CHE 301 Sedimentation PDF

Department of Chemical Engineering Ladoke Akintola University of Technology, Ogbomoso 2015/2016 Session Sedimentation Basic separation Techniques The creation of a mixture of chemical species from the sep...

Department of Chemical Engineering Ladoke Akintola University of Technology, Ogbomoso 2015/2016 Session Sedimentation Basic separation Techniques The creation of a mixture of chemical species from the separate species is a spontaneous process that requires no energy input. The inverse process, separation of a chemical mixture into pure components, is not a spontaneous process and thus requires energy. A mixture to be separated may be single or multiphase. If it is multiphase, it is usually advantageous to first separate the phases. Basic separation techniques is diagrammatically depicted in figure 1 Figure 1.1: Basic separation techniques: (a) separation by phase creation; (b) separation by phase addition; (c) separation by barrier; (d) separation by solid agent; (e) separation by force field or gradient. The most common separation technique, shown in Figure 1.1a, creates a second phase, immiscible with the feed phase, by energy (heat and/or shaft-work) transfer or by pressure reduction. Common operations of this type are distillation, which involves the transfer of species between vapor and liquid phases, exploiting differences in volatility (e.g., vapor pressure or boiling point) among the species; and crystallization, which exploits differences in melting point. A second technique, shown in Figure 1.1b, adds another fluid phase, which selectively absorbs, extracts, or strips certain species from the feed. The most common operations of this type are liquid–liquid extraction, where the feed is liquid and a second, immiscible liquid phase is added; and absorption, where the feed is vapor, and a liquid of low volatility is added. In both cases, species solubilities are significantly different in the added phase. Less common, but of growing importance, is the use of a barrier (shown in Figure 1.1c), usually a polymer membrane, which involves a gas or liquid feed and exploits differences in species permeabilities through the barrier. Osmosis, filtration, pervoration, gas permeation are some of the example in this category. Also of growing importance are techniques that involve contacting a vapor or liquid feed with a solid agent, as shown in Figure 1.1d. Most commonly, the agent consists of particles that are porous to achieve a high surface area, and differences in species adsorbability are exploited. Example are adsorption, chromatography and ion exchange. Finally, external fields (centrifugal, thermal, electrical, flow, etc.), shown in Figure 1.1e, are applied in specialized cases to liquid or gas feeds, with electrophoresis being especially useful for separating proteins by exploiting differences in electric charge and diffusivity. Sedimentation This section describes mechanical devices used to separate one bulk phase from another. It is different from seperations where one or more chemicals are removed from a feed mixture. Sedimentation is the partial separation of suspended solid particles from a liquid by gravity settling. This process may be divided into the functional operations of thickening and clarification. The purpose of thickening is to increase the concentration of suspended solids while that of clarification is to produce a clear effluent.’ Concentration of suspension may settle in one or two different ways. In Figure 2a, a stage in the sedimentation process is illustrated. A is clear liquid, B is suspension of the original concentration, C is a layer through which the concentration gradually increases, and D is sediment. The sedimentation rate remains constant until the upper interface corresponds with the top of zone C and it then falls until the critical settling point is reached when both zones B and C will have  disappeared. A second and rather less common mode of sedimentation as shown in 2b, is obtained when the range of particle size is very great. The sedimentation rate progressively decreases throughout the whole operation because there is no zone of constant composition, and zone C extends from the top interface to the layer of sediment. 238 CHEMICAL ENGINEERING Clear liquid Clear liquid Constant composition variable zone composition Zone of Sediment (4 (b) Figure 5.1. Sedimentation of concentrated suspensions (a) Type 1 settling ( b ) Type 2 settling In the first, after an initial brief acceleration period, the interface between the clear liquid Figure 2: Sedimentation of concentrated suspension and the suspension moves downwards at a constant rate and a layer of sediment builds up at the bottom of the container. When this interface approaches the layer of sediment, its rate of fall decreases until the “critical settling point” is reached when a direct interface is formed between the sediment and the clear liquid. Further sedimentation then results For a given solid and liquid, the main factors which affect the rate of sedimentation are the solely from a consolidation of the sediment, with liquid being forced upwards around the solids which are then forming a loose bed with the particles in contact with one height of the suspension, the diameter of the containing vessel, and the volumetric concentration another. Since the flow area is gradually being reduced, the rate progressively diminishes. In Figure 5. l a , a stage in the sedimentation process is illustrated. A is clear liquid, B is suspension of the original concentration, C is a layer through which the concentration and the shape of the vessel. gradually increases, and D is sediment. The sedimentation rate remains constant until the upper interface corresponds with the top of zone C and it then falls until the critical settling point is reached when both zones B and C will have disappeared. A second and rather less common mode of sedimentation as shown in Figure 5. l b , is obtained when Settling Velocity the range of particle size is very great. The sedimentation rate progressively decreases throughout the whole operation because there is no zone of constant composition, and zone C extends from the top interface to the layer of sediment. The main reasons for the modification of the settling rate of particles in a concentrated Mathematical models used to describe the behavior of particles that separate from fluids, primarily suspension are as follows: because of gravitational forces, invariably are based on the terminal velocity of the particle, 𝑢" , (a) If a significant size range of particles is present, the large particles are settling relative to a suspension of smaller ones so that the effective density and viscosity of the fluid are increased. which is defined as the fluid velocity that renders a particle, subject to gravitational force, (b) The upward velocity of the fluid displaced during settling is appreciable in a concen- trated suspension and the apparent settling velocity is less than the actual velocity motionless when suspended unhindered in an upward-flowing fluid stream. At that condition, the relative to the fluid. (c) The velocity gradients in the fluid close to the particles are increased as a result of the change in the area and shape of the flow spaces. drag force on the particle plus the buoyant force balance the force of gravity. / $%& ' () *(+ 0 𝑢" = Equation 1 ,-. (+ the drag coefficient 𝐶3 in equation 1 is related to the drag force 𝐹% on the projected area, 𝐴6 , of a spherical particle by 0 7%& 80 𝐹% = 𝐶3 𝜌; Equation 2 $ 9 where: 𝑑6 is particle diameter; 𝜌= is particle density; 𝜌; is fluid density; 𝑢" is terminal velocity (or settling velocity in a quiescent fluid); 𝑔 is acceleration due to gravity; and 𝐶3 is the dimensionless drag coefficient. A number of factor influences the calculation of the drag coefficient. This includes the rotation of falling particles, collisions with walls and other particles, Brownian motion (random particle motion occasioned by the collision of very small particles with surrounding gas molecules or atoms). Hence hindered settling in lieu of free settling is often considered. Reynolds number region 9$ Stokes’ law 𝐹% = 3𝜋𝜇𝑢𝑑6 which applies at 𝑁CD < ~2 gives 𝐶3 =. Subtituting in equation 1 HIJ gives the settling velocity for a spherical particle of diameter 𝑑6 as 0 ( *( '%& & + 𝑈" = Equation 3 LMN Equation 3 can be used for Reynolds numbers from 0.001 to 2 For Reynolds numbers between 500 and 200,000, the drag coefficient is almost independent of the Reynolds number, and the corresponding settling velocity and drag force for a spherical particle are, respectively, 𝐶3 ~0.44 𝑎𝑛𝑑 𝐹% = 0.055𝜋𝑑69 𝑢9 𝜌;. Newtons law is applicable here. This results in / %& ' (& *(+ 0 𝑢" = 1.74 Equation 4 (+ *X.Y Between the Stokes and the Reynolds regions, where NRe lies between 2 and 500, 𝐶3 ~18.5𝑁CD. this results in X.ZL 0.153𝑔X.ZL 𝑑6L.L$ 𝜌6 − 𝜌; 𝑢" = Equation 5 𝜌;X.9\ 𝜇 X.$, Although the range of applicability of the above settling equations has been stated, a commonly used concept is to use a single criterion based on the highest Reynolds number for which the equation applies, which for Stokes’ law is 2. The criteria is based on a general procedure that eliminates the terminal velocity factor, 𝑢" , from the Reynolds number by substituting one of the settling equations. This results in an empirical equation L , 𝜌; 𝜌6 − 𝜌; 𝐾^ = 34.81𝑑6 Equation 6 𝜇;9 where 𝑑6 is in inches and 𝜇; is in cP, with densities in lb/ft3. The constant Kc, which is listed in Table 2 along with the range of applicability of the settling equations, can be used to determine if the equation is suitable for the particle size in question. Having obtained Kc, it is then convenient to calculate the settling velocity from a general settling velocity equation, L L_` 9*` 𝑢" = 4𝑔 𝑑6 𝜌6 − 𝜌; /3𝑏𝜇;` 𝜌;L*` Equation 7 where the constants are Table 1: Constants values for Kc Law B N Stokes 24 1.0 Intermediate 18.5 0.6 Newton 0.44 0 Table 2: Ranges of settling equations Newton’s law Intermediate law Stoke’s law dp 100,000-1,500 1,500 -100 100-3 NRe 200,000-500 500-2 2-0.0001 Kc >= 43.6 3.3