How to Calculate Component Flow Rate from Composition

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.

Solution

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?