-
Copyright © 2011 by ASME 1
Proceedings of the ASME 2011 International Mechanical
Engineering Congress & Exposition IMECE2011
November 11-17, 2011, Denver, Colorado, USA
IMECE2011-64473
Design and Simulation of a Hybrid Entrained-Flow and Fluidized
Bed Mild Gasifier Part 1 – Design Considerations and Development of
a Multiphase Model
A.K.M. Monayem Mazumder, Ting Wang and Jobaidur R. Khan
Energy Conversion & Conservation Center University of New
Orleans
New Orleans, LA 70148-2220, USA
ABSTRACT A mild gasification process has been developed to
provide
an innovative form of clean coal technology, which can be
utilized to build a new, highly efficient, and compact power plant
or to retrofit an existing coal-fired power plant in order to
achieve lower emissions and significantly improved thermal
efficiency. The core technology of the mild gasification power
plant lies on the design of a compact and effective mild gasifier
that can produce synthesis gases with high energy volatiles through
a hybrid system: utilizing the features of both entrained-flow and
fluidized bed gasifiers. The objectives of this study are to (a)
describe the features and design considerations of this mild
gasifier and (b) develop a multiphase computational model to guide
the design of the mild-gasifier by investigating the thermal-flow
and gasification process inside a conceptual mild gasifier. Due to
the involvement of a fluidized bed, the Eulerian-Eulerian method is
employed to calculate both the primary phase (air) and the
secondary phase (coal particles). Multiphase constitutive equations
developed from kinetic theory are employed for calculating the
effective shear viscosities, bulk viscosities, and effective
thermal conductivities of granular flows to simulate the
hydrodynamic and thermal interactions between the solid and gas
phases. Multiphase Nativer-Stokes equations and seven global
reaction equations with associated species transported equations
are implementd to simulate the mild gasification process. Part 1 of
this paper documents the design principle of the mild gasifier as
well as the development of the computational model starting from
single phase, then using multiple phases, and finally including all
reactions in the multiphase flow. NOMENCLATURE c concentration
(mass/volume, moles/volume) cp heat capacity at constant pressure
(J/kg-K) cv heat capacity at constant volume (J/kg-K) D mass
diffusion coefficient (m2/s) DH hydraulic diameter (m) Dij mass
diffusion coefficient (m2/s) Dt turbulent diffusivity (m2/s) E
total energy (J) g gravitational acceleration (m/s2) G incident
radiation
Gr Grashof number (L3.ρ2.g.β.∆T/ µ2) H total enthalpy (W/m2-K) h
species enthalpy (W/kg-m2-K) J mass flux; diffusion flux (kg/m2-s)
k turbulence kinetic energy (m2/s2) k thermal conductivity (W/m-K)
m mass (kg) MW molecular weight (kg/kgmol) M Mach number p pressure
(atm) Pr Prandtl number (ν/α) q heat flux qr radiation heat flux R
universal gas constant (8314.34 J/Kmol-K) S source term Sc Schmidt
number (ν/D) t time (s) T temperature (K) U mean velocity (m/s) X
mole fraction (dimensionless) Y mass fraction (dimensionless) x, y,
z coordinates Greek letter β coefficient of thermal expansion (K-1)
ε turbulence dissipation (m2/s3) εw wall emissivity κ von Karman
constant µ dynamics viscosity (kg/m-s) µk turbulent viscosity
(kg/m-s) ν kinematic viscosity (m2/s) v' stoichiometric coefficient
of reactant v" stoichiometric coefficient of product ρ density
(kg/m3) ρw wall reflectivity σ Stefan-Boltzmann constant σs
scattering coefficient τ stress tensor (kg/m-s2) Subscript i
reactant i j product j r reaction r
-
Copyright © 2011 by ASME
2
INTRODUCTION Coal has been widely utilized to produce electric
power.
Approximately 49 percent of electricity in the United States is
produced by coal. Unfortunately coal is dirty and burning coal
releases a large amount of greenhouse gases (CO2 and NOx) and other
pollutants such as SOx, soot, mercury, and ashes. Therefore, it is
essential to continuously develop new technologies to utilize coal
more cleanly. The method of using coal can be categorized into four
main processes: (a) combustion, (b) pyrolysis, (c) liquefaction,
and (d) gasification. In combustion, coal is directly burned to
produce heat. In pyrolysis, coal is decomposed through heating in
the absence of oxygen. Volatile matters inside the coal will be
released when coal is heated, leaving only carbon (char) and tar.
In liquefaction, coal is converted into liquid fuel. In
gasification, coal is converted into synthetic gas (syngas).
Gasification is a process that converts any carbon-based materials,
such as coal, pet-coke, biomass, or various wastes, into a syngas
through an oxygen-limited reaction. After removing sulfur and other
contaminants, the cleaned syngas can be used as a fuel to produce
electricity or valuable products such as chemicals, fertilizers,
and transportation fuels. One of the advantages of using
gasification technique is that the syngas fuel can be cleaned
before combustion occurs, resulting in significantly reduced
emissions. This study is hence focused on gasification technology.
Coal Gasification
Figure 1 presents the typical stages of coal gasification. The
gasification of coal particles involves three major steps: (a)
thermal decomposition (pyrolysis and devolatilization), (b) thermal
cracking of the volatiles, and (c) char gasification. Coal
particles undergo pyrolysis when they enter the hot combustion
environment. Moisture within the coal boils and leaves the coal’s
core structure when the particle temperature reaches the boiling
point. The volatiles are then released as the particle temperature
continues to increase. This volatile-releasing process is called
devolatilization. The long-chained volatiles are then thermally
cracked into lighter, shorter-chained volatile gases, such as H2,
CO, C2H2, C6H6, CH4, etc. These lighter gases can react with O2,
releasing more heat, which is needed to continue the pyrolysis
reaction.
With only char and ash left, the char particles undergo
gasification with CO2 or steam to produce CO and H2, leaving only
ash. The heat required for the pyrolysis and devolatilization
processes can be provided externally or internally by burning the
char and/or volatiles.
Devolatilization
Devolatilization is a decomposition process of hydrocarbon
materials when coal is heated. Devolatilization rates are
influenced by temperature, residence time, particle size, and coal
type. The heating causes chemical bonds to rupture and both the
organic and inorganic compounds to decompose. The process starts at
a temperature of around 100°C (212°F) with desorption of gases,
such as water vapor, CO2, CH4, and N2, which are stored in the coal
pores. When the temperature reaches above 300°C (572°F), the
released liquid hydrocarbon called tar becomes important.
Gaseous
hydrocarbons, CO, CO2, and steam are also released. When the
temperature is above 500°C (932°F), the fuel particles are in a
plastic state, through which they undergo drastic changes in size
and shape. The coal particles then harden again and become char
when temperature reaches around 550°C (1022°F). As heating
continues, H2 and CO are released through gasification.
C + H2O + Volatile
Pyrolysis (No oxygen)
C + Volatile
H2O
C
Volatile
Devolatilization
Lighter products CO, H2, C6H6
Thermal Cracking
Mild Gasification
CO, CO2, H2
CO2, H2O
Gasification
Figure 1 Simplified global gasification processes of coal
particles (sulfur and other minerals are not included in this
figure). Heat can be provided externally or internally through
combustion of char, volatiles, and CO.
The pyrolysis conditions affect the physical properties of
chars. It is reported that the heat transfer coefficient decreases
10 times during fast heating of the coal particles mixed with a hot
solid heat carrier. This reduced heat transfer rate to the particle
surface results in a temperature plateau on the level of about
400°C (752°F) and lasts throughout devolatilization process.
In general, the larger the particle size, the smaller the
volatiles yield. This is because in larger particles, more
volatiles may crack, condense, or polymerize, with some carbon
deposition occurring during their migration from inside the
particle to the particle surface. High pressure has a similar
effect on the devolatilization rate. Anthony et al. [1] reported
that devolatilization rates are higher at lower pressures. An
increase in pressure increases the transit time of volatiles rising
to the particle surface. Types of Gasifiers
There are many types of gasifiers. The operating principles of
two commonly used gasifiers (the entrained-flow and fluidized bed
gasifier) are used in designing the studied mild gasifier, so only
these two types of gasifiers are briefly introduced below.
Entrained-Flow Gasifier
In the entrained-flow gasifier, a dry, pulverized coal, an
atomized liquid fuel, or a fuel slurry is gasified with oxygen
(much less frequent: air) in a co-current or counter-current flow
at a speed of 10-15 m/s. The gasification reactions take place in a
dense cloud of very fine particles. Most coals are suitable for
this type of gasifier because of the high operating
-
Copyright © 2011 by ASME
3
temperatures and the high heat transfer rates to the individual
particles, resulting from that fact that the coal particles are
well separated from one another. All entrained-flow gasifiers
remove the major part of the ash as a slag because the operating
temperature is typically well above the ash fusion temperature. A
smaller fraction of the ash is produced either as a very fine fly
ash or as a black ash slurry. Fluidized Bed Gasifier
In a fluidized bed gasifier, air or oxygen is injected upward at
the bottom of a solid fuel bed, suspending the fuel particles. The
fluidized bed acts like a multiphase, granular flow field. The fuel
feed rate and the gasifier temperature are lower compared to those
of entrained-flow gasifiers. The operating temperature of a
fluidized bed gasifier is also lower: around 1000°C (1830°F), which
is roughly only half of the operating temperature of a coal burner.
This lower temperature has several advantages: lower NOx emissions,
no slag formation, and low syngas temperature, which can result in
a cheaper syngas cooling system being used prior to gas clean up,
meaning higher cycle efficiency. Fluidized bed gasifiers require a
moderate supply of oxygen and steam. Complete, Partial, Full, and
Mild Gasification
For clarification, the terms of full, partial, and mild
gasification are defined below:
Complete and Partial gasification describe how much char is left
unreacted. Complete Gasification implies that all the char is
completely gasified, while Partial Gasification indicates that a
portion of the char is remained unreacted.
Full and Mild gasification describe the level (i.e., the
products' molecular weight or length of molecular chain) of thermal
cracking, which is typically affected by the temperature level and
residence time of reaction. Full Gasification indicates that the
feedstock undergoes complete de-volatilization, gasification, and
thermal cracking into a composition consisting of light species
like CO, H2, and CH4 as the major combustible components of the
so-called syngas, while Mild Gasification preserves the heavy
volatiles without further thermally cracking the volatiles into
lighter components. To be specific, the operation of "Mild
Gasification" refers to controlling the temperature and residence
time to achieve varying levels of gasification between
pyrolysis-only (0% gasification) and full gasification (100%
gasification). It is a comprehensive process to design such a
gasifier that can control the level of thermal cracking that
occurs.
MOTIVATION AND OBJECTIVE
The sole function of all of the gasifiers used for electrical
power generation is to produce syngas, consisting of light gases
such as CO, H2, and CH4 as the major fuels. The major reason for
wanting to produce light gases is to avoid condensation of tars or
heavy volatiles in the gas cleaning systems, which are usually
operated at temperatures lower than the volatiles' dew points.
Therefore, if gas cleaning can be performed at a temperature higher
than the volatiles' dew points, it becomes interesting to
investigate the feasibility of producing mildly-gasified syngas
with a large portion of this
syngas consisting of heavier volatiles with higher energy
density to save the energy consumed for thermally cracking the
volatiles to lighter gases. The recent successful development of a
pilot gas cleanup system by RTI International in Eastman's coal
gasification facility in Kingsport, Tennessee with support from the
U.S. Department of Energy [2] provides the necessary technology
breakthrough to utilize the mildly-gasified syngas studied in this
paper. This system could remove sulfur, ammonia, mercury, arsenic,
selenium and chlorine at temperatures between 600oF and 1000oF. It
will be a great achievement if all the operating temperatures can
be above 960oF --- this is the temperature above which almost all
the volatiles will remain in the vapor phase. The RTI warm gas
clean up system has been incorporated into the Polk Power Station
IGCC plant in Tampa, Florida for commercial testing [3]. The
conceptual system diagram of an integrated mild-gasification
combined cycle (IMGCC) is shown in Fig. 2. Note that IMGCC is
different from the conventional partial gasification system, which
uses a carbonizer to produce the char, in that it uses large
amounts of energy to thermally crack the volatiles fully to very
lighter gases instead of preserving the volatiles and gases with
higher-energy densities.
CO2 + Exhaust
Steam
air
N2
Condenser
Combustion Chamber
Compressor
Cyclone
Char
O2
Sulfur / H2SO4/Other sulfur products
Volatiles
Volatiles + Char
Volatiles
Gas Cooler
CO2Capture
Water
air
Warm Desulfurizer
and gas cleanup
Coal + Biomass
Turbine
HRSG
Steam TurbineBoiler
Steam
Char
Vola tiles + Char
IMGCC (Integrated Mild Gasification Combined Cycle)
Burner
Mild-Gasifier
Legends of Arrows Gases (O2, CO2, Volatiles) Sulfur or Sulfur
products Water Vapor (Steam) Liquid Water Char/Coal/Biomass
ASU
K
Figure 2 A system diagram of an integrated mild-gasification
combined cycle (IMGCC)
In addition to the energy savings, there are several other
attractive advantages for using mildly-gasified syngas: since a
typical mildly-gasified syngas contains approximately 6 times more
energy than a fully-gasified syngas, the sizes of the mild gasifier
and gas cleaning systems can be shrunk down by about 80%. Then, the
remaining unreacted char can be used in the boiler of a
conventional pulverized coal (PC) power plant with negligible
sulfur content (See Fig. 2). This advantage leads to the
possibility of using mild gasification technology to retrofit
existing PC power plants by replacing the coal feedstock with the
char produced by a mild gasifier. The mildly-gasified syngas can be
burned in the gas turbine after it goes through the gas cleaning
systems. The exhaust of the gas turbine can produce steam via a
heat recovery steam generator (HRSG) to produce steam to generate
electricity via a steam turbine, like a traditional combined cycle.
Only this time, the steam produced by the HRSG is mixed with the
steam produced with the boiler
-
Copyright © 2011 by ASME
4
of the existing PC plant operated in a Rankine cycle. This
retrofit can significantly increase the plant efficiency from about
30% to 50% (HHV) as well as drastically reduce the emissions per kW
output because the syngas can be cleaned before combustion more
economically than is possible after combustion due to the low
volume flow rate of mild-gasified syngas and increased overall
cycle efficiency. Furthermore, the scrubber of the original PC
plant could be removed, reducing the overall plant operating and
maintenance (O&M) cost. This approach was first proposed by
Wormer as the Mild Air-Blown Gasification Integrated Combined Cycle
(MaGIC) [4]. However, in MaGIC, the gasifier is operated under the
air-blown condition without using an air separation unit (ASU). In
an IMGCC system, either air-blown or oxygen-blown operation can be
implemented. The core technology of the mild-gasification power
plant is a compact and effective mild gasifier that can control the
level of thermal cracking that occurs. This need motivates this
study with the objectives to (a) discuss the design considerations
and describe the features of this mild gasifier and (b) develop a
multiphase computational model with chemical reactions in granular
flows to guide the design of the mild-gasifier by investigating the
thermal-flow and gasification process inside a conceptual
mild-gasifier.
DESCRIPTION OF THE STUDIED MILD GASIFIER
The conceptual design of a 100kW, laboratory scale mild
gasifier, as shown in Fig. 3, is a hybrid system which combines
features of both an entrained-flow and a fluidized bed gasifier.
The entrained-flow feature is characterized by the centralized
draft tube. Through the draft-tube's bottom inlet, coal and a
limited amount of air are introduced to produce heat, which is used
to drive out the volatiles during the journey moving upward through
the draft tube. Surrounding the draft tube is the fluidized bed.
The draft tube is 4 inches (10.15 cm) in diameter to prevent the
volatiles inside from contacting the oxygen in the fluidization air
in the fluidized bed, but this setup allows heat to be transferred
from the draft tube to the fluidized bed through the draft tube
wall. Above the draft tube, a deflector 8 inches in diameter is
installed to block the particles from being entrained out of the
fluidized bed. The height and width of the bench-top mild gasifier
is 34.25 inches (87 cm) and 18 inches (45.75 cm), respectively.
There are three velocity inlets, two for the fluidized gas and one
for the coal and transport gas. The diameter of the left and right
horizontal gas inlets is 3 inches (7.65 cm) and the vertical coal
inlet is 2 inches (5 cm) in diameter. There are four outlets, two
for char and two for the produced syngas. The diameter of the left
and right horizontal syngas outlets is 5 inches (12.7 cm) and the
char outlet is 1.5 inches (3.8 cm) inclined 45 degrees. The
fluidized bed is 10 inches (0.254m) deep. To create fluidization
inside the gasifier, a total of 28 perforated interior surfaces of
0.15 inches (0.38 cm) diameter each are created side by side,
equally spaced. The computational model developed in this study
will be used to guide design iterations of this preliminary
conceptual design in the future.
Figure 3 Schematic diagram of the cold-flow model of the
conceptual Mild Gasifier, a variation derived from the Wormser's
design [5]. COMPUTATIONAL MODEL Computational Fluid Dynamics (CFD)
is an economical and effective tool to study coal gasification.
Coal gasification is a multiphase reactive flow phenomenon. It is a
multiphase problem between gases and coal particles and also a
reactive flow problem, which involves homogeneous reactions among
gases and heterogeneous reactions between coal particles and gases.
The Eulerian-Eulerian method is adopted in this study because the
concentrations of coal particles are dense in the fluidized bed and
tracking each particle with the Lagrangian method is not practical
given current computational capability. Furthermore, the available
correlations describing the interactions between particles and
gases in the Lagrangian method are all limited to a single particle
or very diluted particle concentration conditions and they can’t be
used for very dense condition in a fluidized bed. In the studied
mild gasifier, even though the condition inside the draft tube is
similar to an entrained-flow gasifier and the Lagrangian-Eulerian
method could be used here, however, since the Lagrangian-Eulerian
method can't be used to obtain a solution within the fluidized bed,
while Eulerian-Eulerian can be used in both the entrained-flow and
fluidized bed portions of the gasifier, employing the
Eulerian-Eulearian method is believed to be the most appropriate
choice.
The solid particles are placed in the domain of the fluidized
bed like a bed of granular material. The mixture of the gas phases
of different species passes through this bed and converts this
granular material from a static solid-like state to a dynamic
fluid-like state. This process is known as "fluidization". Both
homogeneous (gas-gas) reactions and heterogeneous (gas-solid)
reactions are simulated in this study.
-
Copyright © 2011 by ASME
5
Model Development Due to the complexity of this simulation, this
study is
performed by starting from a single phase, then using multiple
phases, and finally including all reactions in the multiphase flow,
using the approach given below:
1. Single gas phase of thermal-flow behavior (no solids and no
reactions.)
2. Single gas phase with chemical reaction assuming
instantaneous gasification (no solids)
3. Multiphase of thermal-flow behavior (no reaction) 4.
Multiphase of reactive thermal-flow (complete
simulation) The central-plane geometry of the 2-D Mild Gasifier
used
in the simulation is shown in Fig. 4. Physical Characteristics
of the Problem
The physical characteristics of the problem are modeled as
follows,
1. The flow inside the domain is two dimensional,
incompressible, and turbulent.
2. Gravitational force is considered. 3. Gas species involved in
this study are Newtonian fluids
with variable properties as functions of temperature. These
variable properties are calculated by using a piecewise-polynomial
method.
4. A mass-weighted mixing law for specific heat and the
incompressible, ideal gas law for density are used for gas species
mixtures.
5. The walls are impermeable and adiabatic. 6. The no-slip
condition (zero velocity) is imposed on all
wall surfaces.
Figure 4 Schematic of the 2D simulated Mild Gasifier
Multiphase Flow Regimes In the Eulerian-Eulerian approach, the
different phases are
treated mathematically as interpenetrating continua. The concept
of a phasic volume fraction is introduced in this approach. These
volume fractions are assumed to be continuous functions of space
and time and their sum is always equal to one. For each phase,
conservation equations are derived to obtain a set of equations
which have similar structure for all phases. These equations are
closed by providing constitutive relations that are obtained from
empirical information, or, in the case of granular (solid) flows,
by application of kinetic theory.
The Eulerian model allows for the modeling of multiple,
separate, interacting phases. It solves a set of "n" momentum and
continuity equations for each phase. Where n is the number of
phases. The pressure and inter-phase exchange coefficients are
coupled in this model.
Governing Equations
The unsteady equations for conservation of mass, momentum, and
energy using the Eulerian multiphase model are presented below: The
continuity equation for phase "q" is
( ) ( ) ( ) qn
1pqppqqqqqq Smmvρρt
+−=ε⋅∇+ε∂∂ ∑
=
&&v (1)
Where, qv
v = the velocity of phase "q"
pqm& = the mass transfer from phase "p" to phase "q"
qpm& = the mass transfer from phase "q" to phase "p" εq =the
volume fraction of phase "q" Sq =the source term of phase "q" The
momentum balance for phase "q" is
( ) ( ) ( )( )
vm,qlift,qq
n
1pqpqppqpqpqqq
qqqqqqqqq
FFF
vmvmRgρ
τpvvρvρt
vvv
v&
v&
vv
vvv
+++
−++ε+
⋅∇+∇ε−=ε⋅∇+ε∂∂
∑=
(2)
Where, qτ , is the stress-strain tensor of phase "q" given
by
( ) Iv32vv qqqq
Tqqqqq ⋅⋅∇⎟
⎠⎞
⎜⎝⎛ μ−λε+∇+∇με=τ
vvv (3)
The inter-phase force, pqR
v depends on the friction, pressure,
cohesion, and other effects, and is subject to the conditions
that qppq RR
vv−= and 0Rqq =
v. This inter-phase force is given by:
( )∑∑==
−=n
1pqppq
n
1ppq vvKR
vvv (4)
μq = the shear viscosity of phase "q"
-
Copyright © 2011 by ASME
6
λq = the bulk viscosity of phase "q" qFv
= an external body force of phase "q"
lift,qFv
is the lift force acting on a secondary phase "p" in a primary
phase "q" is computed from, ( ) ( )qpq, vvv5.0 vvv
v×∇×−−= pqqliftF ερ (5)
qvm,F
v is the inertia of the primary phase mass encountered by
the accelerating particles or droplets or bubbles exerted by a
"virtual mass force" on the particles. The virtual mass effect is
significant when the secondary phase density is much smaller than
the primary phase density. It is negligible in this study.
pqRv
= an interaction force between phase "p" and "q" ∇P = the
pressure gradient shared by all phases
pqvv = the inter-phase velocity
gv = acceleration due to gravity Kpq = the inter-phase momentum
exchange coefficient
One of the major differences between the single phase
momentum equation and the Eulerian multiphase momentum equation
is the inter-phase momentum exchange coefficient. For a solid phase
"s" the conservation of momentum equation is
( ) ( )
( )( )( )
svm,slift,s
n
1lslsllslsslls
sss
sssssssss
FFF
vmvmvvK
gρτ
ppvvρvρt
vvv
v&
v&
vv
v
vvv
+++
−+−+
ε+⋅∇+
∇−∇ε−=ε⋅∇+ε∂∂
∑=
(6)
Where, ps = the solid pressure of the solid phase "s" Kls = Ksl
= the momentum exchange coefficient between fluid or solid phase
"l" and solid phase "s". slK can be written in the following
general form,
s
sssl
fKτρε
= (7)
Where, f = the drag function, and is defined differently for the
different exchange-coefficient models, while τs = the "particulate
relaxation time," and is defined as:
l
2ss
s 18dμ
ρ=τ (8)
Where, ds = the diameter of particles of phase "s" The
definition of the drag function "f" includes a drag
coefficient, CD, that is based on the relative Reynolds number,
Res, the equation of which, again, is different for each of the
exchange coefficient models. The model of Syamlal and O'Brien [5]
is given by:
2s,r
lsD
v24ReCf ε= (9)
Where, vr,s = the terminal velocity for the solid phase "s" And
CD = the drag coefficient with the following form derived by dalla
Valle [28]:
2
s,rsD
vRe8.463.0C ⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛+= (10)
The Syamlal and O'Brien model is based on measurements of the
terminal velocities of particles in fluidized or settling beds,
with correlations that are a function of the volume fraction and
relative Reynolds number, given below:
l
slsls
dvvRe
μ−ρ
=vv
(11)
Where the subscript "l" denotes the fluid phase, the subscript
"s" denotes the solid phase, and ds is the diameter of the solid
particles.
The terminal velocity correlation for the solid phase "s" has
the following form:
( ) ( ) ⎟⎠⎞⎜
⎝⎛ +−++−= 2s
2ss2
1s,r AAB2Re12.0Re06.0Re06.0Av (12)
With 4.14lA ε=
And 85.0for8.0B l1.28l ≤εε=
Or 85.0forB l2.65l >εε=
This model is appropriate when the solid shear stresses are
defined according to Syamlal and O'Brien [5]. For granular
(solid) flows in the compressible regime, i.e.
where the solid volume fraction is less than its maximum allowed
value, a solid pressure is calculated independently. The solid
pressure is composed of a kinetic term and a second term due to
particle collisions: ps = εs ρs θs + 2 ρs (1 + ess) εs² go,ss θs
(13) Where ess = the coefficient of restitution for particle
collisions, go,ss = the radial distribution function, and θs = the
granular temperature.
The radial distribution function, go, is a correction factor
that modifies the probability of collisions between grains when the
solid granular phase becomes dense. This function may also be
interpreted as the non-dimensional distance between spheres: go =
(s + dp)/s (14) Where s = the distance between grains and dp = the
diameter of the grain particle.
There is no unique formulation for the radial distribution
function in the literature, but the following empirical
functions
-
Copyright © 2011 by ASME
7
derived by Syamlal et al. [6] and Lebowitz [7] can be used with
discretion. For "n" solid phases,
( ) ( ) ( )lk2s
lk
n
1k k
k
skl,o
dd1
ddd
3
11g
+ε−
⎟⎟⎠
⎞⎜⎜⎝
⎛ ε
+ε−
=∑
= (15)
Due to translation and collision, the solid stress tensor
contains bulk and shear viscosities arising from particle
momentum exchange.
The solid bulk viscosity accounts for the resistance of the
granular particles to compression and expansion. It has the
following form from Lun et al. [8]:
( )2
1s
ssss,ossss e1gd34
⎟⎠⎞
⎜⎝⎛
πθ
+ρε=λ (16)
The collisional and kinetic parts and the optional
frictional
part are added to give the solid shear viscosity: μs = μs,col +
μs,kin + μs,fr (17)
The collisional part of the shear viscosity is modeled from
Gidaspow et al. [9] and Syamlal et al. [6]
( )2
1s
ssss,ossscol,s e1gd54
⎟⎠⎞
⎜⎝⎛
πθ
+ρε=μ (18)
The kinetic part of the shear viscosity is modeled as from
Syamlal et al. [6]
( ) ( ) ( ) ⎥⎦
⎤⎢⎣⎡ ε−++
−πθρε
=μ ss,osssssss
sssskin,s g1e3e15
21e36
d (19)
Schaeffer's expression can be used if the frictional
viscosity is included in the calculation:
D2
sfr,s I2
sinp φ=μ (20)
ps = the solids pressure φ = the angle of internal friction I2D
= the second invariant of the deviatoric stress tensor.
The granular temperature, θs, for the solid phase "s" is
proportional to the kinetic energy of the fluctuating particle
motion. The transport equation derived from kinetic theory takes
the following form derived by Ding and Gidaspow [10]
( ) ( )
( ) lsssss
sssssss
sskv:τIp
vρρt2
3
φ+γ−θ∇⋅∇+∇⎟⎠⎞⎜
⎝⎛ +−=
⎥⎦⎤
⎢⎣⎡ θε⋅∇+θε
∂∂
θθv
v
(21)
Where
sss v:τIpv
∇⎟⎠⎞⎜
⎝⎛ +− = the generation of energy by the solid
stress tensor
( )ssk θ∇θ = the diffusion of energy ( skθ is the diffusion
coefficient)
sθγ = the collisional dissipation of energy
lsφ = the energy exchange between the fluid or solid phase "l"
and the solid phase "s"
To describe the conservation of energy in the Eulerian
multiphase model, a separate enthalpy equation is written for each
phase:
( ) ( )
( )∑=
−+++⋅∇−∇+
∂
∂ε−=ε⋅∇+ε
∂∂
n
1pqpqppqpqpqqqqq
qqqqqqqqq
hmhmQSqv:τ
tp
hvρhρt
&&vv
v
(22)
Where, hq= the specific enthalpy of the phase "q" Qpq= the rate
of heat transfer between the phase "p" and "q"
hpq= the inter-phase enthalpy The rate of heat transfer between
the phase "p" and "q" is to be a function of the temperature
difference, Qpq = hpq ( Tp – Tq) (23) Where, hpq= hqp = the heat
transfer coefficient between the phase "p" and "q." The heat
transfer coefficient is related to the Nusselt number, Nup, of
phase "p" and is given by:
2p
ppqqpq d
Nuk6h
εε= (24)
Here, kq= the thermal conductivity of the phase "q". The Nusselt
number is determined from one of the many correlations reported in
the literature. In the case of fluid-fluid multiphase flows, the
correlation of Ranz and Marshall [11, 12] the Nusselt number is
found by:
31
21pp PrRe6.00.2Nu += (25)
Where, Rep is the relative Reynolds number based on the diameter
of the phase "p" and relative velocity. The relative Reynolds
number for the primary phase "q" and secondary phase "p" is defined
as:
q
pqpq dvvReμ
−ρ=
vv
(26)
Where Pr is the Prandtl number of the phase "q" defined as Pr =
(Cpq μq/kq).
In the fluid-solid multiphase flows (or granular flows), the
Nusselt number correlation given by Gunn [13], applicable within a
porosity range of 0.35 to 1.0 and a Reynolds number of up to 105,
is given as:
( )( )
( ) 317.0s2ff312.0
s2ffs
PrRe2.14.233.1
PrRe7.015107Nu
ε+ε−+
+ε+ε−= (27)
-
Copyright © 2011 by ASME
8
Where the subscript "f" is for the primary fluid phase "f" and
the subscript "s" is for the secondary solid phase "s". The heat
transfer coefficient is always multiplied by the volume fraction
(ε) of the primary phase as it should tend to zero whenever one of
the phases is not present within the domain. k-ε Mixture Turbulence
Model:
The standard k-ε model is the simplest and most robust of
turbulence two-equation model in which the solution of two separate
transport equations allows the turbulent velocity and length scales
to be independently determined. The turbulence kinetic energy (k),
and its rate of dissipation (ε), are obtained from the following
transport equations:
( ) ( )
ε−+⎟⎟⎠
⎞⎜⎜⎝
⎛∇
σ
μ⋅∇=
⋅∇+∂∂
mmk,k
mt,
mmm
ρGk
kvρkρt
v
(28)
( ) ( )
( )ε−ε+
⎟⎟⎠
⎞⎜⎜⎝
⎛ε∇
σ
μ⋅∇=ε⋅∇+ε
∂∂
εε
ε
m2mk,1
mt,mmm
ρCGCk
vρρt
v
(29)
Where the mixture density ρm, mixture velocity mvv ,
turbulent
viscosity μt,m, and production of turbulence kinetic energy Gk,m
are computed from volume fraction and mass weighted equations.
ε
=μ μ2
mmt,kCρ (30)
( )( ) mTmmmt,mk, v:vvG vvv ∇∇+∇μ= (31)
The constants in these equations are the same as those of
standard k-ε model for the single phase. C1ε, C2ε, Cμ, σk and σt
are constants and have the following values: C1ε = 1.44, C2ε =
1.92, Cμ = 0.09, σk = 1.0, and σt = 1.3. Enhanced Wall
Function:
The k-ε model is mainly valid for high Reynolds number, fully
turbulent flow. Special treatment is needed in the region close to
the wall. The enhanced wall function is used in this study.
Modeling Species Transport in Multiphase Flows:
The global instantaneous gasification mechanism is modeled to
involve the following gaseous species: C, O2, N2, CO, CO2, H2O,
C6H6, H2, and volatiles (CH2.121O0.585). For each phase "q", the
conservation equations for chemical species in multiphase flows can
be solved through Eq. 32:
( ) ( )
( ) RmmSRJYvY
tn
1ppqqp
qi
qqi
q
qi
qqi
qqqqi
qq
ijji +−+ε+ε+
ε⋅∇−=ρε⋅∇+ρε∂∂
∑=
&&
vv
(32)
Where =qiR the net rate of production of homogeneous species "i"
by chemical reaction for phase "q" =ijpqm& the mass transfer
source between species "i" and "j"
from phase "q" to "p" εq = the volume fraction for phase "q"
=qiS the source term, or rate of addition of mass from the
dispersed phase plus any user-defined sources R = the heterogeneous
reaction rate
The species model panel for multiphase species transport
simulations allows inclusion of volumetric, wall surface, and
particle surface reactions.
The multiphase mass transfer model accommodates mass transfer
between species of different phases. Each mass transfer mechanism
defines the mass transfer phenomenon from one entity to another
entity.
The general expression for the source term for species "k" in
the phase "i" is given by: ∑∑ γ−γ=+=
ki
kk
ki
kkki
ki
r
rj
rj
p
pj
pjrp
ki MRMRSSS (33)
Where, "γ" is the stoichiometric coefficient, "p" represents the
product, and "r" represents the reactant.
Calculating momentum sources is more complicated than
calculating mass sources. The general expression for the net
momentum source rate of the reactants is given by:
∑
∑γ
γ=
rrj
rj
r rrj
rj
net M
uMu j
vv (34)
The general expression of momentum source for the phases "i" is
given by: ∑γ−=
i
ir
irj
rjnetp
ui uMRuSS
vvv (35)
The net enthalpy of the reactants is given by:
( ) ( )
ba
fbbb
faaa
net MbMahHMbhHMa
H+
+++= (36)
Where, "hf" represents the formation enthalpy, and "H"
represents the enthalpy. Finally, the general expression for the
heat source term is given by:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛γ+γ−= ∑ ∑
i i
ir p
pj
fpj
pj
rj
rj
rjnetp
Hi hMHMRHSS (37)
Chemical Reaction Model:
In the finite-rate model, the chemical reactions (shown in Table
1) involve both homogeneous (gas-gas) and heterogeneous (solid-gas)
reactions. Reaction rates based on the Laminar Finite-Rate Model
and Eddy-Dissipation Model are calculated and compared. The minimum
of the two results is used as the homogeneous reaction rate. For
the heterogeneous reaction (gas-solid), only the finite rate is
used.
-
Copyright © 2011 by ASME
9
In a manner similar to a previous study by Silaen and Wang [15],
seven global gasification reactions are used, including three
heterogeneous and four homogeneous reactions. The volatiles are
modeled with a two-step thermal cracking and gasification process
via benzene (C6H6). Their reaction rates in the form of R = ATn exp
(-E/RT), are shown in Table 1. Table 1 Global gasification
reactions model (n=0)
R # Reactions A (kg / m²-s) E (J / kmol) R 1 C(s) + ½ O2 → CO
92.32 8.4×10+7 R 2 C(s) + CO2 → 2CO 23.3 1.15×10+8 R 3 C(s) + H2O →
CO + H2 24.9 1.125×10+8 R 4 CO + ½ O2 → CO2 2.2×10+12 1.67×10+8 R 5
CO + H2O (g) → CO2 + H2 2.75×10+10 8.38×10+7
R 6 CH2.121O0.585 → 0.585CO + 0.853H2+0.069C6H6 1.0×10+15
1.0×10+8
R 7 C6H6 + 3O2 → 6CO + 3H2 1.0×10+15 1.0×10+8
The Eddy-Dissipation model assumes that the chemical reaction is
faster than the time scale of the turbulence eddies. Thus, the
reaction rate is determined by the turbulence mixing of the
species. The reaction is assumed to occur instantaneously when the
reactants meet. The net rate of production of species i due to
reaction r, Ri,r, is given by the smaller of the two given
expressions below,
⎟⎟⎠
⎞⎜⎜⎝
⎛
ν′κε
ρν′=R,wr,R
RRi,wr,ir.i M
YminAMR (38)
∑∑
ν ′′κε
ρν′= Nj j,wr,j
P Pi,wr,ir.i
M
YABMR (39)
Where, YP is the mass fraction of any product species, P YR is
the mass fraction of a particular reactant, R A is an empirical
constant equal to 4.0 B is an empirical constant equal to 0.5ν′i,r
is the stoichiometric coefficient for reactant i in reaction r
ν″j,r is the stoichiometric coefficient for product j in reaction r
The Finite-Rate Model computes the chemical source terms using
Arrhenius expressions and ignores the effects of turbulent
fluctuations. The net source of chemical species i due to reaction
Ri (kg/m3-s) is computed as the sum of the Arrhenius reaction
sources over the NR reactions that the species participate in, and
is given as:
∑
=
=RN
1rri,iw,i R̂MR (40)
Where Mw,i is the molecular weight of species i and Ri,r is the
Arrhenius molar rate of creation/destruction of species i in
reaction r.
The r-th reaction can be written in a general form as:
∑∑
==
⇔N
1ii
"ri,
N
1i
k
ki
'ri, MυMυ
R rf,
rb,
(41)
Where kf,r = forward rate constant for reaction r kb,r =
backward rate constant for reaction r.
The molar reaction of creation/destruction of species i as a
result of reaction r, which is ri,R̂ (kgmol/m
3-s) in Eq. (40), is given as:
( ) [ ] [ ] ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−= ∏∏
==
r "rj,
r 'rj,
N
1j
ηrj,
N
1jrb,
ηrj,rf,
'ri,
"ri,ri, CkCkυυΓR̂ (42)
Where, Cj,r = molar concentration of each reactant and product
species j in reaction r (kgmol/m3)
'j,rη = forward rate exponent for each reactant and product
species j in reaction r "j,rη = backward rate exponent for each
reactant and product
species j in reaction r. Γ represents the net effect of external
forces on the reaction rate. Heterogeneous Reaction The particle
reaction, R (kg/m2-s), is expressed as R = D0 (Cg – Cs) = Rc(Cs)N
(43) Where D0 = bulk diffusion coefficient (m/s) Cg = mean reacting
gas species concentration in bulk (kg/m³) Cs = mean reacting gas
species conc. at particle surface (kg/m²) Rc = chemical reaction
rate coefficient (units vary) N = apparent reaction order
(dimensionless). The concentration at the particle surface, Cs, is
not known, so it is replaced by other quantities, and the
expression is recast as follows:
N
0gc D
RCRR ⎥⎦
⎤⎢⎣
⎡−= (44)
This equation has to be solved by an iterative procedure,
with the exception of the cases when N = 1 or N = 0. When N = 1,
Eq. 44 can be written as
c00cg
RDDRC
R+
= (45)
The reaction stoichiometry of a particle undergoing an
exothermic reaction in a gas phase is given as: particle species j
(s) + gas phase species n → products. Its reaction rate is given
as:
rj,jrprj, RYηAR = (46)
where
-
Copyright © 2011 by ASME
10
rN
r0,
rj,nrkin,rj, D
RpRR ⎟
⎟⎠
⎞⎜⎜⎝
⎛−= (47)
and where the quantities rj,R = rate of particle surface species
depletion (kg/s)
Ap = particle surface area (m²) ηr = effectiveness factor
(dimensionless) Rj,r = rate of particle surface species reaction
per unit area (kg/m²-s) pn = bulk partial pressure of the gas phase
species (Pa) D0,r = diffusion rate coefficient for reaction r
Rkin,r = kinetic rate of reaction r (units vary), and Nr = apparent
order of reaction r. The effectiveness factor, r, is related to the
surface area, and can be used in each reaction in the case of
multiple reactions. D0,r is given by
( )[ ]p
0.75p
r1,r0, d2TT
CD ∞+
= (48)
Equation 48 is a modification of the relationship given by Smith
[14] by assuming negligible change in gas density. The kinetic rate
of reaction r is defined as Rkin,r = Ap Tβe-(Er/RT) (49) The rate
of particle surface species depletion for reaction order Nr = 1 is
given by:
rkin,r0,r0,rkin,
njrprj, RDDR
pYηAR+
= (50)
And for reaction order Nr = 0, the rate of depletion is given
by:
rkin,jrprj, RYηAR = (51)
COMPUTATIONAL SCHEME Computational Grid
The geometry is generated and meshed in GAMBIT Version 2.4.6,
using a 2-D structured grid (Fig. 5). For the grid sensitivity
study, a total of 6,960 cells for the Fluidized Bed Mild Gasifier
are employed initially (Fig. 5a) followed by denser grids of 30,876
(Fig. 5b) and 65,355 (Fig. 5c) cells for the final case. The y+
values of the first near-boundary grid vary between 20 and 50 in
the draft tube and are between 50 and 150 in the fluidized bed and
freeboard regions. The enhanced-wall function will automatically
fill in the near-wall turbulence structure below the first
near-wall grid points.
Boundary and Inlet Conditions
The following boundary conditions on the surface geometry have
been assigned. a. Velocity inlet: At all the inlet surfaces, the
velocity,
temperature, and the mass fractions of all species of the gas
mixture are specified.
b. Pressure outlet: The outlet surface is assigned as a constant
pressure boundary. Pressure, temperature, and species mass
fractions of the gas mixture just downstream of the outlet (outside
the domain) are specified. This
information does not affect the calculations inside the
computational domain but will be used if backflow occurs at the
outlet.
(a) 2D structured meshes (6,960 cells)
(b) 2D both structured and unstructured meshes (30,876)
(c) 2D both structured and unstructured (65,355 cells) Figure 5
Three different mesh sizes for grid-sensitivity study
-
Copyright © 2011 by ASME
11
c. Walls: The outside surfaces are defined as a wall boundary.
The walls are stationary with the no-slip condition imposed (zero
velocity) on the surface and are assumed to be well insulated with
zero heat flux (i.e., the adiabatic condition).
d. Fluidized bed – The bed is initially filled with char (C)
with a depth of 10 inch. The char outlets are designed to allow
controlling of the bed depth by valves. In the CFD simulation, the
char draining rate is controlled by changing the char outlets’
pressure values.
e. Patching temperature: Akin to using a lighter to ignite
combustion inside a combustor, a high temperature is needed to
start (ignite) the reactions by setting the temperature of the
cells near the injectors to 1000 K. Figure 6 shows the boundary
conditions of the final
multiphase reactive flow case. Indonesian coal is used as
feedstock at the draft inlet. To simplify the simulation model, the
contents of ash and sulfur are not included. The detailed inlet
conditions for heterogeneous (gas-solid) reaction with volatiles
are given in Table 2.
Figure 6 Boundary and inlet conditions Table 2 Flow condition at
inlets of the fluidized bed and draft tube
Inlet Position Fluidized bed inlet Draft tube inlet
Flow Air C solid, air, volatiles Mass fraction at inlet: O2 N2
CH2.121O0.585 (volatiles)
0.233 0.767 0.000
0.120 0.395 0.485
velocity or mass flow rate per unit depth 2.8 (m/s) 40.64
(kg/s)
Numerical Procedure The commercial CFD software package,
ANSYS
FLUENT 12.0, was used in this study. The governing equations are
discretized spatially with second-order accuracy to yield discrete
algebraic equations for each control volume. The volume fraction of
solid phase is calculated using the QUICK scheme. The SIMPLE
algorithm [16] is used in this study to couple the pressure and
velocity.
The primary phase (gas) enters the computational domain through
the inlets. The iterations are conducted alternatively between the
primary and the secondary (solid) phases. The primary phase is
updated in the next iteration based on the secondary phase
calculation results, and the process is repeated. Unsteady flow
calculations are performed.
The computations were conducted via two clusters with 12 nodes
on each cluster. The physical iteration time step size is chosen to
be 10-4 seconds. Typically, 40,000 time steps are required in six
calendar days to achieve convergence with 20 iterations in each
time step.
The computation is conducted in transient mode. The results and
analyses including a grid sensitivity study are presented in Part 2
of this paper. CONCLUSIONS
In this paper, the design considerations of a conceptual mild
gasifier were explained. The mild gasifier possesses a hybrid set
of characteristics, utilizing features of both the entrained-flow
and fluidized bed gasification processes. The draft tube is
intended for driving quick pyrolysis and devolatilization processes
and the fluidized bed is used to control the percentage of char
gasification (partial or complete) as well as the degree of
mild-gasification between zero gasification (pyrolysis only) and
100% full gasification.
To help guide continuous design iterations, a comprehensive
multiphase reactive flow model has been developed to investigate
the thermal-flow behavior and gasification process inside the
preliminary conceptual mild gasifier. The Eulerian-Eulerian method
is used to calculate the flow characteristics of both the primary
phase (air and gaseous species) and the secondary phase (coal
particles). The reason that the Eulerian-Eulerian method is adopted
in this study instead of Lagrangian-Eulerian method is because the
concentrations of coal particles are dense in the fluidized bed and
tracking each particle with the Lagrangian method is not realistic
given current computational capability.
The Navier-Stokes equations and seven species transport
equations are solved with three heterogeneous (gas-solid) and four
homogeneous (gas-gas) global gasification reactions with two
volatile reactions. For each homogeneous reaction, both the
Finite-Rate and Eddy-Dissipation reaction rate are solved, and the
smaller of the two rates obtained is used. Complicated multiphase
constitutive equations developed from kinetic theory are employed
for calculating the effective shear viscosities, bulk viscosities,
and effective thermal conductivities of granular flows to calculate
the hydrodynamic and thermal interactions between the solid and gas
phases. The inlet, exit, and wall boundary conditions are
described, and the computation is conducted in transient mode. The
results and analyses are presented in Part 2 of this paper.
-
Copyright © 2011 by ASME
12
ACKNOWLEDGMENTS This study was partially supported by the
Louisiana Governor's Energy Initiative via the Clean Power and
Energy Research Consortium (CPERC) under the auspices of Louisiana
Board of Regents and partially supported by the Department of
Energy contract NO. DE-FC26-08NT01922.
REFERENCES 1. Anthony, D.B., Howard, J.B., Hottel, H.C. and
Meissner,
H.P., 1975, "Rapid Devolatilization of Pulverized Coal," 15th
International Symposium on Combustion, Tokyo, Japan, August 25-31,
1975, pp 1303-1317.
2. Gupta, R., Turk, B., and Lesemann, M., 2009, "RTI/
Eastman Warm Syngas Clean-up technology: Integration with Carbon
Capture," Presented at the 2009 Gasification Technologies
Conference.
3. Gupta, R., Jamal, A., Turk, B., and Lesemann, M., 2010,
"Scaled and Commercialization of Warm Syngas Cleanup Technology
with Carbon Capture and Storage," Presented at the 2010
Gasification Technologies Conference, Washington, D.C.
4. Wormser, A., 2008, "Converting PC to Very-high-
efficiency IGCC: the MaGICTM of Mild Gasification," Modern Power
System, November 2008, pp 21-26.
5. Syamlal, M. and O’Brien, T.J., 1989, "Computer
Simulation of Bubbles in a Fluidized Bed," AlChE Symposium
series, Vol. 85, No. 270, pp 22-31.
6. Syamlal, M., Rogers, W., and O’Brien T. J., 1993, MFIX
Documentation: Volume 1, Theory Guide. National Technical
Information Service, Springfield, VA, DOE/METC-9411004,
NTIS/DE9400087.
7. Lebowitz, J.L., 1964, "Exact Solution of Generalized
Percus-Yevick Equation for a Mixture of Hard Spheres," Journal
of Experimental and Theoretical Physical Review, Vol. 133, No. 4A,
1964, pp A895-A899.
8. Lun, C.K.K., Savage, S.B., Jeffrey, D.J., and Chepurniy,
N., 1984, "Kinetic Theories for Granular Flow: inelastic
particles in Couette flow and slightly inelastic particles in a
general flowfield," Journal of Fluid Mechanics, Vol. 140, 1984, pp
223-2565.
9. Gidaspow, D., Bezburuah, R. and Ding, J., 1992,
"Hydrodynamics of Circulating Fluidized Beds, Kinetic Theory
Approach," Fluidization VII, Proc. of the 7th Engineering
Foundation Conf. on Fluidization, pp 75–82.
10. Ding, J. and Gidaspow, D., 1990, "A Bubbling
Fluidization Model Using Kinetic Theory of Granular Flow," AlChE
Journal, Vol. 36, No. 4, 1990, pp 523-538.
11. Ranz, W. E., and Marshall, W. R., March 1952, Jr.
Evaporation from Drops, Part I. Chemical Engineering Progress, Vol.
48, No. 3, pp 141–146.
12. Ranz, W. E., and Marshall, W. R., April 1952, Jr.
Evaporation from Drops, Part II. Chemical Engineering Progress,
Vol. 48, No. 4, pp 173–180.
13. Gunn, D.J., 1978, "Transfer of Heat or Mass to Particles
in
Fixed and Fluidized Beds," Journal of Heat Mass Transfer, Vol.
21, 1978, pp 467-476.
14. Smith, I.W., 1982, "The Combustion Rates of Coal Chars:
A Review," Nineteenth International Symposium on Combustion,
Vol. 19, No. 1., 1982, pp. 1045-1065
15. Silaen, A. and Wang, T., 2010, "Effect of Turbulence and
Devolatilization Models on Gasification Simulation in an
Entrained-Flow Gasifier" International Journal of Heat and Mass
Transfer, Vol. 53, pp. 2074-2091.
16. Patankar, S.V., Numerical Heat Transfer and Fluid Flow,
McGraw Hill, 1980.
