Overview of Binary Distillation in C&PE 611
C&PE 611: Unit Operations Design
Introduction to Binary Distillation
Text References: Wankat Ch 3, SHR Ch 7
Institution: Department of Chemical & Petroleum Engineering, The University of Kansas
Distillation Terminology
Condenser: A heat exchanger that condenses vapor into liquid.
Reflux Drum: A vessel where condensed vapor is collected for refluxing back into the distillation column.
Reflux: The process of returning a portion of the condensed vapor back to the distillation column to enhance separation.
Reflux Ratio (R): A measure of the amount of liquid returned to the column as reflux compared to the distillate produced.
Distillate (D): The product collected at the top of the distillation column.
Overhead Vapor: The vapor that exits the top of the distillation column before being condensed.
Stages, Plates, Trays: Refers to the various levels within the distillation column where vapor-liquid equilibrium occurs.
Boilup: The rate at which vapor is generated in the reboiler.
Boilup Ratio (VB): Ratio of the vapor flow rate to the liquid bottoms flow rate in the column.
Reboiler: A heat exchanger used to vaporize the liquid at the bottom of the column.
Bottoms (B): The product collected at the bottom of the distillation column.
Feed (F): The mixture fed into the distillation column for separation.
Light Key (LK): The more volatile component in a binary mixture.
High Key (HK): The less volatile component in a binary mixture.
Distillation Nomenclature
Variables:
$n$: Plate number in the top rectifying section.
$m$: Plate number in the lower stripping section.
$L$: Liquid flow rate in the top rectifying section.
$V$: Vapor flow rate in the top rectifying section.
$L_{the}$: Liquid flow rate in the lower stripping section.
$V_{the}$: Vapor flow rate in the lower stripping section.
$R$: Reflux ratio; can be expressed as $R = rac{L}{D}$.
$VB$: Boilup ratio represented as $VB = rac{V_{the}}{B}$.
$N$: Number of equilibrium stages.
$LK$: Light key (more volatile compound).
$MVC$: More volatile compound.
$x$: Mole fraction of the MVC in liquid.
$y$: Mole fraction of the MVC in vapor.
Binary VL Systems
From TXY Plot to XY Plot: From the temperature-composition diagram (TXY) or pressure-composition diagram (PXY), the XY plot can be constructed for graphical calculations useful in flash/distillation.
Example: In a system of acetonitrile (1) and nitromethane (2).
XY Plot: Relative Volatility Relationship
If $ rac{ ext{α}}{A,B}$ is constant across the composition range and if Raoult’s Law applies:
As the XY curve approaches $y = x$, separation becomes increasingly difficult as $ ext{α}
ightarrow 1$.Separation improves when $ ext{α} > 1$.
Text Reference: SHR Section 4.2
Practical Considerations in Binary Distillation
Condenser Type
Types:
Total Condenser (Type a): Where all vapor is condensed into liquid.
Partial Condenser (Type b): Only a fraction of vapor is condensed.
Mixed (Type c): Combination of both total and partial condenser configurations.
Reboiler Type
Types:
Kettle Type: Uses external heat for boiling the bottoms.
Steam (Condensate): Employs steam to aid in vaporizing the liquid bottoms.
Vertical Thermosyphon: Relies on natural convection to circulate vapor and liquid.
Binary Distillation: McCabe-Thiele Method
Concept: This method graphically represents the equilibrium stages of the distillation process.
Key Components:
Overhead Vapor: The vapor phase collected after condensation.
Total Reflux: Occurs when all overhead vapor is returned to the column without withdrawal of distillate.
Reflux Drum: Where the condensed liquid is collected before it returns to the distillation process.
Stages and Mole Fractions:
Top stage mole fraction: $x_1 = rac{D}{D ext{(R + 1)}}$.
Bottom stage mole fraction: $x_B$.
Plotting the Operating Lines
Rectifying Line:
Plot straight line considering variables of $x_D$ and overall mass balance.
Use equilibrium expressions for calculations.
Stripping Line:
Based on bottoms mole fractions and reboil ratios.
q-Line:
Represents conditions of feed entering the column: can differ based on vaporization conditions.
Stepping Off Stages Procedure
Process:
Plot lines on XY diagram.
Calculate intersections to determine number of stages needed for desired separation.
Adjust for line switch after reaching specific points in analysis.
Limiting Conditions in Distillation
Total Reflux (Nmin): No distillate withdrawal; maximum reflux ratio.
Minimum Reflux Condition: Requires infinite stages; unrealistic operationally; assessed via pinch point analysis.
Pinch Point: Defines operational limits regarding component recovery.
Distillation Column Sizing
Diameter Calculation
Similar to sizing of absorbers using relationships found in equations (6-44).
Theoretical base for design a packed column.
Tray Efficiency and Height Calculation
Efficiency: Actual number of trays correlates with tray efficiency:
$N{Actual} = rac{Nt}{E0}$ where $Nt$ is the theoretical number of trays.
Height of Column: Derived from equations considering spacing and configurations.
Additional Design Considerations
Pressure Drop: Pressure drop concerns need consideration, aiming below specific limits to ensure effective and safe column operation.
Operational Parameters: Gathering precise flow conditions, component characteristics, and estimating operational costs.
Conclusion
This concise distillation study aids understanding of both theoretical principles and practical considerations necessary for efficient separation in chemical engineering operations, specifically focusing on binary distillation systems. Students are encouraged to delve deeper into each section, ensuring familiarity with equations, graphical interpretations, and operational guidelines inherited in distillation practices.
C&PE 611: Unit Operations Design
Introduction to Binary Distillation
Binary distillation is a unit operation used to separate a liquid mixture of two components into two product streams through selective vaporization and condensation. The goal is to achieve a higher concentration of the more volatile component in the distillate and a higher concentration of the less volatile component in the bottoms.
Text References: Wankat Ch 3, SHR Ch 7
Institution: Department of Chemical & Petroleum Engineering, The University of Kansas
Distillation Terminology
Condenser: A heat exchanger located at the top of the distillation column that removes heat from the overhead vapor, causing it to condense into a liquid. Condensers can be total (all vapor condensed) or partial (some vapor remains).
Reflux Drum: A vessel where the condensed overhead vapor is collected. A portion of this liquid is returned to the column as reflux, while the remainder is withdrawn as distillate.
Reflux: The process of returning a portion of the condensed overhead liquid back to the top of the distillation column. This liquid flows down the column, counter-current to the rising vapor, providing additional contact and enhancing the separation efficiency by washing down less volatile components.
Reflux Ratio (R): A critical operating parameter defined as the molar flow rate of liquid returned to the column () divided by the molar flow rate of distillate produced (). A higher reflux ratio generally leads to better separation but requires more energy.
Distillate (D): The product stream withdrawn from the reflux drum, characterized by a higher concentration of the more volatile component.
Overhead Vapor: The vapor stream that exits the top of the distillation column before being sent to the condenser. Its composition is typically enriched in the light key component.
Stages, Plates, Trays: These refer to discrete physical or theoretical levels within the distillation column where vapor and liquid streams contact each other and approach vapor-liquid equilibrium (VLE). Each stage facilitates mass transfer, allowing the more volatile component to transfer from liquid to vapor, and the less volatile component from vapor to liquid.
Boilup: The rate at which vapor is generated in the reboiler, which then rises through the stripping section of the column.
Boilup Ratio (VB): The ratio of the vapor flow rate from the reboiler () to the liquid bottoms flow rate (). Similar to reflux ratio, it influences separation efficiency in the stripping section.
Reboiler: A heat exchanger located at the bottom of the distillation column that provides the necessary heat to vaporize a portion of the liquid bottoms, creating the vapor flow that rises through the column. This liquid stream becomes the bottoms product.
Bottoms (B): The product stream collected at the bottom of the distillation column, typically enriched in the less volatile component.
Feed (F): The mixture that is introduced into the distillation column for separation. The feed can be introduced as a liquid, vapor, or a mixture of both, and its thermal condition significantly impacts column operation.
Light Key (LK): In a binary mixture, the component that is more volatile and preferentially vaporizes, thus concentrating in the distillate.
Heavy Key (HK): In a binary mixture, the component that is less volatile and preferentially remains in the liquid phase, thus concentrating in the bottoms.
Distillation Nomenclature
Variables: These variables are used in mass and energy balance equations and graphical methods like McCabe-Thiele.
: Plate number, typically counted upwards from the feed plate in the top rectifying section.
: Plate number, typically counted downwards from the feed plate in the lower stripping section.
: Liquid molar flow rate in the top rectifying section ().
: Vapor molar flow rate in the top rectifying section ().
: Liquid molar flow rate in the lower stripping section ().
: Vapor molar flow rate in the lower stripping section ().
: Reflux ratio; can be expressed as (dimensionless).
: Boilup ratio represented as (dimensionless).
: Total number of equilibrium stages in the column (dimensionless).
: Light key (more volatile compound).
: More volatile compound (often used interchangeably with LK for binary systems).
: Mole fraction of the MVC in the liquid phase (dimensionless).
: Mole fraction of the MVC in the vapor phase (dimensionless).
Binary VLE Systems
Understanding binary Vapor-Liquid Equilibrium (VLE) is fundamental to distillation design. This involves experimental or predicted relationships between liquid and vapor compositions at equilibrium at a given temperature and pressure.
From TXY Plot to XY Plot: The temperature-composition diagram (TXY) or pressure-composition diagram (PXY) provides information on boiling points and compositions. From these, an XY plot (equilibrium curve) can be constructed, which shows the equilibrium vapor mole fraction (y) versus equilibrium liquid mole fraction (x) at a constant pressure. This XY plot is crucial for graphical calculations in flash distillation and the McCabe-Thiele method for multistage distillation.
Example: In a system of acetonitrile (1) and nitromethane (2), an XY plot would show how the vapor composition of acetonitrile relates to its liquid composition at equilibrium.
XY Plot: Relative Volatility Relationship
Relative volatility ( or alpha) is a measure of the ease of separation of two components in a mixture. For components A and B, or simplified to , where is the vapor-liquid equilibrium ratio ().
If is constant across the composition range and if Raoult’s Law applies (ideal solution behavior):
As the XY curve approaches (the 45-degree diagonal line), separation becomes increasingly difficult because ext{ ext{α}}
ightarrow 1. When , the components have identical vapor pressures, and no separation is possible by distillation.Separation improves significantly when ext{ ext{α}} >> 1 (e.g., ext{ ext{α}} > 1.1 - 1.2), indicating a large difference in volatility between the components, making them easier to separate.
Text Reference: SHR Section 4.2
Practical Considerations in Binary Distillation
Condenser Type
The choice of condenser affects the overall energy balance and the definition of the operating lines.
Types:
Total Condenser (Type a): All the overhead vapor is condensed into liquid. This simplifies calculations as the vapor leaving the top stage is in equilibrium with the reflux liquid, and .
Partial Condenser (Type b): Only a fraction of the vapor is condensed, with the remaining vapor withdrawn as distillate. The partial condenser itself acts as an equilibrium stage, meaning the vapor product is in equilibrium with the liquid reflux.
Mixed (Type c): A less common configuration involving a combination, perhaps with part of the vapor condensed and returned to the column, and another part condensed and withdrawn, or specific setups for handling non-condensable gases.
Reboiler Type
The reboiler provides the heating required to generate vapor in the column. Its design impacts heating utility requirements and operational stability.
Types:
Kettle Type: A shell-and-tube heat exchanger where the liquid bottoms accumulate in a vessel (kettle) and are boiled, generating vapor that returns to the column while the concentrated liquid is drawn off as product.
Steam (Condensate): Uses steam as the heating medium in a heat exchanger (e.g., kettle or thermosyphon reboiler) to vaporize the liquid at the column's bottom. The steam condenses, and the condensate is returned.
Vertical Thermosyphon: Relies on natural convection to circulate liquid from the column bottom through the reboiler tubes and back into the column, where flash vaporization occurs. It's often energy-efficient due to its passive circulation.
Binary Distillation: McCabe-Thiele Method
Concept: The McCabe-Thiele method is a simplified graphical technique used to determine the number of theoretical equilibrium stages required to achieve a desired separation of a binary mixture in a continuous distillation column. It makes several assumptions, including constant molar overflow (CMO), which implies constant molar flow rates of liquid and vapor within each section of the column.
Key Components: The method involves plotting three main lines on an XY equilibrium diagram: the equilibrium curve, the rectifying operating line, the stripping operating line, and the q-line.
Equilibrium Curve: Represents the vapor-liquid equilibrium relationship ( vs. ) for the binary mixture at the column's operating pressure.
Operating Lines: Represent the mass balance relationships between the vapor and liquid streams within the rectifying and stripping sections of the column. These lines define the compositions of streams moving between stages.
Overhead Vapor: The vapor phase collected after condensation, whose composition ( or if total condenser) is a target for separation.
Total Reflux: An extreme operating condition where all overhead vapor is condensed and returned to the column (, R
ightarrow ext{ ext{∞}}). Under total reflux, the operating lines coincide with the diagonal, leading to the minimum number of theoretical stages () required for a given separation.Reflux Drum: Where the condensed liquid is collected before it returns to the distillation process or is withdrawn as distillate ().
Stages and Mole Fractions: The method graphically steps off stages, alternating between the equilibrium curve and the operating lines, starting from one end of the column (e.g., distillate composition) until the desired bottoms composition is reached.
Top stage mole fraction: For a total condenser, the distillate composition () is equal to the liquid leaving the first stage, and also the vapor leaving the top stage, so . For a partial condenser, the vapor distillate is in equilibrium with the liquid reflux.
Bottom stage mole fraction: The bottoms composition () is the target composition for the liquid leaving the reboiler.
Plotting the Operating Lines
Rectifying Line: This operating line describes the relationship between liquid and vapor compositions in the rectifying (top) section of the column, above the feed plate. It is derived from a material balance around the top of the column and the reflux drum.
Plot a straight line on the XY diagram. It has an intercept on the -axis at and passes through the point (if total condenser). Its slope is .
Use equilibrium expressions for calculations to ensure that the stages stepped off represent equilibrium conditions.
Stripping Line: This operating line describes the relationship between liquid and vapor compositions in the stripping (bottom) section of the column, below the feed plate. It is derived from a material balance around the bottom of the column and the reboiler.
Based on bottoms mole fractions () and reboil ratios. This line extends from the reboiler composition to the intersection with the rectifying line, and its slope is related to the boilup ratio.
q-Line: The q-line represents the thermal condition of the feed stream as it enters the distillation column. It connects the rectifying and stripping operating lines at the feed plate.
It is a straight line passing through the feed composition . Its slope is , where is the fraction of feed that is liquid (or the amount of heat required to vaporize one mole of feed at its bubble point divided by the molar latent heat of vaporization).
Different q-Line conditions:
Saturated liquid feed (): Vertical line.
Saturated vapor feed (): Horizontal line.
Partially vaporized feed (0 < q < 1): Line with a negative slope.
Subcooled liquid feed (q > 1): Line with a positive slope (steeper than vertical).
Superheated vapor feed (q < 0): Line with a positive slope (less steep than horizontal, typically very shallow).
Stepping Off Stages Procedure
Process: Once the equilibrium curve, rectifying operating line, stripping operating line, and q-line are plotted on the XY diagram:
Start at the desired distillate composition () on the line (for a total condenser).
Draw a horizontal line from to the equilibrium curve ().
From the equilibrium curve, draw a vertical line down to the rectifying operating line ().
Repeat steps 2 and 3, stepping off stages between the equilibrium curve and the operating line. Each step represents one theoretical equilibrium stage.
When the stepping crosses the q-line (which marks the feed plate), switch from the rectifying operating line to the stripping operating line for subsequent stages.
Continue stepping until the desired bottoms composition () is reached or passed. The total number of steps represents the number of theoretical stages needed.
Limiting Conditions in Distillation
Understanding these conditions helps in determining the feasible operating range and optimizing column design.
Total Reflux (): This occurs when all the condensed overhead vapor is returned to the column without any distillate withdrawal (, R
ightarrow ext{ ext{∞}}). Under this condition, the operating lines coincide with the diagonal. Total reflux provides the minimum number of theoretical equilibrium stages () required for a given separation. While not practiced for production, it sets a theoretical lower bound for column size.Minimum Reflux Condition (): This condition signifies the lowest possible reflux ratio at which the desired separation can theoretically be achieved. At minimum reflux, the operating line for either the rectifying or stripping section touches the equilibrium curve at some point, called a