Distillation Cheatsheet

Cheatsheet Content

### Distillation Basics - **Definition:** Separation process based on differences in volatility of components in a liquid mixture. - **Key Principle:** Vapor phase is enriched in more volatile components, liquid phase in less volatile components. - **Applications:** Petrochemical industry, alcoholic beverages, air separation. - **Assumptions (Ideal Distillation):** - Constant molar overflow (CMO): Molar heats of vaporization are equal. - Adiabatic column. - No heat of mixing. - Equimolar counterdiffusion. ### Relative Volatility ($\alpha$) - **Definition:** Ratio of vapor pressures of two components or ratio of K-values. $$\alpha_{AB} = \frac{P_A^o}{P_B^o} = \frac{y_A/x_A}{y_B/x_B}$$ where $P^o$ is vapor pressure, $y$ is vapor mole fraction, $x$ is liquid mole fraction. - **Significance:** - $\alpha > 1$: Separation is possible. - $\alpha = 1$: No separation possible (azeotrope). - Higher $\alpha$ means easier separation. - **For binary mixtures:** $$y = \frac{\alpha x}{1 + (\alpha - 1)x}$$ This equation generates the equilibrium curve. ### Flash Distillation (Equilibrium Distillation) - **Process:** Liquid mixture is partially vaporized by reducing pressure or increasing temperature. Vapor and liquid phases are then separated. - **Material Balance:** - Overall: $F = V + L$ - Component A: $F z_F = V y + L x$ where $F$ is feed, $V$ is vapor, $L$ is liquid, $z_F$ is feed mole fraction. - **Operating Line (Equilibrium Flash):** $$y = -\frac{L}{V}x + \frac{F}{V}z_F$$ - **Solution Method:** Graphically, plot equilibrium curve and operating line. Intersection gives $x$ and $y$. Requires trial-and-error if $V/F$ or $L/F$ is unknown. ### Differential Distillation (Rayleigh Distillation) - **Process:** Batch operation where vapor is continuously removed from a still, leading to a continuous change in liquid composition. - **Rayleigh Equation:** $$\ln \frac{L_1}{L_2} = \int_{x_2}^{x_1} \frac{dx}{y^* - x}$$ where $L_1, x_1$ are initial liquid amount and composition, $L_2, x_2$ are final. $y^*$ is equilibrium vapor composition. - **For constant relative volatility ($\alpha$):** $$\ln \frac{L_1}{L_2} = \frac{1}{\alpha - 1} \ln \left[ \frac{x_1(1-x_2)}{x_2(1-x_1)} \right] + \ln \left[ \frac{1-x_2}{1-x_1} \right]$$ ### Continuous Distillation (Tray/Packed Columns) - **Components:** Reboiler, condenser, trays/packing, feed, distillate, bottoms. - **Sections:** Rectifying (enriching) section above feed, Stripping section below feed. #### Material Balances - **Overall:** $F = D + B$ - **Component A:** $F z_F = D x_D + B x_B$ where $D$ is distillate, $B$ is bottoms, $x_D, x_B$ are their compositions. #### Operating Lines - **Rectifying Section (Top):** $$y_{n+1} = \frac{R}{R+1}x_n + \frac{x_D}{R+1}$$ where $R = L/D$ (reflux ratio). - **Stripping Section (Bottom):** $$y_{m+1} = \frac{\bar{L}}{\bar{V}}x_m - \frac{B x_B}{\bar{V}}$$ where $\bar{L}$ and $\bar{V}$ are liquid and vapor flows in stripping section. #### Feed Line (q-line) - **Definition:** Relates feed condition to the intersection of operating lines. - **Slope:** $\frac{q}{q-1}$ - $q = 1$ (saturated liquid feed): vertical - $q = 0$ (saturated vapor feed): horizontal - $0 1$ (subcooled liquid): positive slope - $q ### Azeotropic & Extractive Distillation - **Azeotrope:** A mixture that boils at a constant temperature and composition, making separation by simple distillation impossible. - **Azeotropic Distillation:** Add a third component (entrainer) that forms a new, lower-boiling azeotrope with one of the original components, which is then separated. - Example: Benzene added to ethanol-water to remove water. - **Extractive Distillation:** Add a high-boiling, non-volatile solvent that alters the relative volatilities of the original components, allowing separation. The solvent is usually added near the top of the column. - Example: Phenol or furfural for separating paraffins and aromatics. ### Packed Columns - **Mechanism:** Continuous contact between liquid and vapor phases over a packing material. - **Height of a Transfer Unit (HTU):** Measure of separation efficiency for a given packing. $$H_{OG} = \frac{G_M}{K_G a P_{avg}}$$ where $G_M$ is molar gas flow, $K_G a$ is overall mass transfer coefficient, $P_{avg}$ is average pressure. - **Number of Transfer Units (NTU):** Measure of separation difficulty. $$N_{OG} = \int_{y_1}^{y_2} \frac{dy}{y^* - y}$$ - **Total Packing Height:** $Z = H_{OG} \times N_{OG}$ - **HETP (Height Equivalent to a Theoretical Plate):** Relates packed column height to theoretical stages. $HETP = Z / N_{theoretical}$. ### Distillation Design Considerations - **Column Diameter:** Based on vapor velocity to avoid flooding and weeping. - **Flooding:** Excessive vapor velocity, liquid backs up in column. - **Weeping:** Low vapor velocity, liquid falls through perforations in trays. - **Pressure Drop:** Important for vacuum distillation. - **Energy Integration:** Heat pumps, recompression, side reboilers/condensers to reduce energy consumption. - **Control:** Temperature, pressure, flow rates to maintain product specifications.