Many engineers are familiar with the decline curve analysis, which was developed by Arps ^[6] in the 1940s and was later refined by Fetkovich. ^[7] The decline curves tell us that the value of the decline index b changes from 0 to 1. The decline curve equation, which is applicable during the depletion stage is given by:

where

• q _i = oil rate at the beginning of depletion, STB/day

• D _i = initial decline rate, 1/day

• t = time, days

• b = decline exponent, dimensionless

It has been noted that for a bottom water drive reservoir, b = O.5. ^{[6] [7]} In a bottom water drive reservoir, if the reservoir is operated at, or below, the critical rate, then one can have a uniform sweep of the reservoir as water moves upward, resulting in high ultimate recovery. Nevertheless, to achieve this, the wells have to be operated at, or below, critical rates at all times. This means that as more and more oil is produced, oil column height reduces, and hence, the well will be choked back and its oil production rate reduced to prevent water coning. Based on this scenario, a finite 40-acre reservoir with a bottom water drive was chosen. Various vertical well critical rate correlations listed in Table 8-1 were used to calculate critical rates. ^{[1] [5]} For example, using Schols correlation the critical rate was calculated at the first day. ^[5] The...