SO2 enhanced desorption from basic aluminum sulfate desulphurization–regeneration solution by falling-film evaporation

To find the optimal structure of the converging–diverging tube and develop a high-efficiency falling-film evaporator, the heat and mass transfer performances of falling-film evaporation with converging–diverging tubes of different dimensions were studied. The optimal converging–diverging tube was used in falling-film evaporation desorption of the basic aluminum sulfate desulphurization–regeneration solution, and different influential factors on the desorption effect were analyzed. It was found that converging–diverging tubes with large falling-film flow rate performed well in the heat and mass transfer of falling-film evaporation, and their rib height largely affected the heat and mass transfer performances. At the same rib height and rib pitch, the longer the converging segment of the converging–diverging tube was, the better the heat transfer performance was. The evaporation heat transfer coefficient and evaporation mass transfer rate in the optimal converging–diverging tube were 1.6 and 1.38 times larger than the smooth tube, respectively. The optimal converging–diverging tube was used in falling-film evaporation desorption of basic aluminum sulfate desulphurization–regeneration solution, at a perimeter flow rate of 0.114–0.222 kg m−1 s−1, the desorption efficiency inside the tube was up to 94.2%, which was 10.3–10.5% higher than that of the smooth tube. At the inlet sulfur concentration of 0.02–0.1 kmol m−3, the desorption efficiency was up to 94.1%, which was 12.0–16.3% larger than that of the smooth tube. At the heating temperature of 371.15–386.15 K, the desorption efficiency was up to 93.4%, which was 6.7–11.5% larger than that of the smooth tube. Smaller falling-film flow rate, higher sulfur concentration, or higher heating temperature was more constructive to SO2 desorption. Correlations were obtained to predict the mass transfer coefficient and SO2 desorption efficiency. This study develops a new type of falling-film evaporator for SO2 desorption from basic aluminum sulfate desulphurization–regeneration solution and provides a basis for process design and industrial application.


Introduction
Along with rapid socioeconomic development, great achievements have been made in ue gas desulfuration technology throughout the world. Statistics show that about 85% of existing ue gas desulfuration technology is wet technology, which has become the major technical trend of ue gas desulfuration. 1 However, the nonrenewable wet desulfuration technology is limited by the nonrenewability of absorbents, large consumption, and generation of secondary waste, such as limestone suspension 2 and seawater. 3 Thus, the key to renewable wet desulfuration technology is to discover renewable desulfurization agents. The existing renewable desulfurization agents primarily include magnesia-magnesium sulte, sodium citrate, organic amine, sodium sulte, and basic aluminum sulfate. Research on the desulphurization method of some agents has been carried out and some defects have been found. As for magnesia-magnesium sulte method, the calcination of magnesium sulte into magnesia and SO 2 requires temperatures up to 650-900 C 4 and the byproduct magnesium sulfate can hardly be decomposed. 5 In the sodium citrate method, sodium sulte (or sodium bisulte) can be easily oxidized into sodium sulfate, which will be separated out as crystals that block the equipment and tubes. 6 In case of the organic amine method, despite its high efficiency of up to 95%, its desorption rate is rather low. 7 In the strong sodium sulte method, the large dosage of absorbent and the tendency of oxidation into sodium sulfate lead to its low desorption rate; also, sodium sulfate is hard to separate and even the separated sodium sulfate contains sodium sulte crystals, which cause secondary pollution. 8 In comparison, basic aluminum sulfate is very stable and can be prepared from cheap raw materials at low prices.
Basic aluminum sulfate, as a promising desulfurization agent, has attracted wide attention from the research eld. For instance, basic aluminum sulfate has been used to absorb SO 2 from ue gas, [9][10][11][12] which proves the high absorptive ability, and our team has carried out the mechanism research. 13 However, research has been rarely conducted on desorption of the basic aluminum sulfate desulphurization-regeneration solution, which is a key step in the renewable wet desulfuration process. Thus far, water bath heating 14 assisted by mechanical agitation, 15 microwaves, 16 ultrasonic waves [17][18][19] or vacuum-pumping 20 has been applied for enhanced desorption, exhibiting some improvements. However, these methods are limited by nonuniform heating and long desorption time; moreover, the relevant research is still at the laboratory stage, which is hard to industrialize. To overcome the above limitations and meet the requirements for industrialization, we nd it necessary to adopt high-efficiency heat and mass transfer falling-lm evaporator.
The converging-diverging tube has a periodic alternation of converging segments and diverging segments and thus, it exhibits enhanced heat and mass transfer performances. [21][22][23][24] It has been used in various heat transfer facilities, such as condensers, air preheaters, waste heat boilers and oil coolers, and has been well-promoted in sulfuric acid, fertilizer, chemical and other industries. [25][26][27] As an excellent enhanced heat transfer unit, the converging-diverging tube is primarily used for single phase liquid enhanced heat transfer inside and outside the tube, 28,29 but has not been used in falling-lm evaporation. In view of these considerations, we propose a regenerative process using falling-lm evaporation within the converging-diverging tube, aiming to address the design and industrial application regarding the use of converging-diverging tubes in SO 2 enhanced desorption of basic aluminum sulfate desulphurization-regeneration solution. Thus, to nd the optimal structure of the converging-diverging tube and develop a high-efficiency falling-lm evaporator, the heat and mass transfer performances of falling-lm evaporation with converging-diverging tubes of different dimensions were studied. The optimal converging-diverging tube was used in falling-lm evaporation desorption of the basic aluminum sulfate desulphurizationregeneration solution, and different inuence factors on the desorption effect were analyzed.

Experimental apparatus
Measurements of heat and mass transfer performances of falling-lms were carried out in the experimental apparatus shown in Fig. 1. This system is primarily used to detect the heat and mass transfer performances of falling liquid lms in vertical tubes. The main structure dimensions of the heat transfer tubes that contain four dimensions of convergingdiverging tubes and a smooth tube are listed in Table 1. The structural scheme of the converging-diverging tubes is illustrated in Fig. 2. The uid in the heating tank was heated by an electric heating unit to the preset temperature; then, the uid was pumped by a water pump through a ow adjustment valve into the top water reservoir, which was connected by an adjustment valve with air. Aer the uid owed to the test section, falling liquid lms were formed on the inner surface of the heat transfer tube. The vapor generated in the heat transfer tube was pumped by a vacuum pump into the condensers. Then, the condensate liquids entered a metering tank for measurement. The unevaporated liquid entered the metering tank. The outer section of the heat transfer tube was supplied with saturated steam with certain pressure and temperature. The steam-condensed, water generated during the experiments, was passed by vapor-liquid separator into a metering tank.

Experimental procedure
When the heating steam temperature outside of the heat transfer tube was constant at 373.15 K, the medium (water) was preheated to the boiling point. Then, falling liquid lm experiments inside the four dimensions of converging-diverging tubes and the smooth tube were conducted by changing the water ow rate. By analyzing the heat transfer coefficient and mass transfer rate of liquid lm evaporation, we determined which converging-diverging tube had the optimal heat transfer and mass transfer performances. Then, with basic aluminum sulfate desulphurization-regeneration solution as the medium, aer it was preheated near the boiling point, we carried out falling-lm evaporation desorption experiments inside the optimal converging-diverging tube with the smooth tube as a comparison, and the inuence factors on the desorption performance were investigated. The SO 3 2À concentrations before and aer the desorption of desulphurization-regeneration solution were computed by the iodometric method. 30

Data analysis
The peripheral ow rate of liquid lms (G) and the liquid lm Reynolds number (Re) inside the heat transfer tube were computed using the following equations: where m l is the mass of liquid lms, kg; d i is the inside diameter of the heat transfer tube, m; s is the experimental time of heat transfer in the falling-lms, s; p ¼ 3.1415926; and m i is the dynamic viscosity of liquid lms, kg m À1 s À1 . Heat transfer was analyzed by a thermal resistance analytical method. 31 In each experimental period, with the endothermic quantity of uid within the heat transfer tube as the heat transfer quantity, the evaporation heat ux density of falling-lms (q) and the total heat transfer coefficient of evaporation in falling-lms (K h ) were computed as follows: where m v is the mass of liquid lm evaporation, kg; r 0 is the vaporization latent heat of liquid lms under saturation temperature, kJ kg À1 ; A 0 is the area of outside surface of the tube, m 2 ; T is the heating steam temperature in the ring gap outside the tube, C; t is the liquid lm temperature inside the tube, C. The steam condensation heat transfer coefficient (h o ) outside the heat transfer tube was computed by the Nusselt lmwise condensation experimental correlation: 32 where r 0 , l 0 and m 0 are the density (kg m À3 ), thermal conductivity (W m À1 K À1 ) and dynamic viscosity (kg m À1 s À1 ) of the heating steam condensation liquid, respectively; L is the valid height of the vertical tube, m; t o is the outside wall temperature, C; g is the gravitational acceleration, m s À2 ; Re 0 is the Reynolds number of the heating steam condensation liquid outside the tube. The evaporation heat transfer coefficient of the falling-lms inside the tube (h) was computed as follows: where d o , d i and l s are the outside diameter (m), inside diameter (m) and thermal conductivity (W m À1 K À1 ) of the heat transfer tube, respectively. The dimensionless falling-lm evaporation heat transfer coefficient (h + ) was computed as follows: where v i is the kinematic viscosity of liquid lms (m 2 s À1 ) and l i is the thermal conductivity of liquid lms (W m À1 K À1 ). The liquid lm evaporation mass transfer rate (u v ) was computed as follows: The physical model of falling-lm mass transfer is illustrated in Fig. 3. Under the stable state, the SO 2 in the basic aluminum  sulfate desulphurization-regeneration solution was continually desorbed out. Based on the SO 2 component balance, the equation obtained was as follows: 33 where DC m is the impetus of mass transfer.
where U is the volumetric ow rate of liquid lms, m 3 s À1 ; C is the SO 3 2À concentration in the liquid lms, kmol m À3 ; N is the convection mass transfer rate of SO 2 , kmol m À2 s À1 ; A is the area of liquid lms, m 2 ; K m is the total mass transfer coefficient, m s À1 ; l is the height of falling-lms, m; C l is the SO 3 2À concentration at the liquid lm height l, kmol m À3 ; C * l is the dissolved SO 2 concentration in solution that was balanced with the SO 2 pressure in gas at the liquid lm height l, kmol m À3 ; C l+Dl is the SO 3 2À concentration at the liquid lm height l + Dl, kmol m À3 ; C * l+Dl is the dissolved SO 2 concentration in solution that was balanced with the SO 2 pressure in gas at the liquid lm height l + Dl, kmol m À3 .
In the experiments, during desorption of desulphurizationregeneration solution, a larger vapor evaporation quantity indicates smaller SO 2 concentration, which can be ignored; hence, C* approaches 0. Then, we obtain the following equation: where C 0 and C 1 are the SO 3 2À concentrations at the inlet and outlet of the liquid lms, respectively, kmol m À3 . The dimensionless mass transfer coefficient of the falling-lms (Sh) is computed as follows: where D is the diffusion coefficient of SO 2 in solution, m 2 s À1 .
Under the same conditions, the mass transfer coefficient at any position within the tube is considered to be the same and is equal to the total mass transfer coefficient. The SO 3 2À concentration at the liquid lm height l was computed as follows: The SO 2 desorption efficiency of desulphurization-regeneration solution (h) is dened as follows:

Uncertainty analysis
The uncertainty analysis of the experimental data was performed using the method reported by Kline et al. 34 According to the uncertainty transfer and calculation method of indirect measurement, the assumption is as follows: where each variable is independent of the others, and their uncertainty is (dx 1 , dx 2 , dx 3 .dx n ). The calculation formula of the relative uncertainty of indirect measurement is computed as follows: In this experiment, the volumetric ow rate of the uid was monitored by a rotameter with the accuracy of AE1.5%, the temperature was measured by a platinum resistance temperature sensor with an accuracy of AE0.1 K, the mass was measured by pressure sensors with sensitivity of AE0.1 g, and the time was counted to the nearest 0.1 s of the stopwatch. The relative uncertainty of the evaporation heat transfer coefficient of the falling-lms was obtained by combining eqn (6) and eqn (16); the evaporation mass transfer rate was obtained by combining eqn (8) and eqn (16); the mass transfer coefficient was obtained by combining eqn (11) and eqn (16). Through uncertainty propagation analysis, the maximum uncertainties of the heat transfer coefficient, mass transfer rate and mass transfer coef-cient in the experiments were computed to be 6.71%, 2.0% and 8.18%, respectively.

Heat and mass transfer performances with convergingdiverging tubes of different dimensions
To test the accuracy of the experimental system, we used a smooth tube as the control, and validated the reliability of the system by comparing with previous experimental results. Fig. 4 shows a comparison between falling-lm evaporation and the Chun & Seban empirical formula 35 with the largest error below AE6%. The experimental results of falling-lm evaporation based on the system are consistent with the previous ndings, indicating that this system is highly reliable.   5 shows the curves of evaporation heat transfer coefficients of falling-lms along with the liquid lm ow rate of 0.07-0.18 kg m À1 s À1 for the four converging-diverging tubes and the smooth tube. Clearly, with an increase in the ow rate, the falling-lm evaporation heat transfer coefficients inside all the converging-diverging tubes increase. Compared with the smooth tube, converging-diverging tubes exhibited good heat transfer performance in the range of ow rate of 0.12-0.18 kg m À1 s À1 . This indicates that the converging-diverging tubes are appropriate for falling-lm evaporation with large liquid lm ow rate, while the smooth tube is better for falling-lm evaporation with small liquid lm ow rate. This is because for a small liquid lm Reynolds number, the lm thickness plays a dominant effect on the evaporation heat transfer coefficients of falling-lms. The converging-diverging tube has a periodic alternation of converging segments and diverging segments, which leads to the periodical "increase and decrease" of lm thickness during the falling-lm process, but the average lm thickness is larger than that of the smooth tube with constant lm thickness, so the heat transfer performance is weakened. As the liquid lm Reynolds number increases, the turbulence of liquid lms in the converging-diverging tubes is intensied, so the role of turbulence-induced heat transfer surpasses that of the lm thickness and the falling-lm evaporation heat transfer coefficient gradually increases. As for different dimensions, the falling-lm evaporation heat transfer coefficients of both converging-diverging tubes 3# and 4# are better than tubes 1# or 2#. This is because tubes 3# and 4# have larger rib heights, which help to efficiently induce the disturbance of liquid lms. 36 Moreover, the falling-lm evaporation heat transfer coefficients of converging-diverging tubes 3# and 2# are better than tubes 4# and 1#, respectively. This is primarily because the heat transfer performance is enhanced in the converging segment and weakened in the diverging segment according to eld synergy theory. Thus, at the same rib height and rib pitch, the longer the converging segment of the converging-diverging tube is, the better the heat transfer performance is. 37,38 At the liquid lm ow rate of 0.17 kg m À1 s À1 , tube 3# has an evaporation heat transfer coefficient 1.6 times larger than that of the smooth tube. Fig. 6 shows the relationship curves between the perimeter ow rate and the evaporation mass transfer rate of falling-lms for the four converging-diverging tubes and the smooth tube. The evaporation mass transfer rates of falling-lms inside all the converging-diverging tubes increase with an increase in the perimeter ow rate of the liquid lms. This is primarily because the evaporation mass transfer rate of falling-lms is largely associated with the evaporation heat transfer coefficient as a larger evaporation heat transfer coefficient promotes heat absorption by liquid lms, leading to the increase in evaporation of the liquid lms and thus the evaporation mass transfer rate. Moreover, with the increase in ow rate, the evaporation mass transfer rates of both tubes 3# and 4# surpass those of tubes 1# and 2# or the smooth tube; thus, tubes 3# and 2# are better than tubes 4# and 1#, respectively. When the perimeter ow rate of liquid lms is 0.173 kg m À1 s À1 , the evaporation mass transfer rate of the falling-lms in tube 3# is 0.0094 kg m À2 s À1 , which is 1.38 times larger than the smooth tube. Thus, according to the comparative analysis of the heat and mass transfer performances inside the four convergingdiverging tubes, converging-diverging tube 3# is optimal.   aluminum concentration of 20 kg m À3 and basicity of 20%, the relationship between the average mass transfer coefficient and liquid lm ow rate in the basic aluminum sulfate desulphurization-regeneration solution is illustrated in Fig. 7. With the rise in ow rate, the falling-lm average mass transfer coefficients of the converging-diverging tube 3# and the smooth tube both increase. Under the same conditions, the falling-lm average mass transfer coefficient inside the convergingdiverging tube is 44-67% higher than the smooth tube. The main reason is that the converging-diverging tube promotes the uid disturbance near the wall, enhances turbulence and reduces the thickness of the viscous bottom layer. During the falling-lm desorption of basic aluminum sulfate desulphurization-regeneration solution, SO 2 desorption efficiency gradually decreases with the liquid lm perimeter ow rate (Fig. 7). At the same inlet sulfur concentration, as the ow rate increases, the outlet sulfur concentrations inside the converging-diverging tube 3# and the smooth tube gradually become higher. This is primarily because besides the mass transfer coefficient, the falling-lm desorption is also correlated with the ow rate. It is positively correlated with the mass transfer coefficient and negatively correlated with ow rate. Thus with an increase in the ow rate, though the mass transfer coefficient is improved, the effect of ow rate surpasses that of the mass transfer coefficient, weakening the desorption. Under the same ow rate, the outlet sulfur concentration of the falling-lms in the converging-diverging tube is lower than that in the smooth tube. At the liquid lm perimeter ow rate of 0.114 kg m À1 s À1 , the outlet sulfur concentration is 64% lower and the desorption efficiency (up to 94.2%) is 10.5% higher in the converging-diverging tube than in the smooth tube. At the ow rate of 0.222 kg m À1 s À1 , the sulfur concentration is 48% lower and the desorption efficiency (up to 88.7%) is 10.3% higher in the converging-diverging tube than in the smooth tube. Moreover, when the desulphurization-regeneration solution ows along the tube length, the sulfur concentrations rst decline rapidly and then slowly, indicating that the higher sulfur concentrations contribute to desorption.
3.2.2 Effect of the different sulfur concentrations. At the heating temperature of 381.15 K, perimeter ow rate of 0.162 kg m À1 s À1 , aluminum concentration of 20 kg m À3 and basicity of 20%, the relationship between the average mass transfer coefficient and inlet sulfur concentration in basic aluminum sulfate desulphurization-regeneration solution is illustrated in Fig. 8. With the rise in inlet sulfur concentration, the falling-lm average mass transfer coefficients of both the converging-diverging tube 3# and the smooth tube increase. This is primarily because the mass transfer coefficient is correlated with the sulfur concentration gradient at the lm thickness direction of the desulphurization-regeneration solution according to lm theory. At the same ow rate, as the inlet sulfur concentration increases, the concentration gradient at the lm thickness direction rises. Thus, the mass transfer coefficient increases for both tubes, but the falling-lm average mass transfer coefficient inside the converging-diverging tube 3# is 44-69% higher than that in the smooth tube. During the falling-lm desorption of basic aluminum sulfate desulphurization-regeneration solution, SO 2 desorption efficiency gradually increases with the inlet sulfur concentration (Fig. 8). In comparison, at the inlet sulfur concentration of 0.02 kmol m À3 , the outlet sulfur concentration is 61% lower and the desorption efficiency (up to 89.3%) is 16.3% higher in the convergingdiverging tube than in the smooth tube. At the inlet sulfur concentration of 0.1 kmol m À3 , the sulfur concentration is 67% lower and the desorption efficiency (up to 94.1%) is 12.0% higher in the converging-diverging tube than in the smooth tube.
3.2.3 Effect of the different heating temperatures. At the perimeter ow rate of 0.162 kg m À1 s À1 , sulfur concentration of 0.06 kmol m À3 , aluminum concentration of 20 kg m À3 and basicity of 20%, the relationship between the average mass transfer coefficient and heating temperature is illustrated in Fig. 9. With the rise of heating temperature, the falling-lm average mass transfer coefficients of both the convergingdiverging tube 3# and the smooth tube increase. This is primarily because the mass transfer coefficient is also correlated with SO 2 diffusion coefficient of the desulphurizationregeneration solution according to lm theory, and the diffusion coefficient is proportional to the desulphurization-regeneration solution temperature. With the rise of heating temperature, the desulphurization-regeneration solution  This journal is © The Royal Society of Chemistry 2018 temperature increases. Thus, the mass transfer coefficient increases for both tubes, but the falling-lm mass transfer coefficient inside the converging-diverging tube is 33-44% higher than in the smooth tube. During the falling-lm desorption of basic aluminum sulfate desulphurization-regeneration solution, SO 2 desorption efficiency gradually increases with the heating temperature ( Fig. 9). At the same ow rate and inlet sulfur concentration, as the heating temperature rises, the outlet sulfur concentrations in the converging-diverging tube 3# and the smooth tube gradually drop. At the heating temperature of 371.15 K, the outlet sulfur concentration is 29% lower and the desorption efficiency (up to 83.4%) is 6.7% higher in the converging-diverging tube than in the smooth tube. At the heating temperature of 386.15 K, the outlet sulfur concentration is 63% lower and the desorption efficiency (up to 93.4%) is 11.5% higher in the converging-diverging tube than in the smooth tube.
3.2.4 Correlation derived from the data. As discussed above and shown in Fig. 7-9, the mass transfer coefficient of the falling-lm evaporation for the converging-diverging tube 3# are higher than that for the smooth tube. Thus, the correlation should be used to predict the mass transfer coefficients of falling-lm evaporation in the converging-diverging tube 3#. For engineering purposes, we tried to model K m in functions of important inuencing parameters only. The Sherwood numbers and SO 2 desorption efficiency of the falling-lm evaporation inside the converging-diverging tube 3# and smooth tube are calculated as follows: For the converging-diverging tube 3# The validity of using eqn (17)- (20) to predict the experimental mass transfer coefficient and SO 2 desorption efficiency are shown in Fig. 10 and 11, respectively. As shown in Fig. 10, for the correlation on the mass transfer coefficients inside the converging-diverging tube, 93% of the data falls within AE20% error; for the smooth tube, 100% are within AE20% error. As shown in Fig. 11, for the correlation on the SO 2 desorption efficiency inside the converging-diverging tube and smooth tube, 100% of the data falls within AE10% error. Overall, good agreement has been observed between experimental data and theoretical prediction.

Conclusions
We developed a new type of falling-lm evaporator for SO 2 enhanced desorption experiments. To nd the optimal structure of the converging-diverging tube and develop a high-efficiency falling-lm evaporator, the heat and mass transfer performances of converging-diverging tubes with different dimensions were studied. It was found that converging-diverging tubes with large liquid lm ow rate performed well in the falling-lm Fig. 9 Effect of the heating temperature on the mass transfer coefficient and SO 2 desorption efficiency.  evaporation, and their rib heights largely affected the heat and mass transfer performances. At the same rib height and rib pitch, the longer the converging segment of the converging-diverging tube was, the better the heat transfer performance was. The evaporation heat transfer coefficient and evaporation mass transfer rate in the optimal converging-diverging tube were 1.6 and 1.38 times larger than the smooth tube, respectively. The optimal converging-diverging tube was used in the falling-lm desorption of desulphurization-regeneration solution: the mass transfer coefficient increased and SO 2 desorption efficiency decreased with an increase in the ow rate, but both increased with an increase in sulfur concentration or heating temperature. Smaller ow rate, higher sulfur concentration, and higher heating temperature were more constructive to SO 2 desorption. The mass transfer coefficient in the converging-diverging tube was 33-69% higher than that in the smooth tube, and thus the SO 2 desorption efficiency was greatly improved. At the perimeter ow rate of 0.114-0.222 kg m À1 s À1 , the desorption efficiency in the converging-diverging tube was up to 94.2% and was 10.3-10.5% higher than that in the smooth tube. At the inlet sulfur concentration of 0.02-0.1 kmol m À3 , the desorption efficiency was up to 94.1% and was 12.0-16.3% larger than that in the smooth tube. At the heating temperature of 371.15-386.15 K, the desorption efficiency was up to 93.4% and was 6.7-11.5% larger than that in the smooth tube. Moreover, correlations were obtained to predict the mass transfer coefficient and SO 2 desorption efficiency. This study forms a basis for the process design and industrial application of converging-diverging tubes into a new type of falling-lm evaporator for SO 2 desorption of basic aluminum sulfate desulphurization-regeneration solution.

Conflicts of interest
The authors declare no competing nancial interest.
Area of outside surface of the tube, m 2 A Area of liquid lms, m 2 C SO 3 2À concentration in the liquid lms, kmol m À3 C* Dissolved SO 2 concentration in solution that was balanced with the SO 2 pressure in gas, kmol m À3 C 0 SO 3 2À concentrations at the inlet of the liquid lms, kmol m À3 C 1 SO 3 2À concentrations at the outlet of the liquid lms, kmol m À3 C l SO 3 2À concentration at the liquid lm height l, kmol m À3 C * l Dissolved SO 2 concentration in water that was balanced with the SO 2 pressure in gas at the liquid lm height l, kmol m À3 C l+Dl SO 3 2À concentration at the liquid lm height l + Dl, kmol m À3 C * l+Dl Dissolved SO 2 concentration in water that was balanced with the SO 2 pressure in gas at the liquid lm height l + Dl, kmol m À3 DC m Impetus of mass transfer, kmol m À3