Productivity Models of Infill Complex Structural Wells in Mixed Well Patterns

The mathematical models of productivity calculation for complex structural wells mainly focus on the single well or the regular well pattern. Previous research on the seepage theory of complex structural wells and vertical wells in mixed well pattern is greatly insufficient. Accordingly, this article presents a methodology of evaluating the productivity of infill complex structural wells in mixed well patterns. On the basis of the mirror-image method and source–sink theory, two semi-analytical models are established. These models are applied to the productivity prediction of an infill horizontal well inhorizontal-vertical well pattern and an infill multilateral well inmultilateral-vertical well pattern, respectively, in which the interference of other wells, the randomicity of well patterns, and the pressure drawdown along the horizontal laterals are taken into account. The semi-analytical models’ results are consistent with those calculated by the Eclipse reservoir simulator with the relative error of less than 15%. Results indicate that the bottom hole flowing pressure decreases logarithmically while the wellbore flow rate increases monotonically from the toe to the heel of the horizontal well. Due to the pseudo-hemispherical flow at each endpoint and the pseudo-linear flow at the center of the horizontal well, the drainage area at each endpoint is relatively larger than that at the center. The radial inflow at each endpoint of the horizontal segment is considerably greater than that at the center, which presents the U-shape distribution. The proposed methodology enhances and promotes the theory of productivity evaluation for complex structural wells in mixed well patterns.