Introduction to Simultaneous Heat & Mass Transfer

Introduction to Simultaneous Heat & Mass TransferMr. Muhammad Usmanusmanchem08@yahoo.comDepartment of Chemical EngineeringUniversity of Engineering & Technology, LahoreRecommended Books

Principles of Mass Transfer & Separation Processes By Binay K. Dutta; Prentice Hall of India (PHI: 2007)Recommended BooksUnit operations of Chemical Engineering by Warren L. MCCabe, Julian C. Smith & Peter Harriott, 7th Edition; McGraw Hill International Editions

Recommended BooksSeparation Process Principles by Seader, Henley & Roper, 2nd & 3rd Editions; John Wiley & Sons (2010)

Recommended BooksSeparation Process Engineering by Phillip C. Wankat, 3rd Edition; Prentice Hall Publishers (2012)

Recommended BooksCoulson and Richardsons CHEMICAL ENGINEERING, Volume 2; 5th Edition Butterworth Heinemann Publishers

Recommended BooksPERRYS CHEMICAL ENGINEERS Handbook; 7th & 8th Edition, McGraw Hill Publishers (1997)

Recommended BooksPlant Design & Economics for Chemical Engineers by Peters & Timmerhaus; 4th & 5th Edition, McGraw Hill International Editions

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Simultaneous Heat & Mass TransferIn chemical engineering, we often encounter the situations where heat & mass are transferred simultaneously rather than independently.where there is Mass transfer, there is essentially the Heat transfer but Vice versa may not necessarily be trueExamples of SHMT PhenomenonIn Evaporation & Condensation phenomenon; rates of mass transfer strongly depend on the rates of heat transfer. In Distillation, Absorption, stripping, adsorption etc. rate of mass transfer may or may not depend strongly on the rate of heat transfer.

Heat

Constant Molal OverflowThis is the most important assumption often used to simplify the mathematical modeling of distillation systems especially for binary systems (also for MC systems).one mole of heavy component condenses from vapor to liquid on a tray releasing amount of heat called heat of condensation which is just equal to the heat of evaporation of a lighter component, which after absorbing it; will go from liquid to vapor phaseCMO (constant Molal Overflow)

If a molecule vaporizes by absorbing the heat of condensed molecule; Do I see any net Heat effect in the distillation column?EurekaEurekathose fools! I designed the Distillation Column without Enthalpy Balances while they were saying Distillation is a SHMT Phenomena

Hey! MR. Constant Molal overflowyou need to leave the house now. You know, 1st we were only two. Now there are so many components with usthere is not enough room for you.CMO: seems like you are getting Real.!

Critical Thinking?Is it possible for two different components to have exactly same heat of vaporization or condensation?

Can a Mathematical Model build with CMO represent a real world model?

If not, why we always go for this assumption?Equilibrium [1,2]A system will be in complete equilibrium only when system is in

fi is known as the fugacity of species i in any phase. It can be proved that when multiple phases at T,P are in equilibrium; fugacity of species i is same in every phaseThermal equilibriumTsystem = TsurrondingsMechanical EquilibriumPl = PvChemical Equilibriumfil = fivFugacity [1]From the usual criterion of phase equilibria we know that multiple phases at same T,P are in equilibrium only when il = iv = . = i

fi or..iig..?Where i is known as chemical potential (partial molar Gibbs Free Energy) of species i in any phase.iig= Giig + RT ln yiDifferentiating,diig=dGiig + RT d lnyiUsing fundamental property relation we know thatdGiig=ViigdP - SiigdTdGiig=ViigdP (constant T)fi or..iig..?Also for ideal gasdGiig=ViigdP (constant T)dGiig= (RT/P) dPdGiig= RT d lnPdiig=dGiig + RT d lnyidiig= RT d lnP + RT d lnyidiig= RT d lnyi Pdiig= RT d lnfi(fugacity)fi= yi P

fi or..iig [1,2]diig= RT d lnfiIntegrating,iig= RT lnfiSo if, il = iv = . = iThen,fil = fiv=..=fi

Solution of Simultaneous Equations Multiple equations can be solved only if no. of variables to be solved is at least equal to the independent equations relating those variables.If we have 3 independent equations relating 4 variables, system is called underspecified and cant be solved for the 4 variables.In order to solve this system, we at least need to specify one variable so that we are left with 3 unknown variables & hence 3 equations. This system can now be solved.If more variables are specified than are really needed, system is called over specified.Gibbs Phase Rule [1,2]It tells us the no. of variables to be specified in order to completely specify the state of a system.

F=2- +N= no. of phases N= no. of components

How many variables are required for a pure component existing in two phases?McCabe Thiele Method [3,4,5]Graphical Method

Equilibrium Curve1st step is to draw a x-y diagram with a diagonal line and plot the equilibrium data.

Material Balance LinesDraw the operating lines (obtained through simple material balance) of both the Rectification Section (Top Section) and Stripping Section (Bottom Section) of the column.

Thermal Condition of Feed [5]

Slope of q lineThe q Line has a slope of (q/q-1). If we know the value of q slope can be calculate and q line can be located on McCabe Thiele Diagram.

Locate q Line

Example [5]

Assumptions of McCabe Thiele method [5]The two components have equal and constant molar enthalpies of vaporization (latent heats).Component sensible-enthalpy changes (cpdt) and heat of mixing are negligible compared to latent heat changes.The column is insulated, so heat loss is negligible.Column pressure is uniform (thus, no pressure drop).

Pinch Point [6]A point where operating line coincides the equilibrium line is called pinch point. The location of pinch point in any column may vary depending upon ideality of the system (shape of Equilibrium Curve), no. of components and reflux ratio (i.e. slope of operating lines or internal flow rates of liquid & vapor).When reflux is reduced, slope of operating line (L/D) is reduced and it ultimately touches the equilibrium line. At equilibrium, the gradient for separation is zero hence infinite no. of stages are required to pass from this point.

Location of Pinch Point [3,4,6]If system is Ideal (equilibrium curve is concave downward) Binary (comprising of only two components)At minimum RefluxPinch point lies at Feed Plate.Identify Pinch Point?

[Ref: 4,5,6]ReferencesKoretsky M.D. 2013. Engineering & Chemical Thermodynamics. 2nd ed. John Wiley & Sons, Inc.Smith J.M. Introduction to Chemical Engineering Thermodynamics. 7th ,4th ed., McGraw Hill, Inc.McCabe W.L. et al. Unit operations of chemical engineering. 7th ed., McGraw Hill, Inc.Dutta B.K., Principles of Mass Transfer & Separation Processes., Prentice Hall of India.Seader J.D., Henley E.J., Roper D.K. Separation Process Principles. 3rd ed., John Wiley & Sons, Inc.Perry R.H., Green D.W., Perrys Handbook of Chemical Engineers. 7th ed., McGraw Hill, Inc.