Cumulative Distribution and Residence Time Distribution Curves

residence time distribution

cumulative distribution

μ

1

0.45

μ

2

5.15

σ

1

0.38

σ

2

0.35

Consider the following mixture distribution:

f(x)=

1

5

2π

-

2

x

2

e

+

1

σ

1

-

2

(x-

μ

1

)

2

2

σ

1

e

+

3

σ

2

-

2

(x-

μ

2

)

2

2

σ

2

e

.

You can change this distribution's properties by setting values for

μ

1

,

μ

2

,

σ

1

, and

σ

2

. This Demonstration plots this distribution. For specific values of

μ

1

,

μ

2

,

σ

1

, and

σ

2

, one can obtain a bimodal distribution, which mimics the residence time distribution (

RTD

) of a batch reactor.

This Demonstration also computes the cumulative distribution curve,

F(x)

, which as expected exhibits two plateaus in the case of a bimodal

RTD

. The cumulative distribution is given by the following definition:

1-F(x)=

∞

∫

x

E(u)du

, where

E(u)

is the residence time distribution.