distillation-column

name	distillation-column
description	Distillation column design — McCabe-Thiele, Fenske-Underwood-Gilliland, tray efficiency, reflux ratio, packing HETP, binary/multicomponent VLE, reboiler/condenser duties, ASME, AIChE correlations.
metadata	{"priority":7,"promptSignals":{"phrases":["distillation column","McCabe-Thiele","distillation design","reflux ratio","distillation tray","HETP"],"minScore":3}}

Distillation Column Design — Complete Skill

VLE Fundamentals

Vapor-Liquid Equilibrium (VLE) — binary: y_i = K_i × x_i [K_i = equilibrium ratio; y = vapor mole fraction; x = liquid mole fraction] K_i = P_i_sat / P_total [Raoult's Law; ideal vapor + liquid; P_sat from Antoine equation] Antoine: log(P_sat) = A - B/(C + T) [T in °C; P in mmHg or kPa; constants from NIST]

Relative volatility: α_12 = K₁/K₂ = (P₁_sat/P₂_sat) [α > 1: component 1 more volatile] y₁ = α × x₁ / (1 + (α-1) × x₁) [equilibrium curve for binary system]

Minimum reflux (Underwood): For binary: R_min = (x_D - y_F*) / (y_F* - x_F) × (L/V)_min More precisely via Underwood equation for multicomponent: Σ [α_i × z_F_i / (α_i - θ)] = 1 - q [solve for θ between α values] R_min + 1 = Σ [α_i × x_D_i / (α_i - θ)]

McCabe-Thiele Method (Binary)

Operating lines: Rectifying (above feed): y = (L/V) × x + x_D × (1 - L/V) = (R/(R+1)) × x + x_D/(R+1) L/V = R/(R+1); R = L/D (reflux ratio)

Stripping (below feed): y = (L̄/V̄) × x - x_B × (L̄/V̄ - 1) L̄ = L + q × F; V̄ = V - (1-q) × F [q = feed quality; q = 1 liquid; q = 0 vapor]

q-line (feed quality): y = q/(q-1) × x - z_F/(q-1) q = 1: vertical q-line (saturated liquid feed); q = 0: horizontal (saturated vapor)

Graphical procedure:

1. Plot equilibrium curve y vs. x
2. Draw rectifying and stripping operating lines
3. Draw q-line; find intersection
4. Step-off stages between equilibrium curve and operating lines
5. Count theoretical stages N_T

Minimum stages (Fenske equation at total reflux): N_min = ln[(x_D/(1-x_D)) × ((1-x_B)/x_B)] / ln(α_avg) [Fenske]

Fenske-Underwood-Gilliland (FUG) — Multicomponent

Fenske (total reflux): N_min = log[(x_LK_D/x_HK_D) / (x_LK_B/x_HK_B)] / log(α_LK_HK) LK = light key; HK = heavy key components

Underwood (minimum reflux): Find θ: Σ [α_i × z_F_i / (α_i - θ)] = 1 - q → R_min + 1 = Σ [α_i × x_D_i / (α_i - θ)]

Gilliland correlation: X = (R - R_min) / (R + 1); Y = (N - N_min) / (N + 1) Y = 1 - exp[(1 + 54.4X)/(11 + 117.8X) × (X-1)/X^0.5] [Molokanov fit; 1971] Typical: R = 1.05–1.5 × R_min; N = 1.5–2.0 × N_min

Tray Design

Efficiency (Murphree tray efficiency): E_MV = (y_n - y_{n+1}) / (y_n* - y_{n+1}) [y_n* = equilibrium with x_n] Typical: E_MV = 0.65–0.85 (hydrocarbon systems); 0.50–0.75 (aqueous)

Actual stages required: N_actual = N_theoretical / E_overall [E_overall = 0.5–0.9 from O'Connell correlation]

O'Connell correlation: E_overall = 0.492 × (μ_L × α)^(-0.245) [μ_L = liquid viscosity [mPa·s]; α = relative volatility]

Tray hydraulics: Vapor flow (F-factor): F = u_a × √ρ_v ≤ F_max (from vendor; typically 1.0–2.5 Pa^0.5) Weir height: h_w = 0.04–0.08 m (affects liquid holdup and residence time) Downcomer velocity: < 0.1 m/s (liquid loading limit) Active area: 60–80% of tray area; 15% downcomer area each side

Tray spacing: 0.45–0.90 m (standard 0.60 m); tighter for lower Mtotal (short column); wider for high foam

Packed Column Design

Height Equivalent Theoretical Plate (HETP): HETP = Z_packed / N_theoretical [m/stage; Z_packed = total packing height] For structured packing (Mellapak 250Y): HETP ≈ 0.3–0.5 m (low-viscosity systems) For random packing (2" Pall rings): HETP ≈ 0.6–1.0 m

Number of Transfer Units (NTU) alternative: H_OG = Z / N_OG [height of transfer unit] N_OG = ∫ dy / (y* - y) [integral over column height] N_OG ≈ N_theoretical × ln(α) / (α - 1) [approximate conversion]

Packing pressure drop: GPDC chart (Eckert/Billet): F_lv = (L/V) × √(ρ_V/ρ_L) [flow parameter] Reading ΔP/Z from GPDC chart (30–100 Pa/m structured; 100–300 Pa/m random)

Flooding: maximum gas velocity F ≤ 0.7–0.8 × F_flood; above = flooding, pressure spike

Energy Balance

Condenser duty: Q_C = V × λ_vap = (R+1) × D × λ_vap [V = vapor leaving top; D = distillate; λ_vap = latent heat]

Reboiler duty: Q_R = V̄ × λ_vap_B = L̄ - V̄ + (1-q) × F × λ_vap_approx [energy balance around column] Material balance: Q_R ≈ Q_C + F × h_F - D × h_D - B × h_B [enthalpy balance; h = molar enthalpy]

Steam consumption: ṁ_steam = Q_R / λ_steam [kg/hr; λ_steam ≈ 2000–2200 kJ/kg for low-pressure steam]

Column Sizing

Diameter (tray column): A_active = V_molar × ρ_V × M_W / (F_max × ρ_V^0.5 × 3600) [m²; back-solve for diameter] D_column = √(4A_total/π) [A_total = A_active + 2 × A_downcomer]

Tower height: H_column = N_actual × H_tray_spacing + top/bottom allowances H_column = N_actual × 0.60 + 3 m (bottom sump) + 2 m (top vapor disengagement)

Standards

Standard	Scope
ASME Section VIII	Pressure vessel (column shell)
AIChE Design Manual	Tray and packed column design
API 2500	Storage of petroleum products (distillation context)
ASTM E1416	Distillation of petroleum products
ISO 11011	Distillation apparatus calibration

Output

Provide: binary/multicomponent system, key components (LK, HK), feed composition z_F and quality q, product specifications (x_D, x_B), minimum reflux ratio R_min (Underwood), operating reflux ratio R (R_min × 1.2–1.5), minimum stages N_min (Fenske), actual stages N_actual (Gilliland), feed tray location (Kirkbride equation), tray efficiency E_MV [%] (O'Connell), column diameter D [m], tray spacing [m], condenser duty Q_C [kW] and reboiler duty Q_R [kW], steam consumption [kg/hr], HETP [m] (if packed), column height H [m], and applicable standard (ASME VIII, AIChE correlation).