Single effect

Instead of considering the pore structure in detail, it would alternatively be possible to characterize the medium by a single "effective... 

Wlien solid soda ash is used to supply all the carbonate v alues in the precipitation step (eq. 9), a ca 10% Na2S solution results from the primary filtration step wliich can be concentrated to 40% Na2S in a three-effect evaporator train. Final concentration to 60%Na2S occurs in a high v acuurn single-effect evaporator. Hiis concentrated solution can then be fed to a Baker to produce a 60% sodium sulfide flake wliich is sold as co-product. 

Because each effect of an evaporator produces almost as much vapor as the amount it condenses, the total evaporation accompHshed per unit of prime steam, or steam economy, iacreases ia almost direct proportioa to the number of effects used. The total heat load is also spHt up betweea the effects so that each effect has a much lower heat duty than a single effect for the same total evaporation load. However, the total available AT is also spHt up similarly so that each effect of a multiple effect requites about as much heating surface as a single effect operating over the same total temperature difference. Thus ia selecting the number of effects to use ia any iastallatioa, steam cost savings and capital cost of effects have to be balanced. Even before... 

Sindlady, heating surface area needs are not direcdy proportional to the number of effects used. For some types of evaporator, heat-transfer coefficients decline with temperature difference as effects are added the surface needed in each effect increases. On the other hand, heat-transfer coefficients increase with temperature level. In a single effect, all evaporation takes place at a temperature near that of the heat sink, whereas in a double effect half the evaporation takes place at this temperature and the other half at a higher temperature, thereby improving the mean evaporating temperature. Other factors to be considered are the BPR, which is additive in a multiple-effect evaporator and therefore reduces the net AT available for heat transfer as the number of effects is increased, and the reduced demand for steam and cooling water and hence the capital costs of these auxiUaries as the number of effects is increased. 

Economic and process considerations usually dictate that agitated thin-film evaporators be operated in single-effect mode. Veiy high temperature differences can then be used many are heated with Dowtherm or other high-temperature media. This permits achieving reasonable capacities in spite of the relatively low heat-transfer coefficients and the small surface that can be provided in a single tube [to about 20 m" (200 ft")]. The structural need for wall thicknesses of 6 to 13 mm (V4 to V2. in) is a major reason for the relatively low heat-transfer coefficients when evaporating water-like materials. 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partiaUv for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihriugliue [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

Thermocompression Evaporators Thermocompression-evap-orator calculations [Pridgeon, Chem. Metall. Eng., 28, 1109 (1923) Peter, Chimin Switzerland), 3, II4 (1949) Petzold, Chem. Ing. Tech., 22, 147 (1950) and Weimer, Dolf, and Austin, Chem. Eng. Prog., 76(11), 78 (1980)] are much the same as single-effect calculations with the added comphcation that the heat suppied to the evaporator from compressed vapor and other sources must exactly balance the heat requirements. Some knowledge of compressor efficiency is also required. Large axial-flow machines on the order of 236-mVs (500,000-ftVmin) capacity may have efficiencies of 80 to 85 percent. Efficiency drops to about 75 percent for a I4-mVs (30,000-ftVmin) centrifugal compressor. Steam-jet compressors have thermodynamic efficiencies on the order of only 25 to 30 percent. 

Similarly, the assumption that the contact area is small enough that the particle can be represented by an elastic half space allows the radii of the two contacting particles to be combined into a single effective radius that represents how the contacting shapes interact. 

Figure 9.18 Continuous crystallizers, a) draft-tube and baffle (DTB), (b) single effect forced-circulation evaporative, (c) Oslo or Krystal type after Rohani, 2001)...

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

What is important to emphasize is that, given the range of known EDCs, their potential to act with more than one mechanism of action, and ability of some chemicals to mediate effects via mnltiple tissues, no single effective test exists for an endocrine disrnpter rather, a snite of approaches is reqnired to capture the spectrum of possible effects. 

When a two- or higher-phase system is used with two or more phases permeable to the solute of interest and when interactions between the phases is possible, it would be necessary to apply the principle of local mass equilibrium [427] in order to derive a single effective diffusion coefficient that will be used in a one-equation model for the transport. Extensive justification of the principle of local thermdl equilibrium has been presented by Whitaker [425,432]. If the transport is in series rather than in parallel, assuming local equilibrium with equilibrium partition coefficients equal to unity, the effective diffusion coefficient is... 

In the strict application of this evaluation mode, a CEA looks at a single effectiveness... 

Cosr-utility analyses avoid the potential ambiguities that can arise with multidimensional outcomes. They can also be seen as an improvement on a single effectiveness measure in what is generally regarded as an inherently multidimensional world. The transparency of the methods used to derive utility is a particular strength of the approach. Cost-utility analyses are primarily justified—some would argue justified—... 

Sixteen other nitrogen-containing chelates were examined by Lambert and Jones ", and a very good correlation is observed between E and AS indicating a single effect to predominate in all instances. 

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