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.

A good knowledge of foam hydraulics and cuttings transport (hole cleaning) is essential for successful applications of foam drilling technology in horizontal wells. Estimating local fluid velocity in a partially blocked eccentric annulus (due to cuttings) is a challenge; so, a new analytical method of calculating local stress and velocity (near cuttings-bed in annulus) in an eccentric annular flow is derived which makes it possible to estimate the bed height for foam drilling in horizontal wells. Therefore, a new equation for local velocity (critical velocity) to initiate particle movement is used in order to predict the bed-height profile in a build-up or horizontal section of wellbore. This investigation also focuses on understanding the effects of drilling parameters on bed height and cuttings concentration. A new transient wellbore hydraulics and cuttings transport model has been developed using the finite difference method of continuity equations for foam and cuttings. In order to predict the cuttings bed formation in horizontal wells, a mechanistic hole-cleaning model consisting of two layers has been utilized. The model is based on torque balance for a particle on the surface of a bed. In addition, a new model has been formulated for the local shear stress by modeling the eccentric annular flow as the infinite number of concentric annuli with variable outer radius. Similarly, using the narrow slot-approximation technique, a local velocity profile has been determined analytically in the eccentric annulus to be applied in the torque balance equations. Subsequently, model predictions of bed height were compared with published experimental data and the model is fine-tuned to minimize discrepancies. Results show the cuttings bed front transitions through the annulus along the build-up and horizontal sections. Model predictions showed a good match with experimental results for concentric horizontal annulus except at higher polymer concentrations (greater than 0.25%). The simulation results show that bed height and cuttings concentration are quite sensitive to the changes in surface foam injection rates and back-pressure, thereby can be best optimized by properly adjusting these input parameters. The results also suggest that hole-cleaning is a function of inclination. The bed height increases with increase in inclination angle until a critical angle of 90°-φ (φ is the angle of repose) after which, it reduces.

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Well drainage areas and shapes for wells in reservoirs with aquifer contact or gas-oil contact (constant pressure boundary) take varying shapes, such as, water coming from one-side (edge water drive) to water coming from 3-sides when the 4th-side is a sealing fault. This information is important in well test interpretations, peripheral flooding, aquifer injection, gas and CO2 aquifer storage, geothermal reservoirs, and any subsurface recovery schemes involving injection-production well pairs. A knowledge of well drainage shapes is helpful in optimizing well placement, well productivity estimations, and to maximize reserves. Results show that for a 2-well 3-sided water-drive reservoir system, each well drains an equal area when the well-rates are equal; however, the drainage areas of a well increases logarithmically with an increasing ratio of its flow rate to that of an adjacent well. In case of a multiple well system, results show that the drainage area of well closer to water contact is smaller than that of an interior well, farther away from the water-contact. Results are presented in graphical form and equations to determine the drainage area and shapes for varying production rate-ratios between wells in a multiple constant pressure boundary rectangular reservoir. An algebraic procedure is presented to generalize results from a 2-well system for extension to a multi-well system with similar multiple constant pressure boundary conditions. The equations yield result within 5% of those obtained from complex streamline simulations. A well's location within its drainage area is needed to determine mean well pressures from MBH (Matthews-Brons-Hazebroek) functions for water drive reservoirs, and to estimate productivity index and cumulative water influx volumes.