Scaling of units

Irrespective of the approach taken to scale-up, the scaling of unit operations and manufacturing processes requires a thorough appreciation of the principles of similarity. Process similarity is achieved between two processes when they accomplish the same process objectives by the same mechanisms and produce the same product to the required specifications. Johnstone and Thring (56) stress the importance of four types of similarity in effective process translation (1) geometric similarity (2) mechanical (static, kinematic, and dynamic) similarity (3) thermal similarity and (4)... 

Irrespective of the approach taken to scale-up, the scaling of unit operations and manufacturing processes requires a thorough appreciation of the principles of sim-... 

The rational rate constant is defined as the rate of growth over unit area, in equivalents per second, of a scale of unit thickness, i.e., Equation (3.98),... 

Increasing in scale of unit equipment. With the increasing demand for ammonia, the scale of unit equipment is continuously increased to decrease the investments and production costs. At present, the production capacity of single-stream equipment has reached 1,850 ton of ammonia per day. 

Table 10 Relative volumes, (in units of = Og on the //-scale), of unit-electron wave packets at various atomic sublevels...

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

It is not possible to apply (C2.1.1) down to the level of monomers and replace by the degree of polymerization N and f by the sum of the squares of the bond lengths in the monomer because the chemical constitution imposes some stiffness to the chain on the length scale of a few monomer units. This effect is accounted for by introducing the characteristic ratio defined as C- — The characteristic ratio can be detennined... 

Here f denotes the fraction of molecules diffusely scattered at the surface and I is the mean free path. If distance is measured on a scale whose unit is comparable with the dimensions of the flow channel and is some suitable characteristic fluid velocity, such as the center-line velocity, then dv/dx v and f <<1. Provided a significant proportion of incident molecules are scattered diffusely at the wall, so that f is not too small, it then follows from (4.8) that G l, and hence from (4.7) that V v° at the wall. Consequently a good approximation to the correct boundary condition is obtained by setting v = 0 at the wall. ... 

Now suppose, as before, that distance is measured on a scale whose unit is comparable with the dimensions of che flow channel, and let v° be some characteristic mass mean velocity in the system, like introduced above... 

Fig. 4.11 (o) Adsorption isotherm for (i) a powder made up of nonporous particles (ii) a solid which is wholly microporous (iii) a powder with the same external surface as in (i) but made up of microporous particles having a total micropore volume given by the plateau of isotherm (ii). The adsorption is expressed in arbitrary units, (b) t-Plots corresponding to isotherms (i) and (iii). The o,-plots are similar, except for the scale of... 

Plot E versus log t for both of these sets of data on the same graph. Now suppose that the units of the 45°C experiment are minutes instead of seconds (this is not the case, but we can pretend that it is). On the basis of this imaginary condition, each of the times at 45°C should be multiplied by the factor 60 sec/min to make the comparison with the 25°C data. Apply this correction to the 45°C data and plot on the original graph. Be sure to select a scale of the original graph so that corrected data can be accommodated also, label various portions clearly. Briefly comment on the results of this manipulation. 

The development of the novel Davy-McKee combined mixer—settler (CMS) has been described (121). It consists of a single vessel (Fig. 13d) in which three 2ones coexist under operating conditions. A detailed description of units used for uranium recovery has been reported (122), and the units have also been studied at the laboratory scale (123). AppHcation of the Davy combined mixer electrostatically assisted settler (CMAS) to copper stripping from an organic solvent extraction solution has been reported (124). 

Farbwerke Hoechst AG and Hbls AG have cooperated in the development of industrial-scale plasma units up to 10,000 kW (7). Yields of acetylene of 40—50 wt % with naphtha feedstock, and about 27 wt % with cmde oil feedstock, have been obtained. Acetylene concentration in the cracked gas is in the 10—15 vol % range. 

Most by-product acetylene from ethylene production is hydrogenated to ethylene in the course of separation and purification of ethylene. In this process, however, acetylene can be recovered economically by solvent absorption instead of hydrogenation. Commercial recovery processes based on acetone, dimetbylform amide, or /V-metby1pyrro1idinone have a long history of successfiil operation. The difficulty in using this relatively low cost acetylene is that each 450, 000 t/yr world-scale ethylene plant only produces from 7000 9000 t/yr of acetylene. This is a small volume for an economically scaled derivatives unit. 

In some respects, hydrometallurgy can be described as wet analytical chemistry carried out on a large scale. Many different dow sheets can be designed with various types of unit operations and most metals can be extracted from a complex ore and recovered at the desired level of purity. A viable hydrometaHurgical process, however, must achieve that goal at an economically acceptable cost. 

The criterion of maintaining equal power per unit volume has been commonly used for dupHcating dispersion qualities on the two scales of mixing. However, this criterion would be conservative if only dispersion homogeneity is desired. The scale-up criterion based on laminar shear mechanism (9) consists of constant > typical for suspension polymerization. The turbulence model gives constant tip speed %ND for scale-up. 

A plot of log([A]g j[A — 1) versus log[B], called a Schild plot, yields a straight line of unit slope and intercept of iCg, the latter often expressed on a scale analogous to that for pH, so that = logif (46—48). 

Pilot-plant start-up is different from principal process plant start because of the smaller scale of the unit, smaller resources committed, lack of advance start-up planning, and limited experience with the pilot-plant process and operation. 

Manufacturing methods must suit the scale of manufacture. By the late 1980s, some 6,000 t of pyridine (1) were consumed in the United States, and nearly 20,000 t worldwide. 

The intrinsic rejection and maximum obtainable water flux of different membranes can be easily evaluated in a stirred batch system. A typical batch unit (42) is shown in Figure 5. A continuous system is needed for full-scale system design and to determine the effects of hydrodynamic variables and fouling in different module configurations. A typical laboratory/pilot-scale continuous unit using computer control and on-line data acquisition is shown in Figure 6. 

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