Based on the Mathematical point of view, the problems concerning the optimum well spacing are investigated. Therefrom, two methods for determinating the most profitable number of wells to be drilled are introduced as follows,
(1) The solution by means of the linear programming (L. P.) and
(2) The mathematical analystic solution.
For the L. P. calculation, the linear constraints on the well pressure, oil originally in place and processing capacities are fixed, and the objective=profit function are simultaneously formulated.
Then using the simplex tableau, the optimal solutions to obtain the most profitable production scheduling are derived for the given number of wells and limited production life of the oil field.
By plotting the present value profits versus the various number of wells to be solved on the graph paper, the optimum well spacing for any oil field is quantitatively estimated.
On the other hand, assuming the petroleum production declines exponentially, the present value profit is represented as the contineous function of the number of wells. Then the primary differential calculation. is applied to determine the most profitable number of wells. In spite of the lack of considerations concerning the complicated reservoir conditions, it is thought that this method has the advantage to be straightfoward and practical in its application.
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