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Direct Simulation of the Motion of Particles in Flowing Liquids
Industrial Problems
Particulate flows of solids in fluids are widely
used for different purposes in different industries. The practical applications
often involve more than the hydrodynamics of particle laden flows; heat
transfer, chemical reactions, gas-liquid-solid flows, phase changes and other
complications must be addressed in practical applications. Particle movers in
direct simulations open the door to a much more realistic treatment of these
complicating features than the multiphase flow modeling which was used in the
past.
Among the practical applications without complicating features, many are
suitable for direct simulation; sedimenting and fluidized suspensions,
lubricated transport and hydraulic fracturing of hydrocarbon reservoirs span
this field and present grand challenges for particle movers.
In sedimentation columns and fluidized beds, the fluidized particles are
held up by a stream of air or liquid under a balance of weight and drag. The
benefits which accrue to fluidizations are that both the transport of heat and
the promotion of chemical reactions can be greatly enhanced by bringing over
fresh fluid to the particles; this is an excellent way to dry grains, to coat
particulates or promote the combustion of coal. The use of catalyst particles
in a fluidized bed to promote the conversion of light crudes to gasoline
(catalyst cracking) is a multi-billion dollar technology at the foundation of
the refining business.
Fluidized beds may bubble, offsetting the advantages of mixing by substantial
bypass of particle contact by the fluid. Introducing spouts can improve the
mixing, and draft tubes can improve the stability helping to avoid bubble
formation. A detailed understanding of the fluid dynamics of bubbling with a
potential for evaluating the continuum approaches taken in the past can be
achieved by particle movers in direct simulation. It may be hopeless to analyze
spouted beds with a draft tube in any way other than direct simulation.
Lubricated transport of viscous materials is another application area with
grand challenges. Nature's gift is that lubricated flows are stable; the low
viscosity constituent migrates to the walls, where the shearing is greatest.
This effect produces a lubricated flow, greatly reducing the cost of transport.
The tendency for solid-liquid mixtures in pipes to segregate into solid-rich
core regions surrounded by solid-poor liquid regions near the pipe wall gives
rise to lubrication; coal slurries in water are one example. The problem here
is to determine the nature of forces which push particles away from the wall
and to examine the different ways in which the holdup of the solids may
develop. Flow charts depending on the liquid and solid input are unknown, even
from experiments, but are required for understanding when and how to exploit
the tendency to lubricate.
Lubricated transport of viscous materials will be the topic of an IUTAM
symposium to be held in Trinidad and Tobago in January 1997. The symposium is
being organized by D. Joseph and Harold Ramkissoon. Water lubricated transport
of heavy crudes is perhaps the most studied and best developed of applications
of lubricated transport to technology.
A third rich area of application of solid-liquid flow in which the fluids
rheology plays a crucial role is the fracturing industry. Hydraulic fracturing
is a process often used to increase the productivity of a hydrocarbon well. A
slurry of sand in a highly viscous, usually elastic, fluid is pumped into the
well to be stimulated, at sufficient pressure to exceed the horizontal stresses
in the rock at reservoir depth. This opens a vertical fracture, some hundreds
of feet long, tens of feet high, and perhaps an inch in width, penetrating from
the well bore far into the pay zone. When the pumping pressure is removed, the
sand acts to prop the fracture open. Productivity is enhanced because the
sand-filled fracture offers a higher-conductivity path for fluids to enter the
well than through the bulk reservoir rock, and because the area of contact for
flow out from the productive formation is increased. It follows that a
successful stimulation job requires that there be a continuous sand-filled path
from great distances in the reservoir to the well, and that the sand is placed
within productive, rather than non-productive, formations.
It has been suspected for some time, and experiments have demonstrated, that
the suspended sand does not remain uniformly distributed during pumping of
these slurries. It is found that under the flow conditions expected within the
fracture during pumping, the sand particles migrate rapidly towards the center
plane of the fracture, leaving a clear fluid layer at the fracture walls. This
clear layer lubricates the motion of the slurry, and so increases the rate of
gravity driven, settling and density currents. The net result of these
processes is to cause sand to accumulate at the bottom of the fracture and good
vertical filling to be lost. This in turn reduces well productivity, and can
also interfere with the fracture growth process by blocking downward
extension.
It is sometimes suggested that migration of sand occurs while the slurry is
being pumped down the tubing to reservoir depth. This may cause preferential
injection of solids-rich fluid at the bottom of the reservoir and of
solids-poor fluid at the top. While it is not known if this process actually
occurs, if it did, the consequences to final fracture productivity would be
similar to those described above.
The phenomenon of proppant migration is not currently controlled or exploited
in the fracturing industry. One reason for this is that the relationship
between migration and fluid properties is not understood (there is some
indication from experiments and single particle theories., that the combination
of fluid elasticity and non-uniform shear flow are necessary for rapid
migration). It is therefore not possible confidently to design fluids which,
for example, suppress migration.
The results of a careful theoretical and experimental investigation of the
phenomenon of migration during flow of moderately-concentrated suspensions of
heavy particles in viscoelastic fluids, in particular the identification of the
fluid properties and flow conditions responsible for migration, and of those
which can be controlled to suppress it, would benefit the hydrocarbon industry
by permitting the development of more effective fracturing fluid systems.
Proppant settling in fracturing fluids is also a problem area in fracturing
technology. The settling of particles within the fracture after pumping has
stopped, but before the fracture closes, also impacts final fracture
productivity; loosely speaking, the more settling, the more non-uniform the
coverage of the productive formation and the lower the productivity. Settling
rates are influenced in a poorly understood way by suspending fluid
viscoelasticity.
The current trend in the industry is towards the use of fracturing fluids with
lower concentrations of polymer; this brings cost savings and productivity and
environmental benefits through the use of less material. However, there is a
lower limit on polymer concentrations set, among other factors, by the need to
ensure good particle carrying and suspending properties. A better understanding
of the fluid properties controlling static settling of solids in viscoelastic
fluids could permit further reductions in polymer concentration to be achieved.
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Last updated October 16, 2000 |