Reservoir Simulation

Temporal over-discretization in an Oil-brine two-phase system under non-isothermal conditions

1. Whether non-linearities in fluid flow lead to temporal over-discretization towards characterizing a heterogeneous oil reservoir?

In such cases, whether, the application of temporal over-discretization resulting from the smallest time step would be able to achieve stability, only when, it remains applied over the entire reservoir domain (as against applying the conventional explicit solution schemes that suffer from Courant Number stability constraints)?

2. Whether convergence difficulties occur only in a very small portion of a reservoir simulation domain with an associated small time-step size requirement, while the remaining nodes (having relatively homogeneous regimes) are able to accept much larger time-step sizes?

Further, whether, the location of convergence difficulties also keep changing with time?

In turn, whether, temporal over-discretization in non-linear oil reservoir system would significantly increase the computational burden of reservoir simulation scenarios?

In such cases, whether, an adaptive explicit-implicit method would be able to reduce the computational burden of implicit or Crank-Nicolson time-stepping schemes?

3. Whether temporal over-discretization prevail in an oil-brine front tracking situation (where, an oil-brine interface keeps varying rapidly over a small portion of the solution space)?

In such cases, whether, adaptive sub-gridding techniques be applied to resolve spatial gradients at the oil-brine front? Or, will we end up with higher Courant numbers with finer grids?

To what extent, the concept of sub-timing (where, small time-step sizes are used in portions of a reservoir domain with significant heterogeneities, with larger time-step sizes being applied in other relatively homogeneous locations towards avoiding temporal over-discretization) as against sub-gridding would remain to be efficient in such cases?

Dr Suresh Kumar Govindarajan,

Professor [HAG]

IIT Madras

14-March-2025