How to simulate tray efficiency — real trays vs ideal stages
The same ethanol–water column solved with a **Murphree vapor tray efficiency** of 0.7 instead of ideal equilibrium stages. A real sieve/valve tray never reaches full vapor-liquid equilibrium — the vapor leaving it only partly approaches the equilibrium composition with the tray liquid, mixing in un-equilibrated vapor from the tray below: `y = E·K·x + (1−E)·y_below` (Murphree 1925). At E = 0.7 each of these 12 trays does 70% of an ideal stage's work, so the overhead ethanol is **lower** than an equilibrium column of the same tray count would predict — which is exactly why a real column needs *more* trays than a shortcut (ideal-stage) calculation says. Both HYSYS and Aspen RadFrac expose this per-tray efficiency; set `murphree_efficiency` back to 1.0 to recover the ideal-stage column. The efficiency auto-selects the component-flow Naphtali-Sandholm solver (the reduced-form solvers carry no explicit per-tray VLE row to apply an efficiency to).
- 1Open the ready-made model
Open the "Tray efficiency — real trays vs ideal stages" model in the MaximaLabs workspace — no install, no license. It loads live on the canvas, ready to edit and run.
- 2Confirm the thermodynamics
This process is modeled with the NRTL property package over ethanol, water — already selected, so the phase equilibrium and enthalpy are physically consistent from the first run.
- 3Review the flowsheet
The flowsheet chains COL. Every block is a real, solvable unit op you can reconfigure on the canvas.
- 4Run the simulation
Click Run. The deterministic solver converges the material and energy balances (recycles included) and fills the live stream table — the AI never invents a number.
- 5Read the results and iterate
Inspect the converged streams, tweak a spec, and re-run — or ask the AI copilot to explain a result or diagnose a failed solve in plain English.
- Thermodynamics
- NRTL
- Components
- ethanol, water
- Unit operations
- COL
Opens live on the canvas — free, no install.
Explore the model & flowsheetFrequently asked questions
- What does the Tray efficiency — real trays vs ideal stages model simulate?
- The same ethanol–water column solved with a **Murphree vapor tray efficiency** of 0.7 instead of ideal equilibrium stages. A real sieve/valve tray never reaches full vapor-liquid equilibrium — the vapor leaving it only partly approaches the equilibrium composition with the tray liquid, mixing in un-equilibrated vapor from the tray below: `y = E·K·x + (1−E)·y_below` (Murphree 1925). At E = 0.7 each of these 12 trays does 70% of an ideal stage's work, so the overhead ethanol is **lower** than an equilibrium column of the same tray count would predict — which is exactly why a real column needs *more* trays than a shortcut (ideal-stage) calculation says. Both HYSYS and Aspen RadFrac expose this per-tray efficiency; set `murphree_efficiency` back to 1.0 to recover the ideal-stage column. The efficiency auto-selects the component-flow Naphtali-Sandholm solver (the reduced-form solvers carry no explicit per-tray VLE row to apply an efficiency to).
- Which thermodynamic method does it use?
- The NRTL property package, over ethanol, water — already selected. You can switch the method on the canvas before running.
- Which unit operations are in the flowsheet?
- It chains COL. Every block is a real, solvable unit operation you can reconfigure, add to, or remove.
- Do I need to install software or buy a license?
- No. Tray efficiency — real trays vs ideal stages runs entirely in your browser on MaximaLabs — free, no install, no license. Open the model to load it live and run the deterministic solver.
More guides like this
Tray efficiency: 20 real trays are not 20 stages
Every equilibrium column model quietly assumes each tray reaches equilibrium. Real trays do not, and the gap is not small enough to ignore when you are buying a shell. The same depropaniser is solved twice at 20 trays, a 2.5 reflux ratio and a 50/50 split. As 20 equilibrium stages it puts 99.61% propane overhead. As 20 actual trays on the rate-based model it manages 96.63% — the tower is the same height and the separation is measurably worse, because the model applies an efficiency instead of assuming one. Left to itself it derives that efficiency from the feed's relative volatility and liquid viscosity through the O'Connell correlation; give it a stage_efficiency and it uses yours, and at a punishing Murphree 0.5 the overhead drops further to 95.33%. The practical reading: an equilibrium model sized this column at 20 trays and the tray efficiency spent roughly three points of product purity. Size on equilibrium stages and you will under-build the tower — that is what the efficiency is for. Bounded: this applies a single overall efficiency to every tray, which is a screening treatment. It is not a rigorous rate-based column — for genuine two-film Maxwell-Stefan transfer with per-stage interface composition and energy coupling, use nonequilibrium_distillation instead. O'Connell itself is a correlation fitted to commercial tray data, so it carries that scatter.
Ethanol–water distillation
An 8-stage column concentrating ethanol overhead toward the azeotrope (the headline demo).
Acetone–water distillation
A 12-stage column recovers acetone overhead from a dilute aqueous solvent-recovery feed — a common industrial acetone/solvent-recycling duty.
Distillation column startup dynamics (feed-rate step)
An 8-stage ethanol-water column at a reduced startup feed rate. Solves the steady state normally; switch to the Dynamic solve mode with weir/level-controlled hydraulics enabled and step the feed rate up (e.g. 6 → 9 mol/s) to watch the bottoms draw genuinely rebalance to the new throughput as the tray inventories fill — a feed-rate disturbance no fixed-hydraulics dynamic model (incl. this same column's own default rigorous mode) can show at all. Honest bound: the vapor traffic is held at its steady-state value in this mode, so the distillate draw (condenser-level-controlled off vapor inflow) does not move for a feed-rate-only step — only the liquid/bottoms side responds.
Perry Ch.13 Example 3: butane/pentane splitter
A simple two-cut distillation splitting butane overhead from pentane bottoms, from Chapter 13 of Perry's Chemical Engineers' Handbook.
Perry Ch.13 Example 4: sloppy-butane three-cut splitter
A three-cut column with a side draw producing a deliberately 'sloppy' (off-spec, cheaper-to-make) butane cut between a propane overhead and a pentane-plus bottoms, from Chapter 13 of Perry's Chemical Engineers' Handbook.