a thermo fluid dynamic model of wood particle gasification

A thermo fluid dynamic model of wood particlegasification- and combustion processes

Gernot BoigerICP Institute of Computational Physics, School of Engineering, ZurichUniversity of Applied Sciences, Wildbachstrasse 21, P.O. Box, 8401

Winterthur, Switzerland. [email protected]

ABSTRACT

In order to qualitatively understand and evaluate the thermo- fluid dynamic

situation within a wood gasification reactor, a 1D particle model has been

created. The presented tool accounts for the highly in- stationary, kinetic-

and thermo chemical effects, leading to partial gasification and

combustion of a wood particle embedded within a packed bed collective.

It considers the fluiddynamic situation within the changing porous bulk

structure of the packed bed, its impact on species- and heat transition

mechanisms, the energy- and mass balances of wood, coal, pyrolysis-

gas, woodgas and offgas phases, the thermodynamics of locally

developing gasification- and combustion reaction equilibria, as well as the

presence of the chemical species hydrogen, water, carbon (di-) oxide,

methane, oxygen, solid carbon and gaseous, longer chain hydrocarbons

from pyrolysis.

Model results can be shown to yield very good, qualitative agreement

with measurements, found in literature.

Keywords: Gasification, combustion, thermo chemistry, fluid dynamic,

modelling

NOMENCLATURE

Pre exponential factor wood Greek Symbols pyrolysis (s-1)AP,A Cross section of process air aG Ratio of molar pyrolysis gas cylinder (m2) production rate to total pyrolysis rate (-)AWG,i Frontal area of conical torch i (m2) aj Ratio of reacting component or species j total production rate of j (-)Ag Area of regional border plane g (m2) d Boundary layer thickness (m)CP,A Lateral length of process air cube (m) e

PB Packed bed porosity (-)

Heat capacity of species j at constant ecoal Coal porosity (-) pressure and temperature T

l(J/K mol)

DP Particle diameter (m) hA Kinematic viscosity of process air (m2/s)Dpore Coal pore diameter (m) l Heat conduction coefficient (W/m K)

A ' pyro

Int. Jnl. of Multiphysics Volume 8 · Number 2 · 2014 203

cTp j,

l

DDiff,j Diffusion coefficient of species j rj Density of component j in air (m2/s) (kg/m3) Activation energy wood pyrolysis (J/mol) gO/C Ratio of O to C atoms in fuel (-)fBN Bottle neck factor (-) gH/C Ratio of H to C atoms in fuel (-) Standard molar enthalpy of formation Molar gas density at (J/mol) standard conditions (mol/m3) Boundary layer coefficient between Molar gas density at zones l and l+1 (m) temperature T and pressure p (mol/m3)Dlpores Medium distance between pores (m) Superscripts

MMj Molar mass of component or species PEP Pseudo Equilibrium Phase j (kg/mol)Npores,P Number of coal pores at particle TGP Total Gas Production Phase surface (-)Nj Total number of molecules of species TPP Total Product Phase j within a balance zone (mol) Molar flux of incoming fresh air into Subscripts

particle vicinity (mol/s) Rate of pyrolized carbon atoms (mol/s) i Alternatively: direction, time step, iteration, number of pore Rate of molar coal production (mol/s) BN Bottle neck Rate of molar pyrolysis gas production A Process air (mol/s) Molecular species source term (mol/s m3) P Particle Particle surface normal vector at pore (-) GP Gas production Reaction rate of species j (mol/s m3) W Woodng,i Surface normal vector component of coal Coal plane g (-) Pressure at standard conditions (Pa) j Molecular species Energy flux over plane in air phase (W) k Atomic species O, H, CR Universal gas constant (J/K mol) l Balance zoneReBN Bottle neck Reynolds number (-) g Regional border planeRp Radius of particle (m) PG Pyrolysis gasRW Radius of wooden particle core (m) G GasRWG,PG Ratio of molar wood gas to pyrolysis W* Combined wood and wood gas production (-) gas phase

WG Medium Radius of wood gas bubble (m) Tl Temperature of balance zone or component l (K) Standard temperature (K) Process air velocity at bottle neck (m/s) Process air velocity in zone g (m/s) Wood gas velocity at particle surface (m/s) VP Particle volume (m3) Volumetric flow rate of component j (m3/s) xj Molar fraction of component or species j (-) xi Direction (-) Standard Oxygen content of process air (-)

r

204 A thermo fluid dynamic model of wood particle gasification- and combustion processes

Epyro'

Δ Θhf j, ϑΘG

δ+kl l, 1 ϑG

T p,

nA0

nPyroC

nCoalC

nPGC

nGPnp

nR j,

ΘpQA

ΘTvA

BN

vAg

vPWG

ΘxAO

,

2

Vj

1. INTRODUCTIONUp to this day, medium- and large scale, packed bed gasification plants (see e.g. [1]), haveproven to require a relatively high level of maintenance intensity in order to keep upcontinuous, stationary production. It is still common practice to adjust process parameters via“trial and error methods” to changing input conditions.

This points to the fact that there is yet a demand for a deeper understanding of the relevantthermo-, fluid dynamic sub-processes involved in wood gasification. Thus compact, fast andcomprehensive models of the situation within a packed bed gasifier are still required.

In this work, one such thermo-, fluid dynamic model is being presented and laid out indetail. The model is an addition to the relatively large amount of gasification models,described in literature (see e.g. [2] and [4–6]).

Among previously published works, a rough distinction can be made:• Reactor models, with a focus on global mass- and heat balances, as well as transport

phenomena on the packed bed scale (e.g. [3–4]).• Single particle models, with a more detailed resolution of particle based, sub-processes,

such as drying, pyrolysis, coal and pore formation, gasification and combustion (e.g.[8–9]).

• Kinetic models, which focus on chemical reaction rates but tend to neglect physicaltransport mechanisms (e.g. [5–19]).

The tool, described in this paper, basically falls into the category of single particle approaches,but does not neglect the fluid mechanic and structural coupling to the surrounding packed bed.It focuses on the scale level of about 10-2 m. As shown in chapter 2, the model provides adetailed, 1D depiction of the life span of an individual, reacting pellet or wood chip, theinvolved thermo chemistry, transition kinetics of molecular species, coal- and pore structureformation mechanisms as well as relevant heat- and species balances. In addition (as pointedout in chapter 2.7), the model features a specifically tailored, iterative, numerical solver tohandle the highly transient, thermo chemical situation within the wood gas phase and thepores of the coal phase. This solver does not only, as most other modeling approaches (e.g.[4], [12] and [13]), use a “Gibbs Energy Minimization Method”, but allows the calculation ofa “Pseudo Equilibrium Phase” (PEP), with zero Gibbs free energy. So far, particle moisturecontent, drying effects, as well as the potential influence of non-spherical shape effects andthermal interaction with neighboring particles is either strongly simplified or neglected.

In chapter 3 it will be shown that this implementation, though representing a compact,single particle perspective, can achieve very good qualitative correspondence with packedbed, experimental results, published in literature [7]. Moreover it will be demonstrated thatthe model can be used to reinterpret certain, experimental results [7]. Thus its potential forfurther application is proven.

Chapter 4 then points towards future efforts to incorporate this single particle approachinto a full 3D Eulerian – LaGrangian code, based on OpenFOAM® (see [15–18]).

2. THE MODELIn this chapter the thermo-, fluid dynamic principles and concepts behind the 1D, singleparticle, wood gasification model are laid out and explained step by step.

The most essential, mathematical modelling concepts, range from setting up sensiblebalance zones, realizing the fluid mechanic coupling between single particle and packed bed,over the calculation of pyrolysis kinetics, coal- and pore structure formation mechanisms tothe modelling of species exchange kinetics and the full resolution of the thermo chemicalsituation in terms of gasification and combustion effects.


2.1 BALANCE ZONES AND COMPONENTSThe model distinguishes between four balance zones that transfer molecular species andenergy between each other (see also Figure 1):• The incoming, gaseous process air phase, with ~ 300K, x

O2~ 0.21 and x

N2~ 0.79;

• The shrinking, solid wood phase, being processed by the protruding pyrolysis front;• The produced, solid coal phase with pore structure;• The produced, gaseous wood gas phase, which actually encompasses three kinds of

gaseous mixtures, that are hereby referred to as pyrolysis gas, wood gas and off gas;Pyrolysis gas is hereby regarded as a mixture of longer chain hydrocarbons, namely TARs,of which only the overall, atomic composition, is known. This composition corresponds tothat of wood, according to , but is enriched by oxygen and hydrogen, released by

TAO

γ γCO HC

H

C

O


Figure 1: Wood gas (orange), off gas (pink), coal phase with pores (black) andpyrolysis zone (yellow); Red and orange streamlines represent wood gas andmixed product gas flow respectively

those cellulose components that turn into coal via pyrolysis.Wood gas is the desired, but not exclusive product gas. Within the model, it is created out of

pyrolysis gas by the gasification reactions (thermo chemical stage 1). Its composition remainsto be calculated, but should range within the following limits (see [1]): CO (25%–45%), CO

2

(15%–30%), H2O (g) (3%–20%), H

2(15%–35%), CH

4(4%–10%) and residual TARs (<3%).

Off gas is the undesired, but necessary by-product gas, created at the contact area betweenwood gas and process air. Within the model, it is created out of wood gas by combustionreactions (thermo chemical stage 2). It is composed of CO

2 and H

2O. The off gas production,

via oxidation of wood gas, releases exothermal energy, which heats the entire particle systemand keeps the thermo chemistry going.

2.2 COUPLING BETWEEN PARTICLE AND PACKED BED: MODELLINGTHE PROCESS AIR FLOWEach particle is assigned a cubical region of process air phase with lateral length C

P,A(see

Equ.1), to account for packed bed porosity εPB

, and a frontal, circular, cross section AP,A

within the reactor (see Equ.2).

Eqn. 1

Eqn. 2

πε( )

=−

C D *6 * 1P A P

PB

, 3

π ( )= +AD

f*

4* 1 2 *P A

PBN,

22

In Equ.2 a spherical particle bed structure is assumed. It allows for six free flow bottleneckcross sections per particle, where each has to be shared with two other, neighboring spheres.Each bottleneck cross section is assigned an approximate, representative diameter f

BN*D

P, such

that fBN

is the bottleneck factor. In order to account for the over all porosity, fBN

is calculated as:

Eqn. 3

The velocity distribution of the stationary, compressible 1D gas flow with specific,molecular species source term n

GP, is simply derived by combining the 1D, inhomogeneous

continuity equation, with the ideal gas law and the assumption that the cross sectionalporosity approximately corresponds to the 3D porosity (see Equ.4).

Eqn. 4

2.3 PYROLYSISThe first thing that happens to the pre-heated particle (~700 K) is, that pyrolysis reactions setin at the surface of the spherical piece of fuel. Pyrolysis transforms the cellulose moleculesinto pyrolysis gas and solid coal. Thus, over time, a thickening coal layer is forming at thesurface. The model particle diameter is shrinking, while the pyrolysis front is progressingtowards the particle centre.

First the pyrolysis rate , needs to be calculated in terms of pyrolized carbon atoms pertime. A macroscopic Arrhenius approach, which averages over the entire particle, is chosen,according to [23], to implement the relevant kinetics:

Eqn. 5

Equ.5 introduces the first, highly non-linear relationship to particle temperature Tp. Values

for the activation energy E’pyro

and the pre exponential factor A’pyro

, have been taken out of[20]. The molar mass MM

Wof one carbon atom, being assigned its pre-defined share of

oxygen and hydrogen atoms, is calculated as:

Eqn. 6

A certain fraction of pyrolized carbon atoms αG

, turns into pyrolysis gas, the rest turns intocoal. Since coal mainly consists of solid carbon, all pyrolized oxygen and hydrogen atomsare going into the gas phase. With this definition and a user defined setting of α

G, coal and

pyrolysis gas production rates can be calculated:

Eqn. 7

Eqn. 8

2.4 COAL PORE STRUCTURE MODELWith the assumption of a thickening coal layer, which covers the pyrolysis gas productionfront, the necessity arises to introduce a comprehensive coal pore structure model. Since the

nCPyro

εε

=−

f1BN

PB

PB

3

ε( )( )

( )∂∂

⎡

⎣⎢⎢

⎤

⎦⎥⎥= Θx

v x

T x

n x R

p

*

*AR

GP

PB

ρ ρ( )= −⎡⎣ ⎤⎦( )−

−

n A x x t V MM e' * , , * * *PyroC pyro P W coal coal P W

E

R T t1

'

*pyrp

P

γ γ= + +MM MM MM MM* *W C O C O H C H/ /

α( )= −n n1 *CoalC G

PyroC

α=n n*PGC G

PyroC


velocity of the exiting wood gas at the particle surface vPWG

is of interest, an approximationfor the superficial coal pore area has to be developed.

Assuming isotropic coal porosity εcoal

and constant, circular coal pore cross sections ofdiameter D

pore, the following formulation for the number of pores N

pores at a radial distance

r, from the particle center, has been derived:

Eqn. 9

In Equ.9 the radius of the spherical, wooden particle core is included by RW

.The volumetric flow rate

WG of produced wood gas relates to the molar production rate

of pyrolysis gas (Equ.10) via the molar production rate ratio RWG,PG

and the ideal gas law,such that:

Eqn. 10

Combining Equ.9 and Equ.10 for r = RP,

with RP

being the total particle radius and Npores,P

= Npores

(RP), the velocity of exiting wood gas at the particle surface can then be calculated

as:

Eqn. 11

2.5 SIMPLIFIED FLUID MECHANICS OF THE INTERACTION BETWEENPRODUCT GAS AND PROCESS AIR FLOWHere a compact formulation for the contact area between the two gaseous balance zones, theprocess air phase and the wood gas phase is being proposed. Basically a 1D momentumbalance between the incoming process air flow and the wood gas, protruding out of theparticle, is being solved. In a first step, a representative angle of process air attack iscalculated by force effect averaging, according to Eqn.12.

Eqn. 12

Having defined , the task of approximating the contact area can be reduced to a 0Dproblem. At this point the idea of an average, representative wood gas protrusion radiusWG

is formulated. This radius corresponds to the sum of the wood core radius RW

and thelength of a representative pyrolysis gas/wood gas stream line, which starts at the pyrolysisfront, goes along the very center of a straight coal pore and stops at the contact area to theprocess air phase. Then the assumption of three fluid dynamic stages is introduced: thestable gas bubble stage (stage 1), the gas bubble break up stage (stage 2) and the air intopores stage (stage 3). Within each stage, different physical conditions need to be taken intoaccount and therefore the outflow radius needs to be calculated differently as well. Table 1provides an overview of basic ideas, conditions and calculation methods for the three stages.Table 2 gives additional variables for calculations presented in Table 1, which are not laidout under section “Nomenclature”. Consequentially, Figure 2 gives a more qualitativeimpression of how stages 1-3 are distinguished at the pore scale level. Furthermore Figure 2sketches the relevant oxygen transition areas between process air phase and wood gas phase,for all three stages.

ε( ) ( )= + −⎡⎣⎢

⎤⎦⎥N r

Dr R Rw r

16 *

3** *pores

coal

pore

W2

2

V

ϑ= Θ Θ

i i

V n V RT

T* * *

1*WG C

PG

P WG PG

G

WG,

π=v

V

N D

4 *

* *PWG

WG

pores P pore,2

ϕ

ϕπ

=⎛⎝⎜

⎞⎠⎟arccos

1

ϕr


Even though the calculation of r–WG

in stage 3 involves complex number mathematics,with , the result proves to be a real number.

2.6 MASS AND HEAT TRANSFERThe four balance zones: wood phase, coal phase, process air phase and wood gas phase havebeen introduced in 2.1. They interact through momentum-, mass- and, heat transfer. In thiswork the emphasis lies on the latter two effects. Those are described by setting up coherent(atomic) species balances and sub models for the calculation of species transition kinetics.

−i= 1


Table 2: Variable definitions in addition to Table 1

Stage # Symbol Calculation Unit

2 -

2 PA,WG -

3 m2

3 m3

3 m3

ϒ A WG,ϕ( )v

v

*cosRA

PWG

ρρ

≈ T

TA

WG

WG

A

Κ A WG,

π ε ϕ( )V

P v

3*

4 * * * * *cosWG

coal A WGRA,

ΓA WG, ( )Κ −R R*W A WG W,2

ΗA WG, − Γ + Κ − Γi9 * 12 * 81*A WG A WG A WG,3

,2

,

Table 1: Basic ideas, conditions and calculations behind fluid dynamic stages 1-3

# Basic idea Condition(s) 1 Particle engulfed by stable gas bubble

2 Gas bubble break up after reduction of gas production rates

3 Air penetrates into pores shortly before extinction

r in mWG

∑ π( ) ≥=

A r r4 * *WG i WG i WG

i

N

, ,

2

1

pores p,

εϕ π

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

V

v

MM T

MM T

*

*cos( )**

*

*WG PB

A

WG WG

A A0

1

2

1

4

∑ π( ) <∧

≥

=

A r r

r R

4 * *WG i WG i WG

i

N

WG P

, ,2

1

pores p,

π η

( )

+Δ

+ + ϒ

ϒ +

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

−+ ϒ

+Ρ+Ρ

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎫

⎬

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪

δR kV

N l*

* * **

*

log1 1

* 1 2

1

1 1

PA WG WG

pores P pores A

A WG

A WG

A WG

A WG

A WG

,

,

,

,

,

,

,

<r RWG P Η +Η

Κ1

18*

2

3**A WG

A WG

A WG,3

,

33

,

2.6.1 Atomic species balances and species transition kineticsThe relevant, differential, conservative atomic species balance in tensor notation is shown inEqn.13. This formulation encompasses all relevant (sub-) balance zones (l= wood-, coal-,process air-, wood gas phase, pseudo equilibrium phase PEP, total gas phase TGP and totalproduct phase TPP), directions (i= 1; x

1= x), molecular species (j= CO, CO

2, H

2, H

2O, CH

4

and TARs) and atomic species (k= O, H, C). In stationary, convective, diffusive and chemicalreaction effects are considered. The count of atoms of species k, per molecular species j iswritten as , while the species diffusion coefficient is D

Diff,jand the specific and total molarγ k

j


Figure 2: Sketch of model assumption for three stages of “fluid momentuminteraction” at pore scale, between process air (blue), wood gas (orange) andoxidized off gas (pink). Red, pink and (dashed) blue lines represent wood gas, offgas and air streamlines respectively. Dashed green lines represent the oxygentransition area between the process air zone and the wood gas zone

species reaction rate within phase l are and respectively. The molecular species-specific coefficient α

jrepresents an essential modeling concept and gives the fraction of a

certain species j that takes part in chemical reactions and is thus present within a sub- balancezone, namely the PEP (see 2.6.1). Note that x with subscript j signifies the molar fraction ofa species j and x with a subscript i denotes any direction.

Eqn. 13

2.6.1.1 Atomic species balances within “pseudo equilibrium phase”, “totalgas phase” and “total product phases”Three sub-balance zones are introduced: the pseudo equilibrium phase PEP, the total gas phaseTGP and the total product phase TPP. While TPP simply encompasses all gasification products,including coal, TGP holds only the sum of the gaseous products. PEP is more delicate. In orderto create the PEP, the model postulates the existence of a locally stable chemical state ofequilibrium, which has a Gibbs free energy equal to zero. This is only possible if the locallyavailable, molecular species are not fully mixed and certain species remain unprocessed. Whileall gaseous species together form the TGP, the reacting species in their “pseudo equilibriumstate” of Gibbs free energy equal to zero, form the PEP. Note that α

G is the ratio of pyrolysis

gas production rate to total pyrolysis rate and is thus not to be mistaken for αj.

In Table 3, specializations of Eqn.13 are presented, which account for the molecularspecies balances within the three sub zones. For reasons of mathematical practicality, balanceratios are used, rather than single-species-balances. Table 4 provides additional definitions ofvariables, used in Table 3.

NR jl

,nR jl

,

γ αϑ∂

∂+

∂∂

+∂∂

−⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥ =

n

t

x v

xD

x

xn* *

* ** 0j

kjl

j

lj

Rl G

T p

i

Diff j

lj

i

lR j

,

,

2

2 ,


Tab

le 3

: Sp

ec

ies

ba

lan

ce

ra

tios

for

PE

P, T

GP,

TP

P

Zon

e

B

alan

ce r

atio

S

peci

es in

put

side

Sp

ecie

s ou

tput

sid

ePE

P

PEP

TG

P

TG

P

TPP

TPP

gH

/C

RP

EP

OC/

γα

αα

αγ

γα

αα

γ(

)−

++

+

*1

*2

**

/

**

OC

GG

PG

OOA

WG

OC

GP

Gco

alCC

oal

WG

/,

/

,2

2

++

++

+x

xx

x

xx

x

2*

2*

OPE

PP

EP

HO

PE

PC

OC

OPE

P

PE

PC

OC

OPE

PC

HPE

P2

22

24

RP

EP

HC/

γα

αα

αα

αγ

−+ +

⎛ ⎝⎜ ⎜⎞ ⎠⎟ ⎟

*1

*

**

HC

GG

PG

GP

Gco

alCC

oal

WG

/,

++

++

xx

x

xx

x2

*2

*HP

EP

PE

PH

OP

EP

CH

PE

PC

OC

OPE

PC

HPE

P2

24

24

γγ

αγ

+ +2

*O

COA

WG

GCC

oal

WG

/,

,2

RTG

PO

C/γ

++

++

++

++

γγ

γγ

xx

xx

XX

xx

xX

22

2*

OPE

PP

EP

HO

PE

PC

OC

OPE

POTG

PO

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

/O

CH

C

OC

HC

22

22

//

24

//

RTG

PH

C/γ

αγ+H

C

GCC

oal

WG

/,

γ+

++

++

+γ

γ

γγ

xx

xX

xx

xX

2*

2*

4*

*HP

EP

PE

PH

OC

HPE

PH

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP/

OC

HC

OC

HC

22

4/

/

24

//

RTP

PO

C/γ

γ+

2*

OC

OAW

G/

, 2γ

++

++

++

++

+γ

γ

γγ

xx

xx

XX

xx

xX

X

2*

2*

2*

*OP

EP

PE

PH

OP

EP

CO

COPE

POTG

PO

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

Coa

lTP

P

/O

CH

C

OC

HC

22

22

//

24

//

RTP

PH

C/γ

++

++

++

+γ

γ

γγ

xx

xX

xx

xX

X

2*

2*

4*

*HP

EP

PE

PH

OC

HPE

PH

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

Coa

lTP

P

/O

CH

C

OC

HC

22

4/

/

24

//


Tab

le 4

: Va

riab

le d

efin

itio

ns

in a

dd

itio

n t

o T

ab

le 3

.

Def

init

ion

S

ymbo

l

C

alcu

lati

on

Uni

t

Rat

io o

f m

olar

dif

fusi

on

mol

O2/m

ol p

yro

rate

of

O2

from

pro

cess

air

to w

ood

gas

phas

e to

rat

e of

pyro

lized

car

bon

atom

s

Rat

io o

f m

olar

coa

l

mol

coa

l/mol

pyr

ore

duct

ion

rate

to r

ate

of p

yrol

ized

car

bon

atom

s

Mol

ar r

ate

of n

on-r

eact

ing

m

ol P

G/m

ol P

EP

PG p

er to

tal P

EP

prod

uctio

n ra

te

Mol

ar r

ate

of n

on-r

eact

ing

m

ol O

2/m

ol P

EP

O2

per

tota

l PE

Ppr

oduc

tion

rate

Mol

ar r

ate

of p

rodu

ced

coal

mol

coa

l/mol

PE

P to

tota

l PE

P pr

oduc

tion

rate

γ OAW

G, 2

n nAW

GO P

yro

C, 2

γ CCoa

lW

G,

n nCoa

lW

GC P

yro

C

,

γγ

XC

OH

TGP O

CH

C/

/

α

α(

)−

n

n

1*

*P

GG

CPyr

o

tot

PE

P

XOTG

P

2

αα

γ(

)(

)−

+n

n

n

1*

**

OG

OC

CPyr

oA

WG

O

tot

PE

P/,

22

XC

oal

TPP

α

α(

)(

)−

−n

n

1*

1*

KG

CPyr

o

tot

PE

P


2.6.1.2 Species transition kinetics: process air phase – wood gas phase –coal phaseA qualitatively valid approximation for species transition rates between the balance zones isneeded. The two relevant species transfer mechanisms are O

2transfer from process air phase

to wood gas phase (see Figure 3, (l)) and transfer of H2O (g) and CO

2 from wood gas phase

to the coal surface (see Figure 3, (r)). Figure 3 sketches out the basic model assumption forimplementing the species transition situation of O

2(l) and H

2O plus CO

2(r).

Thus the two main transition regions within the particle vicinity are the contact areabetween the process air phase and the wood gas phase A

A,WGas well as the contact area

between wood gas phase and coal phase AWG,coal

. Both values are coupled to the fluiddynamic interaction model introduced in chapter 2.5 and must be calculated differently as thefluid dynamic situation enters stages 1-3. Table 5 sums up the various transition-areaformulations for stages 1-3 and Table 6 provides additional variable definitions.

Now the diffusion boundary layer thicknesses δA,WG

and δWG,coal

for both transitionmechanisms need to be approximated in order to get a hold on species transition coefficients.A very simple approach, derived from Prandtl’s boundary layer theory [10] is chosen toaccomplish this (see Table 7).

With those pieces of information, the full species transition model, including transitionrates and β-values can be derived. In this work the β variable is used to represent the ratiobetween transition rates of species j from balance zone l to l+1, compared to the total molarinlet rates of species j into balance zone l. The remaining parts of the species transition modelare laid out in Table 7 and Table 8.

2.6.2 Energy balancesThe relevant, differential, conservative energy balance in tensor notation is shown in Eqn.14.This formulation encompasses all relevant balance zones (l= wood-, coal-, process air-, woodgas phase), directions (i= 1; x

1= x) and molecular species (j= CO, CO

2, H

2, H

2O, CH

4and

TARs). Heat transport phenomena are considered via convective and diffusive fluxes ofmolecular species and by heat conduction effects. Heat transition to other zones is derivedfrom the heat conduction formulation, where λ

lis the heat conduction coefficient within zone

l. The contribution of radiation heat exchange is left out because it is mostly relevant duringthe omitted heat up stage. Chemical energy release and in-stationary effects are considered

Figure 3: Sketch of model assumption for species transition situation during fluiddynamic stage 1. Zoomed in on boundary layer level. Green arrows representspecies transition rate vectors. Dashed green lines (l) represent oxygen transitionarea between process air and wood gas AA,WG. Straight black lines representtransition area between wood gas and coal surface AWG,coal


Tab

le 5

: Sp

ec

ies

tra

nsi

tion

are

a c

alc

ula

tion

, de

rive

d f

rom

flu

id-d

yna

mic

mo

de

l ac

co

rdin

g t

o 2

.5

Tra

nsit

ion

mec

hani

sm

S

tage

S

ymbo

l

Cal

cula

tion

Air

-> O

2->

Woo

d G

as

1

, Sta

ble

gas

bubb

le

Air

-> O

2->

Woo

d G

as

2

, Bub

ble

brea

k up

Air

-> O

2->

Woo

d G

as

3

, Por

e pe

netr

atio

n

Woo

d G

as -

>

1,

Sta

ble

gas

bubb

le

A p-

A pore

s,PH

2O

/CO

2->

Coa

l

Woo

d G

as -

>

2,

Bub

ble

brea

k up

Ap-

A pore

s,PH

2O

/CO

2->

Coa

l

Woo

d G

as -

>

3,

Por

e pe

netr

atio

n

H

2O

/CO

2->

Coa

l

ASt

age

AW

G1,

πr

4*

*W

G2

ASt

age

AW

G2,

∑π

()(

)+

+−

=

AD

Dr

r2

**

WG

iW

Gi

pore

i

N

WG

P,

,

1

pore

sP,

ASt

age

AW

G3,

επ

()

()

()

−+

++

−+

−⎡ ⎣⎢

⎤ ⎦⎥A

Ad

rr

rr

rr

rr

16*

*

3*

*1 3

*1 2

**

*P

pore

sP

coal po

re

WG

PW

PW

GW

PW

G,

23

32

22

ASt

age

WG

Coa

l1,

2,

ASt

age

WG

Coa

l1,

2,

ASt

age

WG

Coa

l3

,

επ

()

()

()

−+

++

−+

−⎡ ⎣⎢

⎤ ⎦⎥A

Ad

rr

rr

rr

rr

16*

*

3*

*1 3

*1 2

**

*P

pore

sP

coal po

re

WG

PW

PW

GW

PW

G,

23

32

22

Tab

le 6

: Va

riab

le d

efin

itio

ns

in a

dd

itio

n t

o T

ab

le 5

.

Def

init

ion

S

ymbo

l

C

alcu

lati

on

U

nit

Rat

io b

etw

een

proc

ess

air

spee

d co

mpo

nent

alo

ng th

e

g A

,WG

,i

-di

rect

ion

of s

urfa

ce n

orm

al v

ecto

r of

por

e i t

o w

ood

gas

spee

d at

por

e ou

tlet

Squa

re r

oot o

f ra

tio b

etw

een

proc

ess

air

and

woo

d ga

s

PA,

WG

-de

nsiti

es, r

elat

ed to

tem

pera

ture

dif

fere

nce

with

in th

e tw

o ba

lanc

e zo

nes

Fron

tal a

rea

of c

onic

al w

ood

gas

torc

h of

por

e i

A

WG

,i

m2

Dia

met

er o

f AW

G,i

D

WG

,i

m

ϕ ()

v

v*co

sR A

i

P WG

ρ ρ≈

T TA WG

WG A

ϒΡ

A

*po

reP

AW

Gi

AW

G

,

,,

, πA

2*

/W

Gi,


Tab

le 7

: Sp

ec

ies

tra

nsf

er

mo

de

l fo

r O

2fr

om

air

pha

seto

woo

d ga

s ph

ase

an

d H

2O

or

CO

2fr

om

woo

d ga

s ph

ase

to c

oa

l su

rfa

ce

.

Def

init

ion

Sym

bol/U

nit

Cal

cula

tion

Oxy

gen

diff

usio

n ra

te f

rom

pro

cess

air

phas

eto

woo

d ga

s ph

ase

/(m

ol /s

)

Car

bon-

di-o

xide

and

wat

er d

iffu

sion

rat

e

fr

om w

ood

gas

phas

eto

coa

l sur

face

/(m

ol/s

)

Rat

io o

f O

2tr

ansi

tion

rate

fro

m a

ir p

hase

to

/w

ood

gas

phas

e to

tota

l fre

sh a

ir O

2su

pply

rat

e

(-)

Rat

io o

f m

olar

, H2O

+ C

O2

tran

sitio

n ra

te

/ (

-)

fr

om w

ood

gas

phas

e to

coa

l pha

se to

tota

l

H2O

+ C

O2

prod

uctio

n ra

te

δϑ

ηε

ϑ

()

()

−

=−

δ

Θ

Θ

DA

xx

D

k

Df

vT

TA

xx

**

*

**

**

**

**

*

Diff

OA

WG

AW

G

GA O

OWG

Diff

O

AW

GP

BN

AR A

AP

BA

AW

GG

A OOW

G

,, ,

, ,

0

0,

22

2

2

22

nWG

coal

HO

CO

, ,2

2

βA

WG

O, 2

δϑ

ηε

ϑ=

δ

Θ

Θ

DA

x

D

k

Df

vT

TA

x

**

* **

**

**

**

*

Diff

HO

CO

WG

coal

WG

coal

GH

OC

OW

G

Diff

HO

CO

WG

coal

PB

NA

R A

AP

BA

WG

coal

GH

OC

OW

G

,,

, ,,

,, ,

0

0,

,

22

22

22

22

κε

+

f vT T

f*

* *

AAW

G

Diff

OA

A

PB

R AAA

WG

,

,

00

,

2

γκ

ε+

f

vT T

f*

** *

AWG

Coa

l

HO

CO

OW

GD

iffH

OC

OA

A

PB

R AAW

GC

oal

,

,;

,,

00

,

22

22

2

βWG

Coa

lH

OC

O, ,

22

nAW

G,

0 22

as well. The molar enthalpy of formation of species j at standard pressure and balance zonetemperature T

lis written as ΔhΘ

f,j(T

l). Other notations correspond to the formulation of the

atomic species balance equation (see Eqn.13).


Table 8: Variable definitions in addition to Table 7.

Definition Symbol Calculation/Value UnitRatio of molar CO

2 + H

2O -

production rate by chemical reaction within wood gas phase to molar rate of total fresh air O

2supply

Approximate diffusion boundary dA,WG mlayer thickness modeled according [10] for species transition from air to wood gas.

Approximate diffusion boundary dWG,Coal mlayer thickness modeled according [10] for species transition from wood gas to coal.

Ratio of contact area between air -phase and wood gas phase to reactor cross section per particle

Ratio of contact area between -wood gas phase and coal phase to reactor cross section per particle

Inverse diffusion constant s1/2 m1/2

for O2

diffusion

Inverse diffusion constant s1/2 m1/2

for H2O and CO

2diffusion

γH O CO OWG

, ;2 2 2

fAA WG,

fAWG Coal,

κDiff O, 2

+n

n

WGR H O CO

AO

,

,02 2

2

δk *1

ReA WG

BN

,

δk *1

ReWG Coal

BN

,

A A/A WG P A, ,

A A/WG Coal P A, ,

ηδk

D D f*

*

A WG

Diff O

A

P BN

,

, 2

κDiff H O CO, ,2 2 ηδk

D D f*

*

WG coal

Diff H O CO

A

P BN

,

, ,2 2

Eqn. 14ϑ

ϑ

λ

( )

( )

∂

∂+∂ +

∂∂

⎛

⎝⎜⎜

⎞

⎠⎟⎟

∂

+ ∂∂

− Δ =Θ

T c x

t

x v Dx

xc T

x

T

xn h T

* * ** * * * *

* * 0

l GT p T

p j jl

lj

Rj i G

T pDiff j

lj

i

Tp j l

i

ll

i

lR j f j l

,,

,,

, ,

2

2 , ,

l l

l l

While the energy balances for the wood gas phase, the wood- and the coal phase arederived for a 0D domain, the process air phase balance is a 1D formulation.


2.6.2.1 Energy balance of air phaseFor discretizing the process air phase angularly, along φ, a cylindrical coordinate system,with origin in the particle center, is introduced. For the solution of the energy balance, thecorresponding 1D species balance needs to be solved first. The molecular species balanceequation for the process air phase in its differential and numerical version is shown in Eqn.15and Eqn.16 respectively. Hereby is the molar flux of incoming fresh air into the entirenA

0

particle vicinity with a standard concentration of . Note that the indices i and j representthe temporal and spatial coordinate, respectively.

Eqn. 15

Eqn. 16

On basis of the species balance, the differential version of the process air, energy balance canbe set up as shown in Eqn. 17.

Introducing a numerical solution scheme for Eqn.17 and shifting the terms, such that thelocal process air temperature can be calculated, gives Eqn.18. Table 9 provides additionaldefinitions of variables for Eqn.17 and Eqn.18.

Eqn. 18

2.6.2.2 Energy balance of wood-, product gas- and coal phaseFrom Eqn.17 the 0D, integrated energy balances of the combined wood- plus wood gas phase(denoted by index W*) and the coal phase can be derived. By shifting the terms, thetemperature values of the balance zones can be calculated as seen in Eqn.19 and Eqn.20.Note that the index i represents the temporal co-ordinate and that the index j stands forchemical species in this context. Table 10 provides additional definitions of variables forEqn.19 and Eqn.20.

ΘxOA

2,

ϕϕ ϕ π

β( )

=+

− Θdn

d

nx n

( ) 2 *

1 cos 2

1

2* * *A A A WG

O OA

A

0, , 0

2 2

ϕ ϕϕ π

β ϕ( ) ( )= + Δ+

− Δ− Θn nn

x n2 * *

1 cos 2

1

2* * * *A

i j jAi j A

j

A WGO i O

AA

, , 10

,,

, 0

2 2

π ϕϕ

πϕ

πϕ

β ϕ

( )

( )

( ) ( )

∂∂

+ ∂∂

=

Λ+

+Φ

− Λ+

+ Λ +Φ⎡

⎣⎢⎢

⎤

⎦⎥⎥

λ

λΘ

T

t Nn

T

T v T

x v T

2 ** *

4 * *

1 cos 2* * *

4 * *

1 cos 22 * * * * *

A

A

AA

AA

A WGI

RA WG

A A WGO

AO A

A WGI

RA A

0 ,

, , ,

2 2

πϕ

πϕ

β

( )

( ) ( )

=

=Π

Δ+

Δ+Φ −

+ Λ+

− + Λ

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

λ− − − − −

− − Θ

T

tT

Nn T v T T

T T x T

1*

1 2 *

** * * *

4 * *

cos 2 1* 2 * * * *

i jA

Ai j

Ai j

A i

i jA A

i j A WGI A

R iWG A

i j

Ai

j A Ai j A WG

O iAO A

iA

,

,

1,

,

, , 1 , 1 1, 1

0 1, 1 ,,

, 0

2 2

Eqn. 17

Eqn. 20

2.7 THERMO CHEMISTRY MODELWithin the entire gasification process, two zones of intense thermo chemical reactions playa major role besides the, previously discussed, pyrolysis zone:• Thermo chemical stage 1: The gasification zone• Thermo chemical stage 2: The combustion zone

∑

β

γγ γ

γ

γ

( ) ( )( )

( ) ( )

= − Δ⎛

⎝⎜⎜

⎞

⎠⎟⎟ +

−⎛

⎝⎜⎜

⎞

⎠⎟⎟ + Δ +

Δ + − Δ + −

− Δ +⎡⎣

⎤⎦

−Φ − −Φ −

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

Δ

λ λ α

−−

Θ

−

− −

− −

−

− − − −

T T

N

N

x n

N c

T T c h

h c T h c T

x h x c T

T T T T

t

* 1* *

**

*

2* * *

* * * *

* * * *

* *

*

iW

iW

W

Wi

A WGO i

AO A

Wi

p WT

iA

Coal WGC O i

W p OWC O W

Coal WGC O

Coal p CoalT i

CoalCoalC O Coal p W

T iW

WGC O

WGj

WGj

WGj p j

TWi

j

A WGII i

iW A

i Coal Wi

iW Coal

i

*1*

*

*1

,,

, 0

*1

, *

1,

, 1* , ,

,,

,1

, ,1*

, , *1

,,

1*

1 , *, ,

1*

1

W

W W

W

2 2

2

2 2 2

*

2

*

2

*

β

γ γ

( ) ( )

= − Δ⎛

⎝⎜⎜

⎞

⎠⎟⎟ +

− +

+Φ − +Φ −

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥ Δ

λ α

−−

Θ

−

− −

− − − −

T T

N

N

x n

N c

c T c T

T T T Tt

* 1* *

*

** * * *

* **

iCoal

iCoal

Coal

Coali

A WGO i

AO A

Coali

p CoalT

CoalC O p W

T iW

Coal WGC O p Coal

T iCoal

Coal WGIII i

iWG Coal

i Coal Wi

iW Coal

i

11

,,

, 0

1,

, ,1 ,

, ,1

,,

1 1 ,,

1 1

Coal

W Coal

2 2

2 2


Table 9: Variable definitions in addition to Eqn.17 and Eqn.18.

Definition Symbol Calculation/Value UnitRatio between molar flux of LA 1/sincoming fresh air into the entire particle vicinity and total number of air molecules, already in vicinityConstant for ratio of diffusive s-1/2 m-1/2

heat flux to heat capacity within total process air phasePrandtl number within PrA - process air phase

Average process air velocity m/swithin packed bed

Constant for ratio of gross 1/sconvective species flux into process air phase element j at time i to total number of molecules within that element

nN

A

A

0

ΦλA WG

I, ϑ

ηθ

δ

A

k ND f

*

* *Pr* * *A WG

TA

A WGA A

P BN A,

,

,

A

η ϑλ

θc MM* * *Tp A A A

T

A

,,A A

εv /A PB0

ΠAi j, π

ϕΔ+

Δt

n

N

1 2 * *

*Ai j

A i

,

,

vRA

Eqn. 19


Table 10: Variable definitions in addition to Eqn.19 and Eqn.20.

Definition Symbol/Unit CalculationCoefficient of ratio between heat transition (coal phase - / (J/K mol)wood plus wood gas phase) to fresh air O

2supply at time

step i

Ratio between heat transition / (J/K mol) (process air phase - wood gas phase) to fresh air O

2supply

at time step i

Ratio between heat transition (coal phase - wood gas phase) / (J/K mol)to fresh air O

2supply at time

step i

Ratio between heat transition / (coal phase - wood phase) to (J/K mol)fresh air O

2supply at time step i

Ratio of molar coal transition rate to wood gas phase due to /reduction to molar rate of total (-)fresh air O

2supply

Ratio of molar coal production / rate to molar rate of total fresh (-)air O

2supply

Ratio of pyrolized carbon rate /to molar rate of total fresh (-)air O

2supply

Ratio of molar wood gas / production rate to molar rate (-)of total fresh air O

2supply

Φλ αCoal W

i, *

, ,

ΦλA WG

II i,

,

ΦλCoal WG

III i,

,

ΦαCoal W

i,

,

γ Coal WGC O

,, 2

γ CoalC O, 2

γWC O, 2

γWGC O, 2

αβ+

⎛

⎝⎜⎜

⎞

⎠⎟⎟

++

⎛

⎝⎜⎜

⎞

⎠⎟⎟ Φλ

Θ

A

A A

A

x n

A

A A

**

* *

*

iCoal W

iCoal W

iCoal WG

Coal WiCoal W

O iA WG

OA

AA

iCoal WG

iCoal W

iCoal WG

Coal WGII i

,

, ,

, ,

,, , 0

,

, ,

,,

2 2

λ

βδΘ

A

k x n

* * Re

* * *A

iWG A

iBN

WG AO iA WG

OA

AA

,

,,

, , 0

2 2

λ

βδΘ

A

k x n

* * Re

* * *A

iCoal WG

iBN

Coal WGO iA WG

OA

AA

,

,,

, , 0

2 2

αβ Θ

A

x n

*

* *Coal W

iCoal W

O iA WG

OA

AA

, ,

,, , 0

2 2

n

n

Coal WGCAO

,

,0

2

n

n

CoalCAO

,0

2

n

n

PyroCAO

,0

2

n

n

WGj

AO

,0

2

Gasification and combustion zone are located within the wood gas phase. Allrelevant thermo chemical reactions take place there. The gasification zone is locatedin close proximity to the coal surface (including the pore structure) while thecombustion zone occurs at the contact area between wood gas phase and process airphase.

For closer examination of the phenomena, three additional sub-zones have beenintroduced as description in chapter 2.6.1.

2.7.1 Thermo chemical stage 1: gasification modelThe developed, thermo chemical model resolves the relevant, molecular species compositionx

jfor the three sub-zones: the PEP, the TGP and the TPP. Actually the gas composition within

PEP xjPEP is resolved first. Within PEP, j = H

2O, H

2, CO, CO

2, CH

4and O

2. The calculation

is performed at each numerical time step, assuming that, within PEP a complete chemicalequilibrium is formed. Therefore the time constants of the involved reaction kinetics have tobe significantly smaller, than the chosen numerical time step Δt. By calculating x

jPEP, the

atomic species balance for PEP can be closed. Then the production rates of coal and non-reacting pyrolysis gas are calculated. Finally the atomic species balances for TGP and TPPcan be closed as well (see Table 3).

2.7.1.1 Gasification reactionsA condensation of the most relevant thermo chemical gasification reactions, reveals threebasic mechanisms (see e.g. [1]) that are assumed to exist in complete equilibrium within thepseudo equilibrium phase:

• The Boudouard reaction:

Eqn. 21

• The Methanation reaction:

Eqn. 22

• The Water gas shift:

Eqn. 23

Note the “(g/s)” notation. It hints to the fact that those reactions can occur both asheterogeneous mechanisms with the coal phase C(s) and as homogeneous reactions withpyrolized hydrocarbons within the pyrolysis gas C(g).

Even if no oxygen from the process air penetrates to the particle surface or the pyrolysisgas zone, oxygen will still be present to act as reactant for the formation of the PEP. Its originis the pyrolized wood itself. Thus relevant oxidation reactions have to be included in thecalculation of the gasification equilibrium as well, such that a fourth equilibrium reaction canbe assumed:• The oxidation reaction within the gasification zone

Eqn. 24

Note the constants of equilibria Kjin Eqn.21 – 24. They are sensitive to temperature

and are calculated at each numerical time step. The procedure to obtain the constantsof equilibria is well known (see [6], [11, 12]) and is hereby based on thermodynamiccoefficients a

i,nand b

i,n, published by NASA [14]. Table 11 sums up the

implementation for obtaining Kj. Used indices i, j and n stand for molecular species,

distinct, chemical reactions and the number of the individual, suitable coefficient from[14], respectively. In table 11, γ

i,jare the stoichiometric coefficients of species i in

reaction equation j.

( )+ ← →⎯⎯⎯C g/s CO 2CO2K1

( )+ ← →⎯⎯⎯C g/s 2H CH2K

42

( )+ ← →⎯⎯⎯C g/s H O CO+H2K

23

+ + ← →⎯⎯⎯ +CH H CO+3O 2 CO 3H O4 2 2K

2 210



Table 11: Procedure to obtain the equilibrium constant for reaction j: Kj (see also [11,12]).

Step Definition Symbol/ Calculation Units 1 Thermodynamic aj,n coefficient n for species i in reaction j, [14]2 Thermodynamic bj,n coefficient n for species i in reaction j, [14]

3 Molar, standard enthalpy of reaction j /(J/mol)

4 Molar, standard entropy of reaction j /(J/mol)

5 Molar, standard Gibbs free energy /(J/mol) of reaction j6 Molar, Gibbs free energy of reaction j /(J/mol)7 Equilibrium constant /(-) of reaction j at T

WG

Δ ΘhR j,

∑ γ a( * )i j i n

i

, ,

∑ γ b( * )i j i n

i

, ,

∑⎛

⎝⎜⎜

⎞

⎠⎟⎟ +

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

−

=

Tan

b

TR T* * *j n

WG

n

n

j

WG

WG,

1

1

5,1

∑+ −

⎛

⎝⎜⎜

⎞

⎠⎟⎟ +

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

−

=

Ta T an

b R* ln( ) *1

*j WG j nWG

n

n

j,1 ,

1

2

5

,2

Δ−ΔΘ Θh T

R T

s T

R

( )

*

( )j WG

WG

j WG

Δ +⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥=Θ

Θg T R Tp x

p( ) * * ln

*0j WG WG

i

− Δ⎡⎣⎢⎤⎦⎥

Θ

eg T( )j WG

Δ ΘsR j,

Δ Θg j

Δg j

K j

2.7.1.2 Unknowns and set of equationsThe presented solution for the gasification chemistry within PEP is based upon the idea that,in addition to the six unknowns x

jPEP, four α’

jvalues have to be found as well. For the

calculation within PEP, j’= “G” (gas phase), PG (pyrolysis gas), coal and O2. This makes a

system of ten unknowns: xH2O

PEP, xH2

PEP, xCO

PEP, xCO2

PEP, xCH4

PEP, xO2

PEP, αG

, αPG

, αcoal

, αO2

.The equations and conditions for resolving this problem are presented in Table 12. They

are based upon the assumption of chemical equilibrium for the gasification reactions, theover-all species balance and the H/C as well as O/C balance ratios for PEP.

2.7.1.3 Iterative gasification solverAn iterative gasification solver has been developed to solve the problem, posed in Table12 for the pseudo equilibrium phase. In contrast to Gibbs energy minimizationprocedures, described e.g. in [13], it aims for zero Gibbs free energy and calculatesfractions of potential reactants, that are available, but may not be involved in thereactions, in order to obtain this state. Table 13 lists the corresponding, iterative solutionprocedure, which is performed at each numerical time step. Note that in Table 13, indexi denotes the iterative step.

2.7.2 Thermo chemical stage 2: combustion modelAs postulated by the model, the wood gas phase, with compositions having beencalculated by the gasification solver (see 2.7.1), hits the process air phase at the contactarea A

A,WG, which in turn is calculated as described in Table 5. Oxygen reaches the

wood gas phase via diffusive transport mechanisms (see Table 7). Thus combustionreactions occur in addition to the actual gasification. Here the combustion reactions aremodeled to occur in combination with an intense, internal mixing of the wood gasphase. Consequentially it is assumed, that a global minimization of Gibbs free energy,within the entire wood gas phase takes place. The method of LaGrangian multipliers isused in order to obtain a state of global Gibbs energy minimization for all contributingwood gas phase components and gives the final product gas composition. Theprocedure is not depicted in detail here, since it is equivalent to methods published inliterature e.g. [13].

# Name/Symbol Equation/Condition

1 Boudouard

2 Methanation

3 Water gas shift

4 Oxidation

5 Species balance

6 O/C balance,

7 H/C balance,

8 αG

input user input

9 αO2

restriction

10 αcoal

restriction

= =KK

x

x'

1 CO

CO

11

22

=Kx

xCH

H

2 24

2

= =KK

x

x x'

1

*H O

H CO

33

2

2

=Kx x

x x x x

*

* * *CO H O

H CO CH O

10

2 3

32 2

2 4 2

+ + + + + =x x x x x x 1H O H CO CO CH O2 2 2 4 2

γ α α α α γ γα α α γ

( )− + +

+

−+ + +

+ +=

x x x x

x x x

* 1 * 2 * * /

* *

2 20

O C G G PG O OA WG

O C

G PG K CCoal WG

CO CO H O O

CH CO CO

/,

/

,2 2

2 2 2

4 2

γ α α αα α α γ

− ++

⎛

⎝⎜⎜

⎞

⎠⎟⎟ −

+ ++ +

=x x x

x x x*

1 *

* *

4 2 20H C

G G PG

G PG K CCoal WG

CH H O H

CH CO CO

/ ,4 2 2

4 2

RPEPO C/

RPEPH C/

≤ α ≤0 1O2

≤ α ≤0 1coal

Table 12: Equations and conditions for resolving thermo chemistry within PEP. Notethat the super scripts for PEP are omitted in this table.



Tab

le 1

3: E

qu

atio

ns

an

d c

on

diti

on

s fo

r re

solv

ing

th

erm

o c

he

mis

try

with

in P

EP.

No

te t

ha

t th

e s

up

er

scrip

ts f

or

PE

P a

re o

mitt

ed

inth

is t

ab

le.

#

Ste

p/Sy

mbo

l

Equ

atio

n/C

ondi

tion

1

Est

imat

e st

artin

g va

lue

for

x CO

PE

P,i ,

usi

ng in

form

atio

n fr

om p

revi

ous

iter

atio

ns

2

Cal

cula

te x

H2

PE

P,i

Ins

ert K

CO

PE

P,i

Ins

ert K

11

3

Cal

cula

te R

O/C

PE

P,ius

ing

Tabl

e 1

and

E

qn. 4

0 -

42

4

Cal

cula

te α

i O2

5

Cal

cula

te α

i coal

if α

i O2 =

0 or

αi O

2 =

1,

e

lse

α0co

al=

1;

∑Δ

Δ

−−

==x

in

*1 !

nC

OPE

Pi

n

nni

,1

11

()

()

−+

−+

+−

⎡ ⎣⎢ ⎢

⎤ ⎦⎥ ⎥

⎧ ⎨⎪ ⎩⎪

⎫ ⎬⎪ ⎭⎪K

KK

Kx

KK

xx

1

2*

*4

**

**

11

PE

Pi

CO

PE

Pi

CO

COPE

Pi

COPE

Pi

COPE

Pi

2

,,

2

2,

1'11

,,

+K

x1

*P

EP

iC

O3'

,

KK

KK

**

3'1'2

210

3

γα

αα

γγ

αα

α(

)(

)+

+−−

⎡ ⎣⎤ ⎦

−−

−R

1

2*

**

**

*1

*OA

WG

OC

PE

Pi

Gi P

Gi co

alCC

oal

WG

OC

GG

i PG

,/

,1

1,

/1

2

γα

αα

αγ γ

αα

γ

−+

+⎛ ⎝⎜ ⎜

⎞ ⎠⎟ ⎟−

−−

−R

R

*1

*2

**

**

*

OC

GG

i PG

OiOA

WG

OC

Gi P

GO

CP

EP

i

OC

PE

Pi

CCoa

lW

G

/1

1, /

1/

,

/,

,

2

2

()

()

()

()

++

+

++

xK

xK

xx

Kx

Kx

Kx

x

2*

**

*2

**

**

COPE

Pi

COPE

Pi

COPE

Pi

HPE

Pi

COPE

Pi

HPE

Pi

COPE

Pi

COPE

Pi

,1'

,2

3',

,11

,2

2,

2

1',

2,

2

2

(Con

td)

Tab

le 1

3: E

qu

atio

ns

an

d c

on

diti

on

s fo

r re

solv

ing

th

erm

o c

he

mis

try

with

in P

EP.

No

te t

ha

t th

e s

up

er

scrip

ts f

or

PE

P a

re o

mitt

ed

inth

is t

ab

le. (

Co

ntin

ue

d)

#

Ste

p/Sy

mbo

l

Equ

atio

n/C

ondi

tion

6

Cal

cula

te α

i PG

if (

αi O

2=

0 or

αi O

2 =

1)

a

nd (

αi co

al=

0 or

αi co

al=

1) e

lse

α0co

al=

“us

er d

efin

ed”;

7

Cal

cula

te x

CO

PE

P,i*

Ins

ert K

H2

PE

P,i

Ins

ert R

H/C

PE

P,i

8

Iter

ate

step

1 to

7 to

con

verg

ence

9

Cal

cula

te r

emai

ning

spe

cies

in

;

;

equ

ilibr

ium

with

xC

OP

EP

and

x H2

PE

P

;

10

Che

ck c

onsi

sten

cy o

f at

omic

spe

cies

b

alan

ce r

atio

for

PE

P R

H/C

PE

P

(se

e Ta

ble

1)

Che

ck c

onsi

sten

cy o

f at

omic

spe

cies

bal

ance

rat

io f

or P

EP,

RO

/CP

EP

(se

e Ta

ble

1)

γα

αγ

αγ

αγ

()

()

−+

−

−

R

R

*1

2*

**

*

*

OC

GOi

OAW

Gi K

CAW

GO

CP

EP

i

GO

CP

EP

iO

C

/,

,/

,

/,

/

22 (

)(

)(

)−

+−

−−

⎡ ⎣⎢ ⎢

⎤ ⎦⎥ ⎥

⎧ ⎨⎪ ⎩⎪

⎫ ⎬⎪ ⎭⎪R

KK

KR

KR

Kx

x1

2*

**

4*

**

4*

2*

HC

PE

Pi

PE

Pi

HP

EP

iH

HC

PE

Pi

HC

PE

Pi

PE

Pi

H

PE

Pi

H

/,

1',

,2

/,

1'/

,2

,,

2

22

2

2

−R

Kx

2*

*H

CP

EP

iP

EP

iH

/,

3',

2

γα

αα

αα

αγ

−+ +

⎛ ⎝⎜ ⎜⎞ ⎠⎟ ⎟

*1

*

**

HC

GG

i PG

Gi P

Gi K

CCoa

lW

G/

,

()

=x

Kx

2*

*P

EP

CO

COPE

P1'

2

2

γα

αα

αα

αγ

−+ +

⎛ ⎝⎜ ⎜⎞ ⎠⎟ ⎟=

++

++

xx

x

xx

x*

1*

**

2*

2*

HC

GG

PG

GP

GK

CCoa

lW

G

HPE

PP

EP

HO

PE

PC

H

PE

PC

OC

OPE

PC

HPE

P/

,

!2

24

24

γα

αα

αγ

γα

αα

γ(

)−

++

+=

++

++

+x

xx

x

xx

x

*1

*2

**

/

**

2*

2*

OC

GG

PG

OOA

WG

OC

GP

GK

CCoa

lW

G

OPE

PP

EP

HO

PE

PC

OC

OPE

P

PE

PC

OC

OPE

PC

HPE

P

/,

/

,

!2

22

22

24

=x

Kx

x*

*P

EP

HO

COPE

PHP

EP

3'

22

()

=x

Kx

*P

EP

CH

HPE

P2

2

42

()

=x

Kx

2*

*OP

EP

COPE

P11

2

2


11

Cal

cula

te m

olar

pro

duct

ion

rate

of

n

on-

reac

ting

pyro

lysi

s ga

s

Che

ck c

onsi

sten

cy o

f at

omic

spe

cies

b

alan

ce r

atio

for

TG

P R

H/C

TG

P

(se

e Ta

ble

1)

Che

ck c

onsi

sten

cy o

f at

omic

spe

cies

bal

ance

rat

io f

or T

GP

RO

/CT

GP

(se

e Ta

ble

1)

12

Cal

cula

te m

olar

pro

duct

ion

rate

of

coal

Che

ck c

onsi

sten

cy o

f at

omic

spe

cies

bal

ance

rat

io f

or T

PP R

H/C

TP

P

Che

ck c

onsi

sten

cy o

f at

omic

spe

cies

bal

ance

rat

io f

or T

PP R

O/C

TP

P

α

α(

)−

n1

**

PG

GCpy

ro

γα

γγ

+=

++

++

++

γγ

γγ

xx

xX

xx

xX

2*

2*

4*

*H

C

GCC

oal

WG

HPE

PP

EP

HO

CHPE

PH

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

/,

!/

OC

HC

OC

HC

22

4/

/

24

//

γγ

αγ

γ+ +

=+

++

++

++

+γ

γ

γγ

xx

xx

XX

xx

xX

2*

22

2*

OC

OAW

G

GCC

oal

WG

OPE

PP

EP

HO

PE

PC

OC

OPE

POTG

PO

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

/,

,

!/

OC

HC

OC

HC

22

22

2/

/

24

//

α

()

−n

t1

*(

)G

Cpyro

γγ

=+

++

++

++

γγ

γγ

xx

xX

xx

xX

X

2*

2*

4*

*H

CHP

EP

PE

PH

OC

HPE

PH

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

Coa

lTP

P/

!/

OC

HC

OC

HC

22

4/

/

24

//

γγ

γ+

=+

++

++

++

++

γγ

γγ

xx

xx

XX

xx

xX

X2

*2

*2

*2

**

OC

OAW

GOP

EP

PE

PH

OP

EP

CO

COPE

POTG

PO

CC

OH

TGP

PE

PC

OC

OPE

PC

HPE

PC

OH

TGP

Coa

lTP

P/

,!

/O

CH

C

OC

HC

2

22

22

//

24

//

γ

γn C

HO

H C

O C

()

n Cs

3. QUALITATIVE VERIFICATION AND RESULTSThis chapter focuses on a comparison of model outcome to data from literature and thepresentation of further model results, produced for exemplary parameter combinations.

So far the experimental work, published by Fatehi and Kaviany [7], has been particularlyhelpful to prove the validity of the presented gasification model. The fact, that a remarkable,qualitative agreement between model results and experiments can be shown, proves that asingle particle model can provide valuable information on the state of an entire packed bedreactor.

3.1 FLAME FRONT SPEED AGAINST PROCESS AIR SPEEDThe first criterion for model validity can be obtained by investigating the experimentallyobtained “flame front speed v

FFagainst process air speed v

A”, derived from the fixed bed, up

draft gasifier, seen in Figure 4 and published in [7].Figure 4 shows a direct comparison between the 20-year old, experimental results from

Fatehi and Kaviany, to equivalent results, obtained for two different sets of parameters(assuming pellets and wood chips as fuel), by the hereby presented model. The comparisonreveals that an outstanding, qualitative agreement can be achieved. It proves that the modelcan produce sensible results over a wide range of oxygen/fuel ratios. Note that, in almostexact agreement with experiments, the model gives a process air speed of about 1 m/s thatwould lead to extinguishing the flame.

3.2 TEMPERATURE AT DIFFERENT HEIGHTS AGAINST TIMEThe second kind of experimental evaluation, published in [7], is about mountingtemperature sensors at various heights within the reactor and about monitoring


Figure 4: Flame front speed vFF in mm/s against free flow process air speed vA inm/s. Direct comparison between published, experimental results from [7] (see *,upper left corner) and model results, derived from runs with parameter sets forpellets (blue) and wood chips (red). Single particle model results are scaled by oneconstant fitting parameter only

temperature values over process time (see Figure 5). At close examination, thosetemperature curves reveal five distinct spots of unsteadiness each. They shall hereby bemarked as spots “E”, “A”, “B”, “C” and “D” chronologically. It is obvious that these spotsmark separate events, which tend to occur independently within each layer of fuel particlesin the packed bed.

It can be shown, that those five spots of unsteady temperature evolution, can bereproduced by the model and can thus be explained! Figure 5 provides a direct comparisonbetween measured and modeled results.

3.3 INTERPRETATION OF UNSTEADINESS IN TEMPERATURE CURVESAfter finding a remarkable, qualitative correspondence between published experiments andmodeled results, regarding spots of unsteady temperature evolution against time, the modelcan now be used to explain those phenomena.

Upon examination of additional simulation data, it can be found, that the unsteadiness inspots “A”, “B”, “C” and “D” (as seen in Figure 5) can be explained by additionally plottingthe gas production rates over time, as shown in Figure 6. This way it becomes evident that,whenever the wood gas mixture runs out of a reducing component, a “bump” in thetemperature curve occurs. Hence it can be concluded that at such a spot, a higher, finite stageof oxidation of the local wood gas mixture is reached. Spots “A”, “B”, “C” and “D”correspond to the mixture running out of non-reacting pyrolysis gas (TARs), CH

4, CO and

H2

respectively.In addition to that, the model shows that the temperature curve behaves unsteadily in spot

“E” (see Figure 5), because from here, the coal phase starts to act as an effective heatcapacity.


Figure 5: Modeled results of wood gas temperature, T in K, against time, t in s, (pinkline) in direct comparison to temperature curves, recorded at counter currentgasifier, published in [7]. Spots of unsteady temperature evolution (“E”, “A”, “B”, “C”and “D”) do correspond qualitatively

4. CONCLUSION AND OUTLOOKThe presented 1D, compact, thermo fluid dynamic, single particle gasification andcombustion model, has been validated to yield good, qualitative correspondence to reactorscale experiments. While not giving full quantitative results, the model can still be used toprovide solid guidelines on how to adapt certain process parameters of a gasifier in directresponse to potentially varying fuel input parameters.

A capability to handle additional effects, such as drying, non-sphericity or particle heat-up behavior will be included in future versions of the model.

Furthermore a merging of the gasification model with an adapted version of anOpenFOAM® based, non-spherical, LaGrangian, large particle solver, described in [15], [16,17] and [18], is intended in the near future. The development of such a solver would entailthe possibility to represent e.g. pellets by 3D, non-spherical, LaGrangian particles, within aEulerian framework. The latter could then be set up based on the thermo- fluid dynamicimplementations, elaborated within this paper.

REFERENCES[1] T.B. Reed, M. Markson (2009). A Predictive Model for Stratified Downdraft

Gasification, Progress in Biomass Conversion, Academic Press, New York; Vol.4,(1983), pp. 217–254.

[2] A. Anca-Couce, N. Zobel, (2012). Numerical analysis of a biomass pyrolysis particlemodel: Solution method optimized for the coupling to reactor models, Berlin Instituteof Technology, Department of Energy Engineering, Technologies for RenewableEnergies, Germany. Fuel; Vol.97 (2012) 80–88.

[3] F.V. Tinaut, A. Melgar, J.F. Peerez, A. Horillo (2008). Effect of biomass particle sizeand air superficial velocity on the gasification process in a downdraft fixed bed gasifier.An experimental and modelling study, School of Engineering, University of Valladolid,Spain, Engineering Faculty, University of Antioquia, Colombia, CIDAUT Research


Figure 6: Modeled gas production rates of species i, in moli/sm2, against time, tin s. The correspondence of finite oxidation stages of the wood gas mixture, withspots of unsteady temperature evolution “A”, “B”, “C” and “D” in Figure 5 ishighlighted

N i

and Development Center in Transport and Energy, Spain. Fuel Processing Technology;Vol.89, (No.11), November 2008, pp. 1076–1089.

[4] Ch. Bruch (2001). Beitrag zur Modellierung der Festbettverbrennung in automatischenHolzfeuerungen. PhD thesis. Eidegenoessische technische Hochschule Zuerich,Switzerland, Diss. ETH Nr. 14040, 2001.

[5] N. Prakash, T. Karunanithi (2008). Kinetic Modeling in Biomass Pyrolysis – A Review,Department of Chemical Engineering, Annamalai University, Annamalai Nagar.INSInet Publication, Journal of Applied Sciences Research; Vol.4, (No.12): 1627–1636, 2008.

[6] S. Shabbar, I. Janajreh, (2012). Thermodynamic equilibrium analysis of coalgasification using Gibbs energy minimization method, Masdar Institute of Science andTechnology (MIST), Abu Dhabi. Energy Conversion and Management; Vol.65, (2013),755–763.

[7] M. Fatehi, M. Kaviany, (1994). Adiabatic Reverse Combustion in a Packed Bed,Department of Mechanical Engineering and Applied Mechanics, University ofMichigan. Combustion and Flame; Vol.99, (1994), 1–17.

[8] M. C. Melaaen (1996). Numerical analysis of heat and mass transfer in drying andpyrolysis of porous media. Telemark Institute of Technology, Norway. Numerical HeatTransfer, Part A: Applications; 29:4, 331–355.

[9] A. Galgano, C. Di Blasi, (2004). Modeling the propagation of drying anddecomposition fronts in wood, Dipartimento di Ingeneria Chimica, Universita degliStudi di Napoli. Combustion and Flame,;Vol.139, (2004), 16–27.

[10] Ludwig Prandtl, Fuehrer durch die Stroemungslehre, Vieweg Verlag, H. Oertel (Hrsg.)2002.

[11] G. Job, F. Herrmann, (2005). Chemical potential – a quantity in search of recognition,Institut fuer Physikalische Chemie, Universitaet Hamburg, Abteilung fuer Didaktik derPhysik, Universitaet Karlsruhe. European Journal of Physics; Vol.27, (2006), 353–371.

[12] S. Jarungthammachote, A. Dutta, (2008). Equilibrium modeling of gasification: Gibbsfree energy minimization approach and ist application to spouted bed and spout – fluidbed gasifiers, Energy Field of Study, School of Environment, Resources andDevelopment, Asian Institute of Technology, Thailand. Energy Conversion andManagement, 01/2008; DOI:10.1016/j.enconman.2008.01.006;

[13] S. Gordon, B.J. McBride, (1994). Computer Program for Calculation of ComplexChemical Equilibrium Compositions and Applications, I.Analysis, Sanford Gordon andAssociates, Cleveland Ohio, Lewis Research Center, Cleveland, Ohio. NASAReference Publication 1311, 1994.

[14] B.J. McBride, S. Gordon, M.A. Reno, (1993). Coefficients for CalculatingThermodynamic Transport Properties, Lewis Research Center, Cleveland, Ohio,Sanford Gordon and Associates, Cleveland Ohio, Heidelberg College, Triffin, Ohio.NASA Technical Memorandum 4513, 1993.

[15] M. Mataln, G.Boiger, W. Brandstätter, B. Gschaider, (2008). Simulation of ParticleFiltration Processes in Deformable Media, Part 1: Fluid-Structure Interaction, ICEStroemungsforschung GmbH., Montanuniversitaet Leoben. Int.Journal ofMultiphysics, Vol.2, (No.2), July 2008, pp. 179–189(11).


[16] G. Boiger, M. Mataln, W. Brandstätter, B. Gschaider, (2008). Simulation of ParticleFiltration Processes in Deformable Media, Part 2: Large Particle Modelling, ICEStroemungsforschung GmbH., Montanuniversitaet Leoben. Int.Journal ofMultiphysics, Vol.2, (No.2), July 2008, pp. 191–206(16)8.

[17] G. Boiger, M. Mataln, W. Brandstätter, (2009). Simulation of Particle FiltrationProcesses in Deformable Media, Part 3.1: Basic concepts and particle-fluid forceimplementation of a non- spherical dirt particle solver, ICE StroemungsforschungGmbH., Montanuniversitaet Leoben. Int.Journal of Multiphysics, Vol.3, (No.4), March2010, pp. 407–232(26).

[18] G. Boiger, M. Mataln, W. Brandstätter, (2009). Adaptive time stepping for explicitEuler implementation of spherical and non-spherical particle speed up. ICEStroemungsforschung GmbH., Montanuniversitaet Leoben. Int.Journal ofMultiphysics; Vol.3, (No.3), August 2009, pp. 267–291(25).

[19] C. Di Blasi, (2009). Combustion and gasification rates of lignocellulosic chars.Dipartimento di Ingeneria Chimica, Universita degli Studi di Napoli. Progress inEnergy and Combustion Science; Vol.35, (2009), 121–140.

[20] K.W. Ragland, D.J. Aerts, (1990). Properties of Wood for Combustion Analysis.Department of Mechanical Engineering, University of Wisconsin-Madison.Bioresource Technology; Vol.37, (1991), 161–168.

[21] IUPAC Compendium of Chemical Terminology (the “Gold Book”).doi:10.1351/goldbook.A00446 (Version: 2.3.1).


a thermo fluid dynamic model of wood particle gasification

Documents