# Plug Flow Reactor with Heat Transfer Jacket

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The temperature in a plug flow reactor and the temperature of the heat transfer fluid in the annular region around the reactor (a jacket) are plotted as functions of the cumulative reactor volume. Select "conversion" to plot fractional conversion of (for the reaction ) versus reactor volume. The reactor contents and the heat transfer fluid flow co-currently. A cross-section representation of the reactor (green circle) and the annular region (blue circle, which has a 2 m radius) is shown on each plot. Use sliders to vary the heat transfer fluid feed temperature, reactor radius and heat of reaction. The reactant feed temperature is 305 K. The velocities of the heat transfer fluid and the reactant are fixed, so when the reactor radius increases, the inlet molar flow rate of increases, and the volumetric flow rate of the heat transfer fluid decreases.

Contributed by: Simon M. Lane (April 2014)

Additional contributions by: Rachael L. Baumann, John L. Falconer and Nick Bongiardina

(University of Colorado Boulder, Department of Chemical and Biological Engineering)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Mass balance:

,

,

where is conversion, is volume (), is the reaction rate, is the molar flow rate of component (kmol/hr) that converts velocity of feed to molar flow rate of feed, is the velocity of component (m/s), is the radius of the inner tube (cm), and are the densities of the reactant and coolant (), and is the molar mass of (kg/kmol).

Rate law:

,

,

,

where and are the forward and reverse rate constants (1/hr), is a pre-exponential factor (1/hr), and are the activation energies for the forward and reverse reactions (J/mol), is the ideal gas constant (J/[mol K]), is temperature (K), is the heat of reaction (kJ/mol), and is the inlet concentration of ().

Energy balances:

,

,

where is the heat transfer coefficient (), is the heat exchange area per unit volume of reactor (1/m), is the temperature of the heat transfer fluid (K), is the average molar heat capacity of reacting mixture (kJ/[kmol K]), is the coolant heat capacity (kJ/[kg K]), is the mass flow rate of coolant (kg/hr) which converts velocity of heat transfer fluid to mass flow rate and is the coolant velocity (m/hr).

## Permanent Citation