Turbulent flow slurries

In situations where a low concentration of suspended solids needs to be separated from a liquid, then cross-flow filtration can be used. The most common design uses a porous tube. The suspension is passed through the tube at high velocity and is concentrated as the liquid flows through the porous medium. The turbulent flow prevents the formation of a filter cake, and the solids are removed as a more concentrated slurry. 

One of the most efficient implementations of the slurry process was developed by Phillips Petroleum Company in 1961 (Eig. 5). Nearly one-third of all HDPE produced in the 1990s is by this process. The reactor consists of a folded loop with four long (- 50 m) vertical mns of a pipe (0.5—1.0 m dia) coimected by short horizontal lengths (around 5 m) (58—60). The entire length of the loop is jacketed for cooling. A slurry of HDPE and catalyst particles in a light solvent (isobutane or isopentane) circulates by a pump at a velocity of 5—12 m/s. This rapid circulation ensures a turbulent flow, removes the heat of polymeriza tion, and prevents polymer deposition on the reactor walls. 

In oil and gas well cementing operations, polyethyleneimine phosphonate-derivative dispersants enhance the flow behavior of the cement slurry [422]. The slurry can be pumped in turbulent flow, thereby forming a bond between the well casing and the rock formation. 

A coal slurry is found to behave as a power law fluid, with a flow index of 0.3, a specific gravity of 1.5. and an apparent viscosity of 70 cP at a shear rate of 100 s 1. What volumetric flow rate of this fluid would be required to reach turbulent flow in a 1/2 in. ID smooth pipe that is 15 ft long What is the pressure drop in the pipe (in psi) under these conditions ... 

In highly developed turbulent flow Govier and Winning (Gl) found experimental data to fall within 10% of the conventional Newtonian curve. This means that the effect of the Hedstrom number may be neglected beyond the end of the transition region. Their data were for five clay slurries in two pipe diameters and in. I.P.S.) for Reynolds numbers to 200,000 and Hedstrom numbers to 560,000. 

Figure 6.6. Critical Reynolds number for transition from laminar to turbulent flow of Bingham fluids. The data also are represented by Eqs. (6.56) and (6.5T) (O) cement rock slurry (A) river mud slurries ( ) clay slurry (B) sewage sludge (A) Th02 slurries ( ) lime slurry. [Hanks and Prall, SPE Journal, 342-346 (Dec. 1967)].

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

In the Energy Research and Development Administration s SYNTHOIL process, slurries of coal in recycle oil are hydrotreated on Co-Mo/Si02 Al203 catalyst in turbulent flow, packed-bed reactors. The reaction is conducted at 2,000 to 4,000 psi and about 450° C under which conditions coal is converted to low-sulfur liquid hydrocarbons and sulfur is eliminated as E2S. 

About 80% pyritic sulfur removal has been achieved by microbial desulfurization of Illinois 6 and Indiana 3 coals using T. ferrooxidans in laboratory shake-flask experiments and in a two-inch pipeline loop. The 10 to 25 wt% coal/water slurry was recirculated at 6-7 ft/sec for 7 to 12 days at 70-90°F. Results also show that the rates of bacterial desulfurization are higher in the pipeline loop under turbulent flow conditions for particle sizes, 43 to 200/m as compared to the shake-flask experiments. It is visualized that the proposed coal slurry pipelines could be used as biological plug flow reactors under aerobic conditions. The laboratory corrosion studies show that use of a corrosion inhibitor will limit the pipeline corrosion rates to acceptable levels. 

Wiedmann et al. (1980) have compared the mixing of nonaerated liquids, aerated liquids, and slurries in a turbulent flow. They found that the torque required for stirred, aerated liquids is lower than that for nonaerated stirred liquids because of the decrease in the density of the gas-liquid mixture. The concentration distribution of the particles in aerated suspension becomes more uniform with increasing impeller speed, whereby the torque is higher than that for aerated liquids but lower than that for nonaerated slurries. For gas-liquid-solid systems, very limited data on dispersion of solids and gas phase are available, and further studies are necessary with different designs and for systems with different physical properties. The available literature has been reviewed by Stiegel et al. (1978), Shah et al. (1982), and Shah and Sharma (1986). 

Von Alfthan [22] describes an on-stream x-ray fluorescence system that consists of two flow cells through which the slurry passes. In the classifying flow cell, the slurry flows in a straight path behind a window it then strikes an obstacle that causes slurry mixing as it enters a turbulent flow cell. X-rays excite the slurry in both cells and the resulting fluorescent radiation is a measure of particle size. The system, sold as the Courier 300, measures both x-ray scattering and x-ray fluorescence and is intended primarily as a composition monitor. The measured data can be analyzed to give chemical composition, solids content and maximum particle size. 

To keep the particles in suspension, the flow should be at least 0.15m/sec faster than either 1) the critical deposition velocity of the coarsest particles, or 2) the laminar/turbulent flow transition velocity. The flow rate should also be kept below approximately 3 m/sec to minimize pipe wear. The critical deposition velocity is the fluid flow rate that will just keep the coarsest particles suspended, and is dependent on the particle diameter, the effective slurry density, and the slurry viscosity. It is best determined experimentally by slurry loop testing, and for typical slurries it will lie in the range from 1 m/s to 4.5 m/sec. Many empirical models exist for estimating the value of the deposition velocity, such as the following relations, which are valid over the ranges of slurry characteristics typical for coal slurries ... 

Three-phase fluidized beds and slurry reactors (see Figs. 30g-l) in which the solid catalyst is suspended in the liquid usually operate under conditions of homogeneous bubbly flow or chum turbulent flow (see regime map in Fig. 33). The presence of solids alters the bubble hydrodynamics to a significant extent. In recent years there has been considerable research effort on the study of the hydrodynamics of such systems (see, e.g., Fan, 1989). However, the scale-up aspects of such reactors are still a mater of some uncertainty, especially for systems with high solids concentration and operations at increased pressures it is for this reason that the Shell Middle Distillate Synthesis process adopts the multi-tubular trickle bed reactor concept (cf. Fig. 30e). The even distribution of liquid to thousands of tubes packed with catalyst, however poses problems of a different engineering nature. 

Metzner and Friend [73] measured turbulent heat transfer rates with aqueous solutions of Carbopol, corn syrup, and slurries of Attagel in circular-tube flow. They developed a semi-theoretical correlation to predict the Stanton number for purely viscous fluids as a function of the friction factor and Prandtl number, applying Reichardt s general formulation for the analogy between heat and momentum transfer in turbulent flow ... 

An exception to the generally observed drag reduction in turbulent channel flow of aqueous polymer solutions occurs in the case of aqueous solutions of polyacrylic acid (Carbopol, from B.F. Goodrich Co.). Rheological measurements taken on an oscillatory viscometer clearly demonstrate that such solutions are viscoelastic. This is also supported by the laminar flow behavior shown in Fig. 10.20. Nevertheless, the pressure drop and heat transfer behavior of neutralized aqueous Carbopol solutions in turbulent pipe flow reveals little reduction in either of these quantities. Rather, these solutions behave like clay slurries and they have been often identified as purely viscous nonnewtonian fluids. The measured dimensionless friction factors for the turbulent channel flow of aqueous Carbopol solutions are in agreement with the values found for clay slurries and may be correlated by Eq. 10.65 or 10.66. The turbulent flow heat transfer behavior of Carbopol solutions is also found to be in good agreement with the results found for clay slurries and may be calculated from Eq. 10.67 or 10.68. 

Velocity distribution measurements in the polystyrene slurries showed that k in the slurry is somewhat higher than the clear fluid value of 0.4. Using estimated y values, the Bagnold numbers were <450 in all cases and <40 for the fine particles. It appears Bagnold s criterion does not apply to these turbulent flows. 

Several studies have been reported to determine friction losses in turbulent flow of slurries. Hannah et al. (29) presented an approach in which they compared expressions for the friction pressure of the slurry and clean fluid. In their analysis, they assumed Blasius (30) turbulent Fanning friction factor versus Reynolds number equation for Newtonian fluids. The following expression for estimating slurry friction pressure knowing the clean fluid friction pressure is proposed. 

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