Mass Transfer Operations I
Mass Transfer Operations I CHE 545
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This 14 page Class Notes was uploaded by Jazlyn Schultz III on Friday October 23, 2015. The Class Notes belongs to CHE 545 at University of Idaho taught by Vivek Utgikar in Fall. Since its upload, it has received 30 views. For similar materials see /class/227844/che-545-university-of-idaho in Chemical Engineering at University of Idaho.
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Date Created: 10/23/15
Fall 2008 ChE 545 Mass Transfer Operations I Lecture 1 Fundamental Concepts 0 Chemical processes can be batch continuous or semicontinuous and consist of 0 Key Operations I Chemical reactions I Physical separations 0 Auxiliary Operations I Phase separations I Heat transfer I Size reduction etc I Processes can be represented by block ow diagrams at a basic level Separations are nonspontaneous processes requiring energy expenditure Separations are characterized by a decrease in entropy and increase in availability exergy I Separations can be equilibriumdriven or ratedriven I Separations can be effected through the use of 0 Energy Separating Agents ESA or 0 Mass Separating Agents MSA 0 BSA are usually preferred over MSA due to 0 Possible MSA contamination in product streams 0 Make up requirements for MSA 0 Need to separate MSA for reuse I The extent of separation is limited by the equilibrium the rate of separation dependent upon the mass transfer rate I The material balance for the component 139 in a separation step is P1 Where n is the number of moles F is the feed stream N the number of phases into which the feed is separated The split fraction SF and split ratio SR for a component 139 in the kth separator are de ned as 1 1 n n SFik 7 mm 7 55 quotth quotu where l and 2 represent two outlet phases Split fraction is based on the feed while split ratio is based on the product or outlet stream Separation power or separation factor SP is based on concentrations in two outlet phases or streams SP is always de ned for any component 139 with respect to some other component j 1 Z c c SP 39 39 u Ciro 19 SPs can be related to SFs and SRs Thermodynamic Considerations The minimum work needed to achieve a certain separation can be calculated from the stream availabilities Wmin Zaut nb Zin nb The actual work needed to effect the separations within a finite time requires an additional amount equal to TgASirr to compensate for the lost work LW The second law efficiency for the separation is based on the Wmm and LW Equilibrium Chemical potentials u also known as the partial molar Gibbs free energy for a component are equal in all phases at equilibrium Fall 2008 ChE 545 Mass Transfer Operations I Lecture 13 Isotopic Separation of Uranium Uranium isotopes U235 and U238 can be separated on the basis of their mass hence the mobility differences The separation is effected by converting the elemental uranium into UF5 which is in gaseous state at relatively low temperatures 320K The gas diffusion separation is based on the higher diffusivity of U235F5 through a porous medium Pressurized gas mixture is pumped through a porous barrier for example sintered nickel tube having pores that do not allow bulk convective ow The permeate is enriched in the lighter isotope salt The ideal single stage separation factor is equal to 10043 which is the square root of the ratio of the molecular weights of the two salts Enrichment of 07 U235 natural uranium to 4 with tails containing 025 U235 requires 1200 gas diffusion steps in series The speci c power requirement is 2400 kWhSWU The gas centrifuge process utilizes the centrifugal force to effect the separations of the lighter isotope from the heavier Gaseous hexa uoride salt mixture is fed at the center of a high speed centrifuge The heavier isotope salt is concentrated at the periphery while the lighter isotope collects at the center The separation factor strictly under the centrifugal force is related to the difference rather than ratio of the molecular weights and the peripheral velocity The generalized separation factor for a binary AB mixture is given by z aA B 3951 MA MBNUZT 2RT The separation factor for the hexa uoride salt of the uranium isotopes is 10686 at 60 C for a peripheral velocity of 350 ms which is substantially higher than that for the gaseous diffusion process The speci c power requirement for the gas centrifuge process is 100 kWhSWU which is merely 4 of that for the gas diffusion Specialized Al alloys and maraging steel are used in the construction of the gas centrifuges Fall 2008 ChE 545 Mass Transfer Operations I Lecture 12 LiquidLiquid Extraction A single equilibrium stage in multicomponent liquidliquid systems can be analyzed by an algorithm similar to the RachfordRice algorithm for ash distillation An iterative procedure needs to be followed for the solution If the entering streams feed and solvent are not at identical temperatures then an energy balance also needs to be accounted for Countercurrent liquidliquid extraction single solute can be analyzed graphically using the triangular phase diagrams The graphical procedure consists of Locating the feed F and solvent S points connecting them by a straight line 0 and locating the overall composition of the hypothetical mixed stream M using the inverse lever arm rule Locating the ra inate point RN based on the required duty on the equilibrium curve connecting it to the hypothetical point M by a straight line and extending the line to the other side of the equilibrium curve to locate the extract composition E1 Relative quantities of extract and ra inate are calculated using the inverse O lever arm rule Locating the operating point P 7 intersection of line E1F and SRN O O Locating the ra inate point of the rst stage R1 through the tie line connecting E1 to the point on equilibrium curve drawing the straight line PR1 and extending it to the equilibrium curve to obtain extract from the second stage E2 Repeating the above step to obtain raf nate and extract compositions of the O subsequent stages until the desired separation is reached Maximum and minimum solventtofeed ratios can be obtained from the equilibrium diagram and above construction The maximum amount of solvent that can be used can be calculated by locating the point M at the intersection of the equilibrium curve with SF line near the solvent point Use of additional solvent will result in complete miscibility of the streams The minimum amount of solvent necessary for phase separation is given by the second intersection point of the equilibrium curve with SF line However this solvent ratio may not be suf cient to obtain the desired separation The minimum solvent necessary for the desired separation is obtained by obtaining the intersections of various tie lines with the SRN line Ifthe operating point P is located at the intersection then in nite number of stages are needed for the desired separation Fall 2008 ChE 545 Mass Transfer Operations I Lecture 8 Triangular Diagrams Isotopic separation between U235 and U238 can potentially be accomplished through distillation The vapor pressure of U238F5 is 1000078 times higher than that ofU235F5 Separation between HI and water in the sulfuriodine process for thermochemical hydrogen production can be accomplished through a twostep azeotropic distillation sequence HIwater form a maximum boiling azeotrope containing 57 H1 at atmospheric pressure This forms the bottoms distillate water stream of the rst distillation column This stream fed to another distillation column operating at higher pressures N7 atm can be separated into another maximum boiling azeotrope composition 53 HI and a distillate of H1 H1 stream is decomposed to produce hydrogen Triangular diagrams are valuable in describing ternary systems Distillation boundaries may or may not exist based on the occurrences of azeotropes Product distributions can be predicted on the basis of these diagrams Distillation curves depict the concentration pro les of the distillate stream Distillation curves start from higher boiling components and end at the lowest boiling component Similarly residue curves depict the concentration pro le of the bottoms Residue curves converge at the higher boiling components Fall 2008 ChE 545 Mass Transfer Operations I Lecture 11 Gas Absorption Ternary LiquidLiquid Systems The ow rate of the gas may vary considerably along the height of the absorption column if the inlet gas has a high concentration of the solute and signi cant quantity of the solute is transferred to the liquid phase The gas phase mass transfer coef cient will also vary along the height and the modi ed equation for calculation of the packed height is l V fyl 1 yLM A T K aS 1ym y 1yyy where the primed coef cient indicates UM diffusion A ternary liquidliquid system can be represented by an equilateral triangular diagram a right triangular diagram an equilibrium solute diagram in mass fractions or mass ratios and a Janecke diagram Any one of these diagrams can be used to perform equilibrium stage calculations The inverselever arm rule is used to determine relative quantities of materials corresponding to the end point compositions of a line combining to yield any intermediate point on the line Fall 2008 ChE 545 Mass Transfer Operations I Lecture 4 Flash Distillation Flash distillation is a single stage equilibrium operation in which feed is partially vaporized to obtain enrichment of components in ef uent phases The ef uent phases P are in equilibrium with each other The degree of freedom F in this system is C 5 C being the number of components 0 The number of variables is CP C 6 o The number of independent equations arising out of material balance energy balance and equilibrium considerations is CP P 1 In general C 3 values are known from feed conditions C concentrations in the feed stream mole fractions 2 feed temperature TF and pressure PF and feed ow rate Only two variables need to be speci ed to solve the system ie obtain quantitative description of the system For isothermal ash conditions the system pressure P and temperature T are generally speci ed The system can be reduced to one equation RachfordRice when the K factors are independent of the concentration I ZiaKt 2 wart 1 0 Where 1 is the fraction of feed that is converted to vapor This equation is solved for 11 and the remaining variables concentrations in ef uent phases ow rates heat duty calculated from the independent equations Adiabatic ash operations feature no external heat addition Q 0 The other variable generally speci ed is the ef uent pressure In this case a trial and error procedure is generally adopted by assuming a temperature and solving the RachfordRice equation for l The calculated value of lliS compared with that obtained from energy balance shown below and the guess re ned until an agreement between the two values is obtained hph1 hV hL 1P Where h is the molar enthalpy and the subscripts refer to feed and the ef uent phases Alternatively molar enthalpies are expressed as functions of temperature 1 substituted in RachfordRice equation which is then solved explicitly for temperature However the resultant equation is highly complex and a solution may not be feasible The RachfordRice algorithm can be adapted to treat a system that features 1 vapor and multiple liquid ef uent phases Fall 2008 ChE 545 Mass Transfer Operations I Lecture 10 Absorption and Stripping The number of equilibrium stages N needed for achieving the desired separation can be calculated using the Kremser method AN1 A Fraction Absorbed m SN1 S Fraction Stripped W where ALK V and S KVL are the absorption and stripping factors respectively Rate rather than equilibriumbased methods are used for the analysis of the packed columns The height equivalent of a theoretical plate or stage 7 HETP or HETS is obtained by dividing the packed height by the number of theoretical stages HETP however has no theoretical basis Packed height is also equal to the product of the height of a transfer unit HTU and the number of transfer units NTU HTU and NTU H 0G and NOG for an absorption column based on the overall gas phase mass transfer coef cient are H V as KyaS yin Nos f youty y Where S is the cross sectional area and Kya is the overall volumetric mass transfer coef cient based on the gas phase Other expressions for NTU and HTU are given in Table 67 The overall mass transfer coef cients are related to the individual gas and liquid side mass transfer coef cients by equations such as 1 1 K Kyakya kxa An analytical expression can be obtained for NTU using the material balance provided the equilibrium relationship is linear Otherwise the integral shown above or its analog will have to obtained graphically or numerically Fall 2008 ChE 545 Mass Transfer Operations I Lecture 6 Binary Distillation The condenser can be total liquid draw partial vapor draw or mixed both liquid and vapor draw The partial and mixed condensers provide an additional equilibrium stage for separation The re ux liquid may be in a subcooled state Energy will be expended to heat it to the saturation temperature This energy is obtained from condensation of the vapor in the column The net result is that the column internal re ux Lim is higher than the external re ux L The McCabeThiele construction can be modi ed to solve problems involving multiple feedproduct streams Operating lines can be drawn for each section depending upon the feedproduct speci cations PonchonSavarit method is used when constant molar over ow assumption is not valid for a system This method involves the use of enthalpy concentration H x y diagram Contant temperatures tielines connect the points on H x and H y curves representing equilibrium compositions in liquid and vapor phase The PonchonSavarit method involves o Plotting the enthalpy concentration diagram 0 Locating the feed and distillate points using the re ux ratio 0 Drawing a tie line from the point on H y curve representing the distillate composition to H x curve and determining the equilibrium liquid composition 0 Connecting this point on H x curve to the distillate point located as above the intersection of this line enthalpy operating line with H y curve yields the vapor composition on the second equilibrium stage 0 Repeating the above two steps until feed point is crossed The construction yields the number of stages in the rectification section 0 Drawing the line connecting the feed and distillate points and extending it to bottoms composition obtained from the material balance yields the point representing the bottoms on the enthalpyconcentration diagram The procedure for the recti cation section drawing the enthalpy operating line and the tieline is repeated for the stripping section to obtain the number of stages Fall 2008 ChE 545 Mass Transfer Operations I Lecture 3 Thermodynamics and Equilibrium Activity coef cient y of a component is related to the partial molar excess Gibbs free energy 5 for that component RTln y 6 lt a NTHEgt aNi TPNl gE molar excess Gibbs free energy is a function of composition xis T and P For a regular solution no excess volume or entropy VE SE 0 the activity coef cient is given by RTln 39yi 39IILL Z where 6 is the solubility parameter D is the volume fraction and VL the molar volume in the liquid phase Other expressions are available for the activity coef cients based on the functional relationship for the excess Gibbs free energy These relationships are based on various theories of solution Wilson NRTL UNIQUAC etc Gibbs Phase rule stipulates the number of independent variables that need to be speci ed for xing the equilibrium state of the system consisting of C components and P phases F C 7P 2 The phase rule refers to intensive properties independent of the system size The degree of freedom for a binary vaporliquid system is 2 meaning only 2 variables need to be speci ed out of P T x1 and y1 to x the equilibrium conditions The two independent equations assuming ideality ie Raoult s law are P P P15 x x 1 Pl P25 3 1 1 P T x y and xy diagrarns can be constructed using these equations The region enclosed by T x and T y lines on the T xy diagrarn comprises a two phase region Any point within this region denotes the overall composition of the system abscissa at that temperature ordinate Horizontal line passing through this point connecting the T x and T y curves is called a tie line The intersections of the tie line with the two curves represent the vapor and liquid concentrations at equilibrium with each other The relative amounts of liquid and vapor can be determined using inverse lever rule Altemately y 121952 2 1 an 1x2 Where 0271 is the separation factor relative volatility of component 2 with respect to component 1 and is given by for Raoult s law case P5 Azeotropes constant boiling mixtures x1 yl result due to the nonideality of the system 0 Minimum boiling azeotropes have the azeotrope boiling at a lower temperature than the boiling point of the more volatile component and also the less volatile component These result when activity coefficients of the components are greater than 1 Maximum boiling azeotropes boil at a temperature higher than the boiling point of the less volatile component and also the more volatile component Activity coefficients are less than 1 in this case 0 Fall 2008 ChE 545 Mass Transfer Operations I Lecture 9 Gas Absorption and Stripping The gasliquid system differs from the vaporliquid system in that the gaseous component is present at supercritical temperature and cannot be condensed into a liquid by merely increasing the pressure at the system temperature The standard state fugacity for the gaseous component cannot be equated to the saturation pressure as the saturation pressure is unde ned Instead the empirical Henry s constant H is used in equilibrium relationships Assuming ideal mixtures in both gas and liquid phases yiP H ixi Henry s constant has units of pressure though Henry s law is often written in forms that express the constant as dimensionless or having inverse pressure or other units The equilibrium relationship is valid for physical absorption of the component present in low concentrations It is frequently useful to work in terms of mole ratios rather than mole fractions since molar ow rates of the absorbent and carrier gas are generally constant This is valid when the absorbent is nonvolatile and the carrier gas insoluble in the absorbent The operating line relates the actual concentrations of the component in the two phases in the contacting device The operating line lies above the equilibrium line on an xy XY diagram for absorption and below it for stripping The minimum ow rate of absorbent for a given duty can be obtained from the equation L mm V K fraction of solute absorbed provided the absorbent does not contain any solute at the inlet Kfactor relates the concentrations in the two phases Minimum ow rate of the carrier gas for a given duty in the stripper is given by a similar relationship LI Wm E fraction of solute stripped The required number of stages can be graphically determined from the operating lineequilibrium line diagram Fall 2008 ChE 545 Mass Transfer Operations I Lecture 5 Binary Distillation McCabeThiele graphical method for binary distillation though superseded in industrial practice by computer aided calculations clari es the principles and operation of binary distillation column The simplest con guration of a continuous distillation column is comprised of a recti cation enrichment section a stripping exhausting section a condenser and a reboiler The distillate and bottoms product streams are withdrawn from the condenser and the reboiler respectively The feed stream demarcates the interface between the two sections The operating lines relating the vapor and liquid phase concentrations mole fractions of the light key more volatile component for the two sections are R 1 x xD y Rectification section R1 R1 VB1 1 x x Str1 1n sectlon y VB VB 3 PP g where R is the re ux ratio ratio of overhead stream returned to the distillation column to distillate product and VB is the boilup ratio the ratio of stream returned to column from the reboiler to bottoms product The feed line equation is Feed line Where q is the thermal condition of feed defined as the ratio of the difference between the enthalphy of saturated vapor and feed enthalpy to the difference between enthalpies of the saturated vapor and liquid streams The McCabeThiele graphical method involves o Plotting the equilibrium curve xy diagram and y x line 0 Drawing the qline from the feed concentration on y x line till its intersection with the equilibrium curve 0 Drawing the operating line for the recti cation section from the distillation composition on y x line to the intersection point the slope of this line is RmmRmm where Rmm is the minimum re ux ratio 0 Drawing the actual operating line for the rectification section by assuming a higher re ux ratio than Rm 0 Drawing the operating line for the stripping section from the intersection point of qline and operating line for the rectification section to bottoms composition ony x line 0 Drawing equilibrium stages from the distillate to bottoms composition to determine the number of stages required to achieve the desired separation In nite number of stages are required when the re ux ratio is minimum As the intersection of qline and operating lines lies on the equilibrium curve negligible enrichment is achieved in each stage and the operating lines pinch the equilibrium curve Increasing the re ux ratio reduces the number of stages required for the separation Minimum number of stages are needed at total re ux where operating lines coincide with the y x line There is no feed nor any product streams at total re ux Operating under total re ux allows the determination of the total number of theoretical stages in a column The basis for the above analysis is the key simplifying assumption of constant molar over ow resulting in constant liquid and vapor ows within each section though these are different in the two sections
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