A method is presented for the numerical simulation of wells with arbitrary trajectories using 3D unstructured grids, with a resolution that automatically adjusts to the simulation context: for pressure transient analysis (logarithmic time steps) or low permeability reservoirs a very fine grid is used. The grid is progressively coarsened when early-time transients can be ignored and/or mobility increases. Different discretization controls are applied for full late time consistency between the various resolutions.

A criterion is derived to determine the optimum grid resolution based on the mobility of the fluid in the vicinity of the wellbore and the smallest time step to simulate.

The finest grid uses a full 3D voronoi module around the wellbore, with cells of progressively increasing size away. This module is connected to a coarser background 2.5D voronoi grid for the bulk of the reservoir. Generalized transmissibility derivations accurately account for the well trajectory and estimate the fluxes across potentially non-orthogonal connections.

Progressively coarsened grids are then used to adapt to the problem. For relatively fine grids, generalized derivations of transmissibility and well index values capture the radial effects and avoid the numerical pseudo-skin typically observed with 2.5D grids.

As illustrated with various cases, such approach accurately and consistently simulates wells of complex geometries for all resolutions. The outcome is a new method for generating 3D unstructured grids that automatically adapt to the expected time resolution of the simulation, while ensuring consistency between transient and long-term simulations via original discretization controls.

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