How this calculation works
Equal reactor volumes and feed flows do not guarantee equal conversion. A perfectly mixed tank holds the whole vessel at its outlet concentration, whereas ideal plug flow preserves a concentration change along the reactor. This calculator compares the two ideal steady-state reactors for one irreversible first-order reaction at the same nominal residence time. It uses an entered rate constant and does not fit kinetics from observations.
tau=V/Q; Da=k tau; X_PFR=1−exp(−Da); X_CSTR=Da/(1+Da)A worked example
A one-hundred-litre vessel with flow one hundred litres per hour has residence time one hour. With rate constant one per hour, the Damkohler number is one. Ideal plug-flow conversion is about 63.21 percent, while the single mixed-tank value is fifty percent. Setting rate to zero produces zero conversion in both models without changing residence time.
Good to know
Real residence-time distributions, bypass, pressure change and transport limitations are absent. Heat generation and removal are also excluded, so the comparison does not establish safe or achievable reactor operation. These are ideal educational balances, not equipment approval or a complete design. A real reactor requires kinetics and physical assumptions appropriate to its reaction, phase and operating conditions.
Reference: NPTEL — first order mixed reactor balance (opens in a new tab) ↗
What this calculation answers
Equal reactor volumes and feed flows do not guarantee equal conversion. A perfectly mixed tank holds the whole vessel at its outlet concentration, whereas ideal plug flow preserves a concentration change along the reactor.
This calculator compares the two ideal steady-state reactors for one irreversible first-order reaction at the same nominal residence time. It uses an entered rate constant and does not fit kinetics from observations.
The Integrated reaction order fit calculator infers a rate model from a time series. Reactor comparison instead takes the rate constant as supplied and evaluates two ideal flow patterns.
Use the right input conventions
Working volume is litres, feed flow is litres per hour and rate constant is per hour. The ratio of volume to flow therefore has hours as its unit, making the product k times residence time dimensionless.
The same constant-density, isothermal assumption applies to both reactor types. Entering a gas flow measured at unrelated temperature or pressure would break that common-volume basis.
Interpret the result
The first-order Damkohler number compares reaction opportunity with flow time. Its value determines both ideal conversions, while the remaining outlet fractions expose how much reactant is left under each model.
At positive rate and residence time, the plug-flow ideal gives higher conversion than a single ideal mixed tank for this specific rate law. That comparison should not be generalized to arbitrary reaction orders or thermal behavior.
Work through the example
A one-hundred-litre vessel with flow one hundred litres per hour has residence time one hour. With rate constant one per hour, the Damkohler number is one.
Ideal plug-flow conversion is about 63.21 percent, while the single mixed-tank value is fifty percent. Setting rate to zero produces zero conversion in both models without changing residence time.
Where the model stops
Real residence-time distributions, bypass, pressure change and transport limitations are absent. Heat generation and removal are also excluded, so the comparison does not establish safe or achievable reactor operation.
These are ideal educational balances, not equipment approval or a complete design. A real reactor requires kinetics and physical assumptions appropriate to its reaction, phase and operating conditions.
A few questions, answered
Does this infer the rate constant from measured conversion?
No. Rate constant is entered; the page compares forward predictions for two stated ideal reactor models.
What changes in the comparison?
Double the rate constant while preserving residence time and compare the different nonlinear conversion increases.