A Reservoir/Wellbore‐Coupling Model for the Pressure, Flow Rate, and Optimum Perforation Distribution in Gas Wells

Perforated vertical wells are being used in the petroleum industry around the world. Perforations are the only channel between the wellbore and the reservoir. Accurate prediction of inflow performance for perforated vertical wells is of great significance to reservoir engineering analysis and perforation optimization design. The performance of a perforated vertical well depends on the fluid that enters the well and the fluid flow within the vertical section. The total pressure drop in vertical wells is dominated by gravitational effects, rather than frictional effects as in horizontal wells. Better understanding of the total pressure drop effects in vertical wellbores is helpful for petroleum engineers to design successful horizontal wells and optimize well performance. A considerable amount of analytical and numerical work has been performed on the flow performance of both perforated vertical wells and open-hole horizontal wells. Dikken presented the first semianalytical model that couples the reservoir to the wellbore with turbulent flow in the wellbore. Ouyang proposed a reservoir/wellbore-coupling model by using an analytical reservoir model and a semianalytical wellbore flow model. Ansah et al. developed a finite-element well-inflow model with an asymmetric spiral distribution of cone-shaped perforations around a wellbore to predict the flow performance of perforated vertical-well completions. Pressure-drop calculations have since been discussed in a variety of ways. Islam et al. presented a model allowing for the effect of inflow through perforation within the wellbore, but this model cannot analyze the impact of the perforation distribution on well performance. Landman et al. provided a model that allows for finding the optimal perforation distribution to increase the productivity for a horizontal wells. Hagoort studied an analytical model for single-phase Darcy flow to a single perforation in a semi-infinite porous medium. A considerable amount of analytical work has illustrated that the completion parameters are the main factors that influence the inflow profiles in vertical wells, but there has not been any investigation on the application of these to perforated vertical wells, including wellbore pressure drop. In this study, a mathematical model that couples the pressure and flow rate for perforated vertical well is presented. A basic optimization model is defined and applied to both infinite-conductivity and finite-conductivity wells. The numerical algorithm is recommended to solve the optimization models and the basic data of the “X” well are used for the calculations to help evaluate the models.