Wells are drilled for many reasons. To take water levels (observation or piezometer wells), obtain water samples (monitoring wells), recover contaminated water and/or free product (recovery wells), wells installed to lower water levels (dewatering wells), and wells used to pump abundant amounts of potable water (supply or production wells).
Diameter of the well is often determined by use of the well or how much water is needed, which is influenced by size of the pump. As a rule of thumb, doubling well diameter only provides 10% more water (i.e., increasing the diameter from 6 to 12 inches only adds 10% to well yield). Most of this increase is due to increased well efficiency and less friction at the screen due to lower velocities and ability of the formation to provide water remains constant.
A formation's ability to yield water is called transmissivity, which is measured in feet-per-day multiplied by capture width of the well multiplied by gradient of the water surface.
Piezometers may be as small as 0.5 inch in diameter and are used to record water levels. Monitor wells are commonly 2 inches in diameter to accommodate a small bailer or pump for purging prior to sampling. Domestic wells are often 4 or 6 inches to accommodate economically-priced pumps with yields from a few gallons per minute (gpm) to more than 50 gpm. Production wells yield hundreds or thousands of gpm and have pumps with large impellers from 6 inches to more than 20 inches.
Larger diameters in monitoring wells have an advantage, which can help reduce turbidity of water samples collected if metal concentrations are being analyzed.
Drilling a large-diameter well does not insure high yield. The drilling process greatly disturbs the producing portion of the formation, which plugs pore spaces by smearing the formation.
The method of drilling (mud rotary, hollow stem auger, cable tool, type of drilling fluid, etc.) and development usually play a larger role in well yield than diameter.
For more discussion on well yield and well diameter, refer to Ground Water and Wells by Fletcher Driscoll or many of the other textbooks available on groundwater.