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Batch Reactor Scale-Up Calculator Documentation

Note: This documentation is based on standard chemical engineering principles for reactor scale-up. The actual implementation in the code may vary.

1. Objective

The Batch Reactor Scale-Up Calculator is designed to help engineers determine key operating parameters when scaling a process from a laboratory/pilot scale to a larger production scale. The goal is to maintain process performance and product quality by keeping certain critical parameters constant.

2. Design Basis & Methodology

The calculator uses common scale-up criteria to translate parameters from a small-scale (lab) vessel to a large-scale (plant) vessel.

Key Scale-Up Criteria:

  1. Constant Power per Unit Volume (P/V): Aims to maintain the same level of energy dissipation and turbulence intensity. This is crucial for processes where micromixing is important.

    (P/V)_lab = (P/V)_plant

    Agitator Power P is often related to the Power Number (Np), agitator speed (N), and impeller diameter (D): P = Np * ρ * N³ * D⁵.

  2. Constant Impeller Tip Speed: Aims to maintain the same maximum shear rate in the vessel. This is important for shear-sensitive materials or processes where dispersion is driven by shear.

    (π * N * D)_lab = (π * N * D)_plant

  3. Constant Mixing Time (θ): Aims to achieve the same bulk blending time. This is relevant for processes requiring macroscopic homogeneity.

3. Input Parameters

  • Lab Scale Parameters: Vessel Volume, Liquid Volume, Agitator Speed, Impeller Diameter, Power Input (if known).
  • Plant Scale Parameters: Target Vessel Volume or Liquid Volume.
  • Fluid Properties: Density and Viscosity.
  • Scale-Up Criterion: User selects the basis for the scale-up (e.g., Constant P/V, Constant Tip Speed).

4. Output Results

  • Required Agitator Speed (Plant): The calculated RPM for the large-scale agitator.
  • Required Power Input (Plant): The estimated power draw for the large-scale agitator.
  • Impeller Tip Speed (Plant): The resulting tip speed at the calculated RPM.
  • Reynolds Number (Plant): To confirm the flow regime (laminar, transitional, or turbulent).

5. Limitations and Assumptions

  • Assumes geometric similarity between the lab and plant scale reactors.
  • Does not account for changes in heat transfer, which is a critical and separate scale-up consideration (surface area-to-volume ratio decreases on scale-up).
  • The power number (Np) is assumed to be constant if the flow is turbulent, which may not be true during the transition.

6. Example Calculation

Goal: Scale up a process from a 10 L lab reactor to a 1000 L plant reactor, maintaining constant power per unit volume (P/V).

Given (Lab Scale):

  • Vessel Volume (V_lab): 10 L
  • Impeller Diameter (D_lab): 0.1 m
  • Agitator Speed (N_lab): 300 RPM

Given (Plant Scale):

  • Vessel Volume (V_plant): 1000 L

Calculation Steps:

  1. Calculate Plant Impeller Diameter (assuming geometric similarity): The ratio of diameters scales with the cube root of the volume ratio. D_plant = D_lab * (V_plant / V_lab)^(1/3) = 0.1 m * (1000 / 10)^(1/3) = 0.1 m * (100)^(1/3) ≈ 0.464 m

  2. Calculate Plant Agitator Speed for Constant P/V: For turbulent flow, P/V is proportional to N³ * D². (N³ * D²)_plant = (N³ * D²)_lab N_plant³ = N_lab³ * (D_lab / D_plant)² N_plant = N_lab * (D_lab / D_plant)^(2/3) N_plant = 300 RPM * (0.1 / 0.464)^(2/3) = 300 * (0.2155)^(2/3) = 300 * 0.358 ≈ 107.5 RPM

Result: The plant agitator should run at approximately 108 RPM to maintain the same power per unit volume.

Reference Standards

  • VDI/VDE 2180: Functional Safety in the Process Industry.
  • IEC 61511: Functional Safety - Safety Instrumented Systems for the Process Industry Sector.
  • CCPS (Center for Chemical Process Safety): Guidelines for Safe Storage and Handling of Reactive Materials.
Go to the Batch Reactor Scale-Up Calculator