Calculator Inputs
Example Data Table
| Parameter | Example Value | Unit |
|---|---|---|
| Initial substrate concentration | 25 | g/L |
| Final substrate concentration | 9 | g/L |
| Time interval | 8 | h |
| Initial working volume | 120 | L |
| Feed volume | 10 | L |
| Feed substrate concentration | 80 | g/L |
| Withdrawal volume | 5 | L |
| Withdrawal substrate concentration | 9 | g/L |
| Average biomass concentration | 3.2 | g/L |
| Final product concentration | 6 | g/L |
Formula Used
This calculator uses a mass balance first. That makes the result more reliable when feed or sample withdrawal changes the total working volume.
Final working volume: Vt = Vi + Vf - Vw
Average working volume: Vavg = (Vi + Vt) / 2
Net substrate consumed: Ms = (Si × Vi) + (Sf × Vf) - (Sw × Vw) - (St × Vt)
Volumetric substrate consumption rate: rs = Ms / (Vavg × Δt)
Specific substrate consumption rate: qs = rs / Xavg
Substrate-to-product yield: Yp/s = (P × Vt) / Ms
Where Si is initial substrate concentration, St is final substrate concentration, Sf is feed concentration, Sw is withdrawal concentration, and Xavg is average biomass concentration.
How to Use This Calculator
- Enter the starting substrate concentration and initial working volume.
- Add the ending substrate concentration and the process time interval.
- Fill feed values if fresh substrate entered the system.
- Fill withdrawal values if broth or sample left the system.
- Enter average biomass concentration to calculate specific rate.
- Enter final product concentration if you want yield output.
- Click calculate and review the result block above the form.
- Use the CSV or PDF buttons to export the result summary.
Why This Calculator Helps
Substrate consumption rate is a practical monitoring metric in fermentation, enzymatic conversion, wastewater treatment, and other biological process studies. A simple concentration drop can underestimate or overestimate true substrate usage when feed is added or samples are removed. This page corrects that by using a full balance with volume change.
The volumetric result shows how rapidly substrate disappears per reactor volume and time. That is helpful for comparing batches, checking scale-up consistency, and evaluating control strategy performance. The specific rate adds biomass context, which helps reveal whether faster substrate loss comes from a stronger culture or just more cells in the vessel.
The yield output adds another useful layer. When product concentration is entered, the page estimates how effectively the consumed substrate supports product formation. The depletion percentage also helps teams judge whether the interval captured mild use, heavy drawdown, or a measurement mismatch. Together, these values make the calculator useful for lab review, pilot documentation, and routine production tracking.
FAQs
1. What does substrate consumption rate mean?
It shows how quickly a process uses substrate over time. This page reports both volumetric rate and specific rate when biomass data is available.
2. Why include feed and withdrawal fields?
They improve the balance. Added feed increases available substrate, while withdrawal removes both liquid and dissolved substrate from the system.
3. What if my result is negative?
A negative result means net substrate increased during the interval, or the measurements do not fit the assumed balance. Review inputs carefully.
4. Do I need biomass concentration?
No. Biomass is optional. Without it, the calculator still reports the net substrate consumed and the volumetric consumption rate.
5. What units should I use?
Use concentration in g/L, volume in L, and time in hours. Keep units consistent across every input for valid results.
6. Can I use this for batch and fed-batch work?
Yes. Batch mode uses zero feed and withdrawal. Fed-batch mode uses feed inputs and optional withdrawal values when applicable.
7. What does Yp/s represent?
Yp/s is the substrate-to-product yield. It estimates how much product mass formed per unit of net substrate consumed.
8. What does the chart show?
The Plotly graph displays the concentration change across the interval and the cumulative net substrate consumed over that same period.