# Numerical Solution of the Dispersion Equation for a First-Order Reaction

Numerical Solution of the Dispersion Equation for a First-Order Reaction

The dispersion equation can be written as

df

2

dz

2

df

dz

n-1

0

n

where (i.e., here a first-order reaction is considered), , is the dimensionless axial position in the reactor, is the reactor's residence time, is the reactant's inlet concentration, and is the Peclet number ().

n=1

f=

C

C

0

z

τ

C

0

Pe

Pe=

uL

D

These split-boundary conditions apply: and (i.e., the so-called closed ends' boundary conditions).

f'(1)=0

f(0)-f'(0)/Pe=1

This Demonstration plots the dimensionless exit concentration versus for various values of the number (the blue curve). For very high numbers, one recovers the plug flow reactor (the red curve).

f(z=1)

kτ

Pe

Pe