Appunti Principles of Advanced Separations

Principles of advanced separations

Membrane and Adsorption separations jjojjojjojjojjojjojjo

Author: Emanuele Antognazza

Contents

I Membrane Separations 5

1 Membrane introduction 6

1.1 Industrial example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Materials 7

3 Membrane morphology 10

4 Membrane modules 11

5 General material balance 13

6 Transport in membranes 14

7 Transport through porous membranes 14

7.1 Bulk Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7.1.1 Membrane resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7.1.2 Cake resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.2.1 Liquid phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.2.2 Gas phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8 Transport through dense membranes 21

8.1 Liquid phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

8.2 Gas phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8.3 Separation factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

9 External mass-transfer resistances 27

10 Module flow patterns 29

10.1 Cocurrent configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

10.2 Full mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

10.3 Crossflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

10.4 Effect of the membrane flow pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

10.5 Cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

10.5.1 Two-stage cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

11 Applications 39

11.1 Gas Permeation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

11.2 Dialysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

11.3 Reverse osmosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

11.3.1 Concentration polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

11.4 Pervaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

11.4.1 Separation factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

11.4.2 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

11.4.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

12 Filtrations 50

12.1 Ultrafiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

12.2 Nanofiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

13 Membrane reactors 52

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14 Final summary 53

II Adsorption Separations 54

15 Adsorption introduction 55

15.1 Industrial example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

15.2 Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

16 Solid Adsorbents 57

17 Adsorption equilibria - empirical models 60

17.1 Langmuir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

17.2 Freundlich model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

17.3 Toth model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

17.4 BET model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

17.5 Capillary condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

18 Thermodynamics of adsorption 66

19 Adsorption equilibria - modelling 71

19.1 Direct method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

19.2 Indirect method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

20 Adsorption kinetics 77

20.1 Particle dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

20.1.1 Microparticle - material balance . . . . . . . . . . . . . . . . . . . . . . . . . 78

20.1.2 Macroparticle - material balance . . . . . . . . . . . . . . . . . . . . . . . . . 79

20.1.3 Diffusion coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

20.1.4 Model simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

20.2 Fixed-bed dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

20.2.1 Parameters evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

20.3 Breakthrough curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

20.3.1 Equilibrium model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

20.3.2 Method of characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

20.3.3 Example - regeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

20.3.4 Example - adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

20.3.5 Second order aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

21 Applications 111

21.1 Pressure-swing cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

21.2 Equilibrium model of PSA units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

21.2.1 Purge step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

21.2.2 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

21.2.3 Pressurization step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

21.2.4 Blowdown step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

21.3 Continuous operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

21.3.1 Real countercurrent operation through the solid motion - modelling . . . . . 127

21.3.2 Simulated moving bed system . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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Part I

Membrane Separations

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1 Membrane introduction

In a membrane-separation process, a feed consisting of a mixture of two or more components is partially separated by means of a selectively permeable barrier (the membrane) through which some species move faster than others.

The most general membrane process is shown in Figure 1, where the feed mixture is separated into a retentate (that part of the feed enriched in species that do not pass through the membrane) and a permeate (that part that does pass through the membrane).

Figure 1: General membrane process

The optional sweep is an inert liquid or gas used to facilitate the removal of the permeate, especially if the permeated flow is very small with respect to the retentate one. In some cases, when we have a large amount of permeated species, this component is not necessary.

There is a large variety of barriers that can induce a selection of our species. For example we can have a thin, nonporous, polymeric film (most used one), but may also porous polymer, ceramic, or metal materials, or even a liquid, gel, or gas.

In membrane separations: the two products are usually miscible, the separating agent is a semipermeable barrier, and a sharp separation is often difficult to achieve.

1.1 Industrial example

A large-scale membrane process is the manufacture of benzene from toluene, which requires the separation of hydrogen from methane. In particular, we are focused on the exploitation of toluene for manufacturing benzene, xylenes, and a number of other chemicals, including polyesters.

Toluene can be catalytically disproportionated to benzene and xylenes in an adiabatic reactor °C with the feed entering at T > 510 at a pressure above 34.5 bar.

→ The main reaction is: 2C H C H + C H (isomers) 7 8 6 6 8 10

Figure 2: Reactor section of process to disproportionate toluene into benzene and xylene isomers. (a) Without a vapor-separation step. (b) With a membrane-separation step.

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To suppress coke formation, which fouls the catalyst, the reactor feed must contain a large fraction of hydrogen at a partial pressure of at least 15 bar.

Unfortunately, the hydrogen takes part in a side reaction, the hydrodealkylation of toluene to → benzene and methane: C H +H C H +CH . The reactor outlet is composed of: C H , C H , 7 8 2 6 6 4 8 10 7 8 C H , C H , CH , H (ordered in an ascending relative volatility). 6 6 2 6 4 2

In order to separate the products we have to introduce a flash unit, which allows us to obtain in the vapour phase the most volatile species (C H , CH , H ) and in the liquid one the others 2 6 4 2 (there is a net threshold in the relative volatility scale).

The vapour stream has to be recycled at the reactor because of its H content but a fraction of it has also to be purged in order to avoid 2 a continuous accumulation and production of CH and C H . Notice that a H makeup is always 4 2 6 2 necessary to guarantee the desired inlet concentration at the reactor.

Without using any type of gas purification system (Figure 2(a)) we’ll end up with a huge waste of H (increasing consequently the make up flowrate). It’s important also to underline that even 2 the hydrogen make up is impure (H : 80%, CH : 15%, C H : 5%). 2 4 2 6

To reduce H losses we can implement a gas purification system composed of membrane modules. 2 In particular, the permeation membranes separate the flash vapor (stream S11) into an H2-enriched permeate (S14, the recycled hydrogen), and a methane-enriched retentate (S12, the purge).

Observing Table 1, we notice that thanks to this configuration we can reach:

• Recovery of hydrogen in the permeate: 90%;
• Recovery of methane in retentate: 49%;
• Loss of hydrogen: 10%

There is no need to introduce a sweep since the permeated flowrate is large enough. Concerning the membrane, it’s an aromatic polyamide polymer, 0.3 µmm thick, with the nonporous layer in contact with the feed, and a much-thicker porous support backing to give the membrane strength to withstand the pressure differential of almost 28 bar (recompression is required after the membrane separation).

The effectively permselective layer has to be very thin in order to provide a suitable rate of transport whereas the porous support has the only a mechanical functionality. Overall we have a so called ”composite membrane”.

Table 1: Material Balance for Toluene Disproportionation Plant; Flow Rates in lbmol/h

In general, membrane separators are quite compact, less capital intensive, easier to operate and maintain.

On the other hand, multiple parallel units are usually required due to their modular construction (it’s much cheaper to buy multiple standard modules rather than ask for a single ad hoc module).

In this context, membrane material and corresponding packaging are crucial.

2 Materials

°C) Non-polymeric membranes: inorganic materials are used for high temperatures (> 200 and chemically active mixtures

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• Popular materials: microporous ceramics, metals and carbon
• Examples: microporous glass tubes, silica hollow fibers (3-5 Å pores), sintered metals, pyrolyzed carbon

Polymeric membranes: initially natural and later on synthetic polymers

Synthetic polymers are prepared by different polymerization mechanisms (condensation, free-radical or catalyzed chain addition), resulting in different chain architectures (long linear chains (thermoplastics polymers), branched chains, and highly or partly crosslinked structures (thermosetting polymers)

Classification based on the arrangement of the macromolecules:

• Amorphous (usually transparent, lacking crystalline structure), characterized by a full disordered structure;
• Semi-crystalline (usually opaque, at least partly crystalline), characterized by both crystalline and amorphous regions. Notice that it’s impossible to reach a fully crystalline structure because of the intrinsic polymeric structure (huge macromolecules)

Figure 3: Phase states of polymers

Let’s have a look at Figure 3 and consider a cooling process. Firstly we start observing the crystalline solid trend: we see that the decrease of temperature leads to a decrease also of the volume of the material. Having reached the melting temperature of the material we observe a steep decrease of volume (sort of jump) that leads to a significant shrinking of the material itself (we have a clear phase change at T = T ). Notice also that the volume reduction continues even in the solid m phase.

In the case of a polymer, having crossed T what we see is a solidification, but not necessary a m crystallization (polymers crystallize only if they are characterized by a certain regularity and only in specific regions we can have crystallization). We practically observe the formation of regions of crystalline materials (spherulites) in a disordered/amorphous matrix.

In the particular case of amorphous polymers we don’t have neither the formation of this spherulites and along the so called ”rubbery region” we still have the Volume/Temperature dependence of the liquid phase (so we still have mobility of chains).

But having reached T , the viscosity g of the material is so large that molecules do not move any longer (we block/freeze the mobility of chains), realizing a ”Glassy transition”. From now on the Volume/Temperature dependence is the same of a crystalline solid.

Concerning the free volumes (spaces/cavities among the polymer chains through which molecules can diffuse), passing from T to T we have a progressively decrease of their size, whereas below T m g g they are almost null (3% of the total volume).

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In the case of a semi-crystalline polymer, we observe the formation of spherulites after having crossed T . Even in this case the morphology of the material (distribution of amorphous region m + crystalline region) remains frozen after T , in particular the crystalline portion remains unvaried g whereas the amorphous portion is failed of its mobility.

The extent of the crystallinity is higher the lower is the distance with respect to the crystalline solid behaviour. Slowing down the cooling process allows us to guarantee the correct formation of spherulites, otherwise also polymers that in principle could be able to crystallize will not (there is a time dependence).

Summarizing we can say that T is linked with the phase transition of the material, whereas T m g is related to the change of the mobility of chains.

Concerning the membrane performance, the crystalline portion allows us to increase the mechanical strength of the overall structure but decreases also the permeability of the same (a crystalline material is basically impermeable). Moreover, most polymers are semi-crystalline, with crystallinity from 5 to 90%.

In Table 2 we can observe the most common polymers used in membrane units.

Table 2: Common polymers used in membranes

Some concise information about them:

• Cellulose triacetate is highly crystalline and hydrophobic. Its degree of polymerization DP (number of units forming a single chain) is equal to 300 (A = CH CO). Notice that because c 3 of its high crystallinity, we don’t care about T since it’s not so relevant. g

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• −Polyisoprene has a very low glass-transition temperature, DP = 3000 40000. To increase strength, elasticity, and stability of this material, it is vulcanized with sulfur, a process that introduces cross-links. This will result in a significant decrease of the mobility of the chains
• Aromatic polyamides are high-melting, crystalline polymers. The polyamide structure shown in Table 2 is that of Kevlar, a trade name of DuPont.
• Polycarbonates are mainly amorphous. Since they are thermoplastic, they can be extruded into various shapes, including films and sheets.
• Polyimides are tough, amorphous polymers with high resistance to heat and excellent wear resistance. They can be fabricated into a wide variety of forms, including fibers, sheets, and films.
• Polystyrene is a linear, amorphous, highly pure polymer of about 1000 units of the structure shown in Table 2. It can be annealed (heated and then cooled slowly) to convert it to a °C crystalline polymer with a melting temperature > 240
• Polysulfones are synthetic polymers whose structure contains the SO group, which gives the 2 polymers high strength. Polysulfones are easily spun into hollow fibers.
• Polytetrafluoroethylene (Teflon) is a straight-chain, highly crystalline polymer with DP = 100000, giving it considerable strength. It possesses exceptional thermal stability and can be formed into films and tubing.

Important aspect to underline: when we select a certain material we have also to take into account the affinity of it with respect to the species in our system (it’s not only a matter of free volumes).

Summarizing what we saw concerning the polymer phases (0.01 poise = 1 mP a/s):

• Rubbery – under cooling, the macromolecules undergo slow translational and conformational 15 reorganization at increasing viscosity until T = T (up to 10 poise) aimed to fit into a crystal g lattice compatible with the molecular structure (not too irregular)
• 15 Glassy – if crystallization does not occur before 10 poise or the molecular structure is too irregular, a glass is formed; the temperature at which the rubbery-to-glass transition occurs is called glass transition temperature, Tg
• Semi-crystalline – if the polymer structure is not too irregular, a partial crystallization is taking place below the melting temperature, T being the rest of the material amorphous m

3 Membrane morphology

Polymer membranes can be characterized as dense or microporous.

For dense, amorphous membranes, pores of microscopic dimensions may be present, but they are generally less than a few Å in diameter, such that most