This post would be very simple, yet useful. I found in whole career as process engineer, in most cases, something very simple is very important. As engineer, we almost always deal with mathematics. In this post, I want to share a simple mathematics on how to calculate component flow rate from composition.
We all know that the summation of mol fraction and weight fraction must equal to 1. And sum of individual component flows in any stream cannot exceed the total stream flow. Therefore, we can calculate component flow rate if the composition of all components are well defined, and at least 1 component flow rate is known.
Let’s use example.
The feed stream to a reactor contains ethylene 16%, oxygen 9%, nitrogen 31%, and hydrogen chloride. If the ethylene flow is 5000 kg/h, calculate the individual comment flows and the total stream flow. All percentages are by weight.
There are two methods to solve this problem. The first is to calculate total flow first, then to calculate component flow rate based on each composition. The second method is to use ratio of each composition to calculate flow rate. Let’s start with first method.
First method: calculate component flow from total flow
Percentage of HCl = 100% – (percentage of C2H4 + percentage of O2 + percentage of N2) = 100% – (16% + 9% + 31%) = 44%
Total flow rate = flow rate of ethylene / composition of ethylene = 5000 kg/h/16% = 31,250 kg/h
So, oxygen flow = composition of O2 x total flow rate = 9% x 31,250 = 2813 kg/h
Nitrogen flow = composition of N2 x total flow rate = 31% x 31,250 = 9687 kg/h
Hydrogen chloride flow = composition of HCl x total flow rate = 44% x 31,250 = 13,750 kg/h
Second method: calculate component flow from composition ratio
As a rule, the ratio of flow of one component to other component is the same as ratio of the composition of the two components.
So, for example oxygen flow = composition of O2 / composition of C2H4 x flow rate of C2H4 = 9%/16% x 5000 = 2813 kg/h
We do the same for nitrogen = composition of N2 / composition of C2H4 x flow rate of C2H4 = 31%/16% x 5000 = 9687 kg/h
So, which method do you prefer?