Lecture 5 - Mechanical Engineering

Energy from Biomass 

4S610 

Lecture 5 

Rob Bastiaans

Contents this lecture: Particles 

• Different modes of conversion 

• Time scale of particle conversion 

• Dependence on physics 

• Drying 

• Gasification 

• Combustion 

• Based on equations of lecture 4 

• Simplifications 

/ Mechanical Engineering 

29-11-2012 PAGE 1

Energy from biomass 

Course outline 

1.Biomass macro systems 

2.Biomass micro systems 

3.Practical work 


29-11-2012 PAGE 2

Summary previous lecture 

Basic equations 

• Conservation 

• Peculiarities of species conversion 

• Simplifications 

• Steady 

• One-dimensional 

• Model flow reactors PSR, PFR 

• Important: no model gives you exact answers! 

• Still much research 

• You always have to think 


29-11-2012 PAGE 3

Particle conversion: what happens 

• Heating up and drying by convection/radiation 

• Evaporation and pyrolysis 

• Volatile products: water vapour, hydrocarbons, 

carbon oxides, H, S and N compounds, residual 

char 

• Mixing/diffusion of ambient oxidizer with 

combustibles 

• Ignition, needs high temperature 

• Combustion of volatiles (homogeneous reaction) 

• Combustion of residual char (heterogeneous 

reaction) 

/ Mechanical Engineering 29-11-2012 PAGE 4

Time scales and temperatures for 

pulverized fuel 

• Input fuel particles of 10-100 m 

• Preheating: 200 – 300 o C, < 1 ms 

• Pyrolysis: 300 – 1000 o C, 1-10 ms 

• Combustion of volatile matter: 1200 – 1500 o C, 5 - 

50 ms 

• Char burnout: 1500 – 2000 o C, 50 - 5000 ms 

• Particles fall apart 

• Resulting fly ash, 0.1 – 50 m, coagulation, 

sintering 

/ Mechanical Engineering 29-11-2012 5

Particle heating in different reactors 

• Pulverized fuel (entrained flow reactor): mixing of 

hot flue gas in near burner zone 

• Fluidized bed: heat transferred by particles (sand) 

• Grate furnaces: radiation important heat transfer 

• Fixed bed: convection, conduction and internal 

radiation 


Partial processes of coal combustion in 

firing systems 


Pulverized fuel combustion 

8 / Mechanical Engineering 

29-11-2012

Particle conversion: mechanical integrity 


Modeling conversion of spherical 

particles 

a. Liquid particles 

b. Solid particles 

• Quiescent medium (for validation of 

models g is used) 

• Laminar flow 

• Turbulent flow 


29-11-2012 PAGE 10

Modes of particle combustion 


Modes of particle conversion 

• Shrinking sphere: particle surface combustion, 

products leave particle as they are produced 

• Shrinking core: combustion on a reaction core, 

with build up of an ash/char layer 

• Shrinking density: uniform combustion inside the 

particle, conserved particle size, decrease of 

density 


Conversion rate 

(log –scale) 

Process regimes: Arrhenius plot 

Boundary 

Layer 

Diffusion 

Pore diffusion 

Chemical reaction 

High T 

High 

reaction 

rate 

Low T, limits 

Conversion rate 

III II I 

1/T 


I Shrinking density particle combustion 

• Determine dimensionless numbers 

• Find correct regimes of combustion 

• Mass transfer to particle versus diffusion in the 

particle (Biot number) 

• Chars give Bi < 4 → high external resistance to 

oxidizer diffusion into the particle 

• Reaction controlled by internal diffusion or 

reaction rate (Thiele number) 

• Low Thiele numbers -> low reaction rates -> 

reaction controlled -> shrinking density valid 


Porous particle: 

• Diffusion coefficient 

‣ Outside particle: 

‣ Inside particle: 

Deff D Ox 

D 

eff 

 

 

2 

D 

Ox 

• Steady state 

• One step conversion of carbon to carbon 

dioxide: equimolar, no gas flow 


Particle conversion 

Looking at oxygen concentration: 

1 

t r r 

2 

( YOx 

) ( r uY 

) 

2 

Ox 

 

1 

 

Y 

r D S 

2 

Ox 

( ) 

2 

eff 

r r r 



What would be the equation for the carbon 



Equimolar conditions, no flow 

What about density 



Result: 

1 Y 

r D S 

r r r 

2 

Ox 

0 ( ) 

2 

eff 

Inside particle: 

S k Y 

Ox 

Ox 

Dimensionless coordinate 

and fraction: 

r/ Rp 

Y 

Ox 

/ Y 

Ox, 

 



• Results in the equation: 

• With the Thiele modulus: 

1 

0 ( ) Th 

 

2 2 

2 

 

Th Rp kOx / Deff 

• Th>>1 conversion controlled by diffusion 

• Th

Boundary conditions 

• Boundary condition at centre 

• At the surface: 

 

 

 

0 

YOx 

Deff ( YOx YOx 

, ) 

r 

• With beta a mass transfer coefficient 


Solution 

• This yields: 

• With A, B: 

1 

Aexp( Th ) Bexp( Th 

) 

 

 

A 

B 

 

Bim 

( Bi Th 1)exp( Th) ( Th 1 Bi )exp( Th) 

m 

m 

• And Biot number 

Bi R / D 

m p eff 


Solution: Bi 

Bi R / D 

m p eff 

Bi>>1 pore diffusion limited 

Bi=1 limited boundary layer transport 


Solution: Th 

Th R k / 

p 

Ox 

D 

eff 

Th>>1 diffusion controlled (front) 

Th

Evaluation 

• Porosity not constant 

• Function of t 

• Therefore also function of r 

• Change in gas-density 

• Temporal effects 

• When is the stationary solution relevant 

• Temporal simulations can be done (validate latter) 

• Valid for shrinking sphere as well 

• Change position of boundary condition as function of 

depletion of the boundary 


Summary 

• Typical time scales and particle sizes 

• Arrhenius plot 

• Typical conversion modes 

• Shrinking core 

• Shrinking sphere 

• Shrinking density 

• Understanding present model and assumptions 

• Meaning of dimensionless numbers and what 

happens for a certain combination 

• Thiele 

• Biot 


Break 


29-11-2012 PAGE 27

II Shrinking sphere model for liquid 

particle combustion 

flamefront 

T 

Y Ox 

droplet 

Y F 

r d 

r f 


Mechanical Engineering 29-11-2012 29

Combustion of liquid particles: 

Spalding model (1953) 

• Spherical symmetry 

• Isolated droplet in infinite medium 

• Isobaric process 

• Infinitely fast chemical reaction (vs. diffusion) 

• Constant gas phase transport properties and c p 

• Gas phase quasi-steadiness 

• Constant, uniform droplet temperature (no droplet 

heating) 

• No radiation, Soret, Dufour effects 

• Unity Lewis numbers for all gaseous species 

• No buoyancy 

vD 

/ c p 


General form for different processes 

• Evaporation of liquid droplets 

• Burning of liquid droplets 

• One film model for burning of solid particles 

• Two film model for burning of solid particles 


Droplet evaporation (shrinking sphere) 

T 

 

 

T b 

T d 

Heat up time neglected! 


Evaporation time 

• Determined by 

dm d 

dt 

m 

• With the initial droplet mass 

• Giving: 

md 

 

1 D 6 

3 

dD 

dt 

3 

 

 

6 

m 

 

dD 

dt 

 

2 

D 

2 

m 


Evaporation time:D square law 

• Or 

dD 

dt 

2 

 

 

4 

D 

m 

K 

• With K the evaporation constant, integrating: 

• Giving: 

D 

 

 

D 

2 

2 

0 

dD 

2 

t 

0 

Kdt 

D 

2 

( t) 

D 

2 0 

 

Kt 


Droplet evaporation 


What is K, the mass conversion rate 

• Continuity (outside particle) 

m 

 

v4r 

2 

 

C 

• Energy: 

d dT d 

 

Lec dr dr dr 

p 

2 2 

r r vT 

 

 


Solution strategy 

• Integrate the energy equation twice 

• Find integration constants with B.C.’s: 

• T(r=r s )=T boil 

• T(r->)=T 

• Now T(r) is known 

• Use a heat balance at the droplet surface: 

4r 

2 

s 

dT 

dr 

r 

s 

m h 

evap 


What is K 

• After some math: 

4r 

8 

m ln( Bq 

1) 

K ln( Bq 

1) 

c 

cp 

p 

• With Spalding number for evaporation: 

B 

q 

 

c 

p 

 

T 

 

h 

T 

evap 

b 

 


Droplet evaporation 


Droplet evaporation: exercise 

• Consider a 500 m diameter droplet of n-hexane 

(C 6 H 14 ), evaporating in hot (850 K) nitrogen. The 

boiling point is 342 K. 

• What is the lifetime 

• Try this at home… 


Droplet burning: Temperature profile 


Droplet burning: species profiles 


Spalding transfer number fot liquid 

droplet combustion 

• Relative energy excess scaled with heat of 

vaporization 

B 

0, q 

 

h 

comb 

/ 

h 

c 

p 

evap 

 

T 

 

T 

b 

 

• Typical for combustion of liquid fuels in air, B=1 - 10 


Important results 

• Burn out time, d-square –law 

2 

t D / 

0 

K 

• Flame front distance 

• Flame temperature 

T 

f 

 

T 

b 

r 

r 

f 

s 

 

 

c 

h 

p 

 

 

 

 

ln 1 

B0, 

q 

ln 1 / 

 

evap 

B 

1 

0, 

q 

 

1 


Droplet burning 


Droplet burning experiments 


Droplet combustion: exercise 

• Consider a 100 m diameter droplet of n-heptane 

(C 7 H 16 ), combusting at atmospheric pressure and 

at T=300 K 

• What is the mass burning rate 

• Flame temperature 

• Stand-off distance relative to the droplet radius 


Evaluation 

• Constant burning rate, flame stand off distance 

and flame temperature 

• Single component droplets: good qualitative 

agreement 

• Quantitative agreement by tuning 

• Flame stand off ratio: over-predicted (difficult to 

tune) 

• Solid particles exhibit a d 2 -law as well 

• Conclusion: some errors, improvements over the 

years, but still frequently used 


Spalding transfer number for solid 

particle combustion 

• Surface burning: 

B .... 

• Off-surface burning (two film) 

B .... 


Modes of particle evaporation & 

combustion 

• Shrinking density: uniform combustion inside the 

particle, conserved particle size, decrease of 

density Thiele modulus (Th), Biot number (Bi m ) 

• Shrinking sphere: particle surface combustion, 

ash leaves particle as it is produced Spalding 

transfer number (B) 

• Shrinking core: combustion on a reaction core, 

with build up of an ash layer Solid particles 


Application in turbulent systems 


Application in turbulent systems: factors 

• Particle density important 

• Ratio of inter-particle spacing/flame standoff 

distance 

• Single particle burning – group burning 

• Length scale ratio of turbulent eddies and single 

particles/groups 

• Standard CFD uses some correlations on basis of 

Spalding transfer number 


Application in turbulent systems 


Different modes 


Turbulent vaporization systems 


Turbulent (group) combustion 


Next lecture: Marcel Cremers of Kema 

and emissions 


29-11-2012 PAGE 57

Questions 


29-11-2012 PAGE 58

Lecture 5 - Mechanical Engineering

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