Falling Film Evaporator for Desorption of Basic Aluminum Sulfate SO2

Nov 27, 2017 - So far, more than 200 types of fuel gas desulfuration technology have been developed worldwide. ...... effect of basic aluminum sulfate...
3 downloads 0 Views 2MB Size
Download PDF
Article Cite This: Energy Fuels XXXX, XXX, XXX−XXX

pubs.acs.org/EF

Falling Film Evaporator for Desorption of Basic Aluminum Sulfate SO2‑Rich Solution and Enhancement of Heat and Mass Transfer Kuo Huang,*,†,‡ Xianhe Deng,† and Min Chen§ †

Department of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, Guangdong 510640, People’s Republic of China ‡ Guangzhou Institute of Energy Testing, Guangzhou, Guangdong 511447, People’s Republic of China § Department of Chemistry and Chemical Engineering, Jinggangshan University, Ji an, Jiang xi 343009, People’s Republic of China ABSTRACT: This study was aimed to improve the SO2 desorption effect of basic aluminum sulfate SO2-rich solution. Based on the desorption mechanism, we first used a falling film evaporation method to intensify heat transfer and mass transfer. Based on the falling film desorption heat and mass transfer model, we analyzed the falling film evaporation and desorption of basic aluminum sulfate SO2-rich solution inside the converging−diverging tube and the smooth tube and investigated the heat and mass transfer rules under different conditions. It was found as the quantity of SO2-rich solution increased, the heat transfer coefficient and mass transfer coefficient of falling film evaporation both increased, but the SO2 desorption efficiency decreased. With the rise of the heating temperature, the three indices all increased. With the rise of the inlet sulfur concentration, the three indices all increased. With the rise of the aluminum concentration, the three indices all gradually declined. With the rise of the alkalinity, the three indices all gradually declined. Comparative analysis showed the heat transfer coefficient and mass transfer coefficient of falling film evaporation and SO2 desorption efficiency were 17%−29%, 33%−69%, and 6.7%−16.3% larger inside the converging−diverging tube than the smooth tube, respectively, indicating the basic aluminum sulfate SO2-rich solution significantly outperforms inside the converging−diverging tube in terms of heat transfer and mass transfer. At the heating temperature of 108 °C, liquid film flow rate of 0.005 kg/s, sulfur concentration of 0.06 mol/L, aluminum concentration of 20 g/ L, and basicity of 20%, the SO2 desorption efficiency inside the converging−diverging tube could reach a high level 94.2%, compared with only 83.7% inside the smooth tube. Moreover, correlations were obtained to predict the heat and mass transfer coefficients.

1. INTRODUCTION SO2 emission is one major cause of air pollution and acid rain, and thus becomes one severe restriction on economic and social development. So far, more than 200 types of fuel gas desulfuration technology have been developed worldwide.1 Depending on the dry or wet state of the desulfurization agents and products, these techniques can be divided into dry, semidry, and wet techniques. However, the application of the dry and semidry techniques is largely limited by the low efficiency. Thus, the wet techniques are dominant in fuel gas desulfuration2 and can be subdivided into renewable and nonrenewable techniques depending on the use of desulfurization agents. The widely used industrial nonrenewable wet fuel gas desulfurization techniques include limestone−gypsum technique,3 ammonia desulfuration,4 and seawater desulfuration.5 Despite the high efficiency, these techniques have some inherent limitations, such as secondary pollution due to desulfuration solutions and the problem of wastewater processing. From the perspective of resource recycling, solving the sulfur recycle from desulfuration solutions would contribute to the recycled use of desulfurization agents. Thus, developing renewable desulfurization agents is of great importance for resource conservation and environmental protection. Much research has been conducted on sodium sulfite method,6 magnesium oxide method,7 sodium citrate method,8 and organic amine method.9 However, the development and industrialization of these methods are limited by low © XXXX American Chemical Society

regeneration ability, stability, and equipment investment of desulfurization agents. Basic aluminum sulfate, as a promising desulfurization agent, has been applied into fuel gas purification. Compared with the basic aluminum sulfate− gypsum method,10 the basic aluminum sulfate desorption method11,12 has attracted wide attention owing to high desulfuration efficiency, recycling of desulfuration liquid, low process liquid−gas ratio, and recyclability of recycled SO2. The existing research on basic aluminum sulfate desorption of fuel gas desulfuration is focused on SO2 absorption and starts from the perspectives of mechanism,13 dynamics,14 influence factors,15−19 and inhibitors20 but has rarely concerned SO2 desorption. Experiments on the basic aluminum sulfate desulfuration desorption process with water bath heating show the SO2 desorption efficiency under the optimal conditions is about 70%.21 In these experiments, the use of water bath heating leads to the limitations of nonuniform heating, long heating time, and high energy consumption. Researchers have made efforts to improve the limitations of water bath heating. For instance, Zhang found the desorption efficiency was only slightly improved after the addition of mechanical agitation into water bath heating.22 Gao found the addition of microwave assistance contributed to the deepening Received: July 28, 2017 Revised: November 23, 2017 Published: November 27, 2017 A

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels

Figure 1. Experimental system of falling film flow heat and mass transfer.

tube and analyzed SO2 desorption efficiency and the laws on how heat transfer and mass transfer were affected.

of desorption reaction, and after the desorption in the thermostatic water bath reached the end point, the continual use of microwave could improve the desorption efficiency by 3%−5%.23 Generally, the traditional water bath heating has not been largely improved. Thus, to improve the desorption effect and reduce energy consumption, researchers had to develop novel techniques or methods. Xu et al. used ultrasonic waves to test the effects on the desorption of basic aluminum sulfate SO2-rich solution and found ultrasonic waves promoted the decomposition of only sulfurous acid, but not bisulfite ions.24 Xue et al. also found ultrasonic waves promoted the desorption of SO2 and the SO2 desorption efficiency under experimental conditions was up to 82%.25 Though the above studies reported some improvements, the effects were still not significant and the research was still at the experimental stage and far from industrialization. Our team used the vacuum technique to study desorption of basic aluminum sulfate SO2-rich solution and found the desorption efficiency after 80 min was up to 95%.26 Despite the high desorption efficiency achieved, there are still some limitations such as long desorption time, and our research is still at the laboratory stage. To solve the problems of nonuniform heating and long desorption time, we find it necessary to adopt high-efficiency heat transfer and mass transfer equipment. Falling film evaporator has the advantages of high heat transfer efficiency, small temperature difference, short residence time, and low power consumption. For this reason, it is widely used in chemical industry, nuclear power, power, cooling, and many other industrial fields.27−30 Meanwhile, as an excellent enhanced heat transfer unit, the converging−diverging tube is mainly used for single-phase liquid enhanced heat transfer inside and outside the tube31−33 but has not been used in falling film evaporation. Thus, here falling liquid film evaporation was used to study the falling film desorption of basic aluminum sulfate SO2-rich solution, which might bring about good effects. On the basis of above introduction and for improvement of the desorption effect of basic aluminum sulfate SO2-rich solution, here we used falling liquid film evaporation for the first time into experiments on converging−diverging tube and smooth

2. MECHANISM OF DESORPTION REACTION The basic aluminum sulfate water solution, a colorless transparent solution, is prepared as follows: neutral reaction occurs between powder aluminum sulfate and limestone; after quiet placement, the gypsum precipitate is filtered (reaction 1):11 Al 2(SO4 )3 (aq) + 3xCaCO3(s) + 6x H 2O → (1 − x)Al 2(SO4 )3 ·x Al 2O3(aq) + 3xCaSO4 ·2H 2O(s) + 3xCO2 (g)

(1) (1 − x)Al 2(SO4 )3 ·x Al 2O3(aq) + 3xSO2 (g) ↔ (1 − x)Al 2(SO4 )3 ·x Al 2(SO3)3 (aq)

(2)

Δ

The active component in the basic aluminum sulfate solution that absorbs SO2 is Al2O3, which is expressed as aluminum concentration and basicity. The aluminum content (g/L) is determined as the total aluminum quantity (estimated as Al2O3) in 1 L of basic aluminum sulfate solution. Then, the amount of aluminum expressed as Al2O3 in formula (1 − x)Al2(SO4)3·x Al2O3 is termed as the “basic amount” (g/L). In reaction 1, x is the basicity of the solution, which can be calculated by the following equation (eq 3):34 basicity =

basic amount × 100% total amout of aluminum in solution (3)

The basic aluminum sulfate solution absorbed SO2, forming a SO2-rich solution (reaction 2). Since reaction 2 is reversible, the desorption of SO2 from the SO2-rich solution can be realized by heating. However, since Al2(SO3)3 is unstable in the solution, along with the desorption of SO2 in the SO2-rich solution, SO32− and Al3+ underwent double hydrolysis (reactions 3−6).20,35 Moreover, a trace amount of SO32− was oxidized (reaction 8). SO32 −(aq) + H 2O ↔ HSO32 −(aq) + OH−(aq) B

(4)

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels Table 1. Main Structure Dimensions of Heat Transfer Tubesa tube shape

do (m)

di (m)

L (m)

p (m)

p1 (m)

p2 (m)

e (m)

converging−diverging tube smooth tube

0.019 0.019

0.016 0.017

2.3 2.3

0.014

0.0105

0.0035

0.002

a do = outer diameter; di = inner diameter; L = length of analysis segment; p = pitch spacing/node spacing; p1 = length of converging segment; p2 = length of diverging segment; e = rib height.

SO32 −(aq) + H 2O ↔ H 2SO3(aq) + OH−(aq)

(5)

H 2SO3(aq) ↔ SO2 (g) + H 2O

(6)

Al3 +(aq) + H 2O ↔ Al(OH)3 (aq) + 3H+(aq)

(7)

separator 9 into metering tank 11. And the main structure dimensions of the heat transfer tubes are listed in Table 1. The schematic diagram of the heat transfer tubes is illustrated in Figure 2.

(1 − x)Al 2(SO4 )3 ·x Al 2(SO3)3 (aq) + (3x /2)O2 (g) → Al 2(SO4 )3 (aq)

(8)

The reaction kinetics about SO2 desorption in SO2-rich solution suggests the SO2 desorption effect can be improved mainly by heating and SO2 pressure reduction. In fact, these two methods essentially aim to improve the heat transfer and mass transfer efficiency. In this study, the enhanced heat transfer and mass transfer technique was investigated through the desorption of the basic aluminum sulfate SO2-rich solution.

3. EXPERIMENTAL SECTION 3.1. Preparation of Basic Aluminum Sulfate SO2-Rich Solution. First, many groups of basic aluminum sulfate solutions were prepared by a reported method.20,36 Specifically, the basic aluminum sulfate solutions containing certain amounts of aluminum concentration and basicity were prepared as required, respectively. The masses of aluminum sulfate and calcium carbonate powders were figured out from eq 1, weighed, and stored until used. To containers containing an appropriate amount of deionized water, the aluminum sulfate powders were added and stirred until complete dissolution. After that, the calcium carbonate powders were slowly added under stirring. The aluminum sulfate solution was neutralized by addition of calcium carbonate powder, and after 24 h under stirring, the slurry was filtered to obtain the clear solution. After that, many groups of basic aluminum sulfate SO2-rich solutions containing certain amounts of sulfur concentration were prepared, respectively. Specifically, an appropriate amount of sodium sulfite was weighed and directly added into the fresh basic aluminum sulfate solution, forming a basic aluminum sulfate SO2-rich solution containing a certain amount of sulfur concentration. Meanwhile, a trace amount of sodium thiosulfate pentahydrate was added into the basic aluminum sulfate solution used in all the experiments to hinder sulfite oxidation. Aluminum sulfate, calcium carbonate, sodium thiosulfate pentahydrate (all purity ≥ 99%), and sodium sulfite (purity ≥ 97%) were all purchased from Tianjin Kermel Chemicals Co., Ltd., China. All chemicals and reagents were of analytical reagent grade. 3.2. Experimental Setup and Methods. The experimental system of flowing heat and mass transfer of falling films is illustrated in Figure 1. This system is mainly used to detect the heat and mass transfer performances of falling liquid films in vertical tubes. The fluid in heating tank 2 was heated by electric heating unit 1 to the preset temperature, and then was pumped by pump 3 of flow adjustment valve 4 and flow meter 5 into high water reservoir 6, which was connected by adjustment valve 7 with air. After the fluid flowed to the testing segment, falling liquid films were formed on the inner surfaces of the heat transfer tubes. The vapor generated in the heat transfer tubes was pumped by vacuum pump 16 into condensers 13 and 14. Then the condensate liquid entered metering tank 18 for measurement. The unevaporated liquid entered metering tank 12. The outside of the heat transfer tubes was supplied with saturated vapor with a certain pressure and temperature. The vapor condensation water generated during the experiments was passed by vapor−liquid

Figure 2. Schematic diagram of the converging−diverging tube and smooth tube. The major data measured here included the liquid temperature, liquid mass at the initial stage, and liquid mass after experiment in metering tank 2; the vapor mass due to evaporation from the liquid falling films in metering tank 18 and the mass and temperature of unevaporated liquid in metering tank 12; and the mass of heating vapor condensation outside the heat transfer tube in metering tank 11. All liquid temperatures and heating vapor temperatures were measured by platinum resistance temperature sensors with an accuracy of ±0.1 °C. All liquid masses and vapor masses were measured by pressure sensors with sensitivity of ±0.1 g. Besides, the volume flow rate of the fluid was monitored by a rotameter with the accuracy of ±1.5%. The heating vapor pressure was monitored by a pressure transmitter with the accuracy of ±0.1% FS. The data collection of each group lasted about 20 min, and the time was counted to the nearest 0.1 s of the stopwatch. The working medium was the basic aluminum sulfate solution SO2rich solutions, of which the parameters were configured as follows: SO32− concentration = 0.02−0.1 mol/L, aluminum concentration = 10−30 g/L, and basicity = 10%−30%. The basic aluminum sulfate SO2-rich solutions containing definite concentrations of sulfur and aluminum and basicity used in the experiments were self-prepared. During the experiments, the operating parameters were set as follows: flow rate of liquid film = 0.005−0.011 kg/s; Reynolds number of liquid film = 1500−3100; and heating vapor temperature outside the heat transfer tubes = 98−113 °C.

4. HEAT AND MASS TRANSFER MODEL FOR FALLING FILM DESORPTION The basic aluminum sulfate SO2-rich solution formed falling liquid film on the inner surface of the heat transfer tube, when the outside heating vapor provided condensation latent heat, which was transferred from outside to the inside of the tube. C

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels Since the liquid film was under the boiling state, the heat was mainly used by the heat-absorbing and vapor-absorbing vapor heat during the desorption of the SO2-rich solution. Meanwhile, the SO2 desorbed from the SO2-rich solution was delivered by the liquid-phase to the gas−liquid interface, and finally was separated from the interface, entering the gas phase. Thus, the objective of heat transfer was to rapidly transfer the SO32− in the SO2-rich solution into SO2, and the objective of mass transfer was to rapidly transfer the SO2 desorbed from the rich solution into the gas phase. The physical model of falling film mass and heat transfer is illustrated in Figure 3.

⎡ r ρ 2 gλ 3 ⎤1/4 ⎛ ρ 2 g ⎞1/3 0 0 0 ⎢ ⎥ = 1.76λ 0⎜⎜ 0 2 ⎟⎟ Re0−1/3 ho = 1.13 ⎢⎣ μ 0L(Tk − To) ⎥⎦ ⎝ μ0 ⎠ (11)

where ρ0, λ0, and μ0 are the density (kg/m ), thermal conductivity (W/(m·°C)), and dynamic viscosity (kg/(m·s)) of the heating vapor condensation liquid, respectively; L is the valid height of the vertical tube, m; To is the outside wall temperature, °C; g is the gravitational acceleration, m/s2; Re0 is the Reynolds number of the heating vapor condensation liquid outside the heating tube. The mean evaporation heat transfer coefficient of the falling film inside the tube (h) is computed as 3

h=

do di

1

(

1 K

−

1 ho

−

do 2λ s

( ))

ln

do di

(12)

where do, di, and λs are the outside diameter (m), inside diameter (m), and thermal conductivity (W/(m·°C)) of the heat transfer tube, respectively. The dimensionless evaporation heat transfer coefficient of the falling film (Nu) is ⎛ v 2 ⎞1/3 Nu = h⎜ 3 ⎟ ⎝λ g⎠

(13)

where ν is the kinematic viscosity of liquid films, m2/s; and λ is the thermal conductivity coefficient of liquid films, W/(m·°C). The peripheral flow rate of liquid films inside the tube (Γ) is m Γ= l π d it (14)

Figure 3. Model of heat and mass transfer.

where ml is the mass of liquid films, kg; and π = 3.1415926. The liquid film Reynolds number (Re) inside the heat transfer tube is

4.1. Analysis of Heat Transfer. The mean heat transfer coefficient is analyzed by a thermal resistance analytical method.37 With the heat quantity from heating vapor outside the heat transfer tube as the heat transfer quantity, the mean evaporation heat flux density of falling films (q) is computed as follows: rm q= 0 v A 0t (9)

Re =

4Γ μ

(15)

where μ is the dynamic viscosity of liquid films, kg/(m·s). In this experiment, the Reynolds number of falling films varies between 1500 and 3100. Since the flow patterns of vertical falling liquid films have been extensively studied, research conclusions show that the flow of liquid films can be divided into three states: laminar flow (Re ≤ 80−350), transitional flow (80−350 < Re < 1600−2000), and turbulent flow (Re ≥ 1600−2000).39−41 Thus, the Reynolds numbers in the experiments mostly fall within the turbulent flow falling film regime. 4.2. Analysis of Mass Transfer. Under the stable state, the SO2 in the basic aluminum sulfate SO2-rich solution is continually desorbed out, and the mass per unit time transferred from liquid phase to gas phase is computed as

where mv is the mass of heating vapor condensation outside the tube, kg; r0 is the condensation latent heat of saturated vapor outside the tube, kJ/kg; A0 is the area of outside surface of the tube, m2; and t is the experimental time of heat transfer in the falling film, s. Because the heating vapor outside the tube and the liquid film inside the tube were saturated and changed phase at the same saturation temperature in our tests, the overall heat transfer coefficient of falling film evaporation (K) is given by Newton’s law of cooling as follows: q q K= = (Tk − T ) ΔT (10)

G = U (C0 − C1)

(16)

where G is the mass of SO2 per unit time that was transferred from liquid phase to gas phase in the liquid film, kmol/s; U is the volume flow rate of the liquid film, m3/s; and C0 and C1 are the SO32− concentrations at the inlet and outlet of the liquid film, respectively, kmol/m3. The SO32− concentrations before and after the desorption of SO2-rich solution were computed by the iodometric method.42

where Tk is the heating vapor temperature in the ring gap outside the tube, °C; T is the liquid film temperature, °C; and ΔT is the heat transfer temperature difference between the heating vapor and the liquid film, °C. The mean vapor condensation heat transfer coefficient (ho) outside the heat transfer tube is computed by the Nusselt filmwise condensation experimental correlation:38 D

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels Table 2. Parameters and Estimated Uncertainties parameter

symbol (unit)

uncertainty

evaporation heat flux density (converging−diverging tube) evaporation heat flux density (smooth tube) overall heat transfer coefficient (converging−diverging tube) overall heat transfer coefficient (smooth tube) evaporation heat transfer coefficient (converging−diverging tube) evaporation heat transfer coefficient (smooth tube) overall mass transfer coefficient (converging−diverging tube) overall mass transfer coefficient (smooth tube)

mv (g) ml (g) Tk (°C) T (°C) t (s) U (m3/s) C0 (kmol/m3) C1 (kmol/m3) q (W/m2) q (W/m2) K (W/(m2·°C)) K (W/(m2·°C)) h(W/(m2·°C)) h(W/(m2·°C)) KL(m/s) KL (m/s)

±0.1 g ±0.1 g ±0.1 °C ±0.1 °C ±0.1 s ±1.5% ±2.0% ±2.0% 2.92% 2.92% 3.15% 3.10% 6.59% 5.86% 8.18% 5.35%

mass temperature time flow rate of liquid films SO32− concentration

The desorption rate of total impetus (C − C*) is computed as follows:43 N = KLΔCm

By combining eqs 21 and 23, we get η = 1 − e−AKL / U

(17)

4.3. Error Analysis. Some parameters such as mass, temperature, experiment time, and volume flow rate of liquid films are measured by the devices and sensors directly, while other parameters such as evaporation heat flux density, overall heat transfer coefficient, evaporation heat transfer coefficient, and overall mass transfer coefficient of falling films that we defined in this work are calculated based on the experimental data. Generally the uncertainty resulting from measuring devices and experimental fluctuations of experimental conditions can be analyzed. In order to give a good presentation of the error analysis, the mean relative errors of the key parameters in the experiment are tabulated in Table 2. We apply the principle of uncertainty propagation to each experimental data point.45 Thus, from eqs 9, 10, 12, and 21, the relative error of evaporation heat flux density, overall heat transfer coefficient, evaporation heat transfer coefficient, and overall mass transfer coefficient of falling films are computed as follows:

where ΔCm is the impetus of mass transfer. ΔCm =

(C0 − C0*) − (C1 − C1*)

(

ln

(C0 − C0*) (C1 − C1*)

)

(18)

where C is the concentration in the liquid film, kmol/m3; C* is the dissolved SO2 concentration in solution that was balanced with the SO2 pressure in gas, kmol/m3; and KL is the overall mass transfer coefficient, m/s. From the SO2 component balance, then44 SO32−

G = NA = KLΔCmA

(19)

Then KL =

U (C0 − C1) A ΔCm

(20)

where N is the convection mass transfer rate of SO2, kmol/(m2· s); and A is the area of the inside surface of the tube or liquid films, m2. In the experiments, during desorption of SO2-rich solution, a larger vapor evaporation quantity means smaller SO 2 concentration, which can be ignored, so C* approaches 0. Then we get

KL =

U ⎛ C0 ⎞ ln⎜ ⎟ A ⎝ C1 ⎠

1/2 2 ⎡⎛ ⎛ δr0 ⎞2 ⎛ δt ⎞2 ⎤ δq δm v ⎞ ⎢ ⎥ = ⎜ ⎟ +⎜ ⎟ +⎜ ⎟ ⎝ t ⎠ ⎥⎦ q ⎝ r0 ⎠ ⎣⎢⎝ m v ⎠

(21)

The dimensionless mass transfer coefficient of the falling film (Sh) is ⎛ v 2 ⎞1/3 Sh = KL⎜ 3 ⎟ ⎝D g⎠

C0 − C1 C0

(25)

1/2 2 ⎡⎛ ⎞2 ⎛ ⎛ δT ⎞ 2 ⎤ δq δTk ⎞ δK ⎢ ⎥ = ⎜ ⎟ +⎜ ⎟ +⎜ ⎟ ⎢⎣⎝ q ⎠ K ⎝ Tk − T ⎠ ⎝ Tk − T ⎠ ⎥⎦

(26)

1/2 2 ⎡⎛ ⎛ d i δh 0 1 ⎞ 2 ⎤ d i δK 1 ⎞ δh ⎢ ⎥ =h ⎜ ⎟ +⎜ ⎟ ⎢⎣⎝ do K K ⎠ h ⎝ do h0 h0 ⎠ ⎥⎦

(27)

1/2 2 ⎡ ⎛ ⎛ C ⎞ δC ⎞ 2 ⎤ ⎛ δU ⎞2 ⎛ ⎛ C1 ⎞ δC0 ⎞ δKL 1 1 ⎥ ⎢ ⎜ ⎟ ⎟ ⎜ ⎟ ⎜ = + ⎜ln⎜ ⎟ ⎟ ⎟ + ⎜ln⎜ ⎟ ⎢⎝ U ⎠ KL ⎝ ⎝ C0 ⎠ C0 ⎠ ⎝ ⎝ C0 ⎠ C1 ⎠ ⎥⎦ ⎣

(28)

where the influence of some parameters such as the tube dimensions and geometrical properties of the experimental setup are of minor importance, because of the accurate measurements. Further, the vapor condensation heat transfer coefficient outside the heat transfer tube is calculated by the Nusselt’s film condensation relation, and the error of the relation is ignored.

(22)

where D is the diffusion coefficient of SO2 in solution, m2/s. The desorption efficiency of SO2 (η) is defined as η=

(24)

(23) E

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels The mean relative errors for evaporation heat transfer coefficient and overall mass transfer coefficient of falling films in our experiments are 6.59% and 8.18% for converging−diverging tube and 5.86% and 5.35% for smooth tube, respectively. The converging−diverging tube has larger errors, because it makes the heat and mass transfer coefficients of falling film evaporation larger.

5. RESULTS AND DISCUSSION 5.1. Heat Transfer and Desulfuration Desorption Effect under Different Flow Rates. The falling film evaporation heat transfer coefficient, mass transfer coefficient, and SO2 desorption efficiency of basic aluminum sulfate SO2rich solution inside the converging−diverging tube or smooth tube changing with the Reynolds number of liquid films are illustrated in Figures 4−6, respectively. With the rise of Figure 6. SO2 desorption efficiency changing with the Reynolds number.

the film thickness direction. Comparison shows the evaporation heat transfer coefficient is 22%−28% higher inside the converging−diverging tube (Figure 4). The falling film mass transfer coefficient increases with the rising flow rate for both tubes but is 44%−67% higher inside the converging−diverging tube (Figure 5). Clearly, the falling film flow of SO2-rich solution inside the converging−diverging tube is significantly intensified compared with the smooth tube. The falling film SO2 desorption efficiency declines with the increasing flow rate for both tubes (Figure 6), which is mainly because the desorption efficiency is also correlated with the flow rate in addition to the mass transfer coefficient. Though the mass transfer coefficient increases with the rising flow rate for both tubes, the effect of flow rate is dominant compared with the mass transfer coefficient (eq 24). Thus, the flow rate largely affects the SO2 desorption efficiency. With the rise of flow rate within experimental ranges, the SO2 desorption efficiency decreases from 94.2% to 88.7% inside the converging−diverging tube and from 83.7% to 78.4% inside the smooth tube, but is 10.3% - 10.7% higher inside the converging−diverging tube than the smooth tube. 5.2. Heat Transfer and Desulfuration Desorption Effect under Different Heating Temperatures. The falling film evaporation heat transfer coefficient, mass transfer coefficient, and SO2 desorption efficiency changing with the heat transfer temperature difference (temperature difference between heating vapor and liquid film) or heating temperature are illustrated in Figures 7−9, respectively. With the rise of heating temperature outside the heat transfer tube from 98 to 113 °C, the heat transfer temperature difference increases and evaporation heat transfer coefficient rises for both tubes (Figure 7). The evaporation heat transfer coefficient inside the converging−diverging tube is 22%−25% higher than the smooth tube. Thus, a higher heating temperature contributes to desorption. Moreover, the mass transfer coefficient increases with the rise of heating temperature for both tubes and is 33%− 44% larger inside the converging−diverging tube (Figure 8). The falling film SO2 desorption efficiency increases with the rise of heating temperature for both tubes (Figure 9), which is mainly because the mass transfer coefficients inside the converging−diverging tube and the smooth tube increase by 5.8 × 10−5 and 4.0 × 10−5 m/s, respectively with the temperature rise. Thus, the SO2 desorption efficiency increases

Figure 4. Heat transfer coefficient changing with Reynolds number. Conditions (the same in Figures 5 and 6): Tk = 108 °C; 0.06 mol/L sulfur; 20 g/L aluminum; 20% basicity.

Figure 5. Mass transfer coefficient changing with the Reynolds number.

Reynolds number, the evaporation heat transfer coefficient increases for both tubes, indicating the increasing flow rate contributes to the heat transfer at the film thickness direction of the SO2-rich solution. Since SO2 desorption by sulfurous acid radical (SO32−) in the SO2-rich solution is endothermic, the increasing flow rate accelerates the SO32− to SO2 conversion at F

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels

from 76.8% to 81.8% inside the smooth tube, and is 6.7%− 11.5% higher inside the converging−diverging tube. As for the increasing amplitudes of mass transfer coefficient as well as SO2 desorption efficiency, heating temperature is also an important influencing factor on the falling film SO2 desorption effect of basic aluminum sulfate SO2-rich solution. 5.3. Heat Transfer and Desulfuration Desorption Effect under Different Sulfur Concentrations. The falling film evaporation heat transfer coefficient, mass transfer coefficient and SO2 desorption efficiency changing with the inlet sulfur concentration from 0.02 to 0.1 mol/L are illustrated in Figures 10−12, respectively. With the rise of sulfur

Figure 7. Heat transfer coefficient changing with the heat transfer temperature difference. Conditions (the same in Figures 8 and 9): Re = 2250; 0.06 mol/L sulfur; 20 g/L aluminum; 20% basicity.

Figure 10. Heat transfer coefficient changing with the inlet sulfur concentration. Conditions (the same in Figures 11 and 12): Tk= 108 °C; Re = 2250; 20 g/L aluminum; 20% basicity.

Figure 8. Mass transfer coefficient changing with the heating temperature.

Figure 11. Mass transfer coefficient changing with the inlet sulfur concentration.

concentration, the evaporation heat transfer coefficient increases for both tubes (Figure 10), which is mainly because the SO2 desorption of SO2-rich solution absorbs more heat with the increasing sulfur concentration. The heat transfer coefficient inside the converging−diverging tube is 20%−29% higher than the smooth tube. Moreover, the mass transfer coefficient increases with the increasing sulfur concentration for both tubes, but is 44%−69% higher inside the converging− diverging tube (Figure 11).

Figure 9. SO2 desorption efficiency changing with the heating temperature.

under the same flow rate. With the temperature rise within experimental ranges, the SO2 desorption efficiency increases from 83.4% to 93.4% inside the converging−diverging tube and G

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels

Figure 14. Mass transfer coefficient changing with the aluminum concentration.

Figure 12. SO2 desorption efficiency changing with the inlet sulfur concentration.

The falling film SO2 desorption efficiency rises with the increase of inlet sulfur concentration for both tubes (Figure 12), which is mainly because the mass transfer coefficient increases with the rise of sulfur concentration. The mass transfer coefficients inside the converging−diverging tube and the smooth tube increase by 3.6 × 10−5 and 3.7 × 10−5 m/s, respectively. Thus, within the experimental ranges, the SO2 desorption efficiency increases from 89.3% to 94.1% inside the converging−diverging tube and from 73.0% to 82.1% inside the smooth tube, and is 10.7%−16.3% higher inside the converging−diverging tube. As for the increasing amplitudes, the sulfur concentration is also an important influencing factor on the SO2 desorption effect of basic aluminum sulfate SO2-rich solution. 5.4. Heat Transfer and Desulfuration Desorption Effect under Different Aluminum Concentrations. The falling film evaporation heat transfer coefficient, mass transfer coefficient, and SO2 desorption efficiency changing with the aluminum concentration from 10 to 30 g/L are illustrated in Figures 13−15, respectively. With the rise of aluminum concentration, the evaporation heat transfer coefficient declines

Figure 15. SO2 desorption efficiency changing with the aluminum concentration.

insignificantly, and within the experimental ranges, it is 17%− 26% higher inside the converging−diverging tube (Figure 13). The mass transfer coefficients inside the converging−diverging tube and smooth tube decrease by 1.8 × 10−5 and 0.9 × 10−5 m/s, respectively, but are 44%−54% higher in the converging− diverging tube (Figure 14). A higher aluminum concentration accelerates SO2 absorption and indicates the increases of SO2 absorption quantity and product concentration for the absorption reaction. Since desorption is reversible, absorption is exothermic and desorption is endothermic, a higher desorption reactant concentration requires more heat, and under the same concentration and temperature, the desorption reaction is less complete. Therefore, the desorption efficiency slightly declines with the increasing aluminum concentration (Figure 15). Within the experimental ranges, the SO2 desorption efficiency decreases from 92.0% to 89.3% inside the converging−diverging tube and from 81.9% to 78.5% inside the smooth tube, respectively, but is 10.1%−10.8% higher inside the converging−diverging tube. As for the changing amplitudes, the aluminum concentration has a relatively small impact on SO2 desorption effect of basic aluminum sulfate SO2rich solution.

Figure 13. Heat transfer coefficient changing with the aluminum concentration. Conditions (the same in Figures 14 and 15): Tk= 108 °C; Re = 2250; 0.06 mol/L sulfur; 20% basicity. H

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels 5.5. Heat Transfer and Desulfuration Desorption Effect under Different Basicity. The falling film evaporation heat transfer coefficient, mass transfer coefficient, and SO2 desorption efficiency changing with the basicity from 10% to 30% are illustrated in Figures 16−18, respectively. With the rise

Figure 18. SO2 desorption efficiency changing with the basicity.

4−18, the falling film evaporation process is very complicated due to the multitude of influencing factors. For engineering propose, we try to model h and KL in function of important influencing parameters only. By using the dimensional analysis technique and the regression method, we obtain the correlations for the Nusselt numbers and Sherwood numbers of falling film evaporation within the converging−diverging tube and the smooth tube as follows: for the smooth tube:

Figure 16. Heat transfer coefficient changing with the basicity. Conditions (the same in Figures 17 and 18): Tk = 108 °C; Re = 2250; 0.06 mol/L sulfur; 20 g/L aluminum.

Nu = 8.23 × 10−6Re1.025ΔT 0.608Pr 1/3

(29)

−4

(30)

Sh = 1.076 × 10 Re

0.892

Sc

0.5

for the converging−diverging tube: Nu = 1.2 × 10−5Re1.012ΔT 0.606Pr 1/3

(31)

Sh = 1.479 × 10−3Re 0.608Sc 0.5

(32)

The validity of using eqs 29−32 to predict the experimental heat and mass transfer coefficients is shown in Figure 19a,b, respectively. As shown in Figure 19a, for the correlation on the heat transfer coefficients within the converging−diverging tube and the smooth tube, all the experimental data fall within ±20% error of the calculated values from the correlation equation. Meanwhile, As shown in Figure 19b, for the correlation on the mass transfer coefficients within the smooth tube, 88% of the data falls within ±20% error and 96% falls within ±30% error; for the converging−diverging tube, 96% is within ±20% error and 96% is within ±30% error. Overall, good agreement has been observed between experimental data and theoretical prediction. By comparing the obtained correlations for the falling film evaporation within the converging−diverging tube and smooth tube, the enhancement ratios (γ) of the heat and mass transfer were determined to evaluate the heat and mass transfer performance. They can be defined as

Figure 17. Mass transfer coefficient changing with the basicity.

of basicity, the heat transfer coefficient declines, as in the case of aluminum concentrations, and within the experimental ranges, it is 21%−23% higher inside the converging−diverging tube (Figure 16). The mass transfer coefficients inside the converging−diverging tube and smooth tube decrease by 1.0 × 10−5 and 0.5 × 10−5 m/s, respectively, but are 44%−49% higher inside the converging−diverging tube (Figure 17). As the basicity increases, the active ingredient concentration of SO2 absorption rises, and the desorption reaction under the same concentration and temperature is less complete. Within the experimental ranges, the SO2 desorption efficiency decreases from 92.1% to 89.1% inside the converging−diverging tube and from 81.0% to 79.4% inside the smooth tube, but is 9.6%− 11.0% higher inside the converging−diverging tube (Figure 18). Likewise, the effect of basicity on SO2 desorption of basic aluminum sulfate SO2-rich solution is relatively small. 5.6. Heat and Mass Transfer Correlations of Experimental Values. As indicated above and shown in Figures I

γh =

hcd hs

(33)

γm =

KLcd KLs

(34) DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels

Figure 20. Enhancement ratios of the heat and mass transfer changing with the Reynolds number.

area of the converging−diverging tube is narrowed by 6% compared with the smooth tube, and within the experimental ranges and under the same conditions, this leads to the decrease of 1.5%−2.2% in SO2 desorption efficiency of basic aluminum sulfate SO2-rich solution. However, due to the improvement of falling film turbulence intensity inside the converging−diverging tube, the mass transfer coefficient is significantly improved. Within the experimental ranges, the increase of mass transfer coefficient improves SO2 desorption efficiency by 8.9%−17.8%, and finally SO2 desorption efficiency is 6.7%−16.3% larger inside the converging−diverging tube than the smooth tube. Besides, the enhancement ratio of the mass transfer coefficient is largely affected by the Reynolds number; it gradually declines with the increase of the Reynolds number. Thus, when the converging−diverging tube is used in desorption of basic aluminum sulfate SO2-rich solution, the Reynolds number of the liquid films should be appropriately controlled. Figure 19. Comparison of the experimental data of the converging− diverging tube and the smooth tube versus the calculated values.

6. CONCLUSIONS To improve the SO2 desorption effect of SO2-rich solution, here we used falling liquid film evaporation for the first time into SO2 desorption experiments and analyzed SO2 desorption efficiency and the laws on how heat transfer and mass transfer were affected. It is found that the falling film flow rate, heating temperature, sulfur concentration, aluminum concentration, and basicity all affect the desorption effect of basic aluminum sulfate SO2-rich solutions to varying degrees. The dominant influencing factor is falling film flow rate. The condition of a small falling film flow rate, high heating temperature, high sulfur concentration, low aluminum concentration, and low basicity is more constructive to SO2 desorption. The basic aluminum sulfate SO2-rich solution was desorbed via falling liquid film evaporation, which outperformed traditional desorption methods. The effect was better after the use of the enhanced heat transfer and mass transfer process. At the heating temperature of 108 °C, liquid film flow rate of 0.005 kg/s, sulfur concentration of 0.06 mol/L, aluminum concentration of 20 g/L, and basicity of 20%, the basic aluminum sulfate SO2rich solution inside the converging−diverging tube led to a falling film-based SO2 desorption efficiency up to 94.2%. Moreover, correlations were obtained to predict the heat and transfer coefficients. This study provides a novel clue for

where γh and γm are the enhancement ratios of the heat and mass transfer, respectively; hcd and hs are the heat transfer coefficients within the converging−diverging tube and the smooth tube, respectively, W/(m2·°C); KLcd and KLs are the mass transfer coefficients within the converging−diverging tube and the smooth tube, respectively, m/s. As shown in Figure 20, the enhancement ratio of the heat transfer tends to be stable and is very slightly affected by the Reynolds number, indicating the heat transfer coefficient inside the converging−diverging tube is larger than the smooth tube, mainly because of the alteration of tube structure and dimension. The alteration of tube structure and dimension changes the heat transfer surface area and falling film turbulence intensity. Based on previous theoretical analysis and relevant experimental research conclusions,46,47 it is generally believed that the heat transfer or mass transfer coefficient is not directly affected by the heat transfer surface area. Thus, the increase of heat transfer coefficient inside the converging−diverging tube is mainly attributed to the improvement of falling film turbulence intensity. However, according to eq 24, the heat transfer surface area is an important influencing factor on SO2 desorption efficiency. The heat transfer surface J

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels

ΔT = heat transfer temperature difference between the heating vapor and the liquid film, °C To = outside wall temperature, °C Tk = heating vapor temperature in the ring gap outside the tube, °C U = volume flow rate of the liquid film, m3/s

regeneration of basic aluminum sulfate SO2-rich solution and is critical for process design and industrial application related to desorption of SO2-rich solution.

■

AUTHOR INFORMATION

Corresponding Author

Greek Symbols

*Tel./Fax: +86-020-62874844. E-mail: huangkuo2006@126. com.

γ = enhancement ratios of the heat and mass transfer η = desorption efficiency of SO2, % λ = thermal conductivity coefficient of liquid films, W/ (m·°C) λ0 = thermal conductivity of the heating vapor condensation liquid, W/(m·°C) λs = thermal conductivityof the heat transfer tube, W/ (m·°C) Γ = peripheral flow rate of liquid films inside the tube, kg/ (m·s) μ = dynamic viscosity of liquid films, kg/(m·s) μ0 = dynamic viscosity of the heating vapor condensation liquid, kg/(m·s) ν = kinematic viscosity of liquid films, m2/s π = 3.1415926 ρ0 = density of the heating vapor condensation liquid, kg/m3

ORCID

Kuo Huang: 0000-0003-0735-6731 Notes

The authors declare no competing financial interest.

■

NOMENCLATURE A = area of inside surface of the tube or liquid films, m2 A0 = area of outside surface of the tube, m2 C = SO32− concentration in the liquid film, kmol/m3 C0 = SO32− concentrations at the inlet of the liquid film, kmol/m3 C1 = SO32− concentrations at the outlet of the liquid film, kmol/m3 C* = dissolved SO2 concentration in solution that was balanced with the SO2 pressure in gas, kmol/m3 C0* = dissolved SO2 concentration in solution that was balanced with the SO2 pressure at the inlet of the gas, kmol/ m3 C*1 = dissolved SO2 concentration in solution that was balanced with the SO2 pressure at the outlet of the gas, kmol/m3 D = diffusion coefficient of SO2 in solution, m2/s do = outside diameter of the heat transfer tube, m di = inside diameter of the heat transfer tube, m g = gravitational acceleration, m/s2 G = mass of SO2 per unit time that was transferred from liquid phase to gas phase in the liquid film, kmol/s h = evaporation heat transfer coefficient of the falling film inside the tube, W/(m2·°C) ho = vapor condensation heat transfer coefficient outside the heat transfer tube, W/(m2·°C) K = total heat transfer coefficient of evaporation in falling films, W/(m2·°C) KL = total mass transfer coefficient, m/s L = valid height of the vertical tube, m ml = mass of liquid films, kg mv = mass of heating vapor condensation outside the tube, kg N = convection mass transfer rate of SO2, kmol/(m2·s) Nu = dimensionless evaporation heat transfer coefficient of the falling film q = evaporation heat flux density of falling films, W/m2 r0 = condensation latent heat of saturated vapor outside the tube, kJ/kg Re = liquid film Reynolds number inside the heat transfer tube Re0 = Reynolds number of the heating vapor condensation liquid outside the heating tube Sh = dimensionless mass transfer coefficient of the falling film t = experimental time of heat transfer in the falling film, s T = liquid film temperature (as the outlet liquid temperature inside the tube), °C

Subscripts

■

cd = converging−diverging tube h = heat transfer i = inside of tube m = mass transfer o = outside of tube s = smooth tube

REFERENCES

(1) Zhang, Y. F.; Li, D. L.; Wang, J. The development of flue gas desulphurization technology and its application in China. Environ. Sci. Manage. 2006, 31 (4), 124−128. (2) Jin, S. Y.; Zhao, J.; Bian, G. Y. The advances in application of flue gas desulfurization technologies in foreign countries. Sino-global Energy 2014, 19 (3), 89−95. (3) Jiang, X.; Huang, L.; Wu, X. W. The study on application of flue gas desulphurization technology. Tech. Equip. Environ. Pollut. Control 2003, 4 (3), 82−84. (4) Xu, C. X.; Fu, G. G. Review on ammonia flue gas desulfurization. Electric Power Environ. Protect. 2005, 21 (2), 17−20. (5) Hao, J. M.; Wang, S. X.; Lu, Y. Q. Coal sulfur dioxide pollution control technical manual; Chemical Industry Press: Beijing, 2001; Vol. 4, pp 245−277. (6) Liu, J. Q. The process design and industrial operation of sodium sulfite recycling method to sulfur dioxide in boiler flue gas. Ph.D. Thesis, South China University of Technology, Guangazhou, China, 2007. (7) Guo, R. X. Study progress of flue gas desulfurization with magnesium oxide. Sulphur Phosphorus Bulk Mater. Handl. Relat. Eng. 2009, 3, 10−13. (8) Zhang, J. S. A theoretical inquisition into sodium citrate process for liquid sulphur dioxide production and analyses of problems during production in China. Sulphuric Acid Ind. 1998, 3, 3−6. (9) Tang, Z. G.; Zhou, C. C.; Cheng, C. Studies on flue gas desulfurization by chemical absorption using an ethylenediaminephosphoric acid solution. Ind. Eng. Chem. Res. 2004, 43, 6714−6722. (10) Xiao, D. Y. Application of basic aluminium sulfate gypsum process in Shenyang smelter. Sulphuric Acid Ind. 1988, 3, 19−24. (11) Gao, R. H. New process of flue gas desulfurization by alkali sulphate aluminum regeneration. Sichuan Chem. Ind. 1996, 2, 16−17.

K

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels (12) Nanjing Chemical Industry Research Institute. Basic aluminium sulfate regeneration method for removing low concentration sulfur dioxide flue gas. Chin. Pat. CN85103518, Aug. 26, 1987. (13) Liu, Y.; Jiao, X. F.; Wen, G. An approach to mechanism analysis of wet flue gas desulfuration. Therm. Power Gener. 2006, 35 (1), 25− 27. (14) Lang, L. M.; Zhang, Z. J. Study on chemical kinetics of desulfurization process of basic aluminium sulfate. Inner Mongolia Sci. Technol. Econ. 2015, 15, 109−111. (15) Wen, G.; Yu, X. L. Basic Alkali Aluminum Sulfate in Wet Flue Gas Desulfurization of Alkalinity. J. Inner Mongolia Univ. Technol., Nat. Sci. Ed. 2011, 30 (3), 356−358. (16) Zhang, Z. J.; Lang, L. M. Influence of Temperature and Concentration on Desulphurization of Basic Aluminum Sulfate. Coal Technol. 2016, 35 (5), 304−306. (17) Wang, Q. Y.; Deng, X. H. Absorption of sulfur dioxide by alkali aluminum sulfate solution. Chin. J. Environ. Eng. 2013, 7 (12), 4940− 4944. (18) Wang, S. J. Experimental study on basic aluminum sulfate FGD. Ph.D. Thesis, North China Electric Power University, Baoding, China, 2006. (19) Wen, D. Experiment Research about Basic Aluminium Sulfate Desulphurization of Wet Flue Gas. Ph.D. Thesis, Inner Mongolia University of Technology, Hohhot, China, 2009. (20) Chen, M.; Deng, X. H.; He, F. Q. Removal of SO2 from flue gas using basic aluminum sulfate solution with the byproduct oxidation inhibition by ethylene glycol. Energy Fuels 2016, 30 (2), 1183−1191. (21) Zhang, H.; Zhang, Z. J.; Wen, G.; et al. Experimental study on basic aluminum sulfate adsorption regeneration desulfurization process. Therm. Power Gener. 2013, 42 (12), 72−75. (22) Zhang, S. F. Study on Sulfur Dioxide Absorption and Desorption Characteristics of Basic Sulfate Desulfurization Method [D]. Ph.D. Thesis, Inner Mongolia University of Technology, Hohho, 2015. (23) Gao, Y. Research of Sulfur Dioxide Desorption Characteristics from Basic Aluminum Sulfate Desulfurization Rich Liquid. Ph.D. Thesis, Inner Mongolia University of Technology, Hohhot, China, 2014. (24) Xu, H.; Zhang, S. T.; Lu, X. B.; Liu, Y.; Yu, X. Y. Effect of ultrasound on SO2 desorption from sodium alkali desulphurization regeneration solution. Chem. Eng. Technol. 2010, 33 (2), 231−236. (25) Xue, J. Q.; Li, J. X.; Lu, X.; Mao, W. B.; Wang, Y. J.; Wu, M. Absorption of sulfur dioxide using membrane and enhancement of desorption with ultrasound. Trans. Nonferrous Met. Soc. China 2010, 20 (5), 930−934. (26) Chen, M.; Deng, X. H.; He, F. Q. Study on the Regeneration of Basic Aluminum Sulfate SO2-Rich Solution by Vacuum Desorption. Energy Fuels 2016, 30 (2), 8469−8478. (27) Wang, C. Q.; Lu, Z. Research on Heat and Mass Transfer of Falling Film Generator. J. Tong ji Univ. 2001, 29 (8), 907−913. (28) Xu, Z. Z.; Xia, Z. Z.; et al. Mass Transfer Study of Ammoniawater Falling-film Absorption in Vertical Tube. J. Refrig. 2012, 33 (1), 1−5. (29) Liang, Z. Q.; Xu, M. F.; Yin, Y. G. Effect of falling-film generation outside vertical tube with lithium chloride aqueous solution. CIESC J. 2016, 67 (S2), 87−93. (30) Lanzhou Research Institute of Petroleum Machinery.. Heat exchanger (medium). Hydrocarbon Process. Press 1998, 26−64. (31) Huang, W. J.; Deng, X. H.; Hong, M. N.; et al. Optimization of heat transfer and rib height definition for air flowing in a convergingdiverging tube. Pet. Process. Petrochem. 2005, 36 (12), 54−58. (32) Zhan, H. B.; Zhang, Z. B.; Shao, T. C.; et al. Experimental investigation on the flow resistance and heat transfer performance of the convergent-divergent tube. J. Northeast Dianli Univ. (Nat. Sci. Ed.) 2007, 27 (1), 42−45. (33) Deng, X. H.; Ye, S. Z. The application of new-type heat exchanger in sulfuric acid conversion systems. J. Sulphuric Acid Ind. 1996, 6, 19−23.

(34) Hisano, S.; Sasaki, H.; Tezuka, K.; Watanabe, I. Measuring the basic amount in basic aluminum sulfate solution for removal of SO2 gas. U.S. Pat. 4,251,497 A, Feb. 17, 1981. (35) Sun, Z. G.; Zhao, Y.; Gao, H. Y.; Hu, G. X. Removal of SO2 from flue gas by sodium humate solution. Energy Fuels 2010, 24 (2), 1013−1019. (36) Ruihua, G. New process of BAS regeneration wet FGD. J. Sichuan Chem. 1996, 2, 16−17. (37) LI, W.; Wu, X. Y.; Luo, Z.; et al. Falling water film evaporation on newly-designed enhanced tube bundles. Int. J. Heat Mass Transfer 2011, 54, 2990−2997. (38) Yao, Y. Y.; Chen, C. G.; Chai, C. J. The principles of chemical engineering, 2nd ed.; University Press: Tianjin, China, 2004: p 252. (39) Unterberg, W.; Edwards, D. K. Evaporation from Falling Saline Water Films in Laminar Transitional Flow. AIChE J. 1965, 11, 1073− 1081. (40) Krupiczka, R.; Rotkegel, A.; Ziobrowski, Z. Heat transfer to evaporating liquid films within a vertical tube. Chem. Eng. Process. 2002, 41, 23−28. (41) Alhusseini, A. A.; Tuzla, K.; Chen, J. C. Falling film evaporation of single component liquids. Int. J. Heat Mass Transfer 1998, 41, 1623−1632. (42) East China University of Science and Technology; Chemical Engineering Institute of Sichuan University. Analytical Chemistry, 5th ed.; Higher Education Press: Beijing, 2005; p 158. (43) (a) Yao, Y. Y.; Chen, C. G.; Chai, C. J. The principles of chemical engineering, 2nd ed.; University Press: Tianjin, 2004; pp 101−105. (b) Yao, Y. Y.; Chen, C. G.; Chai, C. J. The principles of chemical engineering, 2nd ed.; University Press: Tianjin, 2004; pp 119−120. (44) Wang, X.; Pan, L. L.; Yan, J. Y.; Chen, H. Y. Establish the Model of Falling Film Mass Transfer Coefficient in the Absorption of SO2 Using H2O2. Chem. Equip. Technol. 2011, 32 (2), 32−38. (45) Taylor, J. R. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements; University Science Books: Sausalito, CA, USA, 1982. (46) Yang, S. M.; Tao, W. Q. Heat Transfer, 4th ed.; Higher Education Press: Beijing, 2006; pp 198−199. (47) Incropera, F. P.; DeWitt, D. P.; Bergman, T. L.; Lavine, A. S. Fundamentals of Heat and Mass Transfer, 6th ed.; Chemical Industry Press: Beijing, 2007; pp 227−229.

L

DOI: 10.1021/acs.energyfuels.7b02206 Energy Fuels XXXX, XXX, XXX−XXX