OPTIMIZATION METHODS IN MINIMIZATION OF EMISSIONS
FROM COMBUSTION
SAARIO, A.1*, MÄKIRANTA, R.2, BACKLUND, A.3 and OKSANEN, A.4
1
Oilon International Oy, P.O. Box 5, 15801 Lahti, Finland
2
Oilon Energy Oy, P.O. Box 5, 15801 Lahti, Finland
3
Metso Power Oy, P.O.Box 109, 33101 Tampere, Finland
4
Tampere University of Technology, Department of Energy and Process Engineering,
P.O.Box 589, 33101 Tampere, Finland
*
Corresponding author, email: [email protected], tel.: +358 3 857 6375
ABSTRACT
Optimization methods have great potential to minimize emissions from combustion in a
systematic and efficient manner. Optimization can be combined both with computational
and experimental approaches. The present paper shows three examples of a successful
application of optimization in the field of combustion.
In the first example, a computational fluid dynamics (CFD)-based mathematical model is
applied to study emission formation in a 40 MWth bubbling fluidized bed boiler burning a
fuel mixture consisting mainly of biomass. After the CFD-based model has been validated
to a certain extent, it is used for optimization. There are nine design variables (nine distinct
NH3 injections in the selective noncatalytic reduction process) and two conflicting
objective functions (minimize NO and NH3 emission in flue gas). Two inherently different
optimization algorithms, viz. a genetic algorithm and Powell’s conjugate-direction method,
are applied in the solution of the resulting optimization problem. The constraints are
incorporated using a penalty function.
In the second example, a CFD-based model is applied to predict NO emission from a 5
MWth gas burner. The sizes of fuel (CH4) injection holes are varied. A method based on the
design of experiments (DOE) is applied to choose the cases to be modeled.
In the third example, a laboratory-scale experimental reactor is applied to study the
formation of NO in fluidized bed combustion conditions. The effect of temperature, O2,
NO, and NH3 on the formation of NO is studied. Taguchi method, which is one of the
methods based on DOE, is applied to select the parameters in the experimental runs.
Keywords: Optimization, CFD, emission minimization, design of experiments
INTRODUCTION
As computing power is currently growing fast, it can be claimed insufficient for the future
just to try to mimic pollution formation phenomena and to model a few arbitrary cases to
answer “what if …” questions. The main focus of the present study is on the combined
approach, consisting of CFD-based modeling and optimization. This efficient and scientific
approach is easily applicable to many types of design and retrofit problems in combustion
devices. It is emphasized that the capability of CFD to yield qualitatively correct results is a
prerequisite for the optimization, and that the optimization by no means compensates the
deficiencies in CFD modeling.
There are a few relatively recent examples of the application of optimization and CFD in
combustion-related problems. For example, Johnson, Landon, and Perry (2001) used 2D
CFD calculations to optimize the shape of a gas-fired combustor for minimum CO
emission. Risio et al. (2005) minimized the NO and unburned carbon emissions of coalfired boilers, whereas Tan, Wilcox, and Ward (2006) minimized the NO, CO, and unburned
carbon emissions from co-combustion of coal and biomass in a pilot-scale combustion rig.
A full review of literature on combustion optimization can be found in Saario (2008, pp. 3–
5).
Methods based on the design of experiments (DOE) are closely related to the optimization.
The great advantage of DOE lies in the reduction of time and resources spent to make
expensive experiments or computations.
OPTIMIZATION
Some basic concepts of optimization are first defined. The objective function is a measure
of quantity that is being minimized or maximized. The design variables are the parameters
that are varied during the optimization. In many practical problems, the design variables
have to satisfy certain requirements. The restrictions that must be satisfied to produce an
acceptable design are called constraints.
Interaction between the optimization algorithm and the CFD solver is shown in Figure 1.
First the optimization algorithm defines the starting values of the design variables, which
can be based e.g. on the current process settings, or they can be random. The design
variables are then passed to the CFD solver for evaluation, after which the objective
function value (or values) is returned to the optimization algorithm. After that the
optimization step is performed, i.e. the new values for the design variables are defined.
Then the whole automated procedure is repeated until a stopping criterion has been met.
Typically in the CFD-based optimization the allocated time or resources are exhausted
before the exact optimum has been found.
Figure 1. Interaction between optimization algorithm and CFD solver.
DESIGN OF EXPERIMENTS
The design of experiments (DOE) is a sampling plan in design-variable space. DOE is
effective in conducting systematic experiments and analyzing the data. DOE can be used
e.g. to approximate the most favorable region in the objective space, to determine the most
important design variables and consequently to reduce the complexity of the optimization
problem, or to create the data base for constructing various simplified lower-accuracy
models (such as polynomials, neural networks, or kriging models). For more information
on DOE see e.g. Wu and Hamada (2000), Queipo et al. (2005), or Shyy et al. (2001).
FIRST EXAMPLE – MINIMIZATION OF NO AND NH3 EMISSION IN
INDUSTRIAL BOILER
A sketch of the 40 MWth BFB boiler studied is shown in Figure 2. The selective
noncatalytic reduction (SNCR) process is applied by injecting a mixture of ammonia and
air into the freeboard. Here, a mixture of ammonia and air is injected from 7.5 m level
where there are eight injections (see Figure 3), and from 6.5 m level where there is one
injection on the rear wall. The chemical properties of fuel mixture (mainly biomass sludge)
and the boiler operating conditions are summarized in Saario (2008, p. 10).
A complex real-world design optimization problem is solved. As a first task, the grid
dependency of CFD-based model predictions were studied. Then, suitable submodels were
identified and the predictions were validated to a certain extent against the measurements of
temperature and of NO and NH3 concentrations obtained from the boiler. The results
related to model validation are presented elsewhere (Saario, 2008; Saario and Oksanen,
2008a, 2008c). After verifying that the model is capable of producing correct trends, it is
applied to the minimization of NO and NH3 emission of the boiler.
The functioning of SNCR process is strongly dependent on local conditions in the boiler,
especially on temperature. Hence, by optimizing the amount of ammonia injected and the
location of injections, a significant emission reduction may be achieved.
Figure 2. Boiler sketch.
Figure 3. Location and numbering of NH3
injections at height of 7.5 m (contours correspond
to NH3 concentration (ppmvol). View from boiler
roof.
Formulation of multiobjective optimization problem
The problem to be solved is a multiobjective optimization problem. As typically is the case
in real-world problems, also here we have more than one objective and the objectives are
conflicting with each other (minimize both NO and NH3 emission). Objective function
vector f(x) is given in the present study by
f(x) = (f1(x), f2(x))T
(1)
where f1(x) and f2(x) measure the concentrations of NO and NH3 (ppmvol) in flue gas,
respectively. The design variable vector, x, is given by
x = (X1, X2,…, X9)T
(2)
where Xi stands for the concentration of NH3 (vol-%) in the ith injection. The feasible set, S,
is defined as
{
S = x ∈ ℜ 9 | 0 ≤ X i ≤ 6.60 for all i = 1, 2, ..., 9, g ( x ) = mflow
M NH3
M flow
9
Xi
∑ 100 − m
i =1
NH3, max
≤ 0}
(3)
The upper design variable bounds are set at 6.60 vol-% for all i = 1, 2,…, 9. This value is
based on the preliminary optimization studies and engineering intuition. If design variable
bounds were too large, much of the search time would be wasted in exploring regions far
from the feasible set, whereas too tight bounds might not allow finding the optimum.
Constraint g(x) is an inequality constraint, M is the molar mass, and mflow stands for the
total mass flow of the mixture of NH3 and air from a single injection. Symbol mNH3,max
stands for the maximum total amount of NH3 available for the injections.
Solution of multiobjective optimization problem
The weighting method, where a weighted sum of the objective functions is optimized, has
been by far the most popular approach in combustion-related MOO studies, probably
because it is intuitive to the user. In the weighting method it is impossible to obtain points
in a nonconvex portion of the Pareto set in the objective space (Das and Dennis, 1997;
Marler and Arora, 2004). Moreover, specifying the weights is not straightforward. An even
spread of weights does not guarantee an even spread of points in the Pareto set in the
objective space (Cohon, 1978; Das and Dennis, 1997).
Instead of the weighting method, here the MOO problem is converted into a singleobjective optimization problem using the achievement scalarizing function (in the
following shortened to achievement function) introduced by Wierzbicki (see Miettinen,
1999, pp. 107–112 and Wierzbicki, 1982), which overcomes the typical disadvantages of
the weighting method discussed above. An achievement function is a function satisfying
certain requirements and the form applied here is closely related to the Tchebycheff
distance metric (min-max formulation). For more information on different distance metrics
see Cohon (1978, pp. 186–187).
A few definitions are needed at this point. A vector consisting of the objective function
values that are desirable or reasonable to the decision maker is called a reference point
vector zref. An ideal objective vector zid is obtained by minimizing each of the objective
functions individually subject to constraints. A vector consisting of the maximum objective
function values in the Pareto set is called a nadir objective vector znad. Vectors zid and znad
are used here to normalize the objective functions so that their objective values are
approximately of the same order of magnitude. Here, the optimization problem is
formulated as
⎛
⎛ f i ( x ) − ziref
minimize ⎜⎜ max ⎜⎜ nad
id
x∈S ′
⎝ i =1, 2 ⎝ zi − zi
2
⎞
⎛ f ( x ) − ziref
⎟⎟ + ρ ∑ ⎜⎜ i nad
− ziid
i =1 ⎝ zi
⎠
⎞
⎞
⎟⎟ + r (max(0, g ( x )))2 ⎟
⎟
⎠
⎠
(4)
The first term in Eq. (4) is the achievement function which projects the reference point
vector zref onto the Pareto set. The second term is the normalized augmentation term, which
prevents from generating solutions that are only weakly Pareto optimal (for details see
Miettinen (1999, pp. 100–102). The third term is the quadratic exterior penalty function,
which penalizes infeasible solutions and becomes more severe with increasing distance
from feasibility. The augmentation coefficient, ρ, is set at 0.0001, and the penalty
parameter, r, is set at 20 000.
Optimization algorithms
The most relevant features of an optimization algorithm are its ability to find the optimum
as well as the number of function evaluations required to find the optimum. Generally
speaking, it is difficult to know in advance which algorithm is best suited for a certain
problem at hand and for a certain initial guess. Two fundamentally different optimization
algorithms, viz. a genetic algorithm and Powell’s conjugate-direction method, are applied
to solve the optimization problem formulated in Eq. (4). Here, in most of the cases a hybrid
optimizer is used to exploit the benefits of the different algorithms; five GA runs with
different initial populations (600 CFD evaluations per run) are performed first (global
search), after which the search is continued from the best solution found, using Powell’s
conjugate-direction method (local search).
Results – multiobjective optimization
The interactive reference-point method is used to generate the Pareto optimal solutions. In
interactive methods the decision maker and the analyst communicate and analyze obtained
solutions and their interactions during the optimization. Here, the role of decision maker
was undertaken by two research engineers from a boiler manufacturing company.
Predicted points in objective space are shown in Figure 4. The point “SOO NO” is obtained
from the solution of a single-objective optimization problem. The point “SOO NH3” is
obtained by solving a single case (all NH3 injections turned off), which was specified by
applying reasoning and knowledge of the process. After solving the end points of the Pareto
set in the objective space, zid can be determined as zid = (zidNO, zidNH3) = (53.1, 0.0). Then,
znad is obtained from the payoff table (see Miettinen, 1999, pp. 16–18), which yields znad =
(znadNO, znadNH3) = (108.2, 47.5). Points “MOO I” and “MOO II” refer to the solutions of the
MOO problem using two different reference points (zref in Eq. (4)). Interestingly, here an
approximation of the Pareto optimal set is obtained as a “by-product” during interactive
optimization by plotting all the cases calculated during optimization (grey points in Figure
4).
Figure 4. Predicted points in objective space. All feasible points and points which exceed mNH3,max at
maximum by 5% are shown.
Figure 5 shows the design variables corresponding to “SOO NO”, “MOO I”, and “MOO II”
shown in Figure 4. As expected, to minimize the NO emission only, plenty of NH3 should
be injected (see Figure 4a). It is interesting to note that in all the three Pareto optimal
solutions the amount of NH3 differs significantly between the injections. Figure 5 shows
also that when both objectives are considered, NH3 is more evenly distributed between the
injections than in the “SOO NO” case.
(a)
(b)
(c)
Figure 5. Predicted Pareto optimal solutions in design space. The dashed line indicates injection settings of
current operating point.
Results – optimization algorithms
Genetic algorithms are based on the concepts of natural selection and survival of the fittest.
GAs use a stochastic population-based approach, in which several search points exist
simultaneously. The effects of population size and mutation probability on the GA
convergence rate are studied in Figure 6. In the present study it seems better to evolve
smaller populations for more generations than the opposite, whereas the effect of mutation
probability is less important.
Figure 6. Convergence of GA as function of population size and mutation probability. Plotted curves are
averages of best individuals of five independent GA runs started with different random seeds.
Although not shown here, it is observed that the convergence rate of Powell’s method is
greater than that of GA, but the solution is found to depend on the chosen starting point
(see Saario, 2008, pp. 93–96).
SECOND EXAMPLE – MINIMIZATION OF NO IN GAS BURNER
NO formation in a 5 MWth low-NOx natural gas burner shown in Figure 7 is studied using
CFD. The combustion chamber is cylindrical with the length of 5.2 m and diameter of 2.4
m. There are nine fuel lances in the burner. The sizes of the fuel injection holes are chosen
as the design variables and NO emission at the exit of the combustion chamber is the
objective function.
Figure 7. Low-NOx natural gas burner.
Both thermal- and prompt-NO mechanisms were taken into account in the CFD model.
Other issues related to CFD-modeling are summarized elsewhere (Mäkiranta et al., 2005).
Altogether 21 different settings for the design variables were modeled. These cases were
selected on the basis of DOE methods, and in principle the results could be applied to
construct a simplified response surface model describing NO formation.
The predicted maximum temperature and the predicted NO emission in all 21 cases are
shown in Figure 8. It can be seen that the model captures the well-known dependency
between high combustion temperature and high NO emission. However, as the case
modeled is extremely complicated, quantitative results on NO emission should not be
expected. Moreover, it was found difficult to achieve convergence in the present case.
Figure 8. Predicted maximum temperature and predicted NO emission in all 21 cases.
THIRD EXAMPLE – NO FORMATION IN EXPERIMENTAL REACTOR
A laboratory-scale experimental reactor is used to examine the formation of NO in the
bubbling fluidized bed combustion conditions, including char. The vertical experimental
reactor is made of steel tube with the height of 100 cm and inner diameter of 4.1 cm (for
more information see Backlund, 2007). The factors studied are the concentrations of O2,
NO, and NH3 as well as the combustion temperature. The levels of these parameters (or
factors) are altered simultaneously and the concentration of NO in the flue gas (response
data) is measured. The aim is to find the parameters affecting the outlet NO concentration
the most. It is important to notice that NO is not only fed into the reactor but also formed
from char and NH3.
Taguchi’s method
If every combination was tested, four factors with three levels would require 81 (34) test
runs. Here, one of DOE-methods, Taguchi’s method, is used to plan the experiment and to
study design parameters. Taguchi’s method is one example of robust parameter design.
Orthogonal arrays are used to decrease the amount of required test runs. The reduction of
runs is based on the insignificance of higher order interactions (Wu and Hamada, 2000, p.
214). The analysis of results is done using response tables, which are formed for the means
(M) and signal-to-noise (SN) ratios. The mean is an average response of test repetitions for
each parameter combination and the SN ratio measures the process robustness. The
response tables show the factors having the biggest effect on the outlet NO concentration.
Using Taguchi’s method and orthogonal arrays the total amount of test runs is reduced from
81 to nine. Table 1 shows an inner-outer array, which is a combination of design matrices
for the control and noise factors in Taguchi’s terminology (Wu and Hamada, 2000). In this
experiment no specific noise factor is studied. For more information on Taguchi’s method
see e.g. Roy (2001) or Wu and Hamada (2000).
Run
T
(ºC)
XO2
(vol-%)
XNO
(ppmv)
XNH3
(ppmv)
R1
XNO,OUT,R1
(ppmv)
R2
XNO,OUT,R2
(ppmv)
R3
XNO,OUT,R3
(ppmv)
MNO,OUT
(ppmv)
SN
(db)
1
850
0
0
0
0
0
0
0
–
2
850
10
100
100
94
104
103
100
-40
3
850
20
200
200
180
178
183
180
-45
4
900
0
100
200
28
23
20
24
-28
5
900
10
200
0
143
158
166
156
-44
6
900
20
0
100
45
47
58
50
-34
7
950
0
200
100
44
51
45
47
-33
8
950
10
0
200
112
96
105
104
-40
9
950
20
100
0
74
77
83
78
-38
Table 1. Inner-outer array. Nine test runs with four factors and three levels. R1, R2, and R3 denote outlet NO
concentrations in three test repetitions. Calculated mean and SN ratio are shown in last two columns. Detailed
information on how to compose array can be found in Backlund (2007).
Results
Figure 9 shows the main effects plot of means. The figure shows that the concentrations of
O2 and NO affect the level of outlet NO concentration the most (biggest difference between
the highest and lowest outlet NO concentration). NH3 concentration has the next biggest
effect and the temperature has the smallest effect on the outlet NO concentration. With the
help of Figure 9 the best, average, and worst test run can be identified. The lowest outlet
NO concentration is considered to be the optimum output. Hence the optimum levels are
950 ˚C for temperature, zero concentrations of O2 and NO, and 100 ppmv of NH3.
Figure 9. Main effects plot of means. The y-axis represents the average NO outlet concentration (MNO,OUT)
for every level of every factor. The markers circle (●), triangle (▲), and square (■) are used to represent the
best, average, and worst level of every factor, respectively.
Also the main effects plot of SN ratios can be composed (see Backlund, 2007, p. 46). With
the help of this figure the levels for factors can be chosen in order to minimize the variation
of outlet NO concentration. The optimal test run can be chosen in order to decrease both the
variation and the outlet NO concentration. Choosing levels for the concentrations of O2 and
NH3 is simple, but a compromise is needed when choosing levels for temperature and NO
concentration. It has to be done in order to reduce either the outlet NO concentration or the
variance. Interactions between the factors are problematic and more test runs would be
required to study these interactions.
CONCLUSIONS
The present study shows that the combination of CFD-based modeling and optimization is
clearly superior in terms of the efficiency and quality of results compared with the widely
applied approach in which CFD is typically used to calculate only a few intuitively selected
cases, the best of which is then considered to be the “optimum” solution.
In the first example, a combination of CFD-based mathematical model and interactive
multiobjective optimization is applied to find the optimal settings of nine ammonia
injections in order to minimize NO and NH3 emissions from a real-world industrial boiler.
With respect to the current operating point, approximately 12% reduction in NO emission is
obtained while maintaining NH3 emission at an acceptable level. At the optimum solution,
the amount of NH3 is not even between NH3 injections but it varies strongly.
The interactive reference-point method is used to find a satisfactory Pareto optimal solution
at a relatively low computational cost. Also, an approximation of the Pareto optimal set is
obtained as a “by-product” during interactive optimization.
The optimization problem is solved using both a genetic algorithm (GA) and Powell's
conjugate-direction method (Powell's method). Using the GA is found to be a robust
method in the case of the present problem. However, using the GA is computationally
expensive and its convergence rate may be strongly dependent on the chosen parameters,
such as population size. The GA and Powell's method are applied here mostly in the form
of a hybrid method (first the GA for the exploration of design space, then Powell's method
for local refinement near the optimum), which is shown to be an effective approach.
In the second example, a CFD-based model is applied to study NO emission in a natural
gas burner. The sizes of the fuel injection holes were selected as design variables and NO
emission at the exit of the combustion chamber was selected as the objective function.
Methods based on design of experiments (DOE) were applied to cut down the number of
CFD calculations required.
In the third example, the effects of temperature, O2, NO, and NH3 on the formation of NO
are studied in bubbling fluidized bed combustion conditions. Test runs were carried out
with a laboratory-scale experimental reactor. Taguchi’s method, one of DOE methods, was
used to plan the experiment and to study multiple variables simultaneously. Applying
Taguchi’s method the number of test runs required was reduced significantly.
The combined approach is easily applicable to many types of design and retrofit problems
in combustion devices. Possible objectives include e.g. the minimization of various
emissions, number of inlets, boiler corrosion, slagging and fouling, boiler size, temperature
and velocity gradients, or costs, or they include the maximization of thermal efficiency or
heat transfer. Possible design variables include e.g. the geometry, fuel feed, fuel quality,
particle size distribution of fuel, air distribution system, swirl angle, injection of additives,
or flue gas recirculation.
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