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

ABSTRACT In order to qualitatively understand and evaluate the thermofluid dynamic situation within a wood gasification reactor, a 1D particle model has been created. The presented tool accounts for the highly instationary, kineticand 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 speciesand heat transition mechanisms, the energyand mass balances of wood, coal, pyrolysisgas, woodgas and offgas phases, the thermodynamics of locally developing gasificationand 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.


Pre exponential factor wood
Greek Symbols pyrolysis (s -1 ) A P,A Cross section of process air a G Ratio of molar pyrolysis gas cylinder (m 2 ) production rate to total pyrolysis rate (-) A WG,i Frontal area of conical torch i (m 2 ) a j Ratio of reacting component or species j total production rate of j (-) A g Area of regional border plane g (m

INTRODUCTION
Up to this day, medium-and large scale, packed bed gasification plants (see e.g.[1]), have proven to require a relatively high level of maintenance intensity in order to keep up continuous, 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 relevant thermo-, fluid dynamic sub-processes involved in wood gasification.Thus compact, fast and comprehensive 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 in detail.The model is an addition to the relatively large amount of gasification models, described in literature (see e.g.[2] and [4][5][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]).

•
Kinetic models, which focus on chemical reaction rates but tend to neglect physical transport mechanisms (e.g.[5][6][7][8][9][10][11][12][13][14][15][16][17][18][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 a detailed, 1D depiction of the life span of an individual, reacting pellet or wood chip, the involved thermo chemistry, transition kinetics of molecular species, coal-and pore structure formation mechanisms as well as relevant heat-and species balances.In addition (as pointed out in chapter 2.7), the model features a specifically tailored, iterative, numerical solver to handle the highly transient, thermo chemical situation within the wood gas phase and the pores 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 of a "Pseudo Equilibrium Phase" (PEP), with zero Gibbs free energy.So far, particle moisture content, drying effects, as well as the potential influence of non-spherical shape effects and thermal 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 packed bed, experimental results, published in literature [7].Moreover it will be demonstrated that the model can be used to reinterpret certain, experimental results [7].Thus its potential for further application is proven.

THE MODEL
In this chapter the thermo-, fluid dynamic principles and concepts behind the 1D, single particle, wood gasification model are laid out and explained step by step.
The most essential, mathematical modelling concepts, range from setting up sensible balance zones, realizing the fluid mechanic coupling between single particle and packed bed, over the calculation of pyrolysis kinetics, coal-and pore structure formation mechanisms to the modelling of species exchange kinetics and the full resolution of the thermo chemical situation in terms of gasification and combustion effects.

BALANCE ZONES AND COMPONENTS
The model distinguishes between four balance zones that transfer molecular species and energy 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 to that of wood, according to , but is enriched by oxygen and hydrogen, released by A thermo fluid dynamic model of wood particle gasification-and combustion processes Figure 1: Wood gas (orange), off gas (pink), coal phase with pores (black) and pyrolysis zone (yellow); Red and orange streamlines represent wood gas and mixed product gas flow respectively those cellulose components that turn into coal via pyrolysis.
Off gas is the undesired, but necessary by-product gas, created at the contact area between wood gas and process air.Within the model, it is created out of wood gas by combustion reactions (thermo chemical stage 2).It is composed of CO 2 and H 2 O.The off gas production, via oxidation of wood gas, releases exothermal energy, which heats the entire particle system and keeps the thermo chemistry going.

COUPLING BETWEEN PARTICLE AND PACKED BED: MODELLING THE PROCESS AIR FLOW
Each 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 ε PB , and a frontal, circular, cross section A P,A within the reactor (see Equ. π ( ) In Equ.2 a spherical particle bed structure is assumed.It allows for six free flow bottleneck cross 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 f BN is the bottleneck factor.In order to account for the over all porosity, f BN is calculated as: 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 sectional porosity approximately corresponds to the 3D porosity (see Equ.4).

PYROLYSIS
The first thing that happens to the pre-heated particle (~700 K) is, that pyrolysis reactions set in at the surface of the spherical piece of fuel.Pyrolysis transforms the cellulose molecules into pyrolysis gas and solid coal.Thus, over time, a thickening coal layer is forming at the surface.The model particle diameter is shrinking, while the pyrolysis front is progressing towards the particle centre.
First the pyrolysis rate , needs to be calculated in terms of pyrolized carbon atoms per time.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 T p .Values for the activation energy E' pyro and the pre exponential factor A' pyro , have been taken out of [20].The molar mass MM W of 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 α G , turns into pyrolysis gas, the rest turns into coal.Since coal mainly consists of solid carbon, all pyrolized oxygen and hydrogen atoms are 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

COAL PORE STRUCTURE MODEL
With the assumption of a thickening coal layer, which covers the pyrolysis gas production front, the necessity arises to introduce a comprehensive coal pore structure model.Since the velocity of the exiting wood gas at the particle surface v P WG is of interest, an approximation for the superficial coal pore area has to be developed.
Assuming isotropic coal porosity ε coal and constant, circular coal pore cross sections of diameter 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 R W .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 R WG,PG and the ideal gas law, such that: Eqn. 10 Combining Equ.9 and Equ.10 for r = R P, with R P being the total particle radius and N pores,P = N pores (R P ), the velocity of exiting wood gas at the particle surface can then be calculated as: Eqn. 11

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

Eqn. 12
Having defined , the task of approximating the contact area can be reduced to a 0D problem.At this point the idea of an average, representative wood gas protrusion radius WG is formulated.This radius corresponds to the sum of the wood core radius R W and the length of a representative pyrolysis gas/wood gas stream line, which starts at the pyrolysis front, goes along the very center of a straight coal pore and stops at the contact area to the process air phase.Then the assumption of three fluid dynamic stages is introduced: the stable gas bubble stage (stage 1), the gas bubble break up stage (stage 2) and the air into pores stage (stage 3).Within each stage, different physical conditions need to be taken into account and therefore the outflow radius needs to be calculated differently as well.Table 1 provides 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 laid out under section "Nomenclature".Consequentially, Figure 2 gives a more qualitative impression of how stages 1-3 are distinguished at the pore scale level.Furthermore Figure 2 sketches the relevant oxygen transition areas between process air phase and wood gas phase, for all three stages.
Even though the calculation of r -WG in stage 3 involves complex number mathematics, with , the result proves to be a real number.

MASS AND HEAT TRANSFER
The four balance zones: wood phase, coal phase, process air phase and wood gas phase have been introduced in 2.1.They interact through momentum-, mass-and, heat transfer.In this work 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.Table 2: Variable definitions in addition to Table 1 Stage # Symbol Calculation Unit

Atomic species balances and species transition kinetics
The relevant, differential, conservative atomic species balance in tensor notation is shown in Eqn.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 total product phase TPP), directions (i= 1; x 1 = x), molecular species (j= CO, CO 2 , H 2 , H 2 O, CH 4 and TARs) and atomic species (k= O, H, C).In stationary, convective, diffusive and chemical reaction effects are considered.The count of atoms of species k, per molecular species j is written as , while the species diffusion coefficient is D Diff,j and the specific and total molar γ k j Figure 2: Sketch of model assumption for three stages of "fluid momentum interaction" at pore scale, between process air (blue), wood gas (orange) and oxidized off gas (pink).Red, pink and (dashed) blue lines represent wood gas, off gas and air streamlines respectively.Dashed green lines represent the oxygen transition area between the process air zone and the wood gas zone species reaction rate within phase l are and respectively.The molecular speciesspecific coefficient α j represents 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-balance zone, namely the PEP (see 2.6.1).Note that x with subscript j signifies the molar fraction of a species j and x with a subscript i denotes any direction.
Eqn. 13 2.6.1.1Atomic species balances within "pseudo equilibrium phase", "total gas phase" and "total product phases" Three sub-balance zones are introduced: the pseudo equilibrium phase PEP, the total gas phase TGP 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 order to create the PEP, the model postulates the existence of a locally stable chemical state of equilibrium, which has a Gibbs free energy equal to zero.This is only possible if the locally available, molecular species are not fully mixed and certain species remain unprocessed.While all gaseous species together form the TGP, the reacting species in their "pseudo equilibrium state" 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 α j .
In Table 3, specializations of Eqn.13 are presented, which account for the molecular species balances within the three sub zones.For reasons of mathematical practicality, balance ratios are used, rather than single-species-balances.Table 4 provides additional definitions of variables, used in Table 3.
2.6.1.2Species transition kinetics: process air phase -wood gas phasecoal phase A qualitatively valid approximation for species transition rates between the balance zones is needed.The two relevant species transfer mechanisms are O 2 transfer from process air phase to wood gas phase (see Figure 3, (l)) and transfer of H 2 O (g) and CO 2 from wood gas phase to the coal surface (see Figure 3, (r)).Figure 3 sketches out the basic model assumption for implementing the species transition situation of O 2 (l) and H 2 O plus CO 2 (r).
Thus the two main transition regions within the particle vicinity are the contact area between the process air phase and the wood gas phase A A,WG as well as the contact area between wood gas phase and coal phase A WG,coal .Both values are coupled to the fluid dynamic interaction model introduced in chapter 2.5 and must be calculated differently as the fluid dynamic situation enters stages 1-3.Table 5 sums up the various transition-area formulations for stages 1-3 and Table 6 provides additional variable definitions.Now the diffusion boundary layer thicknesses δ A,WG and δ WG,coal for both transition mechanisms 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 to accomplish this (see Table 7).
With those pieces of information, the full species transition model, including transition rates and β-values can be derived.In this work the β variable is used to represent the ratio between transition rates of species j from balance zone l to l+1, compared to the total molar inlet rates of species j into balance zone l.The remaining parts of the species transition model are laid out in Table 7 and Table 8.

Energy balances
The 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-, wood gas phase), directions (i= 1; x 1 = x) and molecular species (j= CO, CO 2 , H 2 , H 2 O, CH 4 and TARs).Heat transport phenomena are considered via convective and diffusive fluxes of molecular species and by heat conduction effects.Heat transition to other zones is derived from the heat conduction formulation, where λ l is the heat conduction coefficient within zone l.The contribution of radiation heat exchange is left out because it is mostly relevant during the omitted heat up stage.Chemical energy release and in-stationary effects are considered   Table 6: Variable definitions in addition to Table 5.

Unit
Ratio between process air speed component along the    as well.The molar enthalpy of formation of species j at standard pressure and balance zone temperature T l is written as Δh Θ f,j (T l ).Other notations correspond to the formulation of the atomic species balance equation (see Eqn.13).m layer thickness modeled according [10] for species transition from air to wood gas.

Approximate diffusion boundary d WG,Coal
m layer 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 Eqn. 14 , While the energy balances for the wood gas phase, the wood-and the coal phase are derived for a 0D domain, the process air phase balance is a 1D formulation.

Energy balance of air phase
For 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, the corresponding 1D species balance needs to be solved first.The molecular species balance equation for the process air phase in its differential and numerical version is shown in Eqn.15 and Eqn.16 respectively.Hereby is the molar flux of incoming fresh air into the entire  n A 0 particle vicinity with a standard concentration of .Note that the indices i and j represent the temporal and spatial coordinate, respectively.

Eqn. 15
Eqn. 16 On basis of the species balance, the differential version of the process air, energy balance can be set up as shown in Eqn. 17.
Introducing a numerical solution scheme for Eqn.17 and shifting the terms, such that the local process air temperature can be calculated, gives Eqn.18.Table 9 provides additional definitions of variables for Eqn.17 and Eqn.18.
Eqn. 18 2.6.2.2 Energy balance of wood-, product gas-and coal phase From 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, the temperature 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 for chemical species in this context.Table 10 provides additional definitions of variables for Eqn.19 and Eqn.20.

218
A thermo fluid dynamic model of wood particle gasification-and combustion processes Gasification and combustion zone are located within the wood gas phase.All relevant thermo chemical reactions take place there.The gasification zone is located in close proximity to the coal surface (including the pore structure) while the combustion zone occurs at the contact area between wood gas phase and process air phase.
For closer examination of the phenomena, three additional sub-zones have been introduced as description in chapter 2.6.1.

Thermo chemical stage 1: gasification model
The developed, thermo chemical model resolves the relevant, molecular species composition x j for the three sub-zones: the PEP, the TGP and the TPP.Actually the gas composition within PEP x j PEP is resolved first.Within PEP, j = H 2 O, H 2, CO, CO 2 , CH 4 and O 2 .The calculation is performed at each numerical time step, assuming that, within PEP a complete chemical equilibrium is formed.Therefore the time constants of the involved reaction kinetics have to be significantly smaller, than the chosen numerical time step Δt.By calculating x j PEP , the atomic species balance for PEP can be closed.Then the production rates of coal and nonreacting pyrolysis gas are calculated.Finally the atomic species balances for TGP and TPP can be closed as well (see Table 3).

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

•
The Water gas shift: Eqn. 23 Note the "(g/s)" notation.It hints to the fact that those reactions can occur both as heterogeneous mechanisms with the coal phase C(s) and as homogeneous reactions with pyrolized hydrocarbons within the pyrolysis gas C(g).
Even if no oxygen from the process air penetrates to the particle surface or the pyrolysis gas zone, oxygen will still be present to act as reactant for the formation of the PEP.Its origin is the pyrolized wood itself.Thus relevant oxidation reactions have to be included in the calculation of the gasification equilibrium as well, such that a fourth equilibrium reaction can be assumed:

•
The oxidation reaction within the gasification zone Eqn.24 Note the constants of equilibria K j in Eqn.21 -24.They are sensitive to temperature and are calculated at each numerical time step.The procedure to obtain the constants of equilibria is well known (see [6], [11,12]) and is hereby based on thermodynamic coefficients a i,n and b i,n , published by NASA [14].Table 11 sums up the implementation for obtaining K j .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,j are the stoichiometric coefficients of species i in reaction equation j.
Table 11: Procedure to obtain the equilibrium constant for reaction j: K j (see also [11,12]).
Step Definition Symbol/ Calculation Units 1 Thermodynamic a j,n coefficient n for species i in reaction j, [14] 2 Thermodynamic b j,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 j 6 Molar, Gibbs free energy of reaction j /(J/mol) 7 Equilibrium constant /(-) of reaction j at T WG

Unknowns and set of equations
The presented solution for the gasification chemistry within PEP is based upon the idea that, in addition to the six unknowns x j PEP , four α' j values have to be found as well.For the calculation within PEP, j'= "G" (gas phase), PG (pyrolysis gas), coal and O 2 .This makes a system of ten unknowns: x H2O PEP , x H2 PEP , x CO PEP , x CO2 PEP , x CH4 PEP , x O2 PEP , α G , α PG , α coal , α O2 .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, the over-all species balance and the H/C as well as O/C balance ratios for PEP.

Iterative gasification solver
An iterative gasification solver has been developed to solve the problem, posed in Table 12 for the pseudo equilibrium phase.In contrast to Gibbs energy minimization procedures, described e.g. in [13], it aims for zero Gibbs free energy and calculates fractions of potential reactants, that are available, but may not be involved in the reactions, in order to obtain this state.Table 13 lists the corresponding, iterative solution procedure, which is performed at each numerical time step.Note that in Table 13, index i denotes the iterative step.

Thermo chemical stage 2: combustion model
As postulated by the model, the wood gas phase, with compositions having been calculated by the gasification solver (see 2.7.1), hits the process air phase at the contact area 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 combustion reactions occur in addition to the actual gasification.Here the combustion reactions are modeled to occur in combination with an intense, internal mixing of the wood gas phase.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 is used in order to obtain a state of global Gibbs energy minimization for all contributing wood gas phase components and gives the final product gas composition.The procedure is not depicted in detail here, since it is equivalent to methods published in literature e.g.[13].

QUALITATIVE VERIFICATION AND RESULTS
This chapter focuses on a comparison of model outcome to data from literature and the presentation of further model results, produced for exemplary parameter combinations.So far the experimental work, published by Fatehi and Kaviany [7], has been particularly helpful 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 a single particle model can provide valuable information on the state of an entire packed bed reactor.

FLAME FRONT SPEED AGAINST PROCESS AIR SPEED
The first criterion for model validity can be obtained by investigating the experimentally obtained "flame front speed v FF against 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 comparison reveals that an outstanding, qualitative agreement can be achieved.It proves that the model can produce sensible results over a wide range of oxygen/fuel ratios.Note that, in almost exact agreement with experiments, the model gives a process air speed of about 1 m/s that would lead to extinguishing the flame.

TEMPERATURE AT DIFFERENT HEIGHTS AGAINST TIME
The second kind of experimental evaluation, published in [7], is about mounting temperature sensors at various heights within the reactor and about monitoring temperature values over process time (see Figure 5).At close examination, those temperature curves reveal five distinct spots of unsteadiness each.They shall hereby be marked as spots "E", "A", "B", "C" and "D" chronologically.It is obvious that these spots mark separate events, which tend to occur independently within each layer of fuel particles in the packed bed.
It can be shown, that those five spots of unsteady temperature evolution, can be reproduced by the model and can thus be explained!Figure 5 provides a direct comparison between measured and modeled results.

INTERPRETATION OF UNSTEADINESS IN TEMPERATURE CURVES
After finding a remarkable, qualitative correspondence between published experiments and modeled results, regarding spots of unsteady temperature evolution against time, the model can now be used to explain those phenomena.
Upon examination of additional simulation data, it can be found, that the unsteadiness in spots "A", "B", "C" and "D" (as seen in Figure 5) can be explained by additionally plotting the 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 the temperature curve occurs.Hence it can be concluded that at such a spot, a higher, finite stage of 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 H 2 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 heat capacity.
Figure 5: Modeled results of wood gas temperature, T in K, against time, t in s, (pink line) in direct comparison to temperature curves, recorded at counter current gasifier, published in [7].Spots of unsteady temperature evolution ("E", "A", "B", "C" and "D") do correspond qualitatively Figure 6: Modeled gas production rates of species i, in mol i /sm 2 , against time, t in s.The correspondence of finite oxidation stages of the wood gas mixture, with spots of unsteady temperature evolution "A", "B", "C" and "D" in Figure 5 is highlighted ε

Figure 3 :
Figure 3: Sketch of model assumption for species transition situation during fluid dynamic stage 1.Zoomed in on boundary layer level.Green arrows represent species transition rate vectors.Dashed green lines (l) represent oxygen transition area between process air and wood gas A A,WG .Straight black lines represent transition area between wood gas and coal surface A WG,coal normal vector of pore i to wood gas speed at pore outlet Square root of ratio between process air and wood gas P A,WG densities, related to temperature difference within the two balance zones Frontal area of conical wood gas torch of pore i A

Eqn. 20 2. 7
THERMO CHEMISTRY MODEL Within the entire gasification process, two zones of intense thermo chemical reactions play a major role besides the, previously discussed, pyrolysis zone: • Thermo chemical stage 1: The gasification zone • Thermo chemical stage 2: The combustion zone

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

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

Table 4 :
Variable definitions in addition to Table3.

Table 5 :
Species transition area calculation, derived from fluid-dynamic model according to 2.5

Table 7 :
Species transfer model for O 2

Table 8 :
Variable definitions in addition to Table7.

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

Table 13 :
Equations and conditions for resolving thermo chemistry within PEP.Note that the super scripts for PEP are omitted in this table.

Table 13 :
Equations and conditions for resolving thermo chemistry within PEP.Note that the super scripts for PEP are omitted in