Процессы массопереноса с участием твердой фазы. Учебное пособие

Let us consider the process of membrane separation on example of a binary solution, where component B exists in solvent A. Let solvent to pass through membrane better, than the dissolved substance. Then the initial mixture after contact with the membrane will be divided into two products: concentrate (retinue), enriched with dissolved substance B, and leachate (permeate), with a lower concentration of B component in comparison with the initial mixture (Fig. 4.1).

Using this scheme, we can write the equation of material balance of membrane separation process either for a mixture as a whole, or for component B, respectively:

Process of membrane separation can be characterized by selectivity φ and permeability j. Selectivity is determined as a share of dissolved component B, have not passed through membrane:

If membrane is completely closed for component B, then y = 0,

φ = 1 and reached a complete separation (component B is absent in leachate). If membrane equally passes both components A and B, its

selectivity φ = 0, y = in = x fin and the division is completely absent.

Permeability (i.e. specific productivity or mass flow) - mass of leachate, which passes through the unit of membrane surface (F) per unit of time (in fact – specific mass flow)

Classification of membrane separation methods can be fulfilled on different grounds. So, depending on the nature of the moving forces they can be subdivided into:

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3) electric-membrane (moving force, together with gradients of chemical

→

potentials, is the gradient of electric potential ϕE ).

Pressure-membrane separation is due to the difference of pressures on both sides of membrane. Depending on the size of particles, filtered off by membrane, pressure-membrane processes are divided into:

a)reverse osmosis (10-4- 10-3 µm);

b)ultrafiltration (10-3- 2 ·10-2 µm);

c)microfiltration (2 ·10-2 - 10 µm).

Reverse osmosis. In the basis of this process of separation is the phenomenon of osmosis - spontaneous transition of solvent through membrane into solution. Differential pressure, which appears between solute and solvent after the balance achievement, is called osmotic pressure (Fig. 4.2).

Fig. 4.2. Schematic image of the solvent transfer process and of equilibrium state, arising in a vessel, separated by membrane 3: 1 – position of solvent, 2 - position of solution; p1 and p2 - fluid pressure in the relevant parts of a vessel at the same distance from the bottom, π = ρgH - osmotic pressure.

To undertake the process of reverse osmosis need to create a pressure abundance between solute and solvent greater than osmotic pressure. This will lead to the carrying out the solvent molecules from the solution and, consequently, to the growth of solution concentration (Fig. 4.2). Reverse osmosis is used, mainly, for the separation of solutions of electrolytes. Osmotic pressure can amount to tens and hundreds of atmospheres, and working pressure in a machine even more. So, for sea water π = 25 bar, and the working pressure in a desalination process is approximately 60 atmospheres.

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Ultrafiltration can be used for separation of high-molecular and low molecular weight components of a mixture as the result of passing through the membrane only the last components. Osmotic pressure in such solutions is small and the working pressure shall not exceed, as a rule, ten atmospheres.

Microfiltration is used for the concentration of large colloidal particles from solutions. This process is intermediate between ultrafiltration and common filtering. It should be kept in mind that concentrates, produced during membrane separation, in contrast to filtering, appear in the form of solution, but not precipitate.

Advantages of the pressure-membrane separation processes are: small energy consumption due to the absence of phase transitions (membrane desalination of water demands in 10-15 times less energy than distillation); low temperatures, allowing to share thermally unstable compounds. Their disadvantages are: high operating pressure (especially for reverse osmosis), as well as the falling of selectivity and permeability in case of the growth of solution concentration due to concentration polarization – i.e. to increase in concentration of dissolved substance near membrane surface. For reducing of concentration polarization can be used turbulent flow, mixing, vibration, which leads to equalization of concentrations.

Diffusion-membrane separation is carried out by varying diffusion rate of mixture components through a membrane. Components should have different coefficients of diffusion, consequently, different molecular masses and interaction potentials. Diffusion-membrane processes are used in evaporation through membrane (where initial solution and concentrate are liquids, and leachate - vapor); for separation of liquid solutions, called dialysis (where initial solution and both products are fluids), as well as for separation of gas mixtures.

Electric-membrane processes are used for the separation of ions containing solutions (electrodialysis). Their driving force is the sum of gradients of chemical and electric (e) potentials. So, expression for the flow of component i will have the form:

where ezi - ion charge, φE - electric field potential, µi - chemical potential,

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4.2. Types of Membranes. Theory of Membrane Separation

Membranes, used in industry, must meet the following main requirements: be a device of high selectivity and permeability, chemical resistance, durability, and also be inexpensive. All membranes can be divided into porous and non-porous, called also liquid or diffusion. Porous membranes, depending on original material and procedure of manufacturing, are divided into different types. Classification of membranes is presented in the diagram below.

Membranes

Polymeric

Metallic

Ceramic

Of Micro Porous Glass

Dynamic

Coating

Impregnated

Spraying

Polymeric membranes, made of polymeric materials by washing out of previously entered additives or by the way of α- particles bombing with the following etching with chemical reagents, have a narrow distribution of pores` sizes.

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Metallic membranes can be obtained by leaching of one of the alloy components. Their advantages lie in mechanical strength and homogeneity of the structure.

Ceramic membranes belong to composite materials and are made twoor three-layered. On substrate with a more large pores is spraying a thin membrane forming layer. Their main advantage is chemical resistance, which allows to use ceramic membranes for separation of aggressive environments.

Micro porous glass membranes are produced by acid treatment of the molten glass, which helps to remove separate components out of it. Such membranes also possess chemical resistance and rigid structure.

Coating membranes, depending on the way of producing, are divided into impregnated and spraying. Impregnated membranes are made of porous materials, for example, of cermets, by the way of soaking it with solution of one salt, and then of the other, forming with the first solution insoluble sediment, which reduces the scale of pores to demanded size. Spraying membranes can be obtained by coating on a porous substrate a thin layer of material (usually polymeric), having well adhesion to this substrate, what allows to adjust pores size.

Dynamic membranes are obtained by filtration of solutions, containing colloidal particles, through porous substrates. The sediment of colloidal particles is a membrane layer. The advantages of such membranes are high permeability, durability, easy cleaning (you just need to wash away the membrane layer by solvent, handing it under pressure from the opposite side of membrane, and then in the renewal of the process membrane will self restore).

Non-porous (diffusion, liquid) membranes are, as a rule, correspond to quasi gels, stipulating the separation of substances due to the differences of their diffusion coefficients in the process of passing through the membrane.

Unified theory, which allows to explain this phenomenon and acquire the mathematical description of membrane separation for all types of membranes and methods of membrane separation, does not exist. You can select multiple theories, each of which has limited applicability.

Theory of screening suggests, that coming through the pores particles are small-size, and large are delayed. It applies to the processes of ultrafiltration and microfiltration, carried out through a porous membrane, but is not suitable for reverse osmosis and diffusion membrane separation.

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Diffusion theory, which is based on the difference between diffusion fluxes of various components, applicable only for the diffusion membrane separation through the liquid membrane.

In accordance with the theory of negative adsorption on membrane surface adsorbs only molecules of solvent, and so they pass through the membrane. This theory applies mainly to reverse osmosis.

4.3. Design of Membrane Devices

Devices with porous membranes are classified by the type of membrane elements, which may be flat, tubular, spiral and fibrous.

Design of devices with flat membrane elements can be described on example of apparatus of "Filter press" type (Fig. 4.3). Separating element consists of two membranes 1, arranged on both sides of the drainage plate 2, which is made of high porous material. Between the separating elements are hollow plates (frames) 3. As shown in Fig. 4.3, hollow elements alternate with separating elements, and such a device assembly is clamped from both sides with the help of end plates 4, using the tightening bolts 5. Solution, which has to be divided, consistently passes through all separating elements, then condenses and removes from the apparatus. Leachate after passing through membrane is flowing over drainage plates down and removes from the apparatus.

Fig. 4.3. Membrane device of "Filter press" type: 1 - membranes, 2 - drainage plates, 3 - frames, 4 - end plates, 5 - tightening bolts

Devices of "Filter press" type differ at simplicity of manufacturing, assembling and membranes replacement. Their main drawback is a low

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specific surface of membranes: 60 - 300 m2/m3 (membrane surface per unit of working volume of the machine).

Devices with tubular membrane elements are used for reverse osmosis, but they are especially widely used for ultrafiltration. Tubular membrane element is shown in Fig. 4.4, where indicated: 1 - membrane, 2 - substrate, 3 - porous pipe. Diagram of flows movements – initial solution, concentrate and leachate - is also included in the figure.

Fig. 4.4. Tubular element for membrane separation: 1 - membrane, 2 - substrate, 3 - porous pipe.

Fig. 4.5. Membrane device with tubular elements.

Machine with tubular elements is shown in Fig. 4.5, where in tube plates 1 are hermetically fastened tubular separation elements 2. Initial solution, concentrate and leachate flows are shown on the figure too.

Such an apparatus is similar at sight to casing-tubular heatexchange apparatus. Positive qualities of devices with tube extension elements are as follows: low consumption of materials; good hydrodynamic conditions of membrane functioning, so as ensures uniformity of a solution

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flow at all points of the surface; relatively small hydraulic resistance of separation elements. Disadvantage is a low specific surface of membranes: only 60-200 m2/m3.

Devices with spiral (rolling) membrane elements are made from four layers` plate, rolled up in a spiral and constructively similar to spiral heat exchangers. Schematically spiral membrane element is depicted in Fig. 4.6.

2

13

Fig. 4.6. Schematic image of a spiral membrane element: 1 - membranes, 2 - grid-separator, 3 - drainage layer.

It consists of a grid-separator 2, at which is submitted initial solution and goes out concentrate, two membranes 1 and located between them drainage layer. Solution, passing across the grid-separator, condenses due to removal of the solvent through membranes in the drainage layer, from which goes out the filtrate. Devices, having spiral membrane elements, possess greater specific surface (300-800 m2/m3) and low metal content, but they are more difficult in manufacturing and assembly and also have a significant hydraulic resistance both of grid-separator and drainage layer.

Fig. 4.7. Diagram of membrane apparatus with hollow fibers: 1 - frame, 2 - covers; 3 - pipe lattice, 4 - fibers.

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Devices with fibrous membrane elements represent membranes bundles, made in the form of hollow fibers, whose ends are fixed in tube plates 3 with the help of epoxy resin (Fig. 4.7).

Such devices are used for pressure-membrane processes. Filaments are of outer diameter of 45-1000 microns and a wall thickness of 10-200 mm. Feed of initial solution is possible both inside fibers (Fig. 4.7) and from outside. Advantages of such devices is a high specific surface of membranes (20000-30000 m2/m3), but disadvantage is the need for preliminary cleaning of solutions from mechanical impurities.

Design of devices with liquid membranes depend on the method of membrane creation. So, a layer of liquid membrane can be placed between two flat parallel polymer porous partitions, which allow to pass initial solution, but keep up the gel, from which consist membrane. Design of such device will be identical to machine with the flat porous membranes, for example, "Filter press" on Fig. 4.3.

Membrane can form a liquid film on the surface of a shared fluid (evaporation through membrane), but specific surface of a membrane in this case is small. Much larger specific surface can be ensured, if "membrane liquid" would envelop drops of shared fluid, distributed in a solid phase (emulsion). In this case, for the processes of membrane separation is more suitable to use extractors, for example, hollow spray, rotary-disk and others.

4.4. Calculation of Membrane Devices

Technique of calculation of a concrete membrane device, intended to carry out a definite process of membrane separation, has its own peculiarities. We shall try to highlight the common stages of the calculation of membrane apparatuses and the problems, arising in this context.

At the first stage, solving the system of equations (4.1) - (4.3), we can find three of the unknowns, in the capacity of which, depending on the formulation of the task, may be presented a different set of values. For example, knowing the consumption of initial mixture Lin , its initial

concentration in , as well as required composition of retinue fin and, selecting the membrane with a definite for a given mixture selectivity ϕ ,

you can find the retinue consumption Lfin , as well as the flow W and

composition of the permeate . It should be noted, that the membrane selectivity decreases at the expense of concentration polarization. This

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phenomenon is due to the increase in concentration of component in immediate vicinity of the membrane surface, because the solvent A passes through it better. Reduction of concentration polarization can be achieved by the increase of coefficient of mass delivery of component B from the membrane surface into the bulk of a solution. However, this phenomenon should be taken into account in the qualified calculation of membrane device.

The main task of calculating of apparatuses of membrane separation is finding the surface of a membrane. For majority of masstransfer apparatus, the required surface of a phase is determined by fundamental equation of mass transfer (1.117). And the connection of coefficients of mass transfer with coefficients of mass delivery is given by the relation (1.105), received in the absence of resistance of mass transfer through the interfacial surface. In the processes of membrane separation, on the contrary, the main resistance to mass carry, as a rule, is located in the membrane, and the resistance of mass delivery can be neglected. To reduce the resistance of mass delivery, as well as concentration polarization, the movements of phases are usually organized in a turbulent regime. For calculation of the membrane surface can be used equation (4.4). In case of need, permeability of the membrane j can be qualified with the account of differences in the values of moving (driving) forces and concentrations of permeate in the conditions, for which there were tabular data.

APPENDIX

1. Some Information from the Field of Mathematics

1.1. Scalars, Vectors, Fields

In the tutorial are used the following symbols of different values: scalars are designated by normal letters (a); vectors – by letters with an

→

arrow at the top ( a ).

Scalar – a value, which magnitude can be expressed only as a number. A scalar is specified by one number.

Scalar field - set of values of a scalar function at each point of space. For example, ρ(x,y,z) - field of density, (x,y,z) - temperature field, i(x,y,z) - field of concentration, and etc.

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