Calculator Input Form
Example Data Table
| Parameter | Example Value | Unit | Notes |
|---|---|---|---|
| Feed Mode | Exponential | - | Supports rising substrate demand. |
| Initial Biomass Concentration | 18 | g/L | Measured from current culture. |
| Starting Broth Volume | 120 | L | Working fermenter volume. |
| Target Specific Growth Rate | 0.16 | 1/h | Desired growth target. |
| Biomass Yield | 0.48 | g/g | Biomass formed per substrate consumed. |
| Maintenance Coefficient | 0.015 | g/g/h | Background substrate demand. |
| Feed Substrate Concentration | 650 | g/L | Concentrated feed solution. |
| Residual Substrate Target | 5 | g/L | Small residual target. |
| Safety Factor | 10 | % | Provides operating margin. |
| Projected Initial Feed Rate | 1.2832 | L/h | Calculated from the example inputs. |
| Projected Final Feed Rate at 10 h | 6.3549 | L/h | Exponential profile estimate. |
| Projected Total Feed Added | 31.7071 | L | Approximate ten hour addition. |
Formula Used
This tool estimates feed from biomass demand, substrate yield, maintenance, and usable feed concentration. It supports constant and exponential profiles.
1. Specific substrate demand:
qs = (μ / Yx/s) + ms
2. Initial biomass mass:
Mx,0 = X0 × V0
3. Initial substrate demand:
Rs,0 = Mx,0 × qs
4. Effective substrate concentration in feed:
Seff = Sf − Sres
5. Initial feed rate:
F0 = (Rs,0 / Seff) × (1 + Safety Factor)
6. Constant feed profile:
F(t) = F0
7. Exponential feed profile:
F(t) = F0 × e^(μt)
8. Volume projection:
Constant mode: V(t) = V0 + F0 × t
Exponential mode: V(t) = V0 + (F0 / μ) × (e^(μt) − 1)
9. Dilution rate:
D(t) = F(t) / V(t)
These equations are practical engineering estimates for planning. They do not replace online sensor control, oxygen transfer review, or process-specific kinetic fitting.
How to Use This Calculator
- Select constant or exponential feed mode.
- Enter the current biomass concentration and broth volume.
- Enter the target growth rate, yield, and maintenance coefficient.
- Provide feed substrate concentration and residual substrate target.
- Add a safety factor for practical operation.
- Set projection hours and chart interval.
- Optionally enter feed tank volume and pump limit.
- Press calculate to view results above the form.
- Review the graph, utilization, and tank runtime.
- Download the result as CSV or PDF.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates a fed-batch liquid feed rate from biomass demand, yield, maintenance, and usable substrate concentration in the feed solution.
2. When should I choose constant feed?
Choose constant feed when you want a simple fixed addition rate over a short horizon or when the process plan already uses a steady pump setting.
3. When is exponential feed more suitable?
Exponential feed is useful when biomass is expected to rise at a controlled growth rate and substrate demand should increase with time.
4. Why is residual substrate subtracted from feed concentration?
The subtraction creates an effective concentration term. It prevents the calculation from assuming all feed substrate is immediately available for net demand control.
5. What does the maintenance coefficient change?
Maintenance adds background substrate use even without extra growth. Higher maintenance increases feed demand and can change practical pump requirements.
6. Why is pump utilization important?
It shows whether the planned feed profile stays within pump capacity. Exceeding that limit signals a likely control or hardware mismatch.
7. What is the benefit of feed tank runtime?
Feed tank runtime estimates how long the available feed volume lasts. This helps schedule refill timing and avoids unintended nutrient interruption.
8. Is this enough for final process validation?
No. It is a planning tool. Final settings should also consider oxygen transfer, viscosity, heat removal, sensor response, and real fermentation data.