Solids removal theory

For a variety of reasons, it may be desirable to remove suspended sohds from a water stream. This removal is most commonly done as part of a water injection system for water-flood or enhanced oil recovery. It may also be necessary to remove suspended solids prior to injecting produced water in disposal wells. 

Two different principles have been used to develop equipment for removing suspended sohds from water. Gravity settling uses the density difference between the solid particle and the water to remove the solids filtration traps the solids within a filter medium that allows water to pass. 

The force of gravity may be used to remove sohd particles from water if the density of these particles is not the same as the density of the water. Typically, sohd particles have a density greater than water therefore, they fall relative to the water due to the force of gravity. The terminal settling velocity is such that the gravitational force on the particle equals the drag force resisting its motion due to friction. 

Assuming the particle is roughly spherical, the drag force may be determined as follows  

A = cross-sectional area of particle, ft (ni ), p = density of the continuous phase, Ib/ft (kg/m ), 

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Petrov and Petrov (1998) developed a molecular hydrodynamic theory of film deposition during removal. Their theory correctly assumes a flow pattern - which we identified as a split streamline - between the solid substrate and the monolayer in Figure 10.5 (c). This pattern is indeed the necessary pattern for successful deposition during removal, but it is not the only flow pattern for solid removal at all dynamic contact angles. Petrov and Petrov (1998) address the kinetics of water removal between the solid and the monolayer and the formation of wet or dry monolayers depending on the amount of water entrained. 

The diffusion theory states that matter is deposited in a continuous way on the surface of a crystal at a rate proportional to the difference in concentration between the bulk and the surface of the crystal. The mathematical analysis is then the same as for other diffusion and mass transfer processes and makes use of the film concept. Sometimes, the film theory is considered to be an oversimplification for crystallization and is replaced by a random surface removal theory (20-23). For both theories the rate of crystal growth (dm/dt) is given by equation XVII, where m, is the mass of solid deposited in time t k, the mass transfer coefficient by diffusion. A, the surface area of the crystal, c, the concentration in the supersaturated solution and Cj, the concentration at the crystal-solution interface (3). For the stagnant film and random surface removal model, equations XVIII and XIX can be used, respectively (3,4) D is the diffusion coefficient, x, the film thickness and f, the fractionai rate of surface renewal. 

For gravity settling of solids, water retention time does not directly affect the solids removal, and only settling theory must be considered. Some small retention time is required for evolved gases to flash out of solution and reach equilibrium. This process usually requires less than 30 sec therefore, retention time criteria rarely govern vessel size. 

The theory of the action of drying agents has been considered in Section 1,20. We are now concerned with the practical methods for the removal of water from organic solids and liquids and from solutions of... 

In a 250 ml Erlenmeyer flask covered with aluminum foil, 14.3 g (0.0381 mole) of 17a-acetoxy-3j5-hydroxypregn-5-en-20-one is mixed with 50 ml of tetra-hydrofuran, 7 ml ca. 0.076 mole) of dihydropyran, and 0.15 g of p-toluene-sulfonic acid monohydrate. The mixture is warmed to 40 + 5° where upon the steroid dissolves rapidly. The mixture is kept for 45 min and 1 ml of tetra-methylguanidine is added to neutralize the catalyst. Water (100 ml) is added and the organic solvent is removed using a rotary vacuum evaporator. The solid is taken up in ether, the solution is washed with water and saturated salt solution, dried over sodium sulfate, and then treated with Darco and filtered. Removal of the solvent followed by drying at 0.2 mm for 1 hr affords 18.4 g (theory is 17.5 g) of solid having an odor of dihydropyran. The infrared spectrum contains no hydroxyl bands and the crude material is not further purified. This compound has not been described in the literature. 

A pure transition metal is best described by the band theory of solids, as introduced in Chapter 10. In this model, the valence s and d electrons form extended bands of orbitals that are delocalized over the entire network of metal atoms. These valence electrons are easily removed, so most elements In the d block react readily to form compounds oxides such as Fc2 O3, sulfides such as ZnS, and mineral salts such as zircon, ZrSi O4. ... 

Vinvlbenzvl Iodide—Vinylbenzyl chloride (20 g 0.131 mol) was added dropwise to dry sodium iodide (29.5 g 0.198 mol) in 130 mL dry acetone. The mixture was stirred at 50°C for 40 min, cooled to room temperature, and filtered. The acetone was removed by rotary evaporation, and 100 mL water and 150 mL ether were added to the solid residue. The aqueous layer was washed with ether. The combined ether layers were washed with water containing 2% sodium thiosulfate and dried over magnesium sulfate. The ether was removed by rotary evaporation and the yellow residue was dissolved in 50 mL hexane and cooled to -20°C. Within 1.5 hr, yellow crystals formed. Fast filtering with chilled glassware provided 17.1 g (53.5% of theory) of vinylbenzyl iodide. 

The electron theory of catalysis cannot as yet be regarded as a complete theory. It resembles a building from which the scaffolding has not yet been removed. It is being erected on the foundation of the modern theory of the solid state and thus introduces new concepts and ideas into the theory of catalysis. This does not mean, of course, that it excludes other concepts and ideas prevalent today in other theories of catalysis. On the contrary, it makes use of these while attempting to disclose their physical content. 

The reaction mixture is cooled in a water-ice bath, and a saturated aqueous ammonium chloride solution is added at such a rate as to maintain the temperature below 35°C. Ammonium chloride solution is added in portions until addition produces no further exothermic reaction (Note 3). The supernatant solution is decanted through glass wool onto 400 g of ice in a 4-L separatory funnel. The residual solids are washed with three portions of hexane, approximately 1000 nt total, and the washes are decanted into the separatory funnel. After the phases are separated, the aqueous phase is washed with an additional 500-mL portion of hexane. The combined organic extracts are washed with 500 nl of saturated ammonium chloride, and then with 500 nl. of brine. The organic layer is dried over anhydrous magnesium sulfate and filtered. Most of the solvent is removed by a rotary evaporator and the residual oil is distilled at reduced pressure using an ice water-cooled fraction cutting head. After a small forerun, approximately 390-392 g (94% of theory) is collected as a colorless oil, bp 116°C/1.6 nm (lit. 155°C/17 rim). ... 

Aqueous soap solutions can be obtained in three distinct forms, the sol form containing the ionic micelle, a clear gel, and a white opaque solid the curd. The sol and gel forms of various soaps have been examined by McBain and his co-workers and shown to differ only in elasticity and rigidity, whilst the electrical conductivity, refractive index, concentration of metallic ion and lowering of the vapour pressure are all identical, results to be anticipated on the fibrillar theory. The gel as we have seen is fibrillar in nature and the conversion of a gel into a curd is brought about by the removal of soap fi om solutions in the form of relatively coarse fibres, a process similar to crystallisation. The experiments of Laing and McBain... 

Purification is accomplished by crystallization from a solution prepared from the crude product and 100 mL of water at a maximum temperature of 50°. (The time at this temperature should be kept minimal.) Filtration of the nearly saturated solution through coarse fiber-glass paper (Whatman GF/A) removes impurities of low solubility. At 0° the solid product crystallizes slowly 12 hours are required for complete deposition. The orange solid is collected on a filter and dried under atmospheric conditions (not vacuum). Yield 17.0 g, 66% of theory. Water of hydration is lost under low humidity conditions or under vacuum. Anal. Calcd. for Na6V10O2g 18H2O V, 35.89 H20, 22.84. Found V, 35.51 H20, 22.65%. 

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