Does a Chemical Techicians or Chemical Enginer need to relocate or travel?

Chemical technicians and/or engineers do HAVE to relocate.
But at most companies, the experience the employee gets by
doing a year or two at different plants and locations normally
are very good.
You can work in the field without relocating or traveling, but
it is better if you are open to it. (also gives you a chance to
see other places and people, like an overseas assignment)

Firstly I would like to brief you about the duties and job responsibilities of a chemical engineer. They are as follows:-

Conduct research to develop new and improved manufacturing processes
Develop safety procedures for those working with dangerous chemicals
Develop processes for separating components of liquids and gases, or for generating electrical currents, by using controlled chemical processes
Design and plan the layout of equipment
Conduct tests and monitor the performance of processes throughout production
Troubleshoot problems with manufacturing processes
Evaluate equipment and processes to ensure compliance with safety and environmental regulations
Estimate production costs for management.

Now coming to your question of how frequently they have to travel I would like to tell you that it really depends on the company you are working in. For example companies like shell often sends their
employees abroad to work in their different branch offices while many other companies will train their employees in the initial years and they don't have to travel much.Just to keep you informed Chemical engineers work mostly in offices or laboratories. They may spend time at industrial plants, refineries, and other locations, where they monitor or direct operations or solve onsite problems. Chemical engineers must be able to work with those who design other systems and with the technicians and mechanics who put the designs into practice.Some engineers travel extensively to plants or work sites, both domestically and abroad.