 |
| Titel |
Nonlinearity Analysis for Efficient Modelling of Long-Term CO2 Storage |
| VerfasserIn |
Boxiao Li, Sally Benson, Hamdi Tchelepi |
| Konferenz |
EGU General Assembly 2014
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250093615
|
| Publikation (Nr.) |
 EGU/EGU2014-8513.pdf |
|
|
|
|
|
| Zusammenfassung |
| Numerical simulation is widely used to predict the long-term fate of the injected CO2 in
a storage formation. Performing large-scale simulations is often limited by the
computational speed, where convergence failure of Newton iterations is one of the main
bottlenecks. In order to design better numerical schemes and faster nonlinear solvers for
modelling long-term CO2 storage, the nonlinearity in the simulations has to be
analysed thoroughly, and the cause of convergence failures has to be identified
clearly.
We focus on the transport of CO2 and water in the presence of viscous, gravity, and
heterogeneous capillary forces. We investigate the nonlinearity of the discrete transport
equation obtained from finite-volume discretization with single-point phase-based upstream
weighting, which is the industry standard. In particular, we study the discretized flux
expressed as a function of saturations at the upstream and downstream (with respect to the
total velocity) of each gridblock interface. We analyse the locations and complexity of
the unit-flux, zero-flux, and inflection lines on the numerical flux. The unit- and
zero-flux lines, referred to as kinks, correspond to a change of the flow direction,
which often occurs when strong buoyancy and capillarity are present. We observe
that these kinks and inflection lines are major sources of nonlinear convergence
difficulties.
We find that kinks create more challenges than inflection lines, especially when their
locations depend on both the upstream and downstream saturations of the total velocity.
When the flow is driven by viscous and gravity forces (e.g., during CO2 injection), one
kink will occur in the numerical flux and its location depends only on the upstream
saturation. However, when capillarity is dominant (e.g., during the post-injection
period), two kinks will occur and both are functions of the upstream and downstream
saturations, causing severe convergence difficulties particularly when heterogeneity is
present.
Our analysis of the numerical flux theoretically describes the cause of the convergence
failures for simulating long-term CO2 storage. This understanding provides useful guidance
in designing numerical schemes and nonlinear solvers that overcome the convergence
bottlenecks. For example, to reduce the nonlinearity introduced by the two kinks in the
presence of capillarity, we modify the method of Cances (2009) to discretize the capillary
flux. Consequently, only one kink will occur even for coupled viscous, buoyancy, and
heterogeneous capillary forces, and the kink depends only on the upstream saturation of the
total velocity. An efficient nonlinear solver that is a significant refinement of the works of
Jenny et al. (2009) and Wang and Tchelepi (2013) has also been proposed and
demonstrated.
References
[1] C. Cances. Finite volume scheme for two-phase flows in heterogeneous porous
media involving capillary pressure discontinuities. ESAIM:M2AN., 43, 973-1001,
(2009).
[2] P. Jenny, H.A. Tchelepi, and S.H. Lee. Unconditionally convergent nonlinear solver
for hyperbolic conservation laws with S-shaped flux functions. J. Comput. Phys., 228,
7497-7512, (2009).
[3] X. Wang and H.A. Tchelepi. Trust-region based solver for nonlinear transport in
heterogeneous porous media. J. Comput. Phys., 253, 114-137, (2013). |
|
|
|
|
|
|