Mass transfer

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WHAT IS MASS TRANSFER? Mass transfer is a subject that particularly studies about the relative motion of chemical species with respect to other. For example, it is aimed to investigate the relative motion of one chemical species with respect to another chemical species through the separation and mixing processes. This relative motion is usually due to the driving force of the mechanism. In fact, there are concerns about some specific issues that is necessary to be consider before any actual solutions to any real problems can be made. The issues are: 1. Phase equilibria  When a pure gas is exposed to a pure liquid in constant pressure and temperature, the concentration of the gas increases rapidly in the liquid. However, after a certain time, the rate of increase of the concentration in the liquid becomes gradual and reaches a certain limiting value, considering that the pressure and the temperature of the system remain the same. This stable condition is known as phase equilibria. It depends on the thermodynamic nature of the system only. This shows that phase equilibrium indicates the upper limit for mass transfer of a system, but there are no such restraint exist in heat transfer. 2. Convective mass flux  Mass transfer can be defined in term of material transfer through an interface between two different phases. Meanwhile, diffusion is described as the relative motion of molecule from the center of mass of a mixture, moving at local velocity (Asano, 2006). Therefore, mass fluxes are totally different with diffusional flux, as it is often concluded in primitive mass transfer model. Rather, mass fluxed can be explained as the total of diffusional fluxes at the interface accompanied by convective mass fluxes. In fact, convective mass fluxes can also have an essential effect on the velocity and concentration distribution near interface if the magnitude of the flux is big. This situation can be known as the high mass flux effect. 3. Mixture



Instead of dealing with the system consisting of the pure fluids only in the studies of momentum and heat transfer, the main concern of mass transfer is about the mixed system of fluids. In fact, the simplest case is binary system. Nevertheless, people usually deal with the ternary or multicomponent system. As a result, various definition of concentration have been applied in case-by-case manner, which can drive us to serious misunderstanding in explaining the rate of mass transfer.

4. Effect of latent heat  Latent heat can be described as the heat energy that is needed (absorb or release) to change an object from one state to another state without varying the temperature (Perrot, 1998). Besides involving in the transfer of mass from one phase to another, mass transfer also participate in the transfer of energy associated with phase change. In this perspective, mass transfer is closely interrelated with the heat transfer through the boundary conditions at the interface due to energy transfer is accompanied mass transfer, which will disturb the interface conditions. The effect is considerable and it cannot be neglected. In some cases (i.e: gas absorption in a very low concentration range), latent heat can be neglected as the effect is too minimal.

MASS TRANSFER THEORIES In most cases, operations related to mass transfer is according to turbulent flow, where it is predicted to increase the rate of transfer per unit area or assist disperse one fluid in another and form more interfacial area. Other than that, it is always an unsteady state for mass transfer to a fluid interface, which varying the concentration gradient and mass transfer rate continuously (McCabe, Smith, & Harriott, 2005). Although the differences exist in mass-transfer operations, it is treated by applying same type of equation, which features a mass-transfer coefficient, k (Seader & Henley, 2010). The mass-transfer coefficient, k can be described as the rate of mass transfer per unit area per unit concentration difference.

FILM THEORY The resistance to diffusion which is equivalent to that in a stagnant film of a certain thickness is known as concept of film theory (McCabe, Smith & Harriott, 2005). Coefficient kc varies with the first power of Dv. Complex problems of multicomponent diffusion or diffusion plus chemical reaction uses the film theory. An example of film theory is the mass transfer from a turbulent gas stream to the wall of a pipe which follows the concentration gradient. Laminar layer can be seen near the wall, in where the mass transfer is mainly by molecular diffusion. The concentration gradient is also almost linear. Eddy diffusion increases and turbulence becomes stronger due to the increase distance from the wall increases. At the center of pipe the value of CA is maximum but this CA is not used in the calculation of mass- transfer. But the driving force is taken as CA - CAi, where CA is the concentration reached if the stream was thoroughly mixed. If the gradient near the wall is linear, it can be extrapolated to C A and the distance from the wall at this point is the effective film thickness B T. The resistance to mass transfer is mainly in the laminar boundary layer very close to the wall and B T is only slightly greater than the thickness of the laminar layer. The value of B T depends on the diffusivity of DV and not just on flow parameters, such as Reynold’s numbe r. The concept of an effective film thickness is useful but values of B T must not be confused with the actual thickness of the laminar layer.

MOLECULAR DIFFUSION The movement which occurs due to the influence of a physical stimulus, of an individual component through a mixture is called as molecular diffusion (McCabe, Smith & Harriott, 2005). Diffusion mainly takes place due to the differences between the concentration gradient of the diffusing components. Concentration gradient is defined as the movement of particles from a higher concentration area to lower concentration area. When concentration gradient takes place, it will cause a steady-state flux of the diffusing

components. Besides concentration gradient, there are some other factors which also cause diffusion. Activity gradient (as in reverse osmosis), pressure gradient, temperature gradient, and application of an external force (as in centrifuge) are the factors which causes diffusion. Diffusion can take place through stagnant layers of solid or fluid and also occurs when different compositions of fluid are mixed. There are two steps involved in mixing: i) The eddy motion of characteristic of turbulent flow causes mass transfer. This process is also known as eddy diffusion. ii) Molecular diffusion takes place between the very small eddies. Usually the direction of the bulk flow is parallel to the direction of diffusion.

THEORY OF DIFFUSION – FICK’S LAW OF DIFFUSION The molar flux J is similar to the heat flux q / A and the concentration gradient dc / db is similar to the temperature gradient dT / dx. Hence,

where

= molar flux of component A, kg. mol/ = volumetric diffusivity, = concentration, kg mol/ or or Ib mol/

.h or Ib mol/

b = distance in direction of diffusion, m or ft

The Fick’s law of diffusion above can also be written in different forms. For diffusion in three dimensions, the equation can be written in the form of:

Where

= molar density of the mixture, kg mol/ = mol fraction of A in the L phase

or Ib mol/

CONVECTIVE MASS TRANSFER The diffusional flux is always accompanied by convection mass flux due to the diffusional flux at the interface. In fact, convective mass transfer is one of the major modes that exists in mass transfer design. Convective mass transfer involves the transport of material between boundary interface and a moving fluid or between two relatively insoluble, moving fluids. It can occur in two such cases where: 1. Only in single phase either from or to a phase boundary, e.g: sublimation of moth ball (solid form) into moving air. 2. The two contacting phase, e.g: absorption.

CONVECTIVE MASS TRANSFER COEFFICIENT In the study of convective mass transfer, the mass flux (molar flux) is related with mass transfer coefficient. Below are the equation which can define the situation of convective mass transfer: ) NA CAS CA kc = molar flux = concentration at the phase boundary = concentration at some arbitrary defined point in fluid medium = convective mass transfer coefficient The driving force is the difference between CAS and CA. The convective mass transfer coefficient, kc is described as a function of the properties of the system as well as the velocity and the properties of the fluid.

APPLICATION OF MASS TRANSFER IN PROCESSING INDUSTRIES DISTILLATION Distillation is applied to separate, by vaporization, a liquid mixture of soluble and volatile substances into individual components, or in some cases in a group of component (Kister, 1990). For instance, purification of alcohol can be done by distillation and extracting it from the water and produce pure alcohol as end product of the process by cooling down the alcohol vapor.

Column

 Figure 1: Continuous distillation. Refer to Figure 1, a feed of a liquid mixture is provided continuously to the tank. Once the reboiler is heated up, the liquid mixture is vaporized partially by using the heat transferred by the reboiler. The vapor stream from the low boiler (liquid mixture at the bottom of the column) have to bring close-related countercurrent contact with a downward liquid stream in order to rise the concentration of the low boiler. The liquid must be concentrated enough in case that there is mass transfer of the low boiler from the liquid to the vapor at each stage of the column. It is known that such liquid can be

get by condensing the overhead product and returning it back to the column. It is called reflux, which functions to elevate the purity of the overhead product with some capital, since the vapor produced in the reboiler must be provided to both reflux and overhead product. Usually, the reflux is entering the column at its boiling point. Throughout the column, the liquid and vapor are at their boiling point and condensing temperature respectively. Besides, the temperature will increase when going down the column due to the increase of the boiler concentration or in some cases, the rise of pressure. At the top stage of the distillation column, the vapor coming to this stage is less concentrated compared to the overhead product. At the same time, the reflux, which has the same composition as the overhead product, will have a vapor equilibrium which can make the reflux richer than the product. Hence, vapor that passing through the top stage will be enriched due to the reflux liquid. This makes the reflux less concentrated in the boiler. In the column, some low boiler diffuses into the vapor phase, and a corresponding diffusion of high boiler also occurs at the same time. As a result, the total flow rate of vapor up the column is almost constant. The enrichment of vapor stream as it passes through all the stages of the column in contact with reflux is called rectification. The reflux originates, given its concentration in low boiler is enough to produce the desired product, so it is immaterial. The common source of the reflux is the condensate which will leave the condenser. The condensate will be leaving as the final product partially and the leftover of the condensate will be recycled and entered the column again as reflux. The reflux then have different composition from the vapor leaving as overhead product. From the reboiler, liquid which most of the components have higher boiling point, is taken out due to the small amount of this component slips with overhead product. This liquid is known as bottom product because the equipment of the distillation has no provision to rectifying this stream.

ADSORPTION Adsorption is the adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface. Adsorption takes place on the wall of the pores or at specific sites inside the particle. The pores are small in size which causes the surface area inside is greater in magnitude than external area. Separation occurs due to the differences in molecular weight. Sometimes, the absorbing component (adsorbate) is held strongly enough to permit complete removal of that component from the fluid with very little adsorption of other components. Then regeneration of the adsorbent can be carried out in order to get the adsorbent in concentrated or pure form.

 Figure 2: Equipment for adsorption of solvent vapor.
Source: http://carboncapturescientific.com/technology.php?id=2

Adsorbent particles are placed in a bed 1 to 4ft deep supported on a screen. From one bed to another bed, the feed gasses pass down while the others are being regenerated. Down-flow is preferred by the gases because if up-flow will cause the particles to fluidize, which directly causes attrition and loss of fines. Valves will automatically switch when the concentration of solute reaches a certain fixed value or scheduled time. The gas will be then directed to other valve. Hot inert gases also can be used to in regeneration but usually steam is preferred if the solve is not miscible with water. Temperature increase due to the condensation of steam in the bed. The solution is condensed, separated from the water and sometimes dried before being used. The bed will be cooled and dried with inert gas. Besides that, evaporation of water also helps in cooling down the bed and partially offset the heat of adsorption. The gas flow rate and the desired cycle time is the determining factors for the size of the adsorbent bed. The cross sectional area is always calculated in order to be small. Sometimes, for very large flow rates, a rectangular bed will be installed in the middle of a horizontal cylinder rather than using a vertical tank with a diameter much greater than the bed depth.

CONCLUSION As a conclusion, mass transfer is defined as the shift of chemical substances with respect to the motion of other species. The relative motion is one of the cause of this mechanism. Besides, some consideration must be taken for specific issue before any solution is applied to real problems. Such concerns are phase equilibria, convective mass flux, mixture of the system and last but not least effect of latent heat. Normally, most operations related to mass transfer are according to turbulent flow which it is known to increase the rate of transfer the unit or aid dispersion of one fluid in another and formations of interfacial areas. On the other hand, film theory (mass transfer theory) is described as the resistance to diffusion is equivalent to the stagnant film of certain thickness. Moreover, molecular diffusion is referred as the movement which take place due to the concentration gradient (influence of physical stimulus). Furthermore, convective mass transfer include the transport of material between boundary interphase and moving fluid, or between two relatively immiscible fluids which are in motion. There are many application of mass transfer in processing industries. Distillation and adsorption are example of processing industries.

REFERENCES

Asano, K. (2006). Mass transfer: from fundamentals to modern industrial applications. Weinheim, Germany: Wiley-VCH. Kister, H. Z. (1990). Distillation operation. New York, United State: McGraw Hill. McCabe, W. L., Smith, J. C., Harriott, P. (2005). Unit operations of chemical engineering (7th ed.). United State: McGraw Hill. Seadar, J. D., Henley, E. J. (1998). Separation process principles (2 nd ed.). New York, United State: J, Wiley.

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