LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
mechanicalwith-tool

Pfr Volume

Calculates required plug flow reactor volume for an isothermal constant-density first-order reaction. The template uses tau = -ln(1-X)/k and V = Q tau, while also reporting molar feed and outlet concentration for deterministic reactor sizing checks.

with-tool: The model is given an executable Python calculator script.

Standards

Chemical Reaction Engineering Fundamentals

Tags

deterministicfirst-ordermechanicalpfrreactor-sizing

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

4 inputs

Always given

Included directly in every task prompt.

4

  • Volumetric flow

    volumetric_flow_m3_h

    Volumetric feed flow rate

    0.1 – 5000 m3/h

  • Inlet concentration

    inlet_concentration_kmol_m3

    Inlet concentration of limiting reactant

    0.01 – 20 kmol/m3

  • Required conversion pct

    required_conversion_pct

    Required reactant conversion

    5 – 98 %

  • Rate constant h inv

    rate_constant_h_inv

    First-order reaction rate constant

    0.01 – 10 1/h

Scored outputs

4 outputs

Molar feed kmol h

molar_feed_kmol_h

Molar feed rate of limiting reactant

Scores if within ±3% of the reference value.

Outlet concentration kmol m3

outlet_concentration_kmol_m3

Outlet concentration at required conversion

Scores if within ±3% of the reference value.

Space time h

space_time_h

Required reactor space time

Scores if within ±3% of the reference value.

Required volume m3

required_volume_m3

Required plug flow reactor volume

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

All inputs remain visible at every tier

For this template, difficulty scales through parameter and scenario ranges rather than hidden information.

easy:
All parameters given for a small process reactor
medium:
All parameters given across small and large first-order PFRs
hard:
All parameters given for larger treatment reactor sizing

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • pfr-volume_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior mechanical engineer specializing in process reactor sizing.2 3## Problem4 5Calculate required plug flow reactor volume for an isothermal constant-density first-order reaction.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Volumetric flow rate Q | {{ volumetric_flow_m3_h }} | m3/h |12| Inlet concentration C0 | {{ inlet_concentration_kmol_m3 }} | kmol/m3 |13| Required conversion X | {{ required_conversion_pct }} | % |14| First-order rate constant k | {{ rate_constant_h_inv }} | 1/h |15 16{% if archetype_description is defined %}17### Reactor Context18 19{{ archetype_description }}20{% endif %}21 22{% if tool_available %}23## Available Tool24 25A PFR sizing calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:26 27```bash28python3 /workspace/{{ meta.name }}_calc.py --help29```30 31You may use this tool to verify your calculations or compute values directly.32{% endif %}33 34## Required35 36Calculate the following:37 381. Molar feed rate of limiting reactant (kmol/h)392. Outlet concentration at required conversion (kmol/m3)403. Required space time (h)414. Required plug flow reactor volume (m3)42 43## Constraints44 45- No internet access is available. Work from engineering knowledge and the provided tool.46- Convert percent conversion to decimal conversion X.47- Use molar feed = Q x C0.48- Use outlet concentration = C0 x (1 - X).49- Use first-order PFR space time tau = -ln(1 - X) / k.50- Use required volume = Q x tau.51 52## Output Format53 54Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:55 56```json57{58 "molar_feed_kmol_h": <numeric_value>,59 "outlet_concentration_kmol_m3": <numeric_value>,60 "space_time_h": <numeric_value>,61 "required_volume_m3": <numeric_value>62}63```64 65Write your complete solution to `/workspace/output.md`.66

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Small process reactor

small_process_reactor

Small liquid-phase process PFR

pilot-process-skidspecialty-chemical-line
Parameter ranges
volumetric_flow_m3_h
1 – 50
inlet_concentration_kmol_m3
0.1 – 3
required_conversion_pct
40 – 90
rate_constant_h_inv
0.2 – 3

Large treatment reactor

large_treatment_reactor

Large first-order treatment reactor

industrial-wastewater-reactorprocess-treatment-train
Parameter ranges
volumetric_flow_m3_h
50 – 2000
inlet_concentration_kmol_m3
0.02 – 1
required_conversion_pct
50 – 95
rate_constant_h_inv
0.05 – 1

Example task

industrial-wastewater-reactor-large-treatment-reactor-preview — hard difficulty, all inputs given.

Large first-order treatment reactor. industrial-wastewater-reactor. Required outputs: molar_feed_kmol_h, outlet_concentration_kmol_m3, space_time_h, required_volume_m3

The model sees

Scenario context and visible inputs.

volumetric_flow_m3_h
50 to 2000 m3/h
inlet_concentration_kmol_m3
0.02 to 1 kmol/m3
required_conversion_pct
50 to 95 %
rate_constant_h_inv
0.05 to 1 1/h

Executable tool: pfr-volume_calc.py

The model must infer

Inputs withheld at this difficulty.

Nothing. All inputs are supplied.

The model must produce

The scored JSON answer schema.

{
  "molar_feed_kmol_h": <number>,
  "outlet_concentration_kmol_m3": <number>,
  "space_time_h": <number>,
  "required_volume_m3": <number>
}
  • molar_feed_kmol_h · scored within ±3%
  • outlet_concentration_kmol_m3 · scored within ±3%
  • space_time_h · scored within ±3%
  • required_volume_m3 · scored within ±3%