Construction of High-Order Adaptive Implicit Methods for Reservoir Simulation
Abstract/Contents
- Abstract
- The objective of this work is to construct high-order extensions of the Adaptive Implicit Method (AIM) for Reservoir Simulation. The numerical methods under investigation are mainly applied to the transport equation describing the flow of one or two phases in a porous medium. The Method of Lines (MOL) offers a flexible and computationally efficient framework for general convection-diffusion problems. The convective term can be treated by high-resolution shock-capturing schemes, that are widely used today for the simulation of hyperbolic systems. Moreover, high-order time integration is typically carried out by onestep Runge-Kutta or Linear Multistep methods. A prototype program was developed to test various combinations of space-time discretizations formulated as MOL schemes. Numerical experiments in one dimension show a substantial reduction of the numerical dispersion in comparison with first-order methods. These high-resolution MOL schemes constitute the basic framework for the derivation of high-order AIM. A detailed analysis of the standard AIM scheme reveals an inconsistency at the transition between implicit and explicit regions. The discretization errors are usually comparable to the numerical dispersion. As a result, small “kinks” can be observed in the solution profile. But in most situations, the standard AIM scheme is convergent, and it satisfies strong monotonicity properties. In the context of high-order AIM, it is important to combine implicit and explicit time integration in a consistent manner. We propose a consistency fix that preserves the accuracy at the IE boundaries, and allows us to construct fully high-order AIM. However, the positivity restriction in the implicit regions can be quite severe, even if the implicit time integration is unconditionally stable. This difficulty is overcome by applying artificial viscosity in the implicit regions, which eliminates spurious oscillations and allows for larger time steps.
Description
| Type of resource | text |
|---|---|
| Date created | June 2007 |
Creators/Contributors
| Author | de Loubens, Romain |
|---|---|
| Primary advisor | Tchelepi, Hamdi |
| Degree granting institution | Stanford University, Department of Energy Resources Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
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Preferred citation
- Preferred Citation
- de Loubens, Romain. (2007). Construction of High-Order Adaptive Implicit Methods for Reservoir Simulation. Stanford Digital Repository. Available at: https://purl.stanford.edu/tv465sy1765
Collection
Master's Theses, Doerr School of Sustainability
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