Separation and Purification Technology 62 (2008) 571–581 Contents lists available at ScienceDirect 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. 572 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 574 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. 576 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. 578 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) References [1] A. Irabien, F. Cortabitarte, M.I. Ortiz, Kinetics on flue gas desulfurization at low temperature: nonideal surface adsorption model, Chem. Eng. Sci. 47 (7) (1992) 1533–1543. [2] J.A. Cole, G.H. Newton, J.C. Kramlich, R. Payne, Global evaluation of mass transfer effects, in: Duct Injection Flue Gas Desulfurization, Final Report, U.S. DOE, PETC Contract n◦ DE-AC22-88PC88873. 1990. 581 [3] R. Beittel, R.S. 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