An analysis approach of mass and energy balance in a dual-reactor circulating fluidized bed system

Yangjun Wei,Leming Cheng*,Liyao Li

Institute for Thermal Power Engineering,State Key Laboratory of Clean Energy Utilization,Zhejiang University,Hangzhou 310027,China

Keywords:Mass and energy balance circulating fluidized bed -bubbling fluidized bed Dual-reactor Comprehensive model

ABSTRACT An analysis approach considering gas-solids hydrodynamics,reaction kinetics and reacting species nonuniformity together in a dual-reactor system is presented for better understanding its mass and energy balance.It was achieved by a 3-dimensional comprehensive hydrodynamics and reaction model for the dual-reactor system,which was developed from the successfully verified 3-dimensional comprehensive combustion model for one circulating fluidized bed (CFB) system (Xu and Cheng,2019).The developed model and analysis approach was successfully used on a 1 MW circulating fluidized bed -bubbling fluidized bed(CFB-BFB)dual-reactor system.Results showed the sensible and chemical energy between two reactors as well as the energy distributions in each reactor were balanced and they agreed well with the experimental measurements.The analysis approach indicated energy balance had a close relationship with the mass transfer in the CFB-BFB dual-reactor system.It may be applied in a design and operation optimization for a dual-reactor system.

1.Introduction

An interconnected CFB-BFB (circulating fluidized bed -bubbling fluidized bed) system is widely used in gas-solids reaction applications,including chemical looping technology [1].There are differences in gas-solids hydrodynamics and reaction kinetics between the CFB and BFB.Generally,the endothermic and slower reductions take place in the BFB while the exothermic and faster oxidations occur in the CFB [2,3].

Mass and energy balance between two reactors are design and operation basis.In a CFB-BFB system,chemical energy from exothermic oxidations is transformed into sensible heat in the CFB and the circulating bed materials with the sensible heat are transferred from the CFB to the BFB.Then,the sensible heat compensates the energy of endothermic reductions and the input fuels generate products with chemical energy,which is subsequently transferred to CFB together with the circulating bed materials in the BFB.Auto-thermal operation with high efficiency is still a challenge in a MW-scale dual-reactor unit [4-6].

Mathematical models contribute to a better understanding of the mass and energy transfer.It plays an important role in process optimization and variables parameter analysis.Regarding dualreactor system design,Chenet al.[7],Abadet al.[8],Sharmaet al.[9] and Lyngfeltet al.[10] proposed several large-scale conceptual units from 3 MWth to 200 MWth based on empirical formulas.These 1-D or 1.5-D models were developed mainly upon assumptions,including steady state,perfect gas-solids mix,complete char/gas conversion,ideal cyclone efficiency,non-attrition of particle and isothermal reactors.Ohlemülleret al.[11,12],Sahiret al.[13] and Zenget al.[14] conducted process simulation and compared the predictions with the experimental results.However,those models did not present detailed information on gas-solids hydrodynamics,reaction kinetics and reacting species nonuniformity for the dual-reactor system.

Xuet al.[15-17] developed a 3-dimensional comprehensive combustion model for one circulating fluidized bed (CFB) system.It is hydrodynamically based on the Euler-Euler model combined with energy-minimization multiscale(EMMS)drag model,considering evaporation,devolatilization,fuel combustion reactions in a CFB system.It had been successfully used and verified in largescale industrial CFB boilers [15-17].

Inspired by this work,a comprehensive hydrodynamics and reaction model for a dual-reactor system was developed in this study.Evaporation,devolatilization,char combustion,char gasification and gas homogeneous reactions in the dual fluidized reactors were considered.It was used to analyze the mass and energy balance in a 1 MW CFB-BFB system and 3-D simulation results of pressure distribution,gas-solids suspension density,temperature,species concentration,mass flow rate,enthalpy as well as energy transfer were computed and discussed.

2.CFD Model

2.1.Simulation object -The 1 MW CFB-BFB system

The simulation object is a 1 MW CFB-BFB pilot test rig (Fig.1)[18].It consists of a combustor (1),a cyclone (2),a gasifier (4)and two loop seals (3) and (5).The CFB is a combustor and BFB is a gasifier.The geometry parameters of the system are given in Table 1.The combustor includes a bottom and dilute sections with its total height of 11,200 mm.The gasifier includes a bottom,middle and upper sections with the total height of 7200 mm.There are two paths for mass transfer between (1) and (4),i.e.path (a) combustor to gasifier and path (b) gasifier to combustor.

The 3-D hybrid grids with 359,946 cells and 247,197 nodes were created for the computation.The hexahedral grids are applied in most computational zones while tetrahedral grids are applied in the bottom section of the gasifier.

2.2.Simulation model

Since the comprehensive combustion model has been proved and applied in large-scale CFB boilers successfully [16,17],it is inspired to develop the model further into a dual-reactor system for better understanding the mass transfer and energy balance.The adiabatic wall assumption was taken in the model due to no heating surface of the 1 MW CFB-BFB system.

Fig.1. The structure of the 1 MW CFB-BFB system.

Table 1 Geometry parameters of the 1 MW CFB-BFB system

2.2.1.Gas-solids hydrodynamics

In the 1 MW CFB-BFB system,the solids are fluidized in the combustor and carried to the cyclone,which is similar to a CFB boiler.Different from a conventional CFB boiler,the solids from the cyclone are transferred to another fluidized bed,i.e.gasifier,through a solid returning device(Fig.1(3)).The flow loop is closed by transferring these solids from the gasifier to combustor through another solid returning device (Fig.1(5)).

To obtain the solids suspension density and velocity distributions in the two reactors,the Euler-Euler model combined with the EMMS (energy-minimization multiscale) model in the fluidized-bed reactor was applied.There is not much difference from the hydrodynamics determination method used in the comprehensive CFD model for the large-scale CFB boiler[16].The governing equations and constitutive equations for closing the governing equations are given in Table 2.

In this work,the stress tensor of the gas phase τ=g is calculated by the per-phase RNGk-ε model.The kinetic theory for granular flow (KTGF) is taken into consideration for the stress tensor of thesolid phase.The interphase momentum exchange coefficientKjiis corrected by EMMS drag model.The heat transfer between two phasesQjiis obtained by Gunn model,where 0.35 ＜εs＜1.0 andRes＜105.The gas phase consists of eleven species while the solid phase has seven species.The physical characteristics of the gas mixtures obey the ideal-gas-mixing law while those of solid mixtures depend on the mass-weighted-mixing law.The detailed numerical considerations are given in Table 3.

Table 2 Governing equations and constitutive equations

2.2.2.Chemical reactions

There are combustor and gasifier in the 1 MW dual-reactor system.It is different from the system of the comprehensive CFD model for the large-scale CFB boiler in terms of chemical reactions.

The coal combustion reactions occur in the combustor [15,16].It includes heating and evaporation(12),devolatilization(13),char combustion (14) and volatiles combustion (15)-(18).

To consider simplicity and validity,four main gaseous homogeneous reactions are taken into consideration,including oxidation of CH4,CO,H2and H2S.There are

where ΔHe,ΔHv,ΔHc,ΔHCH4,ΔHCO,ΔHH2and ΔHH2Sare the absorbed or released specific heat of reactions.ΔHevaries by temperature,while ΔHvand ΔHcare influenced by the reaction components.ΔHCH4,ΔHCO,ΔHH2and ΔHH2Sare 802.31 kJ·kmol-1,282.99 kJ·kmol-1,241.84 kJ·kmol-1and 518.19 kJ·kmol-1respectively.

Apart from these,char gasification mainly occurs in the gasifier.The char gasification with steam is given in (19) and Boudouardreaction is given in (20),where ΔHgasificationis influenced by the products,CO2and CO,while ΔHBoudouardis 205.25 kJ·kmol-1.Their reaction rates are given as following [19].

Table 3 Numerical considerations

wherexis the mean carbon conversion rate.

The water gas shift reaction(WGS)was also involved as given in(23).

where ΔHWGSis 41.15 kJ·kmol-1.The reaction rate [19] is

The rate coefficients of the above reaction rates,i.e.(21),(22)and (24),are given in Table 4.

2.2.3.Mass and energy flows

Gas-solids suspension density,pressure,temperature distribution and species concentration will influence the reaction and fuel conversion rates.Developed based on the proven comprehensive CFD model for the large-scale CFB boiler,the mass and energy flows between two reactors as well as in one reactor can be obtained from the 3-D full-loop CFD simulation by obtaining the gas/solid phase flow rate,species properties and distribution,temperature variation,enthalpy flows,reaction rates,etc.

In the gasifier,the coal is gasified to generate higher-purity gas as well as semi-cokes with chemical energy ΔEq.The sensible heat ΔEhof circulating bed materials compensates the energy of endothermic reactions ΔEr,G.While,in the combustor,the semicokes with ΔEqand input coal are combusted and release ΔEr,Creaction energy to heat the circulating bed materials.

The sensible heat ΔEhfor heating gas or solid phase is determined by the circulating solids flow rate .mand the sensible enthalpyhsenof the solids,as given in Eq.(25).

wherehsenis defined as

Yiis the mass fraction of speciesi,Tinitis the initial temperature of solid phase before heating andcp,iis the specific heat of speciesi.

Table 4 Rate coefficients in the char gasification reaction and water gas shift reaction

The reaction energy released/absorbed in one reactor ΔEris calculated by the net heat added and/or removed in the control volumeVk,as given in Eq.(27).

whereShis the sources of energy due to chemical reactions:

In the combustor,the fuel flow rate is the summation of the input coal and the semi-cokes from gasifier.Due to the nonuniformity and incomplete reaction,there exits the thermal efficiencyXCrepresenting the proportion of chemical energy of fuel converted to reaction energy ΔEr,C,as given in Eq.(29).

where ΔEq,coaland ΔEq,scare the chemical energies of full combustion of coal and semi-cokes respectively.They are given in Eq.(30),in whichhcomis the combustion enthalpy of fuel (i.e.coal or semi-cokes).

Similarly,in the gasifier,the endothermic reaction energy ΔEr,Gaccounts forXGpercent of the input energy in the gasifier,as given in Eq.(31).

The overall analysis approach for mass and energy balance in the dual-reactor system is given in Fig.2.

3.Results and Discussion

3.1.Validation of the simulation models

To verify the validity of the model,the simulation was done at an actual test condition and results were compared.

Table 5 gives the operational conditions.Huainan bituminous coal was used as the solid fuel.The proximate and ultimate analyses of this coal are listed in Table 6.The properties of circulating bed materials are given in Table 7.

Fig.3 gives the instantaneous solids concentration distributions of the CFB-BFB system.Dense regions in the bottom section anddilute regions in the upper section are clearly shown in both reactors.The solid concentration in the bottom of gasifier is higher than that in the combustor,while that in the dilute region is lower.It is understandable due to combustor is operated at higher superficial gas velocity than that in the gasifier (Table 5).

Table 5 Operational conditions

Table 6 Proximate and ultimate analyses of the Huainan bituminous coal

Fig.2. Analysis approach for mass and energy transfer in the CFB-BFB system.

Table 7 Circulating bed material

Fig.4 gives the pressure comparison along the reactors between the calculation results and the experimental data[18,21].It can be seen they agree well.This indicates the solid suspension densities profiles of simulation and experiment are matched well and provide a good base for further chemical reaction simulation.

Figs.5 and 6 show the comparison of temperature profiles in the combustor and the gasifier from simulation and experiments individually in about 7 hours[21,22].The temperatures in the bottom (y=1450 mm),middle (y=2000 mm)and upper(y=4000 mm) region of combustor are in a range of 800-950 ℃.Due to combustion and oxidation reactions,Eqs.(14)-(18),the temperature level in the combustor is high.It can be seen the simulation results show a good agreement with the experimental data.

Fig.4. Comparison of pressure profile in the combustor and gasifier.

Fig.3. Contour of instantaneous solid concentration.

Fig.5. Comparison of temperature profile in the combustor.

Fig.6. Comparison of the temperature profile in the gasifier.

Reactions including evaporation,devolatilization,char gasification occurred in the gasifier,i.e.Eqs.(12),(13),(19),(20)and(23),which are endothermic and slow.Therefore,the temperatures simulated in the dense region (y=3000 mm,y=3600 mm) and dilute region (y=9600 mm) of the gasifier are in a range of 650-750°C.There are about 100°C higher than those of experimental data in the gasifier.This deviation may come from the adiabatic wall assumption.Since the specific heat of the solid flow (cp,s=715-725 J·kg-1·K-1)is smaller,the heat loss is carried by the circulating bed materials and accumulated in the bottom of the gasifier,where the solid inventory is higher than that in the combustor.Thus,the effect of heat loss on the temperature is greater in the bottom section of the gasifier.

Table 8 shows the comparison of gas volume fraction at the gasifier outlet [21].During experiments,the 0.35% O2and a small proportion of N2are mainly from air leakage in the gasifier.Apart from them,the relative errors for H2,CxHy,CO and CO2were 12%,-5%,-7% and -17%.This suggests the simulation results match well with the experiment data.

The well-matched results from simulation and experiments on hydrodynamics and reaction species approve the validity of thecomprehensive CFD model for a dual-reactor system,favoring the following mass and energy analysis.

Table 8 Gas volume fraction at the gasifier outlet

3.2.Mass and energy balance

3.2.1.Mass transfer between two reactors

To operate the system steadily it is essential for proper mass and energy transfer between two reactors.Fig.7 shows the steady results of mass transfer between the combustor and the gasifier in the period of 240 s.The mass flow rates in Fig.7(a) and (b) represent the mass flow rate transferred in path(a)and(b)respectively.It consists of the circulating bed materials and semi-cokes.The average mass flow rates in the path (a) and (b) are 2160 kg·h-1and 1980 kg·h-1respectively.This range is consistent with the design value of 2000 kg·h-1.The nuance of the mass flow rate in two paths is within acceptable 10%,which may come from the sampling interval of 0.1 s (time step:1×10-3s) and the different content of the solid species.However,it can be seen the mass flow rates vary intermittently due to pressure fluctuations.Since.ms=ρsεsvsA,it is determined by the pressure balance of the system [23].According to the calculated results,εsvaries in a range of 0.0-0.20,while vsvaries among 0.0-2.0 m·s-1.They are within a reasonable range.Therefore,the dual-reactor system reaches a steady circulating state at 1980-2160 kg·h-1.

According to Eq.(4),the sensible heat ΔEhcarried by circulating bed materials is determined by the mass flow rate .mand the sensible enthalpy.In Fig.7,due to incomplete reaction in the combustor and gasifier,the mass fraction of semi-cokes in the circulating bed materials are about 0.15%-0.30% in path (a) and 0.90-1.03%in path (b),which corresponds to 2.7-9.7 kg·h-1and 16.2-33.4 kg·h-1semi-cokes respectively.Correspondingly,the chemical energies of semi-cokes ΔEq,scare 0.022-0.080 MW and 0.135-0.278 MW in path (a) and (b) respectively.It can be concluded the sensible and chemical energy transfer has close relationships with the mass transfer in the CFB-BFB system.

Fig.7. Mass flow rate and mass fraction of circulating bed materials:(a) in path (a);(b) in path (b).

3.2.2.Energy transfer between two reactors

The mass and energy flow chart of the 1 MW CFB-BFB system is given in Fig.8.It can be seen both sensible heat and chemical energy are transferred between two reactors,together with the circulating bed materials and semi-cokes.

The coal of 100 kg·h-1with ΔEq,coal=0.60 MW,the cooled raw gas and circulating bed materials with ΔEh=0.62 MW are fed into the gasifier.The sensible heat of bed materials reduces due to endothermic reactions when it enters the gasifier,including Eq.(12),(13),(19),(20) and (23).The coal generates 0.18 MW semicokes (ΔEq,sc),0.33 MW higher-purity gas and 0.122 MW tar at 650-750°C.Then,the cooled circulating bed materials with ΔEh=0.51 MW and semi-cokes with ΔEq,sc=0.18 MW flow to combustor through path (b).

Fig.8. Mass and energy flows in the 1 MW CFB-BFB system.

Fig.9. The energy distribution of the 1 MW CFB-BFB system.(a)In the combustor;(b)in the gasifier(inner circle:released energy;outer ring:absorbed energy;Δ:relative error).

The semi-cokes with 0.054 MW chemical energy are gasified in path (b).The left semi-cokes (ΔEq,sc=0.126 MW) and 51 kg·h-1coal (ΔEq,coal=0.31 MW) are combusted by the preheated air in the combustor,as given in Eqs.(12)-(18).The released reaction energy is consumed to heat the circulating bed materials and maintain a high-temperature level at 800-950°C in the furnace.And the circulating bed materials obtain sensible heat ΔEhof 0.62 MW.In the exhaust gas of the combustor,0.29 MW sensible heat and 0.06 MW chemical energy of unburnt gas products are emitted.0.06 MW semi-cokes are unconverted in the combustor,of which 0.036 MW is gasified in path(a).The energy loop is closed by returning the ΔEh=0.62 MW of the heated circulating bed materials and ΔEq,sc=0.024 MW of the unburnt semi-cokes to the gasifier.There are 4% acceptable energy error in each reactor.The ΔEq,scin path (a) and (b) are consistent with the discussions in Section.3.2.1.The sensible and chemical energy flows between two reactors are balanced due to the transfer of the circulating bed materials and semi-cokes.

3.2.3.Energy distribution in the reactors

Fig.9 gives the energy distributions in the combustor and gasifier.The reaction energy released/absorbed in the combustor and gasifier,ΔEr,Cand ΔEr,G,are 0.26 and -0.01 MW respectively.It can be seen ΔEr,Cheats the air,circulating bed materials and solids fuels with 53%,42% and 4% heat in the combustor respectively.These circulating bed materials are subsequently transferred into gasifier through path (a) and then released the sensible heat ΔEhthere.In the gasifier,ΔEhof circulating bed materials is absorbed by cooled raw gas (40°C),solids fuels and endothermic reactions(ΔEr,G).The corresponding proportions are 73%,18%and 9%respectively.The results indicate the released and absorbed energy in each reactor are balanced.

As discussed above,there are 2.7-9.7 kg·h-1semi-cokes unburnt in the combustor and 16.2-33.4 kg·h-1semi-cokes generated in the gasifier.The char conversion in the combustor and gasifier are 89%-96% and 70%-84% respectively.Thus,the ΔEr,Cand ΔEr,Gaccount forXCandXGproportions of the input energy in the combustor and gasifier(Eqs.(29)and(31)).Therefore,the mass transfer rate and fuel conversion play a key role in affecting the energy balance in each reactor.

With the mass and energy analysis discussed above,this comprehensive 3-D full-loop CFD model considering gas-solids hydrodynamics,reaction kinetics and reacting species non-uniformity may be able to predict and optimize the design,operation and maintenance for a dual-reactor system.

4.Conclusions

A novel analysis approach for mass and energy balance in the dual-reactor system using a comprehensive 3-D full-loop CFD simulation was developed.The gas-solids hydrodynamics parameters,temperature level and chemical reaction species can be simulated by the model.Good agreement between the computed results and test results from the 1 MW CFB-BFB system verify the validity.Mass and energy balance analysis shows the close relationship of energy and mass rate between the two reactors.The model may be used to predict design,operation and maintenance for a dualreactor system.

Nomenclature

ACross-sectional area,m2

CMole concentration,mol·m-3

Cμ Constant in turbulence model

cpSpecific heat,J·kg-1·K-1

DDiffusion coefficient for speciesiin the mixtures,m2·s-1

dGranular diameter,m

EhSensible heat/heat flux,J·s-1

ErReaction energy/heat,J·s-1

EqChemical energy of full combustion

essCoefficient of restitution

J Diffusion flux,kg·m-2·s-1

g Acceleration due to gravity,m·s-2

g0Radial distribution function

hEnthalpy,J·kg-1or J·kmol-1

KeqEquilibrium coefficient

KjiInterphase momentum exchange coefficient from phasejtoi

kPre-exponential factor

MMolecular weight,kg·mol-1

NuNusselt Number

PPressure,Pa

PrPrandtl number

QjiHeat transfer from phasejtoi,kJ·m-3·s-1

R Volumetric rate,kg·m-3·s-1

rReaction rate,mol·m-3·s-1

ReReynolds number

ScSchmidt number

ShEnergy source,J·m-3·s-1

TTemperature,K

VControl volume

XMass fraction in coal

XCorXGThermal efficiency in the combustor or gasifier

xMean carbon conversion degree

YMass fraction

y Y-axis of the model geometry

α Volume fraction

ε Dissipation rate of turbulent kinetic energy

εsSolid volume fraction

Θ Granular temperature

κ Turbulent kinetic energy

λ Thermal conductivity,W·m-2·K-1

μ Viscosity,kg·m-1·s-1

ξ Bulk viscosity

ρ Density,kg·m-3

τ=Stress-strain tensor

φ Factor in char combustion

ψ Factor in char stream gasification

Subscripts

C Char in coal or combustor

e Evaporation

g Gas phase

G Gasifier

iGas/solid phase or species

jGas/solid phase

kNumber of the control volume

s Solid phase

sc Semi-cokes

v Devolatilization

Superscript

com Combustion enthalpy

sen Sensible heat

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors are grateful for the financial support of the National Key Research and Development Program of China(2018YFB0605403).