion model with literature-taken parameters no. 1 [30]. Owing to the fact that the reaction rate from CBK/G is actually the sum of char-CO2, char-H2O, and char-H2 rates, as thethe sum overall of char-CO gasification2 and rate char-Hfor the empirica2O rates.l kinetic-diffusion Based on the model literature, was formulated the char-H as 2 reaction rate isthe generally sum of char-CO very low2 and compared char-H2O rates. to theBased other on the gasification literature, the reactions. char-H2 reaction Therefore rate its impact was neglectedis generally in very the low empirical compared model. to the other The finalgasification gasification reactions. reaction Therefore rate its impact for the empirical was neglected in the empirical model. The final gasification reaction rate for the empirical kinetic-diffusionkinetic-diffusion model model is is therefore therefore defined defined as follows: as follows:

RCO2 + H2O + H2 = RCO2 + RH2O (9) RCO2+H2O+H2 = RCO2 + RH2O (9)

(a) (b)

Figure 6. (a)Figure reaction 6. (a rates) reaction of CBK/G rates of CBK/G and kinetic-diffusion and kinetic-diffusion models models withwith literature literature paramete parametersrs no. 1 no.from 1 Table from 6. Table (b) reac-6.( b) reaction tion rates of CBK/G and kinetic-diffusion models with optimized kinetic parameters. rates of CBK/G and kinetic-diffusion models with optimized kinetic parameters. The choice is relevant because at atmospheric pressures separated active sites for CO2 Theand choiceH2O can is be relevant assumed becauseand consequently, at atmospheric the total reaction pressures rate separatedcan be the sum active of the sites for CO2 individual rates [59–61]. Based on Figure 6, one can notice a strong overprediction by the and H2O can be assumed and consequently, the total reaction rate can be the sum of the individualkinetic-diffusion rates [59 –model61]. Basedwith literature-taken on Figure6 ,kinetic one can parameters notice no. a strong 1. In such overprediction a case, the by the char conversion factor would be strongly overpredicted. The figure clearly indicates that kinetic-diffusionapplying literature model kinetic with parame literature-takenters can lead to kineticsubstantial parameters errors. Figure no. 6b 1.depicts In such the a case, the Energies 2021, 14, x FOR PEER REVIEW char conversion factor would be strongly overpredicted. The figure clearly11 of indicates21 that

applying literature kinetic parameters can lead to substantial errors. Figure6b depicts the optimized global model based on the results of CBK/G. In this case, a coefficient of optimizeddetermination global model is equal based to on 97.2%. the results The optimized of CBK/G. kineticIn this case, parameters a coefficient can of be deter- found in Table6. minationFigure is equal7 depicts to 97.2%. the The reaction optimized rate kinetic of char parameters oxidation can for be the found kinetic-diffusion in Table 6. model with literatureFigure 7 parametersdepicts the reaction from Table rate 6of and char CBK/E, oxidation whereas for the Figurekinetic-diffusion8 depicts themodel reaction rate withof literature char gasification parameters for from the Table kinetic-diffusion 6 and CBK/E, model whereas with Figure literature 8 depicts parameters the reaction from Table6, rateand of char for CBK/G.gasification One for can the observekinetic-diff a veryusion strongmodel impactwith literature of the appliedparameters parameters from on the Tablereaction 6, and rate.for CBK/G. In Figure One8 can the observe results a havevery strong been presentedimpact of the in applied two sub-figures parameters because the on the reaction rate. In Figure 8 the results have been presented in two sub-figures because reaction rates with literature parameters no. 3 and no. 4 are an order of magnitude smaller the reaction rates with literature parameters no. 3 and no. 4 are an order of magnitude than for parameters no. 1 and no. 2. It is clear that prior to any simulation, char conversion smaller than for parameters no. 1 and no. 2. It is clear that prior to any simulation, char conversionparameters parameters have to have becarefully to be carefully adjusted adjusted in order in order toaccurately to accurately predict predict the the behavior be- of the haviorrate of of the surface rate of reactions. surface reactions.

FigureFigure 7. Comparison 7. Comparison of char-O of char-O2 reaction2 reaction rates for rateskinetic-diffusion for kinetic-diffusion model with model4 sets of with literature 4 sets of literature parametersparameters from from Table Table 6 and6 forand CBK/E. for CBK/E.

(a) (b) Figure 8. (a) Comparison of gasification reaction rates for kinetic-diffusion model with two sets of literature parameters no. 1 and no. 2. (b) Comparison of gasification reaction rates for kinetic-diffusion model with two sets of literature param- eters no. 3 and no. 4 and for CBK/G.

5.2. CFD Results This sub-section presents the CFD results for the BYU reactor focusing on the char conversion aspect. Four sets of literature-taken kinetic parameters and one set of opti- mized parameters based on the CBK/E and CBK/G models are analyzed. Figure 9 presents the molar fraction concentrations of CO, H2, CO2, and H2O along the centerline of the BYU reactor.

Energies 2021, 14, x FOR PEER REVIEW 11 of 21

optimized global model based on the results of CBK/G. In this case, a coefficient of deter- mination is equal to 97.2%. The optimized kinetic parameters can be found in Table 6. Figure 7 depicts the reaction rate of char oxidation for the kinetic-diffusion model with literature parameters from Table 6 and CBK/E, whereas Figure 8 depicts the reaction rate of char gasification for the kinetic-diffusion model with literature parameters from Table 6, and for CBK/G. One can observe a very strong impact of the applied parameters on the reaction rate. In Figure 8 the results have been presented in two sub-figures because the reaction rates with literature parameters no. 3 and no. 4 are an order of magnitude smaller than for parameters no. 1 and no. 2. It is clear that prior to any simulation, char conversion parameters have to be carefully adjusted in order to accurately predict the be- havior of the rate of surface reactions.

Energies 2021, 14, 1729 11 of 20

Figure 7. Comparison of char-O2 reaction rates for kinetic-diffusion model with 4 sets of literature parameters from Table 6 and for CBK/E.

(a) (b)

FigureFigure 8. (a) Comparison 8. (a) Comparison of gasification of reaction gasification rates for reaction kinetic-diffusion rates for model kinetic-diffusion with two sets of literature model parameters with two sets no. 1 and no. 2. (b) Comparison of gasification reaction rates for kinetic-diffusion model with two sets of literature param- etersof no. literature 3 and no. 4 parametersand for CBK/G. no. 1 and no. 2. (b) Comparison of gasification reaction rates for kinetic- diffusion model with two sets of literature parameters no. 3 and no. 4 and for CBK/G. 5.2. CFD Results 5.2. CFD Results This sub-section presents the CFD results for the BYU reactor focusing on the char conversion aspect. Four sets of literature-taken kinetic parameters and one set of opti- This sub-sectionmized presentsparameters thebased CFD on the results CBK/E forand theCBK/G BYU models reactor are analyzed. focusing Figure on 9 the presents char conversion aspect.the Four molar sets fraction of literature-taken concentrations of CO, kinetic H2, CO parameters2, and H2O along and the one centerline set of optimized of the BYU parameters basedreactor. on the CBK/E and CBK/G models are analyzed. Figure9 presents

Energiesthe molar 2021, 14, x fractionFOR PEER REVIEW concentrations of CO, H2, CO2, and H2O along the centerline12 of 21 of the

BYU reactor.

(a) (b)

(c) (d)

Figure 9. CFD results (a) CO, (b) H2, (c) CO2 and (d) H2O mole fraction distribution along the centerline for five different Figuresets of 9. kineticCFD parameters. results (a) CO, (b) H2,(c) CO2 and (d)H2O mole fraction distribution along the centerline for five different sets of kinetic parameters. An extreme impact of the applied char conversion kinetic parameters on the overall gas composition can be observed. One can notice that the slope of the curves varies in the An extreme impactreforming of the zone applied which corresponds char conversion to the strength kinetic of the gasification parameters reactions. on Judging the overall gas composition canby be Figures observed. 7 and 8, Onethe second can set notice of kinetic that parameters the slope provides of the highest curves reaction varies rate. in the reforming zone whichAs correspondsa result, in Figure to9 for the the second strength set of ofkinetic the parameters gasification the CO reactions. and H2 mole fraction Judging by curves have the highest slopes in the reforming zone and consequently, the highest Figures7 and8, the secondamount setof CO of and kinetic H2 produced, parameters while they provides have the lowest the amount highest of CO reaction2 and H2O. rate. As As for the third set of kinetic parameters, the gasification rate is the slowest (Figures 7 and 8), a result, in Figure9 for the second set of kinetic parameters the CO and H 2 mole fraction hence the lowest slope of the CO mole fraction curve in the reforming zone can be ob- curves have the highestserved slopes and the in smallest the reforming amount of the zone final andCO produced. consequently, One can notice the highestthat the opti- amount of CO and H2 produced,mized whilekinetic parameters they have and thethe fourth lowest set of amount literature-taken of CO parameters2 and H are2O. the Asmost for the third set of kinetic parameters,accurate ones with the respect gasification to the experimental rate is theresults. slowest The phenomenon (Figures that7 anda given8), set hence of data can be fitted equally well by more than one pair of kinetic parameters is referred the lowest slope of theto as CO the molecompensation fraction effect. curve This was in already the reforming mentioned by zone [62–66]. can The be impact observed of gas- and the smallest amountification of the reactions final CO is less produced. pronounced Onein the lean can zone notice and at that the beginning the optimized of the flame kinetic zone where devolatilization and char oxidation prevail. However, the contribution of these reactions in these zones is also non-negligible. Figure 10 depicts the devolatilization process of particles with 6 representative diameters. For clarity, each sub-figure consists of 50 particles. A considerable influence of the particle diameter on the onset of devolati- lization and the overall time of devolatilization can be observed. The sooner the volatiles are released, the sooner the surface reactions begin to occur. One can notice that the axial distance for which the volatiles are released varies from x = 0.2 m to x = 0.5 m. Therefore, different kinetics of the surface reactions will result in different strength of the surface Energies 2021, 14, 1729 12 of 20

parameters and the fourth set of literature-taken parameters are the most accurate ones with respect to the experimental results. The phenomenon that a given set of data can be fitted equally well by more than one pair of kinetic parameters is referred to as the compensation effect. This was already mentioned by [62–65]. The impact of gasification reactions is less pronounced in the lean zone and at the beginning of the flame zone where devolatilization and char oxidation prevail. However, the contribution of these reactions in these zones is also non-negligible. Figure 10 depicts the devolatilization process of particles with 6 representative diameters. For clarity, each sub-figure consists of 50 particles. A Energies 2021, 14, x FOR PEER REVIEW considerable influence of the particle diameter on the onset of devolatilization and the13 of 21

overall time of devolatilization can be observed. The sooner the volatiles are released, the sooner the surface reactions begin to occur. One can notice that the axial distance for which the volatiles are released varies from x = 0.2 m to x = 0.5 m. Therefore, different kinetics of reactionsthe surface in this reactions region. will As result a result, in different different strength amounts of the of surface CO, H reactions2, CO2, and in this H2 region.O are to be expected.As a result, Judging different by Figure amounts 10a–c, of CO, it is H also2, CO evident2, and H that2O arefor tosmaller be expected. particles Judging recirculation by is muchFigure more 10a–c, intense. it is also evident that for smaller particles recirculation is much more intense.

FigureFigure 10. Particle 10. Particle tracks tracks of volatiles of volatiles mass mass fraction fraction for for the the optimized optimized kinetic-diffusion kinetic-diffusion modelmodel during during devolatilization devolatilization of of 50 particles50 particles for 6 representative for 6 representative diameters diameters (a) 1 (µm,a) 1 µ (m,b) (17b) µm, 17 µ m,(c)( cmean-36) mean-36 µm,µm, ( (dd)) 51 51 µm,µm, ((ee)) 75 75µ µm,m, (f )(f 85) 85µm. µm. Judging by Figure 11, the applied kinetic parameters have also a non-negligible effect Judging by Figure 11, the applied kinetic parameters have also a non-negligible effect on the temperature distribution inside the reactor. Due to more intensive gasification on reactionsthe temperature for the literature distribution parameters inside the no. reac 2 andtor. no. Due 3, to because more ofinte theirnsive endothermic gasification re- actionscharacter, for the the literature temperature parameters is substantially no. 2 lower,and no. especially 3, because in the of reformingtheir endothermic zone, where charac- ter,gasification the temperature reactions is dominate.substantially lower, especially in the reforming zone, where gasifi- cation reactions dominate.

Figure 11. CFD results: temperature distribution along the centerline for five different sets of ki- netic parameters. Energies 2021, 14, x FOR PEER REVIEW 13 of 21

reactions in this region. As a result, different amounts of CO, H2, CO2, and H2O are to be expected. Judging by Figure 10a–c, it is also evident that for smaller particles recirculation is much more intense.

Figure 10. Particle tracks of volatiles mass fraction for the optimized kinetic-diffusion model during devolatilization of 50 particles for 6 representative diameters (a) 1 µm, (b) 17 µm, (c) mean-36 µm, (d) 51 µm, (e) 75 µm, (f) 85 µm.

Judging by Figure 11, the applied kinetic parameters have also a non-negligible effect on the temperature distribution inside the reactor. Due to more intensive gasification re- actions for the literature parameters no. 2 and no. 3, because of their endothermic charac- Energies 2021, 14, 1729 13 of 20 ter, the temperature is substantially lower, especially in the reforming zone, where gasifi- cation reactions dominate.

FigureFigure 11. 11. CFDCFD results: results: temperature temperature distribution distribution along along the centerline the centerline for five for different five different sets of setski- of netickinetic parameters. parameters.

Table7 presents the char conversion factor results for the kinetic-diffusion model with kinetic parameters from Table6. As was already mentioned, CBK/E and CBK/G models can handle only monodisperse particles. Therefore the optimized kinetic parameters inherently correspond to the mean particle diameter. On this basis, Table7 regards both the mean particle diameter comparison and all particle fractions with regard to the experiment. Judging by the results, the optimized kinetic parameters for the mean particle diameter are in excellent agreement with the experiment. Char conversion factors for all particle fractions for the optimized parameters and literature parameters no. 4 are in close agreement with the experiment. Future enhancement of CBK/E and CBK/G models to account for polydisperse particles would improve the accuracy of simulations, providing more exact reaction rates. As a result, optimized kinetic parameters would directly correspond to all particle fractions.

Table 7. CFD results: char conversion degree for surface reaction model with different kinetic parameters with regard to experiments.

Char Conversion Degree % Simulation Results Simulation Results Experiment Mean Particle Diameter All Particle Fractions All Particle Fractions 36 µm 1–85 µm 1–85 µm Literature parameters 1 100% 100% Optimized parameters 83% 77% Literature parameters 2 100% 99% 82% Literature parameters 3 27% 59% Literature parameters 4 80% 74%

The accuracy of the optimization procedure for the axial in-reactor gas composition (Figure9) has been additionally assessed with error analysis. A maximum and average value of absolute errors for non–optimized and optimized models are presented. The absolute error is defined as:

∆e = xexp − xnum (10)

where xexp and xnum are the experimental and numerical values of the specific variables (e.g., CO/H2/CO2/H2O mole fraction), respectively. Table8 presents the quantitative assessment of the procedure. Judging by the results, the application of the modified parameters and literature parameters no. 4 results in one of the lowest errors with respect to the experimental data. Energies 2021, 14, 1729 14 of 20

Table 8. Error analysis of CO, H2, CO2 and H2O concentration along the centerline (Figure9).

Kinetic CO H CO H O Parameters 2 2 2 Max ∆e Av. ∆e Max ∆e Av. ∆e Max ∆e Av. ∆e Max ∆e Av. ∆e (%) (%) (%) (%) (%) (%) (%) (%) Lit. parameters 1 17.91 6.74 12.80 7.89 10.22 5.87 16.82 11.84 Mod. parameters 18.48 4.82 7.95 5.47 10.15 4.72 20.22 9.58 Lit. parameters 2 20.20 7.94 14.40 8.98 10.15 5.98 19.73 13.04 Lit. parameters 3 11.11 5.71 11.36 7.51 10.14 5.38 19.24 10.35 Lit. parameters 4 12.50 4.90 8.33 5.40 10.16 4.77 20.68 8.99

Figures 12–14 present molar fraction gas concentrations along radial traverses for axial distances x = 0.13 m, x = 0.20 m, x = 0.28 m, x = 0.34 m, x = 0.51 m, x = 0.81 m, x = 1.12 m and x = 1.73 m. These traverses are visualized in Figure 15. In most cases, the model results Energies 2021, 14, x FOR PEER REVIEW 15 of 21 with the optimized kinetic parameters are in closest agreement with experimental data. As mentioned, H2O mole fraction results are calculated from hydrogen balance and should not

Energies 2021, 14, x FOR PEER beREVIEW considered as credible reference data. The impact of the applied parameters15 onof 21 the radial ondistribution the radial is distribution less substantial is less than substantial for the axial than distribution. for the axial This distribution. observation This is observa- sensible tionbecause is sensible the gasification because reactionsthe gasification that dominate reactions the that reforming dominate zone the proceed reforming axially zone along pro- withceedon axially the the mainstream. radial along distribution with Another the is mainstream.less observationsubstantial Another than regards for theobservation theaxial changesdistribution. regards in radialThis the observa- concentration.changes in ra- dialOne tionconcentration. may is noticesensible that because One from may the the gasification notice axial distancethat re actionsfrom x the =that 0.51 axial dominate m, distance the the molar reforming x = distribution 0.51 m,zone the pro- molar of species dis- tributionstabilizesceed axiallyof in species the along radial stabilizes with direction. the mainstream. in the There radial areAnother di insignificantrection. observation There changes regardsare insignificant inthethe changes yield. changes in Thisra- means in the yield.thatdial after This concentration. the means devolatilization that One after may noticethe process, devolatilization that gasificationfrom the axial process, reactions,distance x gasification= which0.51 m, beginthe molarreactions, to dominatedis- which in beginthe reformingtribution to dominate of species zone, in arestabilizes the radially reforming in the uniform. radial zone, direction. Onare theradially There other are uniform. hand, insignificant substantial On changesthe other changes in the hand, in sub- the yield. This means that after the devolatilization process, gasification reactions, which stantialradial direction changes (Figures in the radial 12 and direction 13) for the (Figures axial distances 12 and 13) x < for 0.51 the m axial can be distances observed. x These< 0.51 begin to dominate in the reforming zone, are radially uniform. On the other hand, sub- mchanges canstantial be are observed. changes most abrupt in These the radial up changes to direction the radialare (Figures most distance abrupt 12 and 0.04 up13) m tofor wherethe the radialaxial the distances boundarydistance x <0.04 0.51 of the m where flame theis located boundarym can (Figurebe observed. of the 16 ).flame These changesis located are (Figuremost abrupt 16). up to the radial distance 0.04 m where the boundary of the flame is located (Figure 16).

FigureFigure 12.15. Map15. Map of of8 radial8 radial traverses traverses in in axisymmetric axisymmetric BYU BYU reactor. reactor.

Figure 13.FigureCFD 12. results: CFD results: CO, HCO,2, COH2, CO2 and2 and H H2O2O molemole fraction fraction distribution distribution along along the radial the traverse radial traversex = 0.13 m, x x == 0.20 0.13 m m, and x = 0.20 m and x = 0.28x = 0.28 m for m for five five different differentsets sets of kinetic kinetic parameters. parameters.

Figure 12. CFD results: CO, H2, CO2 and H2O mole fraction distribution along the radial traverse x = 0.13 m, x = 0.20 m and x = 0.28 m for five different sets of kinetic parameters.

Energies 2021, 14, x FOR PEER REVIEW 15 of 21

on the radial distribution is less substantial than for the axial distribution. This observa- tion is sensible because the gasification reactions that dominate the reforming zone pro- ceed axially along with the mainstream. Another observation regards the changes in ra- dial concentration. One may notice that from the axial distance x = 0.51 m, the molar dis- tribution of species stabilizes in the radial direction. There are insignificant changes in the yield. This means that after the devolatilization process, gasification reactions, which begin to dominate in the reforming zone, are radially uniform. On the other hand, sub- stantial changes in the radial direction (Figures 12 and 13) for the axial distances x < 0.51 m can be observed. These changes are most abrupt up to the radial distance 0.04 m where the boundary of the flame is located (Figure 16).

Figure 12. Map of 8 radial traverses in axisymmetric BYU reactor.

Energies 2021, 14, 1729 15 of 20

Figure 13. CFD results: CO, H2, CO2 and H2O mole fraction distribution along the radial traverse x = 0.13 m, x = 0.20 m and x = 0.28 m for five different sets of kinetic parameters.

Energies 2021, 14, x FOR PEER REVIEW 16 of 21 Energies 2021, 14, x FOR PEER REVIEW 16 of 21 Energies 2021, 14, x FOR PEER REVIEW 16 of 21

Figure 13. CFD results: CO, H2, CO2 and H2O mole fraction distribution along the radial traverse x = 0.34 m, x = 0.51 m and FigureFigure 14. 14.CFD CFD results: results: CO,CO, HH22, CO CO22 andand H H2O2O mole mole fraction fraction distribution distribution along along the theradial radial traverse traverse x = 0.34 x = m, 0.34 x = m, 0.51 x =m 0.51 and m Figure 13. CFD results: CO, H2, CO2 and H2O mole fraction distribution along the radial traverse x = 0.34 m, x = 0.51 m and x =x 0.81= 0.81 m m for for five five different different sets sets of of kinetic kinetic parameters. parameters. andx x= =0.81 0.81 m m for for five five different different sets sets of kinetic of kinetic parameters. parameters.

FigureFigure 15. 14. CFD CFD results: results: CO, CO, H H2,2 ,CO CO2 2and and H H2O2O molemole fractionfraction distributiondistribution along the radial traversetraverse xx == 1.121.12 mm and and x x = = 1.74 1.74 Figure 15.14. CFD results:results: CO,CO, HH22,, COCO22 andand HH22OO molemole fractionfraction distributiondistribution along along the the radial radial traverse traverse x =x 1.12= 1.12 m m and and x =x 1.74= 1.74 m m for five different sets of kinetic parameters. form form five forfive different five different different sets sets of sets kineticof ofkinetic kinetic parameters. parameters. parameters.

FigureFigure 16. 16. CFD CFD results: results: contourcontour plotplot ofof temperature with axial andand radialradial distances.distances. Figure 16. CFD results: contour contour plot of temperat temperatureure with axial and radial distances.

FigureFigure 17 17 showsshows thethe contourcontour plots of temperature, CO,CO, HH22,, andand COCO22 molemole fractions, fractions, 2 2 whilewhileFigure Figure Figure 17 18 18 shows presents presents the the thecontour contourcontour plots plots of of temperature, H2O, O22 molemole CO, fractions,fractions, H , and andand CO the the moledevolatiliza- devolatiliza- fractions, whiletiontion reaction reactionFigure 18rate. rate. presents Five Five regions regions the contour cancan bebe noticedplotsnoticed of inH the2O, reactor:O2 mole thethe fractions, leanlean zone, zone, and the the the recirculation recirculation devolatiliza- tionzone,zone, reaction the the flame flame rate. zone, zone, Five the the regions post-flamepost-flame can be zone, noticed and in the the reforming reactor: the zone.zone. lean InIn the zone,the lean lean the zone, zone, recirculation equiv- equiv- alence ratios are lower than stoichiometric conditions, which corresponds to high O2 con- zone,alence the ratios flame are zone, lower the than post-flame stoichiometric zone, and conditions, the reforming which correspondszone. In the lean to high zone, O2 equiv-con- tent (Figure 18b). This zone is mainly composed of O2 and H2O, which are introduced in alencetent (Figure ratios 18b).are lower This thanzone stoichiometricis mainly composed conditions, of O2 andwhich H2 O,corresponds which are introducedto high O2 con-in the primary and secondary streams. The flame zone begins downstream of the lean zone, tentthe primary(Figure 18b). and secondary This zone streams.is mainly The composed flame zone of Obegins2 and downstreamH2O, which ofare the introduced lean zone, in the primary and secondary streams. The flame zone begins downstream of the lean zone, Energies 2021, 14, 1729 16 of 20

Figure 17 shows the contour plots of temperature, CO, H2, and CO2 mole fractions, while Figure 18 presents the contour plots of H2O, O2 mole fractions, and the devolatiliza- Energies 2021, 14, x FOR PEER REVIEW tion reaction rate. Five regions can be noticed in the reactor: the lean zone, the recirculation17 of 21 zone, the flame zone, the post-flame zone, and the reforming zone. In the lean zone, equivalence ratios are lower than stoichiometric conditions, which corresponds to high O2 content (Figure 18b). This zone is mainly composed of O2 and H2O, which are introduced reachingin the primary very high and secondarytemperatur streams.es–3000 The K—owing flame zone to begins the downstreamhigh O2 content of the in lean the zone, primary stream.reaching CO very and high H2 content temperatures–3000 are relatively K—owing low. In to the the post-flame high O2 content zone, in which the primary follows the flamestream. zone, CO the and temperatures H2 content are are relatively lower than low. in In the the flame. post-flame This zone, region which is also follows characterized the flame zone, the temperatures are lower than in the flame. This region is also character- by a very rich mixture. CO and H2 are mainly formed in this region because of the com- binedized effect by a very of the rich water–gas mixture. COshift and reaction H2 are and mainly the formed gasification in this reactions. region because The next of the zone is combined effect of the water–gas shift reaction and the gasification reactions. The next dominated by reforming reactions. In this region, there are lower temperatures, extremely zone is dominated by reforming reactions. In this region, there are lower temperatures, small gradients, and low conversion rates. CO and H2 continue to increase slowly ap- extremely small gradients, and low conversion rates. CO and H2 continue to increase proachingslowly approaching the equilibrium the equilibrium conditions. conditions. The last The region last region is characterized is characterized by a by strong a strong recircu- lationrecirculation of the gas of and the gascoal and particles, coal particles, the recirculation the recirculation zone. zone. This Thisis located is located between between the lean, flame,the lean, post-flame flame, post-flame zones and zones the reactor and the reactorwall. wall.

FigureFigure 17. CFD 17. CFD results, results, contours contours for for the the optimized optimized kinetic parameters:parameters: (a ()a temperature) temperature (K), (K), (b) CO(b) moleCO mole fraction, fraction, (c)H2 (c) H2 molemole fraction, fraction, (d) CO (d) CO2 mole2 mole fraction. fraction. EnergiesEnergies 2021,2021 14, x, 14 FOR, 1729 PEER REVIEW 17 of 2018 of 21

FigureFigure 18. CFD 18. CFD results: results: contours contours for for the the optimized optimized kinetic parameters:parameters: (a ()Ha) 2HO2O mole mole fraction, fraction, (b)O (b2 )mole O2 mole fraction, fraction, (c) (c) devolatilizationdevolatilization rate rate (kmol/m (kmol/m3s).3 s).

6. Conclusions6. Conclusions AnAn optimization optimization procedureprocedure for thefor empiricalthe empiri charcal conversion char conversion kinetic-diffusion kinetic-diffusion model, based on the detailed CBK/E and CBK/G models, was presented. The numerical model model, based on the detailed CBK/E and CBK/G models, was presented. The numerical was validated against the experimental data from the BYU gasifier. The BYU reactor modelreference was measurementsvalidated against are suitable the experimental for this purpose data sincefrom in-reactorthe BYU measurementgasifier. The BYU data reac- torare reference available measurements which is vital when are one suitable considers for thethis credible purpose and since effective in-reactor assessment measurement of the datapredictive are available capabilities which of is the vital CFD when model. one The co followingnsiders the main credible conclusions and effective can be drawn: assessment of •the Thepredictive optimization capabilities procedure of investigatedthe CFD model. in the currentThe following allows enhancing main conclusions the modeling can be drawn:strategy by obtaining adjusted kinetic parameters of the kinetic-diffusion model only • Thefor optimization the specific operating procedure conditions. investigated in the current allows enhancing the model- • ingThe strategy use of theby obtaining optimization adjusted procedure kinetic resulted parameters in a better of agreementthe kinetic-diffusion between the model model results and the experimental data in terms of the gas composition and char only for the specific operating conditions. conversion factor. In order to further improve the accuracy of the procedure, future • Theresearch use of should the optimization consider the application procedure of resu the intrinsic-basedlted in a better char agreement conversion modelsbetween the modelwith Langmuir-Hinshelwoodresults and the experimental (LH) kinetics. data in terms of the gas composition and char • conversionThe applied factor. kinetic In parametersorder to further of char-oxidation improve the and accuracy char-gasification of the procedure, reactions future researchproved should to have consider a significant the application impact in the of gasificationthe intrinsic-based process simulations.char conversion The mod- elsmajor with effect Langmuir-Hinshelwood could be observed on the(LH) final kinetics. gas composition and the char conversion • Thefactor, applied but also kinetic on the parameters gas composition of char-oxidation in the flame zone. and char-gasification reactions proved to have a significant impact in the gasification process simulations. The major effect could be observed on the final gas composition and the char conversion factor, but also on the gas composition in the flame zone. • Due to the versatile character of the method, the presented optimization procedure can be applied in other areas of interest, provided that both complex and simple mod- els are available. Energies 2021, 14, 1729 18 of 20

• Due to the versatile character of the method, the presented optimization procedure can be applied in other areas of interest, provided that both complex and simple models are available.

Supplementary Materials: The following are available online at https://www.mdpi.com/1996-107 3/14/6/1729/s1. Author Contributions: Conceptualization: J.M., N.M.; Funding acquisition: J.M.; Investigation: J.M.; Methodology: J.M.; Project administration: N.M.; Software: N.M.; Supervision: N.M.; Visualization: J.M.; Writing—original draft: J.M.; Writing—review and editing: N.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Science Center (Poland) as part of Preludium 15 under the project designated with the number 2018/29/N/ST8/00799. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: Calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing, grant No. 492. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

BYU Brigham Young University CBK Carbon burnout kinetic model CBK/E Carbon burnout kinetic model for oxidation CBK/G Carbon burnout kinetic model for gasification CFD Computational fluid dynamics C2SM Competing two-step reaction model Daf Dry-ash-free DNS Direct numerical simulation FG-DVC Functional-group, depolymerization, vaporization, cross-linking model LES Large eddy simulation LH Langmuir-Hinshelwood kinetics RANS Reynolds averaged Navier-Stokes equations SIMPLE Semi-implicit method for pressure linked equations WSGG Weighted sum of gray gas model

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