07/03/2013
Distillation Equilibrium (Review) Flash Distillation Multistage Distillation
MRB
Single Equilibrium Stage – Ethanol-Water, P = 1 atm
Vapor
F, zEtOH Liquid
V, yEtOH L, xEtOH
F is the total moles of ethanol and water fed to the stage. V is the total moles in the vapor stream exiting the stage. L is the total moles in the liquid stream exiting the stage. zEtOH is the mole fraction of ethanol in the feed. yEtOH is the mole fraction of ethanol in the vapor stream. xEtOH is the mole fraction of ethanol in the liquid stream.
Feed Mole-Fraction Relationships • Note that a feed mole-fraction, zF,can be a subcooled liquid, a saturated liquid, a two-phase mixture, a saturated vapor, or a superheated vapor. • The feed phase is dependent upon the temperature, pressure, and the composition (mole fraction).
zF and x,y Relationships •
• • • • •
Assuming that the equilibrium stage is at the same temperature and pressure of the feed: If zF is a subcooled liquid, then zF is simply xF and there is no y. If zF is a superheated vapor, zF is yF and there is no x. If zF is a saturated liquid, zF is essentially xF with a single vapor bubble formed of new mole fraction y. If zF is a saturated vapor, zF is essentially yF with a single liquid drop formed of new mole fraction x. If zF is in the two-phase region, the system will separate into a liquid and vapor of new mole fractions x and y, respectively. zF is not equal to either x or y, but x and y be determined from the T vs. x,y data or plot.
Mass Balance – Lever Rule
Vapor
F, zA Liquid
V, yC L, xB
Mass Balance – Lever Rule Let F = the moles of feed of composition zA L = the moles of liquid of composition xB V = the moles of vapor of composition yC Then the mass balances before and after separation are
and
FzA Lx B Vy C
Eq. (2-6)
F LV
Eq. (2-7)
Mass Balance – Lever Rule Substituting Eq. (2-7) into Eq. (2-6) and rearranging yields L yC z A V zA x B
Eq. (2-8)
where L/V is the ratio of liquid to vapor. Comparing the numerator and denominator with the twophase diagram indicates that the distance between points A and C and points A and B are equivalent to the magnitudes of the liquid-phase and vapor-phase quantities, respectively. L AC Graphically, this is V BA :
Mass Balance – Lever Rule
Temperature-Composition Diagram for Two-Phase System 100
95 Superheated Vapor Phase Two Phase
T( oC)
90
85
V L B A C
T sy s
Isotherm
80 Subcooled Liquid Phase
75
xB
0.0
0.2
zA
yC
0.4
0.6 x or y
0.8
1.0
Mass Balance – Further Relationships From inspection, other useful relationships can be determined: Fraction feed remaining as liquid q
L L y zA C L V F yC x B
Fraction feed vaporized f
V V z xB A L V F yC x B
Note for a Two-Phase Mixture… •
At vapor-liquid equilibrium, the temperatures of the vapor and liquid are equal.
•
When a two-phase mixture separates at vapor-liquid equilibrium conditions, the vapor phase will be at saturated vapor conditions and the liquid phase will be at saturated liquid conditions.
•
We will use this assumption when we do our multi-stage solutions – the vapor and liquid streams exiting a stage will be assumed to be at saturated conditions.
•
Thus, the liquid fed from one stage to another stage can be assumed to be a saturated liquid and the vapor feed to another stage can be assumed to be a saturated vapor.
Enthalpy vs. Composition – Ponchon-Savarit Plot • Presents the temperature equilibrium relationship for enthalpy vs. x and y. • Pressure is constant. • Enthalpy will be required in future problems utilizing energy balances. • Note the units of concentration!
• • •
For a non-ideal system, where the molar latent heat is no longer constant and where there is a substantial heat of mixing, the calculations become much more tedious. For binary mixtures of this kind a graphical model has been developed by RUHEMANN, PONCHON, and SAVARIT, based on the use of an enthalpycomposition chart. It is necessary to construct an enthalpy-composition diagram for particular binary system over a temperature range covering the two-phase vapor-liquid region at the pressure of the distillation.
Enthalpy vs. Composition –Ponchon-Savarit Plot
What is the enthalpy of a (two phase) feed stream at 1 kg/cm2 pressure, 82°C, 0.6 wt% ethanol?
Enthalpy vs. Composition – Enthalpy Determination • The major purpose of an enthalpy diagram is to determine enthalpies.
• We will use enthalpies in energy balances later. • For example, if one were given a feed mixture of 35% ethanol (weight %) at T = 92oC and P = 1 kg/cm2 and the mixture was allowed to separate into vapor and liquid, what would be the enthalpies of the feed, vapor, and liquid?
Enthalpy vs. Composition – Enthalpy Determination
425
295
90
Lecture 5
14
Equilibrium Data – How to Handle? •
Tabular Data • •
•
Graphical • • •
•
Generate graphical plots Generate analytical expressions (curve fit)
y vs. x (P constant) – McCabe-Theile Pot T vs. x,y (P constant) – Saturated Liquid, Vapor Plot Enthalpy vs. composition (P constant, T) – Ponchon-Savarit Plot
Analytical expressions • • • • •
Thermodynamics: Equations of state/Gibbs free energy models Distribution coefficients, K values Relative volatility DePreister charts Curve fit of data
Analytical Expressions for Equilibrium
• There are several disadvantages to using graphical techniques: • One cannot readily plot multi-component systems graphically (maximum is typically three). • Separator design often has to be done using numerical methods; thus, analytical expressions for equilibrium behavior are needed.
• We will now look at other representations for handling equilibrium data analytically…
Other Equilibrium Relationships – Distribution Coefficient Another method of representing equilibrium data is to define a distribution coefficient or K value as: K A yA / x A
Eq. (2-10)
KA is typically a function of temperature, pressure, and composition. The distribution coefficient K is dependent upon temperature, pressure, and composition. However, for a few systems K is independent of composition, to a good approximation, which greatly simplifies the problem. KA K(T,p) Eq. (2-11)
Other Equilibrium Relationships – DePriester Charts • One convenient source of K values for hydrocarbons, as a function of temperature and pressure (watch units), are the DePriester charts • The DePriester plots are presented over two different temperature ranges.
Using DePriester Charts – Boiling Temperatures of Pure Components
• One can determine the boiling point for a given component and pressure directly from the DePriester Charts – one can then determine which component in a mixture is the more volatile – the lower the boiling point, the more volatile a component is.
• For a pure component, K = 1.0. • Assume one wishes to determine the boiling point temperature of ethylene at a pressure of P = 3000 kPa…
Tbp = - 9.5 oC
Lecture 5
Question – DePriester Charts • What are the equilibrium distribution coefficients, K, for a mixture containing:
Ethylene n-Pentane n-Heptane at T = 120 oC and P =1500 kPa?
Lecture 5
Answer – DePriester Charts • The equilibrium distribution coefficients, K, are: K Ethylene 8.5 n-Pentane 0.64 n-Heptane 0.17
at T = 120 oC and P =1500 kPa.
Question – Volatility • What can one say about the volatility of each component from the K values? K Ethylene 8.5 n-Pentane 0.64 n-Heptane 0.17
Answer – Volatility •
What can one say about the volatility of each component from the K values? K T boiling Ethylene 8.5 -35.5 oC n-Pentane 0.64 153 oC n-Heptane 0.17 >200 oC
K A yA / xA
•
The boiling point temperatures of the pure components at P = 1500 kPa have also been determined from the DePriester charts for K = 1.0 for each component (n-heptane’s is off the chart).
•
From the K values and the boiling point temperature of each pure component, one can say that the volatility follows the trend that ethylene>n-pentane>nheptane.
Other Equilibrium Relationships – DePriester Equation While the DePreister charts may be used directly, they have been conveniently fit as a function of temperature and pressure: ln K
a p2 a p3 a T1 a T2 ln p 2 a a T6 p1 2 2 T T p p
Eq. (2-12)
where T is in oR and p is in psia. Table 2.4 (p. 26, Wankat) contains the K fit constants along with their mean errors (again, watch units!). Eq. (2-12) provides an analytical expression which can be used in numerical analyses. We will use this later for bubble and dew-point temperature calculations.
Other Equilibrium Relationships – Mole Fraction – Vapor Pressure Relationship If one does not have equilibrium data, K can be approximated using other more common thermodynamic data quantities such as vapor pressures. From Raoult’s law for ideal systems: p A x A (VP) A
Eq. (2-14)
where pA is the pressure due to component A in the mixture and (VP)A is the vapor pressure of pure component A, which is temperature dependent. From Dalton’s law of partial pressures: yA
pA p
Eq. (2-15)
Combining Eqs. (2-15) and (2-14) and rearranging yields: y A (VP) A xA p
Eq. (2-16)
Other Equilibrium Relationships – Distribution Coefficient – Vapor Pressure Relationship The left-hand side of Eq. (2-16) is the definition of the distribution coefficient K; thus,
KA
(VP) A p
Eq. (2-17)
Eq. (2-17) allows one to obtain K’s from the vapor pressures of the pure components, which can be readily found for many chemical species using the Antoine equation:
ln(VP) A A
B TC
Eq. (2-18)
where A, B, and C are constants, which can be found in many thermodynamic texts for many chemical species. Vapor pressure correlations can also be found in “The Properties of Gases and Liquids” (5th Ed. Poling, Prausnitz, O’Connell) Caution must be used when applying this K relationship since many systems are non-ideal. Actually, systems are often less ideal in the liquid phase because of the intimate contact of the chemical species, and these are handled by the liquid-phase activity coefficient, γA:
KA
A (VP) A p
Eq. (2-19)
The activity coefficient can be obtained from correlations, e.g, Van Laar, Wilson, etc. (see thermodynamic texts).
Other Equilibrium Relationships – Relative Volatility K values are strongly dependent on temperature; however, this temperature behavior maybe somewhat similar, especially for similar chemical species, over certain temperature ranges. Consequently, if one takes the ratio of the K’s for two components, the temperature dependence will be less (see HW problem 2-D5). This ratio, defined as the relative volatility, αAB, for a binary system is:
AB
K A y A /x A K B y B /x B
Eq. (2-20)
If the temperature dependence for the K values is identical, then αAB will be independent of temperature. However, for all but the most ideal situations, αAB will have some temperature dependence. Why is it termed relative volatility? Because, if Raoult’s law is valid:
AB
(VP) A (VP) B
Eq. (2-21)
Thus, if (VP)A > (VP)B, component A is the more volatile and αAB > 1. Likewise, KA > KB; thus, one can determine the more volatile component by comparing K’s. If A is more volatile, its K value will be greater than B’s K value.
Other Equilibrium Relationships – Relative Volatility It will be convenient later on in separation problems to express the relative volatility in terms of the mole fractions and vice-versa For binary systems, the mole fractions are related by
yB 1 yA and x B 1 x A
Eq. (2-4)
and substituting these into Eq. (2-20) yields:
AB
or
y A (1 x A ) (1 y A )x A
AB K A
Eq. (2-22)
1 xA 1 yA
Solving Eq. (2-22) for yA and xA yields:
yA
AB x A 1 ( AB 1) x A
and xA
yA
AB ( AB 1) y A
Eq. (2-23)
Flash Distillation •
Flash distillation is the simplest method of separation.
•
A feed stream is “flashed” into a chamber or “flash drum” and the liquid and vapor are allowed to separate under equilibrium.
•
It is “flashed” by throttling the feed stream through a nozzle or valve into the chamber – the pressure drops through the valve.
•
The more volatile component will be concentrated in the vapor stream – the less volatile in the liquid stream.
•
The system is very close to a single “equilibrium stage”.
•
Separation is usually not very high for a single equilibrium stage.
Flash Distillation – Solution • Flash distillation problems can be solved using three sets of equations: –Equilibrium relationship –Mass balance –Energy balance
Flash Distillation – Equilibrium Parameters • • • • • • • • •
Feed Composition – z Vapor-Phase Composition – y Liquid-Phase Composition – x Upstream Feed Temperature – T1 Feed Temperature – TF Drum Temperature – Td Upstream Feed Pressure – P1 Feed Pressure – PF Drum Pressure – Pd
Flash Distillation – Mass Parameters • • • • • •
Feed Flow Rate – F Vapor Flow Rate – V Liquid Flow Rate – L Feed Composition – z Vapor-Phase Composition – y Liquid-Phase Composition – x
Flash Distillation – Energy Parameters • • • • • • • •
Heater Input – QH Flash Drum Heat Input – Qflash Feed Enthalpy– hF Vapor Enthalpy – HV Liquid Enthalpy – hL Upstream Feed Temperature – T1 Feed Temperature – TF Drum Temperature – Td
Flash Distillation – Mass Balances
• Overall mass balance
F VL • Component mass balance
Fz Vy Lx
Flash Distillation – Operating Line
Solving the overall mass balance for y yields
L F y x z V V which is termed the operating line. It relates the composition of the streams leaving the stage or drum.
Common problem specifications.
• Liquid to vapor ratio L/V • Fraction of feed vaporized f = V/F • Fraction of feed remaining as liquid q = L/F
Operating Line Form – Fraction Vaporized From the overall mass balance L F V 1 V/F 1 f V V V/F f
then
1- f 1 y x z f f
Operating Line Form – Fraction Remaining as Liquid or
L L L/F q V F - L 1 - L/F 1 - q and 1 q z y x 1- q 1 q
Operating Lines – Linear! • Slope
L 1 f q V f 1 q
• y Intercept F 1 1 z z z V f 1- q
• x intercept F 1 1 z z z L 1- f q
So How Do Solve? • We often know all of the system parameters except the compositions of the vapor and liquid leaving the stage or flash drum – two unknowns, y and x. • We have two equations: – Equilibrium Relationship – Mass Balance (Operating Line)
• With two equations and two unknowns we can solve the problem!
McCabe-Thiele Analysis
Flash Distillation – Typical Problem •
One will usually be given the feed stream, F, or it can be assumed.
•
One will usually be given the feed composition, z, in mole or weight fraction.
•
One will also typically be given one of the following: x, y, T d, f = V/F, q = L/F, L/V, or TF.
•
One will usually be given the pressure, Pd, in the flash drum, or it will be chosen such that the feed is above its boiling point at T d, so that some of it vaporizes.
•
What is given in the problem determines the type of problem and the method of solution.
Flash Distillation – Problem Type 1a: Sequential Solution •
If one of the equilibrium conditions – x, y, or Td – in the drum is specified, then the other two can be found from the equilibrium relationships using: – Equilibrium data and plots or – K values or – Relative volatility relationships
•
Once we have x and y, we can then solve for the streams – F, V, and L – using: – Overall mass balance and – Component mass balance
•
We can then solve the energy balances to determine QH, TF, and T1 (Qflash = 0, since we typically assume an adiabatic drum) using enthalpies from: – Heat capacities and latent heats of vaporization or – Enthalpy-composition plots
•
This method of solution is known as a sequential solution method since the energy balance is decoupled from the equilibrium and mass balances.
Flash Distillation – Problem Type 1b: Sequential Solution •
If the stream parameters are specified, usually as fraction of feed vaporized – f = V/F – or the fraction of feed remaining as liquid – q = L/F –, then the problem can be solved for x, y, Td, F, V, and L by a simultaneous solution using: – Equilibrium relationships and – Mass balances
•
We can then solve the energy balances to determine Q H, TF, and T1 using enthalpies from: – Heat capacities and latent heats of vaporization or – Enthalpy-composition plots
•
This method of solution is also known as a sequential solution method since the energy balance is still decoupled from the equilibrium and mass balances.
Flash Distillation – Problem Type 2: Simultaneous Solution
•
If the temperature, TF, of the feed is given, then the problem requires a simultaneous solution for all of the other parameters using: – Equilibrium relationship and – Mass balance and – Energy balance
•
This method of solution is known as a simultaneous solution method since the energy balance is not decoupled from the equilibrium and mass balances.
Flash Distillation – Pressures •
The pressure, Pd, in the flash drum is chosen such that the feed is above its boiling point at Td, so that some of it vaporizes.
•
The pressure, P1, is chosen such that the upstream feed is below its boiling point and remains liquid at T1.
•
Likewise, the feed pressure, PF, must be chosen so that the feed is below its boiling point and remains liquid.
•
The pump and heater assist in adjusting the required pressures and temperatures of the system.
•
If the feed is already hot enough, the heater may not be needed, and if the pressure of the flash drum is low enough, the pump may not be needed.
Column Distillation
• Flash distillation provides a method of separation, but the amount of separation obtained is limited. • What if we need to have a greater separation to obtain essentially pure components? • We could place flash drums in series or as a cascade…
Flash Drums in Cascade
Lecture 9
Flash Drums in Cascade • One can obtain a high level of separation using cascading flash drums. • The problem with this arrangement is that we generate a large number of intermediate liquid and vapor streams, which would need to be separated. • One could feed these intermediate streams to another flash drum cascade, but even more intermediate streams are formed, and so on and so on. • Let’s look at what we can do with the intermediate streams…
Flash Drums in Counter-Current Cascade – Use of Intermediate Steams
Lecture 9
Flash Drums in Counter-Current Cascade – Isobaric Operation
Flash Drums in Counter-Current Cascade – Reflux and Boilup
Lecture 9
Flash Drums in Counter-Current Cascade – Intermediate Heat Exchange
Lecture 9
Distillation Column
Lecture 9
Distillation Column – External Balance
Lecture 9
Column Distillation – Typical Specified Variables •
Column pressure, Pc.
•
Feed flow rate, F.
•
Feed composition, z.
•
Feed temperature, TF; enthalpy, hF; or quality, q = L/F.
•
Reflux temperature,TR; or enthalpy, hD.
•
Reflux ratio, L/D; or distillate composition, xD.
•
Bottoms composition, xB.
Column Distillation – Tools for Solution • Equilibrium relationships • Mass balances • Energy balances
Column Distillation – Methods of Solution • External column balances – Overall – Condenser – Reboiler
• Internal column balances – Stage-by-stage calculations
