# “MODELLING & SIMULATION O

“MODELLING & SIMULATION OF BINARY DISTILLATION COLUMN”
CONTENTS
* Introduction
* Vapour Liquid Equilibrium
* Types of Distillation
1. Batch Distillation
2. Continuous Distillation
* Simple Distillation
* Flash Evaporation
* Fractional Distillation
* Types of Azeotropes
* Separation of Azeotropes
* Steam Distillation
* Vacuum Distillation
* Extractive Distillation
* Theoretical plates
* Methods of calculating no. of stages
1. Fenske Equation
2. McCabe-Thiele Method
* Modelling of McCabe-Thiele Method
* Assumptions of McCabe-Thiele Method
* Introduction to Simulation
* Flow Chart of Simulation Program
* Problem
* Discussion & Conclusion
* 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. Types of distillation include simple distillation (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 contain more of the less volatile material. Distillation columns are designed to achieve this separation efficiently.
Although many people have a fair idea what “distillation” means, the important aspects that seem to be missed from the manufacturing point of view are that:

* 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 its vapor (gas phase) are in equilibrium with each other, a condition or state where the rate of evaporation (liquid changing to vapor) equals the rate of condensation (vapor changing to liquid) on a molecular level such that there is no net (overall) vapor-liquid inter conversion. 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 concentration of a vapor in contact with its liquid, especially at equilibrium, is often given in terms of vapor pressure, which could be a partial pressure (part of the total 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. 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; if a vapor with components at certain concentrations or partial pressures is in vapor-liquid equilibrium with its liquid, then the component concentrations in the liquid 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 concentration (or vapor pressure) in the vapor phase, but there is a correlation. Such VLE concentration data is often known or can be determined experimentally for vapor-liquid mixtures with various components. In certain cases such VLE data can be determined or approximated with the help of certain theories such as Raoult’s Law, Dalton’s Law, and/or Henry’s Law.
Such VLE information is useful in designing columns for distillation, especially fractional distillation, which is a particular specialty of chemical engineers. Distillation is a process used to separate or partially separate components in a mixture by boiling (vaporization) followed by 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 compared in the vapor and liquid phases, concentrations of each component are often expressed as mole fractions. A mole fraction is number of moles of a given component in an amount of mixture in a phase (either vapor or liquid phase) divided by the total number of moles of all components in that amount of mixture in that phase.
Binary mixtures are those having two components. Three-component mixtures could be called ternary mixtures. There can be VLE data 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 pressure, such as 1 atm or whatever pressure a process of interest 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 maintained the overall pressure, the mixture is said to boil and the corresponding temperature is the boiling point (This assumes excess 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.
Thermodynamic Description of Vapor-Liquid Equilibrium

The field of thermodynamics describes when vapor-liquid equilibrium is possible, and its properties. Much of the analysis depends on whether the vapor and liquid consist of a single 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 within the liquid and vapor, and are the temperatures within the liquid and vapor, and and are the molar Gibbs free energies (units of energy per amount of 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. Under this view, equilibrium is described by the following equation:

where and are the fugacities of the liquid and vapor, 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 convenient to use the quantity , the dimensionless fugacity coefficient, which is 1 for an ideal gas.

Multicomponent systems

In a multicomponent system, where the vapor and liquid consist of more than one type of molecule, describing the equilibrium state is more complicated. For all components in the system, the equilibrium state between the two phases is described by the following equations:

where and are the temperature and pressure for each phase, and and are the partial molar Gibbs free energy also called chemical potential (units of energy per amount of substance) within the liquid and vapor, respectively, for each phase. The partial molar Gibbs free energy is defined by:

where is the (extensive) Gibbs free energy, and is the amount of substance of component .
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, 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 increasing proportion of B in the gas phase). This results in a slowly changing ratio A : B in the distillate.
If the difference in vapor pressure between the two 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 component A has distilled off, the boiling liquid is enriched in component B.
Continuous Columns

In contrast, continuous columns process a continuous feed 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 continuously (without interruption) fed into the process and separated 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 fraction, which has 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.
Continuous distillation differs from batch distillation in the respect that concentrations should not change over time. Continuous distillation 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, the number of trays or the height of packing). Reflux is a flow from the condenser back to the column, which generates a recycle that allows a better separation with a given number of trays. 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, a column with a low reflux ratio must have a large number of stages, thus requiring a taller column.
Continuous distillation requires building and configuring dedicated 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:

1. The nature of the feed that they are processing

* Binary column – feed contains only two components.
* Multi-component column – feed contains more than two components.

2. The number of product streams they have

* Multi-product column – column has more than two product streams.

3. Where the extra feed exits when it is used to help with the separation

* Extractive distillation – where the extra feed appears in the bottom product stream.
* Azeotropic distillation – where the extra feed appears at the top product stream.
4. The type of column internals

* Tray column – where trays of various designs are used to hold up the liquid to provide better contact between 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 a condenser which cools and condenses the vapors. Therefore, 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.
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 neglected due to the insignificant contribution of the less volatile component. In this case, the distillate may be sufficiently pure for 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 known as the feed tray. The feed tray divides the column into a top (enriching or rectification) section and a bottom (stripping) 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, the heating source may be the output streams of other columns. The vapour raised in the reboiler is re-introduced into the unit at the bottom of the column. The liquid removed from the reboiler is known as the bottoms product or 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 column and this is called the reflux. The condensed liquid 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 (or partial) evaporation is the partial vaporization that occurs when a saturated liquid stream undergoes a reduction in pressure by passing through a throttling valve or other throttling device. This process is one of the simplest unit operations. If the throttling valve or device is located at the entry into a pressure vessel so that the flash evaporation occurs within the vessel, then the vessel is often referred to as a flash drum.

If the saturated liquid is a single-component liquid (for example, liquid propane or liquid 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, isobutane and 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 evaporation of a single-component liquid is an isentropic i.e., constant entropy) process and is often referred to as an adiabatic 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
= upstream liquid enthalpy at upstream temperature and pressure, J/kg HdV
= flashed vapor enthalpy at downstream pressure and corresponding saturation temperature, J/kg HdL
= residual liquid enthalpy at downstream pressure 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 percent vaporized cp
= 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
= liquid heat of vaporization at downstream pressure 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 is used in the desalination of brackish water or ocean water 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 salt-free water. The residual salty liquid from that first stage is introduced into a second flash evaporation stage at a pressure lower than the first stage pressure. More water is flashed into steam which is also subsequently 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 multi-stage 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 process using a single equilibrium stage. It is very different and more complex than the flash evaporation of single-component liquid. For a multi-component liquid, calculating the amounts of flashed vapor and residual liquid in equilibrium with each other at a given 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);
ß is the fraction of feed that is vaporised;
Ki is the equilibrium constant of component i.
The equilibrium constants Ki 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 Rachford-Rice equation has been solved for ß, the compositions xi and yi can be immediately calculated as:

The Rachford-Rice equation can have multiple solutions for ß, at most one of which guarantees that all xi and yi will be positive. In particular, if there is only one ß for which:
Then that ß is the solution; if there are multiple such ß’s, it means that either Kmax<1 or Kmin>1, indicating respectively that no gas phase can be sustained (and therefore ß=0) or conversely that no liquid phase can exist (and therefore ß=1).

It is possible to use Newton’s method for solving the above Rachford-Rice equation, but there is a risk of converging to the wrong value of ß; it is important to initialize the solver to a sensible initial value, such as (ßmax+ßmin)/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, which are guaranteed to converge but can be slower.
The equilibrium flash of multi-component liquids is very widely utilized in petroleum refineries, petrochemical and chemical plants and natural gas processing plants.

Fractional Distillation

Fractional distillation is the separation of a mixture into its component parts, or fractions, such as in separating chemical compounds by their boiling point by heating them to a temperature at which several fractions of the compound will evaporate. It is a special type of distillation. Generally the component parts boil at less than 25 °C from each other under a pressure of
one atmosphere (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 blue lines). If you reboil that liquid C2, it will give a vapour 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 liquids is obviously to do a succession of boiling-condensing-reboiling 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.
Whether or not this is possible depends on the difference between 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.
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, 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-?-trope/) is a mixture of two or more liquids (chemicals) in such a ratio that its composition cannot be changed by simple distillation. This occurs because, when an azeotrope is boiled, the resulting vapor has the same ratio of constituents as the original mixture.
Because their composition is unchanged by distillation, azeotropes are also called (especially in older texts) constant boiling mixtures. The word azeotrope is derived from the Greek words ??e?? (boil) and t??p?? (change) combined with the prefix a- (no) to give the overall meaning, “no change on boiling.”
Types of Azeotropes

Each azeotrope has a characteristic boiling point. The boiling point of an azeotrope is either less than the boiling points of any of its constituents (a positive azeotrope), or greater than the boiling point of any of 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 78.1°C is the minimum temperature at which any ethanol/water solution can boil. In general, a positive azeotrope boils at a lower 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% hydrogen chloride and 79.8% water (by weight). Hydrogen 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 which any hydrochloric acid solution can boil is 110°C. In general, 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 binary azeotropes. Those consisting of three constituents are called ternary azeotropes. Azeotropes of more than three constituents 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.
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 separate the constituents of an azeotrope, the separation of azeotropic mixtures (also called azeotrope breaking) is a topic of considerable 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 of the constituents of an azeotrope is not generally the ratio of small integers. For example, the 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.
Azeotropic Distillation

Other methods of separation involve introducing an additional agent, called an Entrainer, that will affect 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 to the water/ethanol azeotrope. 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, which reacts strongly with water to form the nonvolatile compound, calcium hydroxide. Nearly all of the calcium hydroxide can be separated by filtration and the 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.
Anhydrous calcium chloride is used as a desiccant for drying a wide variety of solvents since it is inexpensive and does not react with 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 the other constituent is unaffected. In this way, for example, it is possible to break the water/ethanol azeotrope by dissolving potassium acetate in it and distilling the result.

Examples of azeotropes
Proportions are by weight:

* nitric acid (68%) / water, boils at 120.5°C at 1 atm (negative azeotrope)
* perchloric acid (28.4%) / water, boils at 203°C (negative azeotrope)
* hydrofluoric acid (35.6%) / water, boils at 111.35°C (negative 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%) / halothane (66%) a mixture once commonly used in anaesthesia.
* benzene / hexafluorobenzene forms a double binary azeotrope.

Complex Azeotrope Systems

The rules for positive and negative azeotropes apply to all the examples discussed so far. But there are some examples that don’t fit into the categories of positive or negative azeotropes. The best known of these is the ternary azeotrope formed by 30% acetone, 47%chloroform, and 23% methanol, which boils at 57.5°C. Each pair of these constituents forms a binary azeotrope, but chloroform/methanol and acetone/methanol both form positive azeotropes while chloroform/acetone forms a negative 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 system is called a double azeotrope, and will have two azeotropic compositions and boiling points. An example is water and N-methylethylenediamine.
Steam Distillation

Steam distillation is a special type of distillation (a separation 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 is introduced into the distillation apparatus. By adding water or steam, 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. After distillation the vapors are condensed as usual, usually yielding a 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 constituent independently exerts its own vapor 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 partial pressures of the two immiscible liquids just exceeds 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 below the point at which decomposition occurs. For example, the boiling point of 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 distillation is employed in the manufacture of essential oils, for instance, perfumes. In this method, steam is passed through the plant material containing the desired oils. It is also employed in the synthetic procedures of complex organic compounds. Eucalyptus oil and orange oil are obtained by this method on the industrial scale.
Steam distillation is also widely used in petroleum refineries and petrochemical plants where it is commonly referred to as “steam stripping”.
Other industrial uses of steam distillation include the production 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 liquid mixture to be distilled is reduced to less than its vapor pressure(usually less than atmospheric pressure) causing evaporation of the most volatile liquid(s) (those with the lowest boiling points). This distillation method works on the principle that boiling occurs when the vapor pressure of a liquid exceeds the ambient pressure. Vacuum distillation is used with or without heating the solution.

Applications

Laboratory-scale vacuum distillation is used when liquids to be distilled have high atmospheric boiling points or chemically change at temperatures near their atmospheric boiling points. Temperature sensitive materials (such as beta carotene) also require vacuum distillation to remove solvents from the mixture without damaging the product. Another reason vacuum distillation is used is that compared to steam distillation there is a lower level of residue build up. This is important in commercial applications where temperature transfer is produced using heat exchangers.
Vacuum distillation is sometimes referred to as low temperature distillation. Typical industrial applications utilize the heat pump cycle to maximize efficiency. This type of distillation is in use in the oil industry where common ASTM standards are D1160, D2892, D5236. These standards describe typical applications of vacuum distillation at pressures of about 1-100 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 distillation.[6] Vacuum distillation columns (as depicted in the drawing to the right) typically used in oil refineries have diameters ranging up to about 14 meters (46 feet), heights ranging up to about 50 meters (164 feet), and feed rates ranging up to about 25,400 cubic meters per 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 to effect the same separation between the overhead and bottoms products. Lower pressures increase relative volatilities in most systems.
A second advantage of vacuum distillation is the reduced temperature requirement at lower pressures. For many systems, the 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 residence time especially in columns using packing rather than trays.
* Increasing capacity, yield, and purity.
Another advantage of vacuum distillation is the reduced 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 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 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. 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, absorption, 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 provides good contact between the vapor and liquid phases present in industrial-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 = the number of theoretical plates or trays E = the plate or tray efficiency
So-called bubble-cap or valve-cap trays are examples of the vapor and liquid contact devices used in industrial distillation columns. Another example of vapor and liquid contact devices are the spikes in laboratory Vigreux fractionating 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 and liquid contacting would occur as the vapor flowing upwards through the perforations would contact the liquid flowing downwards through the perforations. In current modern practice, as shown in 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 each tray.
To design a distillation unit or a similar chemical process, the number of theoretical trays or plates (that is, hypothetical equilibrium 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 and calculating material balances, heat balances and equilibrium flash vaporizations for each of the succession of equilibrium stages until the desired end product composition is achieved. The calculation process 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 industrial distillation column, the N t required to achieve a 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 of plates required. Hence, the calculation of N t is usually repeated at various reflux rates. N t is then divided by the tray efficiency, 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.
There is a very important distinction between the theoretical plate terminology used in discussing conventional distillation trays and the theoretical plate terminology used in the discussions below of packed bed distillation or absorption or in chromatography or other applications. The theoretical plate in conventional distillation trays has no “height”. 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 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 numerically equal to the absorption bed 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 as Raschig rings or structured sheet metal. Liquids tend to wet the surface of the packing and the vapors contact the wetted surface, where mass transfer occurs.

Chromatographic Processes

The theoretical plate concept was also adapted for chromatographic processes by Martin and Synge. The IUPAC’s Gold Book provides a definition of the number of theoretical plates 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 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 equation was derived by Merrell Fenske in 1932, a professor who served as the head of the chemical engineering department 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 Xb = mole fraction of more volatile component in the bottoms aavg
= 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 aavg. is simply a. If the relative volatility is not constant from top to bottom of the column, then the following approximation may be used:

where: at = relative volatility of light key to heavy key at top of column ab = 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 derivation of another form of the Fenske equation for use in gas chromatography is available on the U.S. Naval Academy’s web site. Using Raoult’s law and Dalton’s Law for a series of condensation and evaporation cycles (i.e., equilibrium stages), the following form of 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 graphical approach presented by McCabe and Thiele in 1925, the McCabe-Thiele method is considered the simplest and perhaps most instructive method for analysis of binary distillation. This method uses the fact that the composition at each theoretical tray (or equilibrium 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 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 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 value of liquid phase composition. Also draw vertical lines from the horizontal axis up to the x = y line for the feed and for the desired 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 (?y/?x) 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 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 intersects the green operating line of the rectifying section operating line.
Finally, as exemplified in Figure 1, draw the steps between operating lines and the equilibrium line and then count them. Those steps represent the theoretical plates (or equilibrium stages). The required number 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-liquid equilibrium data and enthalpy-concentration data, 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.
Simulation

Computer simulation is the discipline of designing a model of an actual or theoretical physical system, execution the model on a digital computer, and analyzing the execution output. Simulation embodies the principle 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 around them by simulating (with toys and figurines) most of their interactions with other people, animals and objects. As adults, we lose some of this childlike behavior but recapture it later on through computer 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 primary subfields: Model design, Model execution and 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 including declarative, functional, constraint, spatial or multimodal. 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, simulation is defined as the process of creating a model (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 tests, prototypes, etc).

Why Do Simulation?

You may wonder whether simulation must be used to study dynamic systems. There are many methods of modeling systems which involve the solution of a closed form system. Simulation is often essential in the following case:
1. The model is very complex with many variables and interacting component;
2. The underlying relationships are nonlinear;
3. The model contain random varieties;
4. The model output is to be visual as in a 3D computer 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 systems without resorting to a “bag of tricks” where one must choose 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

These tools rely on a transaction-flow approach to modeling systems. Models consist of entities, recourses, and control elements. Discrete simulators are generally designed for simulating processes such as 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 standard stock and flow approach developed by Professor Jay W.Forrester at MIT in the early 1960s.

Hybrid Simulator

These tools combine the features of continuous simulators and discrete 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 Rm, 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<iostream.h>
#include<math.h>
#include<conio.h>
# 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 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 { double t1,t2,t3,tn,y1,y2,temp;
double 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 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;
}
}
{cout<<“ENTER THE VALUE OF PRESSURE n “;
cin>> p1;
cout<<“ENTER THE VALUE OF MOLE FRACTION OF FIRST COMPONENT X1 n”;
cin>>x1;
x2=1-x1;
}

class activity { double b12,b21,alpha,tou12,tou21,G12,G21;
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);
G21=exp( -alpha*tou21);
}

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<<“THE VALUE OF ACTIVITY COEFFICIENT FOR THE FIRST COMPONENT IS n”;
cout<<gamma1<<“n”;
}

void main ()
{ // double xxd,xxf,xxw,rr,qq,n=0,ix,iy,xx2,t,p,x2,y2;
clrscr();
cout<<“ENTER THE MOLE FRACTION OF TOP PRODUCT: n”;
cin>>xxd;
cout<<“ENTER THE MOLE FRACTION OF BOTTOM PRODUCT: n”;
cin>>xxw;
cout<<“ENTER THE MOLE FRACTION OF FEED: n”;
cin>>xxf;
cout<<“ENTER THE REFLUX RATIO: n”;
cin>>rr;
// cout<<“enter the operating conditions :”<<endl;
cout<<“ENTER THE TEMPERATURE OF FEED IN CENTIGRADES:n”;
cin>>t;
cout<<“ENTER THE PRESSURE OF FEED IN kPa:n”;
cin>>p;
qq=setq();
ix=inter();
iy=enri(ix);
x2=equili(xxd);
for(;x2>xxw;n++)
{
if(n==0)
{
if(x2>=ix)
y2=enri(x2);
else
y2=stri(x2);
}
else
{
x2=equili(y2);
if(x2>=ix)
y2=enri(x2);
else
y2=stri(x2);
}
conc_prof[n]=x2;
temp_prof[n]=bubl_t(conc_prof[n]);
}
cout<<“THE THEORETICAL NUMBER OF PLATES ARE “<<endl;
cout<<n<<“n”;
for(int ii=0;ii<=n;ii++)
cout<<conc_prof[ii]<<“n”;
for( ii=0;ii<=n;ii++)
cout<<temp_prof[ii]<<“n”;

getch();
}
double bubl_t (double ax )
{
//clrscr();
double a1,a2,a3,a4,T;
double g1,g2;
bubl b;
activity a;
a1=b.anto(p,1);
a2=b.anto(p,2);
T=(a1*ax)+(a2*(1-ax));
while(1)
{
a1=b.ant(T,1);
a2=b.ant(T,2);
a3=T;

a.set_tou(T);
a.set_G();
a.set_gamma(ax,(1-ax));
g1=a.gamma1;
g2=a.gamma2;
a2=pj_sat(p,ax,g1,g2,a1,a2);
T= b.anto(a2,2);
a4=(T-a3);
if( a4<0 )
a4=a4*-1;
if(a4 <.001)
break;
}
a3=(ax*g1*a1)/p;
return T;
}
double dew_t(double ay,int flag )
{
double a1,a2,a3,a4,T ;
double g1,g2,y1,y2;
bubl b;
activity a;
// cout<<“ENTER THE VALUE OF PRESSURE n”;
// cin>>b.p1;
// cout<<“ENTER THE VALUE OF MOLE FRACTION Y1 n”;
y1=ay;
y2=1-y1;
a1=b.anto(p,1);
a2=b.anto(p,2);
T=(a1*y1)+(a2*y2);
g1=1;
g2=1;
while(1)
{
a1=b.ant(T,1);
a2=b.ant(T,2);
a3=T;
b.x1=(y1*p)/(g1*a1);
b.x2=1-b.x1;
a.set_tou(T);
a.set_G();
a.set_gamma(b.x1,b.x2);
g1=a.gamma1;
g2=a.gamma2;
a1=pj_satb(p,y1,g1,g2,a1,a2);
T=b.anto(a1,1);
a4=(T-a3);
if(a4<0)
a4=a4*-1;
if(a4 <.001)
break;
}
if(flag==1)
return T;
else
return
b.x1;
}
double pj_sat(double pj1,double pjx,double pjg1,double pjg2,double pjp1,double pjp2)
{
double z1,z2;
z1=pjx*pjg1*pjp1/pjp2;
z2=(1-pjx)*pjg2;
z2=pj1/(z1+z2);
return z2;
}

double pj_satb(double pj1,double pjy,double pjg1,double pjg2,double pjp1,double pjp2)
{
double z1,z2;
z1=pjy/pjg1;
z2=((1-pjy)*pjp1)/(pjg2*pjp2);
z2=pj1*(z1+z2);
return z2;
}

double setq()
{
bubl b;
clrscr();
double hg,hl,hf,t1,t2,qe,fl,fg;
int ch;
cout<<“ENTER THE CONDITION OF FEEDn”;
cout<<“1. Liquid n”;
cout<<“2. Saturated liquidn”;
cout<<“3. Mixture of saturated liquid & saturated vaporn”;
cout<<“4. Saturated vaporn”;
cout<<“5. Superheated vaporn”;
// cout<<“enter the feed condition : n”;
cin>>ch;
double bub_ret,dew_ret;
bub_ret= bubl_t(xxf);
hl=liq(bub_ret);
dew_ret=dew_t(xxf,1);
hg=vap(dew_ret);
switch(ch)
{
case 1:
hf=liq(t);
t1=hg-hf;
t2=hg-hl;
qe= t1/t2;
break;
case 2:
hf=hl;
qe=1;
break;
case 3:
cout<<“enter the total number of moles in the liquid feed :n”;
cin>>fl;
cout<<“enter the total number of moles in the vapor feed :n”;
cin>>fg;
hf=(hl*fl)+(hg*fg);
t1=hg-hf;
t2=hg-hl;
qe= t1/t2;
break;
case 4:
hf=hg;
qe=0;
break;
case 5:
hf=vap(t);
t1=hg-hf;
t2=hg-hl;
qe= t1/t2;
break;
};

return qe;
}
double liq(double th)
{
double t1, cl1=88.92;
// cl=(xxf*cl1)+((1-xxf)*cl2);
t1=th-t;
t1=cl1*t1;
return t1;
}
double vap(double th )
{
float t1,t2,t3,t4,v1=33536.268,v2=41157.68,y2 , cl1=87.18, cl2=75.44914;
t1=th-t;
t2=cl1*t1;
t3=cl2*t1;
t2=t2+v1;
t3=t3+v2;
t1=xxf*t2+(1-xxf)*t3;
return t1;

}
double inter()
{
double t1,t2,t3,t4;
t1=rr/(rr+1);
t2=xxf/(qq-1);
t3=qq/(qq-1);
t4=xxd/(rr+1);
return (t4+t2)/(t3-t1);
}
double equi(double ax )
{
double t1,t2,t3,g1;
bubl b;
activity a;
t1=bubl_t(xxd);
t3=b.ant(t1,1);
t2=dew_t(ax,2);
a.set_tou(t1);
a.set_G();
a.set_gamma(t2,t2-1);
g1=a.gamma1;
return (ax*p)/(g1*t3);
}
double enri(double x)
{
double t1,t2,t3;
t2=(rr+1);
t1=rr/t2;
t3=xxd/t2;
t1=(t1*x)+t3;
return t1;
}
double stri(double x1)
{
double s,t1,t2,t3,t4,i;
t1=iy-xxw;
t2=ix-xxw;
t3=-ix+x1;
t4=t1/t2;
s=t4;
t4=t4*t3;
t1=iy+t4;
i=s*ix;
i=-i+iy;
// cout<<“the slope”<<s<<endl;
// cout<<“the intercept”<<i;
return t1;
}

double equili(double y)
{
double a;
a=4.5;
double t1,t2;
t1=(a-(a*y) +y);
t2=y/t1;
return t2;
}

Bibliography

Mass-Transfer Operations-Robert E. Treybal

Unit Operations in Chemical Engg.-McCabe Smith Herriot

www.wikipedia.com

www.scienceworld.com