Bulk stream

Bulk stream must contain different acid—base or groups with different reactivities than impurities. 

Catalytic combustion is feasible for purification processes only when impurities are at concentrations <10% of lower flammabiUty limit and when bulk stream already consists of oxidation products, eg, airstreams, off-gases, and other inerts. 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

The two-phase mixture in the boundary layer near the heating surface can hardly be in thermodynamic equilibrium with the bulk stream. Thus, the magni-... 

In a fluidized bed reactor, entrained particles leaving in a dilute phase stream are conventionally and desirably either partially or wholly condensed into a bulk stream and returned to the bed via a centrifugally driven cyclone system. At equilibrium, or when steady state operation is attained, any particle loss rate from the cyclones, as well as the remaining bed particle size distribution, are functions of (a) the rate of any particle attrition within the system and (b) the smallest particle size that the cyclone system was designed to completely collect (i.e., with 100% efficiency), or conversely the largest size which the system cannot recover. These two functions result in an interdependency between loss rate and bed particle size distribution, eventually leading to an equilibrium state (Zenz Smith, 1972 Zenz, 1981 Zenz Kelleher, 1980). 

Results of the Edehzhie survey (a hybrid survey) have been used to adjust suggested protected area boundaries and make compromises in light of mineral potential. There is a high kimberlite potential on the Horne Plateau, as suggested by the presence of indicator minerals and a small diamond recovered from a bulk stream sediment sample (Day et al., 2007). 

We consider a plane with length / and width w, which is exposed to a flowing solution with a dissolved component i at a bulk concentration c. The direction of the bulk stream of flow is parallel to the plane in the direction of the j-axis the x-axis is perpendicular to the plane, as shown in Figure 4. The bulk velocity of the flow far from the plane is denoted as v. The z-axis is considered immaterial, due to a sufficiently large value of w compared with the dimensions of the velocity and concentration perturbations. / is assumed to be much larger than the diffusion layer thickness (<5,). 

In reverse osmosis, where the solutes retained are relatively low in molecular weight and have a significant osmotic pressure, concentration polarization can result in osmotic pressures considerably higher than those represented by the bulk stream concentration. Higher pressures are required to overcome the osmotic pressure (Figure 6). 

Equation 3 Indicates that a semilog plot of flux against concentration should be a straight-line intercepting the horizontal axis at the gel concentration (C ). When the bulk-stream concentration (C ) equals the gel concentration (C ) there is no driving force for removal of solute from the membrlne. The gel layer increases in thickness until the flux is zero. Figure 10 provides experimental confirmation for a number of protein solutions and colloidal suspensions ( ). The Intercepts with the horizontal axis are reasonable values for the gel concentration. 

For exothermic reaction, heat is released and particles are hotter than the surrounding fluid, hence the nonisothermal rate is always higher than the isothermal rate as measured by the bulk stream conditions. However, for endothermic reactions the nonisothermal rate is lower than the isothermal rate because the particle is cooler than the surrounding fluid. 

The overall process of coal combustion involves the following three steps in sequence transport oxygen from the bulk stream of gas to the outer surface of the particles, diffusion of oxygen through the ash layer to the reaction interface, and finally reaction with the combustible matter in the unreacted core. The overall flux of oxygen per unit surface area can be expressed as follows ... 

In laminar gas flow, the reactant concentrations and gas velocity are zero at the substrate surface and increase to the bulk concentration and bulk stream velocity at some distance, 6, from the substrate surface and is given by, ... 

Mass transfer in the feed and strip solutions is limited by the extent of concentration polarization. On the feed side of the membrane, concentration polarization refers to an increase in the concentration of solutes at and near the feed-membrane interface because of evaporation of water into the membrane pores (Fig. 1). The resulting solute concentration gradient between the membrane-feed interface, where the concentration is greatest, and the bulk solution induces diffusive transport of rejected solutes back through the concentration polarization boundary layer into the bulk stream. Bulk solution is simultaneously transported to the membrane wall by convection. When equilibrium has been established under a given set of operating conditions (stream flow rate, temperature, fluid dynamics imposed by membrane module design), the rate of back diffusion is equal to the rate at which the solutes are carried to the membrane surface by convective flow. ... 

On the strip side of the membrane, concentration polarization refers to an increase in the water concentration at and near the strip-membrane interface because of condensation of permeate into the strip solution. At equilibrium, the solutes (osmotic agent) diffuse from the bulk stream towards the membrane wall at the same rate as their concentration is reduced by permeate condensation. Water is transported away from the membrane by convection. 

When a reaction occurs on a catalyst particle, it is necessary for the reactants to get to the catalyst. Sometimes this transfer is hindered by mass transfer, and then the concentration near the catalyst is not the same as it is in the bulk stream. This phenomena is demonstrated with the problem posed in Eqs. (8.21)-(8.22), except that now the rate of reaction is evaluated at a concentration that is near the catalyst. The concentration Cs is the concentration on the surface, expressed as the kmol of a species per volume of the catalyst. In your Chemical Reactor Design courses, you will learn various ways to represent this concentration. The net effect, however, is that Eq. (8.21) is changed to Eq. (8.45) ... 

The error obtained when anisokinetic sampling conditions are chosen can be caused by two factors misalignment of the sampling probe and different velocity In the sample tube than In the bulk stream. The magnitudes of both types of error are dependent on the particle diameter through Stokes number. The Stokes number for the sampling tube Inlet Is defined by ... 

Many of the larger diameter particles will lose momentum In collisions with the wall at the bend and become deposited on the tube wall. The smaller particles will remain suspended In the gas with minimal disturbance due to the bend. On the other hand, this effect may also be caused by a segregation of particle diameters In the bulk stream, with particles having a larger diameter migrating away from the center of the stream. Particles with... 

To evaluate the rate and adsorption equilibrium constants in equations such as (9-32) rate data are needed as a function of concentrations in the fluid phase. Data are required at a series of temperatures in order to establish the temperature dependency of these constants. The proper concentrations to employ are those directly adjacent to the site. In the treatment that follows we shall suppose that these local concentrations have been established from the measurable concentrations in the bulk stream by the methods to be given in Chaps. 10 and 11. Our objective here is to find the most appropriate rate equation at a catalyst site. 

Example 9-2 Olson and Schuler determined reaction rates for the oxidation of sulfur dioxide, using a packed bed of platinum-on-alumina catalyst pellets. A differential reactor was employed, and the partial pressures as measured from bulk-stream compositions were corrected to fluid-phase values at the catalyst surface by the methods described in Chap. 10 (see Example 10-1). The total pressure was about 790 mm Hg. 

Average transport coefficients between the bulk stream and the particle surface in a fixed-bed reactor can be correlated in terms of dimensionless groups which describe the flow conditions For mass transfer the group kj p(G is a function of the Reynolds number dpGIfi and the Schmidt number pIp. Chilton and Colburn suggested plotting 7 vs dpGfp., where... 

Equation (11-92) is also applicable for the whole catalyst pellet when diffusion resistance is negligible. Furthermore, it gives the selectivity at any location within the pellet. The selectivity will vary with position in the pellet as Cg/C changes. Diffusion resistance causes to decrease going from the outer surface toward the center of the pellet. Since B is formed within the pellet and must diffuse outward in order to enter the bulk stream, Cg increases toward the pellet center. Equation (11-92) shows qualitatively that these variations in and Cg both act to reduce the global, or pellet, selectivity for B. 

This expression is analogous to Eq. (4-5) for homogeneous reactions. Note that Cj, is the concentration of reactant in the bulk stream. 

The above discussion holds for both liquid drops in gas or gas bubbles in liquid. It is especially difficult to remove small gas bubbles from liqiads because of the high bulk fluid viscosity. A useful technique for gas removal involves use of thin liquid Rims or use of parallel plates in die bulk stream to minimize die vertical distance for a bubble to travel before coalescing with other gas volumes. 

Favor Sequences that Recover the Most Valuable Species as a Distillate Product. By forcing the product aw y from the bulk stream, higher purities generally will result. Recovety as a distillate product is desirable because it avoids the higher temperatures present in the teboiler which could lead to degradation. 

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