Assume that groundwater production from wells located beyond a distance, say rx, that is large relative to the spacing between adjacent image wells may be treated as an equivalent, continuous, constant production rate per unit of ground surface area. By means of the Theis [1935] equation and the usual symbol nomenclature, the result is s (rx, •o) --QNw (t/S) [e -• --u•W(u•)], where s(r•, •o) is the drawdown at the observation point due to all image wells beyond distance rx, and Nw is the density of wells per unit area. This equation is useful for calculating the minimum radius rx m,n of the image well model in which image wells must be included for a given pumping time t to keep the truncation error due to omitted image wells less than some predesignated value s(rx, •o) .... On the other hand, if an image well model exists and is composed of a fixed number of image wells for approximating an areally infinite system, then the equation will give the maximum allowable pumping time for a given allowable truncation error s(rx, •o) .... Time drawdown estimates for wells in bounded

For a given production rate from a proposed well field, well construction and replacement costs decrease with fewer and larger wells spaced farther apart, while pumping lift costs increase. A method for minimizing the sum of these two costs uses a two‐dimensional uniform grid of wells to select a combination of well spacing and well capacity that minimizes costs for a given demand. Uncertainty in field permeability at future well sites is treated by averaging the possible outcomes over all wells in accord with a probability density function for permeability values. The method assumes an annual cycle whereby the water table declines owing to pumping in a dry season and is recharged to its initial state during a wet season.