The dynamic solution of multiphase flow through porous media is of
special interest to several fields of science and engineering, such as petroleum,
geology and geophysics, bio-medical, civil and environmental, chemical engineering
and many other disciplines. A natural application is the modeling of
the flow of two immiscible fluids (phases) in a reservoir. Others, that are broadly
based and considered in this work include the hydrodynamic dispersion (as in
reactive transport) of a solute or tracer chemical through a fluid phase. Reservoir
properties like permeability and porosity greatly influence the flow of these
phases. Often, these vary across several orders of magnitude and can be discontinuous
functions. Furthermore, they are generally not known to a desired level
of accuracy or detail and special inverse problems need to be solved in order
to obtain their estimates. Based on the physics dominating a given sub-region
of the porous medium, numerical solutions to such flow problems may require
different discretization schemes or different governing equations in adjacent regions.
The need to couple solutions to such schemes gives rise to challenging
domain decomposition problems. Finally, on an application level, present day
environment concerns have resulted in a widespread increase in CO₂capture and
storage experiments across the globe. This presents a huge modeling challenge
for the future. This research work is divided into sections that aim to study various
inter-connected problems that are of significance in sub-surface porous media
applications. The first section studies an application of mortar (as well as nonmortar,
i.e., enhanced velocity) mixed finite element methods (MMFEM and
EV-MFEM) to problems in porous media flow. The mortar spaces are first
used to develop a multiscale approach for parabolic problems in porous media
applications. The implementation of the mortar mixed method is presented for
two-phase immiscible flow and some a priori error estimates are then derived
for the case of slightly compressible single-phase Darcy flow. Following this,
the problem of modeling flow coupled to reactive transport is studied. Applications
of such problems include modeling bio-remediation of oil spills and other
subsurface hazardous wastes, angiogenesis in the transition of tumors from a
dormant to a malignant state, contaminant transport in groundwater flow and
acid injection around well bores to increase the permeability of the surrounding
rock. Several numerical results are presented that demonstrate the efficiency
of the method when compared to traditional approaches. The section following
this examines (non-mortar) enhanced velocity finite element methods for solving
multiphase flow coupled to species transport on non-matching multiblock grids.
The results from this section indicate that this is the recommended method of
choice for such problems.
Next, a mortar finite element method is formulated and implemented
that extends the scope of the classical mortar mixed finite element method
developed by Arbogast et al [12] for elliptic problems and Girault et al [62] for
coupling different numerical discretization schemes. Some significant areas of
application include the coupling of pore-scale network models with the classical
continuum models for steady single-phase Darcy flow as well as the coupling
of different numerical methods such as discontinuous Galerkin and mixed finite
element methods in different sub-domains for the case of single phase flow [21,
109]. These hold promise for applications where a high level of detail and
accuracy is desired in one part of the domain (often associated with very small
length scales as in pore-scale network models) and a much lower level of detail at other parts of the domain (at much larger length scales). Examples include
modeling of the flow around well bores or through faulted reservoirs.
The next section presents a parallel stochastic approximation method
[68, 76] applied to inverse modeling and gives several promising results that
address the problem of uncertainty associated with the parameters governing
multiphase flow partial differential equations. For example, medium properties
such as absolute permeability and porosity greatly influence the flow behavior,
but are rarely known to even a reasonable level of accuracy and are very often
upscaled to large areas or volumes based on seismic measurements at discrete
points. The results in this section show that by using a few measurements of
the primary unknowns in multiphase flow such as fluid pressures and concentrations
as well as well-log data, one can define an objective function of the
medium properties to be determined, which is then minimized to determine the
properties using (as in this case) a stochastic analog of Newton’s method. The
last section is devoted to a significant and current application area. It presents a
parallel and efficient iteratively coupled implicit pressure, explicit concentration
formulation (IMPEC) [52–54] for non-isothermal compositional flow problems.
The goal is to perform predictive modeling simulations for CO₂sequestration
experiments.
While the sections presented in this work cover a broad range of topics
they are actually tied to each other and serve to achieve the unifying, ultimate
goal of developing a complete and robust reservoir simulator. The major results
of this work, particularly in the application of MMFEM and EV-MFEM
to multiphysics couplings of multiphase flow and transport as well as in the
modeling of EOS non-isothermal compositional flow applied to CO₂sequestration,
suggest that multiblock/multimodel methods applied in a robust parallel
computational framework is invaluable when attempting to solve problems as
described in Chapter 7. As an example, one may consider a closed loop control
system for managing oil production or CO₂sequestration experiments in huge
formations (the “instrumented oil field”). Most of the computationally costly activity occurs around a few wells. Thus one has to be able to seamlessly connect
the above components while running many forward simulations on parallel
clusters in a multiblock and multimodel setting where most domains employ an
isothermal single-phase flow model except a few around well bores that employ,
say, a non-isothermal compositional model. Simultaneously, cheap and efficient
stochastic methods as in Chapter 8, may be used to generate history matches of
well and/or sensor-measured solution data, to arrive at better estimates of the
medium properties on the fly. This is obviously beyond the scope of the current
work but represents the over-arching goal of this research. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/6575 |
| Date | 20 October 2009 |
| Creators | Thomas, Sunil George |
| Source Sets | University of Texas |
| Detected Language | English |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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