ENVIRONMENTAL CONTAMINATION AND GEOMECHANICAL SIMULATION
One of the most important problems facing society today is the environment's protection from various sources of contamination. In order to prevent or remove contamination from the air, earth, and water, large-scale computational models are needed that can accurately predict and help control the transport of contaminants. Contamination is found at all length scales. The strongly nonlinear properties of transport models make the scale-up necessary for global simulation extremely difficult.
Another problem that poses a critical threat to the country's economic stability is our rapidly growing dependence on foreign energy sources. The United States produces less than one-half of its petroleum and does not have the overall supplies or increased production capabilities needed to fully support its energy requirements for any extended period of time. Substantial additions must be made to reserves through the location of new sources via exploration or the development of ways to enhance the production of known resources with better technology. The Bush administration has recently acknowledged these needs by recommending significant increases in the Department of Energy's budget aimed at improving enhanced oil recovery (EOR) technology.
These broad topics, although quite different in societal motivation and concerns, actually possess many common technical issues from a computational mechanics standpoint. The research areas of subsurface contaminant transport, geographical exploration, and enhanced production of fossil fuels exhibit a common thread for the need to understand and predict the movement of fluids or mechanical disturbances through heterogeneous porous media on many length scales. They all require large-scale simulations on enormous computational domains. Each of these problems has been mentioned in the context of grand challenges in computational science. They each hold the potential for significant impact through major advances in computational mechanics.
STATUS OF GEOMECHANICAL SIMULATION
Although the increase in computing capabilities and advances in computational mechanics has allowed significant progress in these area's simulation capabilities, existing models are not adequate to address many of the important aspects of these problems. Basic capabilities have been established to predict certain aspects of contaminant transport, petroleum recovery, and seismic exploration. However, models involving less restrictive assumptions are needed to understand and predict the physical processes and to address societal problems effectively.
Currently, basic trends and large-scale movements of contaminants through fairly homogeneous media can be predicted. However, the multiphase flow properties of transport in unsaturated zones are not well understood, nor is the transition from unsaturated to saturated flow with contaminants that form separate phases. The mass transport between phases needed to model migration and vaporization of volatile organic contaminants in the unsaturated zone is not currently modeled sufficiently well to develop efficient monitoring techniques for gasoline spills or leaks. Tools are still needed to model varying soil properties well enough to accurately predict flow in heterogeneous media. Although restoration techniques are beginning to be addressed by both microbial and chemical flooding techniques, the growth/decay, absorption/desorption, or heterogeneous flow parameters are not well enough known to develop effective remediation strategies.
In primary or secondary petroleum recovery where multiphase flow occurs to natural formation pressure or to artificial water flooding, the basic mechanisms are understood, and massive field-scale simulations can aid greatly in developing field production strategies. However, an average of 60 to 70 percent of the original oil is left in the reservoir after this production; this residual oil is the target for EOR techniques. It involves injecting fluids or chemicals into the pores of the reservoir rock, which reduces the surface tension or viscosity that traps the oil and allows the previously trapped hydrocarbon to flow toward production wells. Modeling of the complex fluid/fluid or fluid/rock interactions involved in these physical and chemical processes leads to large coupled systems of nonlinear equations. Although significant progress has been made in these applications, they still require major advances in computational mechanics before the effect of a field-scale EOR process in a heterogeneous reservoir can be routinely predicted.
Although billions of dollars are spent each year on geophysical prospecting techniques, this application still remains one of the least understood problems in computational mechanics due to its lack of uniqueness and the difficulty in solving the so-called inverse problem. The probability of locating a reserve with seismic exploration can clearly be increased, but the ability to predict the earth's internal structure on any fine scale is still well beyond contemporary modeling techniques. Seismic techniques can currently identify the major structural traps that could potentially contain hydrocarbons. However, refined computational mechanics techniques could greatly aid in the detection of more subtle stratigraphic traps or pressure cells and significantly increase petroleum reserves.
PAST COMPUTATIONAL ADVANCES
Current modeling capabilities in these important applications have been made possible through a variety of advances in computational mechanics. Numerical solution of the convection-dominated models used for both contaminant transport and petroleum recovery is quite difficult. The complicated fluid/fluid interactions that govern the multiphase or multicomponent flow processes occur in narrow moving regions of interaction, which often involve small viscous or diffusive phenomena. They are strongly nonlinear and strongly coupled systems that must be solved simultaneously. The enormous computational domains and complex inverse procedures to obtain the parameters for flow have posed, in general, significant challenges to the computational mechanics community.
Large upstream-weighted cell-centered finite difference codes have been developed and optimized in the petroleum industry. Efficient solution of the large coupled systems of nonlinear partial differential equations has required advances in linearization and quasi-linearization techniques, block eliminations, and iterative solution methods, as well as in data storage and retrieval.
The need to treat complex boundaries and flow regimes in contaminant transport has led to the use of finite element methods for these applications. Advances in the use of finite elements in fluids have appeared in recent years. Since governing fluid/fluid interactions occur in moving zones, techniques such as streamline diffusion methods are becoming more popular and hold great promise. Efficient linear solution techniques such as multigrid methods have been used recently
to solve the nonstructured matrices arising from triangular and irregular grids.
Petrov-Galerkin methods, with the choice of test function based on stabilizing the transport terms, have been used with some success. Similarly, Eulerian-Lagrangian techniques and the modified method of characteristics have proven quite useful in treating transport in porous media. These methods require accurate fluid velocities. Mixed finite element methods have been used to yield accurate approximations of the latter, even under heterogeneous and unstable flow conditions.
Many of the phenomena governing transport in porous media are highly localized in time and space. Although local grid refinement is common in finite element codes, its use in large structured finite difference codes has been greatly restricted due to the increased complexity of the resulting matrices. Recently, the combination of domain decomposition techniques and local refinement in time and space has been applied efficiently in large industrial cell-centered codes using finite difference discretization.
Effective solution of the inverse seismic problem requires accurate and efficient solution of the ''forward" problem where the response to input sources is calculated on a specified set of geological structures. The forward problem must be solved repeatedly with different structural locations in the course of solving the inverse problem associated with determining the true subsurface configuration from measured surface data. Given the vastness of the earth's interior, the choice of a reasonable computational domain requires the introduction of artificial computational boundaries. Until recent advances were made in the development of absorbing boundary conditions, computed reflections from such computational boundaries destroyed information about subsurface structure. Improvements have also been made in the modeling of reflections from interior stratigraphic discontinuities. Such advances in computational mechanics for the forward problem now allow the inverse problem to be addressed meaningfully.
The emergence of vector-based supercomputers has revolutionized the solution of each problem mentioned above. Different applications can take advantage of differences in hardware architectures, thus requiring distinct algorithm developments. For example, the CYBER 205 architecture performs quite well for seismic problems where extremely long vectors can be manipulated effectively. Although the CRAY computers cannot take advantage of very long vectors as well as the CYBER 205, the cycle time is significantly better and
the reservoir simulation codes perform extremely well on the CRAY. Highly vectorized codes have been developed for each of the major vector computers by taking advantage of their particular architectural features. Although some codes have been ported to the emerging parallel architecture computers, the machines' parallelizing compilers are not well developed. The choice of the granularity level for code development on parallel algorithms for complex problems is not clear, but the potential for massively parallel machines is enormous.8
Much research is needed in the development of more accurate and useful models in the environmental and energy areas. A major goal is a better understanding of the model properties, especially in the nonlinear regime and how they scale through various representative lengths. There is the need to fully develop the ability to use the computer as a laboratory to test model concepts, parameters, sensitivities, etc., in order to obtain better knowledge of the properties of the models and the processes they represent. If these large-scale simulators are to be used as a tool to build intuition and understanding, overall computational efficiency is essential. Visualization techniques that allow the scientist or engineer to view the results of his/her calculations in real time are also critical in this computational laboratory concept.
One of the major difficulties in accurate earth transport modeling is its heterogeneous nature at many different length scales. It is very difficult to obtain effective global parameters from those that vary rapidly on smaller-length scales, even for linear problems. The nonlinear properties of models greatly complicate their development. Volume averaging, homogenization, geostatistical averaging, and the current use of micromodels are to develop effective parameters. Extensive comparison between fine-grid and coarse-grid simulations using effective parameters will be necessary for a major breakthrough. In the scale-up process the basic constitutive laws must also be described differently to relate the different effective flow properties at various length scales. The homogenization from Navier-Stokes models at a pore scale to Darcy's law at field scale is an important example of this idea. The effects of heterogeneity and viscous fingering, however,
See Appendix 3, Parallel Computation.
may require qualitatively different diffusion terms on various scales.
Although the importance of reliability is clearly acknowledged in many fields such as structural design, it is not emphasized enough in the environmental and energy areas. To evaluate and control environmental damage, there is a distinct need to develop bounding calculations for the transport of contaminants. Designing waste disposal strategies requires the ability to certify the reliability of the computational models. Also, if the local moving interfacial phenomena in EOR methods are not resolved, there will be no guarantee that the production strategy will be successful, much less optimal.
As noted earlier, adaptive strategies have received considerable attention in many areas of computational mechanics. The use of a priori and a posteriori error estimators has proven to be quite effective for many application areas. These concepts must be developed more fully for nonlinear dynamic applications and must be utilized in energy and environmental problems.
A promising area for major advances in adaptive strategies for large-scale codes is the use of domain decomposition techniques. Adaptive local grid refinement methods are being developed for accurate treatment of localized phenomena. Combinations of these with domain decomposition techniques can achieve the benefit of adaptivity without the loss of efficiency. Global decomposition of the computational domain into pieces for parallel solution or decomposition of the problem on coarser-grained physical criteria each allows for more efficient solution algorithms. Also, different constitutive equations can be used on different domains to address scale dependencies. Major advances in these various forms of domain decomposition can help to exploit the enormous potential of the parallel architecture supercomputers.
Although massively parallel computing can potentially break the speed barriers of serial computers, significant advances in utilizing parallelism will require extensive research. The compilers for these parallel architecture computers are far from being able to determine automatically the optimum granularity for parallelism. Similarly, even if a granularity is given, there is a great need for algorithm development for efficient utilization of the computers' parallel capabilities.
Finally, major advances in computational mechanics will be considerably more effective if they are achieved in a multidisciplinary environment. Significant progress can be made by interaction of scientists or engineers who understand the aspects of the physical problem, mathematicians and
numerical analysts who know the mathematical and numerical properties of the mathematical model, and computer scientists who can help take full advantage of the architecture of the specific computer to be used.
Significant advances in computational mechanics as described above could have enormous payoffs in the areas of energy and environment. The ability to model and understand the physics of flow on increasing length scales in heterogeneous media could allow major breakthroughs in the ability to control the expanding contamination of our environment and to develop effective remediation strategies. Although we are far from these capabilities now, they are possible through scientific advances and are critical to maintaining environmental integrity. The rapid progress being made in computer hardware computational capabilities finally allows enough physics to be incorporated into the complex EOR models to permit accurate flow descriptions at various scales. The algorithm development to utilize this hardware growth is lagging severely. The enormous potential of enhanced modeling to increase significantly our accessible petroleum reserves can be achieved only through major advances in computational mechanics.