How to simulate distributed pipeline cool-down (indexed equation model)
A hot gas cools along a buried pipeline — modeled as a custom unit op whose internals are a distributed 1-D indexed equation system, the gPROMS-style array + indexed-equation modeling capability solved by the sandboxed equation engine. Twenty axial segments compute the full temperature profile T[0..20] (the inlet drives the boundary T[0]; each segment loses heat toward the ground temperature); the outlet temperature is the end of that profile. Demonstrates writing a distributed model as one indexed template rather than 20 hand-written equations.
- 1Open the ready-made model
Open the "Distributed pipeline cool-down (indexed equation model)" 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 PENG-ROBINSON property package over methane — already selected, so the phase equilibrium and enthalpy are physically consistent from the first run.
- 3Review the flowsheet
The flowsheet chains PIPE. 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
- PENG-ROBINSON
- Components
- methane
- Unit operations
- PIPE
Opens live on the canvas — free, no install.
Explore the model & flowsheetFrequently asked questions
- What does the Distributed pipeline cool-down (indexed equation model) model simulate?
- A hot gas cools along a buried pipeline — modeled as a custom unit op whose internals are a distributed 1-D indexed equation system, the gPROMS-style array + indexed-equation modeling capability solved by the sandboxed equation engine. Twenty axial segments compute the full temperature profile T[0..20] (the inlet drives the boundary T[0]; each segment loses heat toward the ground temperature); the outlet temperature is the end of that profile. Demonstrates writing a distributed model as one indexed template rather than 20 hand-written equations.
- Which thermodynamic method does it use?
- The PENG-ROBINSON property package, over methane — already selected. You can switch the method on the canvas before running.
- Which unit operations are in the flowsheet?
- It chains PIPE. 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. Distributed pipeline cool-down (indexed equation model) 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
Polymerization reactor comparison: CSTR cascade vs. tubular (PFR)
The same monomer feed, split 50/50 into two trains at equal total reactor volume: a 3-stage CSTR cascade (each stage blending its own new polymer with the MWD already carried by the stream from the stage before it) versus a single tubular (PFR) reactor. Both converge to a real, different Mn/Mw/PDI — the PFR reaches higher conversion at the same total volume, but its cumulative polydispersity is measurably broader than the cascade's, because chain length drifts continuously with conversion along the tube while each CSTR stage makes its own local production under one fixed monomer concentration. See the 'Polymerization Reactors' docs page for the full reasoning.
Helium liquefaction (Linde-Hampson cycle)
A Joule-Thomson liquefaction loop: helium is compressed, aftercooled, precooled well below its ~40-51 K JT-inversion temperature, then throttled through a valve into a flash drum that draws off liquid helium while the cold vapor recycles back to the compressor suction — the same JT-cycle physics as the platform's LNG/refrigeration loops, run on a fluid whose inversion curve makes precooling mandatory before the throttle can cool it at all.
Cement kiln calcination + CO2 liquefaction
Preheated limestone (CaCO3) enters an indirectly-heated rotary kiln that calcines it toward CaO, releasing a CO2-rich off-gas; the gas is knocked free of moisture, then compressed and cooled to liquefy the CO2 for transport/storage. Honesty notes: (1) oxy-fuel combustion itself isn't modeled — this codebase's fired-heater unit hardcodes standard dry-air combustion stoichiometry, so the kiln's heat input is represented the way this solver's rotary-kiln model actually works, an indirect utility-temperature wall duty, not a simulated oxy-fuel flame; (2) the calcination conversion shown (~21%) is the real, kinetically-limited result of this model's validated Arrhenius parameters at this residence time/temperature, not a claim of complete calcination — a real cement plant's preheater-tower-plus-kiln train achieves far higher calcination degree than one rotary-kiln unit alone models here; (3) CO2 must be compressed above roughly 5.2 atm before it can be liquefied by cooling at all (it has no liquid phase at 1 atm at any temperature), which the compressor stage here reflects.
NGL fractionation: single-shell Petlyuk dividing-wall column
A natural-gas-liquids cut (ethane / propane / n-butane) split into three on-spec products by ONE thermally-coupled dividing-wall column instead of two columns in series. This uses the native Petlyuk unit op: a prefractionator whose reflux and boilup are supplied by the main column (the single condenser + single reboiler), solved by an outer Wegstein loop that converges the bidirectional vapor/liquid coupling to self-consistency — the coupling legacy sequential-modular solvers approximate with two connected columns whose recycle fails to converge. Honesty note: the vapor-split and liquid-split ratios are specified inputs (not solved from tray hydraulics), and this is an outer-loop coupling of two rigorous MESH sub-solves, not a single monolithic Petlyuk MESH.
Ethanol–water distillation
An 8-stage column concentrating ethanol overhead toward the azeotrope (the headline demo).
Flash separation
An isothermal flash drum at 358 K splitting an ethanol–water feed into ethanol-rich vapor and water-rich liquid products.