Optimizing in-situ char gasification kinetics in reduction zone of pulverized coal air-staged combustion

Combustion and Flame 194 (2018) 52–71

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Optimizing in-situ char gasification kinetics in reduction zone of pulverized coal air-staged combustion Denggao Chen, Zhi Zhang, Zhenshan Li∗, Zian Lv, Ningsheng Cai Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 22 August 2017 Revised 17 January 2018 Accepted 12 April 2018

Keywords: Staged combustion Electric-heated down-firing furnace Char gasification kinetics CFD-aided optimization

a b s t r a c t Reliable kinetics of char gasification are of great importance for accurate prediction of the reductive atmosphere in air-staged combustion of pulverized coal, which is critical in controlling nitrogen and sulfur species for the optimized design and operation of boilers and burners. In this study, a new method of obtaining char gasification kinetics from realistic air-staged combustion experiments is proposed. Firstly, a real combustion atmosphere, including the temperature and concentration fields of air-staged combustion in an actual boiler, is simulated in an electric-heated down-firing furnace by controlling the stoichiometric ratio of air to coal. In-situ char gasification is observed by obtaining gas and solid reaction data from staged combustions with stoichiometric ratios in the range of 0.6–0.9 at temperatures of 120 0–140 0 °C. Secondly, a detailed char combustion/gasification model with emphasis on coupling between the discrete phase and gas phase is developed and verified. The single film model based on nth order Arrheniustype equations is used in the char combustion/gasification model, with consideration of particle boundary layer diffusion. The effect of reduced reactivity of the char at high degrees of conversion is included in the kinetic model. Thirdly, the in-situ char gasification kinetics are determined via a CFD-aided rigorous mathematical optimization process. A direct search algorithm is used to accelerate the optimization process. Finally, the determined kinetics are verified at wide ranges of temperatures, residence times, and stoichiometric ratios. Compared with char gasification kinetics from ex-situ char gasification experiment using the same coal, it is demonstrated that the kinetics of in-situ char gasification are very different from kinetics derived from ex-situ char gasification experiment. Therefore, reliable kinetics of in-situ gasification are necessary when predicting the fuel conversion and gas phase species in modern air-staged pulverized coal combustion boilers. © 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Abbreviations

1. Introduction

CFD DTF E-DFF EFR LCV OFA RMSE TGA UDF

The design goal of low-NOx pulverized coal combustion application is to produce region of fuel rich zone that is depleted in O2 so that a subset of the formed NOx can be reduced [1–3]. A proven and widely used technique is air-staged combustion, which divides the furnace into three reaction zones: the main combustion zone, reductive zone, and burnout zone. In the main combustion zone, the supplied air is less than the theoretical amount for coal burnout; thus, the oxygen in the air is consumed rapidly by volatile combustion and char oxidation. In the reductive zone, char oxidation with O2 is replaced by gasification with CO2 and H2 O, producing the reductive gases of CO and H2 . This reductive atmosphere has a strong relationship with NOx reduction [4], H2 S high-temperature corrosion of water-wall [5,6], and slagging [7,8]. Therefore, predicting the reductive gases in air-staged combustion is of huge significance.

∗

computational fluid dynamics drop tube furnace electric-heated down firing furnace entrained flow reactor Low calorific value of coal (J kg−1 ) over fired air root mean squared error thermo-gravimetric analysis user defined function

Corresponding author. E-mail addresses: [email protected], [email protected] (Z. Li).

https://doi.org/10.1016/j.combustflame.2018.04.015 0010-2180/© 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

Nomenclature Aj Ap,k Ashcoal Ashsample C¯i C0 cp D0, i Di,k dp,k dp,0 dp,HTPy dp,Com. d¯p,HT Py d¯p,0 E ET Fother fw,0 fmin fp H HR h0i hi hk Ji kCon kc,k,j kSurf. kPy kTur MWr m mm mchar mp,k nn dmp,k,j mp,k,0 mvol ni,j P Pg,i Pr Ps,i R Re Ri

pre-exponential factor for reaction j (kg m−2 s−2 Pa−n ) particle external surface area of particle size k (m2 ) ash fraction of the raw coal (wt%) ash fraction of the sample (wt%) averaged molar concentration of species i (mol m−3 ) diffusion constant heat capacity of particle (J kg−1 ) diffusion coefficient of species i diffusional reaction rate coefficient of species i of particle size k particle diameter of particle size k (m) initial coal particle diameter (m) particle diameter after high temperature pyrolysis (m) particle diameter in combustion or gasification (m) average size of particle after high temperature pyrolysis (m) average size of initial particle (m) activation energy (J mol−1 ) total energy (J) Other interaction forces water mass fraction of initial coal particle objective function heat fraction absorbed by particle mass fraction of H in ultimate analysis of coal (wt%, daf) reaction heat (J kg−1 ) heat of formation of species i (J mol−1 ) sensible enthalpy of species i (J mol−1 ) convection heat transfer coefficient for particle size k (W m−2 K−1 ) diffusion flux of species i (kg m−2 s−1 ) heat conductivity (W m−1 K−1 ) chemical reaction rate of char reaction j for particle size k (kg m−2 s−1 Pa−1 ) surface reaction rate (kg m−2 s−1 ) pyrolysis rate (kg kg−1 s−1 ) turbulence kinetic energy molecular weight of reactant (r = R) and product (r = P) (kg kmol−1 ) exponent factor for coal conversion correlation model exponent factor for particle size model mass fraction of char in raw coal particle mass of particle size k (kg) exponent factor for particle density model Particle mass change due to reaction j (kg) initial particle mass of size k (kg) mass fraction of volatile in raw coal reaction order of species i in reaction j pressure (Pa) partial pressure of species i in the bulk gas (Pa) Prandtl number partial pressure of species i on the particle surface (Pa) universal gas constant (8.314 J mol−1 K−1 ) Reynolds number net rate of production of species i by gas phase reaction (kg m−3 s−1 )

RCO2 /CO r¯ j,k S

SR SR1 SRr,i

TExp . Tp Tg vf Tp, k Tr up,k v wj XChar XCoal,k XHTPy x Yi Yd p,k Y¯r y z

h x mp, k mp, k, j m˙ p,k,0

t

production ratio of CO2 to CO in char oxidation averaged gas phase chemical reaction rate of reaction j for particle size k source term for mass (Sm ), momentum (Smv ), species (Si ), radiation heat (Srad ), reaction heat (Sh,r ), and particle heat source (Sh ) stoichiometric ratio of air to coal stoichiometric ratio of air to coal of the main combustion zone stoichiometric ratio in terms of mass for reaction j (drying, pyrolysis, oxidation, gasification) of species i (water, volatile, O2 , CO2 , CO, H2 ) experiment temperature (◦ C) particle temperature (K) gas temperature (K) volume fraction particle temperature for particle size k (K) gas radiation temperature (K) particle velocity of particle size k (m/s) velocity (m s-1 ) mixing rate of reaction j char conversion fraction (wt%, daf) coal conversion fraction for particle size k (wt%, daf) coal conversion after high temperature pyrolysis (wt%, daf) number of carbon atom in one pseudo volatile species species mass fraction (kg kg−1 ) Volume fraction of particle size larger than dp, k averaged species mass fraction (kg kg−1 ) (r = R, reactant; r = P, product) number of hydrogen atom in one pseudo volatile species number of oxygen atom in one pseudo volatile species reaction heat of volatile (x = vol), char (x = char), CO2 gasification (x = CO2 ) and HO gasification (x = H2 O) (J kg−1 ), particle mass change in the calculated cell (kg) particle mass change due to reaction j for particle size k (kg) initial particle mass flow rate at the injection point of particle size k (kg s−1 ) time step (s)

Greek symbols α HTPy coal swelling factor after high temperature pyrolysis β temperature exponent t time(s) ρ gas density (kg m−3 ) ρ p, k particle density of size k (kg m−3 ) εp particle emissivity ε dissipation rate σ Stephan-Boltzmann number (W m−2 K−4 ) λ gas thermal conductivity (W m−1 K−1 ) μ fluid viscosity (Pa s) τ¯¯ stress tensor υi diffusion volume for species i υ r stoichiometric constant of reactant r υ  r stoichiometric constant of product r  mechanical factor σi,N2 binary pair characteristic length

53

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D. Chen et al. / Combustion and Flame 194 (2018) 52–71

D

diffusion collision integral.

Subscripts 0 initial CO carbon monoxide CO2 carbon dioxide H2 hydrogen H2 O water i index for species i j index for reaction j k index for particle size k P product p particle R reactant s particle surface From a modeling point of view, few studies have focused on the role of gasification reactions in air-staged combustion systems. Most modeling studies on air-staged combustion only consider the char oxidation and neglect gasification [9–18], meaning that the reducing atmosphere in the reduction cannot be predicted accurately. Recently, char gasification has gained attention in the field of oxy-fuel combustion conditions with high concentrations of CO2 and H2 O. Hecht et al. [19] found that char gasification can enhance char conversion and moderate the particle temperature. Chen et al. [20] reported that char consumption can be increased by gasification reactions depending on particle temperature and oxygen concentration. Kim et al. [21] claimed that gasification may result in a decrease in particle temperature of up to 220 K, and a similar finding was reported by Niu and Shaddix [22]. In the field of entrained flow gasification, many works have focused on gasification conditions at high pressures and high syngas concentrations [23– 28]. However, the effect of char gasification in air-staged pulverized fuel combustion system is not well known. Previous works on gasification are mostly based on thermal gravimetric analysis (TGA) [29–32], fixed beds [33–35], and fluidized beds [36–38], which use ex-situ char and entail low heating rates and the concentrations of the gasification agents such as CO2 and H2 O are unchanged in the reaction gas. Drop tube furnaces (DTFs) or entrained flow reactors (EFRs) have been used for pulverized coal combustion research, as they provide similar reaction conditions to those of practical systems while eliminating the effect of turbulence. Few studies have attempted to determine gasification kinetic parameters from EFR experiments. Goetz et al. [39], Dershoewitz [40], Kajitani et al. [28], and Gonzalo-Tirado et al. [41] derived gasification kinetics from DTF gasification experiments. In summary, the gasification works in the literatures all use ex-situ chars in their gasification experiments. Ex-situ char is prepared by different approaches: a. Ex-situ char 1: Raw coal is injected into pyrolysis facility in inert atmosphere, and the generated char samples are cooled and collected for gasification experiments in another reactor. b. Ex-situ char 2: The char is firstly prepared with inert or gasification agents such as CO2 or H2 O, and then tested in gasification experiment without cooling in one reactor [36,37,41,42]. It is well known that the preparation condition has a large effect on the gasification reactivity of char [29,43], and most of the published studies used fresh char as the sample and diluted CO2 or H2 O as the gasification agent. All the ex-situ chars are rather different from the in-situ chars in the reductive zone of an actual boiler. In actual boiler, char particles are produced in high heating rate pyrolysis and then experience an initial oxidizing stage with O2 . Oxidation of O2 consumes amorphous carbon with higher reactivity compared with the remaining graphite carbon, leading to a decrease in char gasification reactivity [44] in the reduction zone. At the same time, the particle temperature

fluctuates because of char burning in the main combustion zone. It has been reported [45] that the temperature/heat history has a significant effect on char reactivity, and the thermal annealing effect will result in lower reactivity. Whether kinetic data derived from ex-situ char can give an acceptable prediction for in-situ char gasification is not clear. Apart from the difference in char characteristics, the gasification gas condition in previous works is also different from actual boiler. In air-staged combustion, gasification agents of CO2 and H2 O in the reduction zone come from the oxidation of volatile and char with O2 in the main combustion zone. Gasification reactions towards H2 O and CO2 in the reduction zone occurs simultaneously, and both the concentrations of reactants (CO2 /H2 O) and products (CO/H2 ) vary when gasification proceeds. The gasification reaction will be inhibited by products of CO and H2 [46,47]. However, in previous works, single gasification agent, CO2 or H2 O, with the dilution of inert gas, N2 or Ar, is used for gasification experiment. Kinetics for CO2 gasification and H2 O gasification were separately derived from separate experiments. The kinetics of char gasification in gas mixture of CO2 and H2 O do not equal to the sum of the two pure-gas reaction rates [48]. Besides, the prediction of gasification products of CO and H2 has not been verified. Therefore, it is necessary to study the gasification behavior and derive reliable kinetics of in-situ char that has been prepared in the same atmosphere and temperature with the real conditions of actual airstaged combustion of pulverized coal. The objective and insight of this study are obtaining the reliable gasification kinetics of in-situ char under real conditions of air-staged combustion, aiming at providing parameters for the CFD modeling of air-staged combustion of pulverized coal in order to accurately predict the reducing atmosphere such as CO and H2 . Firstly, an electric-heated down-firing furnace (E-DFF) is designed to simulate the air-staged combustion of an actual boiler, thus investigates the in-situ char gasification in realistic conditions. The in-situ char gasification is achieved in two aspects: On the one hand, char entering reductive zone is generated with the same reaction process and temperature history of an actual boiler. On the other hand, instead of feeding inert gas diluted CO2 or H2 O gas, in this work, the gasification agents are directly generated from coal combustion in the main combustion zone. Gas concentrations of CO, CO2 , H2 , and coal conversion are measured at different stoichiometric ratios, temperatures and reaction time. Secondly, a CFD numerical simulation framework considering both coal and gas reactions is used to simulate combustion in the E-DFF. Gasification kinetics are determined through a CFD-aided optimization method by using the experiment data as benchmark. The Hooke–Jeeves search algorithm is used to accelerate the optimization process. Finally, the effect of reduced reactivity of the char at high degrees of conversion is compared with literature. The determined kinetics are compared with kinetics from ex-situ char gasification experiment using the same coal. It is found that the experiment method has an obvious effect on determined gasification kinetics. 2. Experiments 2.1. Experimental facility and measurements To simulate air-staged combustion in a boiler, an E-DFF was designed. A schematic diagram of the E-DFF is shown in Fig. 1. The main part is a vertical furnace electric-heated by 24 uniformly distributed SiC rods with an auto-temperature controller. A 2.5-mlong alumina tube (99% purity, 2.0 m heated length, i.d.: 60 mm) was placed inside the furnace as the reaction tube. A water-cooled injection gun was fixed on top of the furnace to inject the coal particles into the hot reaction zone. Gaps between the injection gun and reaction tube were sealed to prevent air leakages, which could

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

55

Fig. 1. Schematic diagram of the E-DFF and air-staged pulverized coal combustion furnace.

change the atmosphere of combustion. Over-fire air (OFA) is injected inside the tube by an inner alumina tube (i.d.: 10 mm). Pulverized coal is continuously fed by a micro coal feeder, and this is dispersed and carried into the injection gun by air from the mass flow controller. The typical coal feeding rate is about 150 gh−1 with 0.6–1.2 Nm3 h−1 air. Air-staged combustion was achieved by a carefully designed stoichiometric ratio of air to coal (SR1 ) in the main combustion zone and burnout zone. Because a pulverized coal stream (instead of a single particle) was used for the air-staged combustion in the E-DFF, the upper furnace near the injection port corresponds to the main combustion zone of an actual boiler, as shown in Fig. 1. The zone between the main combustion zone and the OFA outlet corresponds to the reduction zone, and the zone below the OFA port corresponds to the burnout zone. In this way, air-staged combustion in an actual boiler was simulated in the E-DFF system. As showing in Fig. 1, simulation using LES method [75] shows that the flow in the injection region is turbulent due to the high injection velocity and combustion. However, after the reaction length of 0.3 m, the flow becomes laminar, thus both the temperature and species field becomes steady. Thus, the sampling starts from reaction length of 0.3 m. To collect solid and gas samples at different reaction distances, a water-cooled, N2 -quenched stainless sampling gun was inserted vertically from the bottom. As is shown in Fig. 2, the gaps between reaction tube and injection gun and sampling gun was sealed. The gap between reaction tube and the alumina tube is less than 10 mm (the diameter of the reaction tube is 60 mm). In all experiments, very few ash particles were observed in this gap. Therefore, almost all gas and particles can be collected. From simulation, we found that only the flow field near the inlet of the “Alumina tube” is affected. Besides, the inner “cold sampling gun” is surrounded by thermo insulation layer and alumina tube to increase the heat resistance. By this way, the heat transfer

between cold sampling gun and high temperature reaction tube is minimized, and as a result, the temperature distribution of the reactor is hardly affected. In experiment, when sampling in the reductive zone, the OFA tube is removed. And when sampling in the burnout zone, the OFA tube is inserted. The collected samples were separated, dried and further analyzed to quantify the gas species concentrations (in volume fraction) and characteristic char properties. The concentrations of gas species were measured by Fourier Transform Infrared spectroscopy (FTIR: CO, CO2 ), gas chromatography (GC: H2 ), and a magnetic oxygen analyzer (O2 ). The coal conversion (XCoal ) was calculated from thermo-gravimetric analysis result with the ash-tracer method [49]:

 XCoal =

1−

AshCoal AshSample



(1 − ACoal ) × 100%

(1)

where Ashcoal and Ashsample denote the ash content in the fed coal and the sample, respectively. The stability of air feeding and coal feeding affects the combustion stability inside the reaction tube. This is directly characterized by online gas monitoring. As Fig. 3 shows, the continuous onlinemonitored CO, H2 , and CO2 in the reductive zone are rather steady for SR1 = 0.7 and SR1 = 0.8 at reaction distance of 0.9 m with furnace temperature of 1400 °C. This experiment setup was also used for coal pyrolysis, char oxidation, and also ex-situ char gasification experiment in this work. The feeding rate was much smaller than staged combustion making that the coal or char particle reacts in the form of single particle with near constant gas reactant species concentrations.

56

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

Fig. 2. Sampling process of E-DFF experiment.

Fig. 3. Online measured gas concentrations in E-DFF experiments. Fig. 4. Size distribution of the prepared coal sample.

Table 1 Coal properties. Proximate analysis (wt%, ad)

Ultimate analysis (wt%, daf)

M

V

FC

A

C

H

O

N

S

5.18

35.81

52.21

6.80

83.16

4.88

9.90

1.27

0.78

2.2. Coal properties and experimental conditions A bituminous coal was used in all experiments. Its proximate and ultimate analysis followed the standard of GB T-212−1 [50] and GB T-31−1 ,391 [51], as listed in Table 1. The original coal was ground and repeatedly size-graded to a 45–106 μm cut. Char samples were made from this coal using the E-DFF at 1400 °C, following the method of Goetz [39]. The particle size distribution (PSD) was measured by a laser particle size analyzer to provide data for modeling. The PSD of the prepared coal sample is shown in Fig. 4. The Rosin–Rammler distribution model was applied to fit the distribution. In this work, varies experiments were conducted: First, air-staged combustion. Different stoichiometric ratios of air to coal in the main combustion zone (SR1 ) were designed, for obtaining reaction data for determination of in-situ char gasification kinetics.

Second, two kinds of ex-situ char gasification experiments were conducted on the E-DFF using the same coal and following the method of Goetz [39] and Gonzalo-Tirado [41]. However, the coal or char feeding rate was reduced to 0.2 g min−1 , and the air was change to 18.9% CO2 (N2 balanced) gas. 18.9% was determined according to stoichiometric combustion of this coal. Third, char oxidation experiments were conducted following the method of Ballaster and Jimenez [52]. The coal feeding rate was 0.2 g min−1 , and the air was change to 4% O2 (N2 balanced) gas. The char conversion was measured. Besides, coal pyrolysis experiment was also conducted to obtain high temperature volatile yield. The detailed conditions of these experiments are listed in Table 2. 3. Combustion and gasification modeling In air-staged combustion, as the coal is fed into the reaction zone, it will experience pyrolysis, oxidation, and gasification in sequence. Coal particles experience a complex temperature history because of the exothermic char oxidation and endothermic char gasification. The concentration field and temperature field inside the E-DFF changes with reaction proceeds, and their effect on char

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

57

Table 2 Experimental conditions of E-DFF experiments. No.

Experiment type

SR1

Temperature (°C)

Reaction length La (m)

Measurementb

1 2 3 4 5 6

Air staged Combustion Pyrolysis Gasification Gasification Oxidation

0.6,0.7,0.8,0.9 0.6 N2 18.9% CO2 18.9% CO2 4.0% O2

1400 120 0/130 0/140 0 750–1400 120 0/130 0/140 0 120 0/130 0/140 0 110 0/120 0/130 0

0.3/0.5/0.7/0.9/1.0 0.3/0.5/0.7/0.9/1.0 1.0 0.3/0.5/0.7/0.9 0.3/0.5/0.7/0.9 0.15/0.2/0.3/0.4/0.6/0.8/1.0

CO, H2 , CO2 , O2 XCoal , CSample , PSD XCoal , CSample , PSD XCoal XCoal XCoal

a

Length from coal injection port to sampling gun inlet port. CO/H2 /CO2 /O2 in volume fraction, XCoal in weight fraction of dry ash free basis (daf); CSample is carbon weight fraction in solid sample of dry ash free basis (daf). b

gasification should be considered. To accurately describe the concentration and temperature fields inside the E-DFF, CFD modeling of the air-staged combustion of pulverized coal was conducted. The detailed models are introduced in the following sections. 3.1. Governing equations Gas phase modeling is based on the conservation equations of mass, species, momentum, and energy, and the state equation of ideal gas:

∂ρ  ) = Sm + ∇ · (ρ ν ∂t

(2)

∂ (ρYi ) + ∇ · (ρ ν Yi ) ∂t = −∇ · Ji + Ri + Si (i = Vol,O2 , CO2 , CO, H2 , H2 O)

P = ρ RT

⎧ ⎪ ⎪ ⎨

(3)

  ∂ (4) (ρ ν ) + ∇ · (ρ ν ν ) = −∇ P + ∇ · τ¯¯ + Smv ∂t   ∂  hi Ji + τ¯¯ · ν (ρ ET ) + ∇ · (ν (ρ ET + P ) ) = ∇ · kCon ∇ T − ∂t i +Srad + Sh,r + Sh

where Aj , Ej denote the pre-exponential factor and activation energy, respectively, β j is the temperature exponential factor, Nj is the number of reactants in reaction j, Ci is the molar concentration of reactant i, and ni, j is the reaction order of species i in reaction j. Chemical reaction kinetics of Jones and Lindstedt [53] and Westbrook and Dryer [54] was used (see Table 3). The reverse reaction of R3 is calculated from equilibrium. The volatile species given by pyrolysis is assumed to be a pseudo-species of Cx Hy Oz . Its oxidation is described by R1 and R3. The CH4 combustion kinetics are used for volatile combustion, and this volatile species is still transported in CFD simulation. The determination of pseudo volatile species and its kinetics are discussed in pyrolysis model. The mixing rate is calculated based on the work of Magnussen and Hjertager [55] as:

(5) (6)

Here, ρ , Yi , P, T ,v, τ¯¯ , R denote the density, mass fraction of species i, pressure, temperature, velocity, stress tensor, and gas constant. Sm is the mass source added into the continuum phase from the discrete phase, such as coal pyrolysis, char oxidation, and gasification. Ri is the net rate of production of species i by gas phase reaction, and Si is the net rate of production of species i from the dispersed phase. Smv is the external body force source arising from, for example, the interaction with the discrete phase. k is the conductivity, hi is the sensible enthalpy of species i, Ji is the diffusion flux of species i, and E is energy. Srad is the source of energy due to radiation, Sh, r is the source of energy due to chemical reaction, and Sh is the source of energy due to the dispersed phase. 3.2. Gas phase reactions

w j = Aρ

ε kTur

min

Y¯R,1



Y¯R,2

, ,··· ,B Np ⎪ v1,r MWR,1 v2,r MWR,2 

⎪ ⎩

i=k

r¯ j,k = A j Tg β j exp(−E j /RTg )

Nj

i=1

n C¯i i, j ( j = 1, 2...5 )

(7)

⎪ ⎭ vi,r MWP,i ⎪ (8)

where Y¯R and Y¯P denote the averaged mass fraction of the reactant and product, respectively, MWP,i is the molecular weight of product i, and A, B are constants (set to 4.0 and 0.5, respectively). The source of energy from the gas phase reaction Sh, r is calculated as follows:

Sh,r = −

 h0 i Ri (i= Vol, CO,H2 , CO2 ,H2 O,O2 ) MWi

(9)

i

where h0i is the enthalpy of formation of species i. 3.3. Discrete phase model 3.3.1. Coal pyrolysis The series of physical and chemical processes of coal particles in combustion can be modeled by the governing equations of heat and mass during drying, pyrolysis, char oxidation, and gasification. The mass loss from drying is calculated by deducing the water mass fraction fw, 0 from the initial particle mass mp, k, 0 as:

dm p,k = m p,k,0 (1 − fw,0 ) dt

(10)

The mass loss during pyrolysis is calculated by: The finite rate and eddy dissipation (FR/ED) model is used for the modeling of gas phase reaction. In this model, the net rate of production of species i is taken as the minimum of the averaged chemical reaction rate and mixing rate. The averaged chemical reaction is calculated by Eq. 7. The effect of turbulence on gas phase reaction is calculated by the mixing rate of Eq. 8. The chemical reaction rate is calculated by Arrhenius’ equation as:

Y¯P

⎫ ⎪ ⎪ ⎬



m p,k,0 − m p,k dm p,k = m p,k,0 kPy (1 − fw,0 ) XHT Py − dt m p,k,0

 (11)

where kPy is the pyrolysis rate, which is modeled by the chemical percolation devolatilization (CPD) model. A detailed description has been given by Fletcher [56,57]. The 13 C NMR (nuclear magnetic resonance spectroscopy) parameters of coal were calculated using the correlation equations developed by Genetti [58]. Mass loss in pyrolysis is limited by the volatile yield at high temperature XHTPy .

58

D. Chen et al. / Combustion and Flame 194 (2018) 52–71 Table 3 Global reaction mechanism for gas phase species (unit: J, kmol, K, s, m). A

β

E

n

4.40E + 11

0

1.26E + 08

[Cx Hy Oz ]0.5 [O2 ]1.25

H2 +0.5O2 ⇒ H2 O

1.41E + 12

−1

1.67E + 08

[H2 ]0.5 [O2 ]2.25

R3

CO+H2 O ⇒ CO2 +H2

2.75e + 09

0

8.37e + 07

[CO]1 [H2 O]1

R4

CO2 +H2 ⇒ CO+H2 O

1.44e + 07

0

1.03e + 08

[CO2 ]1 [H2 ]1

R5

CO + 0.5O2 ⇒ CO2

7.08E + 13

0

1.67E + 08

[CO][H2 O]0.5 [O2 ]0.25

No.

Reaction

R1

Cx Hy Oz + ( x+y/22−z )O2 ⇒ xCO +

R2

y H O 2 2

The particle mass loss from pyrolysis is transferred into the continuous phase in the form of a pseudo-species of Cx Hy Oz . Values of x, y, z are calculated based on the assumption that all H and O are released from coal:

x= y= z=

XHT Py − H − O MWvol XHT Py MWC H XHT Py

Di,k =

MWvol MWH

O MWvol XHT Py MWO

(12)

where XHTPy is the high-temperature volatile yield. Mvol is the volatile molecular weight which is assumed from reference [55]. The calculated volatile was C1.65 H2.92 O0.37 , with H/C = 1.77 which was between (H/C )C2 H2 = 1 and (H/C )C2 H4 = 2. As there’s no kinetics for this pseudo species, we used published kinetics of real hydrocarbon. This pseudo species was still transported in CFD. Simulation using kinetics of CH4 ,C2 H6 ,C2 H4 ,C2 H2 from the work of Jones and Lindstedt [53], and Westbrook and Dryer [54] were compared. The predicted results were hardly affected by the kinetics, indicating that the kinetics of volatile combustion has negligible effect on the prediction of gasification in the reductive zone, as long as a proper kinetics of a real hydrocarbon is used. Therefore, the kinetics of CH4 was chosen. The enthalpy of formation is calculated from the heat balance. The total heat released from char and volatile combustion equals the coal combustion heat of LCV (low calorific value). Char combustion heat is taken as carbon combustion heat. The heat of volatile combustion is thus calculated as:

LCV − hchar mchar hVol = mVol hchar = 32.79MJ/kg

(13)

D0, i MWC φ Rd p,k (TGas + Tp,k )/2

(14)

where Di (Pg,i -Ps,i ) is the diffusion rate of the reacting gas from bulk to the char surface, and kc,i (Ps,i )n is the apparent chemical

(15)

where MWC is the molecular weight of carbon, φ is a mechanical factor taken as 2 in Field’s work, and R is the universal gas constant. The diffusion coefficient D0, i is calculated by [61]:



D0,k,O2

 1.75

0.001 TGas + Tp,k /2 MWO02.5 =   1 / 3  1 / 3 2 p ( υ )O2 + ( υ )N2



D0,k,i =

 1 . 5

0.001858 TGas + Tp,k /2 pσi,2N D

MWi0.5

(i = CO2 ,H2 O) (16)

2

where υ is the diffusion volume for simple molecules, σi,N is the 2

binary pair characteristic length, and D is the diffusion collision integral. An exponential function is added to account for the rate decrease due to char consumption. The modified chemical reaction rate is expressed as:



kc ,k, j = A j exp(−E j /RTp,k ) 1 − XChar,k + δ

m

( j = O2 , CO2 ,H2 O) (17)

where the small value of δ is added to prevent the rate dropping to zero when char conversion is close to 1. The exponent m and δ will be determined from the experimental results. XChar,k denotes char conversion, and is calculated by:



3.3.2. Char oxidation and gasification The char reaction is modeled by the kinetic-diffusion controlled model [63,64]. It is based on the concept that the particle mass consumption rate equals to the particle surface chemical reaction rate kc, i (Ps, i )n and diffusion rate of reactants to the particle surface in the boundary layer. So the particle consumption rate is calculated by Eq. (14). The chemical reaction rate and mass transfer rate are coupled through the term of Ps, i . The particle consumption rate is controlled by the smaller one of the chemical reaction rate and diffusion rate. In char oxidation, the chemical reaction rate is much larger than diffusion rate, thus it is diffusion controlled. According to work of Gonzalo-Tirado, etc [41], the chemical reaction rate of gasification is near an order of magnitude smaller than diffusion rate. Thus, it is chemical reaction controlled. The kinetic-diffusion controlled model was used for both char oxidation and gasification reaction.

dm p,k = A p,k kSurf = A p,k Di,k (Pg,i −Ps,i ) dt = A p,k kc,k, j (Ps,i )n (i = O2 , CO2 , H2 O)

reaction rate with reaction order n. Pg,i and Ps,i are the partial pressures of reactant i in the bulk gas and at the particle surface, respectively. The diffusional reaction coefficient Di is calculated from the work of Field [59] and Baum [60] as:

XChar,k =



1 − fw,0 − Xk,HT Py m p,k,0 − m p,k





1 − fw,0 − Xk,HT Py m p,k,0

(18)

The chemical reactions of char combustion and gasification are expressed as global reactions [48,62]:

Oxidation : C + O2 → CO/CO2 Product ratio of CO2 /CO

kc, k,O2 = AO2 exp(EO2 /RTp,k )

Rk, CO2 /CO = 0.02P0O.221 exp(3070/Tp,k )

Gasifiction : C + CO2 → 2CO kc, k,CO2 = ACO2 exp(ECO2 /RTp,k )



1 − XChar,k + δ

m

Gasifiction : C + H2 O → CO+H2



1 − XChar,k + δ

m

kc,k,H2 O = AH2 O exp(EH2 O /RTp,k ) (19)

The product ratio of CO2 /CO in char combustion is from the work of Tognotti et al. [63]. According to the work of Karlström et al. [64], an apparent reaction order of 1 in Eq. (14) provides a good prediction for most of the chars tested in oxidation. For gasification, determination of reaction order n needs experiment data of different CO2 concentrations. In the air-staged combustion, CO2 comes from coal combustion in the main reaction zone, and the

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

59

Fig. 5. Determination of char oxidation kinetics.

Fig. 6. Initial particle sizes and its volume fraction used in simulation.

variation of CO2 concentration at different conditions are small. Therefore, the reaction order of gasification cannot be determined. Our simulation with different reaction orders showed that the reaction order had rather small effect on the predicted result of CO and H2 , therefore, reaction order 1 was used. The method introduced by Ballaster et al. [52] was used to determine char oxidation kinetics using char oxidation experimental data. The experimental and simulated results are shown in Fig. 5. The determined oxidation kinetics are AO2 = 0.0095kgm−2 s−1 Pa−1 EO2 = 66.6 kJ mol−1 . As the particles are considered to be spherical, the external surface area A p,k = π d2p,k . The net consumption rate of char particles due to combustion and gasification can be calculated through the combined control of chemical reaction and diffusion as:

The particle size evolution during conversion is modeled. In pyrolysis, the particle size may change because of swelling [65]. The size and density evolution during pyrolysis is modeled by:

dm p,k dm p,k,O2 dm p,k,CO2 dm p,k,H2 O = + + dt dt dt dt  kc,k,O2 D0,k,O2 kc,k,CO2 D0,k,CO2 2 = π d p,k Pg,O2 + Pg,CO2 D0,k,O2 + kc,k,O2 D0,k,CO2 + kc,k,CO2 kc,k,H2 O D0,k,H2 O + Pg,H2 O D0,k,H2 O + kc,k,H2 O



(20)

Thus, predicting the char conversion is equivalent to predicting the mass loss due to O2 combustion and CO2 , H2 O gasification. From Eqs. (14)–(20), the key factors affecting the modeling of char conversion are the particle size dp , particle temperature Tp , and the kinetic parameters A, E, and m. 3.3.3. Particle size evolution The injected coal particles are divided into ten groups of d p,k,0=1,...,10 = 16, 32, 48,..., 144, 160μm. Here k is the index for particle size. The volume fraction of each size dp, k, 0 is calculated from the fitted Rosin-Rammler (RR) model in Fig. 4. as:

(V olumeFaction)d p,k,0 = Y(d p,k,0 −8) − Y(d p,k,0 +8) 

=e d p,k,0

−( ¯

−

d p,k,0 8 d¯p,0

n



−e

−

d p,k,0 +8 d¯p,0



1+

 XCoal,k  aHT Py − 1 d p,k,0 XHT Py 

ρ p,k =

6m p,k,0 1 − Xcoal,k

(22)

 (23)

π d3p,k

where dp, k is the particle size during pyrolysis and XHTPy is coal conversion after high-temperature pyrolysis. The value of XHTPy is the averaged coal conversion of 120 0 °C, 130 0 °C and 140 0 °C from pyrolysis experiments. aHTPy is the coal swelling factor, calculated by:

aHT Py =

d¯p,HT Py d¯p,0

(24)

where d¯p,0 is the averaged particle size of raw coal. d¯p,HT Py is the averaged particle size after high-temperature pyrolysis. The particle size and density evolution during char combustion and gasification are modeled by Smith’s equations [66,67]:



d p,k = d p,k,HT Py 1 − XChar,k

mm

 nn ρ p,k = ρ p,k,HT Py 1 − XChar,k

(25) (26)

where 3 mm + nn = 1. Here, dp, k, HTPy , ρ p, k, HTPy is particle size and density after high temperature pyrolysis. The values of dp, k, HTPy , aHTPy , XHTPy, k , mm, and nn are determined experimentally from the measured PSDs. 3.3.4. Particle temperature The particle temperature is calculated from the heat balance of convection, radiation, and reaction as:

n

(21)

n

)



d p,k =

Here, Yd = e d p,0 is the Rosin-Rammler (RR) model and used to model the particle size distribution of the coal sample. Yd is volume fraction of particle size that is larger than dp, k, 0 . d¯p,0 is the average particle size of coal sample and n is spread factor that are determined by fitting RR model to measured particle size distribution, as shown in Fig. 2. The particle size and its volume fraction used for simulation is shown in Fig. 6.

    dTp,k 4 = π d2p,k hk Tg − Tp,k + π d2p,k ε p σ Tr4 − Tp,k dt   dm p,k,O2 dm p,k,CO2 dm p,k,H2 O − fp HO2 + HCO2 + HH2 O dt dt dt m p,k c p

(27)

where mp, k , cp , ɛp denote the particle mass, heat capacity, and emissivity, respectively. Tp, k , Tg , Tr denote the particle, gas, and gas radiation temperatures, respectively. σ is the Stefan–Boltzmann constant. HO2 , HCO2 and HH2 O denote the reaction heat due to O2

60

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

combustion and CO2 , H2 O gasification, respectively. HO2 is calculated as HO2 = (HO2 ,CO + HO2 ,CO2 RCO2 /CO )/(1 + RCO2 /CO ). HO2 ,CO2 gives the reaction heat when the combustion product is CO2 ; HO2 ,CO is the equivalent when the product is CO. fp is the heat fraction that is absorbed by solid particles in combustion and gasification. hk is the convection transfer coefficient, calculated via [68]:

hk =



λg



1/3

2.0 + 0.6Re1g,/d2 Pr

d p,k

p,k

(28)

g

where λg is the thermal conductivity of gas, Reg,d

p,k

is the Reynolds

number of the gas based on particle diameter, and Prg is the Prandtl number of the gas. As the time step t for particle trajectories is small, an approximate solution is applied to calculate particle temperature changes within one time step. It is assumed that the particle mass and temperature change slowly within each time step, and so some terms are treated as constants. The integration from time t to time t + t can be expressed as:





Tp,k (t + t ) = α p,k + Tp,k (t ) − α p,k e−γP,k ·t

(29)

where:

α p,k =

hk π d2p,k Tg + Hreac + π d2p,k ε p σ Tr4 3 hk π d2p,k + hπ d2p,k ε p σ Tp,k

 Hreac,i = f p

γ p,k =

π

d2p,k

dm p,i,O2 dm p,i,CO2 dm p,i,H2 O HO2 + HCO2 + HH2 O dt dt dt

( hk + ε p σ

3 Tp,k

)

m p,k c p

(30)

 (31)

(32)

3.4.1. Mass transfer The mass transfer is computed by examining the change in mass of a particle as it passes through the calculated control volume. This mass exchange appears as a source of mass in the continuous phase continuity equation and as a source of a chemical species in the species conservation equation. It is computed as

(33)

(36)

where SRr, rea is defined in terms of the mass of reactant per mass of char and SRr, pro is defined in terms of the mass of product per mass of char. For char oxidation and gasification, the detailed chemical reaction formulas are:

1 × char(s ) + SRr,O2 × O2 (g ) = SRr,CO2 × CO2 (g ) 1 × char(s ) + SRr,O2 × 0.5O2 (g ) = SRr,CO × CO(g ) 1 × char(s ) + SRr,CO2 × CO2 (g ) = 2SRr,CO × CO(g ) 1 × char(s ) + SRr,H2 O × H2 O(g ) = SRr,CO × CO(g )+SRr,H2 × H2 (g ) SRr,O2 = MWO2 /MWC SRr,CO2 = MWCO2 /MWC SRr,CO = MWCO /MWC SRr,H2 = MWH2 /MWC (37) Both oxidation and gasification contribute to char conversion. Their respective contributions to particle mass change can be calculated according to Eqs. (14)–(20) as m p,O2 , m p,CO2 , and m p,H2 O . Thus, the species sources added into the continuous phase in Eq. (3) by the char reactions are calculated as:

SC O2 = SCO =

The above mass, species, and energy sources of the discrete phase are added into the continuous phase through a coupling algorithm. The mass, species, momentum, and heat transfers between the discrete and continuous phases are introduced in the following subsections.

 m p,k m˙ m p,k,0 p,k,0

1 × char(s ) + SRr,rea × reactant(g ) = SRr,pro × product(g )

SO2 = −

3.4. Coupling between the discrete and continuous phases

Sm =

For drying and pyrolysis, SR = 1 because the particles release water and volatile gases into the continuous phase without consuming gases from the continuous phase. For char combustion and gasification, the chemical reaction formula can be summarized as:

SRr,O2

R

CO2 /CO +0.5 RCO /CO +1 2



SRr,CO2

 SRr,CO2



m p,k,O2

m p,k,0

RCO /CO 2 RCO /CO +1 2

0.5 RCO /CO 2



m˙ p,k,0

m p,k,O2 −SRr,CO2 m p,k,CO2

m˙ p,k,0  m p,k,0 +1 m p,k,O2 +SRr,CO m p,k,H2 O +2SRr,CO m p,k,CO2

SRr,H2 O m p,k,H O 2 m˙ p,k,0 m p,k,0 SRr,H2 m p,k,H O 2 m˙ p,k,0 m p,k,0

m p,k,0

(38) m˙ p,k,0

SH2 O = − SH2 =

3.4.3. Momentum transfer The momentum source in Eq. (4) is computed by:

Smv =

 k





18μCD Re p (u p,k − u ) + Fother m˙ p,k t 24ρ p,k d2p,k



(39)

where μ is the viscosity of the fluid, ρ p, k is the particle density, dp, k is the particle diameter, Rep is the particle Reynolds number, up, k is the particle velocity, u is the fluid velocity, CD is the drag coefficient, m˙ p,k is the particle mass flow rate, t is the time step, and Fother denotes other interaction forces.

k

where mp, k is the particle mass change in the calculated cell and m˙ p,k,0 is the initial particle mass flow rate at the injection point. 3.4.2. Species transfer The species exchange between the discrete and continuous phase appears as a source of mass in Eq. (2) and as a source of a chemical species in Eq. (3). It is calculated as:



Si,k =

r,k

SRr, j,i m p,k,i  k

Sm =



Si,k

m p,k,0



m˙ p,k,0

(34)

3.4.4. Heat transfer Reaction heat released from char combustion and absorbed in drying and gasification is transferred into the continuous phase through the heat source Sh . The overall heat exchange from the reaction and thermal energy change is calculated by:

Sh =

 m˙ p,k,0   (1 − f p )Hrec,k − m p,k,in m p,k,0 k  TP,k,   out −m p,k,out HLat − m p,k,out c p dT + m p,k,in Tref

k

TP,k,

in

 c p dT

Tref

(40) (35)

r,k

where SRr, i is the stoichiometric ratio in terms of mass for reaction r (drying, pyrolysis, oxidation, and gasification) of species i (water, volatile, O2 , CO2 , CO, H2 ).

where m p,k,in and m p,k,out denote the particle mass at the inlet and outlet of the control volume, respectively. cp is the particle heat capacity, TP,k,in and TP,k,out are the particle temperatures at the inlet and outlet of the control volume, respectively, Tref is the reference temperature, fp is the heat fraction absorbed by the particle from

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

char oxidation and gasification, and HLat is the latent heat of drying. Hrec,k is the char reaction heat from combustion and gasification, and is calculated as:

Hreac = (1 − f p )   m p,k,O2 Hchar + m p,k,CO2 HCO2 + m p,k,H2 O HH2 O

(41)

3.5. Modeling approach Comparison showed that simulations with 3D grid and 2D grid give the same result. Therefore, a 2D axisymmetric grid was used. Grid independence tests with mesh sizes of 21,244, 32,010, 42,434, 50,110 and 61,242 showed that 50,110 gave stable results and acceptable calculation cost. The near wall mesh was refined, making the y + value of the wall is generally lower than 1. Models discussed in Section 3 were realized in commercial CFD code of FLUENT. For the E-DFF experiment setup, the air jet from the injector is fasted dissipated after injected into reaction tube. As is shown in Fig. 1, LES simulation showed that the flow near the injection port is turbulent, and becomes laminar in the reaction tube. Therefore, a turbulence model is needed. As LES takes much high computational cost than Reynolds-averaged Navier–Stokes (RANS) method, thus in this work, the RANS method was used. Simulations with different turbulence models showed negligible differences. Therefore, the k − ε model with low Reynolds number model of Yang Shin [69] was used. The P-1 [70] radiation model with absorption coefficients calculated by the weight-sum-of-gray-gas model (WSGGM) [71,72] was used. The char oxidation and gasification models were implemented in FLUENT by user-defined functions (UDFs) with the macros of DEFINE_DPM_LAW. The UDFs were verified when it was implemented into FLUENT. The calculation was based on the Eulerian–Lagrangian formulation for the continuous gas phase and dispersed particle phase. The interaction of a particle with turbulence was modeled by the random walk model. Simulations with particle injection number of 320, 640, 960 and 1920 showed very small difference. Therefore, the injection number of 320 was chosen. During the simulation, the SIMPLE algorithm was applied for the coupling of the velocity and pressure fields. The governing equations were discretized by the second-order upwind scheme. Iterative calculations were carried out until the solution satisfies a pre-specified tolerance.

61

the reduced gasification rate at high char conversion. Third, activation energy and pre-exponential factor were optimized at temperatures of 1200 °C, 1300 °C and 1400 °C. Finally, the determined kinetics were verified at all temperatures, SR1 s and reaction distances. The determined kinetics were compared with results of ex-situ char gasification experiment and literature. To reduce computational cost in and increase the repeatability, the optimization algorithm of the Hooke–Jeeves direct search method [73] was adopted, as is shown in Fig. 8. The optimizing procedure takes the following steps: Step 1: Initialization. Set the initial parameters and search step 0 , m0 , δ 0 ] and ϕ 0 = length as ϕ 0 = [A0CO , EC0O , A0H O , EH O 2

2

2

2

0 , m 0 , δ 0 ] . [A0CO , EC0O , A0H O , EH 2 2 2 2O Step 2: Heuristic search. Carry out a search in six indepenj dent directions. Each time, a single direction of vector ϕi is

changed to ϕi

j+1

= ϕ j ± ϕik , and ϕik = (0, ..., ϕik , ..., 0 ).

The input for the simulation is ϕi . The objective function value of each direction is given by the Root Mean Squared Error (RMSE) of the experimental and simulated results. The RMSE is calculated as:

fi,j+1 min

j+1

1 = RMSE = 4

 S=v fCO ,v fH2 ,v fCO2 ,XCoal



5 2 1  Sn,Exp. − Sn,Simu . 5 n=1

(42) where Sn, Exp. and Sn, Simu. are the volume fractions of CO, H2 , CO2, and coal conversion from the experiments and simulations, respectively. The RMSEs of CO, CO2 , H2 , and XCoal are calculated from five data points and averaged to give the overall RMSE. j+1 After searching in all six directions, the minimum fi,min is taken j+1

j+1

j

as fmin . If fmin < fmin , jump to step 3 and conduct a pattern search. Otherwise, if |ϕ m | < σ is not true, decrease the step length to ϕ k+1 = ε × ϕ k , where ε = 0.5 in this case.

Step 3: Pattern search. Calculate the pattern search vector S = ϕ j+1 − ϕ j , increase the value of j to j + 1, and start the search from the new base vector of ϕj . Apply the new vector j+1 ϕ j + S to the simulation. The search continues until fmin < j

4. Optimization methodology for kinetic parameters In this work, as is shown in Fig. 7, the realistic gasification kinetics are determined through a CFD-aided optimization method. This includes obtaining experimental data from E-DFF experiments, CFD simulation of the experiment using models in Section 3, deriving gasification kinetics by optimizing process, and verification of the kinetics. Firstly, air-staged combustion experiments were designed and conducted to obtain data for kinetics determination. First, SR1 was varied in the range of 0.6–0.9 to investigate the effect char conversion on gasification rate. Second, experiments at temperatures of 1200 °C, 1300 °C and 1400 °C were conducted to provide data for the determination of activation energy and pre-exponential factor. Third, pyrolysis and oxidation experiments were done on drop tube furnace for determination of model parameters for pyrolysis and oxidation. Secondly, gasification kinetics were determined through CFDaided optimization process. First, the combustion in E-DFF was simulated by models discussed in Section 3, using initial gasification kinetics from literature listed in Table 6. An objective function was defined to calculate the errors of the prediction. Second, the exponential factor of m was optimized at difference SR1 to model

fmin is false, and the algorithm returns to step 2 to repeat the heuristic search. Step 4: Stop judgment. The heuristic and pattern searches are repeated until the search step length meets the stop judgment of |ϕ m | < σ , where σ is a small user-defined convergence criterion. Applying the above Hooke–Jeeves optimization process according to the procedure shown in Fig. 4, the optimized kinetic parameters can be obtained. 5. Results and discussion 5.1. Profiles of gas phase species and coal conversion Profiles of the gas phase species and coal conversion along the reaction distance from 0.1–2.0 m under experimental conditions of SR1 = 0.7 and SRT = 1.2 at a temperature of 1400 °C are plotted in Fig. 9(a). It can be seen that the oxygen concentration decreases rapidly and then approaches zero near 0.25 m. There is a corresponding rise in the CO2 concentration, which indicates that the char is burning fast. Based on the oxygen concentration in the gas phase, the main combustion zone is marked in Fig. 9. From the rising levels of CO and H2 in the gas phase, it can be concluded

62

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

Fig. 7. Determining kinetic parameters through optimization.

Fig. 8. Flowchart of the direct search optimization method.

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

63

Fig. 9. Measured data from air-staged combustion in E-DFF: (a) Gas species along the distance; (b) Coal conversion along the distance; (Symbol: Experimental result; Line: Simulated result; Condition: T = 1400 °C, SR1 = 0.7 SRT = 1.2).

that char gasification occurs just after the depletion of oxygen, and the zone with depleted oxygen that is rich in CO and H2 corresponds to the reduction zone. It can be seen from Fig. 9(a) that there is a continuous increase in CO and H2 and a continuous decrease in CO2 , that is, there is a changing concentration profile for both gas reactants and gas products during char gasification in the reduction zone. The gas profiles in the E-DFF are the same as in an actual boiler. The profile of coal conversion is shown in Fig. 9(b), where it can be seen that fresh char is burned by oxygen in the air. The char for gasification is the remaining char, and gasification consumes about 22% of the fed coal. This char remaining from combustion is generated by the same temperature history and conversion process as an actual boiler, that is, the char in gasification is in-situ char from air-staged combustion. As gasification is slower than pyrolysis and combustion, the slope of the conversion curve in the reduction zone is much shallower. As discussed above, the char and gas reactants of gasification in the reductive zone come from combustion in the main combustion zone, and the gas species changes with gasification. Thus, it is important to model both the char conversion and gas reaction. To fully model the coal conversion process in E-DFF experiments, CFD simulations using models in Section 3. The simulated results from one CFD simulation case are shown in Fig. 9(a) and 9(b) as lines. The predicted concentrations of O2 , CO2 , CO, H2 and coal conversion agrees well with experimental results, indicating that the selected models gives a reasonable prediction of the combustion process in experiment. Char conversion was calculated from measured coal conversion as:

XChar =

XCoal − XHT Py × 100% 1 − XHT Py

(43)

where XHTPy is the high-temperature volatile yield expressed as the coal conversion of dry ash free base. Char conversion by combustion in the main combustion and burnout zones, and gasification in the reductive zone, at different temperatures and SR1 values at a reaction distance of 1 m are calculated as: SR ×100−X

Maincombustionzone : XC har,C ombustion1 = 1100−XHT PyHT Py × 100% Reductivezone : XChar,Gasi f ication = XChar,L − XC har,C ombustion1 Burnoutzone : XC har,C ombustion2 = XChar,Out − XChar,L (44) where XChar, L denotes char conversion at reaction distance L = 1 m and XChar, Out denotes char conversion at the outlet of the reactor (L = 2 m). Char conversion by oxidation and gasification at differ-

Fig. 10. Char conversion at different SR1 from air-staged combustion in E-DFF.

ent temperatures and SR1 values are plotted in Fig. 10. The char gasification rate increases with the temperature, and so the char conversion by gasification almost doubles from 1200 to 1400 °C at SR1 = 0.6. The activation energy can be determined from different temperatures. At the same temperature, higher values of SR1 imply that more char is converted by oxidation in the main combustion zone than by gasification in the reductive zone. It was found that gasification reactivity decreases with coal conversion [68]. Thus, gasification experiments using ex-situ char cannot simulate real gasification reactions in the reduction zone of an actual boiler.

5.2. Evolution of particle size To model the particle size evolution during coal conversion, Eqs. (22)–(26) are used to describe the evolution of particle size and density, with the parameters for models (22)–(25) derived from the experimental mean particle size evolution in the pyrolysis, char oxidation and gasification. The volume mean diameters are plotted in Fig. 11 with respect to the coal conversion fraction. The black line is the fitting result for the particle size evolution model of coal pyrolysis, and the red line is the particle size evolution of char oxidation and gasification. These two models are in good agreement with the experimental data. The obtained parameters are d¯p,HT Py = 78.27μm, aHT Py = 1.356, XHT Py = 46.15wt%, drybasis, and

64

D. Chen et al. / Combustion and Flame 194 (2018) 52–71 Table 4 Kinetic parameters for SR1 = 0.6, 0.7, 0.8, 0.9 with T = 1400°C. T(°C)

SR1

Avg. XChar (wt% daf)

A CO2 (kgm−2 s−1 Pa−1 )

ECO2 (kJmol−1 )

AH2 O (kgm−2 s−1 Pa−1 )

EH2 O (kJmol−1 )

1400 1400 1400 1400

0.6 0.7 0.8 0.9

25.8 44.3 62.9 81.4

3.715 2.927 2.111 1.686

220.0 220.0 220.0 220.0

6.75E−02 5.21E−02 3.92E−02 2.88E−02

180 180 180 180

timized at SR1 = 0.6, 0.7, 0.8, 0.9 with a temperature of 1400 °C according to the method in Fig. 8. The initial values are set as ACO2 = 3.715 kg m−2 s−1 Pa−1 , ECO2 = 220 kJ mol−1 , AH2 O = 6.75e−2 kg m−2 s−1 Pa−1 , EH2 O = 180 kJ mol−1 , and m = 1,

δ = 0. The same set of ϕij+1 is used for the CFD simulations of all four SR1 . As the temperature is the same for all four conditions, ECO2 and EH2 O remain unchanged during optimization. The objective function is calculated as the average of the RMSEs at SR1 = 0.6, 0.7, 0.8, and 0.9 as:

fmin,m 1 = 4

 SR1=0.6,0.7,0.8,0.9

1 4

 S=v fCO ,v fH2 ,v fCO2 ,XCoal



5 2 1  Sn,Exp. − Sn,Simu . 5 n=1

(45)

simulations.

The optimized value of m = 1.56 and δ = 0.2. Other parameters are ACO2 = 13.870 kg m−2 s−1 Pa−1 , ECO2 = 220 kJ mol−1 , AH2 O = 0.251 kg m−2 s−1 Pa−1 , EH2 O = 180 kJ mol−1 . The simulated results show good agreement with the experimental data, as shown in Fig. 12.

5.3. Optimizing exponent m

5.4. Optimizing pre-exponential factor and activation energy

Previous studies obtained the char gasification kinetics with experimental samples of ex-situ char given by a constant concentration of CO2 or H2 O. However, in the air-staged combustion of pulverized coal combustion, the char located in the reduction zone is that which remains after the fresh char from coal pyrolysis has been burned by oxygen in the main combustion zone. The amount of air provided varies with SR1 , and the amount of char consumed by oxygen oxidation will differ accordingly. This results in different coal conversion at the exit of the main combustion zone or inlet of the reduction zone. It has been observed by some researchers [29,42] that char gasification reactivity can be significantly affected by char conversion. In this study, Eq. (17) is used to describe the effect of the coal conversion fraction on the char gasification kinetics, and a series of experiments at different SR1 values is conducted to obtain the model parameters. First, the kinetics of ACO2 , ECO2 , AH2 O , and EH2 O were optimized at SR1 values of 0.6, 0.7, 0.8, and 0.9, with initial values of ACO2 = 1 kg m−2 s−1 Pa−1 , ECO2 = 220 kJ mol−1 , AH2 O = 1 kg m−2 s−1 Pa−1 , EH2 O = 180 kJ mol−1 , and m = 0. That is, the gasification rate is not related to char conversion. However, this cannot achieve acceptable agreement for the simulated CO, H2 , CO2 , and XCoal for all four SR1 values. To achieve good agreement, the value of A for each condition must be adjusted independently. The adjusted parameters of each condition are listed in Table 4. The value of ACO2 more than halved from SR1 = 0.6 to 0.9, as the theoretical coal conversion increased from 60% to 90%. In terms of the carbonaceous structure of char, highly reactive amorphous carbon is primarily consumed during oxidation, leaving graphite carbon of low reactivity in char. This graphitization reduces the subsequent gasification rate. The graphitization is found to increase with the increasing of char conversion [44]. To improve the prediction accuracy of the determined kinetics, the values of ACO2 , ECO2 , AH2 O , EH2 O , and m are op-

In this section, the pre-exponential factor and activation energy are optimized at temperatures of 120 0°C, 130 0 °C, and 140 0 °C with SR1 = 0.6. A and E are simultaneously optimized at the three temperatures. The process is still conducted according to Fig. 8. 0 , m0 ] = The initial parameters are set as ϕ 0 = [A0CO , EC0O , A0H O , EH O

Fig. 11. Evolution of particle mean diameter (D43) during coal pyrolysis, char oxidation, and gasification.

α = 0.261. These two models are applied in the CFD combustion

2

2

2

2

[13.870, 220, 0.251, 180, 1.56, 0.2] and m, δ are fixed at 1.56 and 0.2, respectively. These parameters vary according to the Hooke– Jeeves optimization method, and are input into the CFD simulation to obtain simulated results. The simulated results are evaluated through the averaged RMSEs of three temperatures as:

=

fmin,AE = Avg.(RMSE1200 ◦ C , RMSE1300 ◦ C , RMSE1400 ◦ C )   1 1 3

120 0 ◦ C,130 0 ◦ C,140 0 ◦ C



XCoal

4

S=v fCO ,v fH2 ,v fCO2 ,

5 2 1  Sn,Exp. − Si,Simu . 5

(46)

n=1

To clarify the optimization process, fmin , AE is calculated with different combinations of ACO2 , ECO2 and AH2 O , EH2 O on squared sub-grids (20 × 20). These results are plotted as a 3D and 2D contour against ACO2 , ECO2 and AH2 O , EH2 O in Figs. 13 and 14. The optimization process is also plotted. From the chemical reaction rate equation, kc = A exp(−E/RT )(1 − XCoal + 0.2 )1.56 , any decrease in E or increase in A leads to a greater reaction rate, and vice versa. This greater reaction rate results in faster gasification and higher CO, H2 , concentrations and Xcoal , and thus leads to higher values of fmin , AE . Obviously, changing E leads to even bigger reaction rate changes, as this is the argument of the exponential function. Thus, the slope in the E direction is steeper than that for A. Although some combinations of A and E will lead to the same kc for a single temperature, there is only one set of A and E for which the simulated

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

65

Fig. 12. Simulated results of each condition with optimized m.

results agree well with the experiments at all three temperatures, because the reaction rate is strongly affected by temperature. In this study, these kinetics were determined by searching for the point that minimizes the objective function value. Despite some deviations from the CFD calculation, a unique objective function value is determined from the given kinetics. The objective function value is an implicit function of kinetics. Thus, in this study, the Hooke–Jeeves direct search algorithm was adopted, as it requires only the independent variable values (i.e., the kinetics in this study) and the objective function. As shown in Fig. 5, the algorithm mainly consists of heuristic and pattern search modules. In every heuristic search, objective function values are calculated in four directions, only one of which is valid. For the pattern search, only the last point is invalid. Thus, the pattern search can obviously reduce the number of invalid calculations and accelj+1 j erate the search. In Fig. 13, the points for which fmin < fmin are j+1

valid moves, indicated by black arrows. Trial points where f min > j fmin

(shown as gray dots) do not contribute to a valid move. As shown in Fig. 13, the search starts from [ACO , ECO , AH O , EH O ] = 2 2 2 2 [13.870, 220, 0.251, 180], and the pattern search quickly finds a direction that continuously decreases the objective function value (two lines in the E direction). Finally, the optimal point is attained. For the optimization of the CO2 gasification kinetics, the valid moves are mostly made by the pattern search with few trial points. The number of simulations of invalid moves is reduced, which accelerates the optimization. For the optimization of H2 O gasification kinetics, only a few steps are required to find the optimal point, as the initial point is rather close. The optimal kinetics from the Hooke–Jeeves search are ACO2 = 62.3 kg m−2 s−1 Pa−1 , ECO2 = 253.1 kJ mol−1 and

AH2 O = 0.465 kg m−2 s−1 Pa−1 , EH2 O = 190.5 kJ mol−1 with an objective function value of 0.073. Different initial kinetics were used for optimization:

ϕ 0 = [A0CO2 , EC0O2 , A0H2 O , EH0 2 O ]

= [1, 220, 1, 180] = [1.3, 235.9, 2750, 317.7] = [7.55, 148.5, 0.0232, 145.2]

(47)

The optimized kinetics always fall in the smallest circle in Fig. 13b, d. Within this circle, the change in fmin , AE becomes relatively small. The calculated fmin , AE s are in a narrow range of 0.073–0.08 for all initial points. The relative errors the predicted CO, H2 concentration and XCoal are less than 10%, indicating that any pair of A and E in this circle provides good prediction. In this region, the effect of the gasification kinetics is small, and the error between the simulated and experimental result is comparable to the uncertainties from the experiments and CFD models. Thus, the objective function values cannot be reduced further by the optimization process. The ranges of A and E for which CO2 gasification remains in this circle are:

ACO2 = 59.7 − 65.1kgm−2 s−1 Pa−1 , ECO2 = 250.5 − 254.2kJmol−1 ; AH2 O = 0.412 − 0.495kgm−2 s−1 Pa−1 , EH2 O = 188.4 − 191.3kJmol−1 (48) Repeated optimization processes with the same initial kinetics were conducted, the difference of optimized kinetics of each run was rather small. As Fig. 13b, d shows, the monotonous to kinetics, thus, we can always get nearly the same optimizing results at different runs.

66

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

Fig. 13. Objective function value distribution and Hooke–Jeeves optimization process for CO2 and H2 O gasification: CO2 gasification: (a) 3D surface colored by objective function value; (b) contour of objective function value H2 O gasification: (c) 3D surface colored by objective function value; (d) contour of objective function value. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Fig. 14. Simulated results at different conditions with determined kinetics.

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

67

Table 5 Optimized kinetics. C + CO2 = 2CO C + H2 O = CO + H2

kCO2 = A CO2 exp(−ECO2 /RTp )(1−XChar + 0.2)1.56 kH2 O = AH2 O exp(−EH2 O /RTp )(1−XChar + 0.2)1.56

From the above optimization process, the optimal kinetics of CO2 and H2 O gasification are determined for temperatures of 120 0 °C, 130 0 °C, 140 0 °C and SR1 values of 0.6, 0.7, 0.8, 0.9. The results are listed in Table 5. The parameters from Table 5 were used to simulate all the combustion cases for verification. The CO, H2 concentrations and XCoal at different SR1 values and temperatures are plotted in Fig. 14 alongside the experimental data. In the simulations, the chemical reaction rate is calculated as kc = Aexp(-E/RTp ) (1XChar + 0.2)1.56 . Despite the changes in particle temperature, the chemical reaction rate decreases as the coal is converted. Thus, the gasification rate (in kg s−1 ) is higher at the beginning. For this reason, the CO volume fraction curve is initially stiff. There is good agreement between the simulated results and the experimental results, indicating that the determined kinetics and improved char reaction model provide good predictions of gasification at different temperatures and SR1 values.

5.5. Comparison of in-situ and ex-situ gasification kinetics Although the kinetics of in-situ char gasification in the reduction zone of air-staged combustion have rarely been reported, many results have been obtained in the field of entrained flow gasification. Thus, in this section, data from gasification experiments in DTFs (or EFRs) are reviewed and compared. Representative results are compared with those presented in this study. The experimental conditions, coal properties, and derived kinetic data from some representative literatures are summarized in Table 6. Goetz et al. [39] prepared char through the pyrolysis of pulverized coal in a DTF at 1454 °C with inert gas, and collected char samples for gasification experiments. Bituminous char, sub-bituminous char, and lignite char were gasified in different concentrations of CO2 or H2 O with N2 as a balance gas at different temperatures and residence times. An apparent model based on the particle external surface considering the chemical reaction rate and diffusion rate was used. Kinetic parameters were derived by Arrhenius’ fitting method at different temperatures. The reaction order of CO2 was determined from gasification rates at different CO2 concentrations. The work of Dershowitz [40] is similar to that of Goetz, although there are differences in the coal types, temperatures, and CO2 or H2 O concentrations. The work of Kajitani et al. [28] considered a pressurized DTF with a total pressure of 20–30 atm, and derived parameters for a random pore model. In the above studies, the char samples for gasification were all prepared from separate pyrolysis experiments, i.e., ex-situ char. The collection cools the char particles and leads to changes in the morphology and reactivity of char particles. Gasification experiments using TGA and fluidized beds have found that the gasification rate is obviously affected by char preparation method [36,37,42]. Recently, Gonzalo-Tirado et al. [41] conducted coal gasification in an EFR. In their work, the coal was directly carried into the reaction tube by a diluted CO2 gas stream. The coal gasifies after pyrolysis in the reaction zone, and thus this method prevents the effect of cooling on reactivity. However, the char for gasification is still fresh, and there is no char combustion and temperature variation before gasification. Therefore, this is still an ex-situ char method. For simplicity, here, gasification experiment using prepared char, such as the work of Goetz, is defined as ex-situ experiment 1 (ex-situ Exp.1), and gasification experiment using coal, such as the work of Gonzalo-Tirado is

A CO2 = 62.3 kg m−2 s−1 Pa−1 AH2 O = 0.465 kg m−2 s−1 Pa−1

ECO2 = 253.1 kJ mol−1 EH2 O = 190.5 kJ mol−1

defined as ex-situ experiment 2 (ex-situ Exp.2). Experiment of this work is defined as in-situ Exp. 5.5.1. Comparison of kinetics derived from in-situ and ex-situ experiment Kinetics of gasification were derived from two kinds of ex-situ experiment introduced in Section 2, using coal or char the same with the E-DFF air-staged combustion experiment. Figure 15 shows the experimental and simulated result of ex-situ Exp.1 and ex-situ Exp.2. The methods of deriving these kinetics are the same to Goetz and Gonzalo-Tirado. The derived CO2 gasification kinetics of ex-situ Exp.1 and ex-situ Exp.2 are:

Ex − situEXP.1 : Ex − situEXP.2 : In − situEXP. :

A =38.2kgm−2 s−1 Pa−1 A =16.4kgm−2 s−1 Pa−1 A =62.3kgm−2 s−1 Pa−1

ECO2 = 267.4kJmol−1 ECO2 = 223.8kJmol−1 ECO2 = 253.1kJmol−1

As showing in the Arrhenius plot of Fig. 16, the gasification rates are ranked as: Ex − situ.2 >In − situ>Ex − situ.1. In ex-situ 2 experiment, the injected coal particles pyrolysis at high temperature, producing high reactivity porous char. Therefore has the largest gasification rate. In the in-situ gasification, char generated from pyrolysis is firstly oxidized by O2 , resulting in reduction of char reactivity. Therefore, the gasification rate in the reductive zone is lower than the fresh char of ex-situ 2. For ex-situ char 1, the char is prepared through high temperature pyrolysis, but cooled to room temperature. The cooling process leads to the morphology changes and reduction of char reactivity. Thus, the reaction rate of ex-situ 1 is the lowest. 5.5.2. Effect of char conversion on char reactivity To compare the published kinetic parameters listed in Table 6 more directly, the gasification rates of 60 μm diameter char particles at 1400 °C with 20% CO2 or 10% H2 O (volume fraction, total pressure 1 atm) were calculated and plotted in Fig. 17. The CO2 molar concentration was calculated from the state equation of an ideal gas for Dershowitz’s results. A coal density of 1300 kgm−3 was assumed to transfer Kajitani and Dershowitz’s results (weight loss rate, g g−1 s−1 ) into an external surface gasification rate (kg m−2 s−1 ). The particle size was assumed to be constant. The calculated results with respect to coal conversion are plotted in Fig. 17. For the works of Goetz, Dershowitz, and Gonzalo-Tirado, kinetic parameters were derived from the overall conversion of char without considering the deactivation effect of char conversion. They also did not improve the correlation of the reaction rate to include the deactivation effect. Thus, the gasification rate is constant for all char conversion fractions. Kajitani used a random pore model for the char gasification process, and so the gasification rate decreases with char conversion as the surface area varies with conversion in this model. Considering the coal type, lower ranks commonly lead to higher gasification rates [74]. In the reviewed works, the gasification rates of lignite and sub-bituminous coal are higher than those of bituminous coal. As Kajitani’s experiments were conducted at high pressures (20–30 atm), the rate for bituminous coal is higher than that of lignite. The gasification rate of the in-situ char of bituminous coal in this study is comparable to that reported by Goetz. Gasification rates for SR1 = 0.6, 0.7, 0.8, 0.9 were calculated from Table 4 and plotted against the theoretical char conversion of each SR1 (i.e.: XChar,Theoretical = (SR1,i − XHTPy )/(1 − XHTPy ) × 100%). Obviously, the gasification rate decreases with char

68

Table 6 Kinetics from coal or char DTF (or EFR) gasification experimentsa . Conditions

Dp (μm)

Coal Type

VM(dry)

C (daf)

H (daf)

O (daf)

A CO2

ECO2

nC O2

Goetz et al. [39]

Char gasification 1092–1447 °C 1 atm 15%, 30%, 60% CO2 (N2 balance)

38–75

Lig.

42.4

71

5.7

20.1

6.51E−02

165.3

0.91

44.7 38.8 38.4

75–150

Sub-Bit. Bit.1 Bit.2 Lig.

74.3 73.9 83.7 94.3

5.2 5.1 5.6 1

18.8 15.4 6.4 3.1

0.103 1.278 0.137 5.81E + 04

177.8 235.9 224.8 97.1

0.26

31

Bit.

29.5

82.7

5

10.1

2.54E + 07

257

0.56

26a

44 38 44 44 53–63

Bit. Bit. Bit. Bit. Sub-Bit.

44.3 36.1 36.9 28.7 57.1

77.8 80.8 78.4 82.5 76

6.6 4.8 5.6 5.1 3.8

13.8 13.3 14.9 10.5 19

6.60E + 08 1.12E + 08 1.19E + 09 6.78E + 04 7.55

280 240 262 163 148.5

0.43 0.48 0.46 0.73 0.45

10 1 1 3

45–106

Bit.

37.8

83.2

4.9

9.9

62.3

253.1

1

Dershowitz [40]

Kajitani et al. [23,28]

Gonzalo-Tirado et al. [41]

This study

Char gasification 1200 °C, 1500 °C, 1840 °C 1 atm 26%, 53–63% CO2 32–35%, 65% H2 O (Ar balance) Char gasification 1400 °C 20–30 atm 40% CO2 5% H2 O

Coal gasification 1040–1300 °C 1 atm 0.7%, 3%, 10%, 50%, 100% CO2 (N2 balance) Coal combustion (Air) with different SR1 1 atm 1400 °C, 1300 °C, 1200 °C

AH2 O

EH2 O

nH2 O

2.75E + 03

317.7

1

3.07E + 10

109.6

1.19

2.45E + 07

214.0

0.86

0.465

190.5

1

a Units of ACO2 used by Dershowitz are g s−1 g−1 (mol cm−3 )−0.26 ; Kajitani used MPa−n s−1 with a random pore model; others used kg m−2 s−1 Pa−nCO2 . Activation energies all in kJ mol−1 . Initial dimensionless parameters in random pore model are 26,10,1,1. Lig., Bit., and Sub-Bit. denote lignite, bituminous, and sub-bituminous coal, respectively. Char indicates that char was prepared externally and then used for gasification experiments; coal indicates that coal was directly fed into the reactor.

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

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D. Chen et al. / Combustion and Flame 194 (2018) 52–71

69

Fig. 15. Experimental and simulated results of ex-situ Exp.1 (left) and ex-situ Exp.2 (right).

predict the rate at low conversion fractions or over-predict the rate at high conversion fractions. 6. Conclusions A novel characteristic of this work is the implementation of in-situ char gasification with CO2 and H2 O simultaneously in an E-DFF by simulating the real combustion conditions of air-staged combustion in an actual boiler. At the same time, a CFD-aided optimization method has been developed to derive the kinetics of in-situ char gasification. The conclusions from this work are as follows:

Fig. 16. Arrhenius plot of in-situ and ex-situ kinetics.

conversion. The coal oxidation in the main combustion zone consumes amorphous carbon with higher reactivity than the remaining graphite carbon, leading to a decrease in char reactivity. Parameters that do not consider this deactivation effect either under-

1. In-situ char gasification kinetics were determined through a series optimization method based on experiment and CFD simulations of the realistic air-staged combustion on E-DFF. By comparing the optimized kinetic parameters for each stoichiometry ratio (0.6, 0.7, 0.8, 0.9), the gasification rate was found to decrease with an increase in coal conversion. An improved model was used to model the char gasification rate due to coal conversion; this model is expressed as kc = Aexp(-E/RTp )(1−XChar + 0.2)1.56 . The pre-exponential factor and activation energy for in-situ char gasification were

Fig. 17. Calculated gasification rate of 60 μm particles at 1400 °C with 20% CO2 (a) or 10% H2 O (b) vs. char conversion fraction (Note that Kajitani used pressurized DTF and random pore model).

70

D. Chen et al. / Combustion and Flame 194 (2018) 52–71

optimized from experimental data at different temperatures (1200 °C, 1300 °C, 1400 °C), giving kinetic parameters of ACO2 = 59.7 − 65.1kgm−2 s−1 Pa−1 , ECO2 = 250.5 − 254.2kJmol−1 ; . AH2 O = 0.412 − 0.495kgm−2 s−1 Pa−1 , EH2 O = 188.4 − 191.3kJmol−1 2. By comparing in-situ char gasification kinetics derived from realistic air staged combustion experiment and ex-situ kinetics from gasification experiment of the same coal, it is found that the in-situ gasification rate is 0.46 times of that from ex-situ experiment 2, and 4.54 times of that from ex-situ experiment 1. In ex-situ experiment 2, raw coal is directly used for gasification, and prepared cooled char is used in ex-situ experiment 1. This indicating that kinetics derived from ex-situ char gasification experiments cannot give an accurate prediction of the reductive gases like CO and H2 in air-staged combustion. 3. Char gasification rate was found to decrease with the increase of stoichiometry ratio in air-staged combustion, which mainly due to the reduction of char activity at a high coal conversion. Char kinetics from published drop tube furnace works were found to be constant at different coal conversions, making it impossible to provide good predictions of char gasification for the different stoichiometry ratios involved in the airstaged combustion of pulverized coal. 4. It has been shown that gasification reactions in the reduction zone consume 13–60 wt% of the char mass and contribute 2.4– 17.4 vol% CO and 0.4–3.7 vol% H2 . Detailed values depend on the temperature and stoichiometry ratio. In typical air-staged combustion of pulverized coal, the stoichiometry ratio is 0.7 and the OFA ratio is 0.3. At a temperature of 1400 °C, more than 46% char will be consumed and produce 11.6 vol% CO and 2.3 vol% H2 . These values might be even higher in a highly reducing location that is rich in coal particles. It is obvious that char gasification is very important for modern staged combustion systems. Author declaration This manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. There are no known conflicts of interest associated with this publication. We confirm that we have provided a current, correct email address which is accessible by the Corresponding Author and which has been configured to accept email from: [email protected]. Acknowledgment This research was funded by the National Key Research and Development Project (2016YFB0600802-A) and the National Natural Science Foundation of China (51376105, 91434124, 51561125001). References [1] T. Abbas, M. Costa, P. Costen, S. Godoy, F.C. Lockwood, J.J. Ou, C. Romo-Millares, J. Zhou, NOx formation and reduction mechanisms in pulverized coal flames, Fuel 9 (1994) 1423–1436. [2] L.L. Baxter, R.E. Mitchell, T.H. Fletcher, R.H. Hurt, Nitrogen release during coal combustion, Energy Fuels 1 (1996) 188–196. [3] B. Coda, F. Kluger, D. Förtsch, H. Spliethoff, K. Hein, L. Tognotti, Coal-nitrogen release and NOx evolution in air-staged combustion, Energy Fuels 6 (1998) 1322–1327. [4] M. Taniguchi, Y. Kamikawa, T. Tatsumi, K. Yamamoto, Staged combustion properties for pulverized coals at high temperature, Combust. Flame 11 (2011) 2261–2271. [5] Z. Zhang, D. Chen, Z. Li, N. Cai, J. Imada, Development of sulfur release and reaction model for CFD modeling in sub-bituminous coal combustion, Energy Fuels 31 (2017) 1383–1398. [6] J.C. Nava-Paz, A.L. Plumley, O.K. Chow, W. Chen, Waterwall corrosion mechanisms in coal combustion environments, Mater. High Temp. 3 (2002) 127–137. [7] S. Li, K.J. Whitty, Physical phenomena of char–slag transition in pulverized coal gasification, Fuel Process. Technol. 95 (2012) 127–136.

[8] S. Li, Y. Wu, K.J. Whitty, Ash deposition behavior during char− slag transition under simulated gasification conditions, Energy Fuels 3 (2010) 1868–1876. [9] H. Zhou, G. Mo, D. Si, K. Cen, Numerical simulation of the NOx emissions in a 10 0 0 MW tangentially fired pulverized-coal boiler: influence of the multi-group arrangement of the separated over fire air, Energy Fuels 5 (2011) 2004–2012. [10] C.R. Choi, C.N. Kim, Numerical investigation on the flow, combustion and NOx emission characteristics in a 500 MWe tangentially fired pulverized-coal boiler, Fuel 9 (2009) 1720–1731. [11] X. Zhang, J. Zhou, S. Sun, R. Sun, M. Qin, Numerical investigation of low NOx combustion strategies in tangentially-fired coal boilers, Fuel (2015) 215–221. [12] H. Liu, Y. Liu, G. Yi, L. Nie, D. Che, Effects of air staging conditions on the combustion and NOx emission characteristics in a 600 MW wall fired utility boiler using lean coal, Energy Fuels 10 (2013) 5831–5840. [13] M. Kuang, Q. Zhu, Z. Li, X. Zhang, Numerical investigation on combustion and NOx emissions of a down-fired 350 MWe utility boiler with multiple injection and multiple staging: effect of the air stoichiometric ratio in the primary combustion zone, Fuel Process. Technol. 109 (2013) 32–42. [14] L.I. Díez, C. Cortés, J. Pallarés, Numerical investigation of NOx emissions from a tangentially-fired utility boiler under conventional and overfire air operation, Fuel 7 (2008) 1259–1269. [15] T. Le Bris, F. Cadavid, S. Caillat, S. Pietrzyk, J. Blondin, B. Baudoin, Coal combustion modelling of large power plant, for NOx abatement, Fuel 14 (2007) 2213–2220. [16] C. Yin, S. Caillat, J. Harion, B. Baudoin, E. Perez, Investigation of the flow, combustion, heat-transfer and emissions from a 609 MW utility tangentially fired pulverized-coal boiler, Fuel 8 (2002) 997–1006. [17] N. Modlinski, Computational modeling of a utility boiler tangentially-fired furnace retrofitted with swirl burners, Fuel Process. Technol. 11 (2010) 1601–1608. [18] H. Liu, C. Tang, L. Zhang, H. Zhu, L. Nie, D. Che, Effect of two-level over-fire air on the combustion and NOx emission characteristics in a 600 MW wall-fired boiler, Numer. Heat Transf., Part A 9 (2015) 993–1009. [19] E.S. Hecht, C.R. Shaddix, A. Molina, B.S. Haynes, Effect of CO2 gasification reaction on oxy-combustion of pulverized coal char, Proc. Combust. Inst. 2 (2011) 1699–1706. [20] L. Chen, S.Z. Yong, A.F. Ghoniem, Oxy-fuel combustion of pulverized coal: characterization, fundamentals, stabilization and CFD modeling, Prog. Energy Combust. Sci. 2 (2012) 156–214. [21] D. Kim, S. Choi, C.R. Shaddix, M. Geier, Effect of CO2 gasification reaction on char particle combustion in oxy-fuel conditions, Fuel 120 (2014) 130–140. [22] Y. Niu, C.R. Shaddix, A sophisticated model to predict ash inhibition during combustion of pulverized char particles, Proc. Combust. Inst. 1 (2015) 561–569. [23] S. Kajitani, N. Suzuki, M. Ashizawa, S. Hara, CO2 gasification rate analysis of coal char in entrained flow coal gasifier, Fuel 2 (2006) 163–169. [24] Y.C. Choi, X.Y. Li, T.J. Park, J.H. Kim, J.G. Lee, Numerical study on the coal gasification characteristics in an entrained flow coal gasifier, Fuel 15 (2001) 2193–2201. [25] X. Guo, Z. Dai, X. Gong, X. Chen, H. Liu, F. Wang, Z. Yu, Performance of an entrained-flow gasification technology of pulverized coal in pilot-scale plant, Fuel Process. Technol. 5 (2007) 451–459. [26] N. Crnomarkovic, B. Repic, R. Mladenovic, O. Neskovic, M. Veljkovic, Experimental investigation of role of steam in entrained flow coal gasification, Fuel 1 (2007) 194–202. [27] H. Watanabe, M. Otaka, Numerical simulation of coal gasification in entrained flow coal gasifier, Fuel 12 (2006) 1935–1943. [28] S. Kajitani, S. Hara, H. Matsuda, Gasification rate analysis of coal char with a pressurized drop tube furnace, Fuel 5 (2002) 539–546. [29] T. Liu, Y. Fang, Y. Wang, An experimental investigation into the gasification reactivity of chars prepared at high temperatures, Fuel 4 (2008) 460–466. [30] Q. Li, C. Zhao, X. Chen, W. Wu, Y. Li, Comparison of pulverized coal combustion in air and in O2 /CO2 mixtures by thermo-gravimetric analysis, J. Anal. Appl. Pyrolysis 1-2 (2009) 521–528. [31] P. Salatino, O. Senneca, S. Masi, Gasification of a coal char by oxygen and carbon dioxide, Carbon 4 (1998) 443–452. [32] G. Liu, P. Benyon, K.E. Benfell, G.W. Bryant, A.G. Tate, R.K. Boyd, D.J. Harris, T.F. Wall, Porous structure of bituminous coal chars and its influence on combustion and gasification under chemically controlled conditions, Fuel 6 (20 0 0) 617–626. [33] D.J. Harris, I.W. Smith, Intrinsic reactivity of petroleum coke and brown coal char to carbon dioxide, steam and oxygen, Symp. (Int.) Combust. 1 (1991) 1185–1190. [34] L. Ren, J. Yang, F. Gao, J. Yan, Laboratory study on gasification reactivity of coals and petcokes in CO2 /steam at high temperatures, Energy Fuels 9 (2013) 5054–5068. [35] S. Wu, J. Gu, L. Li, Y. Wu, J. Gao, The reactivity and kinetics of Yanzhou coal chars from elevated pyrolysis temperatures during gasification in steam at 90 0–120 0 C, Process Saf. Environ. Prot. 6 (2006) 420–428. [36] F. Wang, X. Zeng, R. Shao, Y. Wang, J. Yu, G. Xu, Isothermal gasification of in situ/ex situ coal char with CO2 in a micro fluidized bed reaction analyzer, Energy Fuels 8 (2015) 4795–4802. [37] Y. Guo, Y. Zhao, D. Gao, P. Liu, S. Meng, S. Sun, Kinetics of steam gasification of in-situ chars in a micro fluidized bed, Int. J. Hydrogen Energy 34 (2016) 15187–15198. [38] H. Liu, H. Zhu, M. Kaneko, S. Kato, T. Kojima, High-temperature gasification reactivity with steam of coal chars derived under various pyrolysis conditions in a fluidized bed, Energy Fuels 1 (2009) 68–75.

D. Chen et al. / Combustion and Flame 194 (2018) 52–71 [39] G.J. Goetz, N.Y. Nsakala, R.L. Patel, T.C. Lao, Combustion and gasification characteristics of chars from four commercially significant coals of different rank, Combustion Engineering, Inc., Windsor, CT, 1982. [40] M.S. Dershowitz, High temperature gasification of coal char in carbon dioxide and steam, Massachusetts Institute of Technology, 1979. [41] C. Gonzalo-Tirado, S. Jiménez, J. Ballester, Gasification of a pulverized sub-bituminous coal in CO2 at atmospheric pressure in an entrained flow reactor, Combust. Flame 1 (2012) 385–395. [42] F.F. Peng, I.C. Lee, R.Y.K. Yang, Reactivities of in situ and ex situ coal chars during gasification in steam at 10 0 0–140 0 °C, Fuel Process. Technol. 3 (1995) 233–251. [43] K. Jayaraman, I. Gokalp, E. Bonifaci, N. Merlo, Kinetics of steam and CO2 gasification of high ash coal–char produced under various heating rates, Fuel (2015) 370–379. [44] Y. Sekine, K. Ishikawa, E. Kikuchi, M. Matsukata, A. Akimoto, Reactivity and structural change of coal char during steam gasification, Fuel 2 (2006) 122–126. [45] S. Dong, P. Alvarez, N. Paterson, D.R. Dugwell, R. Kandiyoti, Study on the effect of heat treatment and gasification on the carbon structure of coal chars and metallurgical cokes using Fourier transform Raman spectroscopy, Energy Fuels 3 (2009) 1651–1661. [46] R.C. Everson, H.W. Neomagus, H. Kasaini, D. Njapha, Reaction kinetics of pulverized coal-chars derived from inertinite-rich coal discards: gasification with carbon dioxide and steam, Fuel 7 (2006) 1076–1082. [47] H. Mühlen, K.H. van Heek, H. Jüntgen, Kinetic studies of steam gasification of char in the presence of H2 , CO2 and CO, Fuel 7 (1985) 944–949. [48] D.G. Roberts, D.J. Harris, Char gasification in mixtures of CO2 and H2 O: Competition and inhibition, Fuel 17-18 (2007) 2672–2678. [49] M. Costa, J. Azevedo, Experimental characterization of an industrial pulverized coal-fired furnace under deep staging conditions, Combust. Sci. Technol. 9 (2007) 1923–1935. [50] Proximate analysis of coal (GB/T 212-2008), https://www.chinesestandard.net/ Default.aspx?PDF- English- ID=GB/T%20212- 2008. [51] Ultimate analysis of coal(GB/T 31391-2015), https://www.chinesestandard.net/ Default.aspx?PDF- English- ID=GB/T%2031391- 2015. [52] J. Ballester, S. Jiménez, Kinetic parameters for the oxidation of pulverised coal as measured from drop tube tests, Combust. Flame 142 (3) (2005) 210–222. [53] W.P. Jones, R.P. Lindstedt, Global reaction schemes for hydrocarbon combustion, Combust. Flame 3 (1988) 233–249. [54] C.K. Westbrook, F.L. Dryer, Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames, Combust. Sci. Technol. 1-2 (1981) 31–43. [55] B.F. Magnussen, B.H. Hjertager, On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion, Symp. (Int.) Combust. 1 (1977) 719–729. [56] T.H. Fletcher, A.R. Kerstein, R.J. Pugmire, D.M. Grant, Chemical percolation model for devolatilization. 2. Temperature and heating rate effects on product yields, Energy Fuels 1 (1990) 54–60.

71

[57] D.M. Grant, R.J. Pugmire, T.H. Fletcher, A.R. Kerstein, Chemical model of coal devolatilization using percolation lattice statistics, Energy Fuels 2 (1989) 175–186. [58] D.B. Genetti, An advanced model of coal devolatilization based on chemical structure, Brigham Young University, 1999. [59] M.A. Field, Rate of combustion of size-graded fractions of char from a low-rank coal between 1200°K and 2000°K, Combust. Flame 3 (1969) 237–252. [60] M.M. Baum, P.J. Street, Predicting the combustion behavior of coal particles, Combust. Sci. Technol. 5 (1971) 231–243. [61] R.H. Perry, D.W. Green, Perry’s chemical engineers’ handbook, McGraw-Hill, New York, 2008, pp. 5–49. [62] Z. Huang, J. Zhang, Y. Zhao, H. Zhang, G. Yue, T. Suda, M. Narukawa, Kinetic studies of char gasification by steam and CO2 in the presence of H2 and CO, Fuel Process. Technol. 8 (2010) 843–847. [63] L. Tognotti, J.P. Longwell, A.F. Sarofim, The products of the high temperature oxidation of a single char particle in an electrodynamic balance, Symp. (Int.) Combust. 23 (1991) 1207–1213. [64] O. Karlström, A. Brink, M. Hupa, L. Tognotti, Multivariable optimization of reaction order and kinetic parameters for high temperature oxidation of 10 bituminous coal chars, Combust. Flame 10 (2011) 2056–2063. [65] T.H. Fletcher, Swelling properties of coal chars during rapid pyrolysis and combustion, Fuel 11 (1993) 1485–1495. [66] I.W. Smith, The combustion rates of coal chars: a review, Symp. (Int.) Combust. 1 (1982) 1045–1065. [67] I.W. Smith, The kinetics of combustion of pulverized semi-anthracite in the temperature range 140 0–220 0 K, Combust. Flame 3 (1971) 421–428. [68] W.E. Ranz, Evaporation from drops: part 1, Chem. Eng. Prog. 48 (1952) 141–146. [69] Z. Yang, T. Shih, New time scale based k-epsilon model for near-wall turbulence, AIAA J. (7) (1993) 1191–1198. [70] P. Cheng, Two-dimensional radiating gas flow by a moment method, AIAA J. 2 (1964) 1662–1664. [71] E.H. Chui, G.D. Raithby, Computation of radiant heat transfer on a no-orthogonal mesh using the finite-volume method, Numer. Heat Transf., Part B 23 (1993) 269–288. [72] J. Murthy, S. Mathur, A finite volume method for radiative heat transfer using unstructured meshes, Asian Pacific Confederation of Chemical Engineering Congress Program (2013) pp. 486–486. [73] R. Hooke, T.A. Jeeves, “Direct Search” solution of numerical and statistical problems, J. ACM (JACM) 2 (1961) 212–229. [74] A. Molina, F. Mondragón, Reactivity of coal gasification with steam and CO2 , Fuel 15 (1998) 1831–1839. [75] Jatale, A., et al., Application of a verification, validation and uncertainty quantification framework to a turbulent buoyant helium plume flow, Turbul. Combust. 95(2015) 143–168