A simplified semi-analytical productivity index for a horizontal well with a non-linear trajectory in a vertical plane

A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simulation and line source solutions, thus converting the analytical index equation into a semianalytical equation. The application of the semi-analytical equation to a horizontal well, undulating in a vertical plane, to predict its productivity was demonstrated using an example. This model is the first productivity index equation with the capability to handle a horizontal well with a non-linear trajectory.