Membrane Contactors: Fundamentals, Applications and Potentialities, Volume 11 (Membrane Science and Technology)

Introduction It is well understood today that our society has to face the challenge of modifying the traditional industrial growth to a sustainable growth, if we want to keep developing for generations. In principle, adverse environmental impact can be notably reduced by optimizing the existing activities. Present design methods are effectively devoted, in most cases, to managing wastes better, to introducing methods for pollution abatement, and to realizing cleaner processes for cleaner products. Nevertheless, these positive effects are expected to be offset by the on going growth. Traditional environmental management and pollution prevention will not suffice in the long run; newer approaches, which are radically innovative and integrated, are needed. The chemical and engineering community is already paying significant attention to the request for technologies that would lead us to the goal of technological sustainability. A promising example with a lot of interest by process engineers is the strategy of process intensification. It consists of innovative equipment, design and process development methods that are expected to bring substantial improvements in chemical and any other manufacturing and processing, such as decreasing production costs, equipment size, energy consumption, waste generation, and improving remote control, information fluxes and process flexibility. How to implement this strategy is, however, not obvious. An interesting and important case is the continuous growth of modem membrane engineering whose basic aspects satisfy the requirements of process intensification. Membrane operations, with their intrinsic characteristics of efficiency and operational simplicity, high selectivity and permeability for the transport of specific components, compatibility between different membrane operations in integrated systems, low energetic requirement, good stability under operating conditions and environment compatibility, easy control and scale-up, and large operational flexibility, represent an interesting answer for the rationalization of chemical productions. Many membrane operations are practically based on the same hardware (materials), only differing in their software (methods). The traditional

2 Introduction membrane separation operations (reverse osmosis, micro-,ultra- and nanofiltration, electrodialysis, pervaporation etc.), already largely used in many different applications, are today conducted with new membrane systems such as catalytic membrane reactors and membrane contactors. At present, redesigning important industrial production cycles by combining various membrane operations suitable for separation and conversion units, thus realizing highly integrated membrane processes, is an attractive opportunity because of the synergic effects that can be attained. Interesting examples already exist in water desalination plants, in downstream processing of biological and biotechnological productions, etc. This strategy starts to penetrate also in new areas such as the petrochemical industry, the electronic industry. Limits however exist to the traditional membrane operations, as p.e. the level of feed concentrations which can be reached in a RO system or on the recovery factors in the same RO desalination units. New unit operations moreover might be invented and/or developed in same cases which better satisfy the requirement of the process intensification strategy. Among other new unit operations involving membranes, membrane contactors are expected to play a decisive role in this scenario. The key concept is to use a solid, microporous, hydrophobic (or hydrophilic) polymeric matrix in order to create an interface for mass transfer and/or reaction between two phases: large exchange area and independent fluid dynamics allow an easily controlled operation. These membrane systems, in the form generally of low cost hollow fibres, provide a high interfacial area significantly greater than most traditional absorbers between two phases to achieve high overall rates of mass transfer. In addition, whereas the design of the conventional devices is restricted by limitations in the relative flows of the fluid streams, membrane contactors give an active area, which is independent of the liquid fluid dynamics. Membrane crystallizers, membrane emulsifiers, membrane strippers and scrubbers, membrane distillation systems, membrane extractors, etc. can be designed and integrated in the production lines together with the other existing membranes operations for advanced

Introduction 3 molecular separation, and chemical transformations conducted using selective membranes and membrane reactors, overcoming existing limits of the more traditional membrane processes (for example the osmotic effect of concentration by reverse osmosis). It is amazing to note that, although the above mentioned systems are quite "young", the potentialities of membrane systems have been already discovered and suggested at the beginning of the XX Century [ 1]. In Table 1 are summarized the most traditional membrane contactors developped in these last years.

Table 1. Membrane contactors systems Membrane strippers Membrane scrubbers Membrane extractors Supported liquid membranes Membrane distillation Osmotic distillation Membrane emulsifiers Phase transfer catalysis

A first example might be considered the supported liquid membranes where the microporous hydrophobic membranes act as support to the liquid phase containing appropriate carriers for the selective transport of the species dissolved in the solutions facing the membrane; other most recent examples are membrane distillation contactors. In all the operations mentioned the role of the membranes is crucial; they not only serve as an ideal contactors between the two phases they separates, but contribute more to the efficiency of the overall processes.

4 Introduction

The relative simplicity of the hardware of these systems is combined with a certain complexity on the contrary of their software. A multidisciplinary background is certainly necessary for a deep basic knowledge of the membrane contactors properties in their various configurations and in their various applications. Transport phenomena in porous media, interphacial phenomena in liquid-.liquid, gasliquid, in gas-gas phases, basic properties of polymeric materials, as also of colloids and gels, are necessary and must be well integrated with a knowledge of fundamentals of chemistry as of the thermodynamics and kinetic aspects. In this book we will present the basic aspects of the various membrane contactors already existing, and their applications. The overall potentialities of these new technologies will be also temptatively discussed.

References

[1] P. A. Kober. Pervaporation, perstillation and percrystallization., Contribution read at the meeting of the Soc. Expt. Biol. Med., Feb. 21 (1917)

Chapter I. Basic principles of membrane contactors

1. Generalities on membrane contactors operations The term "membrane contactor" is used to identify membrane systems that are employed to "keep in contact" two phases. On the contrary of the more "traditional" idea of membranes as media for performing separations thanks to their selectivity, membrane contactors do not offer any selectivity for a particular species with respect to another, but simply act as a barrier between the phases involved, by allowing their contact in correspondence of a well defined interfacial area [ 1-9]. Being the two phases separate by the membrane, there is no mix of them and dispersion phenomena do not occur. The species are transferred from one phase to the other by only diffusion. The membranes are usually microporous and symmetric and can be both hydrophobic and hydrophilic. In the case of hydrophobic materials, the membrane can be wetted by non polar phases (e.g., non polar organics) or filled by gas, while the aqueous/polar phase can not penetrate into the pores (see Figure 1).

6 Chapter 1

Figure 1. Interface between a non polar/gas phase and a polar phase in a hydrophobic membrane.

In this way, it is possible to define the area of contact in correspondence of the pores mouths. In order to avoid the mixing of the two phases, it is important to carefully control the operating pressures. First of all, the pressure of the aqueous/polar phase has to be equal to or higher than the pressure of the wetting/filling phase. This permits to eliminate any possibility of dispersion as drops of one phase into the other phase. Moreover, the interfacial area can be established at the pore mouth only if the penetration of the aqueous/polar phase into the membrane pores is prevented. The hydrophobicity of the material is not, in fact, a warranty for keeping the pores aqueous/polar phase-free. If a critical value of pressure, called generally

breakthrough pressure, is exceed, the membrane loses its hydrophobic character and the aqueous/polar phase starts to wet it [10-12]. For a particular material the breakthrough

Basic Principles of Membrane Contactors 7 pressure depends on the pore radius, surface/interfacial tension, contact angle between the

membrane and the fluid, and can be calculated by using the Laplace's equation (see Chapter 2). In figure 1, as well as in all the other figures, for simplicity, straight pores are considered for symmetric membranes. In practice, membrane pores have an un-defined shape, mainly related to the tortuosity of the membrane along its thickness. With asymmetric membranes in which the pore size reduces along the thickness, it is possible to keep in non-dispersive contact the two phases also by working, at the bigger pores side, at pressures higher than the breakthrough value. In fact, being the breakthrough pressure inversely dependent on the pore size, there is a partial wetting of the membrane for the bigger pores, whereas the smaller pores continues to be aqueous/polar phase free. The interfacial area is now established within the pores (see Figure 2).

Figure 2. Interface between a non polar/gas phase and a polar phase in a partially wetted asymmetric membrane.

8 Chapter 1

The hydrophobicity of the membrane can also vary because of the interactions with the phases involved that lead to changes in the membrane structure and morphology. This last aspect can be minimized by using composite membranes with a non-porous thin layer coated on the microporous surface that prevents the penetration of the aqueous/polar phase (Figure 3) [13-17].

Figure 3. Composite membrane with a dense thin layer coated on the microporous surface. The non-porous thin layer allows also to enlarge the range of the operating pressures, but, in order to do not increase too much the resistance to the mass transport, it has to be highly permeable for the trasferred species. The membrane wetting can be partial or complete; in the first case the two phases are in contact somewhere in the membrane pores, whereas for complete wetting the two phases are mixed and the membrane contactor loses its function.

Basic Principles of Membrane Contactors 9

When hydrophilic materials are used, the aqueous/polar phase wets the membrane pores while the non polar/gas phase is blocked at the pore mouth. In this configuration the interface is established at the pore mouth at the non polar/gas phase side and the dispersion as drops between the phases is avoided by working with pressures of the non polar/gas phase equal to or higher than the wetting phase pressure (Figure 4).

Figure 4. Interface between a non polar/gas phase and a polar phase in a hydrophilic membrane.

As for the hydrophobic membranes, the interface is kept at the pore mouth until the breakthrough pressure is not exceed. As reported by Sirkar [10], two liquid phases can be in contact also by means of a composite hydrophobic-hydrophilic membrane where the polar phase wets the hydrophilic

10 Chapter 1 part and the non polar phase enters the hydrophobic one (Figure 5). The interface is now located at the hydrophobic-hydrophilic interface and can be well defined by operating with one of the two phases at higher pressure, taking care in not exceeding the critical pressure value.

Figure 5. Interface between a non polar/gas phase and a polar phase in a composite hydrophilic hydrophobic membrane. Until now, we did not consider any reaction between the phases involved. When the species present into the two phases react, an interface where the reaction occurs can be formed and it can correspond with the phase interface or can be located into one phase.

Basic Principles of Membrane Contactors 11

Table 1 summarizes the main characteristics of the membranes used in membrane contactors. A more detailed analysis on the membrane materials is reported in Chapter 2.

Table 1. Membranes used in membrane contactors i

Microporous membranes Hydrophobic Hydrophilic Symmetric Asymmetric Composite (hydrophilic-hydrophobic or dense-microporous)

All operations that are based on the mass transport between two contacting phases can be in principle carried out by membrane contactors. For example, liquid-liquid extraction, the removal of gases/volatiles dissolved in a liquid phase by stripping with a gaseous stream or the addition of a gas/volatile contained in a gaseous stream into a liquid. In the following, the different types of membrane contactors that can be used depending on the specific application are described. Table 2 reports about them in terms of phases involved and driving force.

12 Chapter 1 Table 2. Membrane contactors systems Membrane Supported strippers/scrubbers/ liquid extractors

Membrane Osmotic Membrane Phase transfer distillation distillation emulsifiers catalysis

membranes

Phase 1 Gas/Liquid

Gas/Liquid

Liquid

Liquid

Liquid

Liquid

Phase 2 Liquid

Gas/Liquid

Liquid

Liquid

Liquid

Liquid

Driving Concentration force gradient

Partial Partial pressure/conc, pressure ~radient ~radient

Partial pressure gradient

Pressure gradient

Concentration gradient

In all different types of membrane contactors the species to be transferred encounters several resistances during its passage from one phase to another. In general, these resistances are offered by the phases and the membrane. Depending on the particular system, the mass transfer can be controlled by the resistance offered by the phase/phases, by the membrane or by both. Although a more detailed analysis of the equations that regulate the mass transfer will be furnished in next Chapters, a discussion on the resistances involved and general expressions for calculating the mass flux are also shortly reported in the following.

1.1. Membrane strippers/scrubbers and membrane extractors

In both membrane strippers and scrubbers a liquid is in contact with a gas, the difference between the two systems being the direction in which the species are transferred: from the liquid to the gas and viceversa, respectively. These systems are used for the transport of

Basic Principles of Membrane Contactors 13

volatile species contained in the phases. A generic species i moves from a phase to the other due to a partial pressure gradient. In the case of streams containing different volatile species, a simultaneous transfer can be achieved. For example, dissolved oxygen can be removed from water by stripping with a CO2 stream while, due to the partial pressure gradient, the C02 diffuses into the water. The membranes are usually hydrophobic and gas-filled, because the volatile species have higher effective diffusion in gas than in liquid and, thus, the resistance offered by the membrane is strongly reduced, with a consequent improvement of the mass transport. These systems can be considered as alternative to traditional packed and bubble columns.

Figure 6. Hydrophobic membrane contactors as strippers.

Figure 7. Hydrophobic membrane contactors as scrubbers.

14 Chapter 1

Membrane extractors can be used for carrying out liquid-liquid extractions, usually conducted in columns, mixer-settler or centrifugal devices. The driving force is due to a difference of concentration and the membranes can be both hydrophobic and hydrophilic, depending on the affinity of the species to be transferred with the streams involved. The choice is dictate by the need to reduce the membrane resistance. For example, if the species has higher affinity with the polar phase, then the membrane will be hydrophilic with the pores filled with the polar stream. If there is higher affinity with the non-polar phase, the membrane will be hydrophobic. The possibility to simultaneously transfer different solutes is valid also for these systems. The figure below refers to a concentration of the species i higher in phase

Figure 8. Transfer of the species i from the phase 1 towards the phase 2.

Basic Principles of Membrane Contactors 15

In membrane strippers/scrubbers/extractors, a generic species contained in phase 1 that moves towards phase 2 encounters a first resistance in the phase 1-self close to the membrane surface, then the resistance of the membrane and, finally, the resistance in phase 2 close to the other membrane side. The presence of these resistances leads to a concentration profile for the species, as depicted in Figure 9, that determines the driving force available for the transport.

Figure 9. Concentration profile for a species that moves from the phase 1 towards the phase 2.

A general expression used to calculate the flux of the species is the following [5]:

J = K'(CI-Ce)

(1)

with

X =f(kl, km, k2)

(2)

where:

J, flux; C1,C2, concentrations in the two phases;

16 Chapter 1

K, overall mass transfer coefficient," kl, k2, phases mass transfer coefficients," kin, membrane mass transfer coefficient.

1.2. Supported liquid membranes In supported liquid membranes the micropores of the membrane are usually filled by an organic phase and the membrane is located between two aqueous phases. One of the aqueous phase is the feed to be treated, the other representing the stripping phase. The removal of the species from the feed to the stripping phase occurs by diffusion through the organic phase and the stripping one, the concentration difference being the driving force (Figure 10).

Figure 10. Supported liquid membrane with aqueous feed and strip and organic phase into the micropores.

The effectiveness of the process is mainly depending on the affinity between the species and the organic phase. In order to increase the mass transport rate, a facilitated transport can be achieved by introducing a carrier in the organic phase. The carrier reversibly complexes

Basic Principles of Membrane Contactors 17

with the species and the carrier-species complex moves from the feed side to the strip side. Once at the strip side, being the reaction reversible, the carrier releases the species that is removed (Figure 11) [ 18-20].

Figure 11. Transfer of the species i by means of a carrier. In this way, the species leaves the feed stream both as uncomplexed, by permeating through the organic layer, and as a complex, by means of the carrier (Figure 12).

Figure 12. Permeation of the species i both as free and as a complex.

18 Chapter 1

The transport of the species by means of the carrier is faster than the simple diffusion of the species into the organic phase. The transport rate is, thus, enhanced and, if the carrier is high specific for the species of interest, high selectivities can be reached. For this configuration the membranes used are hydrophobic and the interfacial areas are established at the pore mouth of the membrane (on both sides) by properly acting on the aqueous pressures. In order to keep the membrane pores organic-filled, it is essential that the organic phase/carrier is immiscible with the aqueous streams. The properties of the immobilized solution (volatility, viscosity, degree of miscibility with the feed/strip phase) and of the carrier (stability, selectivity) are, in fact, at the basis of the performance of these systems. The membrane micropores can be also filled by an aqueous phase in which the carrier is dissolved; in this case, the membrane is hydrophilic and separates two organic phases immiscible with the aqueous one (Figure 13).

Figure 13. Supported liquid membrane with organic feed and strip and aqueous phase into the micropores.

Basic Principles of Membrane Contactors 19

Although most of the applications of supported liquid membranes refer to liquid phases [21-25], gaseous phases can be also treated by this type of membrane contactor [26-27].

In supported liquid membranes the membrane micropores are usually liquid-filled and the mass transfer resistance offered by the membrane mainly matches with the mass transfer resistance offered by the liquid. The two phases also contribute to the overall resistance to the mass transport and the general expression for the mass flux is the same reported above (eqs. 1 and 2). The mass flux through the membrane will be now dependent on the diffusion coefficient of the species in the liquid and, for a liquid containing a carrier, on the diffusion coefficient of the complex species-carrier in the liquid.

A typical expression describing this flux is [18]:

J = km'AC + kmcomplex "Afcomplex

(3)

where:

J, flux through the membrane; kmcomp+ex,membrane mass transfer coefficient for the complex; AC, difference of concentration of the species across the membrane; ACcomplex,difference of concentration of the complex across the membrane.

1.3. Membrane distillation

Membrane distillation is the only example of membrane contactor where the driving force is related to a temperature gradient across the membrane. The membranes used are

20 Chapter 1

hydrophobic and the feed streams are aqueous solutions. The stripping can be performed by using an aqueous stream at the permeate side (direct-contact membrane distillation) or by applying vacuum or by sending a strip gas. The first type of stripping has been the mostly applied. In this case, the hydrophobic membrane separates the two aqueous solutions (feed and strip). By imposing a temperature difference across the membrane (the feed solution is heated and the strip solution is cooled), a partial pressure gradient is created from the hot to the cold side. Due to this gradient, the water molecules evaporated at the warm side of the membrane migrate through the membrane micropores and, then, condensate at the permeate side (Figure 14) [28-29]. Membrane distillation can be effectively used for producing ultrapure water or for concentrating aqueous solutions and can be view as an alternative process to traditional distillation columns.

Figure 14. Scheme of the membrane distillation.

Basic Principles of Membrane Contactors 21

In membrane distillation the mass transport is strictly related to the difference of temperature imposed across the membrane thickness. The resistances offered by the phases and the membrane create now a temperature profile (see Figure 15) that determines the partial pressure gradient available for the transport. The values of the partial pressures at the membrane interfaces are, in fact, dependent on the temperatures values at the interfaces.

Figure 15. Temperature profile in membrane distillation. The equations that describe the membrane distillation operations are based both on mass and energy balances. The water vapour mass flux through the micropores is calculated by:

J = km'(Pz-P2)

(4)

where:

J, flux through the membrane; PI,P2, water vapour partial pressures at the membrane interfaces.

22 Chapter 1

The membrane mass transfer coefficient for flux of vapour/gas molecules through micropores is usually derived as function of the Knudsen and molecular mass transfer coefficients.

Referring to the heat flux, at steady-state it can be written as [30]:

Q = Hv(Th-Tc)

(5)

where:

Q, heat flux; Th, To, temperatures at the hot and cold side," H, membrane heat transfer coefficient," r,, temperature polarization coefficient

The temperature polarization coefficient is due to the resistances offered by the boundary layers adjacent to the membrane surfaces and is defined as:

r = (Thm-Tcm)/(Th-Tc)

(6)

where:

Thin,, Tcm, temperatures at the membrane interfaces. Usually, iterative procedures are implemented for solving the above equations.

1.4. Osmotic distillation

Osmotic distillation performs the same work of the membrane distillation but uses a different method for creating the partial pressure gradient. In this case, the operation is carried out at ambient temperature and the gradient is achieved by sending at the strip side an

Basic Principles of Membrane Contactors 23

aqueous solution containing non-volatiles compounds (usually salts, as CaC12). The difference in solute concentrations between the solution to be treated and the strip side leads to a vapor pressure difference which causes the transport of the water vapor molecules (Figure 16). The membranes used are hydrophobic. The possibility to concentrate a solution at ambient temperature is quite important for streams containing labile or easily denaturated compounds [31].

Figure 16. Scheme of the osmotic distillation. Working at ambient temperature, no heat flux is usually considered and the water vapour mass flux through the micropores can be calculated by the same equations derived for membrane distillation (equ. 3 and 4).

Osmotic distillation can suffer from concentration

polarization phenomena that consist in the increase of the concentration of the species contained in the aqueous solution at the membrane surface with respect to their bulk

24 Chapter 1

concentration. The phenomenon is usually described by means of a concentration polarization coefficient, CPC, defined as the ratio between the concentration of the species at the membrane surface and its concentration in the bulk:

CPC

= C,,,/Cb

(7)

This phenomenon also occurs in membrane distillation, but its effect on the water vapour flux through the membrane can be neglected, being the driving force directly dependent on the difference of temperature. Osmotic distillation is also applied for the removal of volatile compounds (e.g., alcohols) from water streams. In this case, the aqueous strip can be pure water [31]. The resistances offered by the two phases and the membrane lead to a concentration profile that determines the driving force for the transport.

1.5. Membrane crystallizers

Membrane crystallizers represent a particular application of membrane and osmotic distillation. These systems, in fact, are based on the same principles that regulate the above operations but are specifically mentioned here because the feed solutions they treat are close to the saturation values and usually are the results of previous treatments. The aim of membrane crystallizers is to perform the crystallization of the solutes of interest by removing water from the almost saturated feeds. An important task of the process is to avoid the

Basic Principles of Membrane Contactors 25

formation and precipitation of crystals on the membrane surface that could cause pore blocking. This type of membrane contactor is altemative to conventional methods used for producing crystals, such as evaporation.

1.6. Membrane emulsifiers

Membrane emulsifiers employ both hydrophobic and hydrophilic membranes for creating microemulsions. These systems are not used to keep in contact the two phases, but to force one phase into the other. We report here about them as a type of membrane contactors because the membrane properties required for carrying out this operation are similar to those needed in membrane contactors processes. In membrane emulsifiers, one side of the membrane is in contact with the liquid phase emulsified ("dispersed phase") while the other side is in contact with the liquid phase that contains the emulsified phase ("continuous phase"). The dispersion phase is forced, by applying a pressure, to permeate through membrane into the continuous phase where it is emulsified (Figure 17).

26 Chapter 1

Figure 17. Emulsion formation by means of a microporous membrane. The driving force is, thus, related to the difference of pressure between the two phases. During the process it is important that the membrane surface is not wetted by the dispersed phase and the choice of the membrane strongly depends on this aspect. For example, for oil/water emulsions, the membrane used is hydrophilic, whereas for water/oil emulsions is hydrophobic [32-34]. In membrane emulsifiers the flux is directly proportional to the difference of pressure between the two phases and mainly depends on the membrane resistance and the resistance offered by the continuous phase. A generic expression is:

J = K'(P1-P2)

(8)

with K= f(km, k2)

(9)

where:

PI, P2, pressures of the dispersed and continuous phase.

Basic Principles of Membrane Contactors 27 1.7. Phase transfer catalysis Membrane contactors can be also used to carry out catalytic reactions. In this case, the membrane, that can be both hydrophilic and hydrophobic, is catalytically active (e.g. enzymes are immobilized into its micropores). When two liquid phases (aqueous/organic) are kept in contact, a compound of one phase can diffuse to the catalytic sites where reacts and the formed products can be stripped in the other phase, without mixing of the two streams (Figure 18). This type of system is an example of the so-called "phase transfer catalysis" [35]. The process is regulated by a difference of concentration, for both reactants and products.

Figure 18. Schematic representation of the phase transfer catalysis. The concept can be applied also to systems in which both streams contain reactants. Now both reactants have to diffuse towards the catalytic sites and products can move towards both streams, the degree of affinity between products and streams controlling their distribution

28 Chapter 1 (Figure 19). These types of membrane contactors can be, thus, effective also for three-phase reaction where a gas and a liquid come in contact on the catalytic membrane (solid).

Figure 19. Separate feed of reactants and products diffusion towards the two phases. Phase transfer catalysis couples the transport of the species with the reaction. The flux of reactants towards the catalytic sites as well as the flux of products from the reaction zone towards the phases is always depending on the resistances offered by the phases and the membrane. For a product that is formed in themembrane pores on the catalytic sites and that moves towards one of the phases (e.g., phase 1), the flux can be described as:

Jp = K (Cpr - C m )

(10)

w i t h X = f(kmc, kl)

(11)

where:

Basic Principles of Membrane Contactors 29

Jp, flux of the product P; Cec, Cm, concentrations of P in the catalytic membrane pores and in the phase I," kmc, catalytic membrane mass transfer coefficient.

For the case of a phase 1 containing the reactant that moves towards a membrane with a catalytic surface and a phase 2 where the formed products are recovered (see Figure 20), the equations that describe the fluxes are:

JR = K'(CR1-CRm)

(12)

with K = f(kl)

(13)

where:

Jl~ flux of the reactant R; CRI, GRin, concentrations of R in the phase 1 and at the catalytic membrane surface.

Jp = K'(Cpm-Cp2)

(14)

with K = f(km, k2)

(15)

where:

Jp, flux of the product P; CPm,CP2, concentrations of P at the catalytic membrane surface and in the phase 2;

30 Chapter 1

Figure 20. Concentration profiles of the reactant contained in the phase 1and of the products for a membrane with a catalytic surface and a phase 2 with high affinity for products. The different examples of membrane contactors described, with the exception of membrane emulsifiers, can be further grouped into three main classes: -

Carrier-free, that include all membrane contactors working without any carrier;

-

Carrier-charged, that include membrane contactors where carriers are used to facilitate the transport ;

-

Reactors, that include membrane contactors where a reaction occurs within the membrane pores.

Table 3 shows the general equations describing the mass flux through the membrane for the different classes.

Basic Principles of Membrane Contactors 31 Table 3. General equations describing the mass transport through the membrane for the different classes of membrane contactors Membrane contactors

Equation for the mass flux

Carrier-free

J = km AC or J = km AP

Carrier-charged

J = km AC + km complex ACcomplex

Reactors

J = kmc AC

2. Advantages and disadvantages of membrane eontactors Membrane

contactors

have different interesting properties that make them more

advantageous with respect to traditional operations. For example, it is possible to work with a well defined and constant interfacial area. This means that the exchange area is known and all the device works with the same efficiency. The constance of the interfacial area with changes in the operating conditions or fluid properties leads also to a higher efficiency with respect to conventional units. Moreover, a higher interfacial area can be provided in a small volume, that corresponds to higher compactness, and, thus, to reduced size and weight. The typical interfacial area per unit of volume of membrane contactors varies between 1500-3000 m2/m 3, whereas for conventional contactors this ratio is in the range of 100- 800 m2/m 3 [36]. It is important to point out that the higher interfacial area is the major responsible of the enhanced efficiency in membrane contactors with respect to traditional devices. As a matter of fact, the mass transfer coefficients reachable in membrane contactor are usually the same or sligthly lower than those of conventional systems. Ding et al. [37] compared the ka (with a representing the interfacial area) achievable in membrane contactors with those related to a

32 Chapter 1 high-efficiency rotating column and a conventional extractor. From the above comparison it resulted a ka value of 0.053 s -1 for membrane contactors versus 0.0007 and 0.00005 s-1 for the rotating column and the conventional extractors, respectively. Another positive aspect is that there is no dispersion between the two phases and, thus, no need to separate the two phases downstream the process and no need to work with fluids of different densities. Furthermore, being the two phases separate by the membrane, phenomena as flooding, loading, foaming are avoided, leading to a higher flexibility in changing the operating flowrates that can be varied, also independently, in a wider range of values. In gas-liquid transfer, the size of the gas bubbles introduced into the liquid bulk is depending on the micropores size. By ensuring a minimal distance between adjacent pores, any possible coalescence is avoided. This implies that very small bubbles of gas reach the liquid and, then, a better dispersion is achieved. The same concept is valid for the microemulsions production. In membrane distillation, ultrapure water and high recovery factors up to crystals production can be obtained at relatively low temperatures with respect to the classical distillation (the temperature of the feed stream is usually of the order of 35~ and the temperature of the strip phase is in the range of 15-25~

Moreover, azeotropic mixtures, hardly separated by

distillation column, can now be treated. Solutions containing compounds that can deteriorates with temperatures (pharmaceutical compounds, vitamins, aromes) can be processed by osmotic distillation. By carrying out a reaction with membrane contactors, it is possible to reduce the mass transport resistances of the reactants towards the catalyst sites (the phases are in direct contact with the catalytic zone and the reactants do not have to diffuse through the

Basic Principles of Membrane Contactors 33

other phase before reaching the catalyst, as usually happens in multiphase reaction systems). The system can be also used to simultaneously separate the products. In this way, the conversion of reversible reactions can be increased and the further reactions of the desired products are avoided. As all membrane operations, membrane contactors are flexible, easy in the scale-up and control, modular in design, do not present any moving part and are generally characterized by low pressure drops. Unfortunately, these systems offer some disadvantages too! First of all, the presence of the membrane is cause of a further resistance to the mass transport. However, this resistance can significantly be reduced by operating properly. This aspect will be treated in more details in next Chapters. Other drawbacks related to the membrane are its limited life-time and the risk of fouling, that sometimes implies pre-treatments before the process. The limited operating pressures allowed, based on the breakthrough value, is another weak point of these systems. Specifically for the supported liquid membranes, the stability of the solvent and the lifetime and selectivity of the carrier, represent hard problems to solve. Finally, as it will be discussed in next Chapters, sometimes during the operations channeling and bypassing can not be completely avoided, with a consequent reduction of the mass transport efficiency. In Table 4, for each type of membrane contactor is reported the corresponding conventional unit operation.

34 Chapter 1

Table 4. Membrane contactors systems and corresponding conventional operations Membrane contactors

Conventional operations

Membrane strippers/scrubbers

Packed and bubble columns

Membrane extractors

Packed columns, mixer-settler, centrifugal devices

Supported liquid membranes

Packed and bubble columns, mixer-settler, centrifugal devices

Membrane distillation and osmotic distillation Distillation columns Membrane crystallizers

Evaporators

Membrane emulsifiers

High pressure homogenizers

Phase transfer catalysis

Chemical reactors

Table 5 summarizes the main advantages and disadvantages of membrane contactors.

Basic Principles of Membrane Contactors 35

Table 5. Positive and negative aspects of membrane contactors Positive

Negative

Well defined and constant interfacial area

Further resistance offered by the membrane

High interfacial area in small volumes

Membrane limited life-time

Reduced size and weight

Membrane fouling

No dispersion between phases

Pre-treatments before the process

No need of phase separation downstream

Limited operating pressures, based on the breakthrough value

No need to work with fluids of different densities

Channeling and bypassing of fluids

No flooding, loading, foaming

Limited stability of the solvent and of the lifetime and selectivity of the carrier in supported liquid membranes

Wide range of operating flow-rates Flow-rates can be varied independently No coalescence phenomena Controlled and very small size of the bubbles and the emulsions produced Lower operating temperatures with respect to distillation processes Azeotropic mixtures can be easier treated than in conventional units Reaction and separation carry out simultaneously Flexible, easy in scale-up, control and automatization Modular design and no moving parts

36 Chapter 1 References [ 1] Z. Qi and E.L. Cussler. Microporous hollow fibers for gas absorption. I. Mass transfer in the liquid, J. Membrane Sci., 23 (1985) 321-332 [2] Z. Qi and E.L. Cussler. Microporous hollow fibers for gas absorption. II. Mass transfer across the membrane, J. Membrane Sci., 23 (1985) 333-345 [3] E.L. Cussler. Hollow fiber contactors, in J.G. Crespo and K.W. Boddeker (Eds.), Membrane Processes in Separation and Purification, Kluwer Academic Publishers, The Netherlands (1994) 375-394 [4] A. Kiani, R.R. Bhave and K.K. Sirkar. Solvent extraction with immobilized interfaces in a microporous hydrophobic membrane. J. Membrane Sci., 20 (1984) 125-145 [5] A. Gabelman and S.T. Hwang. Hollow fiber membrane contactors. J. Membrane Sci., 159 (1999) 61-106 [6] B.W. Reed, M.J. Semmens and E.L. Cussler. Membrane Contactors, in: R.D. Noble and S.A. Stern (Eds.), Membrane Separation Technology: Principles and Applications, Elsevier, Amsterdam (1995) 467 [7] E. Drioli and A. Criscuoli. Microporous inorganic and polymeric membranes as catalytic reactors and membrane contactors, in: Nick Kanellopoulos (Ed.), Membrane Science and Technology Series, 6 entitled: "Recent advances in gas separation by microporous membranes", Elsevier, Amsterdam (2000) 497-510 [8] A. Criscuoli, E. Curcio and E. Drioli, Polymeric membrane contactors, in: S.G. Pandalai (Ed.), Recent research developments in applied polymer science, Transworld Research Network Publication by Research Signpost, ISBN: 81-7895-102-9, Kerala, 37/66 (2), 7 (2003) 1-21

Basic Principles of Membrane Contactors 37 [9] E. Drioli, A. Criscuoli and E. Curcio. Membrane contactors and catalytic membrane reactors in process intensification. Chem. Eng. Technol., Vol. 26 N. 9 (2003) 975-981 [10]R. Prasad and K.K. Sirkar. Membrane-based solvent extraction, in: W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Chapman and Hall, New York (1992) 727-763 [11]H. Kreulen, C.A. Smolders, G.F. Versteeg and W.P.M. van Swaaij. Determination of mass transfer rates in wetted and non-wetted microporous membranes. Chem. Eng. Sci., 48 (1993) 20932102 [12]A. Malek, K. Li and W.K. Teo. Modeling of microporous hollow fiber membrane modules operated under partially wetted conditions. Ind. Eng. Chem. Res., 36 (1996) 784-793 [13]H. Kreulen, C.A. Smolders, G.F. Versteeg and W.P.M. van Swaaij. Microporous hollow fibre membrane module as gas-liquid contactors. Part 2. Mass transfer with chemical reaction. J. Membrane Sci., 78 (1993) 217-238 [14]J.S. Cha, V. Malik, D. Bhaumik, R. Li and K.K. Sirkar. Removal of VOCs from waste gas streams by permeation in a hollow fiber permeator. J. Membrane Sci., 128 (1997) 195-211 [15] K. Li, D. Wang, C.C. Koe and W.K. Teo. Use of asymmetric hollow fibre modules for elimination of H2S from gas streams via a membrane absorption method. Chem. Eng. Sci., 53 N. 6 (1998) 1111-1119 [ 16]D. Bhaumik, S. Majumdar and K.K. Sirkar. Pilot-plant and laboratory studies on vapor permeation removal of VOCs from waste gas using silicone-coated hollow fibers. J. Membrane Sci., 167 (2000) 107-122 [17]S. Majumdar, D. Bhaumik and K.K. Sirkar. Performance of commercial-size plasmapolymerized PDMS-coated hollow fiber modules in removing VOCs from N2/air. J. Membrane Sci., 214 (2003) 323-330

38 Chapter 1 [18]M. H.V. Mulder. Basic Principle of Membrane Technology., second edition, Kluwer Academic Publishers, The Netherlands (1996) 339-357 [19]A.J.B. Kemperman, D. Bergeman, Th. Van den Boomgaard and H. Strathmann. The stability of supported liquid membranes: A state of the art literature review. Sep. Sci. Technol., 31 (1996) 2733-2762 [20]R.W. Baker. Membrane Technology and Applications, McGraw-Hill, New York (2000) 405-442 [21]D.L. Bryant, R.D. Noble and C.A. Koval. Facilitated transport separation of benzene and cyclohexane with poly(vinyl alcohol)-AgNO3 membranes. J. Membrane Sci., 127 (1997) 161-170 [22]W.S.W. Ho and T.K. Poddar. New membrane technology for removal and recovery of metals from waste waters and process streams. Proc. of the AIChE Spring National Meeting, Atlanta, March 5-9 2000, 38-43 [23]X.J. Yang, A.G. Fane, J. Bi and H.J. Griesser. Stabilization of supported liquid membranes by plasma polymerization surface coating. J. Membrane Sci., 168 (2000) 29-37 [24]S.H. Lin and R.S. Juang. Mass.transfer in hollow fiber modules for extraction and back-extraction of copper(II) with LIX64N carriers. J. Membrane Sci., 188 (2001) 251-262 [25]A. Gherrou, H. Kerdjoudj, R. Molinari and E. Drioli. Facilitated co-transport of Ag(I), Cu(II) and Zn(II) ions by using a crown ether as carrier: influence of the SLM preparation methos on ions flux. Sep. Sci. Technol., 37 N. 10 (2002) 2317-2336 [26]A. Figoli, W.F.C. Sager and M.H.V. Mulder. Facilitated oxygen transport in liqid membranes: review and new concepts. J. Membrane Sci., 181 (2001) 97-110 [27]J.D. Way and R.D. Noble. Facilitated transport, in: W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Chapman and Hall, New York (1992) 833-866

Basic Principles of Membrane Contactors 39 [28]R.W. Shofield, A.G. Fane and C.J.D. Fell. Gas and vapor transport through microporous membranes. II. Mebrane distillation. J. Membrane Sci., 53 N.1 &2 (1990) 173-185 [29]K.W. Lawson and D.R. Lloyd. Membrane distillation. J. Membrane Sci. 124 (1997) 25 [30]M. Gryta and M. Tomaszewska. Heat transport in the membrane distillaton process. J. Membrane Sci., 144 N. 1&2 (1998) 211-222 [31]P.A. Hogan, R.P. Canning, P.A. Peterson, R.A. Johnson and A.S. Michaels. A new option: osmotic distillation. Chem. Eng. Prog., (1998) 49-61 [32]V. Schroder, O. Behrend and H. Schubert. Effect of dynamic interfacial tension on the emulsification process using microporous, ceramic membrane. J. Colloid and Interf. Sci., 202 (1998) 334-340 [33]R.A. Williams, S.J. Peng, D.A. Wheeler, N.C. Morley, D. Taylor, M. Whalley and D.W. Houldsworth. Controlled production of emulsions using a crossflow membrane. Part II: Industrial scale manufacture. Trans IchemE, 76 part A (1998) 902-910 [34] V. Schroder and H. Schubert. Production of emulsions using microporous, ceramic membranes. Colloid and Surf. A: Physochemical and Eng. Aspects 152 (1999) 103-109 [35]S.J. Taverner and J.H. Clark. Recent highlights in phase transfer catalysis. Chem. Ind., (1997) 2227 [36]P.S. Kumar, J.A. Hogendoorn, P.H.M. Feron and G.F. Versteeg. New absorption liquids for the removal of CO2 from dilute gas streams using membrane contactors. Chem. Eng. Sci., 57 (2002) 1639-1651 [37]H.B. Ding, P.W. Carr and E.L. Cussler. Racemic leucine separation by hollow-fiber extraction. AIChE J., 38 n.10 (1992) 1493-1498

Chapter 2. Membrane materials

I. Introduction

The membrane itself represents the core of any membrane process. A large variety of membranes exists, depending on their structure, transport properties and separation mechanism; all those different characteristics are generally originated by dissimilar raw materials or preparation methods. The class of synthetic membranes includes organic (polymeric) and inorganic membranes. Due to the possibility to modulate their intrinsic properties (thermal, mechanical and chemical stability, selectivity and permeability etc.), polymeric membranes have attracted much more interest. A large part of membranes in use for membrane contactors applications are polymeric; the most significant exception probably concerns the use of ceramic membranes in the emulsification process. The microstructure of a membrane is also a critical subject, and strictly depends on the preparation procedures: commonly, one can discriminate between symmetric and asymmetric membranes. Symmetric membranes may be dense or have straight or sponge-like pores: such a kind of microporous structures are widely employed in membrane distillation and related operations, in membrane absorption, stripping and extraction processes, as support for liquid membranes, in membrane emulsification technology. Asymmetric membranes show a thin dense skin layer with or without pores on the top of a high porous sublayer: the thickness of the selective skin offers the advantage of a low resistance to the transport through the membrane. In phase transfer catalysis, if pores in the dense layer are small enough to retain the catalyst- but large enough to freely pass substrates and products - asymmetric membranes provide an interesting support for its immobilization.

Membrane Materials 41

In the next paragraphs, a survey on some polymeric and inorganic materials and on the preparation and characterization techniques for membranes used as contactors is presented. It is beyond the scope of this book to give details on this extremely complex matter, and readers are referred to specific handbooks in this field. Information on commercial modules used in membrane contactors applications are furnished in Chapter 3.

2. Membrane polymers

When producing porous membranes, the selection of the material is mainly driven by the necessity to achieve a high chemical and thermal stability. Microporous polymeric membranes are prepared by various techniques: sintering, stretching, track-etching, phase inversion. The processing requirements and related characteristics of the resulting membrane also determine and limit the choice of the polymeric materials. Typology and main characteristics of the polymers frequently used as material for microporous membranes are given in table 1.

3. Preparation methods

Different methodologies are available to prepare membranes. This paragraph will provide a brief description of sintering of powders, stretching of films, track-etching and template leaching techniques. The most common method for preparing porous membranes, the phase inversion process, is discussed with more details.

42 Chapter 2 Table 1. Frequently used materials for microporous membranes Polymer

Chemical structure

Main characteristics

Polycarbonate

o\\

)?-o-o

\-'-~/

CH 3

\-----/

Cellulose acetate CH2OAc o

High wet/dry strength; mechanical properties suitable for track-etching preparation method Very hydrophilic; sensitive to thermal and chemical degradation; low tensile strength

OAc Nylon H

I N

~

(CH2) s ~

C

Polysulfone

\ -- I

CH 3

\ -- I

\ -

I

Inherently wettable; subject to hydrolytic degradation; better chemical stability when using aliphatic polyamides pH and temperature resistant; poor hydrocarbon resistant

Membrane Materials 43

Polyethersulfone

High thermal and chemical stability

F

Polyetherketone

High thermal and chemical resistance

Polyetheretherketone

High thermal and chemical resistance; only soluble at room temperature in concentrated inorganic acids. Excellent thermal stability; good chemical resistance

to,O- ~ Polyimide 0

/c NX

0

c\ C//N

c

,,

0

0

0

Polypropylene

HI CH3 1 I C--C H

H

Polyvinylidenefluoride F

H

I

I

C--C

I

F

Chemically resistant; hydrophobic

I

H

High temperature resistant; inherently hydrophobic

44 Chapter 2 Polytetrafluoroethylene F:

F

I

I

t2--C

I

F

I

F

High temperature and chemical (acid) resistant; cannot be irradiated; inherently hydrophobic

3.1. Sintering Sintering is a simple technique: a powder of polymeric particles is pressed into a film or plate and sintered just below the melting point. The process yields to a microporous structure having porosity in the range of 10-40% and a rather irregular pore size distribution (figure 1). The typical pore size, determined by the particle size of sintered powder, ranges from 0.2 to 20 ~tm.

Figure 1. Scanning electron micrograph of a PTFE membrane prepared by sintering.

3.2. Stretching Microporous membranes can be also prepared by stretching a homogeneous polymer film made from a partially crystalline material. Films are obtained by extrusion from a polymeric powder at temperature close to the melting point coupled with a rapid draw-down. Crystallites in the polymers are aligned in the direction of drawing; after annealing and cooling, a mechanical stress is applied perpendicularly to direction of drawing. This manufacturing process gives a relatively uniform

Membrane Materials 45 porous structure with pore size distribution in the range of 0.2-20 ~tm and porosity of about 90% (figure 2).

Figure 2. Gore-Tex PTFE membrane prepared by stretching (pore size ~ 0.2 ~tm).

3.3. Track-etching Microporous membranes with uniform and perfectly round cylindrical pores can be obtained by track-etching. Homogeneous thin films, usually with thickness of 5-15 ~tm, are exposed to the irradiation of collimated charged particles, having energy of about 1 MeV. These particles damage the polymeric matrix; the film is then immersed in an acid or alkaline bath, where the polymeric material is etched away along the tracks so leaving perfect pores with a narrow size distribution Figure 3). Typical pore size ranges between 0.02 and 10 ~tm; however, the surface porosity generally is below 10%.

Figure 3. Polycarbonate membrane prepared by track-etching.

46 Chapter 2 3.4. Template leaching Porous structures can be obtained by leaching out one of the component from a film. This technique allows producing porous glass membranes suitable for emulsification process. A homogeneous melt of three components (i.e. SiO2, B203, and Na20) is cooled from 1300-1500~ down to 500-800~

As a consequence, demixing is induced in the system that splits into two

phases: one consisting mainly of Si02 which is not soluble in mineral acids, and the other phase is richer in B203, that is subsequently leached out of the structure resulting in a microporous matrix. Porous alumina membranes made by anodic oxidation contain parallel circular pores with a narrow pore size distribution. They are formed by an electrochemical process involving the oxidation of high purity aluminium foils in presence of an acid electrolyte, followed by etching in a strong acid bath. In this process, an electrical circuit is established between a carbon cathode and a thin film of aluminium which serves as the anode, resulting in the oxidation of the aluminium to form alumina according to the reaction: 2AI + 3 H 2 0 --~ Al202 + 3 H 2

(1)

In appropriate electrolyte solutions, the film that is formed has a uniform columnar array of hexagonally close packed alumina cells, each containing a circular pore (figure 4). Pores form in the oxide film because of field assisted dissolution of the alumina from the base of each pore. With appropriate process conditions, membranes can be formed with pore diameters between 0.01 and 0.3 pm, pore densities between 108 and 10 II cm "2 and thicknesses up to 200 ~tm (figure 5).

Membrane Materials 47

Figure 5. A microporous aluminum membrane prepared by anodic oxidation.

Microlithography and reactive ion etching is a further technique to produce porous membranes. A silicon nitride coating (= 1 ~m) is deposited on a silicon wafer by chemical vapor deposition. By spin-coating, on the top of the nitride layer a photosensitive lacquer is applied. The lacquer is then exposed to UV radiation and developed in a NaOH solution resulting in a print of the mask pattem in the lacquer layer; perforations are extended to silicon nitride layer by reactive ion-etching. The

48 Chapter 2

resulting membranes are characterized by a narrow pore size distribution, with pore diameters typically in the range of 0.5-10 pm. Alternatively, the exposed polymer layer can be degraded by irradiation with X-rays (figure 6).

Figure 6. A silicon microsieve prepared by X-ray lithography process.

3.5. Phase inversion technique

Membranes are prepared by phase inversion technique from polymers that are soluble at a certain temperature in an appropriate solvent or solvent mixture, and that can be precipitated as a continuous phase by changing temperature and/or composition of the system. These changes aim to create a miscibility gap in the system at a given temperature and composition; from a thermodynamic point of view, the free energy of mixing of the system becomes positive. The formation of two different phases, i.e. a solid phase forming the polymeric structure (symmetric, with porosity almost uniform across the membrane cross-section, or asymmetric, with a selective thin skin on a sub-layer) and a liquid phase generating the pores of the membrane, is determined by few and conceptually simple actions: 1. by changing the temperature of the system (cooling of a homogeneous polymer solution which separates in two phases): temperature-induced phase separation technique (TIPS); 2. by adding non-solvent or non-solvent mixture to a homogeneous solution: induced phase separation (DIPS);

diffusion-

Membrane Materials 49

3. by evaporating a volatile solvent from a homogeneous polymer solution prepared using solvents with different dissolution capacity. Although these procedures are practically dissimilar, the basic of membrane formation mechanism is governed, in all cases, by similar thermodynamic and kinetic concepts: variations in the chemical potential of the system, diffusivities of components in the mixture, Gibbs free energy of mixing and presence of miscibility gaps. TIPS and DIPS processes, often utilized also in combination to prepare membranes, are discussed in details in the following paragraphs.

3.5.1. Phase separation: a thermodynamic description

Free Gibbs energy of a system is defined as a state function of enthalpy (H) and entropy (S)" (2)

G = H - TS

where T is the temperature of the system. In general, G depends on temperature, pressure and number of moles ni of each components in the system: (3)

G = G ( r , P , nl,n 2 ..... nk)

and the change in Gibbs free energy for a multi-component systems is given by: dG = OG

dT +

dP +

P,ni

T,n,

dn~ i=1

(4)

T,P,nj

In equation (3)"

= ~t~

"~

P,n, = - S

"~

T,ni = V

~

(5)

T,P,nj

and, therefore: k dG = - S d T + VdP + ~ l.tidn i i=l

(6)

50 Chapter 2 For a two-component mixture, being T and P constant, the Gibbs free energy per mole Gm is given by the sum of the chemical potentials of both components 1 and 2: G m = Xl,s

-'b

X2,L/2

(7)

When nl moles of component 1 are mixed to n2 moles of component 2, the change in the free energy of mixing AGm per mole of mixture is: A G m = x1A].I 1 +

x2A,L/2

(8)

For an ideal solution, the chemical potential of each component is expressed by: (9)

/.ti =/.t o + R T In x~

where/.t o is the molar free energy of pure components. This circumstance is graphically illustrated in figure 7.

Gm 0

x2

~10

~2

Figure 7. Gibbs free energy of mixing for a two-components system at constant T and P.

Membrane Materials 51

From equation (8) follows that: A/~ i = RTlnx

(10)

i

and A G m = R T ( x I In x I + x 2 In

X2 )

(11)

Since lnxi is negative (being xiAPmin is:

88 Chapter 2 rmax

~x4Ap

_z \ _

rmax

Q= I Xr~ -8ft6-rr:['x)dx:n2AP r(AP)

I X4 f(x)dX r(AP)

(45)

Derivative of equation (44) with respect to AP, with opportune rearrangements and substitutions give the final expression for the pore size distribution function (mathematical details in [47]):

f(r)=

d(AP)

AP

In equation (45), constants

(46)

2 ~'~1~"~2

take into account information about the structural properties of the

membrane, the testing fluid properties and the fluid membrane interactions. For a normalized distribution, the n-th moment

(r") is mathematically defined as:

rmax

(47)

rmm where rminand rmaxare the radii of the smallest and largest pores in the membrane. The first moment of the distribution corresponds to the average pore radius. As disadvantage, the characterization method shows a loss in resolution in the pore size distribution (that can be offset by opportune adjustments of the weighting factors) as the pore sizes decrease to values well below the largest pore size. Moreover, this method needs an appropriate pore model describing the membrane structure (eq. (46) is valid for non-interconnecting, cylindrical pores). Liquid-liquid displacement represents a variant of the method above described. In this case, membrane pores are filled by a liquid that is displaced by a second immiscible liquid. A typical liquid pair is water/iso-butanol. Pores with diameters in the range of 5-100 nm can be adequately detected. With respect to gas-liquid displacement, liquid pairs are characterized by lower interfacial tensions compared to gas-liquid pairs, and reduced pressures are needed to penetrate pores with the same size. Further details can be found in literature [45, 48, 49].

Membrane Materials 89 6. 6. 4. P e r p o r o m e t r y

Perporometry is based on the phenomenon of capillary condensation of liquid in micropores. The vapour pressure of a liquid depends on the radius of curvature of its surface, according to Kelvin's equation: (48)

ln P_f-l_ = 27"V cosO Po RTrk

where p and p0 are the vapour pressures in the capillary and under standard conditions, respectively, y is the surface tension between the capillary liquid and air, V is the molar volume of the liquid, 0 the contact angle, R the gas constant, T the absolute temperature and rk the Kelvin radius, little smaller than the actual pore radius due to the presence of an absorbed layer of condensable gas. By applying a partial pressure difference across the membrane, pores can be blocked with liquid by capillary condensation; this principle is coupled to the measurement of the free diffusive transport through the open pores. A scheme of the experimental set-up is reported in figure 30. A mixture of oxygen and nitrogen (e.g. air) is applied on the feed side, while nitrogen flows on the permeate side as carrier gas. This creates a concentration gradient of oxygen across the membrane. On both lines, an organic compound (e.g ethanol) is also applied as condensable gas; in order to avoid swelling phenomena, the organic vapour should exhibit a low affinity with the membrane. At both sides of the membrane, the absolute pressure is 1 atm and the relative pressure of the organic vapour is the same. Evaporator IP GC Analysis

N2, Ethanol

I N2, O2, Ethanol

Evaporator

Figure 30. A permporometry setup.

. DIFFUSION CELL

[

Membrane

90 Chapter 2 The size distribution of active pores is therefore obtained by measuring the gas flow through the membrane. For pore radii of 1-25 nm and at atmospheric pressure, the flux of the i-th component through a pore with radius ri, determined by Knudsen diffusion, can be expressed as: j, = 2 [ 8~ Ap n,r, 3 V MwRT A mr 6

(49)

where Mw is the molecular weight of the gas, R the gas constant, T the absolute temperature, Ap the partial pressure gradient across the membrane, Am the membrane surface area, x the tortuosity of pores, 8 the membrane thickness, and ni the number of pores having radius ri. Integrating over the entire distribution of pore radii, few manipulations allow obtaining the pore size distribution:

-d-~-~ rnun

L drm,n -3V 8---~ Apr3mm

(50)

Quantitative analysis are preferentially carried out during desorption process, since it is more difficult to reach equilibrium during adsorption process: the gas (oxygen, in the discussed case) flux as a function of the Kelvin radius through Nucleopore membranes (pore size given by manufacturer: 15 nm) is reported in figure 31.

Membrane Materials 91 '

I

'

I

i

I

'

I

i

i

'

i

E ~

3

6 i

0

0

4

8

I

12

16

Kelvin radius (nm)

Figure 31. Oxygen flux versus Kelvin radius for a Nucleopore membrane. After [45 ].

This technique characterizes only active pores in the range of 2-40 nm. More details are in [50, 51,

52,53].

6.6.5. Thermoporometry Thermoporometry is based on the calorimetric measurement of a solid-liquid transition in a porous material in order to determine the pore size distribution [54, 55, 56, 57]. In pores totally filled with a liquid, the curvature of the liquid-solid interface Cs is related to the change of temperature T by: r~

,

92 Chapter 2 where V is the volume of the pore, AS is the surface area of the solid-liquid interface, ), is solidliquid surface tension. The liquid-solid interface is almost spherical and its curve Cs is: 2

(52)

Cs " - ~

r-t

where t is the thickness of the layer of condensate fixed to pore wall. Equations (51) and (52) link the pore radius r to a decrease in solidification temperature T-T0. In case of water, in the range of-40 70 0

E !_.

e,,

~

60

X

o

50

I

0

50

I

i

100

150

I

I

I

200

250

300

Gas flowrate (ml/min)

Figure 18. Influence of the gas flow rate on oxygen removal. After [20].

350

160 Chapter 4 References [ 1] Perry's Chemical Engineers' Handbook. R.H Perry, D. W. Green and J.O. Maloney (Eds), 6th edition, McGraw-Hill Book Co., New York (1984) [2] H. Kreulen, C.A. Smolders, G.F. Versteeg and W.P.M. van Swaaij. Microporous hollow fibre membrane modules as gas-liquid contactors. Part 2. Mass transfer with chemical reaction. J. Membrane Sci., 78 (1993) 217-238 [3] Z. Qi and E.L. Cussler. Microporous hollow fibers for gas absorption. II. Mass transfer across the membrane. J. Membrane Sci., 23 (1985) 333-345 [4] P.S. Kumar, J.A. Hogendoorn, P.H.M. Feron and G.F. Versteeg. New absorption liquids for the removal of CO 2 from dilute gas streams using membrane contactors. Chem. Eng. Sci., 57 (2002) 1639-1651 [5] M. Mavroudi, S.P. Kaldis and G.P. SakeIlaropoulos. Reduction of CO2 emissions by a membrane contacting process. Fuel, 82 (2003) 2153-2159 [6] K.K. Sirkar. Other new membrane processes, in: W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Chapman and Hall, New York (1992) 885-912 [7] M.H.V. Mulder. Basic Principle of Membrane Technology., second edition, Kluwer Academic Publishers, The Netherlands (1996) 225-228 [8] M.-C. Yang and E.L. Cussler. Designing hollow-fiber contactors. AIChE J., 32 (1986) 1910-1915 [9] S.R. Wickramasinghe, M.J. Semmens and E.L. Cussler. Mass transfer in various hollow fiber geometries. J. Membrane Sci., 69 (1992) 235-250 [10]

M.J. Costello, A.G. Fane, P.A. Hogan and R.W. Schofield. The effect of shell side

hydrodynamics on the performance of axial flow hollow fibre modules. J. Membrane Sci., 80 (1993) 1-11

Gas - Liquid Systems 161

[ 11 ]

K.L. Wang and E.L. Cussler. Baffled membrane modules made with hollow fiber fabric. J.

Membrane Sci., 85 (1993) 265-278 [ 12]

S.R. Wickramasinghe, M.J. Semmens and E.L. Cussler. Hollow fiber modules made with

hollow fiber fabric. J. Membrane Sci., 84 (1993) 1-14 [ 13]

S.R. Wickramasinghe, M.J. Semmens and E.L. Cussler. Better hollow fiber contactors. J.

Membrane Sci., 62 (1991) 371-388 [ 14]

J. Lemanski, B. Liu and G. G. Lipscomb. Effect of fiber variation on the performance of

cross-flow hollow fiber gas separation modules. J. Membrane Sci. 153 (1999) 33-43 [ 15]

J. Lemanski and G.G. Lipscomb. Effect of shell-side flows on the performance of hollow-fiber

gas separation modules. J. Membrane Sci., 195 (2000) 215-228 [16]

F. Lipniski and R.W. Field. Mass transfer performance for hollow fibre modules with shell-

side axial feed flow: using an engineering approach to develop a framework. J. Membrane Sci., 193 (2001) 195-208 [ 17]

A. Gabelman and S.T. Hwang. Hollow fiber membrane contactors. J. Membrane Sci., 159

(1999) 61-106 [18]

R. Prasad and K.K. Sirkar. Dispersion-free solvent extraction with microporous hollow-fiber

modules. AIChE J., 34 N. 2 (1988) 177-188 [19]

J. Wu and V. Chen. Shell-side mass transfer performance of randomly packed hollow fibre

modules. J. Membrane Sci., 172 (2000) 59-74 [20]

A. Criscuoli, E. Drioli and U. Moretti. Membrane contactors in the beverage industry for

controlling the water gas composition. Annals of New York Acad. Sci., 984 (2003) 1-16 [21 ]

P. Schoner, P. Plucinski, W. Nitsch and U. Daiminger. Mass transfer in the shell side of cross

flow hollo fiber modules. Chem. Eng. Sci., 53 N. 13 (1998) 2319-2326

162 Chapter 4 [22]

D. Bhaumik, S. Majumdar and K.K. Sirkar. Absorption of C O 2 in a transverse flow hollow

fiber membrane module having a few wraps of the fiber mat. J. Membrane Sci., 138 (1998) 77-82 [23]

L. Dahuron and E.L. Cussler. Protein extraction with hollow fibers. AIChE J., 34 (1988) 130

[24]

T. Ahmed and M.J. Semmens. Use of sealed end hollow fibers for bubbleless membrane

aeration: experimental studies. J. Membrane Sci., 69 (1992) 1-10 [25]

T. Ahmed and M.J. Semmens. The use of independenlty selaed microporous hollow fiber

membranes for oxygenation of water: model development. J. Membranse Sci., 69 (1992) 11-20 [26]

R.M.C. Viegas, M. Rodriguez, S. Luque, J.R. Alvarez, I.M. Coelhoso and J.P.S.G. Crespo.

Mass transfer correlations in membrane extraction: Analysis of Wilson-plot methodology. J. Membrane Sci., 145 (1998) 129-142 [27]

T. Leiknes and M.J. Semmens. Vacuum degassing using microporous hollow fiber

membranes. Sep Purif. Technol., 22-23 (2000) 287-294 [28]

R. Gawronski and B. Wrzesinska. Kinetics of solvent extraction in hollow-fiber contactors. J.

Membrane Sci., 168 (2000) 213-222

Chapter 5. Liquid - liquid extractions

1. Introduction The liquid - liquid extractions are hereinafter presented in a similar way of g a s - liquid systems (Chapter 4). As for the gas-liquid systems, in fact, the mass transfer of solutes between two liquid phases in membrane contactors is regulated by the phase equilibria and the mass transfer resistances involved. The non-polar phase (usually, an organic phase) replaces now the gas phase and the liquid -liquid equilibria are considered instead of the gas liquid equilibria. The Chapter provides an analysis of the mass transport in terms of mass balances and calculation of the mass transfer coefficients. This analysis is general and valid for all the applications of membrane contactors where two liquid phases are involved.

2. Mass transfer equations In l i q u i d - liquid extractions, both hydrophobic and hydrophilic microporous, as well as hydrophobic - hydrophilic composite membranes can be used to put in contact the two phases, as discussed in detail below.

164 Chapter 5

2.1. Hydrophobic membranes When a species i is transferred from the non polar phase to the polar phase and a hydrophobic flat membrane is used, the resistances to the mass transfer lead to a concentration profile, as shown in Figure 1. If i is transferred from the polar to the non polar phase, the concentration profile is that of Figure 2. In both cases, the mass transfer resistances are those offered by the boundary layers and the membrane and can be drawn, as in Figure 3, by considering the electrical analogy.

Figure 3. Mass transfer resistances involved in the transport.

Liquid- Liquid Extractions 165 Referring to Figure 1, at steady-state the flux of the species i through the non polar film equals its flux through the membrane, as well as its flux through the polar film and the following equation can be written for the flat membrane:

Ji = kinp (Ci np - f im np) = kim np (Cim np - f ie np) -- kip (Cie p - f i p)

(1)

where:

kinp, mass transfer coefficient in the non polar phase for the species i; kimnp, mass transfer coefficient in the hydrophobic membrane for the species i; kip, mass transfer coefficient in the polar phase for the species i; Cinp, concentration of the species i in the non polarphase; Cimnp, concentration of the species i at the non p o l a r - membrane interface; Cie~p, concentration of the species i at the non p o la r - p o la r interface, non polar side; Ciep, concentration of the species i at the polar - non polar interface, polar side; Cip, concentration of the species i in the polar phase. For the transfer of the species i from the polar to the non polar phase, the fluxes are calculated by the same equation by only changing the sign in each flux (the transfer occurs in the opposite direction). When two liquids are in contact, a generic solute contained into one liquid diffuses through the second until equilibrium is established. The concentration of the solute in the two liquids at the interface, under equilibrium conditions, is related to its distribution coefficient

[1]: C l = m Cz

(2)

where: CI, solute concentration at the interface in the liquid 1; C2, solute concentration at the interface in the liquid 2;

166 Chapter 5 m, solute distribution coefficient.

Figure 4. Liquid-liquid equilibrium. The concentrations of a species i at the liquid - liquid interface (Cie np and Cie p) can be, then, calculated by equation (2):

Cie ,,p = mr Cie p

(3)

The flux of the species i can be also expressed in terms of the overall mass transfer coefficient: J~ ._ K,p (C , ,p - Cinpidea 9 __ Kp (C , pideal - C , p) (4) where: Knp, overall mass transfer coefficient based on non polar phase; Kp, overall mass transfer coefficient based on polar phase; Ci npiaeat, concentration of the species i in the non polar phase ideally in equilibrium with its concentration in the polar phase; Ci piaeat, concentration of the species i in the polar phase ideally in equilibrium with its concentration in the non polar phase.

Liquid- Liquid Extractions 167 Considering equation (2):

Cinp

ideal

= mi Cip

Ci pideal _ Ci n / mi

(5) (6)

The overall mass transfer coefficients can be expressed in terms of single mass transfer coefficients, by combining equations (1) and (4) and taking into account the equilibrium expressions previously reported: 1/Kp = l/kip + 1/(kim np mO + 1/(ki,,p mJ

(7)

1/Knp = m/kip + 1/kimnP+ 1/kinp

(8)

Equations (7) and (8) state that the overall resistance offered to the mass transport is due to the liquid film resistances and the membrane resistance as shown in Figure 3, and are valid also for the transport of the species i from the polar to the non polar phase.

When an hollow fiber configuration is considered with the polar phase in the shell side and the non polar phase at the lumen side the interface is located at the outer diameter of the tubes and equations (7) and (8) change into" 1/(Kp do) = 1~(kips do) + 1/(kim np mi dl,n) + 1/(kinpt mi dO

(9)

168 Chapter 5 (10)

1/(Knp do) : m/(kips do) + 1/(kimnp dim)+ 1/(kinpt dO where:

kips, mass transfer coefficient for the species i in the polar phase at the shell side; kmpt, mass transfer coefficient for the species i in the non polar phase at the tube side; di, inner diameter of the tube; do, outer diameter of the tube; dim, logarithmic mean of the hydrophobic membrane diameters.

2.2. Hydrophilic m e m b r a n e s Figures 5 and 6 show the concentration profiles that occur when the species i is transferred from the non polar and from the polar, respectively, in a hydrophilic flat membrane.

Figure 5. Concentration profile for the species i when it moves from a non polar phase toward a polar phase through a microporous hydrophilic flat membrane.

Figure 6. Concentration profile for the species i when it moves from a polar phase towards a non polar phase through a microporous hydrophilic flat membrane.

Liquid - Liquid Extractions 169

Referring to Figure 5, as for the hydrophobic membrane, at steady state the flux of the species i through the non polar film equals its flux through the membrane and its flux through the polar film:

J, = k,.~ ( c , .p- G . d = k J

(C,~ p - C,m p) = k,p (C, m p - C, p)

(11)

where: Cim p, concentration o f the species i at the p o l a r - membrane interface; k J , mass transfer coefficient in the hydrophilic membrane for the species i.

By considering the equilibrium expression for the liquid - liquid interface, the overall mass transfer coefficients can be related to the single mass transfer coefficients by:

+ 1/(ki.p mO

(12)

1/K.p = mi /kip + mi /ki p + 1/kinp

(13)

1/Kp = 1~kip + 1/ki p

In an hollow fiber configuration with the polar phase in the shell side and the non polar phase at the lumen side the interface is located at the inner diameter of the tubes and equations (12) and (13) become:

1/(Kp dO = if(kips do) + 1/(kimp d'lm) + 1/(kinp, mi dO

(14)

I/(Knp di) = mi/(kips do) + m./(ki p d'tm) + 1/(kinpt dO

(15)

170 Chapter 5 where:

d'tm, logarithmic mean of the hydrophilic membrane diameters. The equations reported until now for symmetric hydrophobic and hydrophilic membranes are valid also in the case of asymmetric membranes, when the membranes are hydrophobic or hydrophilic along all the thickness.

2.3. Partially wetted and hydrophobic-hydrophilic composite membranes Sometimes the membranes can be partially wetted by the liquid phase that should be blocked at the membrane interface and both liquids can coexist into the micropores of symmetric or asymmetric membranes, where the liquid-liquid equilibrium is established. Figure 7 shows the concentration profile for the transport of the species i from the non polar to the polar phase through a partially wetted asymmetric flat membrane. The resistances during the transport are those offered by the non polar film, the hydrophobic membrane, the hydrophilic membrane and the polar film.

Figure 7. Concentration profile for the transport of the species i from the non polar towards the polar phase through a partially wetted asymmetric flat membrane.

Liquid- Liquid Extractions 171 At steady state, the following equation is valid for the flux:

Ji : kinp (Ci rip- Cim np) = kim np (Cim np-Cie np)= ki p (Cie p -- Cim p) : kip (Cim p -- Ci p)

(16)

The overall mass transfer coefficients are calculated by:

1/Kp : I/kip + 1 / ( k J p mO + 1 / k J

+ I/(ki,,pmO

(17)

1/Knp = m~ /kip + 1/kimnp+ m~ / k J +

I/kinp

(18)

For hydrophobic - hydrophilic composite flat membranes the same equations are valid. As already stated in Chapter 4, while for partially wetted membranes (both asymmetric and symmetric), it is quite difficult to determine the location of the interface within the membrane pores, in hydrophobic - hydrophilic composite membranes the interface coincides with the hydrophobic-hydrophilic interface and it is easier to determine the membranes mass transfer coefficients.

For the hollow fiber configuration with the polar phase at the shell side and the non polar phase in the lumen side, the overall mass transfer coefficients are calculated by:

1/(Kp di,,t) = if(kips do) + l/(kim np mr dim) + 1 / ( k J d'lm) + 1/(ki~pt mr di)

(19)

1/(Knp dint) = mr/(kipsdo) + 1/(kim np dhn)+ mr/(ki,,, p d'tm) + 1/( ki,,ptdd

(20)

172 Chapter

5

where:

dmt, interfacial diameter. The hydrophobic - hydrophilic composite hollow fiber membrane section indicating the diameters present in equations (19) and (20) is reported below (Figure 8).

Hydrophilic membrane section .. _. _. _. . . . .

Polar phase

!!!i ::::::i Non polar phase

. . . .

~ x . , .

. . . .

, %,~,.

,\\,q Polar phase

. . . .

. . . . . . . .

. . . .

_... --~

d i

dint

.. w.

I I

I

Hydrophobic membrane section

I

d o

Figure 8. Section of the hydrophobic-hydrophiliccomposite hollow fiber membrane. The overall mass transfer coefficients for the different types of membranes described are summarized in Table 1 and 2.

Liquid- Liquid Extractions 173 Table 1. Expressions of the overall mass transfer coefficients for the different flat membranes Membrane Hydrophobic

1/Kp

1/Knp

1/kip + 1/(kim np mi) + 1/(kinp mi)

mi/kip + 1/kimnP+ 1/kinp

Hydrophilic

1/kip + 1/kimp + 1/(kinp mi)

mi/kip + mi/kim p+ 1/kinp

Partially wetted (symmetric and asymmetric) and hydrophilichydrophobic composite

1/kip+ 1/(kimnp mi) +l/kim p + 1/(kinp mi) mi/kip + 1/kimnp + mi/kim p+ 1/ kinp

Table 2. Expressions of the overall mass transfer coefficients for the different hollow fiber membranes. Operating conditions: polar phase at the shell side and non polar phase in the lumen Membrane Hydrophobic

1/(Kp do) = 1/(kips do) + 1/(kimno mi dim) 1/(Knpdo) = mi/(kips do) + + 1/(kinpt mi di) 1/(kimnp dim)+ 1/(kinpt di)

Hydrophilic

1/(Kp di) = 1/(kips do) + 1/(kimp d'lm) + 1/(kinpt mi di)

Partially wetted (symmetric and asymmetric) and hydrophilichydrophobic composite

1/(Kpdint)= 1/(kips do) + 1/(kimnp mi dim) 1/(Knpdint) = mi/(kipsdo) + + 1/(kimp d'lm) + 1/(kinpt mi di) 1/(kimnp dim)+ mi/(kim p d'lm) + 1/( kinptdi)

1/(Knpdi) - mi/(kips do) + mi/(kimp d'lm) + 1/(kinpt di)

,,,

As in gas-liquid operations, reactive liquids can be used as extractants also in liquid-liquid systems in order to increase the removal efficiency. The enhancement factor (E) is then introduced to takes into account the effect of the chemical reaction on the extraction. If the transfer of the species i occurs from a non polar phase towards a polar phase in which the species reacts, the overall mass transfer coefficient based on the non polar phase for a flat hydrophobic membrane can be calculated by:

i

••••••••••••••••••••••••••••!••••••il•••••••••••••

174 Chapter 5 1/Knp = m/(kipE)

!~i!i i i~ii i iiliii!~I~ii~!ii~!iIi!i iiii/iiii!i/!ili/iii!ii!iil/!iiill~I~I~IIIIIII/

+ l/kimnP+ l/kinp

(21)

Generally, depending on the value of the solute distribution coefficient, the solute might prefer one of the two phases. When the solute strongly prefer a phase (mi is >> 1 or 1

mi > 1

mi t9 t~

0.94

m

I

0.92 0

I 2

i

I 4

molal concentration of

i

I

I

6

8

C12Hz2Oll

Figure 5. Activity coefficient of water in sucrose solutions at 25~

After [ 11].

3. M a s s t r a n s f e r

According to an electrical analogy, mass transport for MD process can be conveniently described in terms of serial resistances upon the transfer between the bulks of two phases contacting the membrane (figure 6). The mass transfer coefficient K is defined as the inverse of the total resistance to the mass transport, expressed as combination of the mass transfer coefficients in the feed side (kf), in the membrane (kM) and in the distillate side (kd):

Membrane Distillation and Osmotic Distillation 197

K =

1

(12)

1/kz +l/k M +l/k d

Mass transfer boundary layers adjoining the membrane generally offer a negligible contribution to the overall mass transfer resistance, whereas diffusion across the polymeric membrane often represents the controlling step. The resistance to mass transfer on the distillate side can be omitted whenever MD operates with pure water as condensing fluid in direct contact with the membrane, or in VMD. The resistances within the membrane are associated to Knudsen, molecular and surface diffusion mechanisms, and viscous transport. A more detailed description of these mechanisms is proposed in the next paragraphs.

~'~

v,scous .~s,s.~.c~

f

BOUNDARY LAYERI RESISTANCE

BOUNDARY LAYER RESISTANCE

-'X

~,,,v

#

Figure 6. Serial and parallel arrangement of resistances to mass transport in MD.

3.1. Mass transfer: boundary layer resistances When solvent molecules are transferred through the membrane, the retained solute tends to accumulate at the membrane surface where its concentration gradually increases. Such a concentration gradient generates a diffusive counterflow that, under steady-state conditions, balances the net convective solute flow into the system: a concentration profile localized in the boundary layer adjacent to the membrane is therefore established (concentration

198 Chapter 6

polarization). In a thermally-driven membrane distillation process, the concentration polarization has generally a limited effect on the process performance [ 12]. Jc

._

Cb

D(dc/dx)

Cp=O

I_.., Figure 7. The development of a concentration profile into the boundary layer under steady-state conditions is known as concentration polarization phenomenon.

Referring to figure 7, and assuming that the solute is completely retained by the membrane, a mass balance across the feed side boundary layer yields to a relation between the molar flux J, the mass transfer coefficient kx (given by D/f, being D the diffusion coefficient and 8 the boundary layer thickness), and solute concentrations Cm and Cb at the membrane interface and in the bulk, respectively:

J=kxlnCm p

(13)

Cb

Concentration polarization phenomenon is usually quantified by a CPC coefficient, defined as: C P C = cm

Cb

(14)

Membrane Distillation and Osmotic Distillation 199

Literature provides several correlations (see review [13]), often derived by analogy with those evaluated for the heat transport, that are practical for determining the mass transfer coefficient. These empirical relationships are usually expressed in the form: S h = ct

Re p S c r

(15)

where: Sh, Sherwood number

Sh =

Re, Reynolds number Re

9

Sc, Schmidt number

kxdh

D

= p v dh

(dh: hydraulic diameter, D: diffusion coefficient)

(p: fluid density, v: fluid velocity, g: fluid viscosity)

Sc = pD

A brief list of mass transfer correlations for Newtonian fluids is given in table 2. The equations for the calculation of the shell side mass transfer coefficient have been already reported in Chapter 4.

Table 2. Predictive equations for mass transfer coefficients for shell and tube configuration Equation (tube side flow)

Comments

Reference

Sh=1.62 (d2v/(LD)) ~

L6v6que equation

[ 14]

Sh = 0.023 Re~

Chilton-Colburn, Re> 105, Sc>0.5

[ 14]

Chilton-Colbum, 104l) and moleculewall collisions predominate over molecule-molecule collisions. In many practical cases, t is comparable to the typical pore size of MD membranes. Dusty Gas Model (DGM) is frequently used for describing gaseous molar fluxes through porous media; the most general form (again neglecting surface diffusion) is expressed as [31 ]"

j D

~_,pjjD_p,jD.

O ke t-Z.,a J--;~;

-1_)-0 "-'~e

1 = -~R V pTi

(18.a)

2

v o~r Pi J, = VP

(18.b)

D ke = 2er 1_[8RT

(18.c)

8RTr ct

3r ~ zM i o

Doe

E

o

rPD~

(18.d)

204 Chapter 6 where jD is the diffusive flux, jv the viscous flux, D k the Knudsen diffusion coefficient, D Othe ordinary diffusion coefficient, p the partial pressure, R the gas constant (8.314 J mol 1 K "1 ), T the temperature, P the total pressure, ~ the gas viscosity, r the membrane radius, e the membrane porosity and x the membrane tortuosity. Underscript e indicates the "effective" diffusion coefficient, calculated by taking into account the structural parameters of the membrane as shown in equations (18.c) and (18.d). Although DGM was derived for an isothermal systems, it is successfully applied in MD working under relatively small thermal gradients by assuming an average value of temperature across the membrane. Simplifications related to particular MD configurations are summarised in table 4.

Table 4. Simplified equations for the mass transfer in MD Configuration

Assumption

Vacuum membrane

Mean pore size Plw2 . . . .

STRIPPING SOLUTION

i i :

"iiiii:: i-i ......-........ 9 .....-........

:-i

i!!i!i!i!iii ii! -.-.-.-.-.-.... 9 .-.-.-.-.-.... -..-.-....-.-. -..-.-.-..-... -..-.-.-..-.-.

Cw2

. : . : . :. .: .: . : . : .

i : : : : : : : .: i : i : : :

Clwl . . . . . . . . . . . . . . . . -.-.-.-....-.

i!iiiiiiiiii: iii . . . . . . . . . . . . . . .

Cwl . . . . . . . . . . . . . . . ..-.-.-..-.-.-. .

.

9

.

.

.

.

..

,i:i: w ::?: .:.:. m - , : . : 9:.:. U J . : . : , iii.: ~ 12:1', . . . . . . . . . . . . . . . . .. . . . . . . -.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........-.-.-

Figure 22. Concentration profile in Osmotic Distillation.

OD is not a purely mass transfer operation: transport involves an evaporation at the feed side and a condensation at the stripping side. A temperature difference at the membrane interfaces is thus created, even if the bulk temperatures of the two liquids are equal. Mengual et a1.(1993) [80] estimated the temperature difference in their aqueous system to be lower than 1~ which would lead to a negligible decrease of the vapour flux.

Membrane Distillation and Osmotic Distillation 239

Assuming a simplified approach, the transmembrane flux can be expressed in terms of membrane permeability Km, partial pressures P'w at feed (1) and stripping (2) fluid-membrane interfaces, and log mean pressure of air entrapped into pores Poir "

j ._ Km

P'wl_-P'w2

(52)

Pair

Water vapour pressure is related to activity by eq. (2). Referring to a series expansion cut at the first order term, and assuming that the temperature difference through the membrane is small, the following relationship can be derived [81 ]"

J = -Pa~,. gm{P~ (T)" [a'~ - o'~2 ]- a~ (T)" IdP~ 1 [ . - ~ . J f (r~-~()}

(53)

where p0 is the vapour pressure of pure liquid, aw is the water activity, and T is the average temperature between the two membrane interfaces. Film-theory model can be used to describe the mass transport through boundary layers: t

t

j = kxPln x ~ kx p a w - a._.......~ x

(54)

~w~

assuming that water activity coefficients ~w are constant in the layers' x is the solute mole fraction, ~ its logarithmic mean value, kx the mass transfer coefficient, p the solution density. Apex refers to value at the membrane interface. Some useful empirical correlations for the calculus of kx are reported in table 11.

240 Chapter 6 Table 11. Correlations for mass transfer coefficient in OD Correlation

ot

[3

k x = co r

-

-

7 1.09+0.17

kx(10 5 m/s) 54+78.10 -3

S h = ct R e # S c r

1.86

0.33

0.33

kf=0.17;0.9;0.37

S h = ct R e ~ S c r

1.62 (shell)

0.33

0.33

1.86 (tube)

Comment (o=0+350rpm aqueous NaC1 solution 0.5+5M For NH3, SO2, HzS: 1+20.10 .3 M Shell: watersucrose 0+70%wt

Reference [80]

[821

[83]

Tube: waterCaC12: 26+40 %wt

Temperature and activity gradients can act in a synergistic way, or can operate in an antagonistic way to each other. Heat transfer phenomena are described as in MD operations. The salts chosen as osmotic pressure agents are in general NaC1 (because of its low cost), MgC12, CaC12 and MgSO4 [84]. In osmotic evaporation carried out at room temperature, transmembrane fluxes generally range between 0.2 and 1 L/mZh [85]. Table 12 offers a short list of typical operative conditions in OD for selected systems.

o . ....,

o o ....,

o m

.....,

d [-

s

o

o

0~

o tr

d~ ~176

o

r~

o~ s

o

e

9.

.~

N.~

8"~" ~o

,~,.~

o

~--.=

e'q

e~

0

t~~ ",~

~r3 e~

O

~

O r

oo

O

~

c;

o

=

Membrane Distillation and Osmotic Distillation 241

~

~--

r o,..~

0

0

r-i

a.

o

!

242 C h a p t e r 6

0 oo

r o

n~ o9

~

~

~

0

0

r-i

t~ 0

t~~ o~.,~

o

0

,~k c~

uaZ

~

0

~c~l

~~

.~.~

oo

~

0 0

o o

~ ~.~.~

~Z

0

r ,.Q

0

o

~

~

~

--

r

0'~

~

~ OD

9

o O

C'4

~

tt% ("4

~

t"--

Membrane Distillation and Osmotic Distillation 243

r....ii @',1 i..iii

t,,i

("4

"u o

C',l

~

::L "~

~ ~Z ~

=~ o

"7 ,5

0

9

~

o ~

~D

L~

t",,I

ri-i

~,5~ru

iii!

~s ~

Oeq

0", i....,.ii

e~

& 0

..

r

~

~. ~ -~ ~

0

9,.,

~

~D

244 Chapter 6 I0. Coupling thermal and osmotic distillation

In order to describe the action of a thermal gradient and a osmotic gradient simultaneously imposed across a microporous hydrophobic membrane, let express the transmembrane flux as in equation (19), and the dependence of the water vapour pressure on temperature and solute concentration by equation (3). In addition, the Clausius-Clapeyron's equation established an exponential dependence between the vapour pressure of a pure component and the absolute temperature of the form:

p~

exp(- R-~-f)

(55)

Let T1 and T2 be the temperatures at the corresponding liquid-vapour interfaces at sides 1 and 2, AT the transmembrane temperature difference, and T the mean temperature. Therefore: T1 = T +AT/2 and T2 = T-AT/2. Analogously, let Aa and 6 the transmembrane activity difference and the mean activity, respectively. Under the usual operative conditions of MD and OD, it can be assumed that:

AT - H C O ;

(13.a)

H C O 3 + O H - < k2,,:k2,2 >CO 2- + H2 0

(13.b)

2 H 2 0 ~ k3,~;k3,2 >H30+ + O H -

(13.c)

CO 2 + 2 H 2 0 ~ k4,~;k4,2 > H C 0 3 + H30+

(13.d)

The overall reaction is: CO 2 + CO 3- + HE0 ~ 2HCO~

(13.e)

354 Chapter 10 Reactions (13.a) - practically irreversible for pH> 10 - and (13.d) - important only at pH