Simple pseudo-steady state productivity index correlations for infinite-conductivity horizontal wells based on a rigorous, semi-analytical model

Abstract

Simple pseudo-steady state (PSS) productivity index (PI) correlations are developed for horizontal wells producing at a constant rate from a closed, rectangular reservoir based on a rigorous infinite-conductivity model (ICM). The main three correlations are functions of the half-length wellbore segments number (mt) only and mt can be determined by the general correlation, which is a function of dimensionless well length (LD). The correlations are developed by using a nonlinear regression technique (with zero error) based on over thousand semi-analytical runs for a rigorous ICM covering 90 cases of different well and reservoir configurations. The 90 cases are averaged with less than 5% error in the total pressure drop calculation for the most of them to reduce the number of correlations and to remove the slight effect of well penetration ratio (PR). The PSS PI correlations are simply used to calculate mt, average pressure drop at transient-state, average starting time of PSS, and average total pressure drop at the beginning of PSS. At PSS, the reservoir outer boundaries are dominant, and the pressure drop will depend on the temporal and the spatial time-independent functions. The simple PSS PI correlations have been verified, and can be easily implemented in a standard spreadsheet code.The results show that LD is directly proportional to PSS PI and more significant than reservoir thickness (h) on horizontal-well productivity evaluation, which confirms the principle of the economic feasibility for drilling horizontal well in the oil industry. The results also show that the horizontal-well productivity by this study is several times higher than its counterparts by the methods reported in the literature because the method used by this study is based on a rigorous infinite-conductivity solution where no significant pressure drop occurs, while the previous methods are based on approximate infinite-conductivity solutions (AICSs). Therefore, there is a big underestimation in productivity calculation by using the previous methods which crucially reflect on reservoir evaluation. The new correlations give accurate PSS PI for over 3000 cases of diverse well and reservoir configurations, besides giving a rough PSS PI for the other cases.