Modeling SO2 absorption into water accompanied with reversible reaction in a hollow fiber membrane contactor

Author’s Accepted Manuscript Modeling SO2 Absorption into Water Accompanied with Reversible Reaction in a Hollow Fiber Membrane Contactor Hesheng Yu, Jesse Thé, Zhongchao Tan, Xianshe Feng www.elsevier.com/locate/ces

PII: DOI: Reference:

S0009-2509(16)30507-3 http://dx.doi.org/10.1016/j.ces.2016.09.020 CES13158

To appear in: Chemical Engineering Science Received date: 1 June 2016 Revised date: 15 August 2016 Accepted date: 16 September 2016 Cite this article as: Hesheng Yu, Jesse Thé, Zhongchao Tan and Xianshe Feng, Modeling SO2 Absorption into Water Accompanied with Reversible Reaction in a Hollow Fiber Membrane Contactor, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2016.09.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Modeling SO2 Absorption into Water Accompanied with Reversible Reaction in a Hollow Fiber Membrane Contactor Hesheng Yua,b*, Jesse Théa,b, Zhongchao Tanb,c*, Xianshe Fengc a

Lakes Environmental Research Inc., 170 Columbia St. W., Waterloo, Ontario, N2L 3L3,

Canada b

Department of Mechanical & Mechatronics Engineering, University of Waterloo, 200

University Ave. W., Waterloo, Ontario, N2L 3G1, Canada c

Department of Chemical Engineering, University of Waterloo, 200 University Ave. W.,

Waterloo, Ontario, N2L 3G1, Canada

[email protected] [email protected]

*

Correspondence to: Dr. Z. Tan, Tel.: 1 519 888 4567.

Abstract The authors developed an efficient flue gas desulfurization (FGD) process employing a hydrophobic polypropylene hollow fiber membrane contactor (HFMC) using deionized water as scrubbing liquid. A novel mathematical reactor model for gas absorption accompanied by a reversible reaction in an HFMC was developed for the first time. This new model employed the resistance-in-series theory, along with partial pore wetting, and a chemical enhancement factor for an instantaneous reversible reaction. This model was validated agreeably with experimental 1 / 43

data. The validated reactor model was then employed to investigate the resistance distribution along the main axis and the effects of temperature on SO2 removal efficiency. It was shown that the reactor model with the assumption of non-wetted pores overestimated the absorption efficiency, and a wetted pore length between 6.25 – 9.75% would yield a very good agreement with the experimental data. The deviations between the predicted and experimental values were less than ± 3.0% with an exception of 3.4% at the highest gas rate for gas flow rates ranging from

to

m3∙s-1, liquid flow rates between

m3∙s-1, and the inlet SO2 concentration of 2000 ppmv. Furthermore, the reactor model described the impact of inlet SO2 concentration on the SO2 removal efficiency within ±0.5% of measured values for liquid rates between

and

m3∙s-1 under a gas flow rate of

m3∙s-1. The resistances of shell side, fiber side and membrane are all important due to high solubility of SO2 and partial pore wetting. The SO2 removal efficiency decreased gradually as the temperature increased from 283 to 333 K based on model predictions.

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Graphic Abstract

Shell Side

Membrane

Lumen Side

SO2

Water

SO2+H2O ⇌ H++HSO3-

Keywords: Sulfur dioxide, Absorption, Partial pore wetting, Reversible reaction, Hollow fiber membrane contactor, Reactor modeling

Nomenclature A c d D E

gas-liquid contact area [m2] concentration [mol∙m-3] diameter [m] diffusivity [m2∙s-1] enhancement factor [ ] 3 / 43

H Henry’s Law constant [m3·Pa·mol−1] K equilibrium constant [mol∙m-3] kf fiber (lumen) side mass transfer coefficient [m∙s-1] KL overall liquid phase mass transfer coefficient [m∙s-1] km membrane mass transfer coefficient [m∙s-1] ks shell side mass transfer coefficient [m∙s-1] L effective fiber length [m] M molecular weight [g·mol−1] P pressure [Pa] Q volumetric flow rate [m3∙s-1] R universal gas constant [m3·Pa·K−1·mol−1] or mass transfer resistance [s·m-1] T temperature [K] u superficial velocity [m∙s-1] VbA molar volume of solute A at its normal boiling temperature [cm3·mol−1] vf void fraction [ ] x ratio of pore length filled with gas phase [ ] y gas volumetric concentration [ppmv] z axial position [m] Abbreviations 2D FGD HFMC HTU NOx ODE PP PVDF RMSE SO2

two dimensional flue gas desulfurization hollow fiber membrane contactor height of transfer unit nitrogen oxides ordinary differential equation polypropylene polyvinylidenefluoride root-mean-square-error sulfur dioxide

Dimensionless Numbers Graetz number of lumen side (inside fiber) Reynolds number of shell side Sherwood number of lumen side (inside fiber) Schmidt number of shell side

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Sherwood number of shell side Greek letters wall thickness of hollow fiber [m] the characteristic Lennard-Jones energy [J] fiber porosity [ ] SO2 removal efficiency [%] Boltzmann’s constant [J·K−1] dynamic viscosity in Eq. (18) [mPa∙s] kinetic viscosity [m2∙s-1] characteristic length [Ǻ] membrane tortuosity [ ] association factor of solvent [ ] diffusion collision integral [ ] Subscripts A, S, SO2 eff exp f G i in Kn L lm m M N, N2 o out ov p s S(IV) T w

SO2 effective experimental Fiber gas phase inner Inlet Knudsen liquid phase logarithm mean Membrane membrane module (cartridge outer) nitrogen outer outlet overall pore of hollow fiber shell side total sulfur compound total, or tube (cartridge inner) in Eq. (17) water

Superscripts 5 / 43

*

saturated

1 Introduction Fossil fuels including coal, oil, and natural gas are projected to remain the primary energy sources around the world in the near future(IEA, 2014; U.S. EIA, 2014, 2015).

As a

consequence, fuel combustion will continue to emit sulfur dioxide (SO2) and nitrogen oxides (NOx) at an astonishing annual rate. Industrial SO2 emissions were 4.991 Mt in the U.S.(U.S. EPA, 2015), and 19.744 Mt in China (China's MEP, 2015) in 2014. SO2 in the atmosphere results in the acidification of ecosystem, which negatively affects agriculture, foresting and public health (You and Xu, 2010; Yu et al., 2015). For example, 29.8% of major cities in China suffered badly from acid rain (the average pH value of rainwater in those cities was lower than 5.6) in 2014 (China's MEP, 2015). The annual economic loss due to air pollution in China was estimated by the World Bank to be 100 - 300 billion US dollars in 2014 (World Bank and Development Research Center of the State Council of China, 2014).

The OECD countries and China have established increasingly stringent regulations and laws for SO2 emission limits to ensure a sustainable consumption of fossil energy (China's MEP, 2012; U.S. EIA, 2015). Advanced flue gas desulfurization (FGD) technologies are important to meet the market demands for efficient and affordable sulfur emission control (Yu et al., 2014). Existing FGD technologies include primarily wet and dry methods, and regenerable processes (Srivastava and Jozewicz, 2001). Large scrubbers are usually utilized in these technologies. They require costly installation and specific operational conditions, and are characterized by low effectiveness and high cost (Bokotko et al., 2005; Iversen et al., 1997). The research presented

6 / 43

here places great emphasis on the development of novel FGD technologies to reduce costs and resulting waste product from traditional control systems.

Hollow fiber membrane contactor (HFMC) emerges as a promising configuration of FGD reactors.

It possesses several advantages including large and constant interfacial areas,

compactness, linear scale-up, and independent regulation of gas and liquid flows (Mansourizadeh and Ismail, 2009). HFMC has been widely used in liquid-liquid extraction (Diban et al., 2008) and liquid degassing (Agrahari et al., 2012; Sengupta et al., 1998). Recently numerous studies have been conducted to capture carbon dioxide using HFMC (deMontigny et al., 2006; Mulukutla et al., 2014). However, previous research on SO2 removal was relatively limited although membrane-based FGD technology has been proven economically and technologically viable on an industrial scale (Klaassen, 2003; Luis et al., 2012). Sun et al. (2008) tested SO2 removal using seawater in a hydrophobic polypropylene (PP) HFMC and concluded that the HFMC had a much lower height of transfer unit (HTU) than conventional packed towers. Park et al. (2008) studied SO2 absorption into different solvents in a small-scale hydrophobic polyvinylidenefluoride (PVDF) HMFC, achieving a high SO2 removal efficiency. Luis et al. (2009) absorbed SO2 into an ionic liquid in a hydrophilic aluminium oxide HFMC, and developed a zero solvent emission process. The HFMCs used in these studies were operated in a parallel flow mode.

However, cross-flow module was known to be superior to the parallel flow design for gas-liquid contact (Dindore et al., 2005; Sengupta et al., 1998; Wang and Cussler, 1993). Firstly, the crossflow design has a better mass transfer performance owing to the absence of fluid maldistribution

7 / 43

in the shell side (Gabelman and Hwang, 1999). Albo and Irabien (2012) concluded that the overall volumetric mass transfer coefficient in a cross-flow HFMC was around 2 times higher than that in a parallel flow module. Secondly, the cross-flow mode provides a lower pressure drop and a larger gas-liquid interfacial area (Sengupta et al., 1998). In order to eliminate uneven distribution of fluid in the shell side, the liquid phase usually flows through the lumen side of the hollow fibers in a parallel configuration. On the one hand, this flow pattern leads to a great pressure drop, thereby affecting the performance of the HFMC. On the other hand, the gasliquid contact area for liquid flowing inside fiber lumens is based on the inner surface area of the hydrophobic hollow fiber, which is less than that for liquid flowing in the shell side. For the above reasons, our previous work (Yu et al., 2015) employed a cross-flow HFMC. Water was chosen from a list of commonly used FGD absorbents because it was cheap and selective to SO2 over CO2 (Sengupta et al., 1990; Teramoto et al., 1999). Additionally, water is an ideal substitute for commercially used seawater in the preliminary experiments (Oikawa et al., 2003), and the current FGD process can be easily adapted to seawater-based FGD method. Preliminary results showed that the HFMC could be a prospective FGD reactor.

This research developed a new reactor model to reduce empirical approaches to the design of the FGD system.

Reactor modeling is an efficient tool in the reactor scale-up and process

optimization. Therefore, it is desired to model the SO2 absorption into water in the cross-flow HFMC for further development of the novel FGD process. Gas absorption in HFMC can be simulated numerically with assumptions of laminar parabolic velocity profile inside hollow fibers, considering the existence of Happel’s free surface in the shell side (Li and Chen, 2005; Mansourizadeh and Ismail, 2009). Conversely, a mathematic model of HFMC is preferred for its

8 / 43

ease to use, accuracy, and expeditious calculation (Albarracin Zaidiza et al., 2014; Hoff and Svendsen, 2014). Such mathematical model is based on the resistance-in-series theory. The effect of a chemical reaction on absorption is generally represented by an enhancement factor (Kreulen et al., 1993; Kumar et al., 2003).

Membrane pore wetting was also taken into

consideration by some researchers in the assessment of the HFMC performance (Mahmud et al., 2000, 2002).

Most modeling studies on gas absorption in HFMC in the literature involve fast 2nd order irreversible reactions (Ortiz et al., 2010; Zhou et al., 2012). The enhancement factor of such chemical reactions is independent of interfacial gas concentration. Furthermore, the concentration of liquid solvent involved in the calculation is usually in great excess of the gas concentration dissolved at the gas−liquid interface, and it can thus be considered unchanged (Kumar et al., 2003). However, SO2 absorption into water involved in the current work is an instantaneous reversible reaction (Chang and Rochelle, 1981), and its expression of enhancement factor is much more complicated than irreversible reactions due to the difficulty in the presentation of bulk liquid (Hikita et al., 1978; Kumar et al., 2003).

The primary objective of this paper is to develop and validate a new mathematical model for wet FGD using water as a scrubbing agent in a HFMC, which does not have the limitations described above. The newly developed model employs the resistance-in-series theory, along with partial pore wetting, and an enhancement factor for an instantaneous reversible reaction. To the authors’ best knowledge, the modelling of gas absorption with reversible reaction in an HFMC is reported for the first time.

The new developed model is then validated by our (Yu et al., 2015)

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experimental data at various operating conditions. The effects of gas and liquid flows, and the inlet SO2 concentration on the absorption efficiency are investigated.

The SO2 removal

efficiency and the distribution of mass transfer resistances in the reactor are then analyzed. The effect of temperature on the FGD performance is also studied using the reactor model.

2 Model Development Figure 1 shows a schematic diagram and an infinitesimal element of the cross-flow HFMC. A

table of nomenclature that is included at the end of the paper provides definitions for the variables and constants used in this study. The gas and liquid streams flow counter-currently into the HFMC for non-dispersive contact on the outside surface of the hollow fibers. The total interfacial contact area is the summation of the outside surface area of the hollow fibers. Assuming plug flow in the HFMC and negligible pressure drop in the gas phase flowing inside the hollow fiber lumens, mass balance on the gas phase in Figure 1 (bottom) leads to Eq. (1). (

)

(

)

(1)

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Central Liquid Distribution Tube

z=0

z=L

L

dz

dT Water Outlet

dM Water Inlet

Potting

Middle Baffle

Hollow Fibers

Flue Gas Inlet

Flue Gas Outlet

z+dz KLdA(cA*-cAL)

z 𝑄𝐺 𝑐𝐴𝐺

𝑄𝐿 𝑐𝐴𝐿

Liquid Phase

𝑄𝐺 𝑐𝐴𝐺

𝑑𝑐𝐴𝐺

𝑄𝐿 𝑐𝐴𝐿

𝑑𝑐𝐴𝐿

Figure 1. Schematic view (top) and an infinitesimal element (bottom) of the HFMC

Assuming ideal gas behavior and applying Henry’s Law for gas sorption into a liquid, Eq. (1) turns into

(

)

(2)

Based on the resistance-in-series model, the overall mass transfer coefficient for reactive absorption with liquid flowing in the shell side can be described as follows (Drioli et al., 2011; Rangwala, 1996). 11 / 43

(3)

where

is the overall resistance of mass transfer, and

,

,

are individual

resistance components in the shell side, lumen side, and the membrane, respectively.

In general, the Lévéque correlation predicts mass transfer coefficients inside hollow fibers with an acceptable accuracy for Graetz numbers (Gz) greater than 4, but the mass transfer coefficient will be overestimated for Gz < 4 (Gabelman and Hwang, 1999). In this study, a modified Lévéque equation developed specifically for low gas flow ratesis used (Mahmud et al., 2004). (4) where (5)

(6)

The diffusivity of SO2 in nitrogen gas (

), which is relevant to the binary gas mixture

used in our study, at low pressures is predicted using the Chapman-Enskog correlation as follows (Poling et al., 2000; Yu and Tan, 2014). (7) where (8) 12 / 43

(9)

(

)

(

(

The values of

and

)

(

)

(

)

(10) (11)

)

are 4.112 and 3.798 Ǻ, respectively; the values of

and

are 335.4 and 71.4 K, respectively (Cussler, 2009; Poling et al., 2000).

Ideally, the hydrophobic polypropylene hollow fibers are not wetted, and the mass transfer coefficient in the membrane may be represented in Eq. (12) (Bocquet et al., 2006; Shen et al., 2012).

(12)

The diffusivity of SO2 in the membrane pores (

) can be described by (Kong and Li, 2001):

(13)

where the Knudsen diffusion coefficient (DKn) is given by (Lawson and Lloyd, 1997): √

(14)

13 / 43

However, partial wetting of the pores in the membrane is inevitable in practice, and it is evidenced by the observation of condensed water droplets during our experiments. Mahmud et al. (2000, 2002) predicted the mass transfer coefficient across the membrane (km) by taking into account pore wetting.

[

(

)

]

(15)

where x is the ratio of pore length filled with gas phase. The non-wetted condition is represented by x = 1, at which Eq. (15) becomes Eq. (12).

The mass transfer in the shell side of the cross-flow HFMC requires a careful evaluation. It is not as unified as that in the lumen side due to the complexity of shell side hydrodynamics. Several correlations have been proposed and the expressions of different dimensionless groups vary between researchers (Schoner et al., 1998; Tarafder et al., 2007; Wang and Cussler, 1993). The correlation by analogy with that developed for closely packed cross-flow heat exchanger, which has been well adopted for different conditions (Pierre et al., 2002; Tarafder et al., 2007; Viladomat et al., 2006), is employed in this work.

(13)

where the Sherwood (Shs), Reynolds (Res), and Schmidt (Scs) numbers on the shell side are described below,

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(14) (15) (16) (

)

The diffusivity of SO2 in water (

(17)

) can be estimated by the Wilke-Chang equation (Wilke

and Chang, 1955) shown in Eq. (18). (

)

(18)

The association factor for water ( ) is 2.26 (Yu and Tan, 2014), and the molar volume of SO2 at the normal boiling temperature (

) is 44.8 cm3·mol−1 (Wilke and Chang, 1955). The physical

properties of liquid water including densities and viscosities at various temperatures are available in the literature (Lide, 2005).

The absorption of SO2 in water can be considered to occur via two reversible reactions as shown in Reactions (19) and (20). Based on the reaction thermodynamics (Wagman et al., 1982), the equilibrium constant of Reaction (20) is approximately 5-6 orders of magnitude lower than that of Reaction (19); hence, the formation of

ions is usually negligible (Hikita et al., 1978).

Reaction (19) can be assumed instantaneous reversible due to its great forward reaction rate constant (Chang and Rochelle, 1981).

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⇌

(19)

⇌

(20)

It is, therefore, reasonable to assume that the Reaction (19) is at equilibrium everywhere inside the HFMC, and the equilibrium constant (K) is described as,

(21)

In view of the electroneutrality of the solution, (22)

The combination of Eqs. (21) and (22) leads to, √

(23)

Then the total concentration of sulfur in the liquid phase, represented as

(

),

is described in Eq.

(24).

(

√

)

(24)

Mondal (2007) experimentally determined the equilibrium constant for the absorption of dilute SO2 into water. The temperature dependence of dissociation constant over 293 – 333 K can be described by Eq. (25).

(

)

(25)

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The Henry’s law constant (H) of SO2 in pure water at different temperatures can be estimated according to

Sander (2014) as in Eq. (29).

This correlation is consistent with Mondal’s

experimental findings (Mondal, 2007).

[

(

)]

(26)

The enhancement factor (E) of Reaction (19) for SO2 absorption is represented by Eq. (27), which is based on surface renewal theory (Chang and Rochelle, 1981; Hikita et al., 1978). This equation is slightly different from the expression based on the film theory, in which the index of the diffusivity ratio of sulfite ion to sulfur dioxide is 1 instead of ½ (Vivian, 1973). Because the diffusivity ratio is usually close to unity, both expressions are expected to give similar results (Chang and Rochelle, 1981).

√

√

√

(27) √

The diffusivity of HSO3- ion in water is

m2∙s-1 at 25 oC, and it is close to the

value at 27 oC (Ebrahimi et al., 2003; Lide, 2005). With the enhancement factor and all individual mass transfer coefficients, Eq. (2) then becomes

[(

√

√ √

)

]

(

)

√

(28)

17 / 43

Furthermore, the overall mass balances for both the gas and liquid streams on the finite element shown in Figure 1 give

(

(

)

))

(

(

)

(

)

(29)

and its differential form is, (

(30)

)

Dividing both sides of (30) by dz, and substituting Eq. (24) produce

(

√

)

(31)

Rearranging Eq. (31) becomes

(

√

)

(32)

The equations of the reactor model are now established. The solutions to the system of ordinary differential equations (ODEs) (28) and (32) with boundary conditions of

and

will allow us to predict the performance of the HFMC for SO2 absorption into water. However, the two ODEs are greatly complicated by the reversible reaction between SO2 and water. Thus, it would be very difficult to obtain an analytical solution to the equations. Instead, the ODEs are solved numerically using a finite difference method. This work used 18 / 43

MATLAB’sbvp4c solver. Figure 2 presents the results, as an example, for the conditions of x = 0.91, inlet SO2 = 2000 ppmv,

m3∙s-1 and

m3∙s-1.

Figure 2. Axial distribution of SO2 concentration in water (left y axis) and in gas phase (right y axis) for experimental conditions of x = 0.91, inlet SO2 = 2000 ppmv, m3∙s-1 and 3 -1 m ∙s

3 Experimental Apparatus for the Model Validation Figure 3 shows the HFMC system for the removal of SO2 using deionized water. Pure N2 (purity grade 4.8) and a SO2 in nitrogen gas mixture (purity 15%) were supplied by Praxair Canada Inc. Flue gas streams containing 1000 to 3000 ppmv of SO2 were simulated by diluting the gas flow from the concentrated SO2 cylinder using pure N2. A stainless steel in-line mixer (Model RK04669-05 from Koflo Corporation) was utilized for mixing. The overall gas flow rate under investigation ranged from 8.3 to 18.1 L∙min-1. The SO2 flow rate was regulated by a mass flow controller with an accuracy of ± 1% full scale (Model 32649-58 from Cole-Parmer Canada). The

19 / 43

N2 flow rate was controlled by a correlated flowmeter with an accuracy of ± 2% full-scale (Model 03229-33 from Cole-Parmer Canada). 3-way valve

Exhaust

Pressure Gauge Filter

HFMC

Gas Analyzer EL3020

Mixer Rotameter

Correlated Flowmeter

MFC

###

Pressure Gauge

Exhaust

Rotameter

Regulator Ice Bath

Pressure Regulator Valve

N2

SO2

Filter Fresh Water

Used Water

Figure 3. Laboratory hollow fiber membrane contactor system for the absorption of SO2 into water

The gas stream was filtered by a 0.2 µm capsule before entering the cross-flow HFMC (LiquiCel® 2.5 × 8 Extra-Flow Module). Table 1 summarizes the specifications of the HFMC. The inlet SO2 concentration of the HFMC was monitored by directing the prepared gas flow to a continuous gas analyzer with a repeatability of ≤ 0.5% of span (Model EL 3020 from ABB Ltd.) 20 / 43

via a by-pass route for each test. An ice bath was placed upstream the analyzer to remove moisture from the sampling gas. The analyzer readings were recorded every 15 seconds, and the inlet SO2 concentration was the average of stable readings in a 3-minute duration prior to the onset of the test. The gas stream was then introduced to the fiber side of the HFMC via a threeway valve, and the SO2 concentration at the HFMC outlet was continuously monitored with the SO2 analyzer. The gas pressure at inlet spanned from 127.5 to 148.2 kPa. The pressure drop in the gas phase through the HFMC was shown to be low, which supports the assumption of negligible pressure drop in the reactor model.

Table 1. The Characteristics of Liqui-Cel® 2.5 × 8 Extra-Flow Membrane Contactor equipped with polypropylene hollow fibers Celgard® X-40 (provided by Polypore International, Inc.)

Cartridge inner diameter (m) (or central distribution tube diameter)

0.022

Cartridge outer diameter (m)

0.05

Effective fiber length (m)

0.16

Number of fibers

11100

Fiber porosity (%)

25

Fiber pore size (m)

3×10-8

Fiber pore tortuosity

2.5

Nominal outer diameter of the fiber (m)

3×10-4

Nominal inner diameter of the fiber (m)

2×10-4

A central water purification system, from the University of Waterloo, provided deionized water for the experiment, which was filtered by a 5.0 µm filter capsule, and delivered to the shell side of the HFMC through a central distribution tube using a peristaltic pump. The temperature of 21 / 43

water was 27 ±0.3 oC. Ideally water contacted the gas phase counter-currently at the pore mouth located on the outside of hollow fiber. However, the pores of hollow fibers were found partially wetted during experiments. The flow rate of water was in the range of 194 - 463 mL∙min-1. The liquid pressure was manipulated by a regulator valve to remain slightly higher than the gas pressure to avoid the formation of gas bubbles in the liquid phase. The transmembrane pressure difference was maintained between 6.895 – 20.68 kPa. The system was operated in a oncethrough manner, and the used absorbent was collected in a liquid tank.

Prior to directing gas flow to the HFMC system, water was allowed to flow through the membrane contactor for 15 min to remove any possible gas trapped from drying and previous testing. It would then take around 15 min for the system to reach steady state. Upon reaching the steady state, the average of the stable readings collected in a 3-min duration at the outlet was utilized as outlet SO2 concentration for a specific experimental condition. After each run, water was drained from the bottom of the HFMC. A dry nitrogen gas was then passed through the system for 45-60 min at a flow rate of 5 L∙min-1 to blow the remaining water out of the shell side of the HFMC, and to remove any condensed water in the pores of the hollow fibers and the gas tubing. The removal efficiency of SO2 is calculated using Eq. (33). At least 5 replicates were conducted separately under each experimental condition.

(

)

(33)

22 / 43

4 Reactor Model Validation and Discussion The reactor model in the current study was validated with experimental data collected at different conditions. The difference between the reactor model and the experiment is indicated by the deviations between experimental data and the calculated results. The verified reactor model was employed to demonstrate SO2 absorption efficiency and the distribution of mass transfer resistances in the HFMC, along the axial direction, followed by an investigation of the effects of temperature on the SO2 removal efficiency. 4.1.

Validation of the Reactor Model

Figure 4 shows a comparison between model calculations and experimental data from our previous work (Yu et al., 2015) for different gas and liquid flow rates at 2000 ppmv of inlet SO2 concentration. The gas flow rate was from between

and

to

m3∙s-1, while liquid rate

m3∙s-1. The error bars are the standard deviations of the

SO2 removal efficiencies. The top graph presents the predicted SO2 removal efficiencies for non-wetted condition (x = 1), under which the model overestimates the reactor performance, especially at relatively higher liquid flow rates. The assumption of non-wetted pores deviates from reality, which is also endorsed by the observation of water condensation during experiments.

Therefore, partial wetting of membrane pores will better represent the real

situation under investigation.

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Figure 4. Comparison between the developed model and experimental results (adapted from Yu et al. (2015)) for different gas and water flow rates at 2000 ppmv of inlet SO2 concentration under the assumptions of a) non-wetted condition (top, x = 1) and b) partially wetted pores (bottom, x = 0.9025 - 0.9375)

24 / 43

In addition to the properties of membrane and solvent, the wetting behavior of the HFMC depends on liquid contact time (Mavroudi et al., 2006), liquid flow rate (Wang et al., 2005), and working pressure (Faiz et al., 2014). In the current study, the effect of contact time on wetting can be excluded as the gas-liquid contacting period for each run is almost the same. It is well documented that higher liquid flow rates lead to a higher membrane wetting, whereas the gas flow rate has insignificant impact on wetting (Boributh et al., 2012). Similar findings have also been reported by El-Naas et al. (2010). Therefore, constant wetting ratio was assumed for a specific liquid flow rate regardless of gas flow rate.

The value of x, the ratio of pore length filled with gas, is adjustable. The actual value is determined by comparing the corresponding calculated results at a specific x with the experimental data. This method for x determination has been adopted by previous researchers for gas absorption in HFMC (Mavroudi et al., 2003). In the current study, the root-mean-squareerror (RMSE) as defined in Eq. (37) is used as the quantitative metric (Hyndman and Koehler, 2006) for the determination of x value. The objective is to obtain minimum RMSE. The bottom graph of Figure 4 shows that the membrane wetting level increases from 6.25% (x = 0.9375) at a water flow rate of 3.23×10-6 m3∙s-1 to 9.75% (x = 0.9025) at 7.72×10-6 m3∙s-1 . This finding corresponds to previous gas absorption studies (Boributh et al., 2012; Mavroudi et al., 2003).

√ ∑ (

)

(34)

Exceedingly high transmembrane pressure difference and capillary condensation are two major causes for the wetting of a HFMC (Albarracin Zaidiza et al., 2015; Keshavarz et al., 2008). The 25 / 43

breakthrough pressure of a membrane is predicted by the Laplace-Young equation (Kumar et al., 2002). Low surface tension, large pore size, and small contact angle favor membrane wetting. The breakthrough pressure of Celgard X-40 PP fiber is approximately 2273 kPa using nominal pore size and the contact angle measured by Wang et al. (2004). Since the transmembrane pressure difference in the current research ranges from 6.895 – 20.68 kPa, it is unlikely for water to directly penetrate into membrane pores. However, the membrane wetting could still occur due to the following reasons. Firstly, the intrusion of non-wetting water meniscus into pores can sometimes enlarge the pore entrance, lowering breakthrough pressure and resulting in partial wetting (Li and Chen, 2005; Mosadegh-Sedghi et al., 2014). The increase in liquid flow rate leads to a reduction in the liquid boundary resistance, thereby favoring the intrusion of water meniscus and raising membrane wetting (Mosadegh-Sedghi et al., 2014). Secondly, SO2 absorption into water is an exothermic reaction (Goldberg and Parker, 1985; Pérez-Salado Kamps et al., 2005), which could result in a progressive temperature increase in the membrane pores. This local heating would decrease the surface tension at the water-SO2 interface. As a result, gradual intrusion of water into the pores may happen (Mavroudi et al., 2006). Furthermore, the Laplace-Young equation is valid only for ideal membrane surfaces. The surface roughness and non-uniform pore size distribution of real PP membrane would be responsible for the wetting at higher liquid flow rates (Lu et al., 2008). Also important, the capillary condensation leads to membrane wetting in this work, which is also supported by the observation of water droplets in the gas phase in every run. The gas flow may carry most condensed water in the gas phase out of the system, but may not be able to remove all water condensation trapped in the membrane pores. The trapped moisture will help create a water layer or reside in the pores in the form of droplets, significantly increasing the membrane resistance (Mahmud et al., 2000).

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With the use of wetting ratio, the developed model agrees with the experimental findings nicely. Experimental data under all conditions are within ±3.0% of the predicted curves with an exception of 3.4% of divergence. This indicates that a constant wetting ratio over the entire investigated gas flow rates is acceptable. It is thus concluded that the partial wetting condition is much closer to the reactor circumstance.

Despite the close agreement between experimental and predicted data at a constant wetting ratio over the investigated gas flowrate range, the model tends to slightly underestimate the membrane contactor performance at higher gas flow rates. In other words, the model somewhat overpredicts the wetting ratio at greater gas rates. A moderately reduced wetting ratio at higher gas flow rate was also reported by El-Naas et al. (2010), and they considered this as an indication of a reduced trans-membrane pressure. In our opinion, the marginally decreased membrane wetting at greater gas flow rate could more likely be due to the enhanced removal of water condensate trapped in the membrane pores. Because such underestimation of membrane wetting is minor, and will not lead to a significant deviation in performance prediction, a constant wetting ratio over the entire gas flow rate range is acceptable and is adopted in the model. In order to consolidate this conclusion, the reactor performance at different inlet SO2 concentrations will be studied subsequently. The wetting ratios at different liquid flow rates in Figure 4 will be employed in the following sections.

Figure 5 displays the HFMC removal performance at different inlet SO2 concentrations (ranging from 1000 to 3000 ppmv) and at a gas flow rate of

m3∙s-1 and a liquid rate in the

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range between

and

m3∙s-1. The error bars are the standard deviations

of the SO2 removal efficiencies. Due to the occurrence of an instantaneous reversible reaction in SO2 absorption into water, the inlet SO2 concentration plays an important role in its absorption into water (Sengupta et al., 1990). As the inlet SO2 concentration increases from 1000 to 3000 ppmv, the SO2 removal efficiency decreases slightly from 98.45% to 96.64% at m3∙s-1, and from 97.93% to 95.07% at

m3∙s-1.

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Figure 5. Validation of the developed reactor model in terms of the effect of inlet SO 2 concentration on SO2 removal efficiency under the cases of a) non-wetted condition (top, x = 1) and b) partially wetted pores (bottom, x = 0.9100.915)

The lines in Figure 5 represent the removal performance at different inlet SO2 concentrations predicted by the new reactor model. Again, the results based on the non-wetted conditions overestimate the SO2 absorption efficiencies, whereas the counterparts obtained for x = 0.915 at a water flow rate of 4.35×10-6 m3∙s-1 and x = 0.91 at 5.50×10-6 m3∙s-1 are in very good agreement with the experimental data (within ±0.5%). Additionally, two other conditions are included in Figure 5 to examine the impact of further reducing gas rate or increasing liquid rate on enhancing desulfurization efficiency. Figure 5 indicates that both reduced gas rate and enhanced liquid rate lead to an improved SO2 removal performance. The increase in SO2 removal efficiency is more obvious at a lower gas flow rate.

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The desulfurization efficiency remains greater than 99.2% for all the inlet concentrations tested at QG = 1.38×10-4 m3∙s-1 and QL = 5.50×10-6 m3∙s-1. Such performance can well meet industrial FGD requirements, revealing that the HFMC absorption can be an alternative to existing technologies. In summary, the membrane pores in the current study are partially wetted and the developed model is fully validated by extensive experimental data.

The wetting ratio increases with

increasing flow rate. 90.25 – 93.75% of the membrane pore length is filled with gas phase (x=0.9025-0.9375) in the current work. 4.2.

SO2 Removal Efficiency and Resistance Distribution along Axial Direction

Our validated reactor model can now be employed as an efficient tool in reactor design, scale-up and process optimization since it saves time and efforts in experimentations. The validated reactor model calculates the SO2 removal efficiency and resistance distribution along the HFMC at different axial positions. Such information is important to reactor selection, scale up and process optimization. Figure 6 shows how the absorption efficiency progressed along the gas flow direction for five conditions. It can be seen that the rate at which SO2 removal efficiency rises to reach plateau depends upon the input parameters/conditions. In general, a greater rate at which removal efficiency increases occurs at a lower gas rate and a smaller inlet SO2 concentration. Figure 6 provides an example herein to demonstrate how the reactor model will benefit the determination of operational parameters.

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Figure 6. The absorption efficiency of SO2 along the axial direction at 27 oC

If a 95% of removal efficiency is desired (as seen in Figure 6), the required fiber length would be 0.104, 0.119, 0.135, and 0.146 m, respectively, at Conditions 1-4. Results from this analysis support that our HFMC experiments could be calibrated to achieve even higher SO2 removal efficiencies. On the other hand, the HFMC with an effective fiber length of 0.16m in the current study cannot fulfill the objective of 95% removal efficiency at Condition 5. The extrapolated value of fiber length according to the last two points of modeling results for such an objective at Condition 5 would be 0.192 m. If the inlet SO2 concentration and m3∙s-1, a gas flow rate slightly greater than

are set at 2000 ppmv and m3∙s-1 is preferred to

maximize the HFMC performance for an objective of 95% SO2 removal efficiency.

Figure 7 given by the validated model shows the change in the shell side mass transfer resistance and the distribution of individual resistance component along the gas flowing direction under 31 / 43

inlet SO2 = 2000 ppm, x = 0.91, absolute value of

m3∙s-1, and

m3∙s-1. The

, represented by the black solid curve, decreases readily along the axial

position due to an increase in the enhancement factor of Reaction (19). The enhancement factor rises from 2.35 at the inlet of the HFMC to 13.83 at the outlet in this case. It indicates the importance of chemical reaction in gas absorption.

Figure 7. Mass transfer resistance in the shell side and distribution of individual resistance along axial position at inlet SO2 = 2000 ppm, x = 0.91, m3∙s-1, and m3∙s-1

The distribution of individual resistance component enables us to understand the importance of each resistance in the mass transfer in the HFMC. It can be observed from Figure 7 that all three resistance components, Rm, Rf and Rs, are important and cannot be ignored. According to the definitions in Eq. (3), the resistances of fiber and membrane become significant due to the high solubility of SO2. The contribution of Rf barely varies with axial position. The share of Rs steadily decreases, whereas that of Rm gradually increases. At the reactor inlet, Rm and Rs are

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equally significant, while at the outlet Rm and Rs accounts for 73.61% and 12.68%, respectively, of the overall mass transfer resistance. The percentage of Rs at the reactor outlet is even lower than that of Rf.

Overall, the wetting ratio of pores is 9% (corresponding to x = 0.91) at QL = 5.5×10-6 m3∙s-1. This minor wetting greatly jeopardizes the mass transfer performance in the HFMC. The value of membrane resistance, Rm, of partially (9%) wetted pores under the experimental conditions described in Figure 7 is 5 times greater than that of non-wetted pores. Therefore, membrane materials with a high hydrophobicity are desired for economically and chemically viable HFMC. 4.3.

Effect of Temperature on SO2 Removal Efficiency

Temperature plays an important role in SO2 scrubbing in a FGD reactor. It affects many parameters including dissociation constant, solubility, diffusivity and viscosity.

Figure 8

illustrates the effects of temperature on SO2 absorption efficiency for 4 representative scenarios at x = 0.910-0.915 and 2000 ppmv of inlet SO2 concentration. The SO2 removal efficiency drops as temperature rises from 283 to 333 K for all cases. This decrease in SO2 removal efficiency is within expectation because both SO2 solubility and the equilibrium constant of Reaction (19) decreases with rising temperature. A lower solubility means that SO2 becomes more difficult to be absorbed by water. According to Eq. (27), the reduction in the reaction equilibrium constant leads to a lower enhancement factor, which in turn, deteriorates the SO2 absorption performance.

The optimal scrubbing temperature should be determined on the basis of the compromise between SO2 removal efficiency and the penalty of reducing temperature. A closer look at Figure 8 provides more information on the rate at which SO2 removal efficiency decreases with 33 / 43

temperature. The rate at a lower temperature is much lower than that at an elevated temperature. For example, the SO2 removal efficiency drops slightly from 98.5% to 97.4% (a reduction of 1.1%) over the first 20 K temperature interval from 283 to 303 K; while from 96.2% to 90.6% (a reduction of 5.6%) at the last 20 K temperature interval between 313 and 333 K. This means that the optimum operating temperature may not be necessarily at low temperatures, and a moderate temperature (e.g. room temperature) is preferred in practice.

Figure 8. The impact of temperature between 283 and 333 K on SO2 removal efficiency based on verified model

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5 Conclusions The removal of SO2 using water was performed in a cross-flow HFMC using water at 27 oC. The new HFMC reactor model for gas absorption with reversible reaction was developed in this study to overcome limitations present in models published in the literature. This model was then validated with experimental data. Simulations using the reactor model produced interesting and relevant results. The membrane wetting increases with an increase in the liquid flow rate.

The reactor model predicted the performances of the HFMC within ±3.0% of experimental data with an exception of 3.4% at gas flow rates from rates between

and

m3∙s-1.

to

m3∙s-1 and liquid

The FGD efficiency decreased with an

increase in the inlet SO2 concentration. The divergence between calculated and experimental values for different inlet SO2 concentrations are less than ±0.5%. The reactor modelling results also show that the mass transfer resistances of membrane, shell side and lumen side are all significant along the axial position due to high gas solubility and partial wetting of fiber pores. A 9% of wetting ratio of pore length at QL = 5.5×10-6 m3∙s-1 increases the membrane resistance by 5 times in comparison with that at non-wetted condition.

The verified reactor model can be used to design new FGD process using HFMC, and determine optimum operating parameters (e.g., gas flow rate and working temperature). The new validated model is a useful tool in reactor scale-up and process optimization.

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Acknowledgements The authors would like to acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) Industrial R&D Fellowships Program, Lakes Environmental, and Ontario-China Research and Innovation Fund (OCRIF 2014). We would also like to acknowledge Mr. Kuang Cheng for his assistance in partial data collection.

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Highlights 

Flue gas desulfurization in a hydrophobic hollow fiber membrane contactor (HFMC);



A novel gas absorption model to design and simulate the process with reversible reaction in HFMC;



Validation of the reactor model using experimental results at various inlet SO2 concentrations, and gas and liquid flow rates;



The deviations between predicted and experimental values are mostly with ±3.0%.



Distribution of mass transfer resistances along axis and effect of temperature on FGD efficiency are investigated by the verified model.

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