In my opinion, this query is devoid of proper background information - or a definitive scope of work for the assignment given. This are typical student problems and mistakes. By not focusing on the scope of work and the specific problem at hand, the query becomes lost in a maze of different options, methods, and generated work efforts without getting to the core of the expected resolution. Specifics such as the raw gas flow rate, temperature, pressure, analysis, and other basic data are missing.
For example, lack of knowledge in the pre-selected processes being compared leaves the student with the idea that one process can serve as a legitimate replacement for the other. In this specific case, this does not seem to be true. TEG dehydration can be successfully used for a gas product having as low a water content as 3-4 lb/MM Scf of product gas. Since your scope is to dehydrate the gas merely for 10 lb/MM Scf in the product gas, than TEG is a valid and logical selection. That being the case, the adsorption process makes no common sense when viewed from practical, logical, and economic point of view. Adsorption processes cannot be controlled in producing a pre-selected water content (10 lb) and holding it at that level on a constant basis. Knowledge and familiarity with adsorption will yield concurrence with the fact that it is not a practical or logical process for pipeline transportation of large gas flow rates. Adsorption (especially using Molecular Sieves) is used to yield a very, ultra-dry product gas - something that is not required in producing a relatively “wet” gas product. It would logically be the process of choice if your scope was to treat the gas prior to liquefaction - especially at cryogenic temperatures - in order to avoid any freeze ups - but not for pipeline transport.
So, from a logical, common sense TEG is an obvious selection. However, this is reached without considering the raw gas flow rate - which could make a difference. If we are dealing with 1.0 MM Scfd, then adsorption could be considered - or deliquescence using calcium chloride. My first advice to you would be to improve your communications skills.