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TECHNICAL PAPERS

Large Eddy Simulations of a Brine-Mixing Tank

[+] Author and Article Information
Piroz Zamankhan1

Laboratory of Computational Fluid & BioFluid Dynamics, Lappeenranta University of Technology, Lappeenranta 53851, Finland;  Power and Water University of Technology, School of Energy Engineering, P.O. Box 16765-1719, Tehran, Iranqpz002000@yahoo.com

Jun Huang, S. Mohammad Mousavi

Laboratory of Computational Fluid & BioFluid Dynamics, Lappeenranta University of Technology, Lappeenranta 53851, Finland

1

Corresponding author.

J. Offshore Mech. Arct. Eng 129(3), 176-187 (Aug 04, 2006) (12 pages) doi:10.1115/1.2426995 History: Received February 09, 2006; Revised August 04, 2006

Traditionally, solid–liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing, and contacting related to power draw. One important application of solid–liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as in the Barents Sea. In this paper large-eddy simulations, of a turbulent flow in a solid–liquid, baffled, cylindrical mixing vessel with a large number of solid particles, are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the sliding mesh. The simulations are four-way coupled, which implies that both solid–liquid and solid–solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic and some dimensions of a standard baffled tank with Rushton radial turbine used in the present attempt. (a) Gas–liquid mixing tank in which the interface is located at H=260mm. (b) Three-phase mixing tank with the solid phase shown to be deposited at the bottom. (c) Different views of the 6 impeller Rushton turbine with its characteristic dimensions.

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Figure 3

(a) The instantaneous velocity vector field in a cutting xz plane passing through the rotor axis of a mixing tank, whose schematic is illustrated in Fig. 1, at the Reynolds number of Retank=58,500. (b) The interface of air and water in the mixing tank is shown, to obtain better visualization. (c) A high resolution version of the velocity vector field in a cutting xy-plane located below the impellers.

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Figure 4

The complex velocity vector field around rotating grains of sodium formate in a solution. In this case, the drag force includes the lift force due to particle rotational velocity relative to liquid vorticity, which is different than the lift force due to velocity gradient. Vectors are color coded by their velocity magnitudes, where the red is for highest velocity and blue represents the lowest.

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Figure 10

(a) A typical configuration of sodium formate granules around the rotating Ruston turbine at Ω=400rpm. Here only about 104 particles are shown. (Inset) A different view of the configuration as illustrated in (a). (b) The configuration of particles after t≈1.5s of simulation. The particles are color coded using their size where the red is for highest diameter and blue represents the lowest. The particles are polydisperes (36) with the average particle size of 668μm. To obtain better visualization of particle size distribution around a blade, the instantaneous configuration as shown in (a) is magnified and presented in the inset. In addition, probability distribution of particles in each size interval for the instantaneous configuration as illustrated in (b) is plotted on the top left of inset.

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Figure 11

(a) Grid for the rotor and blades. (b)–(d) Deformations of the elastic rotor caused by rotating liquid-particle system. The rotor and blades are color coded using the local displacement magnitude where the red color represents significant displacement as large as 3mm.

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Figure 9

(a) A side view of initial configuration of sodium formate grains in the mixing tank. Roughly 1.4×106 initially monosized particles with diameter of 1mm were used in the simulation. The angular velocity of the Ruston turbine is set at Ω=400rpm. (b) Temporal evolution of position of particles. The instantaneous realizations each separated by t≈0.25s. Movements of particles can be clearly seen from (b). Here, only particles whose distances from the based of the tank are larger than 4cm are shown.

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Figure 8

Variations of dimensionless diffusion layer thickness with saturation. (Inset) The typical shape of particle dissolution profile. Note that in the present attempt, the grains are assumed to be dissolving in a partially saturated solution with concentration C∞.

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Figure 7

A diffusion model for the dissolution of a single grain of sodium formate in water. The concentration field within the solid phase, Cs(r)=Cs=constant(r⩽Rp). The concentration jumps across the interface, ΔCeq=Cl0−Cs, at the solid surface. Note that the solution has lower average concentration of sodium formate, C∞, than the equilibrium value Cl0.

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Figure 6

(a) A snapshot of a spill of roughly monosized sodium formate granules onto a flat surface, which collect in a right circular conical shape. The particle diameter is dp=1mm and its physical properties are found in Table 1. The straight line represents the slope of the linear region. In this case, the angle of repose is roughly 33deg. (b) An instantaneous configuration of particles slightly before the 507th particle collides in the pile. In order to obtain an angle of repose of θf≈33deg, the coefficient of static friction is set to 0.65 in the present simulations. A slightly higher coefficient of static friction has to be used to model the sliding movements of particles over a flat surface made of steel. Here, the coefficient of static friction is set to 0.8 for grain-steel sliding contacts. The base of the flat surface is supported so that no movement is possible in any direction and the effects of the gas are neglected. The experimental results are fairly well reproduced by the present model implying the correct physical framework has been incorporated.

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Figure 5

Temporal evolution of the velocity of colliding particles with diameter of dp=5mm. The physical properties including the coefficient of friction are reported in Table 1. The particles are color coded using their velocity magnitudes. Instantaneous configurations in (a) and (b) are each separated by t≈10−6s. Note that in some cases, the rotation rates as large as 2Hz is induced due to frictional contact between rough grains of sodium formate.

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Figure 2

(a) Sodium formate described as white granules with molecular weight of 68.01, and chemical formula of HCOONA is a hazardous material, which is harmful if swallowed or inhaled. (b) A sample of sodium formate used in the computer simulation reported in the present attempt.

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