PII:
Chemical Engineering Science, Vol. 53, No. 15, pp. 2727—2742, 1998
( 1998 Elsevier Science Ltd. All rights reserved
Printed in Great Britain
S0009–2509(98)00081–5
0009—2509/98/$—See front matter
Dynamic modeling of waste incineration
plants with rotary kilns: Comparisons
between experimental and simulation data
M. Rovaglio,* D. Manca and G. Biardi
Dipartimento di Chimica Industriale ed Ingegneria Chimica ‘‘G. Natta’’, Politecnico di Milano,
Italy
(Received 4 September 1996; accepted 31 January 1998)
Abstract—Incineration is not a new technology and has been used to destroy organic hazardous waste for many years. Nevertheless, variability in waste composition and the severity of the
incineration operating conditions may result in many practical operating problems, high
maintenance requirements and equipment unreliability. Moreover, a large number of constraints must be satisfied. These constraints are imposed by permit, by design and by operating
practice. The goal of this work is to present a dynamic model which is able to follow large
variations in process conditions and to be of practical value from a control point of view. This
paper deals in particular with the development of a dynamic model which describes the
behavior of a rotary kiln (primary combustion chamber with heterogeneous combustion) as
well as the corresponding afterburner system (secondary combustion chamber with homogeneous combustion) followed by a heat recovery system which completes the hot section of
a typical incineration plant. Special attention was devoted to a start-up procedure which was
used as a specific application, to check the robustness and reliability of the model itself
effectively. In addition, a number of comparisons with experimental data available from
commercial units are reported to complete the model validation under ordinary feeding
conditions. ( 1998 Elsevier Science Ltd. All rights reserved.
Keywords: Incineration; dynamics; modeling; combustion; control.
INTRODUCTION
Incineration processes are today considered important components of waste management policy all over
the world. The next several decades should see an
increase in the demand for incineration because of
recent limitations placed on the remaining hazardous
waste management options.
Waste incineration offers the following real or at
least potential advantages:
f volume reduction, especially for solids with
a high combustible content;
f detoxification, especially for combustible carcinogens, pathologically contaminated material,
toxic organic compounds, etc.;
f environmental impact mitigation, by destruction
of all the undesired secondary effluents or byproducts which would create further significant
pollution problems;
* Corresponding author. Fax: 00 39 02 70 63 81 73; e-mail:
[email protected].
f energy recovery, especially when large quantities
of waste are available and users of heat or steam
are located nearby.
These advantages have justified the development of
a variety of incineration systems showing greatly
varying degrees of complexity and process schemes to
meet the needs of municipalities, commercial and industrial firms and institutions. The most commonly
used incineration techniques include off-gas treatments, liquid injection and rotary kilns. Although
off-gas and liquid injection incinerators have been the
most popular in Europe and the United States, rotary
kiln incinerators are better suited to handle all physical forms of hazardous wastes and new high temperature chambers are capable of destroying highly toxic
organic wastes (e.g. chlorinated organic compounds,
PCBs) very efficiently. Multiple hearth, fluidized bed
and other technologies such as cement kiln and molten salt combustion seem to be promising but they
need further demonstration to prove that they are
economically, technically and environmentally acceptable (Theodore and Reynolds, 1987).
2727
2728
M. Rovaglio et al.
Incineration is not a new technology and has been
used for treating organic hazardous waste for many
years. However, variability in waste composition and
the severity of the incineration operating conditions
may result in many practical operating problems, high
maintenance requirements and equipment unreliability. In practice, the majority of incinerators are on-site
facilities responsible for destroying a well-defined set
of wastes. These incinerators must be robust enough
to handle large variations in waste composition and
heat release. In contrast, commercial facilities receive
a wide variety of wastes from many generators. These
wastes can vary in physical state (solid, liquid, sludge),
chemical composition and thermodynamic properties. For both commercial and on-site incinerators,
there is a large number of operating constraints. These
constraints are imposed by permit, by design and by
operating practices. Thus, the operator must blend
the waste quality and control the waste flowrates, air
flowrates, water scrubbing flowrates and auxiliary fuel
flowrates such that all the constraints are satisfied.
Moreover, operators seek to maximize the waste
throughput or minimize the auxiliary fuel flow while
maintaining a correct oxygen concentration value in
the outlet gas. Incinerator operators currently attempt to achieve these objectives by intuition and
experience (Behmanesh et al., 1990). Finally, feedstocks to incinerators can be continuous, semi-continuous or batch-wise which means that the time
evolution of process conditions seems to be an important element in evaluating feasible and reliable operations.
The goal of this work is to present a dynamic model
being able to follow and describe large variations in
terms of process conditions while being of real practical value from a control point of view. In the following
presentation, the paper will deal with the development
of a dynamic model capable of describing the behavior of a rotary kiln (primary combustion chamber
with heterogeneous combustion) and the corresponding afterburner system (secondary combustion chamber with homogeneous combustion) plus the heat
recovery system which completes the hot section of
a typical incineration plant. Special attention was
devoted to a start-up procedure which was used as
a specific application, to check the robustness and
reliability of the model itself effectively.
Several comparisons with experimental data available from commercial units are also reported to complete the model validation under normal feeding
conditions.
INCINERATOR MODEL DEVELOPMENT
The basic structure of the plant analyzed in this
paper comprises, as mentioned above, a rotary kiln
followed by a postcombustion chamber (afterburner
system) and the corresponding air pre-heaters which
allow the heterogeneous combustion to be improved
and the auxiliary fuel consumption to be reduced.
This configuration with geometry and plant layout is
shown in Fig. 1. The solid is fed into the rotary kiln
where the bulk of the combustion takes place and
then moves along the chamber in a countercurrent
configuration with respect to the gas flow. The resulting combustion products go to a cyclone postcombustion chamber which allows the total combustion and
destruction of contaminants be completed. At the end
of the plant’s hot section two spiral heat exchangers
are used to preheat the incoming combustion air.
Rotary kilns involve a large variety of combinations of processes such as particulate mixing,
gas—solid or solid-phase reactions with intensive heat
and mass transfer. The kiln analyzed here is operated
with a semicontinuous feed and continuous discharge,
pitched slightly from inlet to outlet and normally
running less than half-full of solid. The upper space
accommodates a countercurrent flow of hot gas which
may serve both to supply the heat to the inlet stream
and to carry out gaseous products. As mentioned
above, the rotary kiln has a secondary chamber to
ensure complete combustion of the waste. In practice,
the kiln acts as the primary chamber to volatilize and
partially or totally oxidize the combustible materials
in the waste. Inert ash is then removed from the lower
end of the kiln. The volatilized combustibles exit the
kiln and enter the secondary chamber where
Fig. 1. The hot section of an incineration process with combustion air preheating.
Dynamic modeling of waste incineration plants
additional oxygen is made available and ignitable
liquid wastes or fuel can be introduced to achieve the
desired operating temperature.
In order to describe the time evolution of a combustion process like this, a simplified but rather general
model can be built up on the basis of the following five
main steps.
¼aste feedstock characterization and combustion
stoichiometry
The feedstock consists of a dry solid fraction
(1!u ) and a moisture fraction u
(mass fracH2O
H2O
tions). Within the dry solid, it is then necessary to
distinguish between a combustible or burning fraction
u which gives rise to gas products, and an inert
BF
fraction representing what will be also the final solid
ash amount. A formal stoichiometry must be associated with the combustible fraction of the solid waste
in order to account for the heterogeneous combustion. This leads to the following stoichiometric relationship:
n!y
C H O S N Cl #l O P mCO#
m n p q x y
O2 2
2
x!a
]H O#qSO #
N #aNO#yHCl.
2
2
2
2
It must be emphasized that, as in the case of the
heterogeneous combustion, CO has been assumed to
be the main oxidation product of carbon. The total
combustion to CO takes place in the gas phase.
2
Furthermore, waste compounds containing nitrogen
are converted to N and NO according to the scheme
2
and the relationship reported by Bowman (1975)
which evaluates the a fraction as a function of kiln
temperature and oxygen excess. The stoichiometric
coefficients are likely to occur in the gas phase and
they will be taken into account further on in the
paper.
2. Solid waste mass balance
The solid waste undergoing the heterogeneous
combustion passes through the rotary kiln incinerator
for a certain contact, or retention time, while the effect
of the mechanical agitation induced by rotation consists of the renewal of the surface area exposed to hot
gases containing oxygen. Here, on this area, both
volatilization and combustion processes take place at
a rate which is largely dominated by the oxygen
transfer rate towards the surface since the temperature
is high enough to reduce the importance of the chemical reactions kinetics. This is why in the model
scheme, the rate of destruction of the waste combustible fraction was computed according to the oxygen
mass transfer from the bulk gas phase to the solid
flame surface where its molar fraction disappears as it
is consumed, also in transient conditions, at the rate it
diffuses. The bulk solid phase movement along the
rotary kiln is not different in nature from that of
similar units. The proper correlations of those cases
and available in literature may be used for the case in
2729
hand. This applies for the retention time as reported
by Freeman (1989):
1.77JbF¸
h"
.
SDN
(1)
Whence the outlet solid flowrate ¼S can be deter065
mined by linking it to the aforementioned retention
time and to the instantaneous solid mass hold-up
within the incinerator:
M
SDN
¼S " 40-*$"M
.
065
40-*$ 1.77JbF¸
h
(2)
This correlation means that despite the transient situation, where the solid movement in the rotary kiln is
concerned, the same relationships as in the steady
state hold true using the instantaneous value of the
variable M . In other words, the transient condi40-*$
tions related to both gas and solid flows are assumed
to be fast with respect to mass and energy dynamic
balances. In agreement with the aforementioned assumptions, the mass balance for the solid phase reads
as follows:
dM
40-*$"¼
(1!u )!R !¼S .
8!45%
H2O
dr
065
dt
(3)
Particular attention must be devoted to the evaluation of R which represents the burned fraction of
dr
the solid waste.
This term is strictly related to the transport phenomena active at the solid surface. The top plane of
the solid phase is evidently the most likely region for
the highest rates of both convective and radiative heat
transfer as well as mass transfer to the contiguous gas
phase (Ferron and Singh, 1991).
This source term, therefore must be calculated in
agreement with the scheme previously mentioned and
is represented as follows:
K (X"6-,!X*/ )PM C
O2
O2 505 A.
(4)
R " x O2
dr
k
O2
The evaluation of A, the interface area for solid oxygen contact, would in principle require the knowledge
of both gas-and solid phase motions inside the rotary
kiln. This area is a function of the kiln geometry and
the operating conditions. The maximum possible interface area would depend also on particle diameter
and solid angle of repose; if one could estimate the
average renewal surface velocity [A (m2/s)] then
r
A"A h.
(5)
r
Jacob and Perlmutter (1980) have already provided
criteria for determining such a renewal surface velocity. Nevertheless, we thought it more reliable and
practical to treat A as an adaptive parameter based on
the interpolation of a data matrix obtained from
steady-state simulations of known kiln performances.
As a matter of fact, if a given commercial unit can
be operated in a specified range of operating conditions with satisfactory performances with respect to
2730
M. Rovaglio et al.
waste residence time and combustion efficiency, the
interface area can be easily derived from steady-state
simulation as a function of the mass holdup and
available oxygen mole fraction by inverting relation
(4), and by noting that, at the steady-state conditions,
the rate of destruction of waste combustible fraction is
closely related to such parameters. From the solidphase balance, eq. (3), one gets
¼
(1!u )!R !¼S "0.
8!45%
H2O
dr
065
(6)
Under the assumption of complete waste destruction:
¼S "¼
(1!u )(1!u )
BF
065
8!45%
H2O
with u
BF
(7)
the waste burning fraction, R follows from
dr
u
BF
R "¼
(1!u )u "¼S
dr
8!45%
H2O BF
0651!u
M
u
BF
" 40-*$
h 1!u
Fig. 2. Flame area as a function of solid holdup and oxygen
mole fraction inside kiln.
BF
(8)
BF
and finally
1M
u
k
BF "
40-*$
O2
A"
h *x
K C PM 1!u
x 505
O2
BF
O2
(9)
In agreement with the assumption already made
about the fast dynamics of solid flows within the kiln,
the same effective area is held under transient conditions.
On the basis of experimental data available and
through the use of a commercial package (CYCOM
6.0), an example of interface area evaluation is reported in Fig. 2. It can be observed that if the total
mass holdup inside the kiln increases, the flame surface achieves a larger value with a variation that is
a function of the bulk oxygen concentration. A small
O mole fraction in the gas phase will obviously
2
require an increase in the surface area for a given mass
holdup and kiln volume in order to achieve the total
burning of the waste load (slow firing conditions). On
the other hand, a large oxygen excess corresponds to
a practically constant required interface area (high
firing rate). Figure 2 also shows a typical domain
where the kiln under examination operates. Comparing the value obtained by the interpolated surface (as
a function of kiln conditions) with the result of Jacob
and Perlmutter’s relationship, the interphase reaction
area is defined as the maximum between these numbers.
Gas-phase mass balances.
Taking into account possible auxiliary fuel, if required, the total gas-phase mass balance, which applies to both the rotary kiln and postcombustion
chamber, becomes
dM
'!4"¼*/ w!*3#¼*/ w!*3#(1!k )R
!*3 N2
!*3 O2
O2 dr
dt
w
#¼ !¼g #¼
065
8!45% H2O
CH4
(10)
while the corresponding mass balances for each component can be specified by
dM
¼'
i"¼*/!
065 y #R »
(11)
i
i 505
dt
+ PM y i
i
i i
with i"CO, CO , H O, SO , N , HCl, NO, O ,
2
2
2
2
2
where y "M /+ M is the gas mole fraction of
i
i i i
species i.
The flows of all the i species forming ¼*/ and the
i
reaction rates R can be determined with reference to
i
the following simplified reaction scheme and assumptions (Niessen, 1978):
`O2 mCO#(n!y) H O
(a) C H O S N Cl &"
m n p q x y
2
2
(x!a)
N #aNO#yHCl.
#qSO #
2
2
2
(b) CH #O P CO #2H O.
4
2
2
2
(c) CH #3 O P CO#2H O.
4 2 2
2
(d) N #O b 2NO.
2
2
(e) CO#1 O P CO .
2
2 2
(g) CO#H ObCO #H .
2
2
2
where reaction (a) represents the previously mentioned overall waste destroying reaction producing
CO as result of heterogeneous combustion. CO will
be immediately converted to CO , should enough
2
oxygen be present to accomplish reaction (e), or otherwise following reaction (f ) when the oxygen amount is
too small. Waste nitrogen is converted to N and NO.
2
The corresponding fractions are determined through
a relationship reported by Bowman (1975) as a function of kiln temperature and oxygen excess. The equilibrium conditions determined by reaction (d) refer to
the afterburner system (homogeneous combustion). If
auxiliary fuel is needed to maintain the required temperature (e.g. postcombustion chamber), reactions (b)
and (c) allow total or partial methane combustion as
a function of the oxygen availability to be taken into
Dynamic modeling of waste incineration plants
account. Reactions (a)—(c) and (e) are very fast and can
be considered under equilibrium conditions (completely displaced towards CO and CO ) within the
2
range of temperatures usually adopted (900—1200°C).
The extent of conversion for such reactions is in practice determined by the oxygen excess. Only reactions
(d) and (f ) have been considered in a kinetic regime,
while the corresponding rate expressions have been
deduced by generalizing the theoretical analysis reported by Westenberg (1971). In particular, by considering the kiln, burner and postcombustion chamber
residence times separately, it is possible to evaluate, at
least qualitatively, the contributions to the production of NO corresponding to the different portions of
the plant. Finally, the outlet flue gas flowrate ¼' re065
ported in eq. (11) can be determined on the basis of
a simple fluid dynamics description as shown later in
the paper.
Energy balances
Inside incinerators the heat is generally transferred
to the walls or to the upper surface of the solid beds
(whenever present) by radiation and convection and
to the lower (covered) surface by the regenerative
action of the rotating kiln walls. The radiating gases in
the kiln free volume (i.e. not occupied by the waste)
are also present within the confines of the burner
and/or waste flames so that they may be considered as
covering the entire free volume. Thus, due to the high
gas temperature, solids and exposed walls receive heat
primarily by radiation from the gas volume while
both convective and regenerative heat flow play only
a minor role in the overall heat transfer process.
On the basis of the following assumptions:
f perfectly mixed conditions;
f equilibrium condition between gas and solid
phase (if present);
f complete combustion (for both waste and auxiliary fuel);
a zero-dimensional model (lumped model) describing
the variation of bulk flow temperature with time can
be derived as follows:
dº
505"¼*/ H*/ #¼
Q
!*3 !*3
8!45% 8!45%
dt
where
#¼ Q !¼g H !sGS(¹4!¹4 )
CH4 CH4
065 065
'
w,*/
!h pD¸(¹ !¹
)!¼s CM (¹ !¹ )
3*&
*/
g
w,*/5
065 pS g
(12)
º "M C (¹ !¹ )
505
40-*$ vS g
3*&
M
Tg
i
C (¹ ) d¹
#M +
vi
'!4 + M
i i i T3*&
T*/!*3
C (¹ ) d¹
H*/ "
p!*3
!*3
T3*&
M
Tg
i
H "+
C (¹ ) d¹.
065
pi
+M
i i i T3*&
P
P
P
(13)
(14)
(15)
2731
Equation (12) implies that waste and fuel are fed at the
reference temperature. GS can be evaluated by means
of the ‘well-stirred combustion chamber’ model reported by Hottel-Sarofim (1968):
PP
GS"
A
K d» dS cos 0q(r)
q
,
.
(1/C e )#(1/e )
nr2
V S
gp
G
(16)
The evaluation of the gas emissivity e refers to the
G
diagram reported by Hottel and Sarofim which only
considers the emission band related to the combustion products: water and carbon dioxide. The emissivity of such components can be calculated through
a polynomial regression of the experimental data as
a function of the sum of the single partial pressures
(P "P #P ) and of the beam length (¸ ):
CW
CO2
H2O
W
11
log (¹e )" + C xn~1
10 G
n
n/1
where x"log (¸ P ).
10 W CW
Coefficients C are deduced by interpolating the
n
diagrams reported by Hottel and Sarofim (1968) and
the resulting values are summarized in Table 1. The
convective heat transfer coefficient is computed by
a Dittus—Boelter relationship
hD
Nu"0.023Re0.8Pr1@3, Nu"
k
(17)
and corrected to take into account possible entry
effects (see Knudsen and Katz, 1958)
A
B
D
.
h "h 1#1.4
in
¸
(18)
As for the transient heat conduction within the furnace walls, the problem can be easily modeled by
means of the classical equation of heat diffusion in one
dimension to be solved for adjacent layers of different
materials and with proper boundary conditions ensuring the continuity of heat fluxes (Biardi et al., 1987).
The real problem lies in choosing which discretization
method is to be adopted and which numerical algorithm to use for integration purposes. While the latter
question is discussed in the next paragraph, it is worth
saying a few words about the former one. Figure 3
Table 1. Polynomial coefficients
for gas emissivity evaluation
C " 9.695]10~3
11
C " 5.407]10~2
10
C " 1.349]10~1
9
C " 2.068]10~1
8
C " 1.496]10~1
7
C "!1.049]10~1
6
C "!2.239]10~1
5
C " 3.061]10~2
4
C " 7.615]10~2
3
C " 4.062]10~1
2
C " 2.44956
1
2732
M. Rovaglio et al.
reported by Owens et al. (1991) where it is clearly
shown that the bed temperature evolution along the
kiln is quite fast and can be considered of relevant
value only for waste with high moisture content
(sludges) or for contaminants desorbing applications.
Fluid dynamic relationships
Q "c JP !P
-%!,
1
%95
,*-/
l2
P "P #c o 065,,*-/
,*-/
1045
2
2
Fig. 3. Refractory and insulating discretization scheme with
nodal arrangement.
shows the case of a chamber wall divided into several
shells or layers of refractory and insulating materials
(onion scheme). The nodal arrangement distinguishes
between volume-averaged temperatures, whose index
is an integer, and surface-averaged temperatures,
whose index is arbitrarily set as an integer plus or
minus a half.
Symbolically, this gives rise to the following thermal balance:
d¹W
KW
n" n A
r Cp
(¹
!¹ )
W W dt
n
*X/2 -/,n~1@2 n~1@2
KW
(¹ !¹
)
! n A
n`1@2
*X/2 -/,n`1@2 n
for n"1, N
(19)
(22)
(23)
l2
P "P
#c o 065,1045
1045
14541*3!3
2
(24)
l2
P
"P #c o 065,41*3!- .
14541*3!l
4
2
(25)
Equations (22)—(25) reflect the level of the fluid dynamic simplification used within the model. Equation
(22), in particular, allows an evaluation of air leakage
due to the vacuum conditions usually maintained
inside a waste kiln and, when necessary, this term will
be included in the corresponding mass and energy
balances. Equations (23)—(25) define the kiln pressure
(P ), the postcombustion pressure (P ) and the
,*-/
1045
first spiral heat exchanger pressure (P
) as
14541*3!a function of the gas flow, the geometry and the
pressure level at the final outlet throat (P ). Values for
1
c are calculated from correlations available in litera*
ture, see, for example, Rovaglio et al. (1990), and
Douglas et al. (1980).
AIR HEATER MODEL DEVELOPMENT
In the plant configuration analyzed here (see Fig. 1),
there is a heat recovery section consisting of a sequence of spiral heat exchangers placed after the
burning system.
These devices have a double function, namely:
with the boundary conditions:
hot side
KW
i A
(¹ !¹ )"h nD¸(¹ !¹ )
l
*/
g
w,*/
*X/2 -/,1@2 1@2
#GSp(¹4!¹4 )
(20)
g
w,*/
where ¹ ,¹
is the internal chamber wall tem1@2
w,*/
perature.
cold side
KW
N A (¹ !¹
)"h A (¹
!¹ )
N`1@2
e e w,065
!."
*X/2 I/,N N
(21)
where ¹
,¹
is the external chamber wall
N`1@2
w,065
temperature, where the overall chamber shell is
divided into N different layers of thickness *X; KW is
n
the thermal conductivity and A represents the log
-/,n
mean surface area.
Finally, it is worthwhile explaining the assumption
about the equilibrium condition between gas phase
and solid bed. This leads to the same temperature for
both phases equal to the outlet temperature since it
has been also assumed to be a CSTR scheme. The
reason for this choice can be related to the results
f air combustion pre-heating to improve the thermal yield of the plant;
f gas cooling to reduce water consumption inside
the scrubbing section.
These apparatuses consist of a metal shell which
covers a cylinder of refractory and insulating material
where, inside the enclosure, a coil of special alloy is
placed. The cold air flows inside the coils while the hot
gas moves along the refractory lined chamber. A general scheme for the examined plant including such
heat exchangers together with a schematic representation of the reference geometry is reported in Fig. 4.
A new set of equations is needed to solve this
problem.
Inside the heat exchangers, the hot gas temperature
can be considered uniform, that is, a CSTR scheme is
assumed to be a consequence of the high turbulence
due to the gas velocity and to the presence of coils:
dº
505"¼ H !¼ H !Q
!Q
f */
f 065
-044%4
%9
dt
(26)
Dynamic modeling of waste incineration plants
2733
Fig. 4. Reference scheme for combustion air pre-heaters.
where H*/ and H065 can be evaluated through eq. (15)
while ¼ represents the hot gas flowrate assumed to
f
be equal for inlet and outlet flows.
The heat losses Q
through the walls can be
-044%4
determined by the correlations reported by Hottel
and Sarofim (1968):
C
A
B
D
1!k3
h
*/
#A
Q
" GS
8!-- 1!k4
8!--,n 4p¹3
-044%4
f
]p(¹4!¹4 )
(27)
f
8!--,n
¹
k" 8!-(28)
¹
f
where the term inside the square brackets defines the
global heat transfer coefficient which takes into account both the convective and the radiative terms. In
a similar manner, the heat exchanged between smokes
and coils can be determined on the basis of the following relationship:
NS
Q " + pGS (¹4 —¹4 )#h A (¹ !¹
)
%9
#0*-4 f
8!--,n
e n f
8!--,n
n/1
(29)
where the external convective coefficient h can be
e
evaluated through the Nu number given by
Nu"0.110Re0.675Pr1@3
(30)
which refers to a system with a cross-flow geometry
(see Incropera and DeWitt, 1988).
In all the previous correlations the variables corresponding to the coils are indicated with a subscript
n implying a discretized description along the coil as
sketched in Fig. 5. This means that the temperature
evolution along the coils can be evaluated through
a system of N equations:
s
¼ H
!¼ H #Q "0
!*3 !*3,n~1
!*3 !*3,n
%9,n
with n"1,2 ,N
(31)
s
where the energy holdup corresponding to each single
element is considered negligible since, with respect to
the space discretization, the air temperature can be
assumed instantaneously to be under the steady-state
conditions.
Finally, the metal coil temperature can be determined on the basis of the heat fluxes congruence at the
2734
M. Rovaglio et al.
the global differential system. In mathematical terms
this means
M
o c (¹W!¹ )
'!4:
w pw n
3*&
.
¼
kW
065
1 A
(¹ !¹ )
l
*x/2 -/,1@2 1@2
Fig. 5. Coils discretization scheme.
wall so that, for each element, the result is
(¹4!¹4 )#h A (¹ !¹
)
pGS
#0*-4,n f
8!--,n
e n f
8!--,n
"h A (¹
!¹ )
*/ n 8!--,n
!*3,n
with n"1, 2 , N
s
(32)
where the internal heat transfer coefficient h is com*/
puted by a conventional Dittus—Boelter relationship.
(33)
Practically, in the case examined here, N was determined to be in the range of 8—10.
Since the overall set of equations constitutes
a coupled system of algebraic and differential equations behaving as a numerically stiff system, due to the
large spectrum of characteristic times involved,
a completely implicit method able to automatically
select the proper integration step was used in order to
achieve a fast and robust numerical solution. The well
known LSODE package (Hindmarsh, 1983) was adopted for these purposes.
ALGORITHM
The overall dynamic model consists of
2(N #N#2)#1 differential equations, namely:
c
1 mass balance for the solid phase [eq. (3)];
1 total mass balance for the gas phase [eq. (10)];
N !1 mass balances for N !1 single components of
c
c
the mixture [eq. (11)];
1 energy balance for the gas phase [eq. (12)];
N!energy balances for the refractory and insulating
layers [eq. (19)];
1 energy balance for the hot gas phase inside the heat
exchanger [eq. (26)].
In addition, 2N #8 algebraic equations which can be
s
summarized as follows:
4 fluid dynamics relationships [eq. (22)—(25)];
4 boundary conditions [eq. (20)—(21)];
N air thermal balances inside coil [eq. (31)];
s
N heat fluxes equality [eq. (32)]
s
complete the structure of the model which must be
numerically integrated to describe the dynamic evolution of the hot section of an incineration process. In
particular N, the number of refractory-insulating elementary layers, can be estimated on the basis of the
minimum spectrum width for the time constants of
MODEL VALIDATION
The results reported below refer to a specific commercial unit of 0.9—1.2 MW total burning capacity
(waste plus auxiliary fuel). Geometry and characteristics are briefly summarized in Table 2. The model
validation, as the title states, is unfortunately based
only on a limited number of variables measured and
available from the plant, namely:
f outlet gas temperature from the rotary kiln,
f outlet gas temperature from the postcombustion
chamber,
f external skin temperature for the rotary kiln,
f external skin temperature for the postcombustion chamber,
f oxygen mole fraction in the postcombustion gas
outlet,
f air temperatures from heat exchangers.
However, the comparison is completed by the knowledge of the transient evolution of some input variables, such as:
— waste flowrate to the rotary kiln,
— fuel flowrates to kiln and postcombustion chamber,
— air flowrate to the spiral heat exchangers.
Table 2. Plant description
Internal length (m)
Internal diameter (m)
Refractory thickness (m)
Refractory conductivity (W/m K)
Refractory heat capacity (J/kg K)
Refractory density (kg/m3)
Insulating thickness (m)
Insulating conductivity (W/m K)
Insulating heat capacity (J/kg K)
Insulating density (kg/m3)
Rotary
kiln
Postcombustion
chamber
4.43
1.515
0.100
1.696
700.0
2550.0
0.120
0.29
500.0
890.0
3.664
1.722
0.110
1.348
600.0
2000.0
0.125
0.198
400.0
475.0
Dynamic modeling of waste incineration plants
With reference to the plant measurements, it must be
specified that the outlet gas temperatures are measured through a thermocouple placed in the outlet gas
exit which has a small diameter with respect to the
unit one. Moreover, both the kiln thermocouples are
shielded from radiation by a special enclosure made in
the refractory material.
Therefore, the temperatures measured can be assumed to represent the average conditions of the outlet smokes. As a consequence of the assumed perfectly
stirred conditions, defined by the turbulent regime,
such temperatures also correspond to the average
temperatures of the units.
Finally, the reported skin temperatures derive from
the average of several measurements taken with
a manual thermocouple placed along the cylinder.
Start-up procedure
The start-up operation is a long transient condition
requiring about one day to achieve the final values of
the operating temperatures (1200°C for the afterburner system). A slow warm-up is necessary to avoid
sudden expansion effects which may compromise the
robustness and the reliability of refractory and insulating materials. Therefore, the burners, operating in
the manual control mode, are brought to their maximum fuel capacities over a period of 2—3 h, with each
starting at a different time. Only when the correct
temperature regime is reached, the waste can be
loaded and a high efficiency of total combustion can
be achieved. Simulations and comparisons with experimental measurements taken during operation can
be of real use in evaluating the reliability of the
model’s basic structure without introducing possible
misunderstandings due to results affected by wrong
waste characterization in terms of feed flowrate, composition or heat of combustion.
A schematic representation of the main input variables during the transient is reported in Fig. 6 referring to the first 11 h of the diagrams. Fuel and air inlet
flowrates correspond to flows imposed by valves operating in the manual mode. The variation of such
variables is modeled as ramp disturbances derived
from the corresponding experimental measurements.
The evolution of the postcombustion fuel flowrate
also includes a perturbation related to a fuel-line
blockage.
Once again, with reference to the first 11 transient
hours, a comparison between experimental data available and model evaluation as a function of time is
reported in Figs 7 and 8 for the outlet gas temperature
from the rotary kiln and the postcombustion chamber, respectively. Both transients show a very satisfactory agreement with the corresponding experimental
data, not only in terms of characteristic times, but also
in terms of absolute values and variations. A further
model validation can be obtained by comparing the
external kiln surface temperatures as reported in Figs
9 and 10. Although the number of available experimental measurements is very limited, the agreement
between predictions and measurements confirms that
2735
significant information about the refractory and insulating temperature profiles can be derived from model
simulations. One example of such profiles is reported
in Fig. 11 as the evolution of temperature with time
and refractory layers.
The aforementioned analysis seems to confirm that
the thermal capacities for both refractory-lined chambers and the flue gas together with the corresponding
transport phenomena were well represented mathematically and that the related portion of the model
can be considered reliable and useful for a further
simulation study.
¼aste feeding conditions
Waste characterization is a major factor in assessing the simulation of incineration processes by a deterministic model. The characterization of wastes is
usually accomplished using the analytical techniques
available although problems do arise since almost all
the traditional analytical methods are only applicable
for the analysis of either pure chemicals or nearly
homogeneous materials. Wastes are typically highly
heterogeneous and proper sample collecting and
handling are obviously critical steps in determining
waste characteristics and simulating the corresponding incineration processes. However, as it is shown
below, reasonable estimates of combustion heat and
ultimate analysis can be considered sufficient for
model simulation purposes. All the simulation results
reported here are refer to a waste characterization as
given in Table 3.
With reference to the previously described plant
operation, waste feeding was commenced about 11 h
after the initial startup, when the kiln temperature was
around 850°C and the corresponding postcombustion
chamber was at 950°C. At that moment the kiln
burner was switched off and the postcombustion
burner was put in the automatic operating mode to
achieve an imposed setpoint of 1200°C. Combustion
air flows and temperatures consequently followed the
pattern described above. A schematic representation
of the input variables evolution during the overall
transient is shown in Fig. 6.
The waste 40 l boxes weighting about 4 kg each are
loaded by a manually actuated feeder at a rate of 1—2
boxes/minute. The average waste flowrate, corresponding to a period of 30 h, was estimated at about
340 kg/h.
A global comparison between available experimental data and corresponding simulation data, including start-up and waste feeding conditions, is
shown in Figs 7—12. It can be observed that the
scattering of the experimental data of the kiln temperature, as shown in Fig. 7, can be explained on the basis
of rapid changes in the waste feed rate as well as in the
composition or heat of combustion. The corresponding simulation calculations refer to the average conditions mentioned earlier since the impact of the kiln
fluctuations on the other variables seems to be very
limited and this approximation does not affect the
2736
M. Rovaglio et al.
Fig. 6. Input measured variables for start-up and loading conditions: (a) waste flowrate to the rotary kiln
(b) fuel flowrates to rotary kiln and postcombustion chamber (c) air flowrate to the 1st spiral exchanger (d)
air flowrate to the 2nd spiral exchanger.
Dynamic modeling of waste incineration plants
2737
Fig. 7. Outlet gas temperature from Rotary kiln.
Fig. 8. Outlet gas temperature from Postcombustion Chamber.
model results. Figure 8 shows good agreement between the experimental postcombustion temperature
and the one predicted by simulation. Transients of
long duration, rapid variations of process variables
and temperature control actions are all perfectly reproduced by the model. The satisfactory results can
also be confirmed by observing the skin temperature
variations for both of the refractory-lined chambers
(see Figs 9 and 10): the typical reaction curves obtained coincide perfectly with the experimental data
and validate not only the correlations adopted to
describe heat fluxes but also the thermo-physical data
used to characterize the corresponding insulating materials. Finally, Fig. 12 shows the time evolution of the
oxygen mole fraction in the outlet section of the afterburner system. The comparison between experimental
data and simulated ones shows an excellent agreement under the waste-feeding condition while the
evident difference during the start-up procedure, indicates a failure of the oxygen sensor which shows an
unrealistically high value of the measured quantity. In
fact, since the auxiliary fuel consumption is known,
a simple material balance clearly demonstrates that
the total air flow needed to satisfy the experimentally
indicated oxygen concentration is 3—4 times greater
than the real maximum flow capacity of the plant
itself. Conversely, the agreement shown for the wastefeeding conditions validates the model described from
the material balance point of view. In particular, eq.
(4), which was adopted to define the burning rate of
the waste, the reaction scheme and the general characterization of the flows together with all the corresponding model assumptions, seems to be more than
acceptable for the correct simulation of the hot
section of an incineration plant. Once the model was
proved reliable and capable of representing the phenomena involved, over a large range of operating
conditions, some important information about unmeasurable variables could be easily deduced. An
example is shown in Fig. 13 which shows the air
2738
M. Rovaglio et al.
Fig. 9. External skin temperature for Rotary kiln.
Fig. 10. External skin temperature for Postcombustion Chamber.
leakage into the rotary kiln throughout the transient
period. Knowledge and control of such a variable will
certainly allow significant improvements to be taken
in the auxiliary fuel consumption.
Heat recovery
Finally, Figs 14 and 15 show the comparison between the experimental and computed values of the
outlet air temperature from the first and second heat
exchanger respectively. In both cases there is a very
good agreement between theory and practice. These
last results, even though quite obvious on the basis of
the previous ones, emphasize the reliability of the
model itself since the presence of thermal and material
recycles does not seem to compromise the robustness
of the model simulation in object.
CONCLUSIONS
A generalized model for the dynamic simulation of
incineration kilns was developed to reproduce the
operating trends of some monitored variables for
a commercial plant.
Dynamic modeling of waste incineration plants
2739
Fig. 11. Refractory temperature profile versus time and grid index.
Table 3. Waste characterization
Component
Mass fraction
Net heat of combustion
H
O
N
C
S
Cl
Inerts
Water
0.0620
0.0900
0.0100
0.2840
0.0050
0.0080
0.1699
0.3711
8500 kJ/kg
Fig. 12. Oxygen mole fraction in the outlet gas from postcombustion.
The above analysis includes start-up procedures
(considered as an important transient condition)
together with more usual waste-feeding operations.
All the results confirm that the model description
can be considered to be generally applicable and
easily extendable to different processes or plant
situations where a reliable dynamic knowledge is
available.
Although the application examples of the
aforementioned model have certainly been obtained
on the basis of several minor assumptions and simplifying hypotheses, the close agreement between
2740
M. Rovaglio et al.
Fig. 13. Air leakage for the Rotary Kiln.
Fig. 14. Combustion air temperature from 1st heat exchanger.
Fig. 15. Combustion air temperature from the 2nd heat exchanger.
Dynamic modeling of waste incineration plants
predicted values and experimental data clearly confirms that such a model can be of real value for
engineering purposes.
In the future, research will be devoted to exploiting
the good quality of the simulated process behaviors in
the application of the model to the definition of improved control strategies. In particular, a control
structure, allowing stable and reliable operations, satisfying legal limits and process conditions and compatible with a maximum waste load, can be defined as
a challenging issue for future study.
NOTATION
A
A
e
A
-/,n
A
n
A
r
A
q
C
p!*3
C
pi
CM
pS
C
pw
C
vS
C
s
C
505
D
F
GS
h
*/
h
e
H*/
!*3
H
*/
H
065
K
KW
n
K
x
k
¸
¸
W
M
'!4
M
i
M
40-*$
N
N
s
interface area, i.e. the flame surface, m2
external skin area, m2
log mean surface area at level n of the discretization grid, m2
wall area at section ‘n’ of the spiral exchanger, m2
average renewal surface velocity, m2/s
total refractory surface, m2
air heat capacity at constant pressure,
J/kg K
gas heat capacity at constant pressure of
component ‘i’, J/kg K
mean solid heat capacity at constant pressure, J/kg K
wall heat capacity at constant pressure,
J/kg K
solid heat capacity at constant volume,
J/kg K
ratio between sink surface and total surface,1
total concentration in gas phase, kmol/m3
internal combustion chamber diameter, m
factor: 1 for undammed kilns;'1 for dammed kilns
gas—wall surface exchange area, m2
internal convective heat transfer coefficient,
W/m2 K
external convective heat transfer coefficient,
W/m2 K
inlet air enthalpy, J/kg
inlet gas enthalpy, J/kg
outlet gas enthalpy, J/kg
absorption coefficient, 1/m
thermal conductivity at level ‘n’ of the discretization grid, W/m K
mass transfer coefficient (m/s) evaluated on
the basis of the following dimensionless relationship: Sh "0.023 Re0.8 Sc1@3
D
D
thermal conductivity, W/m K
internal combustion chamber length, m
free mean path of a photon inside the combustion chamber, ft
gas holdup inside the kiln, kg
molar holdup for component ‘i’ kmol
solid holdup inside kiln, kg
rotational speed of kiln, rps
total number of discrete coil sections
Nu
P
CW
P
%95
P
,*-/
PM
i
Pr
Q
%9
Q
-%!,
Q
-044%4
Q
CH4
Q
8!45%
Re
R
dr
R
i
S
Sc
Sh
¹065
a
¹*/
!*3
¹*/
f
¹
f
¹065
f
¹
g
¹W
n
¹
3*&
¹
w,*/
¹
8!-¹
8!--,n
º
505
v
065
»
505
¼065
a
¼*/
!*3
¼
CH4
¼*/
f
¼065
f
¼*/
i
¼g
065
¼S
065
¼
8!45%
X"6-,
O2
X*/
O2
2741
Nusselt number
partial pressure of CO and H O in the gas,
2
2
atm
external pressure, Pa
internal kiln pressure, Pa
molecular weight of the component, ‘i’
(kg/kmol)
Prandtl number
heat exchanged between smokes and coils,
W
air leakage flowrate, m3/s
heat losses through the exchanger walls, W
methane net heat of combustion, J/kg
waste net heat of combustion, J/kg
Reynolds number
destroying rate of waste combustible fraction, kg/s
production/consumption for reactions in
kinetic regime, kmol/m3 s
kiln slope (degrees from horizontal)
Schmidt number
Sherwood number
outlet air temperature, K
inlet air temperature, K
inlet flue gas temperature, K
flue gas temperature, K
outlet gas temperature, K
outlet gas temperature, K
refractory or insulating temperature for
layer ‘n’, K
reference temperature, K
internal wall temperature: refractory surface,
K
wall temperature of the spiral exchanger, K
wall temperature at section ‘n’ of the spiral
exchanger, K
total internal energy, J
outlet gas velocity, m/s
combustion chamber volume, m3
outlet air flowrate, kmol/s
inlet air flowrate, kg/s
auxiliary fuel flowrate, kg/s
inlet gas flowrate, kmol/s
outlet gas flowrate, kmol/s
inlet component ‘i’ flowrate deriving from
inlet flows or solid/gas reactions, kmol/s
outlet gas flowrate, kg/s
outlet solid flowrate containing ash, inert or
unburned products, kg/s
inlet waste flowrate, kg/s
oxygen bulk mole fraction in the gas phase
oxygen interface mole fraction assumed
equal to zero over all the flame surface
Greek letters
a
waste nitrogen fraction converted to NO
according to Bowman (1975)
b
dynamic angle of repose for the solid material
c
geometry coefficients
i
2742
e
p
e
G
h
k
O2
l
O2
o
o
W
p
q
u
BF
u
H2O
u
O2
u
N2
M. Rovaglio et al.
refractory emissivity
gas emissivity
residence time, s
stoichiometric coefficient for waste combuswhere the waste refers to
tion, kg /kg
O2 8!45%
the combustible fraction and the O con2
sumption refers to CO formation
stoichiometric coefficient for waste combuswhere the waste refers
tion, kmol /kmol
O2
8!45%
to the combustible fraction and the O con2
sumption refers to CO formation
gas density, kg/m3
wall conductivity, W/m K
Stefan—Boltzmann constant, W/m2 K4
gas transmittance
burning mass fraction in the inlet waste
water mass fraction in the inlet waste (moisture)
oxygen mass fraction in the inlet air flowrate
nitrogen mass fraction in the inlet air flowrate
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