Separation and Purification Technology 62 (2008) 571–581
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Separation and Purification Technology
journal homepage: www.elsevier.com/locate/seppur
Modeling of the in-duct sorbent injection process for flue gas desulfurization
F.J. Gutiérrez Ortiz ∗ , P. Ollero
Departamento de Ingenierı́a Quı́mica y Ambiental, Universidad de Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain
a r t i c l e
i n f o
Article history:
Received 18 October 2007
Received in revised form 3 March 2008
Accepted 6 March 2008
Keywords:
Desulfurization
Modeling
Flue gas
Sulfur dioxide
In-duct
Hydrated lime
Pilot plant
Simulation
a b s t r a c t
Dry scrubbing processes, especially dry sorbent injection technology, offer a more economical technology
for retrofitting than wet or semi-wet scrubbing processes. A simple realistic model for the in-duct desulfurization process has been developed. The model has been conceived as an approach useful for both
analyzing results and aiding in design of an in-duct desulfurization process. The model of the process
involved, which is the basis for the discussion in this paper, has been evaluated by comparing the model
results and the experimental data, obtained in a pilot plant study. The predicted values agree reasonably
well with the available experimental data, and the relationships in the model presented have been verified. The sensitivity analysis of variables is relevant for the design and operation of the in-duct process,
allowing a parametric study that reveals the effect of the different operation and design factors. Although
this model is specific to our in-duct pilot plant, it may be used with confidence in commercial DSI (dry sorbent injection) units as it was designed and implemented according to widely accepted engineering rules
in this field. The model has been built in an open structure to allow for rearrangements of and extensions
to the process.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
oxidized to gypsum following the reaction,
Although the most commonly used industrial practice for flue
gas desulfurization (FGD) is a wet scrubbing process, dry scrubbing
processes, especially dry sorbent injection technology, offer a more
economical technology for retrofitting. Dry scrubbers have significantly lower capital and annual costs than wet systems because
they are simpler and demand less water and their waste disposal
is less complex. Dry injection systems install easily and use less
space; therefore, they are good candidates for retrofit applications.
SO2 removal efficiencies are significantly lower than those for wet
systems, between 50% and 60% for calcium-based sorbents. The
SO2 removal is about 93–98%, and even higher for wet-scrubbers.
Dry sorbent injection is viewed as an SO2 control technology for
medium to small industrial boiler applications.
The main reaction binding the SO2 is a simple acid–base reaction:
CaSO3 · 12 H2 O + 21 O2 + 32 H2 O → CaSO4 · 2H2 O
SO2 + Ca(OH)2 → CaSO3 · 21 H2 O + 12 H2 O
Apart from hemihydrate calcium sulfite, different reaction products have been proposed [1]. A small calcium sulfite fraction is
∗ Corresponding author. Tel.: +34 95 448 72 60/61/65/68; fax: +34 95 446 17 75.
E-mail addresses: fjgo@esi.us.es, frajagutor@us.es (F.J. Gutiérrez Ortiz),
ollero@esi.us.es (P. Ollero).
1383-5866/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.seppur.2008.03.012
Dry sorbent injection systems pneumatically inject powdered
sorbent directly into the furnace, economizer, or downstream
ductwork (DSI process). The dry waste product is removed using
particulate control equipment such as a baghouse or electrostatic precipitator (ESP). The flue gas emissions from the coal-fired
boiler are humidified by fresh water in the duct. The water flow
rate is controlled so as to achieve a temperature approximately
10–15 ◦ C above the adiabatic saturation temperature of the gas.
SO2 is removed by the sorbent particles present in the duct and
also by the sorbent deposited in the particle collector device.
The residence time in the duct is usually quite short (between
one and three seconds) and, therefore, a very reactive sorbent is
required.
Scrubbers are classified as “once-through” (no recycle) or
“regenerable” (with recycle), based on how the solids generated
by the process are handled. Once-through systems either dispose
of the spent sorbent as a waste or utilize it as a byproduct. Regenerable systems recycle the sorbent back into the system. Regenerable
processes have higher costs than once-through processes; however,
they might be more desirable if higher desulfurization efficiency is
required. Regenerable systems make it possible to sell pure fly ash,
reduce the total solid finally disposed and simplify the recirculation
of the partially spent sorbent.
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F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
Nomenclature
cross-section area of the duct (m2 )
specific superficial area measured by BET technique
(m2 /g)
0
Cp,g
average specific heat capacity for the gas measured
under constant pressure (J/mol K)
CSO2
SO2 molar concentration in the gas (mol/m3 )
dp
hydrated lime particle diameter (m)
fnj
molar fraction of the substance j in the commercial
hydrated lime (mol/mol)
fpj
weight fraction of the substance j in the commercial
hydrated lime (kg/kg)
ESO2
desulfurization efficiency (%)
EESP
desulfurization efficiency in the ESP (%)
Hr0 (T ) reaction heat at a pressure of 1 atmosphere and at
the temperature T (reaction between Ca(OH)2 and
SO2 ) (J/mol)
RH
relative humidity in the flue gas (%)
L
effective duct length (m)
ṁi
mass flow rate of solid i (kg/s)
ṁf,ash
mass flow rate of fly ash upstream from the duct
inlet (kg/s)
ṁr,ash
mass flow rate of recirculated fly ash (kg/s)
Ni
superficial molar flow rate for the species i
(mol/m2 s)
ṅf
molar flow rate of fresh hydrated lime (mol/s)
ṅr
molar flow rate of recirculated reactive solid (mol/s)
MW
molecular weight (g/mol)
P
pressure (bar)
PV
vapor pressure (bar)
Q
gas flow rate (m3 /s)
R′
recirculation relation corrected for the sorbent (kg
of sorbent recirculated/kg of fresh hydrated lime)
Rg
universal constant for gases (8.314 J/mol K)
R
recirculation ratio (kg of solid recirculated/kg of
fresh hydrated lime), also RR
−r
reaction rate – consumption of Ca(OH)2 –
(mol Ca(OH)2 converted/m3 reactor s)
−rSO2
reaction rate – consumption of SO2 –
(mol SO2 converted/m3 reactor s)
T
temperature (K)
t
time (s)
uj
velocity of the phase j (m/s)
u0
superficial velocity of the gas (m/s)
w
dimensionless axial coordinate in the duct
X
Ca(OH)2 molar conversion (mol/mol)
Yi
molar fraction of the substance i in the gas (mol/mol)
z
axial coordinate of the duct (m)
A
BET
Greek letters
ε
volumetric fraction of the gas or solid phase related
to the duct (m3 /m3 )
superficial area fraction uncovered by product
EF
particle collection efficiency of the ESP (%)
dynamic viscosity (kg/m s)
molar density (mol/m3 )
ash
ash density (kg/m3 )
m
mass density (kg/m3 )
Subscript letters
ash
fly ash
av
average
coll, EF collected in the ESP
f
g, G
lime
purg
r
s, S
s, EF
w
fresh
gas
hydrated lime
purged from the system
recirculated
reactive solid (sorbent partially converted plus reaction product)
ESP outlet
dimensionless axial coordinate in the duct (it varies
from 0 to 1)
In the last two decades some studies have been carried out
to study mass and energy transfer ([2–6]) as well as kinetic
studies [1,7–16] of the dry flue gas desulfurization at low
temperatures.
In today’s highly industrialized environment, it is necessary to
view environmental issues as part of the design objectives rather
than as constraints on operations. Analytical methods, including
software simulation and optimization tools based on process models, that help make air pollution control more effective, can be
valuable assets to chemical and environmental engineers who are
designing and optimizing air pollution control equipment.
The main objectives of the present investigation were to study
the in-duct desulfurization process as well as to develop and verify
a simple realistic model for the process. This paper gives an introduction to the model, which is based on pilot plant data, and it has
been conceived as a feasible approach for both analyzing results
and aiding in the design of an in-duct desulfurization process. Thus,
the model was evaluated by comparing the model results and the
experimental data obtained from a pilot plant.
2. Experimental setup and data
The pilot plant (Fig. 1) is located within a 550 MWe power plant
in southern Spain. It contains a subcritical forced-circulation steam
boiler with a tangential-fire configuration. This boiler burns Colombian and South African bituminous coal with a sulfur content of less
than 0.7 wt.% and produces about 1800 T m/h of superheated steam
at 168 bar y 540 ◦ C. The representative flue gas composition is 6.3%
O2 , 12.3% CO2 , 74.1% N2 , 7.2% H2 O, and 400 ppmv SO2 concentration.
There is a long gas duct upstream from a pilot precipitator to provide enough residence time for in-duct desulfurization (Table 1).
This pilot plant can process up to 12,000 N m3 /h of flue gases that
are drawn upstream and/or downstream from the power plant precipitator at 130–150 ◦ C. Therefore, we can treat flue gases with or
without fly ash in any proportion, thus simulating the performance
of an ash precollector located upstream from the desulfurization
unit. There is also an SO2 injection unit to increase the SO2 gas
concentration from 350 ppm to 3000 ppm. An SO2 analyzer with
three measuring probes – located at the pilot plant inlet, after the
desulfurization unit and downstream from the electrostatic precipitator at the pilot plant outlet – makes it possible to determine the
Table 1
Technical characteristics of the duct sorbent injection
Duct
•Diameter
•Length
Hydrated lime conveyor
Solid recirculation rate
Water flow rate
0.44
50.00
140
2600
700
m
m
kg/h
kg/h
kg/h
F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
573
Fig. 1. Pilot plant flow sheet.
desulfurization efficiency in the duct and in the whole system, i.e.,
including the electrostatic precipitator (ESP).
At around 140 ◦ C, the flue gas is sprayed with water to reduce
its dry temperature to a few degrees above the adiabatic saturation
temperature (about 51 ◦ C). A mixture of fresh hydrated lime and
recirculated product, which can be activated with liquid water in
a pugmill, is injected downstream from the humidification chamber into the cooled and humidified flue gas. The SO2 is removed
in the duct but also in the ESP, which contributes significantly to
the global yield (about 10% of the total) due to a long gas residence
time (around 14 s) and the presence of unconverted hydrated lime.
The dust collected in the ESP is conveyed to the product hopper
by means of a pneumatic device. Both the fresh hydrated lime and
product hoppers discharge through rotary valves into an air slide
where both products are mixed. The air slide in turn discharges the
mixture into the pugmill.
An experimental program was designed to evaluate the performance of the DSI process with respect to the main operating
variables: the calcium to sulfur molar ratio (mol Ca/mol S), the
approach to the adiabatic saturation temperature (◦ C), the solid
recirculation ratio (kg of recirculated solid per kg of fresh hydrated
lime), the SO2 flue gas concentration (ppm), the fly ash content in the flue gas (mg/N m3 ), and the gas flow rate (N m3 /h).
Table 2 shows the two levels considered for the five main variables
used.
The main operating variables for this simple DSI process are the
Ca/S ratio and the approach to the adiabatic saturation temperature. Increasing the Ca/S ratio leads to higher SO2 removal yields
but at the expense of lower sorbent utilization. Upon decreasing
the approach temperature, moisture and sorbent co-exist in the
gas for a longer time, and thus the sorbent continues to react with
Table 2
Factors and levels in the experiences design used to obtain the model
Fresh calcium to sulfur ratio (mol/mol)
Approach to the adiabatic saturation temperature (◦ C)
SO2 concentration (ppm)
Gas flow rate (N m3 /h)
Ash concentration at the system inlet (mg/N m3 )
Recirculation ratio (kg/kg)
1.2–1.7
8–13
350–1000
8000–12000
35–7000
0–10
SO2 , significantly improving the SO2 removal efficiency and sorbent
utilization.
The experimental campaign included more than forty tests to
assess the effect of the different factors. These tests have been used
to obtain the realistic approach of modeling pursued.
We used commercial hydrated lime with a BET surface area of
12.9 m2 /g, a mass average mean diameter of 6.83 m, a total pore
volume of 0.100 cm3 /g and a purity of 96 wt.%. The fly ash had a
mass average mean diameter of 12.20 m, an unburnt amount of
3.02 wt.% and a CaO content of 9.18 wt.%.
This section is more specifically described elsewhere [17,18].
However, Figs. 2–4 summarize some of the experimental results
that were important for attaining the realistic model. Fig. 2 shows
the positive effects of increasing the fresh Ca/S ratio (CASf ) and
of operating close to the adiabatic saturation temperature (AST).
Fig. 3 indicates that the precollection of the fly ash has a clear positive effect on the desulfurization yield. The explanation for this
effect, when recycling, is clear: a high value of fly ash concentration reduces the fraction of free hydrated lime in the recycled solid,
due to the increase in the ash fraction being recycled. However, the
explanation for this effect when there is no recirculation is not, in
principle, so patent. In this case, there is no quantitative decrease in
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F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
Fig. 2. Effects of the Ca/S ratio (CASf) and of the approach to the adiabatic saturation temperature (AST) on the global desulfurization efficiency. SO2 inlet concentrations
vary from 350 ppm to 1000 ppm.
the Ca/S molar ratio. Fly ash probably prevents sorbent conversion,
perhaps by making it difficult for the SO2 to attain active hydrated
lime, especially if particles of hydrated lime and fly agglomerate
themselves. Finally, Fig. 4 records how a recirculation ratio (RR)
of 10 can up to double the desulfurization yield obtained without
sorbent recirculation.
3. DSI model description
Fig. 5 shows a schematic flow diagram of the in-duct process,
where the humidification chamber, the reactor and the particle
device collector can be distinguished. Moreover, some of the flow
rates, concentrations and boundary conditions are also included.
Fig. 3. Effect of the fly ash precollection.
F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
575
Fig. 4. Effect of the recirculation.
3.1. Model hypothesis
It is a quasi-steady process.
There is plug flow in all the phases (gas and solid).
Conditions only change in the axial direction.
Average values of density and flow rate for the gas phase are used.
The loss of pressure along the duct is negligible.
The particle diameter is the average value and it remains constant.
The system is adiabatic, i.e. loss of heat to the exterior is insignificant.
• The hydrated lime is exclusively comprised of Ca(OH)2 , CaCO3
and H2 O.
•
•
•
•
•
•
•
dNCa(OH)2
= εs Ca(OH)2 us
Considered reaction:
Ca(OH)2 (s) + SO2 (g) → CaSO3 · 21 H2 O (s) + 12 H2 O (l)
3.2. Main equations
(a) Mass balance for the gas phase:
dz
= εg g ug
dYSO2
L dw
m3 reactor s
,
(1)
where NSO2 is the superficial molar flow rate for the SO2
(mol/m2 s), ε is the volumetric fraction of the gas phase related
to the duct (m3 /m3 ), g is the gas molar density (mol/m3 ), ug is
the velocity of the gas (m/s), YSO2 is the molar fraction of the SO2
in the gas (mol/mol) and (−r) is the reaction rate – consumption
of Ca(OH)2 – (mol Ca(OH)2 converted/m3 reactor s)
(b) Mass balance for the solid phase:
dz
dNSO2
mol Ca(OH) conv
2
= −(−rSO2 ) = −r
εs Ca(OH)2 us
d(1 − X)
= −(−rSO2 ) = −r
L dw
dX
=r
L dw
(2)
(3)
where X is the conversion of reactive solid and Ca(OH)2 is the
molar density of the hydrated lime (mol/m3 ). The nomenclature
used can be seen in Nomenclature.
The molar concentration of SO2 in the gas (mol/m3 ) – CSO2 –
is calculated in these equations on wet basis. However, the CSO2
experimental data is expressed on dry basis.
Fig. 5. Schematic flow diagram for the in-duct desulfurization process modeled.
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F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
(c) Energy balance:
where the real gas velocity is:
r Hr0 (T )
−
εg g ug Cp,g 0 (T )
dT
=
L dw
(4)
From Eqs. (1) and (2), the following equation is obtained:
εs Ca(OH)2
εg g
(Xw − Xw=0 )
(5)
The boundary condition set for the sorbent conversion at the
duct inlet implies an iterative process for solving the equation, since
it depends on the final conversion of Ca(OH)2 , i.e.:
Xw=0 =
ṅr
Xr
ṅf + ṅr
(6)
where ṅf is the molar flow rate of fresh hydrated lime (mol/s) and
ṅr is the molar flow rate of recirculated reactive solid (mol/s).
Additionally, taking into account that w = z/L, where z is the
axial coordinate for the duct, and L is the length of the duct, we
have the following expression for the average temperature:
Tav
1
=
L
l
T (z) dz =
0
(7)
0
Average gas density (g,av ) as well as average gas flow rate (Qg,av )
is calculated at Tav . Likewise, the relative humidity (RH), which
is a very important operation parameter, is calculated using the
following equation:
RH =
PT · YH2 O
· 100 (%)
(8)
pv (T ) = 10[5.0844−(1668.7166/T (K)−45)] (bar)
(9)
pv (T )
where
is the vapor pressure of water. This equation is valid at temperatures
between 274 K and 373 K.
With respect to the solid sorbent, from the weight composition of the commercial hydrated lime its molar composition and
the equivalent molecular weight are calculated, as well as the
molecular weight of the partially unspent sorbent in the duct and
the recirculated reactive solid, so the sorbent conversion must be
known. Then, the mass flow rate of the reactive solid in the duct
can be calculated from:
ṅf + ṅr
· MWav =
1000
CASf · CSO2 ,w=0 · Qg,av · g,av
fnCa(OH)2
+ ṅr ·
MWav
1000
(10)
3.3. Velocities and residence times
⇒
1 − exp
for t ≥ 10−3 s,
18 · g
dp2 · m,s
us ∼
= ug
·t
(m/s)
(13)
With respect to the reactive solid, in order to calculate the residence time in the system the following consideration must be
introduced:
Let r = ṁr /(ṁr + ṁpurg + ṁs,EF ) = (ṅr · MWr )/((ṅr + ṅf ) · MWr ),
where rN denotes the probability that any particle returns to the
active system (duct) by the (N + 1)th time. Thus, the number of loops
that a particle makes in the system is the sum of all ith probabilities,
i.e.:
S = 1 + r + r2 + r3 + · · · + rN + · · ·
(14)
This series is a geometric progression whose sum is:
∞
ri =
S=
i=0
1
1−r
(15)
As a result, the solid residence time is:
ts = S · tg =
ṅr + ṅf
· tg (s)
ṅf
(16)
Now we can obtain a direct relationship between r and R (recirculation ratio):
R
MWlime
1
= 1 + R′ ·
=1+
1−r
MWr
1 + (ṁf,ash /ṁf ) · (MWlime /MWr )
·
MWlime
MWr
(17)
Thus, increasing the recirculation ratio leads to a higher effective
residence time for the sorbent in the duct, and the internal (or total)
Ca/S molar ratio will be larger:
CAStotal =
fnCa(OH)2
Qg,av · g,av · CSO2
fnCa(OH)2
Qg,av · g,av · CSO2
· (ṅf + ṅr · (1 − Xr ))
· ṅf · 1 + R′ ·
MWlime
· (1 − Xr )
MWr
(18)
where R′ is the recirculation relationship corrected for the sorbent
(kg of sorbent recirculated/kg of fresh hydrated lime), MW is the
molecular weight (g/mol), ṁf is the mass flow rate of fresh hydrated
lime (kg/s) and ṁf,ash is the mass flow rate of fly ash upstream from
the duct inlet (kg/s).
3.4. Kinetic model
We have assumed spherical and uncompressible particles, and
that one particle movement is not influenced by the others. Also, the
gas is considered uncompressible and its movement is exclusively
in the axial direction. Based on the above assumptions, the solid
velocity is:
(12)
L · εg
L
=
(s)
ug
u0
=
In Appendix A, the other main mass flow rates of solid considered in the model are shown.
us = ug ·
tg =
1
T (w) dw
Qg,av · A
u0
=
(m/s),
εg
εg
and A is the cross-section area of the duct. In Appendix A the volumetric fractions involved are indicated.
The gas residence time in the duct is given by the following
expression:
where Hr0 (298 K) = −176, 045 (J/mol).
YSO2 ,w = YSO2 ,w=0 −
ug =
If dp = 5 m
(11)
The kinetic model used is based on the general model proposed
by Shih et al. [13], which assumes that the absorption of CO2 (and,
by extension, absorption of SO2 ) in Ca(OH)2 is controlled by the
superficial reaction that takes place only in the reactive surface
where there is no reaction product. In the general modeling, there
is a parameter (“n”) that can take different values since it is linked
to a function that represents the way the reaction product covers
the solid surface. These researchers chose n = 1 for the sake of simplicity, although the performance with a value of n = 2 would have
F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
been equally correct. There was no other reason. In this latter case
(logarithmic law), the following equation is attained:
dX
= k1 exp(−k2 X),
dt
(19)
where X is the conversion of reactive solid. k2 is related to the
decrease in the conversion rate during the reaction, that is, as long
as the conversion is increasing. The parameter k1 can be interpreted
as the conversion rate when the conversion is very low (null, from
a mathematical point of view). We have selected this mode, which
is similar to the conception in Krammer et al. [11]. Parameters k1
and k2 can depend on the specific superficial area (BET), temperature (T), SO2 concentration (CSO2 ) and relative humidity (RH). Since
these variables change over time while the process is running, it is
not possible to achieve an analytical solution. However, beginning
from the references cited above and a previous study of our own
[18], the following equation is proposed and used:
dX
= KI
dt
BET
12.9
exp
−
12.9KII X
(RH/100)(BET) YSO2
(20)
From the experimental results obtained in the pilot plant, it was
possible to find out the values of the two parameters, KI and KII ,
by minimizing the quadratic deviation between the desulfurization efficiencies calculated using the model and those obtained
experimentally. To do so, the in-duct model and the kinetic model
were implemented in MatlabTM , and an optimization algorithm
with an objective function based on the Nelder–Mead algorithm,
which represents the search of the minimum cited above, was
used. Parameters KI and KII , when fitted, have the following values:
KI = 0.0768; KII = 0.0019.
577
average temperature are calculated, updating thus the water vapor
pressure and, therefore, the relative humidity in the duct. At the
outlet of the third loop (the innermost one), the reaction rate is
calculated as well as the error related to the second loop, which is
compared with the allowed tolerance. In the first loop (the outermost one), the one-dimension matrices of sorbent conversion, SO2
concentration and temperature are updated. As the boundary condition for the calculus of the profile of sorbent conversion is given
at w = 0 (Xw=0 ), which includes the total conversion at the outlet of
the particle collector system (Xr ), it is necessary to use a trial and
error method. The error has been defined, in this case, as follows:
=
ṅr · Xr
− Xw=0
ṅr + ṅf
(21)
The convergence will be achieved when < tolerance. The tolerance can be introduced as an input in the simulation tool. The
value for Xw=0 is updated from the beginning of the second loop,
whereas Xr is calculated at the end of each step run inside the third
loop, once the matrices of values for the sorbent conversion, SO2
concentration and temperature are obtained.
With regard to the solid sorbent conversion, we used the following equations:
o At the duct inlet:
Xw=0 =
ṅr
R′ MWlime
· Xr ,
· Xr =
MWr + R′MWlime
ṅf + ṅr
(22)
o At the duct outlet:
Xr = Xw=0 +
YSO2 ,w=0 · ESO2 ,overall (%)
100
4. Simulation tool
where:
The in-duct desulfurization process can be simulated by means
of a tool programmed in Visual Basic 5.0. This tool [17] can be used
to assist in the design of a real plant. In the simulation, it is possible
to run the combustion and humidification processes previous to
the desulfurization, or only the desulfurization process by setting
the flue gas characteristics at the duct inlet.
For the humidification process, the procedure used to calculate
the water flow rate required consists of computing the absolute
saturation humidity after injecting water (YSat,2 ), obtained on the
one hand from the definition of the vapor pressure (YSat,2 )pv , and,
on the other hand, by solving an energy balance (YSat,2 )BE , with the
constraint of the Tsa (approach to the adiabatic saturation temperature) value, previously set. Thus, beginning from a dew point
related to the vapor pressure of water equal to the process pressure, the value of YSat,2 will be maximum, as calculated by the vapor
pressure definition. However, the YSat,2 value, as calculated by the
energy balance, will be quite a bit lower. As the dew point decreases,
the YSat,2 values will approach each other. The tolerance chosen was
|(YSat ,2 )pv − (YSat,2 )BE | < 0.001.
Finally, the desulfurization process can be run after the two
previous processes indicated above or without those processes. In
this latter case, the gas to be treated consists of air plus SO2 and
fly ash, whose concentrations must be input by the user. The gas
temperature, pressure and flow rate must also be set.
For the desulfurization process, the procedure followed consists
of three nested loops with stepped convergence, in such a way that
the conditions for the more external loops are imposed by the tolerances chosen for the SO2 concentration values (first loop) and
the sorbent conversion (second loop). In the third loop, the integration process for the set of the ordinary differential equations
of the model was performed using the classic fourth-order RungeKutta method. Next, the SO2 concentration and the increase in the
ESO2 ,overall (%) =
CSO2 ,w=0 − CSO2 ,w=1
CSO2 ,w=0
= EDuct (%) · 1 +
·
εg · g
,
εlime · Ca(OH)2
· 100 · 1 +
EESP (%)
100
.
EESP (%)
100
(23)
(24)
ESO2 ,overall is the overall desulfurization efficiency (%) and EESP
is the desulfurization efficiency in the ESP (%), measured as a
fraction of the duct desulfurization (EDuct (%)). EESP is an input
data. The particle collector device was not modeled as part of the
system. In other words, the desulfurization removal and particle
separation efficiencies in the ESP are data required by the simulator. However, to estimate these efficiencies, experimental results
can be looked up [18], although most of them were about 10% of
the total efficiency.
5. Results and discussion
The sensitivity analysis of variables can be pertinent for the
design and operation of the in-duct process. Thus, it is possible to
check the effect of significant independent variables on the results
of the model, mainly on the SO2 removal and on the sorbent conversion. The main runs of sensitivity analysis carried out have consisted
of Ca/S molar ratio, relative humidity, fly ash precollection and recirculation ratio. The data sets of the variables considered were fresh
Ca/S molar ratio (1.0–2.4), relative humidity (50–90%), recirculation
ratio (0–10) and fly ash concentration (0–8 g/N m3 ). Each of these
runs involved a discrete input parameter from a standard condition. The standard conditions for the input parameters are given in
Table 3. In order to remove any disturbance due to ESP in this analysis focused on the duct, we assumed a particle collector device
with particle removal efficiency of 100% but without contributing
to SO2 removal in the system.
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F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
Table 3
Standard conditions for the simulation
Particle mean diameter of hydrated lime
Sorbent specific surface area (BET)
Particle mean diameter of fly ash
Particles removal efficiency in the ESP
Increment of the desulfurization efficiency in the ESP
Duct length
Duct inside diameter
Tolerance for the conversion of Ca(OH)2
Tolerance for the conversion of SO2
Gas temperature at the humidification chamber outlet
Gas humidity at the humidification chamber outlet
Gas flow rate (humid)
SO2 concentration (humid basis), at the duct inlet
Gas residence time
5
12.9
10
100
0
50
0.437
10−7
10−2
60
60
3.5
1000
2.14
m
m2 /g
m
%
%
m
m
–
–
◦
C
%
m3 /s
ppmv
s
Figs. 6–9 show the sensitivity analysis of the DSI process carried out using the modeling approach described. In all cases, higher
fresh Ca/S molar ratio yielded higher desulfurization efficiencies,
but lower sorbent conversion, as expected.
The net effect of the recirculation ratio (RR) on model results can
be examined in Figs. 6 and 7. As can be seen in Fig. 6, with respect
to the once-through configuration, the sorbent recycle leads to an
increasingly higher mass flow of fresh hydrated lime and, for that
reason, to higher desulfurization efficiencies. Thus, a recirculation
ratio of 10 produces an average increment of 20 to 30 efficiency
percentage points in the duct for a fresh Ca/S molar ratio of 1.0 and
2.4, respectively. Indeed, recirculation allows us to make use of the
unspent hydrated lime. However, gains in SO2 removal achieved
at high RR values are lower as RR increases: in relation to an RR
value of 7, an RR of 10 only allows for an increase in SO2 removal
efficiency of 3.5 percentage points. Fig. 7 shows the influence of
RR on sorbent conversion by using a related variable such as the
solid residence time, and also its effect on the total (or internal)
Ca/S molar ratio. In accordance with Eqs. (16) and (17), we see that
higher RR values lead to higher residence times for the solids. First,
these sensitivity curves show a decline in the sorbent conversion as
fresh Ca/S molar ratio is increased because for any such change in
the fresh Ca/S molar ratio, the change in SO2 removal efficiency is
proportionally smaller. However, for a given fresh Ca/S molar ratio,
a higher RR (higher solid residence time) leads to an increase in sorbent conversion in a very significant way because residence time
Fig. 6. Effect of the recirculation ratio on the SO2 removal efficiency (cases run with
fly ash precollection).
for the solid phase enlarges considerably. When RR is higher, the
internal Ca/S ratio is clearly increased, and, for instance, for a fresh
Ca/S molar ratio of 2, the internal or total Ca/S molar ratio is 7 times
this value when we use a recirculation ratio of 10 (equivalent to a
sorbent residence time of 23.57 s) as compared to the once-through
case (equivalent to a sorbent residence time of 2.14 s). In this case,
the number of cycles that, on average, the sorbent particles make
in the system before being purged out of it is 11. In accordance with
Eq. (20), although the average sorbent conversion in the duct is lowered by increasing the recirculation ratio and Ca/S molar ratio due
to instantaneous X and SO2 concentration values becoming higher
and lower, respectively, the number of sorbent moles converted
per duct volume unit and time unit is increased. That is, the continuous sorbent recycle implies a lower sorbent conversion each
time it passes through the duct but the number of loops is quite a
bit higher, thus compensating for the decrease in X variation each
time it passes through the duct.
The model sensitivity to fly ash precollection on the SO2 removal
and on the sorbent conversion is illustrated in Fig. 8, where a recirculation ratio of 10 has been used. As shown, the solids precollection
Fig. 7. Effect of the solid residence time on the sorbent conversion and on the total Ca/S molar ratio (cases run with fly ash precollection).
F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
579
Fig. 8. Effect of the fly ash precollection on the SO2 removal efficiency and on the internal Ca/S ratio (cases run with RR = 10).
produces an increase in desulfurization efficiency between 7 and 10
percentage points. The reason is that the internal Ca/S molar ratio
is considerably higher when fly ash is removed before arriving to
the duct, as can be seen in the figure. In addition, the residence
time for sorbent is higher when there is no fly ash. Hence, sorbent
conversion will be also greater. Furthermore, when the fresh Ca/S
molar ratio is increased, the proportion of sorbent in solid phase
also increases and the residence time of the sorbent is higher, thus
enhancing the desulfurization yield while reducing the sorbent
conversion.
Therefore, to sum up, the unspent sorbent recirculation
increases the utilization of sorbent because it provides multiple
exposures in the gas sinus. As a result, the solid phase recirculation reduces the mass flow of fresh hydrated lime that is inserted
in the process and thus reduces the fresh sorbent cost and the total
residue generated. This effect from the recirculation is even more
marked when fly ash is precollected upstream from the in-duct
process, regardless of the fresh Ca/S molar ratio.
Fig. 9 illustrates the effect of relative humidity when there is a
precollection of fly ash and compares the once-through case with
the recirculation case. As can be seen, an increase in the relative
humidity leads to higher SO2 removal efficiencies since the reaction
rate is faster. The effect is clear. Thus, for a gas nearly saturated with
a relative humidity of 90% (corresponding to a temperature about
2 or 3 ◦ C above the adiabatic saturation temperature), the desulfurization efficiency increases about 10 percentage points as compared
to when there is a relative humidity of 50% (corresponding to an
approach to the adiabatic saturation temperature (AST) around 12
or 13 ◦ C). However, for changes of lower magnitude, this effect is
not as strong as expected, especially if this result is compared with
the experimental ones illustrated in Fig. 3. As shown, from 50% to
60% (equivalent to about a decrease of 3 ◦ C, in the approach to AST),
Fig. 9. Effect of the relative humidity on the desulfurization efficiency for different Ca/S ratios (cases run with fly ash precollection and RR = 10).
580
F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
Fig. 10. Model validation: desulfurization efficiencies calculated and measured.
the gain in the SO2 removal efficiency is only 2–4 percentage points.
In fact, in the simulation tool, the increase in the gas temperature
due to the reaction heat (exothermic reaction) is considered. Thus,
temperature increases as desulfurization efficiency increases. For
the sensitivity analysis, relative humidity decreases along the duct
as much as 9–12 percentage points, corresponding to an increase
in the gas temperature of around 2–4 ◦ C. This is in agreement with
results from other pilot plant studies [19,20]. In a real plant, the
dew point at the outlet of the duct should be controlled, i.e. relative humidity at the duct inlet will be higher than that set at the
duct outlet. Therefore, relative humidity at the duct inlet could be
increased up to 80–90%, approximately.
Finally, as a model validation, some of the experimental tests
were reserved to compare their results with those obtained using
the model proposed. Fig. 10 shows the measured versus the calculated removal efficiency for the duct. It can be seen that almost
all the points lie in a narrow ±5% band. Moreover, the standard
deviation of the predicted values of dimensionless SO2 concentration related to the experimental ones was 0.032, with a correlation
coefficient for data fitting of 0.957.
Although results reported under operating conditions outside of
the real operating window must be viewed very cautiously, since
model parameters were fitted on tests conducted under pilot plant
conditions, the conditions required to attain higher values of SO2
removal than those obtained in the pilot plant could be estimated,
tentatively, by means of simulation. Thus, to achieve a 90% SO2
removal in the duct, the model estimates a hydrated lime with
20 m2 /g of BET area, a recirculation ratio of 12, a Ca/S molar ratio of
2.5 and a relative humidity of 90%, on the basis of the data reported
in Table 3.
If new improvement options for the process with a focus on
increasing the desulfurization efficiency are considered, such as
a reactivation of the total sorbent (fresh and partially converted)
being injected into the duct, the use of a hygroscopic additive or
the direct humectation of solid in the pugmill, in such a way that
the sorbent would be injected with considerably more water, the
kinetic model should be revised.
lyzing results and aiding in the design of a DSI process. A sensitivity
analysis was carried out to check the behavior of the model under a
variety of conditions. The sensitivity results highlight the influences
of the Ca/S molar ratio, the relative humidity, the fly ash precollection and the recirculation ratio of the partially converted sorbent
for prediction of the SO2 removal efficiency and sorbent conversion.
Fly ash precollection proved to have a significant beneficial effect on
the desulfurization yield. Thus, using a medium-efficiency particulate collector, such as a cyclone or a small ESP, makes the collection
of saleable fly ash possible and reduces both the amount of final
solid disposal and the recirculation flow. The recirculation of the
partially converted sorbent results in the reduction of the required
Ca/S ratio, thus increasing the sorbent utilization and reducing the
consumption of the expensive calcium hydroxide sorbent.
An extensive experimental program allowed us to fit a kinetic
model from one more general formulation, and to validate the
in-duct sorbent injection model of desulfurization. The predicted
values agree reasonably well with the available experimental data,
and the relationships in the presented model have been verified.
Although, this model was fitted specifically for our in-duct pilot
plant, it may be used with confidence in commercial DSI units as it
was designed and implemented according to widely accepted engineering rules in this field. The model was built in an open structure
so that in the future it could be changed and extended.
For future research, some simulator aspects can be enhanced,
such as the modeling of the particle device collector (from the
desulfurization point of view), inclusion of an economic module
and the consideration of the particle size distribution, taking into
account the attrition and the molar volume change.
Appendix A
In this supplementary section, other relevant equations
included in the model are shown.
A.1. Mass flow rates for solids
Assuming that, although the entire reactive solid contributes
to the desulfurization efficiency, a part of it is not collected, the
following results are reached:
• Mass flow rate of the reactive solid leaving the duct:
ṁw=1 = (ṅf + ṅr ) ·
·
A simple realistic model for the in-duct desulfurization process
was developed. It was conceived as an approach useful for both ana-
(kg/s)
(A1)
• Mass flow rate of the reactive solid leaving the ESP with the
cleaned gas:
ṁs,EF =
[(ṅf + ṅr ) · (1 − (EF /100)) · MWr ]
(kg/s)
1000
(A2)
• Mass flow rate of the reactive solid collected in the ESP:
ṁcoll,EF =
[(ṅf + ṅr ) · (EF /100) · MWr ]
(kg/s)
1000
(A3)
• Mass flow rate of the reactive solid purged from the system, distinct of ṁs,EF :
ṁpurg =
6. Conclusions
MWw=1
1000
MWw=1
MWlime
= ṅf 1 + R′ ·
1000
MWr
[(ṅf + ṅr ) · (EF /100) − ṅr ] · MWr
(kg/s)
1000
(A4)
• Global balance for the reactive solid in the system:
ṅf ·
MWr
= ṁs,EF + ṁpurg
1000
(A5)
F.J. Gutiérrez Ortiz, P. Ollero / Separation and Purification Technology 62 (2008) 571–581
• Mass flow rate of the reactive solid recirculated to the duct:
′
ṁr = R · ṁf (kg/s)
(A6)
• Mass flow rate of the fly ash recirculated:
ṁr,ash = R′ ·
MWlime
· ṁf,ash (kg/s);
MWr
ṁf,ash is a input data
(A7)
A.2. Volumetric fractions
The volumetric fraction of gas in the duct is:
εg =
1
1+((ṅf + ṅr )/(lime · Qg,av )) + ((ṁf,ash + ṁr,ash )/(ash · Qg,av ))
m3 gas
m3 duct
(A8)
and the volumetric fraction of the reactive solid (hydrated lime)
inside the duct is:
εs =
ṅf + ṅr
ug · lime · A
m3 lime
m3 duct
(A9)
Likewise, the volumetric fraction of the fly ash in the duct is:
εash
ṁf,ash + ṁr,ash
=
ug · ash · A
m3 flyash
m3 duct
(A10)
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