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Ind. Eng. Chem. Res. 2000, 39, 3042-3050
Gas-Liquid Equilibrium-Operational Diagram: Graphical Presentation of Absorption of SO2 in the NaOH-SO2-H2O System Taking Place within a Laboratory Absorber Martin Zidar Hacquetova 8, 1000 Ljubljana, Slovenia
A gas-liquid equilibrium-operational diagram showing the relationships between the concentration of total SO2, combined SO2, and true free SO2, iso-pH, and isopartial pressure of SO2 is presented as a useful tool for graphically presenting the absorption of SO2 in the NaOH-SO2H2O system. The graphical presentation of the absorption of SO2 on an industrial scale is studied on a laboratory scale using a falling film reactor by taking into account scaled-down criteria for the spray culumns of liquid-gas contactors. An example is given where the bulk and the interfacial compositions along the contactor during the absorption of SO2 into 0.005 M NaOH at T ) 298 K are simulated using an absorption model based on the film theory of gas absorption. This is then graphically presented in a design diagram with the concentration of Na+ as a parameter, which is reconstructed from the gas-liquid operational diagram for the NaOHSO2-H2O system. The enhancement factor, the overall mass-transfer coefficient, the resistance to the absorption of SO2 in the liquid and in the gas phase, and the fraction of the liquid resistance along the falling film reactor are also calculated. Introduction The potential hazard of SO2 to human health and its implication in acid rain formation and forest decline have resulted in strict regulations being imposed on coal-fired power plants in an attempt to reduce SO2 flue gas emissions. Fundamental to the understanding and the optimization of industrial-scale flue gas desulfurization wet processes is the simulation of absorbers on a laboratory scale and the development of computer models. Various types of laboratory models can be used for simulating absorbers under different conditions; these include falling films, rotating drums, jets, stirred reactors, and a string of the disks. Criteria that enables the selection of the best model for simulating the operation of a particular industrial gas-liquid contactor are presented in the work of Laurent and Charpentier.1 Important sources of information concerning the chemistry of aqueous solutions of sulfur dioxide and sulfites are studies made within the pulp and paper industries. Developments in sulfite technology such as high-yield, two-stage, bisulfite and alkaline sulfite pulping have allowed the use of sodium, magnesium, calcium, and ammonium bases. To express the concentrations of base and base-bound bisulfite ions, the terms free SO2, combined SO2, and total SO2 used for sulfite solutions are defined by the Technical Association of the Pulp and Paper Institute.2,3 Another important contribution for selecting the appropriate numerical simulation for absorption of SO2 with chemical reaction is made by Glasscock and Rochelle, who compared the predicted effects of chemical reaction on the absorption process for some of the rigorous models (film theory, penetration theory, surface theory, and eddy diffusity theory) and approximate methods. They concluded that, in light of the shorter computation time involved for the steady-state theories and the inherent uncertainty at the present time in the
actual mass-transfer mechanism at a gas-liquid interface, the steady-state model is the most useful for interpreting experimental data and describing acid gastreating process design.4 More recently, the equilibrium-operational diagram in the MgO-SO2-H2O system is described as a graphical way of showing the relationship between the concentrations of the total SO2, combined SO2, and true free SO2, iso-pH, and isopartial pressure of SO2 and as a useful tool for graphically representing the mass balances (each straight distance represents CB absorption of SO2, B′C reaction of magnesium hydroxide with the magnesium bisulfite, and AB′B mixing of flows) in the absorption process. The equilibrium-operational diagram also can be reconstructed into the design diagram with the concentration of combined SO2 as a parameter for analyzing the efficency of a commercial Venturi absorption tower.5,6 The results of these studies form the basis of the present work, the aim of which is to study on a laboratory scale the equilibrium-operational diagram, which shows the relationships between ctot, ccom, Y, pH, pSO2 and a design diagram with ccom as the parameter, as a useful tool for graphically showing the absorption of SO2 on an industrial scale. The study is divided as follows: (i) calculation of the equilibrium concentrations of species in a two-phase NaOH-SO2-H2O system and the construction of an equilibrium-operational diagram and a design diagram for the NaOH-SO2-H2O system at T ) 298 K, (ii) laboratory simulation of the kinetic data of spray columns of liquid-gas contactors and the measurements of the absorption rate of SO2 into NaOH at T ) 298 K, (iii) numerical simulation of the experimental data describing the absorption of SO2 into a NaOH solution, and (iv) showing that a design diagram can be a useful tool for graphically representing experimental and simulated data for interpreting absorption of SO2.
10.1021/ie990711+ CCC: $19.00 © 2000 American Chemical Society Published on Web 07/11/2000
Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 3043
Figure 1. Experimental equipment.
Experimental Work To analyze the graphical presentation of absorption of SO2 on an industrial scale, we proposed studying this on a laboratory scale by taking into account the criteria for scaling down liquid-gas contactors. The criteria are that the laboratory and industrial units have the same mass-transfer coefficients kG and EkL and the same ratio of the specific interfacial surface and liquid holdup a/L. Spray columns of liquid-gas contactors for desulfurization processes where the gas and liquid flow are cocurrent are selected as the industrial unit. The starting point for scaling down is on the same order of magnitude as the parameters taken from the literature7 (2% < L < 20%; 0.5 mol/m2 satm < kG < 2 mol/m2 satm; 0.7 × 10-4 m/s < kL < 1.5 × 10-4 m/s; 0.1 cm2/cm3 < a < 1 cm2/cm3) and expected in the spray columns of liquid-gas contactors. The small falling film reactor similar in design to the cable contactor of ref 8 and shown in Figure 1 was chosen for simulation of the spray column absorbers. This laboratory contactor has the advantage of having a well-defined gas-liquid area, similar to wetted-wall columns, making it suitable for fundamental transfer studies.9 To analyze only the process of absorption of SO2 into solution without taking into account the process of simultaneous particle dissolution (MgO and CaCO3) in the falling film reactor, a solution of NaOH is used. To simulate the enhancement factors in wet limestone flue gas desulfurization processes, a concentration of 0.005 M NaOH is used. Using such an approach, a more accurate study of the graphical presentation of the absorption of SO2 on an industrial scale can be expected. In this study the absorption column is an isolated, thermostated vertical 10 mm diameter glass tube, in the axis of which is stretched a 1.5 mm diameter stainless cable with coils. The height of the cable contactor is 0.76
m. During operation, the NaOH solution is fed in at the top of the distributing chamber by a pump. The liquid then flows down the cable (cocurrently to the gas phase), collects at the bottom of the column in a small stainless steel tube, and exits through the overflow. The gas phase is air-humidified in a saturator, to which a sufficient amount of sulfur dioxide is added to obtain concentrations from 0 to 3000 ppm. Inlet and outlet gas concentrations are measured using a Rosemount NGA 2000 gas analyzer. Iodometric titration is used to simultaneously determine the total S (IV) and the pH of the liquids. The diameter of the liquid sheath around the cable d ) 2(r + s) and the gas-liquid contact area A ) πdh are calculated from the liquid film thickness given by the correlation s/R ) 1.33Re0.35Ar-0.34.10 The gas-side mass-transfer coefficients are obtained by running the reactor with a 1 M NaOH solution. In this way, the liquid mass-transfer resistance is canceled because the reaction between SO2 and OH- is instantaneous and irreversible and the OH- concentration is higher than the critical concentration.11 Experiments are made by keeping the liquid flow rate constant and varying the gas flow rate (0.5-2.0 m3/h), by keeping the gas flow rate constant and varying the liquid flow rate (1.0-9.0 L/h), and by keeping constant gas and liquid flow rates and varying the concentration of SO2 in the gas phase (0-3000 ppm). The gas flow rate, the liquid flow rate, and the inlet and outlet concentrations of SO2 in gas phase are measured and the gas-phase masstransfer coefficients kG ) (G/PA)(yin - yout)/(y - y*)lm calculated. The liquid-side mass-transfer coefficients are determined by absorbing pure carbon dioxide into distilled water and correcting for SO2 proportionally to the power 2/ of the diffusion coefficient. The experiments are 3
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Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000
performed by keeping the liquid flow rate constant and varying the gas flow rate (0.5-2.0 m3/h) and by keeping the gas flow rate constant and varying the liquid flow rate (1.0-9.0 L/h). The concentration CO2 in the liquid phase is determined by using p/m-Analyse of a titroprocessor. The gas flow rate, the liquid flow rate, and the outlet concentration of CO2 in the liquid phase are measured and the liquid-side mass-transfer coefficients kL ) (L/A)(cin - cout)/(c - c*)lm calculated. The overall mass-transfer coefficient KG is obtained by making absorption runs using 0.005 M NaOH at T ) 298 K under the same conditions as those for studying the gas-side mass-transfer coefficients. The gas flow rate, the liquid flow rate, the inlet and outlet concentrations of SO2 in the gas phase, the outlet concentration of the total SO2, and the outlet pH of the liquid phase were measured, and the overall mass-transfer coefficients KG ) (G/PA)(yin - yout)/(y - y*)lm, the enhancement factors E ) (KHe/kL)/(1/KG - 1/kG), and the portion of liquid mass-transfer resistance (RL/(RL + RG) [%] ) (KHe/EkL)/(1/kG + KHe/EkL) were calculated. Absorption Model For developing a computer model of SO2 absorption, the Pasiuk-Bronikowska and Rudzinski method of modeling SO2 absorption into aqueous solutions containing sulfites is a suitable starting point.12 The absorption model is based on the film theory of gas absorption and the stagnant gas and liquid films that surround the phase boundary. In the stagnant film layers a steady-state diffusion is assumed to be coupled with chemical reactions. For sulfite solutions, the reactions accompanying chemical absorption are reversible and instantaneous compared with diffusion.13,14 The thicknesses of the films depend on the hydrodynamic conditions in the gas and liquid bulks. In the gas film no reactions occur and the flux rate of SO2 throughout the gas film is expressed as
NAbs ) kG(pSO2,b - pSO2,i)
(1)
If we consider the dissociation reactions for the SO2,gSO2,aq-HSO3- -SO32- -H2O system, the flux rate throughout the liquid film is
Nabs ) kL((DSO2/DSO2)(cSO2,aq,i - cSO2,aq,b) + (DHSO3/DSO2)(cHSO3,i - cHSO3,b) + (DSO3/DSO2)(cSO3,i - cSO3,b)) (2) In the liquid bulk all of the reactions are assumed to be in equilibrium and the bulk concentrations of the different species form the boundary conditions at the bulk side of the liquid film. The equilibrium concentrations are solved iteratively by using a secant method. At the gas-liquid surface two boundary conditions must be determined: (i) The flux of SO2 through the gas film must be equal to the flux of total sulfur dioxide through the liquid film, while assuming a phase equilibrium at the gas-liquid interface
kG(pSO2,b - pSO2,i) ) kL((DSO2/DSO2)(cSO2,aq,i cSO2,aq,b) + (DHSO3/DSO2)(cHSO3,i - cHSO3,b) + (DSO3/DSO2)(cSO3,i - cSO3,b)) (3)
and (ii) the net flux of charged species must be zero:
-DH3O (dcH3O/dx) ) -DHSO3 (dcHSO3/dx) 2DSO3 (dcSO3/dx) - DOH (dcOH/dx) (4) The enhancement factor, defined as the ratio between the absorption of SO2 with and without chemical reaction, is calculated using the results of the numerical solution:4
E ) (DSO2(cSO2,i - cSO2,b) + DHSO3(cHSO3,i - cHSO3,b) + DSO3(cSO3,i - cSO3,b))/(DSO2(cSO2,i -cSO2,b)) (5) Results and Discussion (a) Equilibrium-Operational Diagram for the NaOH-SO2-H2O System. The concentrations of Na+, H3O+, OH-, SO2,aq, SO2,g, HSO3-, and SO32- are determined using a calculation based on the equilibrium relationships for the SO2,g-SO2,aq-HSO3--SO32--H2O system, the mass balance equation, the charge balance equation, and the Pitzer ion interaction model. The relationships between Y (the excess of SO2 over the amount necessary to form NaHSO3 only, per unit mass of solution (Y ) cSO2 - cSO3)), ctot (the amount of total SO2 per unit mass of solution), ccom (total concentration of Na+ expressed with SO32- and HSO3- using the corresponding stoichiometric factors, per unit mass of solution), pH, and pSO2 are transferred from the MgOSO2-H2O system applied in previous works5,6 to the NaOH-SO2-H2O system studied herein (eqs 6-10).
cH4 + (K1,c + cNa)cH3 + (K1,cK2,c + cNaK1,c - Kw,c ctotK1,c)cH2 + (cNaK1,cK2,c - Kw,cK1,c 2ctotK1,cK2,c)cH - Kw,cK1,cK2,c ) 0 (6) cH3 + cNacH2 - (Kw,c + K1,cpSO2/KHe,c)cH 2K1,cK2,cpSO2/KHe,c ) 0 (7) pSO2 ) KHe,ccH2/(cH2 + K1,ccH + K1,cK2,c)ctot
(8)
ccom ) ctot(K1,cK2,c + 0.5K1,ccH)/(cH2 + K1,ccH + K1,cK2,c) (9) Y ) ctot - 2ccom
(10)
Equations 6 and 7 are the charge balance equations containing the relevant thermodynamic equilibrium constants for the SO2,g-SO2,aq-HSO3--SO32--H2O system together with the mass balance equation expressed in terms of total SO2, Na+ and H3O+ concentrations, and pSO2, respectively. Equation 8 derives from the dissociation and dissolution equilibrium set up in the H2O-SO2 system. Equations 9 and 10 are important for calculating the concentrations of combined SO2 and true free SO2. In eqs 6-10, K1,c ) K1γH2OγSO2/γHγHSO3, K2,c ) K2γHSO3/γHγSO3, and Kw,c ) KwγH2O/γHγOH are the concentration equilibrium constants and KHe,c is the concentration Henry constant, here defined as KHe,c ) KHeγSO2. The thermodynamic constants are taken from the literature (cf. Table 1) and refer to T ) 298 K. For the theoretical description of a NaOH-SO2-H2O system, the Pitzer ion interaction theory is used to calculate the activity coefficients for all of the species in the
Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 3045 Table 1. Coefficients Used in Pitzer’s Equations for the NaOH-SO2-H2O System, Thermodynamic Constants, and Diffusivity Constants at 298 K Thermodynamic Constants at 298 K K1 ) 0.014 K2 ) 7.1 × 10-8 Kw ) 1 × 10-14 KHe ) 0.808 m3‚bar/kmol Pitzer coefficients at 298 K
18 18 18 18
salt
β(0)
β(1)
C(φ)
ref
Na2SO3 NaHSO3 NaOH
0.08015 0.1527 0.0864
1.185 0.3197 0.253
-0.00436 -0.0246 0.0044
16 16 15
i
j
λij
ref
Na
SO2
0.0283
16
Diffusion Constants D DH+ ) 9.31 DSO2 ) 2.0 DHSO3- ) 1.33 DSO32- ) 0.96 DOH- ) 5.24
[10-9 m2/s]
at 298 K 19 19 19 19 19
solution.15 The advantage of this theory is its sound statistical mechanical basis, which results in a better description of the concentration of various species at different temperatures. Reliable Pitzer’s parameters β(0), β(1), C(φ), and λ for the interaction of Na+ with SO2, HSO3-, and SO32- are taken from the work by Millero et al.,16 who investigated the dissociation of H2SO3 in NaCl solutions where I ) 0.1-6.0 M at 25 °C. The validity of this model was checked against literature data on the solubilities of sulfur dioxide in water and in a 0.225 mol of Na2SO3/kg of solution at T ) 298 K3,8 and by comparing the calculated concentrations of combined SO2, total SO2, and pH from the model with experimentally determined data at 298 K in ref 2. The results of a linear regression analysis comparing experimental and computed concentrations show good agreement between the two sets of values at T ) 298 K: pSO2,exp ) 1.054pSO2,model - 0.002(R2 ) 0.998); pHexp ) 0.998pHmodel + 0.009(R2 ) 0.990). A graphical representation of the calculated concentrations in the NaOH-SO2-H2O system at 298 K is displayed in the equilibrium-operational diagram (Figure 2), which is presented as the relationship between Y and ccom for different ctot and pH or pSO2 values. The diagram contains iso-pH curves and isobaric curves of SO2 at 298 K and may be useful for graphically presenting the absorption of SO2 (ccom ) constant), the reaction between SO2 and NaOH (ctot ) constant) and the mixing of flows (using the gravity principle technique). The equilibrium-operational diagram for the NaOHSO2-H2O system can be reconstructed in a design diagram for gas absorption processes including the concentration of Na+ instead of ccom as a parameter (Figure 3). The concentration of Na+ remains constant during the absorption of SO2, but each initial concentration of Na+ yields an equilibrium curve in the absorption process. This equilibrium curve with constant concentration of Na+ can be described either as a function of pSO2 ) f(ctot) with the slope of the equilibrium curve defined by a system of eqs 7 and 8 (this curve describes the equilibrium composition of the gas and liquid phases) or as a function of pH ) f(ctot) with the slope of the equilibrium curve defined by eq 6 (this curve describes the equilibrium composition of the liquid phase only). In this way a family of iso-Na+ equilibrium
curves can be obtained for different concentrations of sodium ions in the liquid phase. Thus, the applicability of the design diagram presented in Figure 2 of ref 6 is extended. The combined SO2 parameter, however, is only appropriate for the absorption of SO2 into sulfite solutions at pH < 9, because it does not take into account the chemical reaction of OH- with SO2 during the absorption of SO2 into sodium base solutions at higher pH values (pH > 10). (b) Laboratory Simulation. The measured gasphase mass-transfer coefficients kG are 1.0 mol/m2‚s‚ bar < kG < 3.0 mol/m2‚s‚bar. The values of kG on a laboratory scale sufficiently simulate the magnitude of the reported kG values (0.5 mol/m2 satm < kG < 2 mol/ m2 satm) for spray columns.7 The measured gas mass-transfer coefficients are higher than the gas mass-transfer coefficients determined by Lorent et al.8 Note that the gas and liquid flows in the laboratory absorber are cocurrent. The gas velocity in the tube is 1.5-7.0 m/s. The gas film mass-transfer coefficients increase with the gas and liquid flow rates according to the correlation
kG [mol/m2‚s‚bar] ) 1.919G [m3/h]0.641 L [m3/h]0.040 (11) The correlation shows the weak influence of the liquid flow rate on the gas-phase mass-transfer coefficient, which is due to the flow regime in the gas phase. The results of a linear regression analysis comparing experimental and calculated data (eq 11) show an acceptable agreement between the two sets of data: kG,regress ) 0.921kG,exp + 0.161(R2 ) 0.927). The measured liquid-phase mass-transfer coefficients kL are 4.0 × 10-5 m/s < kL < 15 × 10-5 m/s. The values of kL on a laboratory scale sufficiently simulate the values (0.7 × 10-4 m/s < kL < 1.5 × 10-4 m/s) of kL for spray columns reported in the literature.7 The liquid-phase mass-transfer coefficients kL increases with the gas and liquid flow rates according to the correlation
kL [m/s] ) 3.09 × 10-3L [m3/h]0.621 G [m3/h]0.106 (12) The liquid-phase mass-transfer coefficients are lower than the liquid-phase mass-transfer coefficients determined by Lorent et al.8 The coefficient kL also depends on the gas velocity. The rate of mass transfer in the liquid phase within the falling film is highly dependent on surface conditions. Vivian and Peaceman7 investigated the characteristics of the CO2-H2O and Cl2-HCl-H2O systems in a wetted-wall column and found that the gas rate had no effect on the liquid-phase coefficient at Reynolds numbers below 2200. Beyond this, the effect of rippling significantly increases the liquid-phase transfer rate. Results of kinetic studies in a cable contactor published by Lorent et al.8 show that the coefficient kL is independent of gas velocity when the Reynolds number varies between 1200 and 3000 as the gas velocity increases from 1.0 to 2.5 m/s. In the present study, a weak influence of gas velocity on the coefficient kL (exponent 0.106) is observed, which can be related to the development of surface rippling. The Reynolds number varies from 1000 to 4000 as the gas velocity increases from 1.8 to 7.2 m/s. The results of a linear regression analysis comparing the experimental and calculated data according to
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Figure 2. Equilibrium-operational diagram of NaOH-SO2-H2O at 298 K.
Figure 3. Design diagram of NaOH-SO2-H2O at 298 K.
correlation (12) shows an acceptable agreement: kL,regress ) 0.924kL,exp + 8.05 × 10-6(R2 ) 0.937). The specific interfacial surface a and the holdup of liquid L are 0.75 cm2/cm3 < a < 0.95 cm2/cm3 and 1.3% < L < 3.3%, respectively. The values of a and L sufficiently simulate the values 0.1 cm2/cm3 < a < 1 cm2/ cm3 and 2% < L < 20% for spray columns reported in ref 7. The overall mass-transfer coefficients KG for the absorption of SO2 into a 0.005 M NaOH solution are
0.3 mol/m2‚s‚bar < KG < 2.0 mol/m2‚s‚bar, and the enhancement factors are 5 < E < 45. The portion of liquid mass-transfer resistance RL/(RL + RG) [%] increases with the input concentration of SO2 and gas flow and decreasing liquid flow rate as shown by correlation (13) and is 10% < RL/(RL + RG) < 80%. A linear
RL/(RL + RG) [%] ) 0.022cg,input [ppm]0.572 G [m3/h]0.400 L [m3/h]-0.620 (13)
Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 3047
regression analysis comparing experimental and calculated data according to correlation (13) gives an acceptable R2 value: (RL/(RL + RG))regress ) 0.960(RL/(RL + RG))exp + 0.0202(R2 ) 0.907). The liquid RL and gas RG mass-transfer resistance controls the absorption of SO2 into the 0.005 M NaOH solution in the laboratory absorber. The range of the liquid and gas mass-transfer resistance of the laboratory absorber is in acceptable agreement with the range of gas and liquid mass-transfer resistance found in the literature17 for wet limestone FGD plants, where the simulations of the enhancement factors for SO2 in the CaCO3-SO2-H2O system vary between 10 < E < 25. (c) Numerical Simulation. The model which describes the absorption process in 0.005 M NaOH is constructed in two parts, calculating the equilibrium concentrations in the liquid and the absorption of SO2 at the gas-liquid interface, respectively, according to the above considerations. The calculation begins at the top of the laboratory absorber. The reactor is divided into n elements of height ∆h where the absorption rates are calculated using the current concentrations in the liquid bulk and partial pressures in the gas bulk as the boundary conditions. In every segment the gas and liquid bulk concentrations are upgraded according to the amount of the different species transferred. The correlations for kL and kG obtained by regressing the experimental results are used in the computations. The following mass balances allow one to calculate the concentrations of the sulfur species in bulk and partial pressure of SO2 along the height of the contactor:
ctot,k+1 ) ctot,k + (Nabsπd∆h)/(L/3600)
(14)
for the liquid bulk and
pSO2,k+1 ) pSO2,k - (PNabsπd∆h)/(Gf/3600)
(15)
for the gas bulk. An equilibrium calculation for the upgraded liquid is followed. The procedure is repeated until the calculated height is equal to the height of the laboratory absorber. In this way the values of partial pressure of SO2, total SO2, pH of the bulk and of the interface, and the enhancement factor are calculated for each height of the falling film absorber. To determine the behavior of the absorption of SO2 and the reaction processes occurring in the laboratory absorber, simplified assumptions are made using the steady-state theory with the dependence of the mass-transfer coefficient to the 1 power of the diffusion coefficient (film theory) instead of the 1/2 power (eddy diffusivity theory). To make the calculation, the diffusity constants at an infinite dilution (Table 1) are used and diffusive transport in the boundary layer is assumed. Although some oxidation of sulfites may occur during the absorption of SO2 because of the high concentration of oxygen in the experiments, made in the one-pass through experiments without the presence of a catalyst (Mn2+, Co2+, Fe3+, and Cu2+), the model assumes no oxidation of sulfites. Despite this, a comparison between the measured output and the simulated data (at 298 K) in bulk shows an acceptable agreement for concentrations of the total SO2 and pH values along the contactor in the range between ctot,b ) 0 and 7 mmol/L and pHb ) 11.7 and 3.1, respectively: pSO2,out,model ) 1.017pSO2,out,exp - 19.75(R2 ) 0.99); pHout,model )
0.890pHout,exp + 0.702(R2 ) 0.93); ctot,out,model ) 0.850ctot,out,exp + 0.48(R2 ) 0.95). In this range of total concentration of SO2 and pH values in bulk, the oxidation was limited and is not taken into account. For this range of output concentrations of the total SO2 and pH values, the bulk and interfacial compositions along the contactor during the absorption of SO2 into 0.005 M NaOH at T ) 298 K are simulated for showing the possibility of a graphical presentation of bulk and interfacial compositions during absorption of SO2 along a falling film reactor in a design diagram. (d) Graphical Presentation. By using a design diagram reconstructed from the equilibrium-operational diagram for a NaOH-SO2-H2O system, by using the experimental data obtained for the absorption of SO2 into Na2SO3 solutions (define the start and end point of absorption of SO2), and by using the absorption model that calculates the relevant concentrations along the reactor during the absorption of SO2, it is possible to graphically represent the absorption process of SO2 in NaOH-SO2-H2O performed either in the laboratory or in industrial liquid-gas contactors. To show this, the experimental data presented in Table 2 are used for a graphical presentation in the design diagram for the NaOH-SO2-H2O system with an iso-Na+ equilibrium curve of 0.005 mol/L at T ) 298 K (Figure 4). The variables in Figure 4 are concentrated in two sets: pSO2, ctot, and cNa (Na+ ) 0.005 mol/L) and pH, ctot, and cNa (Na+ ) 0.005 mol/L). Figure 4 shows an equilibrium curve expressed in two ways: the curve pSO2 ) f1(ctot) calculated by the system of eqs 7 and 8 and the curve pH ) f2(ctot) calculated by eq 6. Points A have the coordinates ctot and pSO2 and describe the gas and liquid compositions, while points B have the coordinates ctot and pH and describe only the liquid composition. Subscripts 0, 1, and 2 describe the top, bottom, and equilibrium conditions of the laboratory absorber. Superscripts bulk and interface describe the bulk liquid and gas phases and gas-liquid interface composition. The coordinates of points A0bulk, A1bulk, B0bulk, and B1bulk are determined experimentally and are presented in Table 2. In the design diagram (Figure 4), both the operational line A0-A1 describing the concentration of SO2 in the gas and liquid phases along the falling film reactor and the operational curve B0-B1 describing the pH and total SO2 in solution along the falling film reactor in the bulk and gas-liquid interface at T ) 298 K are calculated using the absorption model (Figure 4 and Table 2). The operation lines A0-A1 and B0-B1 (Figure 2) describing the bulk composition and the curves describing the composition of the gas-liquid interface intersect at the points A2equilibrium and B2equilibrium. This represents the equilibrium composition in the gas and liquid phases at an infinite height of the laboratory absorber. The coordinates, which describe the composition of the gas-liquid interface, do not lie on the equilibrium curve. The classical design diagrams in the literature7 show the equilibrium relationship between pSO2 and cSO2,aq as described by Henry’s law or a more complicated function of cSO2,aq. In this case the concentrations of SO2,aq in the liquid phase at the gas-liquid interface can be obtained directly from the diagram by solving the equations Nabs ) kG(pSO2,b - pSO2,i) ) kLE(cSO2,i - cSO2,b) and pSO2,i ) kHe,ccSO2,i because the dynamic equilibrium concentration of SO2,aq defined by the dynamic electroneutrality equation (∑ZiJi ) 0) is considered to be equal to the static
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Figure 4. Graphical presentation of absorption of SO2 into a 0.005 M NaOH solution taking place in a laboratory absorber at 298 K. Table 2. Experimental, Kinetic, and Simulation Data of a Laboratory Absorber and the Coordinates of Points A0, A1, A2 and B0, B1, B2 Shown in Figure 4 h [m] L [L/h] G [m3/h] ctot [mmol/L] pH pSO2 [ppm] L/fG [L/kmol]
Experimental Data 0.20 2.6 0.55
0.00 2.6 0.55 0.0 11.7 1170 -117
h [m] kL [m/s] kG [mol/m2‚s‚bar] KG [mol/m2‚s‚bar] E
-117
h [m] E KG [mol/m2‚s‚bar] RL [bar‚m2‚s/mol] RG [bar‚m2‚s/mol] RL/(RL + RG) [%] EkL/kG [L/mmol‚ppm] ctot,b [mmol/L] ctot,i [mmol/L] pHb pHi pSO2 [ppm] pSO2,i [ppm]
0.60 2.6 0.55
-117
Kinetic Data 0.20 7.1 × 10-5 0.97 0.47 14
0.00 7.1 × 10-5 0.97 0.47 14
0.40 2.6 0.55
-117
0.40 7.1 × 10-5 0.97 0.47 14
Simulated Data 0.20 0.40 25 12 0.67 0.50 0.46 0.97 1.03 1.03 31 49 -1808 -855 1.6 2.6 13.5 9.7 11.3 8.5 3.4 3.1 978 869 302 422
0.00 2690 0.97 0.0 1.03 0.0 -200 × 103 0.0 22.0 11.7 5.4 1170 5
0.76 2.6 0.55 3.6 6.8 720 -117
0.60 7.1 × 10-5 0.97 0.47 14 0.60 11 0.49 1.02 1.03 50 -818 3.3 9.8 7.2 3.1 784 390
0.76 7.1 × 10-5 0.97 0.47 14 0.76 10 0.48 1.06 1.03 51 -781 3.8 9.8 6.8 3.1 724 368
Coordinates of Points Shown in Figure 4 pSO2 ) f1(ctot) at 0.005 mol of Na+/L bulk
bulk
A0
A2equilibrium
A1
A0interface
A1interface
h [m]
ctot
pSO2
ctot
pSO2
ctot
pSO2
ctot
pSO2
ctot
pSO2
0
1
0.0
1170
3.6
724
6.6
391
22.0
5
9.8
370
0.00
0.76
pH ) f2(ctot) at 0.005 mol of Na+/L B0bulk
B1bulk
B2equilibrium
B0interface
B1interface
h [m]
ctot
pH
ctot
pH
ctot
pH
ctot
pH
ctot
pH
0
1
0.0
11.7
3.6
6.8
6.6
2.9
22.0
5.4
9.8
3.1
0.00
0.76
equilibrium concentration of SO2,aq defined by the electroneutrality equation (∑Zici ) 0). In the present case a new design diagram for the absorption of SO2 is proposed using pSO2 or pH as a function of ctot and the concentration of the natrium ion as a parameter. The
concentrations of the species SO2,aq, HSO3-, and SO32-, which make up the total SO2 in the liquid side of gasliquid interface, are determined from the dynamic equilibrium concentration of the total SO2, which is defined by the dynamic electroneutrality equation (∑ZiJi
Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 3049
) 0) and is not the same as the static equilibrium concentration of the total SO2 as defined by the electroneutrality equation (∑Zici ) 0). Also, it is impossible to read the concentrations of the total SO2 in the liquid phase at the gas-liquid interface directly from the design diagram pSO2 ) f(ctot) and pH ) g(ctot), and a simulation model is needed to determine the gas-liquid interface composition by solving eqs 3 and 4, pSO2,i ) KHe,c,tot,ictot,i, and pSO2,b ) KHe,c,tot,bctot,b. The ratio EkL/kG ) (pSO2,b - pSO2,i)/(cSO2,i - cSO2,b) varies along the falling film reactor and can be determined from eq 16 using the simulation model
[pSO2,b - pSO2,i]/[ctot,i(cH3O,i2)/(cH3O,i2 + K1,c,icH3O,i + K1,c,iK2,c,i) - ctot,b(cH3O,b2)/(cH3O,b2 + K1,c,bcH3O,b + K1,c,bK2,c,b)] (16) In this case, the ratio EkL/kG decreases from -200 × 103 [L/mmol‚ppm] at the top to -781 [L/mmol‚ppm] at the bottom of laboratory absorber. The enhancement factor E, the overall mass-transfer coefficient KG, the resistance to absorption of SO2 in the liquid phase RL and the gas phase RG, and the fraction of the liquid resistance along the falling film reactor are also calculated using this model. The enhancement factor varies along the height of the laboratory absorber and decreases from E ) 2690 at the top to E ) 10 at the bottom. The enhancement factor E ) 14 determined from experimental data is an average value for the whole contactor. The absorption rate of SO2 is controlled both by the gas film and the liquid film mass-transfer resistance. The fraction of liquid film mass-transfer resistance of laboratory absorber is 0% at the top and 51% at the bottom. The calculated data for the absorption of SO2 is presented in Table 2. Conclusion The gas-liquid equilibrium-operational diagram showing the relationships that exist between the concentrations of the total SO2, combined SO2, and true free SO2, iso-pH, and isopartial pressure of SO2 can be a useful tool for graphically presenting the absorption of SO2 (ccom ) constant), the reaction between SO2 and NaOH (ctot ) constant), and the mixing of flows (using the gravity principle technique) in the liquid-gas contactors. The equilibrium-operational diagram for the NaOH-SO2-H2O system can be reconstructed in a design diagram for gas absorption processes including the concentration of Na+ instead of ccom as a parameter. The possibility of graphically presenting the absorption of SO2 in a design diagram is shown using an example where the bulk and interfacial compositions along the falling film reactor during the absorption of SO2 into 0.005 M NaOH at T ) 298 K are graphically presented in a design diagram of a NaOH-SO2-H2O system. Nomenclature A0, A1, A2, B0, B1, B2 ) points shown in Figure 2 a ) specific interfacial surface [m2/m3] A ) gas-liquid contacting area on the falling film reactor [m2] Ar ) Archimedes number ) (2R)3g/ν2 ci ) concentration of species i [wt %, mol/L, or mmol/L] d ) diameter of the liquid sheath around the yarn [m] Di ) diffusivity of the component [m2/s]
E ) enhancement factor f ) conversion factor equal to 0.0409 kmol/m3 G ) gas flow rate [m3/h] h ) height of the falling film reactor [m] H ) concentration of H3O+ ions [mol/L] K1, K2, Kw, KHe ) thermodynamic constants K1,c, K2,c, Kw,c, KHe,c ) concentration equilibrium constants kG ) gas-phase mass-transfer coefficient [mol/s‚m2‚bar] KG ) overall gas mass-transfer coefficient [mol/m2‚s‚bar] KHe,c,tot ) slope of the equilibrium curve (m3‚bar/kmol) defined by the equation KHe,c,tot ) KHe,ccH2/(cH2 + cHK1,c + K1,cK2,c) kL ) liquid-phase mass-transfer coefficient [m/s] L ) liquid flow rate on the cable [m3/h] Nabs ) SO2 absorption flux [mol/m2‚s] pSO2 ) partial pressure of SO2 [bar or ppm] P ) total pressure [bar] R ) radius of the cable [m] RG ) gas-phase film resistance [bar‚m2‚s/mol] RL ) liquid-phase film resistance [bar‚m2‚s/mol] Re ) liquid Reynolds number ) 4L/2πRν s ) liquid sheath thickness [m] y ) molar fraction of SO2 in gas phase Y ) true free SO2 [wt %] Subscripts 0 ) top of the falling film reactor 1 ) bottom of the falling film reactor b ) bulk com ) combined SO2 exp ) experiment i ) interface in ) input k ) number of differential elements of the falling film reactor out ) output lm ) logarithmic mean mean ) mean value model ) model regress ) regression analysis tot ) total SO2 Superscripts bulk ) bulk condition equilibrium ) equilibrium condition interface ) interface condition Greek Letters ∆ ) difference L ) liquid holdup gi ) activity coefficients of H3O+, OH-, Na+, HSO3-, and SO32ν ) kinematic viscosity [m2/s] β(0), β(1), C(φ), λ ) Pitzer parameters
Literature Cited (1) Laurent, A.; Charpentier, J. C. The Role and Use of Experimental Laboratory-Scale Models for Predicting the Performance of an Industrial Gas-Liquid Reactor. Chem.-Ing.-Tech. 1981, 53 (No. 4), 244-251. (2) Ingruber, O. I. Chemical Equilibria in Heated Sulphite Solutions. Pulp Pap. Mag. Can. 1965, April, T216. (3) Young, C. L. Sulphur Dioxide, Chlorine, Fluorine and Chlorine Oxides; Solubility Data Series; Pergamon Press: Oxford, U.K., 1983; Vol. 12, p 38. (4) Glasscock, D. A.; Rochelle, G. T. Numerical Simulation of Theories for Gas Absorption with Chemical Reaction. AIChE J. 1989, 35 (No. 8), 1271-1281. (5) Zidar, M.; Golob, J.; Veber, M. Absorption of Sulfur Dioxide into Aqueous Solutions: Equilibrium MgO-SO2-H2O and Graphical Presentation of Mass Balances in an Equilibrium Diagram. Ind. Eng. Chem. Res. 1996, 35, 3702-3706.
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(6) Zidar, M.; Golob, J.; Veber, M.; Vlachy, V. Absorption of Sulfur Dioxide into Aqueous Solutions: 2. Gas Liquid Equilibrium of the MgO-SO2-H2O System and Graphical Presentation of Operation Lines in an Equilibrium Diagram. Ind. Eng. Chem. Res. 1997, 36, 4342-4346. (7) Perry’s Chemical Engineers’ Handbook, 7th ed.; McGrawHill: New York, 1997; pp 23-43. (8) Lorent, P.; Gerard, P.; Vanderschuren, J. Sulphur dioxide absorption into sodium sulphite solutions in a cable contactor. Gas Sep. Purif. 1992, 6 (No. 3), 125-131. (9) Gerard, P.; Segantini, G.; Vanderschuren, J. Modeling of Dilute Sulfur Dioxide Absorption into Calcium Sulfite Slurries. Chem. Eng. Sci. 1996, 51 (No. 12), 3349-3358. (10) Lefebvre, S.; Vanderschuren, J.; Verheve, D.; Oneyejekwe, F. Hydrodynamic characteristics of the flow of thin cylindrical liquid films on vertical support. Chem.-Ing.-Tech. 1979, 51, 330331. (11) Danckwerts, P. V. Gas-Liquid reactions; McGraw-Hill: New York, 1970. (12) Pasiuk-Bronikowska, W.; Rudzinski, K. J. Absorption of SO2 into aqueous Systems. Chem. Eng. Sci. 1991, 46 (9), 22812291. (13) Hikita, H.; Asai, S.; Tsuji, T. Absorption of sulphur dioxide into aqueous sodium hydroxide and sodium sulphite solutions. AIChE J. 1977, 23b, 538-544.
(14) Chang, C. S.; Rochelle, G. T. SO2 absorption into NaOH and Na2SO3 aqueous solutions. Ind. Eng. Chem. Fundam. 1985, 24, 7-11. (15) Pitzer, K. S. Activity coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (16) Millero, F. J.; Hershey, J. P.; Johnson, G.; Zhang, J. Z. J. Atm. Chem. 1989, 8, 377. (17) Kiil, S.; Michelsen, M. L.; Kim, D.-J. Experimental Investigation and Modeling of a Wet Flue Gas Desulfurization Pilot Plant. Ind. Eng. Chem. Res. 1998, 37, 2792-2806. (18) Goldberg, R. N.; Parker, V. B. Thermodynamics of Solutions of SO2,g in Water and of Aqueous Sulfur Dioxide Solutions. J. Res. Natl. Bur. Stand. 1985, 90 (No. 5 (Sept-Oct)), 341358. (19) Gage, C. L. Limestone dissolution in modelling of slurry scrubbing for flue gas desulphurisation. Ph.D. Thesis, The University of Texas at Austin, Austin, TX, 1989.
Received for review September 24, 1999 Revised manuscript received February 18, 2000 Accepted April 24, 2000 IE990711+
