Modelling & Simulation of Binary Distillation Column

“MODELLING & SIMULATION OF BINARY DISTILLATION COLUMN” CONTE NTS • • •

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Introduction Vapour Liquid Equilibrium Types of Distillation 1. Batch Batch Distil Distillat lation ion 2. Contin Continuou uouss Distilla Distillatio tion n Simple Distillation Flash Evaporation Fractional Distillation Types of o f Azeotropes Separation of Azeotropes Steam Distillation Vacuum Distillation Distillati on Extractive Distillation Theoretical plates Methods of calculating no. of stages 1. Fens Fenske ke Equ Equat atio ion n 2. McCabe McCabe-Thi -Thiele ele Method Method Modelling of McCabe-Thiele Method Assumptions of McCabe-Thiele Method Introduction to Simulation Flow Chart of Simulation Program Problem Discussion & Conclusion

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Appendix Bibliography

Introduction A process in which a liquid or vapour mixture of two or more substances is separated into its component fractions of desired purity, by the application and removal of heat. Or in other words: Distillation is a widely used method for separating mixtures based on differences in the conditions required to change the phase of components of the mixture. To separate a mixture of liquids, the liquid can be heated to force components, which have different boiling points, into the gas phase. The gas is then condensed back into liquid form and collected. Repeating the process on the collected liquid to improve the purity of the  product is called double distillation. Although the term is most commonly applied to liquids, the reverse process can be used to separate gases by liquefying components using changes in temperature and/or pressure. Distillation is used for many commercial processes, such as production of  gasoline, distilled water, xylene, alcohol, paraffin, kerosene, and many other  liquids. liquids. Types of distillati distillation on include include simple simple distillat distillation ion (described (described here), fractional distillation (different volatile 'fractions' are collected as they are  produced), and destructive distillation (usually, a material is heated so that it decomposes into compounds for collection). Distillation is based on the fact that the vapour of a boiling mixture will be richer in the components that have lower boiling points. Therefore, when this vapour is cooled and condensed, the condensate will contain more volatile components. At the same time, the original mixture will will contai contain n more more of the less less volati volatile le materi material. al. Distil Distilla latio tion n colum columns ns are designed to achieve this separation efficiently. efficiently. Alth Althou ough gh many many peop people le have have a fair fair idea idea what what “dis “disti till llat atio ion” n” mean means, s, the the important aspects that seem to be missed from the manufacturing point of  view are that:

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Distillation is the most common separation technique. It consumes enormous amounts of energy, both in terms of cooling and heating requirements. It can contribute to more than 50% of plant operating costs.

The best way to reduce operating costs of existing units, is to improve their  efficiency and operation via process optimization and control. To achieve this improvement, a thorough understanding of distillation principles and how distillation systems are designed is essential. The Distillation of the Crude Oil in Oil Refinery can be represented by:

Vapor-Liquid Equilibrium Vapor-liquid equilibrium, abbreviated as VLE by some, is a condition where a liquid and and its its vapor (g vapor (gaas phas phasee) are in equilibrium with with each each othe otherr, a condition or state where the rate of evaporation of  evaporation (liquid changing to vapor) equals the rate of condensation of  condensation (vapor changing to liquid) on a molecular  level level such such that that ther theree is no net net (ove (overa rall ll)) vapo vaporr-li liqui quid d inte interr conv conver ersi sion on.. Although in theory equilibrium takes forever to reach, such an equilibrium is  practically reached in a relatively closed location if a liquid and its vapor are allowed to stand in contact with each other long enough with no interference or only gradual interference from the outside.

VLE Data Introduction The The conc concen entr trat atio ion n of a vapo vaporr in cont contac actt with with its its liqu liquid id,, espe especi cial ally ly at equi equili libr briu ium, m, is ofte often n give given n in terms terms of vapo of vaporr pressure pressure,, whic which h coul could d be a partial pressure (part of the total gas pressure gas  pressure)) if any other gas(es) are  present with the vapor. The equilibrium vapor pressure of a liquid is usually very dependent on temperature. temperature. At vapor-liquid equilibrium, a liquid with individual components (compounds) in certain concentrations will have an equilibrium vapor in which the concentrations or partial pressures of the vapor components will have certain set values depending on all of the liquid component concentrations and the temperature. This fact is true in reverse also also;; if a vapo vaporr with with comp compon onen ents ts at cert certai ain n conc concen entr trat atio ions ns or parti partial al  pressures is in vapor-liquid equilibrium with its liquid, then the component concentratio tions in the liquid wil will be set dependent on the vapor  concentrations, again also depending on the temperature. The equilibrium concentration of each component in the liquid phase is often different from its its conc concen entr trat atio ion n (or (or vapo vaporr pres pressu sure re)) in the the vapo vaporr phas phase, e, but but there there is a corr correl elat atio ion. n. Such Such VLE VLE conc concen entr trat atio ion n data data is ofte often n know known n or can can be dete determ rmin ined ed expe experi rime ment ntal ally ly for for vapo vaporr-liq -liqui uid d mixt mixtur ures es with with vari variou ouss comp compon onen ents ts.. In cert certai ain n case casess such such VLE VLE data data can can be dete determ rmin ined ed or  approximated with the help of certain ain theorie ries such as Raoult's Law, Law, Dalton's Law, Law , and/or Henry's and/or Henry's Law. Law. Such Such VLE VLE info inform rmat atio ion n is usef useful ul in desi desig gning ning columns for distillation for distillation,, especially fractional distillation, distillation , which is a particular specialty of  chemical engineers. engineers. Distil Distillat lation ion is a proces processs used used to separa separate te or partia partially lly separa separate te components in a mixture by  boiling (vap (vapor oriz izati ation on)) foll follow owed ed

 by condensation. condensation. Distillation takes advantage of differences in concentrations of components in the liquid and vapor phases. In mixtures containing two or more components where their concentrations are comp compar ared ed in the the vapo vaporr and and liqu liquid id phas phases es,, conc concen entr trat atio ions ns of each each component are often expressed as mole fractions. fractions . A mole fraction is number  of moles of moles of a given component in an amount of mixture in a  phase (either  vapo vaporr or liqu liquid id phas phase) e) divi divide ded d by the the tota totall numb number er of mole moless of all all components in that amount of mixture in that phase. p hase. Bina Binary ry mixt mixtur ures es are are thos thosee havi having ng two two comp compon onen ents ts.. Thre Threee-co comp mpon onen entt mixt mixtur ures es coul could d be call called ed tern ternar ary y mixt mixtur ures es.. Ther Theree can can be VLE VLE data data for  for  mixtures with even more components, but such data becomes copious and is often hard to show graphically. VLE data is often shown at a certain overall   pre press ssur ure, e, such such as 1 atm or what whatev ever er pres pressu sure re a proc proces esss of inte intere rest st is conducted at. When at a certain temperature, the total of partial pressures of  all the components becomes equal to the overall pressure of the system such that vapors generated from the liquid displace any air or other gas which main mainta tain ined ed the the over overal alll pres pressu sure re,, the the mixt mixtur uree is said said to boil to  boil and the the corr corres espo pond ndin ing g temp temper erat atur uree is the the   boili boiling ng point point(T (Thi hiss assu assume mess exce excess ss  pressure is relieved by letting out gases to maintain a desired total pressure). A boiling point at an overall pressure of 1 atm is called the normal boiling  point.  point.

Thermodynamic Description of Vapor-Liquid Equilibrium The The fiel field d of thermodynamics of thermodynamics describes describes when vapor-li vapor-liquid quid equilibriu equilibrium m is  possible, and its properties. Much of the analysis depends on whether the vapor and liquid consist of a single s ingle component, or if they are mixtures .

Pure (single-component) systems If the liquid and vapor are pure, in that they consist of only one molecular  component and no impurities, then the equilibrium state between the two  phases is described by the following equations:

And

where and are the pressures the pressures within within the liquid liquid and vapor vapor,, and and are are the the temperatures with withiin the the liqu iquid and vapo vaporr, and and and are the molar Gibbs molar Gibbs free energies (units of energy per amount per  amount of  substance) substance) within the liquid and vapor, respectively. [4] In other words, the temperature, pressure and molar Gibbs free energy are the same between the two phases when they are at equilibrium. An equivalent, more common way to express the vapor-liquid equilibrium condition in a pure system is by using the concept of  fugacity. fugacity. Under this view, view, equilibrium is described by the following equation:

where where and are the fugacities of the liquid uid and vapor, respectively, respectively, at the system temperature and pressure . [5] Using fugacity is often more convenient for calculation, given that the fugacity of  the liquid is, to a good approximation, pressure-independent, [6] and it is often convenie convenient nt to use the quantity quantity coefficient, which is 1 for an ideal gas. gas .

, the dimensionl dimensionless ess fugacity fugacity

Multicomponent systems In a multicomponent system, where the vapor and liquid consist of more than than one one type type of mole molecu cule le,, desc descri ribi bing ng the the equi equili libr briu ium m stat statee is more more compli complicat cated. ed. For all componen components ts in the system, system, the equilibr equilibrium ium state  between the two phases is described by the following equations:

where

and

are the temperatur temperaturee and pressure pressure for each phase, phase, and

and and are are the the  par parti tial al mola molarr Gibb Gibbss free free ener energy gyals also o called called chemical  potential (units of energy per  amount of substance) substance ) within the liquid and vapor, respectively, for each phase. The partial molar Gibbs free energy is defined by:

wher wheree is the the (extensive) extensive) Gibb Gibbss free free ene energ rgy y, and and substance of component .

is the the amou amount nt of 

Types Of Distillation Columns There are many types of distillation columns, each designed to perform specific types of separations, and each design differs in terms of complexity. One way of classifying distillation column type is to look at how they are operated. Thus we have: 1. Batch and 2. Continuous columns.

Batch Columns In batch operation, the feed to the column is introduced batch-wise. That is, the column is charged with a 'batch' and then the distillation process is carried out. When the desired task is achieved, a next batch of feed is introduced.

Heating an ideal mixture of two volatile substances A and B (with A having the higher volatility, volatility, or lower boiling point) in a batch distillation setup (such as in an apparatus depicted in the opening figure) until the mixture is boiling results in a vapor above the liquid which contains a mixture of A and B. The ratio between A and B in the vapor will be different from the ratio in the liquid: the ratio in the liquid will be determined by how the original mixture was prepared, while the ratio in the vapor will be enriched in the more volatile compound, A (due to Raoult's Law, see above). The vapor goes through the condenser and is removed from the system. This in turn means

that the ratio of compounds in the remaining liquid is now different from the initial ratio (i.e. more enriched in B than the starting liquid). The result is that the ratio in the liquid mixture is changing, becoming richer  in component B. This causes the boiling point of the mixture to rise, which in turn results in a rise in the temperature in the vapor, which results in a changing ratio of A : B in the gas phase (as distillation continues, there is an incr increa easi sing ng prop propor orti tion on of B in the the gas gas phas phase) e).. This This resu result ltss in a slow slowly ly changing ratio A : B in the distillate. If the difference difference in vapor vapor pressure pressure between the two components components A and B is large (generally expressed as the difference in boiling points), the mixture in the beginning of the distillation is highly enriched in component A, and when when comp compon onen entt A has has dist distil ille led d off, off, the the boil boilin ing g liqui liquid d is enric enriche hed d in component B.

Continuous Columns In contr contrast ast,, conti continuo nuous us column columnss proces processs a contin continuou uouss feed feed stream stream.. No interruptions occur unless there is a problem with the column or surrounding  process units. They are capable of handling high throughputs and are the most common of the two types. We shall concentrate only on this class of  columns. Continuous distillation is an ongoing distillation in which a liquid mixture is contin continuou uously sly (with (without out interru interrupti ption) on) fed into into the proces processs and separa separated ted fractions are removed continuously as output streams as time passes during the operation. Continuous distillation produces at least two output fractions, including at least one volatile distillate distillate fraction, fraction, which which has boiled boiled and been separately captured as a vapor condensed to a liquid. There is always a  bottoms (or residue) fraction, which is the least volatile residue that has not  been separately captured as a condensed vapor. Contin Continuou uouss distil distillat lation ion differ differss from from batch batch distill distillati ation on in the respect respect that that concentrati concentrations ons should should not change change over time. Continuou Continuouss distillat distillation ion can be run at a steady state for an arbitrary amount of time. Given a feed of in a specified composition, the main variables that affect the purity of products in continuous distillation are the reflux ratio and the number of theoretical equilibrium stages (practically, (practically, the number of trays or the height of packing). Reflux is a flow from the condenser back to the column, which generates a recyc recycle le that that allo allows ws a bett better er sepa separa rati tion on with with a give given n numb number er of tray trays. s. Equilibrium stages are ideal steps where compositions achieve vapor-liquid

equilibrium, repeating the separation process and allowing better separation given a reflux ratio. A column with a high reflux ratio may have fewer  stages, but it refluxes a large amount of liquid, giving a wide column with a large holdup. Conversely, Conversely, a column with a low reflux ratio rat io must have a large number of stages, thus requiring a taller column. Cont Contin inuo uous us dist distil illa lati tion on requ requir ires es buil buildi ding ng and and conf config igur urin ing g dedi dedica cate ted d equipment. The resulting high investment cost restricts its use to the large scale.

Types of Continuous Columns Continuous columns can be further classified according to: f eed that they are processing 1. The nature of the feed • •

Binary column - feed contains only two components. Mult Multii-co comp mpon onen entt colu column mn - feed feed cont contai ains ns more more than than two two components.

2. The number of product streams they have •

MultiMulti-pro produc ductt column column - colum column n has more more than than two product product streams.

3. Wher Wheree the extra xtra fee feed exit exitss when hen it is used sed to help elp with ith the the separation •

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Extrac Extractiv tivee distil distilla latio tion n - where where the extra extra feed feed appear appearss in the  bottom product stream. Azeotropic distillation - where the extra feed appears at the top  product stream.

4. The type of column internals •

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Tray column - where trays of various designs are used to hold up the liqui liquid d to provid providee better better contac contactt betwee between n vapour vapour and liquid, hence better separation. Packed column - where instead of trays, 'Packing' are used to enhance contact between vapour and liquid.

Simple Distillation

In simple distillation, all the hot vapors produced are immediately channeled into into a conden condenser ser which which cools cools and conde condense nsess the vapors. vapors. Therefor Therefore, e, the distillate will not be pure its composition will be identical to the composition of the vapors at the given temperature and pressure, and can be computed from Raoult's law. law. As a result, simple distillation is usually used only to separate liquids whose  boiling points differ greatly (rule of thumb is 25 °C) [25] or to separate liquids from in volatile solids or oils. For these cases, the vapor pressures of  the components are usually sufficiently different that Raoult's law may be negl neglec ecte ted d due due to the the insi insig gnifi nifica cant nt cont contri ribu buti tion on of the the less less vola volati tile le comp compon onen ent. t. In this this case case,, the the dist distil illa late te may may be suff suffic icie ient ntly ly pure pure for for its its intended purpose.

The liquid mixture that is to be processed is known as the feed and this is introduced usually somewhere near the middle of the column to a tray

know known n as the the feed feed tray tray.. The The feed feed tray tray divi divide dess the the colu column mn into into a top top (enriching or rectification) section and a bottom (stripping) (str ipping) section. The feed flows down the column where it is collected at the bottom in the reboiler. Heat is supplied to the reboiler to generate vapour. The source of heat input can be any suitable fluid, although in most chemical plants this is normally steam. In refineries, refineries, the heating source may be the output streams of other  columns. columns. The vapour vapour raised in the reboiler is re-introduced re-introduced into into the unit at the bottom of the column. The liquid removed from the reboiler is known as the bottoms product or simply, simply, bottoms.

The vapour moves up the column, and as it exits the top of the unit, it is cooled by a condenser. The condensed liquid is stored in a holding vessel known as the reflux drum. Some of this liquid is recycled back to the top of  the the colu column mn and and this this is call called ed the the refl reflux ux.. The The cond conden ense sed d liqu liquid id that that is removed from the system is known as the distillate or top product. Thus, there are internal flows of vapour and liquid within the column as well as external flows of feeds and product streams, into and out of the column.

Flash Evaporation Flash Flash (or partia partial) l) evaporation is the partia partiall vaporization that that occurs occurs when when a saturated saturated liquid liquid stre stream am unde underg rgoe oess a reduc reducti tion on in pres pressu sure re by pass passin ing g through a throttling valve or other throttling device. This process is one of  the simplest unit operations. operations . If the throttling valve or device is located at the entry into a press a  pressure ure vessel so that the flash evaporation occurs within the vessel, then the vessel is often referred to as a flash drum. drum. If the the satu satura rate ted d liqu liquid id is a sing single le-c -com ompo pone nent nt liqu liquid id (for (for exam exampl ple, e, liquid propane liquid propane or liquid ammonia), ammonia), a part of the liquid immediately "flashes" into vapor. Both the vapor and the residual liquid are cooled to the saturation

temperature of the liquid at the reduced pressure. This is often referred to as "auto-refrigeration" and is the basis of most conventional vapor compression refrigeration systems. If the saturated liquid is a multi-component liquid (for example, a mixture of  propane,  propane, isobutane and normal butane normal butane), ), the flashed vapor is richer in the more volatile components than is the remaining liquid.

Flash Evaporation of a Single-Component Liquid The flash flash evapora evaporati tion on of a single single-com -compon ponent ent liquid liquid is an isentr isentropi opicc i.e., i.e., constant entropy) entropy) process and is often referred to as an adiabatic flash. flash. The following equation, derived from a simple heat balance around the throttling valve or device, is used to predict how much of a single-component liquid is vaporized.

X = 100 (HuL – HdL) ÷ (HdV – HdL)

where: X

= weight percent vaporized

HuL

= upst upstrea ream m liqu liquid id enth enthal alpy py at upst upstre ream am temp temper erat atur uree and and  pressure, J/kg

HdV

= flas flash hed vapo vaporr enth nthalp alpy at down downst stre ream am pres pressu sure re and and corresponding saturation temperature, J/kg

HdL

= resi residu dual al liqu liquid id enth enthal alpy py at down downst stre ream am pres pressu sure re and and corresponding saturation temperature, J/kg

If the enthalpy data required for the above equation is unavailable, then the following equation may be used.

X = 100 · cp (Tu – Td) ÷ Hv where: X

= weight perce rcent vaporized

c p

= liquid specific heat at upstream temperature and pressure, J/(kg °C)

Tu

= upstream liquid temperature, °C

Td

= liquid saturation temperature corresponding to the downstream pressure, °C

Hv

= liqu liquid id heat heat of vapori vaporiza zatio tion n at down downst stre ream am pres pressu sure re and and corresponding saturation temperature, J/kg

(Note: The words "upstream" and "downstream" refer to before and after the liquid passes through the throttling valve or device.) This type of flash evaporation e vaporation is used in the desalination of brackish water or  ocea ocean n wate waterr by "Multi-Stage Flash Distillation." The water is heated and then routed into a reduced-pressure flash evaporation "stage" where some of  the water flashes into steam. This steam is subsequently condensed into saltfree water. The residual salty liquid from that first stage is introduced into a seco second nd flas flash h evap evapor orati ation on stag stagee at a pres pressu sure re lowe lowerr than than the the firs firstt stag stagee   press pressure ure.. More More water water is flashe flashed d into into steam steam which which is also also subseq subsequen uently tly

condensed into more salt-free water. This sequential use of multiple flash evaporation stages is continued until the design objectives of the system are met. A large part of the world's installed desalination capacity uses multistage flash distillation. Typically such plants have 24 or more sequential stages of flash evaporation.

Equilibrium Flash of a Multi-Component Liquid The equilibrium flash of a multi-component liquid may be visualized as a simple distillation proc proces esss usi using a sing single le equilibriu equilibrium m stage stage . It is very different and more complex than the flash evaporation of single-component liquid. liquid. For a multi-com multi-componen ponentt liquid, liquid, calculating calculating the amounts of flashed flashed vapo vaporr and and resi residu dual al liqu liquid id in equi equili libr briu ium m with with each each othe otherr at a give given n temperature and pressure requires a trial-and-error  iterative solution. Such a calculation is commonly referred to as an equilibrium flash calculation. It involves solving the Rachford-Rice equation:

Where: zi is the mole fraction of component i in the feed liquid (assumed to be known); β is the fraction of feed that is vaporised; K i is the equilibrium constant of component i. The equilibrium constants K i are in general functions of many parameters, though the most important is arguably temperature; they are defined as:

Where: xi is the mole fraction of component i in liquid phase; yi is the mole fraction of component i in gas phase.

Once the Rachfo hford-Rice equation has been solved compositions xi and yi can be immediately calculated as:

for  β,

the

The Rachford-Rice equation can have multiple solutions for  β, at most one of which guarantees that all xi and yi will be positive. In particular, particular, if there is only one β for which:

Then Then that that β is the solution; if there are multiple such β's, it means that either K max max1, indicating respectively that no gas phase can be sustained (and therefore β=0) or conversely that no liquid phase can exist (and therefore β=1). It is possible to use Newton's use  Newton's method for solving the above Rachford-Rice equation, but there is a risk of converging to the wrong value of  β; it is impo import rtan antt to initi nitial aliz izee the the solv solver er to a sens sensib ible le init initia iall valu value, e, such such as (βmax+βmin)/2 (which is however not sufficient: Newton's method makes no guarantees on stability), or, alternatively, use a bracketing solver such as the  bisection or the Brent method, method , which are guaranteed to converge but can be slower. The equilibrium flash of multi-component liquids is very widely utilized in  in  petroleu petroleum m refineries refineries,, petrochemical and chemical chemical plants plants and natura naturall gas  processing plants.

Fractional Distillation Fractional distillation is the separation of a mixture into its component parts, or fract fractio ions ns,, such such as in sepa separat ratin ing g chemical chemical compounds compounds by thei their  r  boiling  boiling  point by heating them to a temperature at which several fractions of the compound will evaporate. It is a special type of  distillation. distillation. Generally the component parts boil at less than 25 °C from each other under a pressure of 

one atmosphere (atm ( atm). ). If the difference in boiling points is greater than 25 °C, a simple distillation is used.

Using the Phase Diagram

If you boil a liquid mixture C1, you will get a vapour with composition C2, which you can condense to give a liquid of that same composition (the pale   blu bluee line lines) s).. If you you rebo reboil il that that liqu liquid id C2, C2, it will will give give a vapo vapour ur with with composition C3. Again you can condense that to give a liquid of the same new composition (the red lines). Reboiling the liquid C3 will give a vapour still richer in the more volatile component B (the green lines). You can see that if you were to do this once or twice more, you would be able to collect a liquid which was virtually pure B. The secret of getting the more volatile component from a mixture of  liquid liquidss is obviou obviously sly to do a succes successio sion n of boili boilingng-con conden densin sing-r g-rebo eboili iling ng operations. It isn't quite so obvious how you get a sample of pure A out of  this. That will become clearer in a while.

The Vapour This new vapour will again move further up the fractionating column until it gets to a temperature where it can condense. Then the whole process repeats itself. Each time the vapour condenses to a liquid, this liquid will start to trickle  back down the column where it will be reboiled by up-coming hot vapour. Each time this happens the new vapour will be richer in the more volatile component. The aim is to balance the temperature of the column so that by the time vapour reaches the top after huge numbers of condensing and reboiling operations, it consists only of the more volatile component - in this case, B.

Whet Whethe herr or not not this this is poss possib ible le depe depend ndss on the the dif differen ference ce betw betwee een n the the  boiling points of the two liquids. The closer they are together, the longer the column has to be.

The Liquid So what about the liquid left behind at each reboiling? Obviously, if the vapour is richer in the more volatile component, the liquid left behind must  be getting richer in the other one. As the condensed liquid trickles down the column constantly being reboiled  by up-coming vapour, each reboiling makes it richer and richer in the less volatile component - in this case, A. By the time the liquid drips back into the flask, it will be very rich in A indeed. indeed. So, over time, as B passes out of the top of the column into the condenser, the liquid in the flask will become richer in A. If you are very, very careful over temperature control, eventually you will have separated the mixture into B in the collecting flask and A in the original flask. Finally, Finally, what is the point of the packing in the column? To make the boiling-condensing-reboiling process as effective as possible, it has to happen over and over again. By having a lot of surface area inside the column, you aim to have the maximum possible contact between the liquid trickling down and the hot vapour rising. If you didn't have the packing, the liquid would all be on the sides of the condenser, while most of the vapour would be going up the middle and never come into contact with it.

Azeotrope An Azeotrope (pronounced /ay-ZEE-ə-trope/) is a mixture of two or more liquids (chemicals) in such a ratio that its composition cannot be changed by simple distillation. distillation. This occurs because, when an azeotrope is boiled, the resulting vapor has the same ratio rat io of constituents as the original mixture. Because their composition is unchanged by distillation, azeotropes are also cal called led (esp (espec eciially lly in olde olderr text exts) const onstan antt boilin iling g mixt mixtu ures. res. The The word azeotrope is derived from the Greek words ζέειν (boil) and τρόπος (change) combined with the prefix α- (no) to give the overall meaning, “no change on boiling.”

Types of Azeotropes Each azeotrope has a characteristic  characteristic   boiling point. point. The boiling point of an azeotrope is either less than the boiling points of any of its constituents (a   pos posit itiv ivee azeo azeotr trop ope) e),, or grea greate terr than than the the boil boilin ing g poin pointt of any any of its its constituents (a negative azeotrope). A well known example of a positive azeotrope is 95.6% ethanol and 4.4% water (by weight). Ethanol boils at 78.4°C, water boils at 100°C, but the azeotrope boils at 78.1°C, which is lower than either of its constituents. Indeed Indeed 78.1°C 78.1°C is the minimu minimum m temper temperatu ature re at which which any ethano ethanol/w l/wate ater  r  solu soluti tion on can can boil boil.. In gene genera ral, l, a posi positi tive ve azeo azeotr trop opee boils oils at a lowe lower  r  temperature than any other ratio of its constituents. Positive azeotropes are also called minimum boiling mixtures. An example of a negative azeotrope is hydrochloric acid at a concentration of 20.2 20.2% % hydrogen hydrogen chloride chloride and and 79.8 79.8% % wate waterr (by (by weig weight ht). ). Hydr Hydrog ogen en chloride boils at –84°C and water at 100°C, but the azeotrope boils at 110°C, which is higher than either of its constituents. The maximum temperature at whic which h any any hydr hydroc ochl hlori oricc acid acid solu soluti tion on can can boil boil is 110°C 10°C.. In gene genera ral, l, a negative azeotrope boils at a higher temperature than any other ratio of its constituents. Negative azeotropes are also called maximum boiling mixtures. Azeotropes consisting of two constituents, such as the two examples above, are called called binar binary y azeotr azeotrope opes. s. Those Those consis consistin ting g of three three consti constitue tuents nts are called called ternary ternary azeotrope azeotropes. s. Azeotrope Azeotropess of more than three constituen constituents ts are also known. More than 18,000 azeotropic mixtures have been documented. Combinations of solvents that do not form an azeotrope when mixed in any  proportion are said to be zeotropic. zeotropic. When running a binary distillation it is often helpful to know the azeotropic composition of the mixture.

Separation of Azeotrope Constituents Distillation is one of the primary tools that chemists and chemical engineers use to separate mixtures into their constituents. Because distillation cannot separa separate te the consti constitue tuents nts of an azeotr azeotrope ope,, the separa separatio tion n of azeotr azeotropi opicc mixt mixtur ures es (als (also o call called ed azeo azeotr trop opee brea breaki king ng)) is a topi topicc of cons consid idera erabl blee interest. Indeed this difficulty led some early investigators to believe that azeotropes were actually compounds of their constituents. But there are two

reasons for believing that this is not the case. One is that the molar ratio molar ratio of  the constituents of an azeotrope is not generally the ratio of small integers. For example, the azeotrope azeotrope formed by water and acetonitrile contains 2.253 moles of acetonitrile for each mole of water. A more compelling reason for    believing that azeotropes are not compounds is, as discussed in the last section, that the composition of an azeotrope can be affected by pressure. Contrast that with a true compound, carbon dioxide for example, which is two moles of oxygen for each mole of carbon no matter what pressure the gas is observed at. That azeotropic composition can be affected by pressure suggests a means by which such a mixture can be separated.

Azeotropi Azeo tropicc Distilla ist illation tion Other methods of separation involve introducing an additional agent, called an Entr Entrai aine nerr, that that will will affe affect ct the the volatility of one of the azeotrope constituents more than another. When an entrainer is added to a binary azeotrope to form a ternary azeotrope, and the resulting mixture distilled, the method is called azeotropic distillation. The best known example is adding  benzene or cyclohexane or cyclohexane to the water/ethanol azeotrope. With With cyclohexane as the entrainer, the ternary azeotrope is 7% water, 17% ethanol, and 76% cyclohexane, and boils at 62.1°C. Just enough cyclohexane is added to the water/ethanol azeotrope to engage all of the water into the ternary azeotrope. When the mixture is then boiled, the azeotrope vaporizes leaving a residue composed almost entirely of the excess ethanol.

Chemical Action Separation Another type of entrainer is one that has a strong chemical affinity for one of  the constituents. Using again the example of the water/ethanol azeotrope, the liquid can be shaken with calcium oxide, oxide , which reacts strongly with water to form form the the nonvolatile compound, calcium calcium hydroxide hydroxide.. Nearly all of the calcium hydroxide can be separated by filtration and the filtratere filtratere distilled to obtain nearly pure ethanol. A more extreme example is the azeotrope of 1.2% water with 98.8% diethyl ether . Ether holds the last bit of water so tenaciously that only a very  powerful desiccant such as sodium metal added to the liquid phase can result in completely dry ether. ether.

Anhydrous calcium chloride is used as a desiccant desiccant for drying drying a wide variety variety of solv solven ents ts sinc sincee it is inex inexpe pens nsiv ivee and and does does not not reac reactt with with most most non aqueous solvents. Chloroform is an example of a solvent that can be effectively dried using calcium chloride.

Distillation using a Dissolved Salt When a salt is dissolved in a solvent, it always has the effect of raising the  boiling point of that solvent - that is it decreases the volatility of the solvent. When the salt is readily soluble in one constituent of a mixture but not in another, the volatility of the constituent in which it is soluble is decreased and and the the othe otherr const constit itue uent nt is unaf unaffe fect cted ed.. In this this way way, for for examp example le,, it is   pos possi sibl blee to brea break k the the wate water/ r/et etha hano noll azeo azeotro trope pe by diss dissol olvi ving ng potassium  potassium acetate in it and distilling the result.

Examples of azeotropes azeotropes Proportions are by weight : •

• •

• • •

•

•

nitric nitric acid acid (68 (68%) / water , boil boilss at 120. 120.5 5°C at 1 atm atm (ne (negat gative ive azeotrope)  perchloric acid (28.4%) / water, boils at 203°C (negative azeotrope) hydrofluori hydrofluoricc acid (35. (35.6% 6%)) / water ater,, boil boilss at 111.35 1.35°C °C (neg (negat ativ ivee azeotrope) ethanol (96%) / water, boils at 78.1°C sulfuric acid (98.3%) / water, boils at 338°C acetone / methanol / chloroform form an intermediate boiling (saddle) azeotrope diethyl ether (33%) ether  (33%) / halothane (66%) a mixture once commonly used in anaesthesia. anaesthesia.  benzene / hexafluorobenzene forms a double binary azeotrope.

Complex Azeotrope Azeotrope Systems The rules for positive and negative azeotropes apply to all the examples disc discus usse sed d so far far. But But ther theree are some some examp example less that that don' don'tt fit fit into into the the categories of positive or negative azeotropes. The best known of these is the ternary azeotrope formed by 30% acetone, acetone, 47%chloroform, chloroform, and 23% methanol, methanol, which boils at 57.5°C. Each pair of these constituents forms a binary binary azeotrope, azeotrope, but chloroform/ chloroform/metha methanol nol and acetone/me acetone/methano thanoll both form form posi positi tive ve azeo azeotr trop opes es whil whilee chlo chloro rofo form/ rm/ac acet eton onee forms forms a nega negati tive ve azeotrope. The resulting ternary azeotrope is neither positive nor negative. Its boiling point falls between the boiling points of acetone and chloroform, so it is neither a maximum nor a minimum boiling point. This type of system is called a Saddle Azeotrope. Only systems of three or more constituents can form saddle azeotropes.

A rare type of complex binary azeotrope is one where the boiling point and condensation point curves touch at two points in the phase diagram. Such a syst system em is call called ed a doub double le azeo azeotr trop ope, e, and and will will have have two two azeo azeotr trop opic ic compositions and boiling points. An exampl mple is water and Nmethylethylenediamine.

Steam Distillation Steam Steam dist distil illa lati tion on is a spec specia iall type type of distillation of distillation (a separation separation process process)) for temperature sensitive materials like natural aromatic compounds. Many organic compounds tend to decompose at high sustained temperatures. Separation by normal distillation would then not be an option, so water  or steam or steam is introduced into the distillation apparatus. By adding water or  steam, the boiling the boiling points of the compounds are depressed, allowing them to evaporate at lower temperatures, preferably below the temperatures at which the deterioration of the material becomes appreciable. If the substances to be distilled are very sensitive to heat, steam distillation can also be combined with vacuum distillation. distillation . After distillation distillation the vapors are condensed as usual, usually yielding a two-  two-  phase system of water and the organic compounds, allowing for simple separation.

Principle When a mixture of two practically immiscible liquids is heated while being agitated to expose the surfaces of both the liquids to the vapor phase, each constitue constituent nt independe independently ntly exerts exerts its own vapor vapor pressure pressure as a function of  temperature as if the other constituent were not present. Consequently, the vapor pressure of the whole system increases. Boiling begins when the sum of the  parti partial al pressu pressures resof of the the two two immi immisc sciible ble liquids uids just exce exceed edss the atmospheric pressure (approximately 101 kPa at sea level). In this way, many organic compounds insoluble in water can be purified at a temperature well well below below the point point at which which decomp decomposi ositio tion n occurs occurs.. For exampl example, e, the  boiling point of  bromobenzene  bromobenzene is 156 °C and the boiling point of water is 100 °C, but a mixture of the two boils at 95 °C. Thus, bromobenzene can be easily distilled at a temperature 61 C° below its normal boiling point.

Applications Steam Steam distil distillat latio ion n is employ employed ed in the manufa manufactu cture re of essen of  essential tial oils, oils, for  instance, perfumes instance, perfumes.. In this this meth method od,, stea steam m is pass passed ed thro throug ugh h the the plan plantt material containing the desired oils. It is also employed in the synthetic   pro proce cedu dure ress of comp comple lex x orga organi nicc comp compou ound nds. s.Euc Eucaly alyptu ptuss oil and orange oil are obtained by this method on the industrial scale. Steam distillation is also widely used in  petroleum refineries and petrochemical and petrochemical plan plants ts wher wheree it is comm common only ly refer referre red d to as "steam stripping". Othe Otherr indu indust stri rial al uses uses of stea steam m dist distil illa lati tion on incl includ udee the the prod produc ucti tion on of  consumer food products such as sprayable or aerosolized condiments such as sprayable mayonnaise.

Vacuum Distillation Vacuum distillation is a method of  distillation whereby the pressure above the the liq liquid uid mixt mixtur uree to be dist istill illed is redu reduce ced d to less ess than than its its vapor   pressure(usually  pressure(usually less than atmospheric pressure) pressure ) causing evaporation of the most volatile liquid(s) (those with the lowest  boiling points ). This distillation method method works on the principle principle that boiling boiling occurs when the vapor pressure pressure of a liquid exceeds the ambient pressure. Vacuum distillation is used with or  without heating the solution.

Applications Laboratory-s Laboratory-scale cale vacuum distillat distillation ion is used when liquids liquids to be distilled distilled have high atmospheric boiling points or  chemically change at temperatures near their atmospheric boiling points. Temperature sensitive materials (such as beta as beta carotene) carotene ) also require vacuum distillation to remove solvents from the the mixt mixtur uree with withou outt dama damagi ging ng the the prod produc uct. t. Anot Anothe herr reas reason on vacu vacuum um distillation is used is that compared to steam distillation there is a lower level of resi residu duee buil build d up. This This is impo import rtan antt in comm commer erci cial al appl applic icat atiions ons where temperature transfer is transfer is produced using heat exchangers. exchangers . Vacuum distillation is sometimes referred to as low temperature distillation. Typical ypical indust industria riall applic applicati ations ons utiliz utilizee the heat heat pump pump cycle cycle to maximi maximize ze effi effici cien ency cy.. This This type type of dist distil illa lati tion on is in use use in the the oil indust industry ry where common ASTM stan standa dard rdss are are D116 D1160, 0, D289 D2892, 2, D523 D5236. 6. Thes Thesee stan standa dard rdss describe typical applications of vacuum distillation at pressures of about 1100 mbar . Pilot plants up to 60 L can be built in accordance with these standards. Industrial-scale vacuum distillation has several advantages. Close  boiling mixtures may require many equilibrium stages to separate the key components. One tool to reduce the number of stages needed is to utilize vacuum vacuum distillati distillation. on.[6] [6] Vacuum acuum distil distillat lation ion column columnss (as depict depicted ed in the drawing to the right) typically used in oil refineries have diameters ranging up to about 14 meters (46 feet), heights ranging ranging up to about 50 meters (164 feet) feet),, and and feed feed rate ratess rang rangin ing g up to abou aboutt 25,4 25,400 00 cubi cubicc mete meters rs per per day day (160,000 barrels per day). Vacuum distillation increases the relative volatility of the key components in many applications. The higher the relative volatility, the more separable are the two components; this connotes fewer stages in a distillation column in order order to effec effectt the same same separa separatio tion n betwee between n the overhe overhead ad and botto bottoms ms  products. Lower pressures increase relative volatilities in most systems. A second second advant advantage age of vacuum vacuum distil distilla latio tion n is the the reduce reduced d temper temperatu ature re requirement requirement at lower lower pressures. pressures. For many systems, the products products degrade or   polymerize at elevated temperatures. Vacuum distillation can improve a separation by: •

•

Prevention of product degradation or polymer formation because of  reduced pressure leading to lower tower bottoms temperatures, Reduction of product degradation or polymer formation because of  reduced mean resid sidence time especially in columns mns using  packing rather than trays. trays.

Increasing capacity, yield, and purity. Another Another advantage advantage of vacuum vacuum distillati distillation on is the reduced capital capital cost, at the expense of slightly more operating cost. Utilizing vacuum distillation can reduce the height and diameter, and thus the capital cost of a distillation column. •

Extractive Distillation Extractive distillation is similar to azeotropic distillation, except in this case the entrainer is less volatile than any of the azeotrope's constituents. For  example, the azeotrope of 20%acetone 20% acetone with 80% chloroform can be broken  by adding water and distilling the result. The water forms a separate layer in which the acetone preferentially dissolves. The result is that the distillate is richer in chloroform than the original azeotrope.

Theoretical Plate A theoretical plate in many separation processes is a hypothetical zone or  stage in which two phases, such as the liquid and vapor phases vapor phases of a substance, establish an equilibrium with each other. Such equilibrium stages may also be referred to as an equilibrium stage or a theoretical tray. tray. The  performance of many separation processes depends on having a series of  equilibrium stages and is enhanced by providing more such stages. In other  words, having more theoretical plates increases the efficacy of the separation  process be it either a distillation, distillation, absorption, absorption, chromatographic, chromatographic, adsorption or  similar process.

Applications The concept of theoretical plates and trays or equilibrium stages is used in the design of many different types of separation.

In Distillation Columns

The concept of theoretical plates in designing distillation processes has been discussed in many reference texts. Any physical device that that provides good cont contac actt betw betwee een n the the vapo vaporr and and liqu liquid id phas phases es pres presen entt in indu indust stri rial al-scale distillation columns or laboratory-scale glassware distillation columns constitutes a "plate" or "tray". Since an actual, physical plate is rarely a 100% efficient equilibrium stage, the number of actual plates is more than the required theoretical plates.

where:  Na

= the number of actual, physical plates or trays

 Nt E

= the number of theoretical plates or trays = the plate or tray efficiency

So-called bubble-cap or valve-cap trays are examples of the vapor and liquid contact contact devices devices used in industria industriall distillati distillation on columns. columns. Another Another example example of  vapo vaporr and and liqu liquid id cont contac actt devi device cess are are the the spik spikes es in labo labora rato tory ry Vigreux fractionating columns. columns . The trays or plates used in industrial distillation columns are fabricated of  circular steel plates and usually installed inside the column at intervals of  about 60 to 75 cm (24 to 30 inches) up the height of the column. That spacing is chosen primarily for ease of installation and ease of access for  future repair or maintenance.

Typical bubble cap trays used in industrial distillation columns

For example, a very simple tray would be a perforated tray. The desired vapor vapor and liquid liquid contac contactin ting g would would occur occur as the vapor vapor flowin flowing g upward upwardss throug through h the perfor perforati ations ons would would contac contactt the liquid liquid flowin flowing g downwa downwards rds thro throug ugh h the the perf perfor orati ation ons. s. In curre current nt mode modern rn prac practi tice ce,, as show shown n in the the adjacent diagram, better contacting is achieved by installing bubble-caps or  valve caps located at each perforation to promote the formation of vapor   bubbles flowing through a thin layer of liquid maintained by a weir on weir on each tray. To design a distillation unit or a similar chemical process, the number of  theore theoretic tical al trays trays or plate platess (that (that is, hypot hypothet hetica icall equili equilibri brium um stages stages), ), N t, required in the process should be determined, taking into account a likely range of feedstock composition and the desired degree of separation of the components in the output fractions. In industrial continuous fractionating columns, N t is determined by starting at either the top or bottom of the column column and calcul calculati ating ng materi material al balanc balances, es, heat heat balanc balances es and equilibrium flash vaporizations for each of the succession of equilibrium stages until the desire desired d end produc productt compo composit sition ion is achiev achieved. ed. The calcul calculati ation on proces processs requires the availability of a great deal of  vapor-liquid equilibrium data for  the components present in the distillation feed, and the calculation procedure is very complex. In an indust industria riall distil distilla latio tion n column column,, the N t requir required ed to achiev achievee a given given separation also depends upon the amount of  reflux used. Using more reflux decreases the number of plates required and using less reflux increases the number number of plates plates required. required. Hence, the calculatio calculation n of N t is usually repeated at various various reflux reflux rates. rates. N t is then then divide divided d by the tray tray effic efficien iency cy,, E, to determine the actual number of trays or physical plates, Na, needed in the separating column. The final design choice of the number of trays to be installed in an industrial distillation column is then selected based upon an economic balance between the cost of additional trays and the cost of using a higher reflux rate. Ther Theree is a very very impo import rtan antt dist distiincti nction on betw betwee een n the the theo theore reti ticcal plat platee termin terminolo ology gy used used in discus discussin sing g conven conventio tional nal distil distilla latio tion n trays trays and the theoretical plate terminology used in the discussions below of packed bed distillation or absorption or in chromatography or other applications. The theore theoretic tical al plate plate in conve conventi ntiona onall distil distilla latio tion n trays trays has no "heigh "height". t". It is simply a hypothetical equilibrium stage. However, the theoretical plate in  packed beds, chromatography and other applications is defined as having a height.

Distillation and absorption packed beds Distillation and absorption separation processes using packed using  packed beds for vapor  and liquid contacting have an equivalent concept referred to as the plate height or the height equivalent to a theoretical plate (HETP). HETP arises from the same concept of equilibrium stages as does the theoretical plate and is numerical numerically ly equal to the absorption absorption bed length length divided by the number of  theoretical plates in the absorption bed (and in practice is measured in this way).

where: Nt = the number of theoretical plates (also called the "plate count") H = the total bed height HETP = the height equivalent to a theoretical plate

The material in packed beds can either be random dumped packing (1-3" wide) such structured sheet metal. Liquids tend to wet the surface of the as Raschig rings or structured  packing and the vapors contact the wetted surface, where mass transfer occurs.

Chromatographic Processes The theoretical plate concept was also adapted for chromatographic for chromatographic proc rocesse essess by Martin and Synge. Synge. The IUPAC's IUPAC's Gold Book pr Book prov ovid ides es a defi defini niti tion on of the the numb number er of theo theore reti tica call plat plates es in a chromatography column. The same equation applies in chromatography processes as for the packed  bed processes, namely:

where: Nt = the number of theoretical plates (also called the "plate count") H = the total column length HETP = the height equivalent to a theoretical plate

Other Methods for Calculating No. of Trays There are two different methods for calculating the no. of trays in Distillation Column.

Fenske Equation The Fenske equation in continuous fractional distillation is an equation used for calculating the minimum number of theoretical of  theoretical plates required for the separation of a binary feed stream by a fractionation column that is being operated at total reflux (i.e., which means that no overhead product distillate is being withdrawn from the column). The equati equation on was derived derived by Merrel Merrelll Fenske Fenske in 1932, 1932, a profes professor sor who who served as the head of the chemic chemical al engine engineeri ering ng depa depart rtme ment nt at the Pennsylvania State University from 1959 to 1969. This is one of the many different but equivalent versions of the Fenske equation:

where: N

= minimum number of theoretical plates required at total reflux (of  which the reboiler is one)

Xd

= mole fraction of more volatile component in the overhead distillate = mole fraction of more volatile component in the bottoms

Xb αavg

= average relative volatility of more volatile component to less volatile component

For ease of expression, the more volatile and the less volatile components are commonly referred to as the light key (LK) and the heavy key (HK), respectively. If the relative volatility of the light key to the heavy key is constant from the column top to the column bottom, then αavg. is simply α. If the relative volatility is not constant from top to bottom of the column, then the following approximation may be used:

where:

αt αb

= relative volatility of light key to heavy key at top of column = relative volatility of light key to heavy key at bottom of column

The above Fenske equation can be modified for use in the total reflux distillation of multi-component feeds.

Another form of the Fenske Equation A deri deriva vati tion on of anot anothe herr form form of the the Fens Fenske ke equat quatio ion n for for use use in gas gas chromatograp raphy is available on the U.S. U.S. Naval aval Acad cademy' emy'ss web site. Using Raoult's law and Dalton's Law for a series of condensation and evaporatio evaporation n cycles cycles (i.e., (i.e., equilibriu equilibrium m stages stages ), the the foll follow owin ing g form form of the the Fenske equation is obtained:

where: N = number of equilibrium stages Zn = mole fraction of component n in the vapor phase Xn

= mole fraction of component n in the liquid phase = vapor pressure of pure component n

McCabe-Thiele Method The The grap graphi hica call appr approa oach ch pres presen ente ted d by McCa McCabe be and and Thie Thiele le in 1925 1925,, the McCabe McCabe-Th -Thiel ielee method method is consid considere ered d the simple simplest st and perhap perhapss most most instructive method for analysis of binary distillation. distillation. This method uses the fact that the composition at each theoretica theoreticall tray (or equilibrium (or equilibrium stage) stage) is completely determined by the mole fraction of one of the two components. The McCabe-Thiele method is based on the assumption of constant molar  overflow which requires that: • • •

The molal heats of vaporization of the feed components are equal for every mole of liquid vaporized, a mole of vapour is condensed heat effects such as heats of solution and heat transfer to transfer to and from the distillation column are negligible.

Construction and use of the McCabe-Thiele Diagram Before starting the construction and use of a McCabe-Thiele diagram for the distillation of a binary feed, the vapor-liquid vapor-liquid equilibrium (VLE) data must be obtained for the lower-boiling component of the feed.

Figure 1: Typical McCabe-Thiele diagram for distillation of a binary feed

The first step is to draw equal sized vertical and horizontal axes of a graph. The horizontal axis will be for the mole fraction (denoted by x) of the lower boiling feed component in the liquid phase. The vertical axis will be for the mole fraction (denoted by y) of the lower-boiling feed component in the vapor phase. The next step is to draw a straight line from the origin of the graph to the  point where x and y both equal 1.0, which is the x = y line in Figure 1. Then draw the equilibrium line using the VLE data points of the lower boiling component, representing the equilibrium vapor phase compositions for each valu valuee of liqu liquid id phas phasee comp compos osit itio ion. n. Also Also draw draw vert vertic ical al line liness from from the the hori horizo zont ntal al axis axis up to the the x = y line line for for the the feed feed and and for for the the desi desire red d compositions of the top distillate product and the corresponding bottoms  product (shown in red in Figure 1). The next step is to draw the operating line for the rectifying section (the section above the feed inlet) of the distillation column, (shown in green in Figure 1). Starting at the intersection of the distillate composition line and the x = y line, draw the rectifying operating line at a downward slope (Δy/Δx) of  L / (D + L) where L is the molar flow rate of  reflux and D is the molar flow rate of the distillate product. For example, in Figure 1, assuming the molar flow rate of the reflux L is 1000 moles per hour and the molar  flow rate of the distillate D is 590 moles per hour, then the downward slope of the rectifying operating line is 1000 / (590 + 1000) = 0.63 which means that the y-coordinate of any point on the line decreases 0.63 units for each unit that the x-coordinate decreases.

Examples of q-line slopes

The next step is to draw the blue q-line (seen in Figure 1) from fr om the x = y line so that it intersects the rectifying operating line. The parameter q is the mole fraction of liquid in the feed and the slope of the q-line is q / (q - 1). For example, if the feed is a saturated liquid it has no vapor, thus q = 1 and the slope of the q-line is infinite which means the line is vertical. As another example, if the feed is all saturated vapor, q = 0 and the slope of the q-line is 0 which means that the line is horizontal. Some example q-line slopes are presented in Figure 2. As can be seen now, the typical McCabe-Thiele diagram in Figure 1 uses a q-line representing a  partially vaporized feed.  Next, as shown in Figure 1, draw the purple operating line for the stripping section of the distillation column (i.e., the section below the feed inlet). Starting at the intersection of the red bottoms composition line and the x = y line, draw the stripping section operating line up to the point where the blue q-line q-line intersects intersects the green operating operating line of the rectifying rectifying section section operating operating line. Finally, as exemplified in Figure 1, draw the steps between operating lines and and the the equi equilib libri rium um line line and and then then coun countt them them.. Thos Thosee step stepss repr repres esen entt the theoretica theoreticall plates plates (or (or equi equili libr briu ium m stag stages es). ). The The requ requir ired ed numb number er of  theoretical plates is 6 for the binary distillation depicted in Figure 1.  Note that using colored lines is not required and only used here to make the methodology easier to describe. In continuous distillation with varying reflux ratio, the mole fraction of the lighter component in the top part of the distillation column will decrease as the reflux ratio decreases. Each new reflux ratio will alter the slope of the rectifying section operating line. When the assumption of constant molar overflow is not valid, the operating lines will not be straight. Using mass and enthalpy balances in addition to vapor-liqu vapor-liquid id equilibriu equilibrium m data and enthalpy-c enthalpy-concen oncentrati tration on data, operating operating lines can be constructed based on Ponchon-Savarit's method.

Modelling In the Mc Cabe-Thiele method we make the material balance and enthalpy  balance equation by dividing the distillation column into two two parts-the enriching section and the stripping section .This are shown in the diagram as well. The feed enters the column somewhere near the middle, overhead and  bottom products are withdrawn as shown. The column contains a number of    bubble cap plates. The vapour from the top plate passes to a condenser  where it is condensed to a saturated liquid.Some of the liquid from the accumulator is returned as reflux continuously to the top plate.The residual or the bottom product is taken out from the bottom as shown in the figure  below from an example.

Simu imulati lation on Computer simulation is the discipline of designing a model of an actual or  theoretical physical system, execution the model on a digital computer, and anal analyz yzin ing g the the exec execut utio ion n outp output ut.. Simu Simula lati tion on embo embodi dies es the the prin princi cipl plee of  “learning by doing”---to learn about the system we must first build a model of some sort and then operate the model. The use of simulation is an activity that is as natural as a child who role plays. Children understand the world arou around nd them them by simu simula lati ting ng (wit (with h toys toys and and figu figuri rine nes) s) most most of thei their  r  interactions with other people, animals and objects. As adults, we lose some of this this chil childl dlik ikee beha behavi vior or but but reca recapt ptur uree it late laterr on thro throug ugh h comp comput uter  er  simulation. To understand the reality and all of its complexity, we must build artificial objects and dynamically act out roles with them. Computer simulation is the electronic equivalent of this type role playing and it serves to drive synthetic environments and virtual world. Within the overall task of simulation, there are three three primar primary y subfie subfield lds: s: Model Model design design,, Model Model execut executio ion n and Model Model analysis. To simulate something physical, you will first need to create a mathematical model which represents that physical object. Models can take many forms includ includin ing g declar declarati ative, ve, functi functiona onal, l, constr constrain aint, t, spatia spatiall or multim multimoda odal. l. A multimodal is a model containing multiple integrated models each of which represents a level of granularity for the physical system. The next task , once a model has been developed, is to execute the model on a computer --- that is, you need to create a program which steps through time while updating the state and event variables in your mathematical model. There are many ways to “step through time.” You can also execute the program on a massively  parallel computer. this is called parallel and distributed simulation. The term simulation is used in different ways by different people. As used here here,, simu simula lati tion on is defi define ned d as the the proc proces esss of crea creati ting ng a mode modell (i.e (i.e., ., an abstract representation or facsimile) of an existing or proposed system (e.g., a project, a business, a mine, a watershed, a forest, the organs in your body) in order to identify and understand those factors which control the system and/or to predict (forecast) the future behavior of the system.

The Power of Simulation Simulation is a powerful and important tool because it provides a way in which alternative designs, plans and/or policies can be evaluated without having to experiment on a real system, which may be prohibitively costly, time-consuming, or simply impractical to do. That is, it allows you to ask  “what if?” Question about a system without having to experiment on the actual system itself (and hence in our the costs of field f ield tests, prototypes, etc).

Why Do Simulation? You may may wond wonder er whet whethe herr simu simula lati tion on must must be used used to stud study y dyna dynami micc systems. There are many methods of modeling systems which involve the solu soluti tion on of a clos closed ed form form syst system em.. Simu Simula lati tion on is ofte often n esse essent ntia iall in the the following case: 1. The The mode modell is very very comp comple lex x with with many many vari variab able less and and inte interac racti ting ng component; 2. The underl underlying ying relationshi relationships ps are nonlinea nonlinear; r; 3. The model model conta contain in random random varieti varieties; es; 4. The model model output output is to be visual visual as in a 3D comput computer er animation. animation. The power of simulation is that ---even for easily solvable linear systems---a uniform model execution technique can be used to solve a large variety of  syst system emss with withou outt reso resort rtin ing g to a “bag “bag of tric tricks ks”” wher wheree one one must must choo choose se special-purpose and sometimes arcane solution methods to avoid simulation.

Types of Simulation Tools The simulation tools are known as Simulator. The general purpose tools can  be broadly categorized as follows;

Discrete Event Simulators Thes Thesee tool toolss rely rely on a tran transa sact ctio ion-f n-flo low w appr approa oach ch to mode modeli ling ng syst system ems. s. Mode Models ls cons consis istt of enti entitie ties, s, reco recour urse ses, s, and and cont contro roll elem elemen ents ts.. Disc Discre rete te simula simulator torss are genera generally lly design designed ed for simula simulati ting ng proces processes ses such such as call call centers, factory operations, and shipping facilities in which the material or  information that is being simulated can be described as moving in discrete steps or packets.

Agent based Simulator This is a special class of discrete event simulator in which the mobile entities are known as agent.

Continuous Simulators This class of tools solves differential equations that describe the evolution of  a system using continuous equations. These types of simulators are the most appropriate if the material or information that is being simulated can be described as evolving or moving smoothly and continuously, rather than infrequent discrete steps or packets. A common class of continuous simulators is system dynamics tools based on the the stan standa dard rd stoc stock k and and flow flow appr approa oach ch deve develo lope ped d by Profe Professo ssorr Jay Jay W.Forrester at MIT in the early 1960s.

Hybrid Simulator These These tools tools combin combinee the featur features es of conti continuo nuous us simul simulato ators rs and discret discretee simulators. That is, they solve differential equations, but can superimpose discrete events on the continuously varying system. Goldsim is a hybrid simulator.

Problem

Included in table are the data for the McCabe-Thiele method at R=1.029, the reflux ratio used for exact Ponchon-Savarit calculation. It is noteworthy that for either method each at 1.5 times its respective value of  R m, the no. of  stages is essentially the same, and the maximum flow rates which would be used to set the mechanical design of the tower are sufficiently similar for the same final design to result.

Appendix Simulation through C++ #include #include #include # define R 8.314 # define t0 298 # define lpha 2.69 double pj_sat(double pj1,double pjx,double pjg1,double pjg2,double pjp1,double pjp2); double pj_satb(double pj1,double pjy,double pjg1,double pjg2,double pjp1,double pjp2); double bubl_t (double ax) ; double dew_t(double ay,int flag ); double equili(double equili(double y); double setq(); double liq(double th); double vap(double th ); double inter(); double equi(double ax); double stri(double x1); double enri(double x); class bubl bubl { double t1,t2,t3,tn,y t1,t2,t3,tn,y1,y2,temp; 1,y2,temp; double a1,a2,b1,b2,c1,c2; a1,a2,b1,b2,c1,c2; public : double p1,x1,x2; bubl() { a1=16.5938; a2=16.262; b1=3644.3; b2=3799.89;

c1=239.76; c2=226.35; } double anto(double p2sat,int flag) ; double ant(double ta,int flag) ; void read_data(); void show_data(); double solve_y();

}; double bubl::anto(double p2sat,int flag) {double t1,t2; if(flag==2) { t1=a2-log(p2sat); t1=b2/t1; t2=t1-c2; return t2; } if(flag==1) { t1=a1-log(p2sat); t1=b1/t1; t2=t1-c1; return t2; } } double bubl::ant(double ta,int flag) { double t1; if(flag==1) { t1= b1/(c1+ta); t1=a1-t1; t1=exp(t1); return t1; } if(flag==2)

{ t1= b2/(c2+ta); t1=a2-t1; t1=exp(t1); return t1; } } void bubl::read_data() {cout p1; coutx1; x2=1-x1; } /*double bubl::solve_y() bubl::solve_y() { y1=(x1*g1*ant(t3,1))/(ph y1=(x1*g1*ant(t3,1))/(phi1*p1); i1*p1); y2=1-y1; }*/

class activity { double b12,b21,alpha,tou12,tou21,G12,G2 b12,b21,alpha,tou12,tou21,G12,G21; 1; public : double gamma1,gamma2; activity() { b12=-253.88 ; b21=845.21 ; alpha=.2994 ; } void set_tou (double t ); void set_G (); // void read_x (); void set_gamma (double,double ); void show_gamma (); }; void activity :: set_tou ( double t ) { double t1,t2; t2=t+273.15;

t1= 1.987*t2; tou12=b12/t1; tou21=b21/t1; } void activity :: set_G () { G12=exp( -alpha*tou12); -alpha*tou12); G21=exp( -alpha*tou21); } /*void activity:: read_x () { coutx1; coutx2; }*/ void activity:: set_gamma (double x1,double x2 ) { double t1,t2,t3,t4; t1=x1+x2*G21; t2=x2+x1*G12; t1=G21/t1; t1=tou21*t1*t1; t2=tou12/(t2*t2); t2=G12*t2; t1=t1+t2; t1=x2*x2*t1 ; gamma1=exp(t1); t3=x1+x2*G21; t3=tou21/(t3*t3); t3=t3*G21; t4=x2+x1*G12; t4=G12/t4; t4=tou12*t4*t4; t4=t4+t3; t4=x1*x1*t4; gamma2=exp(t4); }

double xxd,xxf,xxw,rr,qq,n=0,ix,iy,xx2,t,p,x2,y2,conc_prof[15],temp_prof[20]; void activity:: show_gamma() {cout