A groundwater model is necessary when a wide variety of influences affect the groundwater situation or complex boundary conditions exist and an analytical solution to the problem is no longer possible.
Possible problem statements for a groundwater model are e.g:
How does the groundwater flow behave when the abstraction rate changes?
What are the groundwater levels in specific area?
What effects does mining-related subsidence have on the groundwater levels?
What are the consequences of a flood wave and how do the floodplains change?
What influence do modifications on water bodies have (stream relocation, changes to the stream bed)?
What happens when new production wells are built and what impact do they have on the existing situation?
etc.
These and many other questions that can be answered with a groundwater model.