Reactor Sizing Calculator

For a first-order reaction, the rate law −rA = k·CA scales directly with concentration, and the design equations for both CSTR and PFR are built from ratios of concentration terms that cancel Feed Concentration out algebraically -- doubling Feed Concentration doubles both the molar feed rate and the rate of reaction by the same factor, leaving the required volume unchanged. This is a genuine property of first-order kinetics, not a coincidence of these particular default values, and this calculator verifies it holds across the full declared input range.

Both design equations contain a term that diverges as conversion approaches 100% -- the CSTR's volume is proportional to X/(1−X), and the PFR's is proportional to ln[1/(1−X)] -- so each additional percentage point of conversion near the high end costs disproportionately more reactor volume than the same percentage-point increase near the low end. This is why real processes often target 90-99% conversion rather than chasing 100%: the last few percent gets extremely expensive in reactor size.

Residence Time (τ = V/v0) is a per-unit-of-fluid property -- how long a given parcel of fluid spends in the reactor -- so it depends only on the reaction kinetics (Rate Constant) and Target Conversion, not on how much total flow you're processing. Reactor Volume, on the other hand, scales directly with Feed Volumetric Flow Rate because processing more flow at the same residence time simply requires a proportionally bigger tank or pipe to hold it all.

A PFR always requires less volume than a CSTR to reach the same conversion with the same first-order kinetics, because a CSTR operates entirely at its (lower) exit concentration throughout its whole volume, while a PFR's concentration -- and therefore its reaction rate -- stays higher through most of its length before dropping off near the exit. That higher average reaction rate lets a PFR reach the same conversion in less volume; the gap between the two grows larger as Target Conversion increases.

Rate Constant is the first-order reaction rate constant at your operating temperature -- it sets how fast the reaction proceeds independent of concentration, with units of inverse time (1/min here). It isn't something this calculator derives; you obtain it from kinetics experiments (measuring concentration decay over time at a fixed temperature) or from published literature values for your specific reaction and temperature, since rate constants for the same reaction can vary by orders of magnitude across different temperatures.