Low conversion is sometimes overcome using several adiabatic reactors with interstage cooling. Several reactors, with heat exchangers for cooling between them, are run up to near the maximum reaction rate until satisfactory conversion is attained. Methanol synthesis from syngas is a typical example where this technique is used:
. This reaction is reversible at 250°C (the temperature where commercial reactors are operated). It is common to use interstage cooling to achieve high conversion and to extract reaction heat.
Consider a reversible exothermic reaction,
, such that the reaction rate,
, and the equilibrium constant,
, are given by the following expressions:
is the conversion (unitless),
is the inlet concentration (in moles/liter),
is the universal gas constant (1.987 cal/mol K), and
is the temperature (in Kelvin).
It is assumed that the product
is independent of temperature and equal to 1000 cal/liter.
This Demonstration displays the loci of the maximum reaction rate (magenta curve), the equilibrium conversion,
(the green curve), and the possible trajectories for a number of adiabatic reactors with interstage cooling. You can vary the number of reactors. The cooling step is represented by the horizontal blue segment. The conversion versus temperature in the PFR (plug-flow reactor) is given by the red line. In addition, the final conversion is displayed. Usually, up to three adiabatic reactors with interstage cooling are sufficient to achieve good conversion. Indeed, this Demonstration shows that when the number of reactors becomes greater than seven, the additional gain in the final conversion is not too large and does not justify using additional reactors and heat exchangers.