Brainer:
First of all, there is nothing "sacred" about a process being off-shore. The process will operate in the same manner as if it were on-shore. Civil engineering, communications, Safety, physical layout, external corrosion, weather, and structural constraints may be factors off-shore, but there is no effect on the process. I have dehydrated gas using TEG on off-shore platforms in Lake Maracaibo as well as West Texas; the process is the 100% the same.
You seldom, if ever, compare a glycol dehydration unit with an adsorption unit. As a ChemEng you should already know that you have to identify your scope of work; what this means is that you have to consider what level of dehydration you intend or hope to achieve. The level of dehydration (& the size of the humid gas stream) is what determines whether you apply one of the other. There may be other process factors - especially economics - involved, but with the sparse amount of basic data you furnish we can't comment any further. If you want details, you have to furnish details beforehand especially basic data.
Glycol dehydration is normally employed to dry gas to positive dewpoints; adsorption - such as with Mol Sieves & Activated Alumina - can achieve dew points down to -150 oF. Additionally, adsorption is a batch-swing type of process, while glycol is a continuous, steady-steady state one. These are all important factors that any Chem Eng should already know and be prepared to take into consideration. The application and the basic data make all the difference on whether they apply or not.
Perhaps you can furnish specific basic data and scope of work information - at least more than one simple sentence. In that event, specifics can be addressed.