Steady state kinetic model for entrained flow CO2 gasification of biomass at high temperature

Journal Pre-proof Steady state kinetic model for entrained flow CO2 gasification of biomass at high temperature M.A. Kibria, Pramod Sripada, Sankar Bhattacharya PII:

S0360-5442(20)30180-8

DOI:

https://doi.org/10.1016/j.energy.2020.117073

Reference:

EGY 117073

To appear in:

Energy

Received Date: 14 October 2019 Revised Date:

23 January 2020

Accepted Date: 29 January 2020

Please cite this article as: Kibria MA, Sripada P, Bhattacharya S, Steady state kinetic model for entrained flow CO2 gasification of biomass at high temperature, Energy (2020), doi: https:// doi.org/10.1016/j.energy.2020.117073. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Steady state kinetic model for Entrained flow CO2 gasification of Biomass at high temperature M.A. Kibria*, Pramod Sripada, Sankar Bhattacharya Department of Chemical Engineering, Monash University, VIC 3800, Australia

Abstract Entrained flow gasification technology is considered as a promising technology for its unique nature; high carbon conversion in short residence time and fewer pollutants emission for utilizing solid fuels towards high-value products. In a two-stage dry feed entrained flow gasifier, CO2 is the predominant gas species that evolves from combustion zone with a concentration around 77% and 18% during oxy and air-fired gasifier respectively. The CO2 rich gas stream acts as a reactant in the reduction zone that produces syngas. This article presents a kinetic model of CO2 gasification of biomass that mimics the reduction zone of a dry feed entrained flow reactor. The model is based on plug flow analogy for heat and mass balance. Explicit calculations are performed to calculate particle residence time. Gas-phase reactions are introduced, and the predicted results are compared against a benchscale entrained flow reactor. The results indicate during high-temperature CO2 gasification condition; the gas-phase chemistry is dominated by the homogenous reverse water gas shift reaction (rWGSR). Particle structure plays an essential role by imposing diffusional effects during char conversion. An increased concentration of CO2 served a dual purpose: raising devolatilization rate and lowering the diffusional limitation. * Corresponding author: M. A. Kibria ([email protected])

Highlights • Reverse water gas shift reaction is a significant reaction during CO2 gasification • Particle structure plays an essential role during char conversion • Higher CO2 level promotes the devolatilization rate • Higher CO2 level decreases diffusional limitation

Key words: Gasification; Entrained flow; Model

1

Nomenclature Specific heat capacity (J/kg.K)

CP C&

Gas Concentration (kmol/m3) Diffusion rate (m2/s) Reactor Diameter (m)

D Dr

Activation energy (J/mol) Fraction of energy that is consumed in particle

E

fh fc

Moles of CO2 required for complete gasification of unit mass of carbon Heat of reaction (J/g) Convective heat transfer rate (W/m2. K) Mass flow rate (kg/s)

∆H

h •

m n T

V S

υ

R

MW MF •

MOLEFLOW Y

t L P

k X Subscript

c mix p g

s v i, j w Pd Rt x

Reaction order Temperature (K) Volume fraction (Dimensionless) Source term in the mass balance Stoichiometric coefficient Reaction rate (kmol/m^3.s) or Gas constant where appropriate Molecular weight (g/mol) Mass fraction Molar flow rate (kmol/s) Mole fraction Time (s) Reactor length (m) Pressure (atm) Pre-exponential factor (1/s or 1/s.atmn where appropriate) Conversion (dimensionless) Carbon Mixture Particle Gas phase Solid phase Volatile Integer number Reactor wall Product Reactants Position

Symbols

εp ε τ φ Ω

σ

ψ

λ

Emissivity of particle (Dimensionless) Porosity (Dimensionless) Tortuosity of particle (Dimensionless) Thiele Modulus (Dimensionless) Collusion diameter (Dimensionless) Stefan–Boltzmann constant (W/m2K4) Structural parameter (Dimensionless) Thermal conductivity (W/m.K) 2

ρ µ

Density (kg/m3) Dynamic viscosity (kg/m.s)

1.0 Introduction The global energy demand is projected to increase by 40% by the year 2035. To mitigate the increasing energy trend, the field of renewable energy resource has been received considerable attention from the government worldwide over the years. It is expected renewable energy resource can provide half of the power generation capacity between 2035 [1]. Biomass, a renewable energy resource, is also the fourth largest source of energy in the world. Biomass can be converted to valuable products through various pathways classified as biochemical or thermochemical routes. Gasification is a thermochemical route in which biomass is partially combusted to produce low calorific value gas, syngas, which is a mixture of CO, H2, CH4, CO2 and contaminates (NH3, H2S, and HCN etc.) [2]. Mainly four significant steps are involved in gasification,i.e., drying, devolatilization, combustion and gasification. Numerous researches have been carried out to explore and understand the effects of the different gasifying agent such as steam, air, oxygen and their combination on the gasification process [3-5]. However, the role of CO2 as an oxidizing agent on the gasification behavior has been explored in a limited number of studies which might be an alternative route to deal with the massive amount of CO2 producing from various industrial stream [6, 7]. CO2 is a significant cause of global warming [8]. Using CO2 as a gasifying agent can serve a dual purpose,i.e., reducing greenhouse gas and producing syngas. In a two-stage dry feed entrained flow gasifier, CO2 is the predominant gas species that evolves from combustion zone with a concentration of around 77% and 18% during oxy and air-fired gasifier respectively [9]. The volumetric ratio of CO2 to H2O is close to 3.5~4 in this case. This designates, the CO2 is the dominant gas species in the flue gases and can act as a reactant in the reduction zone. As a result, it is crucial to understand the role of CO2 during gasification as the reaction between carbon and CO2 is known as the rate limiting step during gasification of solid fuel such as coal or biomass. Gasification reactions of solid carbonaceous material are complex and can be influenced by the thermodynamic and hydrodynamic coupling between solid and gas phase inside the gasifier. A mathematical model can provide detail information about the complex gasification chemistry while the particles change their physical and thermal properties inside the gasifier. Until now, numerous numerical works have been reported in the literature for predicting carbon conversion during different gasification media along with the different level of kinetics and mixing. Ubhayakar et al. developed a one-dimensional model considering the axial mixing of gas [10]. They neglected the solid-phase reactions and considered only the gas-phase reactions of volatile products. Wen and Chaung developed a cell-in-series approach to predict the gasification behaviour of Texaco pilot plant entrained flow gasifier [11]. Each of the cells was considered as a well-stirred reactor for the gas phase whereas the solid phase was considered as plug flow condition. Govind and Shah further refined the model by using momentum balance instead of Stokes law approximation [12]. Both of the studies did a parametric investigation to provide a better understanding of rector performance on carbon conversion. Vamvuka et al. used a plug flow model to study the gasifier performance for the different operating condition [13, 14]. The finite reaction rate for a solid-phase reaction while equilibrium for gas-phase reactions was considered in their model. Furthermore, a more complex

3

numerical model for two/three-dimensional gasifier with turbulence and mixing has been reported using CFD [15-23]. CO2, a dominant gas species in the flue gases, can act as a reactant in the reduction zone of an entrained flow reactor. The influence of CO2 in the gas phase reactions along with the solid phase reactions can significantly affect the syngas composition at the reactor outlet. However, gasification chemistry where CO2 is used as an oxidizing agent during entrained flow condition at high temperature is not well explored in the literature to the authors’ best knowledge. This paper addresses this information gap through detailed mathematical modelling of CO2 gasification of biomass in the reduction zone of an entrained flow reactor at high temperature. The primary purpose of the present article is to justify our published experimental data [6] in terms of a mathematical model so that the involved reactions during direct CO2 gasification of biomass at entrained flow condition can be explored and understood. A secondary purpose is to model the internal mass transport limitation on carbon conversion during high-temperature gasification condition when the particles change their thermal and physical properties.

2.0 Mathematical formulation of solid phase A particle stream of the same diameter and initial temperature of 300 K is injected to an entrained flow reactor. Before particle injection, the reactor is heated to 1473 K with a certain N2 and CO2 flow condition. After injection, the particle temperature will rise and the particle stream will get entrained with the flowing incoming gases. After exceeding onset the devolatilization temperature, pyrolysis will start and pyrolysis gases will be generated. A part of heat energy imposed on the particle stream will be consumed as the heat of pyrolysis. Due to the very high heating rate, the particle temperature will approximately reach the reactor wall temperature while travelling a very short distance. The entire volatile component will be evolved and consecutively char will form. The Char is highly carbon-rich solid with a porous structure which will play a significant role in the syngas production by surface gasification reactions. The gases evolved during the char gasification event will influence all the transport properties of the gas mixture inside the reactor by changing the species mole balance. The change in species mole balance of gas mixture will modify the coupled heat and mass transfer phenomenon among the solid and gas side. As a consequence, the gas concentration of the available species will be changed accordingly. The change of the species gas concentrations will impact the involved homogenous reactions as well. The gasifying agent (CO2) on the particle surface will be consumed by the chemical kinetic rate while satisfying the bulk diffusion and pore diffusion limitation of the porous char. The particle stream will approach toward the end of reactor length. While approaching, all the fixed carbon will be gasified. All the homogenous reactions of equilibrium will try to balance their net effects. Thermal and physical properties of the particles will change with the thermal history of the particle stream carbon conversion. Both the gases and particle stream will have a different residence time inside the reactor. All these events described have their own mathematical formulation based on the position of particle stream. In the numerical model, plug flow analogy is adopted in which the residence time of

4

the particles inside the reactor is calculated explicitly. The transfer of calculated solid residence time to the reactor is achieved by adjusting the reactor diameter.

2.1 Assumptions and limitations The underlying assumptions are made during model development: • •

• • •

• • • • • • •

Although different particles should have different fate depending on particle position inside the reactor, we consider all the particles in a calculated plug have the same fate. The particles are assumed to be spherical with the same diameter. No fragmentation is considered. The particles have uniform temperature in the calculated plug. Any frictional force with particle to the wall is not considered. The particles are very dilute in the system [12]. The mass flow rate of particle and flow rate of injected gases are constant (Steady state) [6]. So, the particle and gas fraction are assumed to be fixed in a calculated plug. Stokes law is assumed to be valid when the explicit calculation of residence time of the particle is performed [24]. Particle density will change during solid conversion. A linear dependence is considered where the true char density is calculated according to IGT correlations [25]. The bimodal pore structure is considered [26]. All the gases inside the system obeyed the ideal gas law and binary diffusion coefficients pairs of the gases in the mixture are considered equal [27]. Any turbulence and recirculating of particle or gases inside the reactor are not considered. Char conversion dependent particle porosity and tortuosity are considered [28]. Gas-phase reactions are considered kinetically controlled and activated when devolatilization ends. Char gasification starts after devolatilization [29]. Sufficient gasifying agent (CO2) is all time present in excess inside the system. Particle thermal property changes with particle temperature [30]. Any heat loss from the system is not considered. The devolatilized gas is considered as a mixture of CO2, CO, H2and CH4 with a constant mass fraction [6].

2.2 Energy conservation For any length in the reactor, the rise in the temperature of the particle stream is modelled as a contribution of convective and radiative heat energy and heat of pyrolysis and heat of gasification [11]. •

m p ( x ) CP (Tp )

dTp dx

= hp DrVs (Tg ( x ) − Tp ( x ) ) + ε pσDrVs (Tg4( x ) − T p4( x ) ) − (∆H v Rv + f h ∆H gasification Rc )

(1)

Discretizing Eq. (1) we can obtain the predicted particle stream temperature for the next plug

Tp ( x+dx)

 h D V (T − T ) + ε σD V (T 4 − T 4 ) − (∆H R + f ∆H  p r s g ( x) p( x) p r s g ( x) v v h gasification Rc ) p( x)  ∆x = Tp ( x ) +  •   m p ( x ) CP (Tp )  

(2)

5

f h is a fraction of energy that would be consumed during gasification reaction. The rest (1- f h ) fraction of energy will be consumed in the gas phase [29]. VP is the volume fraction of particles. The gas-phase temperature is modelled considering a portion of the energy will be consumed or be added to the gas phase energy balance due to the gas phase reactions. If there is no heat loss from the gas phase, then the energy balance for the gas phase can be approximated as [11] •

dTg

m g ( x ) C P ( mix )

dx

(3)

= hg DrVg (Tw − Tg ) + ε gσDrVg (Tw4 − T g4 ) + (1 − f h )∆H gasificati on Rc − S i ∆H i

Discretizing Eq. (3) assuming that the gas temperature changes slowly from one-plug value to the next, we can obtain

Tg ( x+dx )

Here plug.

 h D V (T − T ) + ε σD V (T 4 − T 4 ) + (1 − f )∆H  g r g w g ( x) g r g w h gasification Rc − Si ∆H i g ( x)   ∆x = Tg ( x ) + •   m g ( x ) CP ( mix)  

Si is the source term due to homogenous gas reactions that are involved in the calculating

2.3 Mass conservation In the model, the solid particles are injected with an initial mass flow through a feeder nozzle. As there will be a rapid devolatilization and afterwards char gasification, the solid mass flow at the inlet of each plug will be higher than the outlet flow. The mass that is lost from the particle stream will be added as a source term in the gas phase. At the same time, there will be homogenous reactions in the available gas species in that calculated plug. The mass conservation both for solid and gas phase is calculated as •

•

mP ( x +1) = mP ( x ) − ( Rv + Rc )∆x

(5)

•

•

(6)

•

•

(7)

mv ( x+dx ) = mv ( x ) − Rv ∆x mc ( x+dx ) = mc ( x ) − Rc ∆x

During the gas phase mass conservation calculation, the creation or destruction of species involved in reaction j until Nth reactions is calculated as

6

 N ,reation  π Si =  ∑ (υ Pd − υ Rt )R j Dr2Vg MWi  4  i= j 

(8)

This source term is added in the mass balance equation of gases to incorporate the effects of gasphase reaction •

•

mg ,i ( x + dx) = mg ,i ( x ) + (MFi RV + υi Rc + Si )∆x

(9)

Then the total molar flow, mole fraction and concentration of gas species is calculated as •

•

MLFLOWg =

N , species

∑

mg ,i ( x+ dx) MWi

i •

Yi =

MLFLOW

Cg =

(11) g ,i

•

MLFLOW •

(10)

g

• N , species

m g ,i ( x + dx )t

∑ i

MW i

π

4

(12)

Dr2 L

Based on the assumptions presented in the assumption section, the program follows the following boundary condition while solving the nonlinear equations. As the reactor wall temperature is fixed, the maximum gas temperature could be the wall temperature. At X=0, the particle and gas temperature start from an initial condition (Tg=Ts=300 K). At X= L (full reactor length), the program terminates.

2.4 Particle and gas-phase fraction calculation To evaluate the energy balance and the reactions involved, it is essential to know the particle fraction available inside the reactor during steady-state flow. We assumed that the particle fraction is fixed in the entire reactor. The fraction is calculated as the ratio of the total volume of the injected particles to the reactor volume and expressed as •

mP ( x = 0) t Vs =

(13)

ρ s ( x = 0) π 2 4

Dr L

The gas fraction is calculated as

Vg = (1 −Vs )

(14)

7

2.5 Heat of pyrolysis, gasification and gas-phase reactions The heat of pyrolysis ∆Hv is the net heat required to convert solid biomass into gas, liquid and char. In the numerical model, it is considered as 1.6 kJ/g of dry biomass (Pine) [31]. The heat for gasification reaction

∆Hgasificati onis considered as 14.3kJ/g of Carbon consumed [32].

The gas-phase enthalpy ∆H j of the involved reactions is calculated as the enthalpy changes due to change in reactants to product

∆H j = ∑ H Pd − ∑ H Rt

(15)

Here, a negative value of ∆H j means the reaction involved is exothermic and it will contribute to increasing the gas stream temperature. However, positive ∆H j means the reaction is endothermic and require energy ultimately lower down the gas stream temperature. The enthalpy of each species for the reaction temperature is calculated as [33] H i0 − H i0, 298 .15 = AT +

BT 2

2

CT 3 DT + 3 4

+

4

−

E +F −H T

(16)

2.6 Mixture properties of gases Binary diffusion of CO2 throughout the gas mixture outer the particle surface is modelled as [34] −

DCO2 =

1 − YCO2 n Yi ∑ i =1 DCO2 ,i

(17)

The diffusion of CO2 in each gas species available in the gas mixture is calculated as [35] 1/ 2

 1 1  + 0.001858T 3 / 2    MWi MWj  Dij = Pσ ij2Ω T =

T p + Tg

(18)

(19)

2

Here T is the mean temperature.

(20)

The mixture viscosity of the gases is modelled considering a binary mixture of gases [36] n

µ mix = ∑ i =1

1+

µi 113 .58 µ iT Yi MWi

(21) n

Yj

∑D j =1

ij

8

The viscosity of the individual gases in the gas mixture is modelled described by Chapman and Enskog [37]. All other thermal properties of the mixture gases (i.e. density, thermal conductivity and specific heat) are modelled as [38, 39]

ρmix =

(22)

P n ∑Yi MWi RT i=1 n

λ mix =

∑ λ Y ( MW ) i i

i =1

∑

n i =1

1/ 3

(23)

i

Yi MW i1 / 3

(24)

n

CP(mix) = ∑YiCpi i=1

2.7 Devolatilization model In the present model, the rate of devolatilization is considered as a first-order reaction with the remaining volatile and expressed as

 − Ev  dX v (1 − X v ) = k v exp dt  RTP 

(25)

Where Xv is the volatile conversion and calculated as •

(26)

mv ( x )

Xv = 1−

•

mv ( x=0 ) The unit conversion of Eq. (25) from 1/s to kg/ (s.m ) is calculated considering all the particles in the calculated plug area in which the density of the particle changes from bulk to char density. The change in the density depends on the solid conversion and details of calculating bulk and char density is presented in the proceeding section. Rv = ρ s ( x )

π 4

2

Dr Vs

dX v dt

(27)

The reaction kinetics used in the present simulation for the devolatilization model is taken from ref [40].

2.8 Char consumption model To understand the influence structural changes (porosity and pore structure) of the biomass particles on gasification rate, Random pore kinetic model (RPM) is used to model the char consumption rate [41]. The char conversion is calculated as the ash-free basis and defined as •

Xc =1−

mc ( x )

(28)

•

mc ( x=0 )

9

The gasification rate of char consumption is calculated as [41] dX c = K RPM (1 − X c ) 1 − ψ ln(1 − X c ) dt

(29)

The rate of constant KRPM is modelled by introducing the mole fraction of CO2 on the particle surface [42]

 − Ec   PYCO2 n K RPM = k c EXP  RTP 

(30)

Fig 1: Conceptual drawing of solid flow, single-particle structure and network diagram of diffusional resistance. As seen in Fig 1 (the single-particle), the gasification agent is likely to be consumed by the surface Boudouard reaction with an intrinsic rate while satisfying the diffusional resistance due to the porous nature of the char. As seen in the network diagram, the char consumption rate might be influenced by both pore diffusion (internal) and bulk diffusion (external) limitation. In the present model, the pore diffusion (internal) is modelled as Knudsen diffusion and the bulk diffusion (external) is modelled as binary diffusion of CO2 in the gas mixture. The intrinsic rate of char gasification for per meter of reactor length is calculated considering all the particle available on calculated plug area multiplying by the particle density where particle density changes from char to ash density. Rc ,int rinsic = ρ s ( x )

π 4

2

Dr Vs

dX c dt

(31)

10

The apparent char gasification rate is calculated by introducing the effectiveness factor with the intrinsic rate in which all the internal mass resistive parameters are incorporated and expressed as

Rc = ηRc,int rinsic

(32)

In the present model,effectiveness is calculated with a relation of Thiele modulus [43, 44]

η=

φ=

1 1 1 −   φ  tanh( 3φ ) 3φ 

 − Ec   1 − ψ ln(1 − X c ) ( PYCO2 ) n −1 RTρ s ( x ) (1 − X c )kc EXP (n + 1)  RTP  2 MWC Deff

dp 6

(33)

(34)

The bulk molecular diffusion is modelled while considering the porosity and tortuosity of these pores [26]. D Bulk =

ε − D CO τ

(35) 2

The effective diffusion of CO2 Deff is calculated from Ref [45] while incorporating the bulk molecular diffusion and Knudsen diffusion [46]

Deff =

1

(36)

1 1 + Dk DBulk

The Knudsen diffusion Dk is modelled as [43]

Dk =

d pore 3

8RT πMWCO2

(37)

During gasification of porous char, Knudsen diffusion dominates the gasification rate at high temperature while the bulk diffusion dominates at low temperature. It also depends on the pore structure as the char structure is changing with carbon conversion. The mean pore diameter that incorporates all the structural parameters of the porous particle is calculated as [26]

d pore

4ετ 0.5 = SC ρC

(38)

The change in specific surface area and porosity are modelled as [28]

SC = SC0 (1 − X c ) 1 −ψ ln(1 − X c )

(39)

11

ε = ε 0 + (1 − ε 0 ) X c

(40)

The kinetic parameters used for the intrinsic char consumption rate is taken from authors previous publication [42]

2.9 Modeling gas-phase reactions The identification of involved gas-phase reactions was driven from our previous published direct CO2 gasification of biomass experiment during entrained flow condition at high-temperature. During enrich CO2 atmosphere in the absence of Oxygen; the Boudouard reaction is found to be dominant that can consume char to produce CO. The pyrolysis gas containing H2, CO and CH4 and the product CO during char gasification alter the syngas composition while approaching to the end of the reactor. As CO2 is all time available in excess at high temperature along with H2, there might be a possibility that the water gas shift reaction will be favoured in the backward direction. This will consume a part of H2while producing water vapour (H2O). Depending on the CO and produced H2O concentration, the forward water gas shift reaction will be activated and these two-opposing reactions will try to reach the equilibrium condition. In our experiments, the feed biomass was air-dried. We assumed the only source of water vapour (H2O) in the system is due to the activity of reverse water gas shift reaction. The produced H2O should have a low concentration (maximum 2% in mole fraction as calculated) compared to CO2 to drive the steam gasification reaction of char. As a result, steam gasification on the char surface is ignored in the present study. However, as the water (H2O) will be in the gas phase at high temperature, it might have an affinity to drive the steam reforming reaction of CH4 (MSR) and forward water gas shift reaction (fWGSR) with CO. Under these observations from previous experience, the reactions considered for the present model are (Table 1): Table 1: Reaction rates used in the simulation Rate Reactions Chemistry kmol/m3.s R1 Boudouard C+CO2=2CO R2 fWGSR CO+H2O= CO2+ H2 R3 rWGSR CO2+H2=CO+ H2O R4 (MSR) CH4+H2O=CO+3H2 **

Rate expression

Ref

Expressed in Ref R2=2.75x106exp(-83736/RT)CH2OCCO R3=1.2x1013exp(-318000/RT)CH20.5 CCO2 R4=312exp(-30000/1.987T)*(CCH4CCO.CH23/(Keq.CH2O)) ** Keq=exp (33.1371-25014.0499/T)

[42] [47] [48] [11]

1.98 is multiplied before T due to universal gas constant is cal/mol.K and Equilibrium is calculated and incorporated

2.10 Thermal and physical properties of a particle In the present model, the specific heat capacity (Cp(Tp)) of the biomass particle is temperaturedependent and modelled as Fig.2 [30]. The specific heat of pyrolyzed wood at 523 K is about 1.25 kJ/kg.K and the specific heat increases approximately 1.9 kJ/kg.K in a temperature range of 523- 673 K due to the formation of char.

12

Fig 2: Specific heat capacity of wood at different temperature In the numerical calculation, the mass flow rate of the particle is divided into mass flow as volatile, fixed carbon and ash taken from the high-temperature devolatilization experiment tabulated in Table 2. •

•

(41)

•

•

(42)

mv ( x =0) = m p ( x =0) * MFv mc ( x =0) = m p ( x =0) * MFc •

•

mash( x=0) = m p ( x=0) * MFash

(43)

The change in density of the biomass particle is considered as a function of volatile and char conversion. The initial density, i.e. the bulk density of the particle will change to char or skeleton density when devolatilization is completed. Then the char density will change into ash density when full char conversion is completed. A linear dependency is used to model the intermediate change while solid conversion proceeds. The bulk density was considered as 400kg/m3 for pine bark. The char density was calculated using the IGT char density model[25] which was 2328 kg/m3.The density changes are calculated as

ρ s ( x ) = ρ s ,bulk (1 − X v ) + X v ρ s ,char

(44)

ρ s ( x ) = ρ s ,char (1 − X c ) + X c ρ s ,ash

(45)

Usually, the conversion of the useful component of the biomass is generally closely 100% for gasification applications. As a result, we consider the density of the solid at the outlet is ash density and calculated as dry basis

ρ s ,ash = ρ s ,bulk (1 − Ymoisture ).Yash

(46)

13

2.11 Calculation of solid residence time In this plug flow model, the residence time is calculated as VR

t=

(47)

1

∫

dVR • 0V •

Here V is the volumetric flow rate of the incoming gases after devolatilization. The calculated residence time using Eq. (47) is mainly the residence time of the gas phase. So, it is important to correct the residence time for solid particles. In the present model, the diameter of the biomass particle is considered as 90 µm. The Reynold number is calculated as

Re =

d Puρ mix

(48)

µmix

For the present system, the calculated gas mixture density = 0.268 kg/m3and viscosity is 4.7x105Pa.s The value of gas mixture density and viscosity is calculated based on Eq (22-23) after full devolatilization event at atmospheric pressure and 1200°C. The mixture mole fraction is taken from our previous publication [49]. Assuming the particles are injected with the gas velocity, the calculated Re number is <2 in the whole gasifier. This allows us to apply Stokes’ law as a valid regime for solid flow in the system[24]. According to Newton’s 2nd law and Stokes’ law, the downdraft velocity of the solid can be approximated [11]

(

vs = vs,i e−bt + (vg + vt ) 1− e−bt b=

)

(49)

18µ mix ρ s , H d P2

(50)

The terminal settling velocity of particles in the fluid stream is calculated as

vt =

( ρ s , H − ρ mix )d P2 g

(51)

18µ mix

Integrating Eq. (49) gives us the relation of solid residence time with reactor length t

L = ∫ vs dt = 0

vs ,i  1 − e − bt 1 − e −bt + (v g + vt ) t − b b 

(

)

  

(52)

Based on Eq. (52), the solid residence time is solved by using Newton’s method. While the calculation is performed, the density and the viscosity of the gas mixture are taken after the devolatilization event. The solid density used in Eq. (50) is the average harmonic square root density of solid and defined as [50]

14

2 ρ s2,bulk .ρ s2, ash

ρ s, H =

(53)

ρ s2,bulk + ρ s2, ash

After the solid residence time is calculated, it is essential to transfer the result so that the gas residence time can be corrected for solid using Eq. (47). The transfer is accomplished by adjusting the gasifier diameter Vg .t =

π 4

Dr =

Dr2 L

(54)

Vg .t

(55)

π

4

L

2.12 Carbon conversion The initial carbon present in the feed biomass can contribute both in pyrolysis gas (gas phase) and char (solid phase). The carbon during devolatilization contributes as CO, CO2, CH4. During char gasification, carbon contributes as CO. The initial carbon that can contribute to the gas phase is calculated as

 MFCO 2 MFCO MFCO4 mC , PYR,0 = MWC  + +  MWCO 2 MWCO MWCO 4  •

•  m p ( x =0) * MFv  

(56)

Then the initial carbon present in the particle is calculated as •

•

•

(57)

mC,ini = mC, PYR,0 + mp( x=0) * MFc

The amount of total carbon from the gas phase Eq. (56) and solid-phase Eq. (42) is satisfied with the ultimate carbon content (5% error) of the biomass in dry basis tabulated in Table 2. Table 2: Ultimate and standard proximate analysis of fuel Standard Proximate at Pyrolysis at 1200°C in Ultimate analysis (wt%) 900°C(dbwt%) Entrained flow reactor Moisture 5 Volatile Yield (wt%) 77 C 49.8 Volatile 59.78 Char Yield (wt%) 23 H 5.9 Fixed carbon 23.91 Carbon in Char (wt%) 95 N 0.13 Ash 16.30 Ash in char (wt%) 5 S 0.1 O 42.9 Ash 1.15

During numerical calculation, the carbon in the gas phase due to devolatilization is calculated as •

mC , PYR dx

 MFCO 2 MFCO MFCH 4 = Rv MWC  + +  MWCO 2 MWCO MWCH 4 

   

(58)

The overall carbon conversion is calculated as 15

•

Overall _ conversion =

•

•

mC ,ini − (mC , PYR + mc X c ) •

(59)

*100

mC ,ini 2.13 Solution strategy The solution of the present mathematical model is based on the iterative solution of the energy balance of solid and gas phase while solving the nonlinear equations of devolatilization, chargasification model and gas-phase reaction kinetics. During the calculation of any plug, the primary target of the solution algorithm is to find convergence on the mean temperature and mass balance while satisfying the devolatilized mass, gasified carbon mass, all the transport properties of the available gases and the gas phase reactions involved. At the beginning of the calculation, the residence time of the solids inside the reactor is not known (the transport properties of the gas mixture are unknown based on Eq. (21-24)). As a result, the solid residence time is assumed so that the particle and gas fraction can be calculated. Depending on the flow condition, the devolatilization model is solved for 100% conversion. When the devolatilization model is solved, the transport properties of a gas mixture is known in which the solid residence time can be corrected. The transfer of solid residence time is accomplished by adjusting the reactor diameter, according to Eq. (54). The program is then reinitialized with the corrected plug diameter and residence time and the devolatilization model is solved again. When the change of residence time for subsequent run is <0.1, the residence time, as well as the reactor diameter, is optimized. The gasification and gas-phase reaction model start as soon as the devolatilization model ends. In the subsequent iteration of mean temperature, a secondary algorithm is triggered in which the system mole balance is converged by solving the gas-phase reactions model. The distance travelled by the particle phase is calculated and the program is terminated when the travelled distance is greater than reactor length. To solve the above equations, an explicit segregated coupled solver (ESCS) was developed using C++ program code. The code was tested for a single particle gasification model of authors’ previous publication [49]. The algorithm is extended for multiple particle simulation and presented in Fig 3.

16

Fig 3: ESCS algorithm

3.0 Results The numerical results of the present model are compared with our previous published experimental bench-scale entrained-flow CO2 gasification result of biomass for 10% ~40% CO2 concentration at 1200°C [6]. The entrained flow reactor used for model validation is an electrically heated 2.8-meterlong and has an internal diameter of 100 mm. It is capable of running from 1000- 1600 °C. The feeding system is situated on the top of the reactor. There are three impingers connected in series to collect the solid. A vacuum pump is connected with the last impinge to such the gases inside the 17

reactor. The reactor is coupled with online gas chromatograph to see the outlet gas concentration during experiments. The schematic diagram of the reactor system is presented in the Appendix. All the model parameters are taken from the authors' previous publication [49]. The model prediction and the comparison between the experimental results are presented in Table 3 Table 3: Comparison between numerical and experimental results (Dry basis 1200°C) 10% CO2+ 90%N2 20% CO2+ 80%N2 40% CO2+ 60%N2 Vol% Experiment Model Experiment Model Experiment Model N2 87.22 87.18 78.09 77.00 57.93 56.98 CO2 8.24 7.53 17.27 16.27 34.55 34.90 CO 4.17 4.91 4.41 6.47 7.33 7.94 H2 0.37 0.35 0.24 0.22 0.19 0.12 CH4 0.00 0.04 0.00 0.04 0.00 0.05 Overall carbon conversion 97.20 97.10 98.30 98.9 99.10 99.98 Time(s) 8.17 8.18 8.10 As seen in Table 3, the model prediction and the experimental results are in good agreement. The small discrepancy observed in carbon conversion might be due to the particle size distribution of the feed biomass during experiments and uncertainty associated with the solid collection which is discussed in Ref [6]. At the same time, the discrepancy observed in the gas composition might be due to the allowable tolerance in the Micro-GC reading. The readers should note that, although the present model is a steady-state simulation, the feed rate of biomass during the experiment was not stable as showed in Fig 4(A). These fluctuations also impact the gas-phase reaction resulting in fluctuating outlet gas composition (Fig 4(B) (C)). The results presented in Table 3 for gas composition are the average value of at least 5 individual Micro GC run. The residence time of the particles presented is the minimum residence time as any recirculation of gas or solid was not considered in the model.

18

Fig 4: Experimental data at 1200°CN2 free basis (A) Feed of biomass (B) Micro GC data at 10% CO2 (C) Micro GC data at 20% CO2 (D) Micro GC data at 40% CO2 Furthermore, Carbon, Hydrogen and Oxygen balance was performed for the entire reactor system. Table 4 present the C, H, O balance

Table 4: Elementary balance of the system (1200°C) Elements Condition Experiments Model CO2 % (g/min) (g/min) Carbon 10 1.15 1.11 20 2.03 2.02 40 3.82 3.85 Hydrogen 10 0.035 0.036 20 0.037 0.044 40 0.047 0.055 Oxygen 10 2.54 2.61 20 4.85 4.96 40 9.48 9.78

Absolute Error (%) 4.19 0.37 0.88 2.23 18.12 17.20 2.71 2.34 3.07

As seen in Table 4, the elementary balance of experiments and model predictions are in good agreement. The discrepancy (Absolute error) is in a range of 0.37~4.19% except for Hydrogen content. The model over predicts the H2 (maximum 18%). The potential source of this discrepancy might be the moisture content of the biomass. Although in the model, 4% moisture is considered, this content might vary in the biomass. There might be a strong possibility that the biomass might have high moisture for some particles. The history of a different variable along the reactor length during particle conversion is presented below. Where necessary, the inset of Figures is introduced.

3.1 Temperature and conversion history of the particle The particle stream temperature, gas temperature and the history of different conversion while travelling the reactor length during the whole gasification event is presented in Fig 5. As seen in the Figure, there is no difference between the gas temperature and reactor wall temperature after 1.5% distance from the top of the reactor. At the same time, the rise in particle temperature is tremendously fast. Consequently, the difference between the gas and particle temperature reach close to zero while travelling almost 2% distance from the reactor inlet. The trend is consistent with the reported findings [51, 52]. From the conversion curve, it is evident that complete devolatilization is achieved while the particles travelled 2% of the reactor length. The result indicates devolatilization is extremely fast during entrained flow condition at high temperature. The finding is also consistent with the findings during coal and biomass pyrolysis at high temperature [40, 51, 53, 54]. Form the overall conversion curve; it can be seen that almost 58% of the initial carbon present in the particle contributes to the gas phase during devolatilization. The remaining carbon is gasified by the heterogeneous Boudouard reaction. The char conversion curve shows, increasing CO2 concentration leads to a faster gasification rate in which full carbon conversion is achieved even faster. The result supports our previous finding [6].

19

20

Fig 5: History of particle, gas temperature and different conversions along the reactor length (A) 10%CO2 (B) 20%CO2 (C) 40%CO2 Interestingly it can be seen higherCO2 concentration can promote devolatilization rate according to Fig.6. This is due to the fact that when CO2 concentration is increased, it increases the thermal conductivity of the gas mixture inside the reactor. The increased thermal conductivity of the gas mixture allows increasing the particle temperature much quicker which is also reflected in Fig.5. This affects the devolatilization kinetics which has a direct coupling with particle temperature stipulated by Eq. (25) showed better devolatilization rate.

Fig 6: Effects of CO2 concentration on devolatilization rate 3.2 Gas composition and Gasification Chemistry In the simulation, the outlet gas composition is predicted while solving the involved gas-phase reactions along with the heterogeneous reaction in a successive manner. The gases that have been generated during the pyrolysis will be altered due to the extent of the involved reactions to produce the outlet gas composition. Fig.7 presents the reactor length-dependent evolution of gas species during gasification event. As seen in the Figure, the involved gas-phase reactions are prominent at the beginning of the reactor length. When CO2concentration is increased, the extent of the reactions is much faster so that almost a steady state is achieved even in a shorter distance. A decreasing trend of gas species CO2 and H2 can be observed in which the trend gets sharper when CO2concentration is increased. This is due to the activity of the rWGSR. Thermodynamically, rWGSR is favourable at high temperature [55], which was the scope of our experimental study [6]. During our experiments, the flow rate of supplied CO2 was higher than the feed rate of biomass which confirms the supplied CO2 was all-time excess than the stoichiometry requirement of Boudouard reaction for the available carbon inside the biomass. As a result, the concentration of CO2 is much higher than H2as the only source of H2 is due to the pyrolysis gas. The high concentration of CO2 along with high temperature might push the rWGSR to a forward direction in such a way that all the 21

H2present in the system could be consumed by the excess CO2. However, as soon as rWGSR is activated, H2O and CO are generated as products which play a significant role by imposing resistance through fWGSR in which the extent of rWGSR is slowed down. The nature of fWGSR is such that the reaction is thermodynamic favourable and kinetically unfavourable at low temperature [56]. Catalyst is used to activate the energy requirement of the reaction, which is extensively reviewed in the literature [57, 58]. However, at high temperature, the fWGSR is favoured kinetically although thermodynamically, it shows less conversion of CO [59]. Our gasification experiment was far beyond from low-temperature experiment with enriching CO2 environment. At the same time, the biomass feed was air-dried with 4% moisture which allows us to assume the only source of water vapour inside the reactor (if any) should be contributed by the activity of rWGSR. As a result, the H2O concentration inside the reactor at the initial stage of gasification should be very low which will increase as the rWGSR proceeds. On the opposite hand, species CO should have a higher concentration than H2O as this species is generated during pyrolysis and increases due to rWGSR and Boudouard reaction. However, the reaction kinetic used for MSR reaction was not prominent to consume all CH4 available in the system. A very small quantity of CH4 was predicted by the model though during our experiment, we did not observe any CH4. The discrepancy observed might be due to the very low quantity of CH4 which is very dilute in the gas mixture beyond the detectable range of the Micro-GC.

22

Fig 7 Gas composition along the reactor length (A) 10%CO2 (B) 20%CO2 (C) 40%CO2. In all case, N2 is not shown Fig.8 presents the reaction rate of rWGSR and fWGSR with respect to reactor length. From the figure, it is evident that both the reaction occurred in a distinct manner. The reaction rate of rWGSR is much higher than fWGSR and has a boost when CO2concentration is increased. During the non-isothermal zone in which the mean temperature is still ramping, both the reaction rate showed an increasing trend as the reaction proceeds. The reason for this phenomenon could be both the reactions are sensitive to temperature in which temperature is dominant than reactant concentration to influence the reaction rates. However, at isothermal zone decreasing trend for 23

rWGSR and increasing trend of fWGSR is observed. The decreasing trend of rWGSR can be explained by the fact that CO2and H2 concentration is decreasing due to rapid consumption to produce CO and H2O. As the reaction rate constant is fixed at isothermal zone, the concentration of the reactant influences the reaction rate in which the reaction rate decreases due to rapid consumption of the reactants. As CO is a product of Boudouard reaction as well as the rWGSR, the net production of CO has an increasing trend during the whole event. Species H2Oalso increases as the rWGSR proceeds starting with very low concentration. The production of H2O starts to influence the fWGSR when its concentration increases to a certain limit. Interestingly it can be seen both the reaction reached equilibrium while travelling 6~13% of the reactor length depending on CO2 concentration. The equilibrium is reached even faster when CO2 concentration is increased due to the higher reaction rate forcing each other to neutralize their net effects. As a result, H2O is consumed by fWGSR as soon as it is created by rWGSR, resulting in a stable mole fraction of H2O until it leaves the system.

Fig 8: Gas-phase reaction rate along the reactor length

3.3 Diffusional resistance during char conversion From Fig 1, it can be understood that the intrinsic char consumption rate can be influenced by pore diffusion (i.e. internal diffusion) limitation. The extent of the internal diffusional limitation can be explained by the effectiveness factor and Thiele modulus which is presented in Fig. 9. Form the figure, the lower value of the effectiveness factor leads to a stronger influence of pore diffusion limitation. High CO2 concentration leads to a higher value of effectiveness factor, indicating a lower influence of pore diffusion limitations [49]. Both particle temperature and CO2 concentration on particle surface can influence the heterogeneous Boudouard reaction [49]. The reactivity of char gasification also depends on the 24

mechanism of how the available CO2will be consumed by the active sites of the carbon defined by Eq. (29). Obviously, char from different feedstock and different pyrolysis conditions have different reactivity. During isothermal gasification condition, the intrinsic char consumption rate of Boudouard reaction can be highly influenced by the pore diffusion resistance [60, 61]. Thiele modulus is an indicator which shows the degree of influences. The previous study showed; the pore diffusion limitation can be neglected if the Thiele modulus is <0.4. Conversely, the intrinsic char gasification rate is heavily influenced by pore diffusion limitation if the Thiele modulus is >3 [62]. According to the statement, our numerical results indicate the pore diffusion limitation is controlling the reaction rate until a certain char conversion in the present system of gasification. At the very beginning of the gasification reaction, as shown in Fig.9, there is a sharp increasing trend of Thiele modulus is observed due to the non-isothermal behaviour of particle temperature (still ramping, see Fig.5). During this time, the particle surface temperature is comparatively low than the effective diffusion rate of CO2 on the particle surface to drive the surface reaction. This illustrates chemical reaction rates is the rate-limiting at the very beginning of the char gasification stage due to low surface temperature. However, the particle temperature reached almost reactor wall temperature while travelling a short distance (isothermal zone, see Fig.5), the chemical rate gradually increases and pore diffusion resistance starts to influence the chemical reaction rates. This illustrates the diffusion of the CO2 on the particle surface is the rate-limiting part. Furthermore, when CO2concentration is increased, the pore diffusion resistance eliminates much quicker. It can be understood when the Thiele modulus is <3 in the Figure. For instance, the pore diffusion limitation is significant until 55% of char conversion at 40% CO2 whereas it is dominating until 72% char conversion at 10% CO2. The effectiveness factor gradually increases and approach to unity starting from a very low value. The trends of the effectiveness factor during char conversion is consistent with the reported findings of Ref [63].

25

Fig 9: Thiele modulus and Effectiveness during char conversion

4.0 Conclusion To understand and explore the reaction scheme while direct CO2 gasification of biomass, a kinetic model is developed during entrained flow condition at high temperature. The model is validated against our previous published data showing a small discrepancy in terms of carbon conversion and outlet gas composition. The numerical results eventually confirm the selection of the involved gasphase reactions and the reaction rates used in the present model are comprehensive to describe the actual phenomenon during our gasification experiment. The internal mass transport limitation due to the porous structure of the char during carbon conversion is also modelled and studied. From the numerical results, the following conclusion can be listed: •

• • • • •

During entrained flow condition at high temperature, devolatilization is extremely fast. High level of CO2 concentration can promote the devolatilization rate due to better heat transfer from gas to solid. Almost 58% of the initial carbon contributes to the devolatilized gases. For particle size 90 µm, it takes almost 9s for 100% carbon conversion while travelling 2.4 m of reactor length at 1200°C. The gas-phase chemistry is dominated by reverse water gas shift reaction (rWGSR) at high temperature due to CO2 rich environment. The reverse and forward shift reaction reached equilibrium. When CO2concentration is increased, the equilibrium is reached much quicker. Pore diffusion resistance dominates chemical reaction rate at the beginning of char gasification stage. An increased concentration of the gasification agent can promote chemical reaction rate of Boudouard reaction by eliminating diffusion resistance.

Acknowledgement The authors would like to gratefully acknowledge the financial support received from the Australian Research Council through the Industry Transformation Research Hub Grant IH130100016. The authors also acknowledge the Australian Research Council’s Linkage Infrastructure, Equipment, and Facilities Scheme (LIEF 120100141).

26

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The undersigned author (Dr. M.A. Kibria) declares that there is no conflict of interest among the authors of the Manuscript.

Mahmud Arman Kibria, PhD Research Fellow Department of Chemical Engineering Monash University, Australia