DE - Modeling - Chemical Reaction                               Home : www.sharetechnote.com

 

 

 

Assume that you have a tank which contains the chemicals named A, X, Y, B and all of these are undergoing chemical reactions as shown below.

Your job is to build a set of differential equations predicting the concentration of each chemicals along with time.

 

First, let's build a differential equation for the chemical A. To do this, first identify all the chemical reactions which either consumes or produce the chemical (i.e, identify all the chemical reactions in which the chemical A is involved). And then build a differential equation according to the governing equation as shown below.

 

Next, let's build a differential equation for the chemical X. To do this, first identify all the chemical reactions which either consumes or produce the chemical (i.e, identify all the chemical reactions in which the chemical X is involved). And then build a differential equation according to the governing equation as shown below.

 

 

Next, let's build a differential equation for the chemical Y. To do this, first identify all the chemical reactions which either consumes or produce the chemical (i.e, identify all the chemical reactions in which the chemical Y is involved). And then build a differential equation according to the governing equation as shown below.

 

 

Next, let's build a differential equation for the chemical B. To do this, first identify all the chemical reactions which either consumes or produce the chemical (i.e, identify all the chemical reactions in which the chemical B is involved). And then build a differential equation according to the governing equation as shown below.

 

 

Now we got all the differential equations representing the concentration of each individual chemicals. The last step is to put all the equations together as a simulteneous equation as shown below.