In this dissertation we discuss some upscaling methods for flow and transport
in heterogeneous reservoirs. We studied realization-based multi-phase flow and
transport upscaling and ensemble-level flow upscaling. Multi-phase upscaling is more
accurate than single-phase upscaling and is often required for high level of coarsening.
In multi-phase upscaling, the upscaled transport parameters are time-dependent functions
and are challenging to compute. Due to the hyperbolic feature of the saturation
equation, the nonlocal effects evolve in both space and time. Standard local two-phase
upscaling gives significantly biased results with reference to fine-scale solutions. In
this work, we proposed two types of multi-phase upscaling methods, TOF (time-offlight)-
based two-phase upscaling and local-global two-phase upscaling. These two
methods incorporate global flow information into local two-phase upscaling calculations.
A linear function of time and time-of-flight and a global coarse-scale two-phase
solution (time-dependent) are used respectively in these two approaches. The local
boundary condition therefore captures the global flow effects both spatially and temporally.
These two methods are applied to permeability distributions with various
correlation lengths. Numerical results show that they consistently improve existing
two-phase upscaling methods and provide accurate coarse-scale solutions for both
flow and transport.
We also studied ensemble level flow upscaling. Ensemble level upscaling is up scaling for multiple geological realizations and often required for uncertainty quantification.
Solving the flow problem for all the realizations is time-consuming. In recent
years, some stochastic procedures are combined with upscaling methods to efficiently
compute the upscaled coefficients for a large set of realization. We proposed a fast
perturbation approach in the ensemble level upscaling. By Karhunen-Lo`eve expansion
(KLE), we proposed a correction scheme to fast compute the upscaled permeability
for each realization. Then the sparse grid collocation and adaptive clustering are coupled
with the correction scheme. When we solve the local problem, the solution can
be represented by a product of Green's function and source term. Using collocation
and clusering technique, one can avoid the computation of Green's function for all
the realizations. We compute Green's function at the interpolation nodes, then for
any realization, the Green's function can be obtained by interpolation. The above
techniques allow us to compute the upscaled permeability rapidly for all realizations
in stochastic space.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-7256 |
| Date | 2009 December 1900 |
| Creators | Li, Yan |
| Contributors | Efendiev, Yalchin |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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