Shortcut Results
Distillate Flow, D:
-
Bottoms Flow, B:
-
Min. Stages (Nmin):
-
Min. Reflux (Rmin):
-
Selected Reflux (R):
-
Theoretical Stages (N):
-
Feed Stage Estimate:
-
Hydraulics (Preliminary)
Top Vapor Rate (Vtop):
-
Flooding Velocity (uf):
-
Design Velocity (ud):
-
Required Net Area:
-
Est. Column Diameter:
-
Heat Duties
Condenser Duty (Qc):
-
Reboiler Duty (Qr):
-
Fenske: Nmin = ln[(xD_LK/xD_HK)*(xB_HK/xB_LK)] / ln(α)
Underwood: zLK/(α-θ) + zHK/(1-θ) = 1-q ; Rmin = Σ xD_i α_i/(α_i-θ) -
1
Gilliland: X=(R-Rmin)/(R+1), Y=1-exp(A*(X-1)/sqrt(X)),
N=(Nmin+Y)/(1-Y)
Diameter: u_f = C·√((ρL-ρV)/ρV), u_d = u_f·(flood%), Dcol = √(4·A/π)
Technical Notes
Variable Definitions
-
F, D, B: Flowrates (kmol/h) for Feed,
Distillate, Bottoms.
- q: Feed quality (thermal condition).
-
z, xD, xB: Mole fractions of Light Key (LK).
- α: Relative volatility (LK/HK).
-
Nmin: Minimum theoretical stages (Total Reflux).
-
Rmin: Minimum reflux ratio (Infinite Stages).
- N: Theoretical stages at selected R.
Formulas / Logic
-
Product Split: D = F·(zLK −
xB,LK)/(xD,LK − xB,LK).
-
Fenske (Nmin): Uses average α to estimate
stages at total reflux.
-
Underwood (Rmin): Solves for pinch root θ to
find minimum reflux for specified split.
-
Gilliland (N): Empirical correlation linking N,
Nmin, R, and Rmin.
-
Diameter: Souders-Brown method using C-factor
and densities.
Assumptions / Notes
-
Assumes Binary Mixture (LK/HK) where xHK
= 1 - xLK.
-
Assumes Constant Molar Overflow (CMO) and
constant relative volatility.
-
Stage counts are theoretical; apply efficiency
for real trays.
-
Diameter is a screening estimate only; verify with rigorous
vendor tools.
-
Shortcut sizing is best for early feasibility. For close-boiling
systems, strong non-ideality, pressure-sensitive VLE, or
multi-component feeds, use rigorous equilibrium/Rate-based
design.
-
Hydraulics here uses a single C-factor approach for screening;
actual capacity depends on tray type, surface tension, froth
regime, downcomer design, and entrainment limits.
-
Always ensure pressures are absolute (kPa(a)) and temperatures
in °C are converted internally to K where required.
References
-
Fenske–Underwood–Gilliland (FUG) shortcut method
(binary/constant α screening).
-
Perry’s Chemical Engineers’ Handbook — Distillation and
absorption fundamentals and shortcut methods.
-
Kister, H.Z. — Distillation Design / Distillation Operation
(tray hydraulics, capacity, and design practices).
-
Souders–Brown capacity approach (screening) for vapor velocity /
flooding tendency; final tray capacity requires detailed
correlations and vendor tray type.
-
Company/vendor tray rating tools and rigorous simulators (Aspen
HYSYS/Plus, Pro/II, UniSim) are required for final design
verification.