Understanding the dynamics of multi-phase fluid flow is one of the
long-standing problems of computational fluid dynamics today. It has
great theoretical and practical interest. Problems such as the enhanced
recovery of oil, droplets breakup and coalescence in polymer blends,
hydrocarbon migration, and ground water flow are but a few processs
of interest to petroleum engineers, chemical engineers, hydrologists and
soil scientists. In this proposal we will focus on the application of
the Lattice-Boltzmann Method (LBM) in two frontier areas. One is the
droplets breakup and coalescence in polymer blends, and the other is
multi-phase fluids in porous media with direct applications for the enhanced
recovery of oil. Our ultimate goal is to develop efficient customized
software for practical industrial applications. One of us (Haowen Xi) have
been performing research at Exxon Research Corp. in Annandale, New Jersey for
two years before join Bowling Green State University last year. Both of us
have extensive use of powerful workstations and supercomputers to perform
large scale, realistic numerical experiments. We also possess extensive
backgrounds in the parallelization of fluid dynamics algorithms, having written
a three dimensional code for the simulation of relativisitic fluids which has
high parallel efficiency in implementing a message passing parallel strategy.
We believe, with state of art facility and the highly qualified scientists
and software engineers in the Pharoah project at the OSC, we will be able to
use our expertise in application of rigorous theoretical physics and
mathematical modeling to solve complex industrial problems.
Because nearly all chemically different polymers are relatively immiscible, the mixing of immiscible polymers is a ubiquitous industrial goal. Two broad categories of such materials are rubber-toughened plastic and stiffened elastomers. Both are fine dispersions of one polymer in another. The usual aim is to produce a fine dispersion of submicron-size droplets suspended in another polymer to produce a composite with improved physical properties (Paul D. R and Newman S. , editor,"Polymer Blends", volume 2 (Academic Press: NY 1987; Kleintjens L. A. and Lemstra P. J., editor,"Integration of Fundamental Polymer Science and Technology"). A common example is the rubber-toughening of a brittle glass polymer. The inclusion of rubber serves to stop the propagation of cracks through the brittle material and dissipate energy. The inclusions are most effective when they are small (submicron) and numerous. The common means of mixing immiscible polymers involves the breakup of droplets in shear flow and added block copolymer. The breakup of droplets under shear is well simulated using the three-dimensional Lattice-Boltzmann method code we have developed. ( See our web page.)
At present, one of the biggest challenges in practical industrial applications
is to be able to predict the droplet size distribution in a multi-phase flow
under shear flow. In our recent work ("How Copolymers Promote Mixing of
Immiscible Homopolymers," Journal of Rheol, vol 49, p. 663, 1996) we have
developed a dynamical model of the polymer droplet breakup and coalescence in
a mixing shear flow. Our project of the parallelization of LBM simulation
techniques would have significant impact on our understanding of particulate
suspensions of droplets, complementingpresent experimental and theoretical
knowledge.
In today's world oil market, the economic production of oil and gas resources requires carefully engineered recovery projects of increasing technical complexity and sophistication. Hydrocarbons are found, sometimes at enormous depths, within the confines of tiny pores in rock. Although the pores may be interconnected, the resulting pathways still present a significant resistance to the flow of oil toward a well drilled into the hydrocarbon-bearing strata. In addition, since water resides in some of the pores, hydrocarbons and water are recovered simultaneously at the well-head. Thus, even when large amounts of oil are known to be in a reservoir, often only a relatively small fraction of it can be recovered with the conventional pumping technology. The most common method of enhancing oil recovery, which accounts form much of the oil production in the U.S., is the injection of water at strategic locations to displace the oil toward the production wells. Many oil companies attempt to predict the average, or bulk, flow behavior of the flows through the hydrocarbon-bearing rock of a reservoir. Many times the traditional networks simulation method (Dias M. and Payatakes A. editors, "Dynamics of Fluids in Heirarchical Porous Media" Acadmeic Press, San Diego) predictions over- or under-estimate reservoir performance because they over-simplify the geometry of the porous media and its physics. It thus does not properly model multi phase flow in porous media.
However, in the recent years, the LBM to such problems has gained in popularity. The idea is to numerically solve the Navier-Stokes equation in a realistic disordered geometry, and then study study how the volume-averaged properties of the flow relate to the details at the microscopic level of the porous geometry. For the multi-phase flow (e.g oil-water), the ONLY numerical simulations of porous media (at the level of the Navier-Stoke equations) have been achieved by the Lattice-gas and Lattice-Boltzmann methods (Rothman D. H.: J. Geophys. Res vol 95, p.8663, 1990, Gunstensen A. K and Rothman D. H.: J. Geophys. Res vol 98, p. 6431 1994, and Rothman D. H. and Zaleski S.: "Lattice-gas model of phase separation: interfaces, phase transitions, and multiphase flow", Rev. Modern Phys, vol 66, 1417, 1994). The present proposal is devoted to the development of efficient methods for the parallelization of the porous media systems and to the study of single-phase and two-phase flow through porous media. Our methods will yield a simulation tool which can be used to approach the simulation of porous media which can treat very fine pores. The applicability of the final code to realistic porous media flow and the utility of the simulations to the oil-recovery efforts constitute a major anticipated achievement.