The standard method is campaign-based batch sizing: allocate the total operating time among products, calculate the number of batches each product can complete, and determine the batch volume required for each product. For product (x), the preliminary batch volume is calculated as:

[ V_{\text{batch},x}

\frac{P_x,v_{\text{react},x}}{t_x/t_{\text{cycle},x}} ]

The shared reactor or mixer is then sized to the largest actual batch volume required after practical whole-batch rounding.

Shared equipment is sized by balancing production targets, product-specific volume requirements, cycle times, and campaign schedules. The governing equipment capacity is the maximum batch volume among all products processed in the shared unit.

How Shared Equipment Sizing Works

Define the production campaigns

First, establish the total operating time available for the production program. If products A, B, and C share a pilot plant over 500 hours, their campaign times must satisfy:

[ t_A+t_B+t_C=500\ \text{h} ]

Each campaign time represents the period during which the shared reactor or mixer is dedicated to one product.

Determine product-specific requirements

For each product, identify:

The target production quantity, (P_x), typically in kg
The required reactor or mixer volume per unit mass, (v_{\text{react},x}), in (\text{m}^3/\text{kg})
The complete batch cycle time, (t_{\text{cycle},x})

The cycle time should include filling, processing, emptying, cleaning, and any required sterilization or changeover activities.

Calculate the number of batches

The preliminary number of batches for product (x) is:

[ N_x=\frac{t_x}{t_{\text{cycle},x}} ]

This calculation estimates how many batch cycles can fit within the product's allocated campaign.

Calculate the required batch volume

The total process volume associated with a product target is:

[ P_xv_{\text{react},x} ]

Dividing this volume by the available number of batches gives the preliminary batch volume:

[ V_{\text{batch},x}

\frac{P_xv_{\text{react},x}}{N_x}

\frac{P_xv_{\text{react},x}} {t_x/t_{\text{cycle},x}} ]

For mixers, the same logic applies when the specified volume represents the working volume needed per unit of product.

How the Shared Vessel Size Is Determined

Equalize preliminary batch volumes

When the objective is to find the minimum common equipment size, the preliminary batch volumes can be set equal:

[ V_{\text{batch},A}

V_{\text{batch},B}

V_{\text{batch},C} ]

Together with the total-time constraint, these equations can be solved for the campaign durations and the common preliminary vessel volume.

This identifies a schedule in which each product uses the shared unit efficiently.

Convert batch counts to practical values

The calculated batch counts are often non-integer. In practice, a product cannot normally run a fraction of a batch, so the batch counts must be converted to whole numbers.

The campaign schedule and batch volumes should then be recalculated using those integer batch counts rather than relying only on the continuous mathematical solution.

Select the limiting product condition

After rounding, calculate the actual batch volume required for every product:

[ V_{\text{actual},x}

\frac{P_xv_{\text{react},x}}{N_{x,\text{integer}}} ]

The shared reactor or mixer must be sized for the largest of these values:

[ V_{\text{equipment}}

\max \left( V_{\text{actual},A}, V_{\text{actual},B}, V_{\text{actual},C} \right) ]

The product producing this maximum is the limiting case or governing design condition.

Why Campaign Time Matters

Production targets alone are insufficient

A product with a large production target does not automatically determine the vessel size. Its required volume per batch also depends on its cycle time and the amount of campaign time assigned to it.

A product with a slower cycle may require a larger batch volume because fewer batches can be completed during its campaign.

Equipment utilization affects the result

Allocating more time to one product increases its available batch count and can reduce its required batch volume. However, that time must be taken from another product, so the schedule and equipment size are coupled.

The method therefore sizes the equipment and evaluates the production schedule together.

The approach applies to flexible pilot plants

This calculation is particularly useful when a reactor or mixer is shared across multiple products rather than dedicated to one process. It supports decisions about pilot-plant capacity, campaign planning, and whether a proposed equipment size can meet all production targets.

Understanding the Trade-offs

Continuous solutions are not operating schedules

Equating batch volumes produces a useful preliminary design, but the resulting batch counts may be fractional. Treating those values as executable batches can understate the required capacity.

Whole-batch recalculation is therefore essential.

The largest batch volume is not the only constraint

A vessel's nominal volume is not necessarily its usable working volume. Mixing performance, headspace, heat transfer, solids suspension, foaming, and safe operating limits may require additional capacity beyond the calculated process volume.

The calculated maximum should be treated as the process-volume requirement, followed by normal equipment design allowances.

Changeovers can reduce available time

Cleaning and sterilization must be included in the cycle time when they consume shared equipment capacity. Omitting them overestimates the number of batches and can produce an undersized vessel.

Product transitions may also require longer campaign changeovers than repeated batches of the same product.

Integer rounding can create idle capacity

Rounding batch counts changes the balance between products. One product may have spare campaign time while another determines the final vessel size, so the final schedule should be checked for both capacity and unused operating time.

Making the Right Choice for Your Goal

Use the calculation as a schedule-and-capacity model, then validate the result against practical operating constraints.

If your primary focus is minimum equipment volume: Allocate campaign times so the preliminary batch volumes are equal, then size the unit using the largest recalculated volume after integer batch rounding.
If your primary focus is meeting production targets reliably: Include complete cycle and changeover times, use whole batches, and verify that the selected vessel has adequate working-volume and operating margins.
If your primary focus is maximizing pilot-plant utilization: Compare alternative campaign allocations and select the schedule that meets all targets with the least idle time and acceptable operational flexibility.

The reliable method is to balance campaign time and batch counts, then size the shared reactor or mixer for the largest practical batch volume.

Summary Table:

Sizing factor	How it is used
Campaign time	Allocate available operating hours among products.
Cycle time	Include filling, processing, emptying, cleaning, sterilization, and changeovers.
Batch count	Calculate available batches, then convert results to whole batches.
Batch volume	Divide each product's required process volume by its integer batch count.
Equipment size	Select the largest practical batch volume as the governing capacity.
Design checks	Allow for working volume, headspace, mixing, heat transfer, foaming, and safe operation.

Planning a flexible pilot plant? Contact LABPARK for Educational and Vocational Unit Operations Pilot Plants tailored to your needs. LABPARK supports universities, research institutes, and enterprises with shared reactor and mixer systems for chemical engineering, bioprocess and biotech, and environmental and water treatment applications. Our team can help you balance campaign schedules, batch capacity, cycle times, changeovers, working-volume limits, and future process requirements to select practical, reliable equipment for training, research, scale-up, and production development.