# Cumulative Distribution and Residence Time Distribution Curves

Cumulative Distribution and Residence Time Distribution Curves

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Consider the following mixture distribution:

f(x)=++

1

5

2π

-2

2

x

e

1

σ

1

-2

2

(x-)

μ

1

2

σ

1

e

3

σ

2

-2

2

(x-)

μ

2

2

σ

2

e

You can change this distribution's properties by setting values for , , , and . This Demonstration plots this distribution. For specific values of , , , and , one can obtain a bimodal distribution, which mimics the residence time distribution () of a batch reactor.

μ

1

μ

2

σ

1

σ

2

μ

1

μ

2

σ

1

σ

2

RTD

This Demonstration also computes the cumulative distribution curve, , which as expected exhibits two plateaus in the case of a bimodal . The cumulative distribution is given by the following definition: , where is the residence time distribution.

F(x)

RTD

1-F(x)=E(u)du

∞

∫

x

E(u)