The presence of wells in reservoir simulations can be represented by utilizing a well model within the finite volume framework of the simulator. A commonly applied approach is the Peaceman well inflow model, which places wells at the center of a specified grid cell of the reservoir model. Nonetheless, several studies have investigated the ability of placing wells off-center. Capturing the exact well position can significantly impact the reservoir response of the simulation model, particularly for heterogeneous reservoirs, as spatial heterogeneity plays a more pronounced role when wells are no longer located at the center of the grid cell. Furthermore, exact well position modeling would allow for more realistic well presentation within the reservoir simulator. Although the performed studies have successfully modeled
wells off-center, they are course-grid approaches. Therefore, this study investigates the application of an unstructured grid-based well model to accurately account for both the exact well location within a grid block and the surrounding reservoir heterogeneity in the calculation of a steady-state well index.

To achieve this, an improved well inflow model is established using Gmsh (three-dimensional finite element mesh generator) and the open Delft Advanced Research Terra Simulator (open-DARTS). The model implements an unstructured grid on a locally structured reservoir geometry, where typically five structured blocks are integrated. The model is verified against the Peaceman well inflow model for a center position and values match the Peaceman well model with a 5% accuracy. The model is validated for different well placements, permeability profiles and a considered number of structured reservoir blocks. Additionally, the validation study includes an accuracy assessment of the model against a full unstructured approach. The improved well index model is finally applied to the wells of the Geothermie Delft (GTD) project, enabling well index estimations based on true well trajectories.

Validation of the model shows that both well placement and local reservoir permeability impact the computed well index. A comparison of the proposed well index evaluation with the fully unstructured model indicates that incorporating more surrounding reservoir blocks within the well index calculation leads to closer correspondence with the fully unstructured approach. Additionally, the study reveals that the spatial discretization method within the finite volume framework used in open-DARTS influences well index values and can result in errors, depending on the choice of discretization approach. Finally, the results of the application of the proposed approach to the real trajectory of wells in the Geothermie TU Delft (GTD) project demonstrate that the improved well index model generally yields lower well index estimations than the Peaceman well model. The effect of this difference is further tested by simulating the full reservoir with the newly obtained well index values. These results depict that the well pressure profile for both the injector and producer varies depending on the well model, especially for later simulation times. The improved well model captures more variations in the pressure profile, emphasizing its capability for more accurate well modeling.