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.

Sedimentation Columns and Fluidized Beds

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

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.

Hydraulic Fracturing

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