The cost of water from a well depends upon the capital invested and the annual recurring costs. A large part of the recurring element derives from the cost of pumping. Capital costs and pumping costs are interdependent to the degree that the design of the well affects the drawdown and thus the pumping cost. For example, a short screen section will produce a larger drawdown than a long screen for a given discharge. Thus saving in capital is offset by increased pumping costs. Similarly a screen of small diameter produces large entry and upflow losses and again increased recurring costs. For each chosen design parameter there is an optimum solution for least cost. This paper is concerned with the determination of such least cost solutions.
The principle of the analysis is to produce an equation representing the total cost in terms of a single design parameter and to apply a discounted cash flow procedure to calculate the present value. Differentiation of the present value expression with respect to the chosen design parameter leads to the determination of the optimum value of that parameter for minimum cost.
The analysis depends on certain theoretical or empirical correlations between the parameters involved. These are presented in the paper. A simplified case involving screen length and well depth is discussed in some detail to illustrate the approach. This is followed by a discussion of more complex problems that require analysis by computer.
Determination of the optimum diameter of a well is reviewed in relation to the different components causing well losses. Well losses in very deep wells are examined together with the optimum discharge and diameter of such wells.