Theoretically, ultimate water cut, (WCult), defines well's maximum water production for uncontained oil pay underlain with water. However, in a real multi-well reservoir well's drainage area is contained by a no-flow boundary (NFB) that would control water coning, so: (1) the ultimate water cut concept needs to be qualified, and (2) related to the well spacing size. Moreover, a simple presently-used (WCult) formula derives from other simplifying assumptions ignoring the effects of non-radial inflow, production rate and aquifer size, so: (3) the formula needs to be verified.
The study shows that in multi-well bottom-water reservoirs well production water cut would never stabilize (after initial rapid increase) but would continue increasing at slow rate dependent on the size of well's drainage area, i.e. well spacing size. There is a minimum well spacing size – correlated here with reservoir properties – above which water cut becomes practically stable at the value defined as pseudo WCult. The pseudo WCult formula is developed by considering all previously-ignored effects. Then, the formula is statistically verified in a variety of bottom-water reservoir systems using three-level parametric experimental design and sensitivity analysis of variance. It is found that most of the new physical effects are statistically insignificant so, in practical applications, the pseudo WCult values can be computed from the conventional WCult formula for well spacing greater than the value defined by the minimum well spacing correlation.
The pseudo WCult concept and value has potential practical use for well spacing design in the strong-bottom-water reservoirs with known value of the water cut economic limit, WCec, determined for the breakeven (zero-profit) cost of daily production. When the WC economic margin (WCec – WCult) is large, well spacing has little effect on the final recovery (when water cut becomes equal to WCec). Thus, well spacing could be designed for the same value of recovery by finding optimum number of wells for maximum return on investment using the time-value-of money (NPV) approach. However, when the WC economic margin is small or negative, reservoir development decision should also consider increase of final recovery for smaller well spacing.