A simulation tool for aerosol formation during sulphuric acid absorption in a gas cleaning process

Journal of Aerosol Science 41 (2010) 1066–1079

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A simulation tool for aerosol formation during sulphuric acid absorption in a gas cleaning process A. Wix, L. Brachert, S. Sinanis n, K. Schaber Karlsruhe Institute of Technology (KIT), Institut f¨ ur Technische Thermodynamik und K¨ altetechnik, Engler-Bunte-Ring 21, 76131 Karlsruhe, Germany

a r t i c l e i n f o

abstract

Article history: Received 15 May 2009 Received in revised form 24 August 2010 Accepted 25 August 2010

A simulation tool has been developed to predict sulphuric acid aerosol formation in typical industrial absorption processes for gas cleaning. The underlying model comprises homogeneous nucleation and the growth of a polydisperse droplet collective under the special circumstances of a gas–liquid contact device where heat and mass transfer processes between the bulk phases take place simultaneously. The model is applied to a hot flue gas (200 1C) with sulphuric acid concentrations between 5 and 100 mg m  3 (STP) (STP: standard temperature and pressure). The simulation yields high droplet number concentrations up to 1016 m  3 especially for low gas inlet concentrations of sulphuric acid (5 mg m  3 (STP)), and very small droplet sizes in the range 20–100 nm. The droplet number concentrations decrease and the droplet sizes increase with increasing sulphuric acid inlet concentrations. It is shown that small droplets ( o 20 nm) need relatively high supersaturation for growing. If the saturation in the absorption equipment is not high enough the droplets partially re-evaporate but do not vanish due to the extremely low vapor pressure of concentrated sulphuric acid. The resulting size distributions of the aerosol droplets are not very sensitive with respect to the nucleation model used. This is demonstrated by comparing nucleation models with and without hydrate formation. The new simulation tool allows an estimate of the true sulphuric acid removal efficiency of absorption processes which is often not more than 50% due to aerosol formation. In general, the simulation results enable a deeper insight in the mechanisms of aerosol formation and behavior in absorption processes. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Sulphuric acid aerosols Absorption Process simulation Homogeneous nucleation

1. Introduction When the thermodynamic state of gas–vapor mixtures containing vapors of sulphuric acid and water changes, there is an appreciable tendency for aerosol formation, caused by the extreme hygroscopic properties of sulphuric acid. Consequently, high degrees of supersaturation may arise and aerosol formation will be initiated by homogeneous nucleation. Also, sulphuric acid nucleation plays an important role in tropospheric particle formation. This is why the numerous publications dealing with homogeneous nucleation of H2SO4–H2O mixtures are restricted mostly to temperatures and acid concentrations at tropospheric conditions. In typical industrial exhaust or flue gases, however, sulphuric acid concentrations may be orders of magnitude higher ( 420 mg m  3 (STP)) than under tropospheric conditions, and their temperatures are usually in the range 20–200 1C.

n

Corresponding author. E-mail addresses: [email protected] (L. Brachert), [email protected] (S. Sinanis), [email protected] (K. Schaber).

0021-8502/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2010.08.007

A. Wix et al. / Journal of Aerosol Science 41 (2010) 1066–1079

Nomenclature A ci cN d DG J K M n_ N_ N(1) P q_ r S S T V x y z

interfacial area (m2) mean thermal molecule velocity (m s  1) number concentration (m  3) droplet diameter, (m) change of the Gibbs energy for cluster formation (J) nucleation rate (m  3 s  1) collision frequency (m  3 s  1) molar mass of component (kg kmol  1) specific mole flux (kmol m  2 s  1) mole flux (kmol s  1) monomer number concentration (m  3) pressure (Pa) specific heat flux (J m  2 s  1) radius of a cluster/droplet (m) degree of saturation (dimensionless) degree of saturation in a mixture (nucleation theory), dimensionless temperature (K) molar volume of a mixture (m3 mol  1) mole fraction in a condensed phase (dimensionless) mole fraction in the gas phase (dimensionless) axial coordinate of the contact device (m)

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Constants k R

Boltzmann constant, (1.38  10  23 J K  1) general gas constant (8.314 J mol  1 K  1)

Greek letters

b

s

rate for a cluster to gain a molecule (m  2 s  1) surface tension (N m  1)

Indices A G hom i,k j K K crit L Ph S Dew

aerosol gas phase homogeneous index for a compound index for a droplet class number of components coolant phase critical cluster liquid phase interfacial area saturation/equilibrium dew point

The removal of sulphuric acid from exhaust gases is mainly carried out by absorption processes in gas–liquid contact devices such as packed-columns, jet scrubbers, or spray towers. There, exhaust gases are brought into intense contact with an aqueous scrubbing solution, and in principle three transfer processes simultaneously take place between both phases:

 mass transfer of H2SO4 from the gas into the liquid phase (absorption of H2SO4),  mass transfer of H2O from the liquid into the gas phase (evaporation of water and humidification of the gas phase, if the exhaust gas is not saturated, which is normally the case), and

 heat transfer between both phases (mainly from the gas to the liquid phase decreasing the temperature of the gas phase). During these transfer processes the dew point in the gas flow may be exceeded, the gas becomes supersaturated, nucleation takes place, and acid droplets are formed. Aerosol formation in exhaust gas cleaning processes is highly undesired, as the aerosol often contains a considerable amount of the pollutant. The droplets are carried with the gas stream out of the process, resulting in the exceeding of emission limits or operational problems in downstream equipment. In the chemical industry sulphuric acid absorption devices are usually equipped with aerosol precipitators, often causing expensive investment or operational costs. The design of aerosol precipitators is still based mostly on empirical correlations associated with huge uncertainties, because there are currently no reliable and validated methods available for the quantitative prediction of number concentrations and droplet diameters of technical sulphuric acid aerosols. Additionally, validated strategies for aerosol prevention so far do not exist in process technology. The basic physical principles of sulphuric acid aerosol formation under tropospheric and technical conditions are similar and the initial nucleation step can be described using the same models of the classical theory of homogeneous nucleation. But the initial thermodynamic state and growth conditions in gas–liquid contactors are completely different. In gas cleaning processes often high degrees of supersaturation and consequently high nucleation rates occur, resulting in high droplet number concentrations (41014 m  3), and droplet diameters which are smaller than 200 nm (Sinanis, Wix, Ana, & Schaber, 2008). Aerosol formation in gas–liquid contact devices is a very rapid process which takes place within less than one second. Hence, the growth of aerosol droplets is finished within the typical residence time in a contact device which is usually between 2 and 5 s. That is why special simulation tools are required to describe absorption processes with sulphuric acid aerosol formation. ¨ In recent years the simulation program AerCoDe was developed in cooperation with the ’’Konrad-Zuse-Zentrum fur Informationstechnik, Berlin’’ for the calculation of aerosol formation during acid absorption and it was successfully applied

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¨ ¨ to heterogeneous nucleation processes (Korber & Schaber, 1994; Ofenloch, 2004; Schaber, Korber, Ofenloch, Ehrig, & Deuflhard, 2002). Within the continued development of AerCoDe, a polydisperse model for aerosol formation induced by binary homogeneous nucleation was implemented. The new model was first applied to the calculation of aerosol formation during the evaporation of hot water into a cold gas stream (Wix, Schaber, Ofenloch, Ehrig, & Deuflhard, 2007). The first simulation results for binary homogeneous nucleation which explain and quantify the formation of sulphuric acid aerosols in a gas–liquid contact device are presented here. 2. State of the art on sulphuric acid aerosol formation Due to its significance in nature and technology H2SO4–H2O is a convenient and commonly used system for the investigation of homogeneous nucleation theories. The applications stem from atmospheric physics on the one hand (Shaw, 1989; Vancassel, Sorokin, Mirabel, Petzold, & Wilson, 2004; Yue, 1981; Zhao & Turco, 1995) and industrial processes on the other hand (Amelin, 1967; Schaber, 1995). So far there are only few studies available in the latter field, whereas numerous investigations covering atmospheric conditions can be found in the literature. 2.1. Sulphuric acid absorption processes The first investigation of aerosol formation during the absorption of sulphur trioxide in aqueous sulphuric acid solutions was carried out by Amelin (1967). Schaber pointed out that the generation of supersaturation, and consequently fog formation in absorption processes, is favored if high-strength inorganic acids like HBr, HCl, HNO3, and H2SO4 are absorbed in aqueous solutions (Schaber, 1995). Ana and Sinanis investigated the fog formation during H2SO4 absorption in a flue gas cleaning pilot plant (Sinanis et al., 2008). They used a three-wavelength-extinction measuring method (3WEM) for the determination of the droplet number concentration after droplet enlargement in an additional condensation step. The original properties of the volatile aerosol could not be measured simultaneously with this in-situ measuring technique, because it fails at droplet sizes below 200 nm for non-absorbent droplets. Other optical in-situ measuring methods for volatile aerosols with droplet number concentrations 4108 cm  3 and droplet sizeso200 nm are not available. Measurements using condensation particle counters after dilution of the aerosol (and consequently evaporation of water from the aerosol droplets) enable the determination of number concentrations but not the droplet size distribution under actual process conditions. That means, up to now no experimental method exists which allows a complete characterization of sulphuric acid aerosols under real industrial conditions. 2.2. Homogeneous nucleation of sulphuric acid and water Despite several disadvantages, the classical nucleation theory is still the most important approach for the theoretical description of a spontaneous phase transition. ¨ For pure components it is based on the work of Volmer and Weber (1926), Farkas (1927), Becker and Doring (1935), Frenkel (1955), and Zeldovich (1942). For binary systems, the basics of the theory were mainly investigated by Flood ¨ (1934), Neumann and Doring (1940), Reiss (1950), Binder and Stauffer (1976), and Stauffer (1976). The theoretical description of sulphuric acid nucleation is also based on the classical nucleation theory and the first investigations showed that very low partial pressures of sulphuric acid (  10  7 Pa) are needed for nucleation to take place (Doyle, 1961; Mirabel & Katz, 1974). Several researchers found that in the presence of water vapor, the majority of sulphuric acid molecules exist in the form of hydrates consisting of one sulphuric acid molecule and a variable number of water molecules (Doyle, 1961; JaeckerVoirol & Mirabel, 1988, 1989; Jaecker-Voirol, Mirabel, & Reiss, 1987). Consequently, the formation of hydrates has to be considered for cluster formation, resulting in an extension of the classical theory. The abbreviation CTH is used for the classical nucleation theory considering hydrate formation. In general, hydrate formation has a stabilizing effect on the gas–vapor-mixture, as the nucleation rate is reduced (Jaecker-Voirol & Mirabel, 1988, 1989; Jaecker-Voirol et al., 1987). From the theoretical point of view, hydrate formation can be described in analogy to cluster formation during nucleation (Heist & Reiss, 1974). In order to reduce the computational efforts, several parameterizations for the nucleation rate are available, which are ¨ ¨ based on the classical theory (Kulmala, Laaksonen, & Pirjola, 1998; Vehkamaki et al., 2002; Vehkamaki, Kulmala, & Lehtinen, 2003). Apart from the classical approach, the cluster population can be described by the consideration of cluster-clustercollisions (Arstila, 1997; Sorokin, Vancassel, & Mirabel, 2005). However, due to their complexity these models cannot be used in process simulations so far. Despite extensive theoretical studies, only few experimental investigations are described in the literature. The first ones were carried out by Reiss, Margolese, and Schelling (1976) and Boulaud, Madelaine, Vigla, and Bricard (1977). Some researchers found that the classical theory including hydrate formation reproduces the experimental data satisfactorily

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(Mirabel & Clavelin, 1978; Viisanen, Kulmala, & Laaksonen, 1997). By contrast, Wyslouzil, Seinfeld, Flagan, and Okuyama (1991) report that their experimental data do not agree with CTH (CNT including hydrate formation) at all. Ball, Hanson, and Eisele (1999) compared experimental data with a parameterization based on the CTH (Kulmala et al., 1998) and came to the conclusion that the theory does not describe the influence of the key variables correctly. Obviously, there is still need for a validation of the classical nucleation theory, which is, however, difficult to achieve. The nucleation rate is very sensitive to the state of the gas phase and therefore the input data (i.e. temperature and concentrations of the condensing components) have to be known very accurately. 3. Simulation tool AerCoDe The detailed description of the simulation tool AerCoDe including the governing equations was already published in Ehrig, Ofenloch, Schaber, and Deuflhard (2002) and Ofenloch (2004) and will be omitted here. In the following, the focus is laid on the description of the physical basis of the model including the fundamental assumptions. 3.1. Phase equilibrium of the H2SO4–H2O system The vapor–liquid equilibrium of the sulphuric acid–water system is the major basis to model the gas-to-particle conversion and often a source for uncertainties. The calculation of the phase equilibrium of the H2O–H2SO4 system follows the suggestions of Gmitro and Vermeulen (1964) and Ayers, Gillett, and Gras (1980). The partial pressures are calculated based on the equality of the chemical potentials of the components in both phases. The vapor phase is assumed as an ideal gas. The liquid phase is calculated with the help of the activity which is evaluated using the partial molar properties collected by Giauque, Hornung, Kunzler, and Rubin (1960). In the present approach the partial molar heat capacity, the partial molar enthalpy and the partial molar Gibbs enthalpy are expressed by cubic splines as functions of the weight percentage of sulphuric acid in the mixture. Concerning the pure component term, Ayers et al. (1980) showed that the approach of Gmitro and Vermeulen (1964) to use the enthalpy and the entropy of evaporation at 298.15 K yields inaccurate results as the experimental data that they used were outdated. Hence, Ayers performed experiments in the temperature range 338–445 K and re-evaluated these caloric pure component quantities. In contrast to this method in the present approach the pure component vapor pressure of sulphuric acid is calculated directly with an equation fitted to the experimental data tabulated in Perry (1997) for pure sulphuric acid in the temperature region from 0 to 280 1C. For the vapor pressure of water an empirical equation is used. The deviation from the tabulated values of Wagner and Kretzschmar (2007) in the temperature range from 20 to 150 1C is smaller than 0.17%. The equations for the calculation of the vapor pressures of water and sulphuric acid can be found in the appendix. The differences between the different calculation methods can be seen in Fig. 1. The partial pressures of sulphuric acid over aqueous solutions with different weight percentages of sulphuric acid calculated with the approaches of Gmitro and Vermeulen (1964), Ayers et al. (1980) and this work are opposed to the experimental data given by Perry (1997) at two different temperature levels (20 and 120 1C). Obviously, the method used in this work confirms the statement of Ayers et al. (1980) that the partial pressures calculated by Gmitro and Vermeulen (1964) are about one magnitude too high. The conformity of the present calculations with experimental data from Perry in the whole range of

Fig. 1. Partial pressure of sulphuric acid at 20 and 120 1C in the water–sulphuric acid system.

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concentrations is visible. Thus, the partial pressures of sulphuric acid calculated with the method used in this work are corresponding to data which are actually considered as reliable. 3.2. Process modeling and simulation In process engineering, gas–liquid contact devices like columns, condensers, or venturi scrubbers are commonly used for the transfer of heat and mass between a gas and a liquid phase. The interfacial area in columns is usually provided by internals, e.g. a structured or packed bed, and ensures an intense contact of gas and liquid phase. Fig. 2 shows a simplified flow sheet of a cocurrent absorption process (gas scrubbing) with liquid circulation which is typical for flue gas cleaning. The acid component is dissolved and concentrated in the scrubbing liquid. In order to keep the concentration in the liquid and also the liquid level constant, fresh water is fed and a part of the aqueous (acid) solution is continuously or batchwise discharged. The absorption process takes place along the active gas–liquid contact interface A in the packing section of the absorber on which the circulating liquid is distributed by a spray nozzle. As both phases are neither in thermal nor in material equilibrium at the entry of the column the states of the gas and liquid phases change due to the simultaneous heat and mass transfer along the interface A, or length z, respectively. In sulphuric acid absorption processes for hot flue gases the absorption of the pollutant in the scrubbing liquid is overlapped by the quenching of the gas phase and the partial evaporation of the scrubbing liquid. The gas phase becomes supersaturated when the dew point line in the binary mixture H2O–H2SO4 is crossed at the actual state of the gas phase corresponding to a certain length z. If the critical degree of saturation is exceeded, a spontaneous phase transition and consequently aerosol formation takes place. A supersaturated (metastable) fluid phase is a necessary precondition for the spontaneous phase transition and the key variable for its quantitative description is the degree of saturation, S. It can be defined as the ratio of the sum of the partial pressures of the condensable components and the dew point pressure of the gas phase: PK PK p ðT G ,y1 ,. . .,yK1 Þ p ðT G ,y1, . . .,yK1 Þ S¼ i¼1 iG ¼ PKi ¼ 1 i ð1Þ G pDew ðT ,y1 ,. . .,yK1 Þ p i ¼ 1 is ðT ,y1 ,. . .,yK1 Þ Eq. (1) is a simple descriptive definition of the degree of saturation, as it shows that the gas phase is supersaturated if the amount of condensable components exceeds the equilibrium quantity. It can be calculated without the use of a nucleation theory, solely from the state of the gas phase. Another definition of the saturation ratio results from the classical nucleation theory using the saturation ratios of both components, S1 and S2, and the composition of the critical cluster xcrit (Flood, 1934): crit S ¼ Sx1crit S1x 2

ð2Þ

Although the calculations are rather different, it is shown in the results section that both definitions yield similar values for the degree of saturation. As soon as the critical degree of saturation is exceeded, nucleation takes place and is followed by the growth of the nuclei to droplet size. The process model in the simulation program AerCoDe is based on a locally one-dimensional description of the gas and liquid flow in the contact apparatus, neglecting gradients in radial direction (plug flow). Therefore, potential abscissas for the calculations are the length of the device, z, or the interfacial area provided for heat and mass transfer, A. The structure of the simulation program is illustrated in Fig. 3 with a differential volume element. Five different balance volumes for the gas phase, the liquid phase, the phase interface, the aerosol, and the cooling phase are considered. With the cooling phase, heat losses or the cooling by an external liquid phase in the apparatus can be

Fig. 2. Quench column for hot flue gases as a typical gas–liquid contact device.

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Fig. 3. Simulation program AerCoDe: differential volume element including the five balance volumes, the heat and mass fluxes between the phases and the source/sink terms for the calculation of aerosol formation in gas–liquid contact devices.

1

2

j

crit

Fig. 4. Formation of different droplet classes by homogeneous nucleation in the nucleation window.

simulated. For each of these balance volumes, non-stationary differential mass and energy balances are set up and solved. By the source and sink terms for nucleation and growth, as well as by the heat and mass transfer in between the phases, the change of mass and energy of each phase in the interval dz is calculated. The heat and mass transfer between gas and liquid phase is calculated using the phase interface as a separate balance volume. The temperature and concentration gradients are located therein and the balance variables in the bulk of the adjacent phases are solely a function of the axial coordinate in the contact device. It is assumed that thermodynamic equilibrium exists at the interface (see Chapter 3.1) and that there is no accumulation or conversion of mass and energy. For the calculation of the mass transfer coefficients, empirical correlations for different internals in the contact device are used (Billet, 1991; Onda & Okumoto, 1968). The calculation of the heat transfer results from the use of the Chilton– Colburn-analogy (Chilton & Colburn, 1934). In case of large mass fluxes across the gas–liquid-interface, the Stefan- and Ackermann-correction factors (Ackermann, 1937; Taylor & Krishna, 1993) for the transfer coefficients are taken into account. ¨ Deviations from the ideal plug flow in the contact device are considered with the axial dispersion (Tsotsas & Schlunder, ¨ 1988; VDI-Warmeatlas, 2006; Winterberg, 2000). An external cooling of the contact device or heat losses is realized by a heat flux between liquid and cooling phase. For the aerosol it is assumed that the droplets do not influence each other directly, but indirectly via the heat and mass transfer with the gas phase (Carstens & Zung, 1970; Vogt, 2001). Each droplet is ideally mixed and does not exhibit any temperature or concentration gradients. Apart from the nucleation process, the nuclei formed grow to droplet size and continuously reduce the degree of saturation of the gas phase. The nucleation rate is an extremely sensitive function of the degree of saturation and a simple monodisperse approach, as it has been proven successful for heterogeneous nucleation, cannot be used. Instead, polydisperse modeling is necessary, where the aerosol is divided into an arbitrary number (j) of discrete droplet classes, which in practice is only limited by the computing power. Each droplet class is allocated a fixed position in the contact

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device where it originates and grows subsequently. The section of the column where the different droplet classes are established is defined by the state of the gas phase: it is where the degree of saturation exceeds the critical one Scrit. Within this the so-called nucleation window the nuclei are formed with the size and composition of the critical cluster, which result from the nucleation theory used. The number concentration of a droplet class is calculated by the integration of the nucleation rate. The polydisperse modeling is schematically illustrated in Fig. 4. The critical degree of saturation is defined for a nucleation rate of 1010 m  3 s  1 (Schaber, 1995). Considering residence times in the range of seconds, the number concentration would be about 1010 m  3, which is a relevant and detectable number concentration in technical processes. For the calculation of the droplet growth in gas–liquid contact devices, the temperature and concentration profiles around the droplet are of little importance. Therefore, simple approaches based on the laws of Fick and Fourier are chosen in order to calculate the heat and mass fluxes between gas phase and aerosol droplets. The growth of the droplets is described as diffusion of the condensable components through a concentrically spherical surface (Fuchs, 1959; Maxwell, 1990; Wagner, 1982). The latent heat of condensation is released at the droplet surface and increases the droplet temperature on the one hand. On the other hand it is compensated by thermal conduction to the gas phase (Wagner, 1982). For small droplets it is taken into account that the droplet growth cannot be calculated by diffusion and heat conduction in the continuum. Hence, the heat and mass fluxes are corrected with the Knudsen correction factor (Fuchs & Sugutin, 1970; Smirnov, 1971). The vapor pressures of sulphuric acid and water at the droplet surface are calculated with the Gibbs–Thomson equation (Thomson, 1870), which takes into account that the vapor pressure is increased when the surface is curved. In the population balance for each droplet class the terms for nucleation and growth by condensation are included. The nucleation rate is calculated as follows: rcrit ¼

2sV

ð3Þ

RT ln S 2

DGcrit ¼

16 s3 V 4 2 p ¼ psrcrit 3 ðRTÞ2 ðln SÞ2 3

  DGcrit J ¼ K exp  kT

ð4Þ

ð5Þ

The formula for the nucleation rate consists of two parts: the collision frequency K and the exponential term, which can be interpreted as the probability for the formation of a critical cluster. Especially the latter term is extremely sensitive to the state of the gas phase. If the concentration of component i massively exceeds the concentration of the other nucleating component k, the collision frequency can easily be calculated (Mirabel and Katz, 1974): 2 K ¼ bi ðni ð1Þ þ nk ð1ÞÞ4prcrit

ð6Þ

where ni(1) and nk(1) are the concentrations of the monomers, and bi is the rate of molecules impinging onto the surface of a cluster. It can be calculated from the mean thermal molecule velocity, taken from kinetic gas theory: sffiffiffiffiffiffiffiffiffiffiffiffi 1 RT G ð7Þ bi ¼ ni ð1Þci ¼ ni ð1Þ 4 2pMi For the calculation of the nucleation rate the parameterization of Vehkam¨aki et al. (2003), which considers hydrate formation in the gas phase, was also used, and the influence on the droplet size distribution will be shown in Section 4. The deposition of the droplets is not included in the simulation program. The inertial deposition of droplets can be neglected as long as the droplets are small, and it is assumed that the diffusional deposition can be neglected, which seems reasonable for the low residence times. The balance equations and modeling approaches yield a system of partial, differential-algebraic equations, which is converted into a system of ordinary differential equations by the method of lines and solved using the code LIMEX (Ehrig, Nowak, Overdieck, & Deuflhard, 1999). By the chosen space discretisation, the potential points of origin for the droplet classes are set. 4. Results and discussion 4.1. Simulation of sulphuric acid absorption without homogeneous nucleation In this section, the special features of sulphuric acid aerosol formation in a typical flue gas scrubbing process (quench cooler) as shown in Fig. 2 are presented. The basic data used for simulation are shown in Table 1. These operation conditions have been realized in a pilot plant operated in the laboratory of the institute. Preliminary calculations without considering nucleation and droplet growth show the potential for homogeneous nucleation to take place. If the resulting theoretical degree of saturation and the nucleation rate are too low, nucleation will

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Table 1 Basic operation conditions. G ð1CÞ Tinlet

200

G 1 V_ inert gas ðm3 ðSTPÞh Þ

200

rGH2 O, inlet ðkg m3 ðSTPÞÞrGH2 O,inlet =ðkg=m3 ðSTPÞÞ

0.0258

L Tinlet ð1CÞ

49.6

_ L ðkg h1 Þ M

2988

xLacid

0.0

ðdimensionlessÞ p (bar) Dp (mbar)

1.0 7

8E+24

80

S

S 6E+24

J

40

4E+24

20

2E+24

0 0.0

J / (1 / (m³s))

S / - and S / -

60

0E+0 0.5

1.0

1.5

z/m Fig. 5. Theoretical degrees of saturation (definition as pressure ratio (Eq. (1)) and definition according to the nucleation theory (Eq. (2))) and the 3 theoretical nucleation rate in the quench column, standard operation conditions (Table 1), rG ðSTPÞ. H2 SO4 , inlet ¼ 50 mg m

not occur to an appreciable extent, as the residence time in the column is only about 1 s. The theoretical degree of saturation along the length z of the packing section in the absorption column and the theoretical nucleation rate are shown in Fig. 5 for a sulphuric acid inlet concentration of 50 mg m  3 (STP). The theoretical saturation profiles in the quench column were calculated according to Eqs. (1) and (2). Using Eq. (1), the maximum degree of saturation is 69, while the definition according to the nucleation theory (Eq. (2)) yields a maximum value of 54. Therefore, it can be concluded that both definitions yield values in the same order of magnitude, and in the following the more descriptive definition according to Eq. (1) will be used. The theoretical nucleation rate calculated from Eqs. (3) to (7reaches a maximum value of 7.1  1024 m  3 s  1, so that homogeneous nucleation will take place to a significant and observable extent. The theoretical degree of saturation versus the spatial coordinate z in Fig. 5 reaches a maximum value and drops afterwards again. It has to be emphasized that here the decrease of S cannot be explained by nucleation and droplet growth, because a phase transition is not taken into account in this preliminary calculation. The reasons for this phenomenon are the ongoing heat and mass transfer processes between both phases which finally would end at S =1, corresponding to the thermodynamic equilibrium between both phases at infinite values of A or z, respectively. Thus, supersaturation is a local phenomenon in a gas–liquid contact device which vanishes again at infinite values of A. Of course, such high supersaturations and nucleation rates will not actually be reached in the quench column because nucleation and droplet growth will take place very rapidly after exceeding the critical saturation.

4.2. Simulation of sulphuric acid absorption with homogeneous nucleation For the calculation of aerosol formation in the quench column, 12 droplet classes were used. Their diameters are shown as a function of the position in the quench column in Fig. 6. The different droplet classes originate in a very small nucleation window of less than 10 cm in the column. The critical diameters are approximately 2 nm and the mole fraction of sulphuric acid in the critical cluster is approximately 35%. The droplets grow mainly by the condensation of water vapor until diameters between 10 and 180 nm are reached at the quench column outlet. Fig. 6 also shows the total number concentration of all droplet classes, which promptly rises to 3  1015 m  3 within the nucleation window. The real value will be lower, as coagulation is not calculated with the current program version. In order to give a first estimation for the Brownian coagulation, a monodisperse aerosol with a medium droplet size (d =37 nm) was assumed. In this case the

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200

4E+15

d / nm

150

3E+15

cN d

100

2E+15

50

c N / m-3

1074

1E+15

0 0.0

0.5

1.0

1.5

0E+0

z/m Fig. 6. Diameters of the 12 droplet classes and total number concentration of all droplet classes as a function of the position in the quench column, 3 ðSTPÞ. standard operation conditions (Table 1), rG H2 SO4 , inlet ¼ 50 mg m

1.0 hydrate formation

0.8

Q 0/ -

without hydrate formation 0.6 0.4 0.2 0.0 0

50

100

150

200

250

300

d / nm Fig. 7. Cumulative droplet size distribution calculated for the nucleation rate models with and without hydrate formation, standard operation conditions 3 (Table 1), rG ðSTPÞ. H2 SO4 , inlet ¼ 50 mg m

number concentration would be reduced from 1016 m  3 to approximately 5  1014 m  3 within 1 s assuming a constant collision frequency. Considering aerosol formation in the calculations, the maximum degree of saturation is only 4.5 and the maximum nucleation rate is 3.7  1017 m  3 s  1. In this example, the total pollutant concentration (H2SO4) in the quench column outlet is increased by a factor of 240 due to the aerosol formation, and consequently, emission limits could be exceeded if aerosol formation is not considered and the gas cleaning process is calculated based solely on the mechanism of absorption of H2SO4 in the scrubbing liquid. That means in this case the true H2SO4 removal efficiency ðrH2 SO4 ,inlet rH2 SO4 ,outlet Þ=rH2 SO4 ,inlet by absorption is only 69.2% whereas calculations neglecting the influence of aerosol formation yield 99.8%. That is why in industry after the absorption process special precipitation equipment (filters, wet electrostatic precipitators) is used to separate sulphuric acid aerosol droplets. The cumulative droplet size distribution in the quench column outlet is shown in Fig. 7. It can be seen that more than 98% of the droplets are smaller than 65 nm. The reason for these very small droplets in the quench outlet is the extreme phase equilibrium of sulphuric acid and water and also the competition between nucleation and growth. The high supersaturation that is generated in the absorption process is not caused by a large amount of sulphuric acid and water in the gas phase, but by the phase equilibrium (see Eq. (1)). However, the supersaturation is the driving force for the spontaneous phase transition and causes high nucleation rates. On the other hand, droplet growth is dominated by the partial pressure differences of sulphuric acid and water between the droplets and the bulk gas phase. But these driving forces for mass transfer are very low for low vapor species concentrations. Consequently, due to these special thermodynamic conditions in the system, the supersaturation is not preferentially relieved by droplet growth, but instead a lot of new droplets are formed, which in total reduce the supersaturation of the gas phase. And as a huge number of droplets compete for sulphuric acid and water in the gas phase, the single droplet does not grow significantly. By contrast, if the degree of saturation is caused by a large amount of the condensable components in the gas phase, the supersaturation is reduced quickly by the newly formed droplets, which grow significantly. Consequently, the number

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concentration of the aerosol does not get too large and the aerosol is characterized by only few but large droplets. This is for instance the case when hot water is evaporated (Wix et al., 2007). 4.3. Influence of hydrate formation In order to estimate the influence of hydrate formation of sulphuric acid molecules in the gas phase on the nucleation ¨ et al. (2003) was used. It was set up for rate and the resulting droplet size distribution, the parameterization of Vehkamaki gas phase temperatures between 300 and 400 K, relative humidities between 1% and 100% and sulphuric acid concentrations between 3.3  10  10 mg m  3 (STP) and 8.2  10  4 mg m  3 (STP), resulting in nucleation rates between 105 and 1020 m  3 s  1. Although the sulphuric acid concentrations are significantly lower, and in the absence of more suitable models considering hydrate formation, the parameterization is extrapolated to the acid concentrations in flue gas cleaning processes. For the nucleation models with and without hydrate formation, the theoretical nucleation rate in the quench column is shown in Fig. 8 (operation conditions according to Table 1, H2SO4 inlet concentration= 50 mg m  3 (STP)). As expected, the theoretical nucleation rate is reduced due to the coating of sulphuric acid molecules with water molecules. The difference between the maximum theoretical nucleation rates with hydrate formation (3.1  1022 m  3 s  1) and without hydrate formation (7.1  1024 m  3 s  1) is about two orders of magnitude. It should be mentioned that the run of the theoretical nucleation rate in Fig. 8 only appears to be different to the one in Fig. 5 due to the different scales of the yaxis. Considering the actual nucleation rates that include the depletion of saturation by means of nucleation and growth, the difference is even smaller and yields less than one order of magnitude (9.2  1016 and 3.7  1017 m  3 s  1, respectively). In Fig. 8 the run of the actual nucleation rate exhibits a steep nucleation pulse: The nucleation rate drops fast after the initiation of nucleation as the saturation of the gas phase decreases. As expected, the droplet number concentration (Fig. 9) without hydrate formation is higher than calculated with hydration (3  1015 m  3 compared to 1  1015 m  3) due to the higher theoretical nucleation rate. However, the difference is much smaller than for the nucleation rate and results in a factor of only three. The cumulative size distribution in Fig. 7 consequently shows that without hydrate formation it is shifted to smaller droplet diameters. Summarizing from the technical point of view, there is no significant influence on the number concentration when hydrate formation is considered in the nucleation model. So, in the following the nucleation rate model without hydrate formation will be used. 4.4. Influence of the sulphuric acid concentration in the quench column inlet For a parametric study the acid concentration in the inlet of the quench column was varied between 5 mg m  3(STP) and 100 mg m  3 (STP), covering the typical acid concentrations of industrial flue gases. Fig. 10 shows that for the considered acid concentration range, the maximum theoretical degree of saturation calculated without nucleation and growth increases from 30 to approximately 90. It has to be kept in mind, that from the theoretical degree of saturation no

Fig. 8. Theoretical and actual nucleation rate in the quench column for the nucleation rate models with and without hydrate formation, standard 3 operation conditions (Table 1), rG ðSTPÞ. The solid lines represent the theoretical nucleation rates and the dashed lines show the H2 SO4 , inlet ¼ 50 mg m actual nucleation rates (including depletion of saturation by droplet growth).

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4E+15

3E+15

c N / m-3

without hydrate formation

2E+15

hydrate formation

1E+15

0E+0 0.0

0.5

1.0

1.5

z/m Fig. 9. Total droplet number concentration calculated for the nucleation rate models with and without hydrate formation, standard operation conditions 3 (Table 1), rG ðSTPÞ. H2 SO4 , inlet ¼ 50 mg m

100 80

S/ -

60 40 20 0 0

20

40

60

80

100

ρH 2SO 4 / (mg / m 3(STP)) Fig. 10. Maximum theoretical degree of saturation as a function of the H2SO4 inlet concentration, standard operation conditions (Table 1).

c N / m-3

2E+16

1E+16

0E+0 0

20

40

60

80

100

ρH 2SO4 / (mg / m³(STP)) Fig. 11. Total number concentration of all droplet classes in the quench column outlet as a function of the H2SO4 inlet concentration, standard operation conditions (Table 1).

conclusions regarding the resulting aerosol size distribution can be drawn. It solely shows the potential for nucleation, but the resulting aerosol size distribution is always a product of nucleation in combination with droplet growth. Considering nucleation and growth in the simulations gives the total number concentration of all droplet classes, which is shown in Fig. 11 as a function of the H2SO4 inlet concentration. It can be seen that if the acid concentration in the inlet is increased, the total number concentration of the droplets decreases. In principle, that was unexpected, as for higher acid

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1.0 5 mg /m³(STP) 0.8 25 mg/m³(STP) 100 mg/m³(STP)

Q0 / -

0.6 0.4 0.2 0.0 0

50

100

150

200

250

300

d / nm Fig. 12. Cumulative droplet size distribution in the quench column outlet for various H2SO4 inlet concentrations, standard operation conditions (Table 1).

concentrations the maximum theoretical degree of saturation and consequently the theoretical nucleation rate are higher, which should result in higher total number concentrations. The explanation for this result can be found looking at Fig. 12, which displays the cumulative droplet size distributions for the inlet concentrations 5, 25, and 100 mg m  3 (STP). The comparison shows that the droplet diameters increase when the acid concentration is increased. Obviously there is a larger potential for droplet growth, which is caused by the larger partial pressure of the acid in the gas phase. The phenomenon is at first surprising, but the sulphuric acid flux to a single droplet is directly proportional to the number of molecules which are available in the gas phase. Also, as sulphuric acid is extremely hygroscopic, there is always a flux of water molecules accompanying the acid molecules. Both mass fluxes result in a more significant droplet growth when the acid concentration in the gas phase is higher. That is why for higher acid concentrations the droplets become larger compared to low acid concentrations, and the number concentration (Fig. 11) is smaller.

5. Conclusions and significance The simulation tool AerCoDe in his extended version allows the prediction of sulphuric acid aerosol formation in industrial absorption processes initiated by homogeneous nucleation. Nucleation rates are considerably high under typical operating conditions in gas–liquid contact devices. That is why the aerosol resulting from homogeneous nucleation consists of a large number concentration (  1015–1016 m  3) and comparably small droplets in the range 50 nm. This has been demonstrated for the operating parameters of a typical flue gas cleaning process. Flue gases always contain particles with number concentrations in the range 1012 m  3, which serve as condensation nuclei. Thus, sulphuric acid aerosol formation is always a process in which both, heterogeneous and homogeneous nucleation take place. But due to the extreme hygroscopic properties of H2SO4 and the resulting high supersaturations of the gas phase during an absorption and quench process homogeneous nucleation is the dominating mechanism (Sinanis et al., 2008). Thus, it is justified to focus on homogeneous nucleation in this case. The sensitivity analysis on hydrate formation shows that the actual nucleation rate considering hydrate formation is only less than one order of magnitude lower. With constant sulphuric acid concentrations in the gas phase, this results in a three times lower number concentration and cumulatively larger droplet diameters. The simulations also show that, with higher sulphuric acid concentrations in the quench column inlet and consequently higher theoretical degrees of saturation, the droplet number concentration is lower. This is unexpected, but it can be explained with the comparably larger droplet growth rate due to the higher sulphuric acid concentrations. This example shows that nucleation and droplet growth should not be regarded separately. The new simulation tool allows to estimate the true removal efficiency of sulphuric acid in absorption processes which is often not more than 50% due to aerosol formation. So far it is not possible to compare the simulation results of sulphuric acid aerosol formation with experimental data because those are not yet available. In ongoing experimental investigations the number concentrations of sulphuric acid aerosol droplets at different gas inlet concentrations will be measured and compared with theoretical results. But applying this method only number concentrations of aerosols can be measured in the sulphuric acid–water system because the aerosol droplet sizes decrease by evaporation of water if the aerosol sample is diluted by air. Nevertheless, using the simulation tool AerCoDe the actual droplet size distribution in various thermodynamic states of a process can be estimated if the number concentration is fitted to the experimental results. Thus, the simulation tool which is described here can also serve as a base for a complete characterization of sulphuric acid aerosols.

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Appendix Vapor pressure of H2O: pH2 O B ¼ A C lnðTÞ þ DT 2 T Pa Vapor pressure of H2SO4:   pH SO B ln 25 4 ¼ exp A TC 10 Pa ln

with T in Kelvin

A B C D

H2O

H2SO4

66.36704 6992.61255 6.15866 2.65735E  06

11.90577 7430.42956 39.72264 –

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Further reading Winterberg, M. (2000). Modellierung des W¨ arme- und Stofftransports in durchstr¨ omten Festbetten mit homogenen Einphasenmodellen. Fortschritt-Berichte VDI ¨ Reihe 3 Nr. 654. Dusseldorf: VDI-Verlag.