Membrane

Literature survey

2. LITERATURE REVIEWS

2.1 General aspects of membrane.

A membrane is a permeable or semi-permeable phases which is essentially a barrier between the feed stream for separation and one product stream. The membrane can be solid, liquid and gas and it controls the relative rates of transport of various species through itself producing one product with minimal concentration of certain components and second product concentrated in these components. [K. Scott and R. Hughes, Industrial membrane separation technology, Blackie academic & professional, Glasgow, First edition, 1996.]

Nowadays, membranes are used for different applications in separation processes of one or more products of interest. Also, they are used on a large scale in water treatment, to clean industrial effluents and recover valuable constituents. Furthermore, membranes are employed to concentrate, purify or fractionate macromolecular mixtures in the food and drug industries and to separate gases and vapours. They are also main components in energy conversion systems and drug delivery devices and in artificial organs. The membranes used in different applications differ widely in their structure, function and the way they are operated. [R. W. Baker.” Membrane technology and applications”, J. Wiley & Sons, Chichester, Second edition, England, 2004]

Their intrinsic characteristics of efficiency, operational simplicity and flexibility, relatively high selectivity and permeability for the transport of specific components have been established in a large variety of applications and operations. In addition, their low energy requirements, good stability under a wide spectrum of operating conditions, environment compatibility, easy control and scale–up have been confirmed. For instance, molecular separation, fractionation, purification and emulsifications in liquid and gas phases in wide spectrum of operating parameters (i.e. temperature and pressure) have been carried out.

2.2 Classification of the membrane

The membranes can be classified according to their nature in biological and artificial membranes [Hwang et al, 1975]. Artificial membranes are also classified on surface chemical, structure and production method. On the other hand, structure membranes can be divided according to density, porosity and asymmetry as is given in 2.1.

* Biological membranes

Biological membranes are sheet-like structures composed mainly of lipids and proteins. All biological membranes have a similar general structure. Membrane lipids are organized in a bilayer (two sheets of lipids making up a single membrane) with a thick of approximately 60 to 100 Å. On the other hand, the proteins are scattered throughout the bilayer and perform most membrane functions. Membranes are two-dimensional fluids: both lipids and proteins are constantly in motion. [B. Alberts, A. Johnson,J. Lewis Molecular Biology of the cell (4th ed.). New York: Garland Science. (2002)].

· Artificial membranes

Artificial membrane also known as synthetic membrane; it can be made from organic or inorganic materials including solids such as metal or ceramic, homogeneous films (polymers), heterogeneous solids (polymeric mixes, mixed glasses) and liquids.

Pressure and concentration gradients are the main driving forces of a membrane process in industry. Synthetic membranes utilized in separation processes can have different geometry and flow configurations. The most known synthetic membranes separation processes include water purification, reverse osmosis, dehydrogenation of natural gas and removal of cell particles by microfiltration and ultra filtration [Osada, T. Nakagawa, Membrane Science and Technology, Marcel Dekker, New York, Inc, 1992]

Artificial membranes can be classified according to their surface chemistry, structure (morphology) and production method.

A. Surface chemistry

Synthetic membrane chemistry usually refers to the chemical nature and composition of its surface in contact with a separation process stream. The chemical nature of membrane's surface can be quite different from its bulk composition. This difference can be due to membrane fabrication or by an intended surface post-formation modification.

Membrane surface chemistry creates very important properties such as hydrophilicity or hydrophobicity (relates to surface free energy), presence of ionic charges, membrane chemical or thermal resistance, binding affinity for particles in a solution and biocompatibility (in case of bioseparations) [Marcel Mulder, Basic Principles of Membrane Technology, Kluwer Academic Publishers, second edition Netherlands, 1996].

B. Structure (morphology):

Synthetic membranes can be also classified on their structure (morphology). Three such types of synthetic membranes are commonly used in separation industry: dense membranes, porous membranes and asymmetric membranes.

Dense membrane is usually a thin layer of dense material utilized in the separation processes of small molecules (usually in gas or liquid phase). Dense membranes can be synthesized as amorphous or heterogeneous structures. The membrane structure of a dense membrane can be in a rubbery or a glassy state at a given temperature depending on its glass transition temperature. They are widely used in industry for gas separations and reverse osmosis applications. [Y. Osada, T. Nakagawa, Membrane Science and Technology, Marcel Dekker, New York, Inc, 1992]

Porous membranes are used on separation of larger molecules such as solid colloidal particles, large bio-molecules (proteins, DNA, RNA) and cells from the filtering media. The structure of porous membrane is related to the characteristics of the interacting polymer and solvent, components concentration, molecular weight, temperature and storing time in solution. Porous membranes can be use in the microfiltration, ultra filtration and dialysis applications. [Osada, T. Nakagawa, Membrane Science and Technology, Marcel Dekker, New York, Inc, 1992 .]

Asymmetric membranes are permeable membranes sometimes provide support for the thin of dense membrane layers. The asymmetric membranes are usually produced by a lamination of dense and porous membranes.

C. Membrane separation processes

This classification is based on separation mechanisms and size of the separated particles. The membrane can be used in various processes:

· Microfiltration and ultra filtration) is widely used in food and beverage processing, biotechnological applications and pharmaceutical industry (antibiotic production, protein purification), water purification and waste water treatment, microelectronics industry and others.

· Nanofiltration and reverse osmosis membranes are mainly used for water purification purposes.

· Dense membranes are utilized for gas separations (removal of CO2 from natural gas, separating N2 from air, organic vapor removal from air or nitrogen stream) and sometimes in membrane distillation. In Fig. 2.2. is shown the membrane application according to pore diameter [R. W. Baker.” Membrane technology and applications”, J. Wiley & Sons, Chichester, Second edition, England, 2004]

2.3 General characteristics of the inorganic membranes.

Below are given the stability properties of the membrane according to their chemical composition.

* Chemical stability:

Inorganic membranes have a chemical stability for different ranges of pH and organic solvents. According to this property it may be possible to use strong acid or alkali treatments for cleaning the membrane if it is necessary. Its stability is associated with the strength of its crystal structure, the chemical bonding and the high field strengths from charged cations in ceramics [H. P. Hsieh, Catal Rev.-Sci. Eng. 33, 1991, 1.]

· Thermal stability:

A membrane with high thermal stability can be used in gas separation at high temperature. This property is associated with the stable bond formed when the valence electrons of the metal part are retained by the non-metal atoms. The membranes can be used at high temperature to separate the products from the reactants and/or can act as a catalyst through a chemical reaction [ B. Van Hassel, A. Kawada, T. Sakai, N. Yokokawa, H. Dokiya and H.J.M. Bouwmeester, Solid state Ionics, 66, 1993, 295.; M. Mulder, Basic principles of membrane technology, Netherdands, kluwer, Academic publishers. 1996.]

* Mechanical stability:

The mechanical stability of the inorganic membrane is important for constructing the membrane reactor and is usually high compared to organic membranes. It is particularly relevant for separation process carried out at high pressures. [. Mulder, Basic principles of membrane technology, Netherdands, kluwer, Academic publishers. 1996.]

2.4 Membrane shapes

The membranes inorganic devices (modules) can be fabricated three different forms: flat plates, spiral wounds and hollow fibres.

Flat plates are usually fabricated as circular thin flat membrane surfaces to be used in dead-end geometry modules. [Osada, Y., Nakagawa, T., Membrane Science and Technology, New York: Marcel Dekker, Inc, 1992.].

Spiral wounds are constructed from similar flat membranes but in a form of a “pocket” containing two membrane sheets separated by a highly porous support plate. [Osada, Y., Nakagawa, T., Membrane Science and Technology, New York: Marcel Dekker, Inc, 1992.].

Hollow fibre modules consist of an assembly of self-supporting fibres with a dense skin separation layers and more open matrix helping to withstand pressure gradients and maintain structural integrity. The main advantage of hollow fibre modules is very large surface area within an enclosed volume, increasing the efficiency of the separation process. [Osada, Y., Nakagawa, T., Membrane Science and Technology, New York: Marcel Dekker, Inc, 1992.].

2.5 Candidate materials for oxygen separate membrane technology.

In last decades mixed ionic and electronic conducting (MIEC) membranes have attracted attention due to their ability to separate oxygen from ambient air and possible application in industry. Pure oxygen is used in various industrial processes such as: partial oxidation of methane to syngas (POM) [S.M. Murphy, D. A. Slade, K.J. Nordheden, S.M. Stagg-Williams, J. Membr. Sci. 277,(1-2) 2006, 94; W. Jin, S. Li, P. Huang, N. Xu, J. Shi and Y. S. Lin, J. Membr. Sci, 166, 2000, 1], oxidative coupling of methane (OCM) to form ethylene and ethane [C. Yang, N. Xu, J. Shi, Ind Eng. Chem. Res. 37, 1998, 2601; J.T. Ritchie, J.T. Richardson and D. Luss, AIChe journal, 47, 9, 2001, 2092]; selective oxidation of hydrocarbons [. Kim, Y. L. Yang, A. J. Jacobson, B. Abeles, Solid State Ionics, 106, 1998, 189.]; waste reduction and recovery [N. Miura, Y. Okamoto, J. Mamaki, K. Morinag, N. Yamazoe, Solid state Ionics 79 (1995) 195]. There are also medical applications and oxygen generator [D. Kang, S. Srinivasan, R. Rhorogood and E.Foster, US Patent 5 516359; 1996; P.N. Dyer, R. E. Richards, S. L. Russek, and D. M. Taylor, “Ion transport membrane technology for oxygen separation and syngas production,” Solid State Ionics 134,(2000) 21; W. Jin, S. Li, P. Huang, N. Xu J. Shi and Y. S. Lin, J. Membr. Sci. 166, 2000, 13]

The MIEC ceramic membranes, perovskite-type (ABO3) exhibit extraordinary properties, which makes them very attractive for industrial application. These properties are mentioned below: [W. Yang, H. Wang, X. Zhu, and L. Lin, “Development and application of oxygen permeable membrane in selective oxidation of light alkanes”, Topics in Catalysis 35, 1–2, 2005, 155-167)

1. High oxygen permeability under the operation conditions

2. The oxygen permeation through the membrane do not decreases with time

3. High stability in long-term operation under strongly reducing atmosphere such as mixture of carbon monoxide and hydrogen at elevated temperatures (above 700°C).

4. High mechanical strength for constructing the membrane reactor.

5. The material has low cost for large scale industrial applications.

2.6 A special perovskite (ABO3)

The perovskite mineral as the most abundant solid phase in the Earth's lower mantel (70-80 %), which is at 670 to 2900 km depth. This mineral was discovered in 1839 at the Ural Mountains by the geologist Gustav Rose, who named it after the famous Russian mineralogist Lev Aleksevich Perovski.

The perovskite is one of the most commonly occurring and important structure in materials science. Physical properties of interest among perovskite include superconductivity, colossal magneto resistance, ionic conductivity and a multitude of dielectric properties [J B Goodenough, “Electronic and ionic transport properties and other physical aspects of perovskites” Rep. Prog. Phys. 2004, 67, 1915-1993]. Many of these properties of perovskite depend crucially on the details of different types of distortions which can occur from the ideal structure. These include tilting of the octahedra, displacements of the cations out of the centers of their coordination polyhedral and distortions of the octahedra driven by electronic factors [J B Goodenough, “Electronic and ionic transport properties and other physical aspects of perovskites” Rep. Prog. Phys. 2004, 67, 1915-1993, E. J. BARAN, “Structural chemistry and physicochemical properties of perovskite-like materials”, Catalysis Today, 8 (1990) 133-151, A.S. Bhalla, R. Guo, R. Roy, The perovskite structure –a review of its role in ceramic science and technology, Mat Res Innovat (2000) 4:3–26]EVI. .

The most promising and extensively studied membranes are formed from the perovskite-type families of metal oxides (XIIA2+VIIB4+X2-3). The general chemical formula for perovskite compounds is ABX3, where 'A' and 'B' are two cations of very different sizes and X is an anion that bonds to both cations. The 'A' atoms are larger than the 'B' atoms. The ideal cubic-symmetry structure has the B cation in 6-fold coordination, surrounded by octahedron of anions (X) and the A cation in 12-fold cub octahedral coordination. The A cation is generally an alkali earth metal or a transition metal. The B cation is a transition metal or rare earth metal but can also be found in the family (Al, Ga, Pb, Bi, etc). The relative ion size requirements for stability of the cubic structure are quite stringent, so slight buckling and distortion can produce several lower-symmetry distorted versions, in which the coordination numbers of A cation or B cation or both are reduced. [BARAN, “Structural chemistry and physicochemical properties of perovskite-like materials”, Catalysis Today, 8 (1990) 133-151]

Goldschmidt introduced a so called tolerance factor [J B Goodenough, “Electronic and ionic transport properties and other physical aspects of perovskites” Rep. Prog. Phys. 2004, 67, 1915-1993] to determine how distorted is the cubic structure of perovskite type ABO3. This term is defined as:

(2.1)

Where, , and are the ionic radii of the A-site cation, B-site cation and oxygen anion respectively. When indicates that the structure is cubic and signifies that the ideal cubic structure is distorted to a lower symmetry (e.g. tetragonal, orthorhombic, rhombohedral etc.)

A perovskite with the ideal structure is calcium titanium oxide mineral (CaTiO3) which is shown below in 2.1. Where the red spheres are oxygen atoms, the blue spheres are B-atoms (a smaller metal cation, such as Ti4+), and the green spheres are the A-atoms (a larger metal cation, such as Ca2+). The perfect perovskite structure that is without crystal defects does not exhibit the useful electrical, optical, magnetic and catalytic properties that are being applied in a wide range of technologies [A.S. Bhalla, R. Guo, R. Roy, The perovskite structure –a review of its role in ceramic science and technology, Mat Res Innovat (2000) 4:3–26; BARAN, “Structural chemistry and physicochemical properties of perovskite-like materials”, Catalysis Today, 8 (1990) 133-151].EVI

Clearly, the stability of the perovskite structure depends on the ideal stoichiometry, obtained from the substitution with alionvalent cations on the A or B site or from redox processes associated with the presence of transition metal atoms which can adopt different formal oxidation states. Oxygen vacancies are free to move among energetically equivalent crystallographic sites.

2.6.1 Unit cell.

The crystal structure of a material or the arrangement of atoms within a given type of structure can be described in terms of its unit cell. The unit cell is a tiny box containing one or more motifs, a spatial arrangement of atoms. The unit cells stacked in three-dimensional space describes the bulk arrangement of atoms of the crystal. The crystal structure has a three dimensional shape. The unit cell is given by its lattice parameters, the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions (xi, yi and zi) measured from a lattice point.

2.6.2 Defect theory

Generally almost all inorganic compounds have defects in their crystal structure, which is associated with the reduction in the Gibbs free energy for that compound. This means that the entropy increases to achieve structure stability. [P. Perrot, ”A to Z of Thermodynamics”. Oxford University Press (1998), 336”.; W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, John Wiley & Sons, Toronto, 1976 and A.R. West, Solid State Chemistry and Its Applications, John Wiley & Sons, Chichester, 1984].

The Gibbs free energy is defined as:

(2.2)

Where, is the enthalpy (Joule), is the temperature (Kelvin) and is the entropy (Joule per Kelvin)

Defects in the crystal structure would cause considerable increase in entropy because many possible crystal positions can be occupied by defects. At higher temperatures, a higher defects concentration exhibiting a higher value of entropy in the crystal structure.

Defects are generally classified as electronic defects and structural defects.

Electronic defects are related to the intrinsic ionization or excitation of electrons from valence to conduction bands or their formation to fulfil the electric neutrality criteria [W.D. Kingery, H.K. Bowen, D.R. Uhlmann, “Introduction to ceramic”, John Wiley & Sons, Toronto, 1976].

Crystalline solids have a very regular atomic structure. That is, the local positions of the atoms with respect to each other are repeated at the atomic scale. However, most crystalline materials are not perfect. In other words, the regular pattern of atomic arrangement is interrupted by crystal or structural defects. For example, when one atom substitutes for one of the principal atomic components within the crystal structure, may cause alteration in the electrical and thermal properties of the material.

There are three basic classes of crystal defects: Point defects, line defects and planar defects.

* Point defects are places where an atom is missing or irregularly placed in the lattice structure. Point defects include lattice vacancies, self-interstitial atoms, substitution impurity atoms and interstitial impurity atoms.

Lattice vacancies are empty spaces where an atom should be, but is missing. They are common, especially at high temperatures when atoms are frequently and randomly change their positions leaving behind empty lattice sites. In most cases diffusion (mass transport by atomic motion) can only occur because of vacancies (see Fig. 2.7), which can generate two type of defects: 1) Frenkel defect is produced when an atom or ion leaves its place in the lattice, creating a vacancy, and becomes an interstitial by lodging in a nearby location not usually occupied by an atom. 2) Schottky defect is formed when oppositely charged ions leave their lattice sites, creating vacancies. These vacancies are formed in stoichiometric units, to maintain an overall neutral charge in the ionic solid. The vacancies are then free to move about as their own entities.

2.7 (a) Frenkel disorder in an ionic crystal, where the red square denotes a vacancy left by a cation which has moved to an interstitial site. (b) Schottky disorder.

A self interstitial atom is an extra atom that has crowded its way into an interstitial void in the crystal structure. Self interstitial atoms occur only in low concentrations in metals because they distort and highly stress the tightly packed lattice structure (Fig. 2.7).

A substitutional impurity atom is an atom of a different type than the bulk atoms, which has replaced one of the bulk atoms in the lattice. Substitutional impurity atoms are usually close in size (within approximately 15%) to the bulk atom. An example of substitutional impurity atoms is the zinc atoms in brass (alloy of copper and zinc). In brass, zinc atoms with a radius of 0.133 nm have replaced some of the copper atoms, which have a radius of 0.128 nm (Fig. 2.7).

Interstitial impurity atoms are much smaller than the atoms in the bulk matrix. Interstitial impurity atoms fit into the open space between the bulk atoms of the lattice structure. An example of interstitial impurity atoms is the carbon atoms that are added to iron to make steel. Carbon atoms, with a radius of 0.071 nm, fit nicely in the open spaces between the larger (0.124 nm) iron atoms (Fig. 2.7).

* Linear defects, which are groups of atoms in irregular positions. Linear defects are commonly called dislocations, which are areas were the atoms are out of position in the crystal structure. Dislocations are generated and move when a stress is applied. The motion of dislocations allows slip – plastic deformation to occur.

* Planar defects, which are interfaces between homogeneous regions of the material. Planar defects include grain boundaries, stacking faults and twin region.

Solids generally consist of a number of crystallites or grains. Grains can range in size from nanometers to millimeters across and their orientations are usually rotated with respect to neighboring grains. Where one grain stops and another begins is known as a grain boundary. Grain boundaries limit the lengths and motions of dislocations. Therefore, having smaller grains (more grain boundary surface area) strengthens a material. The size of the grains can be controlled by the cooling rate when the material cast or heat treated. Generally, rapid cooling produces smaller grains whereas slow cooling result in larger grains. For more information, refer to the discussion on solidification.

A disruption of the long-range stacking sequence can produce two other common types of crystal defects: 1) a stacking fault and 2) a twin region. A change in the stacking sequence over a few atomic spacing produces a stacking fault whereas a change over much atomic spacing produces a twin region. A stacking fault is a one or two layer interruption in the stacking sequence of atom planes.

Another type of defect observer in ceramic materials is bulk defects, which occur on a much bigger scale than the rest of the crystal defects above discussed. However, for the sake of completeness and since they do affect the movement of dislocations, a few of the more common bulk defects will be mentioned. Voids are regions where there are a large number of atoms missing from the lattice. Empty spaces can occur for a number of reasons. When voids occur due to air bubbles becoming trapped when a material solidifies, it is commonly called porosity. When a void occurs due to the shrinkage of a material as it solidifies, it is called cavitation. Another type of bulk defect takes place when impurity atoms cluster together to form small regions of a different phase.

2.7 Notation for point defects in crystalline solids

The notation used for defects is from Kröger and Vink and are shown for a number of examples in table 1. [F.A. Kröger and H.J. Vink, Relations between the concentrations of imperfections in crystalline solids, Solid State Phys., 3, 1956, 307] There are vacant lattice sites (called vacancies), ions placed at normally unoccupied sites (called interstitial ions), foreign ions present as impurity or dopant and ions with charge different from those expected from the overall stoichiometry. Electron defect may arise either in the form of ions present with charges deviating from the normal lattice ions, or as a consequence of the transition of electrons from normally filled energy levels, usually the valence band, to normally empty levels, the conduction band. In those cases where an electron is missing i.e. when there is an electron deficiency, this is usually called electron hole (often abbreviated to hole). Usually it is convenient to consider point defects, such as vacancies or electron holes to be moving entities in a lattice even though in reality the ions or electrons move through the lattice in the opposite direction.

The charge of the defects and of the regular lattice particles are defined with respect to the neutral, unperturbed (ideal) lattice and are called effective charges. These are indicated by a dot () for a positive excess charge, by a prime () for a negative excess charge and by a for effectively neutral defects (i.e. ions having their normal charges corresponding with the stoichiometry of the compound).

TABLE 1

Kröger-Vink notation for point defects in crystals. Divalent ions are chosen as example with as a compound formula with , as cation and anion, respectively.

Symbol

Type of Defect

Metal ion vacancy: vacant metal site with effective charge -2 (with respect to the ideal lattice)

ion vacancy: vacant X site with effective charge +2 (with respect to the ideal lattice)

Metal, respectively, X ion on their normal lattice position (neutral)

dopant ion on metal site with effective charge -1 (with respect to the ideal lattice)

dopant ion on metal site with effective charge +1 (with respect to the ideal lattice)

(Quasi)-free electron in conduction band

(Quasi)-free electron hole in valence band

Interstitial metal ion metal with effective charge +2 (with respect to the ideal lattice)

Interstitial X ion with effective charge -2 (with respect to the ideal lattice)

Monovalent metal ion on -position ( localised electron, only possible if the metal M has multiple valencies)

Trivalent metal ion on -position ( localised electron hole, only possible if the metal has multiple valencies)

2.8 Doping strategies

Perovskite structure ABO3 can be happening substitutions at site B by lower valence dopant B'. This will create oxygen vacancies in the lattice (AB1-xBx'O3-δ), which is represented by the symbol δ and it is called oxygen non-stoichiometry. This latter depend on composition, temperature and oxygen partial pressure. At low temperature they remain ordered but at high temperature, typically T > 700°C, they provide path for the migration of the oxygen anions from one side of the membrane to the other side [H.J.M. Bouwmeester, A.J. Burggraaf, “Dense ceramic membranes for oxygen separation” in: P.J. Gellings, H.J.M. Bouwmeester (Eds.), CRC Handbook of Solid State Electrochemistry, CRC Press, Boca Raton, FL, 1997, Chapter 14.]. A counter-balancing flux of electronic charge carriers is present in the material so that the electro neutrality is held. A part of this family of compounds, can also be obtained a wide variety of compounds when A and B atoms are both replaced by A' and B' atoms (i.e. A1-xAx'B1-xBx'O3-δ). These materials have very good mixed ionic-electronic conductivity.

2.9 Mechanism of oxygen transport

Oxygen permeation through MIEC perovskite membrane is a complex process that involves a series of steps, which are illustrates in Fig. 2.3. The oxygen permeation through a membrane is driven by an oxygen partial pressure gradient across it and this process has different steps, which are described to continuation:

(1) Initially, mass transfer of gaseous oxygen from the gas stream to the membrane surface (high pressure side, ). The oxygen is adsorbed on the membrane surface of the high oxygen pressure side [54].

(2) Reaction between the molecular oxygen and oxygen vacancies at the membrane surface . The adsorbed oxygen is dissociated into oxygen ions and electron hole . Different oxygen species are produced as intermediates upon the reduction of molecular oxygen [32, 39, 54, 55].

(2.2)

(3) The oxygen species diffuse from the side of high oxygen pressure to the side of low oxygen pressure of membrane through the combination of mobile oxygen vacancies and electronic defects (holes). Simultaneously, electrons are transported in the opposite direction to maintain electric neutrality [32-40, 54].

(2.3)

(4) Reaction between the lattice and electron hole at the membrane surface (low-pressure side). Therefore, on the permeate side either molecular oxygen is formed at the membrane surface [54, 55].

(2.4)

(5) Finally, the mass transfer of oxygen from the membrane surface to the gas stream (low pressure side) [8, 32, 40, 54].

2.10 Theory of oxygen transport

The basic assumption of the oxygen transport theory is that the lattice diffusion of oxygen or the transport of electronic charge carrier through the bulk oxide determines the rate of overall oxygen permeation.

2.10.1 Bulk diffusion

The Wagner equation is the form used for calculation of the oxygen flux across an ion –conducting membrane. This theory assumes that the overall oxygen permeation is controlled by bulk diffusion or the transport of electronic charge carriers such as oxygen anions, electrons and electron holes. Moreover, the driving force is a gradient of oxygen chemical potential across the membrane [E. ten Elshof, H. J. M. Bowmeester, H. Verweij, Appl. Catal. A: Gen., 130, 1995, 195].

The interaction between the oxygen in the gas phase and the lattice is represented by the following equation, using the Kroger-Vink notation [F.A. Kröger and H.J. Vink, Relations between the concentrations of imperfections in crystalline solids, Solid State Phys., 3, 1956, 307]

(2.5)

It is implicitly assumed that the oxygen vacancies are fully ionized. The interaction between electrons and electron holes can be described by:

(2.6)

Considering equilibrium in eq. 2.5 and 2.6, chemical potential of the different species can be related according to the following relations.

(2.7)

(2.8)

Where denotes the chemical potential of the charge carrier. The single particle flux of charge carries, with neglect of cross terms between fluxes, is obtained by

(2.9)

Where is the Faraday constant, denotes the conductivity, the charge number and the gradient of the electrochemical potential of the charge carrier. The latter includes a gradient in chemical potential and a gradient in electrical potential according to:

(2.10)

In the steady state or equilibrium, no charge accumulation occurs. The flux of ionic and electronic defects can be expressed by the charge balance, as given in equation (2.9)

(2.11)

Combining equation (2.7) with equation (2.9) and taking into account that, one can express the oxygen flux through the membrane as follows:

(2.12)

Or in a more generalized form

Where and , then

(2.13)

Integrating eq. 2.12 with respect to the thickness of the membrane material can be done using the following relation:

Assuming that ( is the distance coordinate) and integrating equation (2.13) with respect to the thickness of the membrane , can be obtained the Wagner equation in the usual form:

(2.14)

Where and represent the high oxygen partial pressure and the low oxygen partial pressure side of the membrane, respectively.

2.10.2 Surface processes

The oxygen exchange reaction between the gas phase and the oxide surface involves a number of reaction steps, each of which may be rate determining. Possible steps are the oxygen adsorption on the oxide surface, oxygen dissociation, (surface) diffusion of intermediate species, charge transfer and incorporation into the lattice (see Fig. 2.8). It is generally assumed that this sequence of reactions applies for both membrane surfaces, in reverse directions. In the presence of a reactive gas, for instance methane, the rate-limiting step may be different than in the case of an helium sweep. It is therefore difficult to derive an appropriate expression for the interfacial oxygen flux.

The Onsager equation [[H.J.M. Bouwmeester, A.J. Burggraaf, “Dense ceramic membranes for oxygen separation” in: P.J. Gellings, H.J.M. Bouwmeester (Eds.), CRC Handbook of Solid State Electrochemistry, CRC Press, Boca Raton, FL, 1997, Chapter 14.].] gives a general expression for the oxygen flux through the solid/gas interface at conditions near to equilibrium:

(2.15)

where is the oxygen chemical potential difference across the interface and denotes the exchange rate in the absence of an oxygen chemical potential gradient. The later parameter is related to the surface exchange coefficient accessible from data of isotopic exchange:

(2.16)

where is the volume concentration of oxygen anions at equilibrium.

The oxygen chemical potential gradient applied across a MIEC is in practice consumed in two ways:

* loss of driving force at either one or both interfaces

* loss of driving force for the bulk diffusion

Decreasing the thickness of the membrane material can enhance the oxygen flux (see eq. 2.14) as long as the interface processes play a negligible role. It is pointless to reduce the thickness further if the limiting mechanism is the surface oxygen exchange. Bouwmeester et al. [[H.J.M. Bouwmeester, A.J. Burggraaf, “Dense ceramic membranes for oxygen separation” in: P.J. Gellings, H.J.M. Bouwmeester (Eds.), CRC Handbook of Solid State Electrochemistry, CRC Press, Boca Raton, FL, 1997, Chapter 14.].] introduced the concept of characteristic membrane thickness in order to distinguish between surface exchange and bulk diffusion controlled kinetics. When the total driving force is shared between these two processes, the membrane has a thickness , defined as:

(2.17)

Where is the electronic transference number, combining eqs. 2.17 and 2.15 with an equation mathematically equivalent to 2.14, one obtains the overall flux equation:

(2.18)

A factor 2 is introduced in the denominator to take into account the fact that for a symmetrical membrane the exchange processes at both interface can be rate limiting. For large membrane thicknesses, eq. 2.18 is equivalent to eq. 2.14 (Wagner's equation). For thicknesses much smaller than , the oxygen flux is independent of the thickness .

2.11 The oxygen flux through La0.6Sr0.4Co0.2Fe0.8O3-δ hollow fibre membrane

Tan and Li researched the oxygen flux for mixed conducting membrane at steady state under the electrochemical potential gradient, when it is controlled by bulk diffusion They describe this process through the following equation [X. Tan and K. Li, Alche J., 48, 7, 2002, 1469].

(2.19)

Where is transport flux of defect i,is effective diffusivity of defect i, is concentration of defect i, is transport number of defect i, is charge number of defect i, is the distance coordinate. According the step (3) in the Fig. 2.9, the oxygen vacancy and electron hole , are the only mobile charged carrier in the mixed conducting membrane [S. Xu, W.J. Thomson, Ind. Eng. Res. 37, 1998, 1290], therefore the eq. 2.19 can be reduced to

(2.20)

Where is transport flux of oxygen vacancy, is electron hole concentration, is oxygen vacancy concentration, is oxygen vacancy bulk diffusion coefficient and is electron hole bulk diffusion coefficient. When the ionic transference number closes to zero in the perovskite ceramic membrane then and , therefore the eq. 2.20 is simplified to [V. Karton, E. N. Naumivich and A. V. Nikolaev, J. Memb. Sci, 111, 1996,149; L. Qiu, T. H. Lee, L. M. Liu, Y. L. Yang and A. J. Jacobson, Solid State Ionics, 76, 1995, 321]

(2.21)

The oxygen permeation can be written based on the stoichiometric relations of oxygen and the oxygen vacancy as eqn. or

(2.22)

The diffusion coefficient of oxygen vacancies ( ) depend on the temperature and the oxygen defect lattice structure (J.B. Goodenough, Fast ionic conduction in solids, Proc. R. Soc. (London), A393, 1984, 214-234). Once the steady-state structure is established under certain temperature, then can be considered a constant and not to be a function of the position from the membrane wall [S. Xu, W.J. Thomson, Ind. Eng. Res. 37, 1998, 1290].

(2.23)

The oxygen flux or molar flow rate for a hollow fibre membrane can be expressed as

(2.24)

or

(2.25)

Where andis outer and inner radius of the hollow fibre membrane, is the length of hollow-fibre membrane module.

Tan and Li also deduced the oxygen flux for mixed conducting membrane (La0.6Sr0.4Co0.2Fe0.8O3-δ) at steady state under the electrochemical potential gradient, when it is controlled by surface reaction.

The following reversible reactions take place at the high and low pressure sides

(2.26)

(2.27)

Where, represents lattice oxygen in the perovskite crystal structure, and and are, respectively, the forward and reverse reaction rate constants for the surface reactions. [Van Hassel, B., A. Kawada, T. Sakai, N. Yokokawa, H. Dokiya, and H. J. M. Bouwmeester, ‘‘Oxygen Permeation Modeling of Perovskites,''Solid State Ionics, 66, 1993,295].

It should be stand up that because of the high electronic conductivity; the electron holes are essentially constant at both surfaces of the membrane, and thus the forward 2.26 and reverse 2.27 reaction rates of the surface reactions are pseudo zero-order at steady state under isothermal conditions [Xu, S. J., and W. J. Thomson, ‘‘Oxygen permeation rates through ion-conducting perovskite membranes,'' Chem. Eng. Sci., 54, 1999, 3839].

Therefore, the local rate of oxygen consumed (step 2) or formed (step 4) in the hollow fibre (Fig. 2.8) can be denoted, respectively.

(2.28)

(2.29)

Substituted the eq. 2.28 or 2.29 into the eq. 2.24 can be correlated the local oxygen permeation rate in a hollow fibre to the partial pressures of oxygen (eq. 2.30)

(2.30)

2.11.1 Correlation between the Chemical diffusion coefficient () and the diffusion coefficient of oxygen vacancies ( ).

The eq. 2.9 can be written in function of neutral oxygen flux (2.31)

Assuming that the fast movement of electron- holes inside the membrane do not reach a steady state electric field gradient, hence

(2.32)

Then, the neutral oxygen flux through the membrane is

(2.33)

Where the chemical potential gradient () can also be expressed in terms of a chemical potential driving force ().

(2.34)

Considering that the chemical potential is also given by

(2.35)

The neutral oxygen flux can be rewritten as

(2.36)

Therefore,

(2.37)

The chemical diffusion coefficient () is given by

(2.38)

Then, the effective transport of neutral oxygen atoms can be expressed in terms of a chemical diffusion process, considering the Fick's first law [H.J.M. Bouwmeester, A.J. Burggraaf, “Dense ceramic membranes for oxygen separation” in: P.J. Gellings, H.J.M. Bouwmeester (Eds.), CRC Handbook of Solid State Electrochemistry, CRC Press, Boca Raton, FL, 1997, Chapter 14.]

(2.39)

Where the driving force for diffusion it is the gradient in neutral oxygen () and the diffusion is dominated by neutral vacancies. Therefore

(2.40)

Substituting the eq. 2.39 into 2.40 and considering can be obtained (2.41)

Equaled the eqs. 2.22 and 2.41 is found

(2.42)

Then, it can be observed that the chemical diffusion is equal to the vacancy diffusion coefficient.

(2.43)

2.12 Mixed conducting ceramic membranes for Syngas production.

The price of crude oil is high owing to the limited reserves that currently exist. In addition, the constantly rising requirements for clean fuels are driving industrials to use natural gas, which offers an interesting energy source when upgraded to higher-value chemicals.

Currently, the most technologically older and cost effective path for large-scale hydrogen production is the direct chemical conversion of fossil fuels to hydrogen. This process is steam reforming of natural gas, which is the principal industrial process for the production of hydrogen; it representing more than a half of world hydrogen production.[F. Mueller-Langer, E. Tzimas, M. Kaltschmitt, S. Peteves, Techno-economic assessment of hydrogen production processes for the hydrogen economy for the short and medium term, International Journal of Hydrogen Energy 32 (2007) 3797 – 3810]

(2.44)

This process is endothermic at pressures between 15-30 bars and temperature between (850-900) °C, which makes process expensive. In addition, this process requires the natural gas desulphurization unit for eliminate the sulphur that have the gas natural. Generally the metal catalysts used for this reaction are easily poisoned by sulphur or coke deposition. Noble metal catalysts, such as Palladium (Pd), Platinum (Pt) or Rhodium (Rh), are less sensitive to carbon deposition, but have a higher tolerance towards sulphur and then they cannot be favourable for obvious economical reasons. A schematic of the process is shown in Fig.2.10

A remedy to these problems resolve is the slightly exothermic catalytic partial oxidation (CPO) reaction:

(2.45)

The main challenge in this case is to produce pure oxygen. It is nowadays achieved in a cryogenic plant but the associated investment costs are very high, therefore limiting the use of this process. Air can be used in place of oxygen but there is a risk of producing harmful compounds and handling large quantities of nitrogen is costly.

One alternative to replace or improve the performance of methane conversion processes, i.e. combining air separation and high-temperature catalytic partial oxidation (CPO) into a single step are dense ceramic membranes made from mixed oxygen-ionic and electronic conducting (MIEC) perovskite oxides, because can be use in many industrial processes that require a continuous supply of pure oxygen. Of particular significance in the partial oxidation of methane to syngas () used MIEC membrane is that have been published outstanding methane conversion levels and 100% CO selectivities in the presence of a reliable catalyst, e.g. supported Nickel (Ni) or Rhodium (Rh). [P.N. Dyer, R. E. Richards,S.L. Russek, and D. M. Taylor, . Ion transport membrane technology for oxygen separation and syngas production, Solid State Ionics, 134 (2000) 21]

The advantages of the dense MIEC membrane reactor technology are following:

* Economically attractive process.

* Elimination of compounds.

· Avoids the premixing of oxygen and natural gas and reduces the formation of hot spots as encountered in a co-feed reactor.

· Air can be used as oxygen supply.

· Oxygen separation and partial oxidation are combined in a single reactor.

· Application in remote locations possible.

2.12.1 Principle of operation

The operating principle of Partial oxidation methane through MIEC perovskite membrane is shown in Fig. 2.11.

In a typical membrane reactor, the pressure differential is provided by air on one side and a reducing gas () side. On the air side, the molecular oxygen is reduced to oxygen anions () and this driven from the high partial pressure side to the low partial pressure side through oxygen vacancies. Then, in the reducing side, methane () is oxidized by oxygen anions () and produce syngas ().

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