Estimator Inputs
Example Data Table
| Case | Reactor | n | X (%) | τ (s) | CA0 (mol/L) | T (C) | k_obs | k_ref | a |
|---|---|---|---|---|---|---|---|---|---|
| A | PFR | 1 | 55 | 40 | — | 350 | 0.0200 | 0.0250 | 0.800 |
| B | CSTR | 1 | 62 | 60 | — | 320 | 0.0272 | 0.0305 | 0.893 |
| C | PFR | 2 | 40 | 25 | 1.20 | 380 | 0.0222 | 0.0280 | 0.793 |
| D | CSTR | 0 | 15 | 90 | 0.80 | 300 | 0.00133 | 0.00160 | 0.831 |
| E | PFR | 1 | 70 | 55 | — | 410 | 0.0216 | 0.0260 | 0.831 |
Formula Used
- CSTR: k = X / (τ · C_A0^(n−1) · (1−X)^n)
- PFR, n = 1: k = −ln(1−X) / τ
- PFR, n ≠ 1: k = [ (1−X)^(1−n) − 1 ] / [ (n−1) · τ · C_A0^(n−1) ]
How to Use This Calculator
- Choose the reactor model that matches your test or plant unit.
- Enter conversion and residence time using consistent operating conditions.
- Select a reaction order; provide CA0 if order is not one.
- Pick a reference method: Arrhenius parameters or a direct reference constant.
- Optionally add feed flow and catalyst mass for rate-per-mass output.
- Submit to see results below the header and above the form.
- Download CSV or PDF to document runs and comparisons.
Operational Purpose and Outputs
This estimator converts measured conversion and residence time into an observed rate constant, then reports activity as the ratio between observed and fresh reference performance. Outputs include k_obs, k_ref, activity a, activity percent, and an optional rate per catalyst mass when you supply feed molar flow and catalyst mass. The result panel is designed for quick comparisons across runs and for documenting performance drift over time. It supports quick screening before detailed kinetic regression.
Reactor Model Selection and Data Quality
Choose PFR for plug-flow test reactors and tubular units where axial mixing is limited, and CSTR for well-mixed vessels or recycle-dominated systems. Because conversion drives the calculation nonlinearly, use steady readings and consistent sampling windows. Avoid using conversions extremely close to 0% or 100%, where small measurement errors can amplify k. If order n is not one, provide a reliable inlet concentration CA0 in mol/L.
Kinetic Reference and Temperature Normalization
For reference kinetics, either enter a known fresh k directly or compute k_ref using Arrhenius parameters at the operating temperature. Ensure A and Ea are consistent with your kinetic model and concentration basis, and use the same temperature definition used in your plant report. Temperature affects k exponentially, so even a 10 °C mismatch can noticeably shift activity. Keep units consistent so the activity ratio remains meaningful.
Interpreting Activity for Maintenance Decisions
Activity values near 1.00 indicate performance close to the reference catalyst, while sustained values below target thresholds can support changeout planning. Many operations flag investigation around a = 0.85–0.90 and schedule regeneration or replacement as activity approaches 0.70–0.80, depending on margin and selectivity. Use the deactivation check to estimate k_d from measured activity or to predict remaining activity at future time-on-stream.
Practical Benchmarks and Sensitivity Checks
Run sensitivity checks by perturbing conversion, residence time, and temperature within plausible instrument uncertainty, then observe the change in activity. If activity swings widely, prioritize improving measurements before acting. Track multiple runs at similar conditions and look for monotonic declines rather than single-point drops. Use the history table and exports for audits, shift handovers, and catalyst vendor discussions, keeping assumptions and data sources noted.
FAQs
What does activity a represent?
Activity a is the ratio k_obs/k_ref. Values near 1 mean performance close to the reference catalyst at the same conditions, while lower values indicate deactivation, fouling, or transport limits affecting the apparent rate.
When should I use the PFR or CSTR option?
Use PFR for tubular or packed-bed tests with limited axial mixing. Use CSTR for well-mixed vessels or strongly recycled systems where the exit composition represents the reactor bulk.
Why is CA0 required only for some reaction orders?
For first-order kinetics, CA0 cancels in the integrated expressions, so conversion and residence time are sufficient. For n ≠ 1, concentration scaling affects k, so CA0 is required to keep units and magnitude consistent.
Can I compare activities across different temperatures?
Yes, if k_ref is computed or provided at each operating temperature. Because k changes exponentially with temperature, always enter the correct temperature so the activity ratio reflects catalyst condition, not a temperature mismatch.
What units should I use for Arrhenius A?
A must be consistent with your chosen rate law and concentration basis, so its units change with reaction order. Use the same A and Ea units used in your kinetic model documentation and keep CA0 in the matching concentration units.
What gets included in CSV and PDF exports?
Exports include the latest result and the stored run history from your session: timestamps, reactor choice, order, conversion, residence time, k_obs, k_ref, activity, and optional deactivation fields. Run a calculation first to enable downloads.