Assumptions and Specifications

The column/side reactors process has a large number of design optimization variables. A number of specifications and assumptions ate made to leduee this number to a manageable level. The design objective is to obtain 95% conversion for fixed fresh feed flowrates of 12.6 mol/s of each reactant. The product purities of distillate stream x c and bottoms stream xb,d are both 95 mol%. The two fresh feedstreams of reactants A and B ate fed into the column at the trays immediately above the lower and upper trap-out trays, respectively. 

The reactors are assumed to be adiabatic, and the holdups of each reactor are the same. We assume that the number of trays between each liquid trap-out tray is the same. Other assumptions are theoretical trays, equimolal overflow, saturated liquid feeds and reflux, total condenser, and partial reboiler. 

Based on these specifications and simplifying assumptions, there are five optimization variables  

Number of trays between each liquid trap-out Alt 

The kinetic, vapor-liquid equilibrium, and economic parameters are the same as those used in Chapter 3. The steady-state design objective is the minimum TAC. 

---

A cloth is first saturated with water, then weighed and hung to dry for a 40 minutes, after which it is weighed again. The room temperature and humidity are recorded. Theoretically, compute the following, stating any assumptions and specifications in your analysis ... 

Also with these assumptions and specifications the whole multiperiod optimisation problem shown in Figure 8.12 will now be decomposed into a series of independent dynamic optimisation problems (Figure 8.13). Referring to Figure 8.12 and Figure 8.13 the optimisation problem for Recycle Loop 1 may now be described as follows ... 

In Section 3.4, as the operations are inserted into alternative flowsheets to manufacture vinyl chloride, rules of thumb or heuristics are utilized. For example, when positioning the direct chlorination operation, it is assumed that because the reaction is nearly complete at 90°C, ethylene and chlorine can be fed in stoichiometric proportions. Furthermore, when positioning the pyrolysis operation, the temperature and pressure are set at 500°C and 26 atm to give a 60% conversion. These assumptions and specifications are based on many factors, not the least of which is experience in the manufacture of vinyl chloride and similar chemicals. In this case, a patent by the B.F. Goodrich Co. [British Patent 938,824 (October 9, 1963)] indicates the high conversion of ethylene and chlorine over a ferric chloride catalyst at 90°C and recommends the temperature and pressure levels of the pyrolysis reaction. The decision not to use ethylene in excess, to be sure of consuming all of the toxic chlorine, is based on the favorable conversions reported experimentally by chemists. In the distillation operations, the choice of the key components, the quality of the feed streams and the distillate products, and the pressure levels of the towers are also based on rules of thumb. In fact, heuristics like these and many others can be organized into an expert system, which can be utilized to synthesize sections of this and similar chemical processes. 

This analysis, for the distillation operation in Figure 20.10, is based on the following assumptions and specifications (a) constant relative volatility, (b) saturated liquid distillate, (c) negligible vapor holdup in the column, (d) constant tray pressure drops (Luyben, 1990), and (e) negligible heat losses except for the condenser and reboiler. When using Nf trays, the column is modeled with 4N-j- -I- 13 variables ... 

An approximate heuristic design procedure is used for the columns in the conventional process. The optimum number of frays is assumed to be equal to 2 times the minimum, and the optimum reflux ratio is assumed to be 1.2 times the minimum. The assumptions and specifications use up 9 of the 12 design degrees of freedom, leaving 3 that can be used to optimize the process. Three design optimization variables were selected ... 

The chemical equilibrium constant at 366 K [(Feq)366] and the relative volatilities (constant or temperature dependent) are specified for each case. Equimolal overflow is assumed in the distillation columns, which means that neither energy balances nor total balances are needed on the trays for steady-state calculations. Other assumptions are isothermal operation of the reactor, theoretical trays, saturated hquid feed and reflux, total condensers, and partial reboilers in the columns. Additional assumptions and specifications are the following ... 

Quantitative Relationship of Conductivity and Antistatic Action. Assuming that an antistatic finish forms a continuous layer, the conductance it contributes to the fiber is proportional to the volume or weight and specific conductance of the finish. As long as the assumption of continuity is fulfilled it does not matter whether the finish surrounds fine or coarse fibers. Assuming a cylindrical filament of length 1 cm and radius r, denoting the thickness of the finish layer as Ar and the specific conductance of the finish k, the conductance R of the finish layer is given by the equation (84) ... 

Calvert et al. []. Air Pollut. Control Assoc., 22, 529 (1972)] obtained an explicit equation by making some simplifying assumptions and incorporating an empirical constant that must be evaluated experimentally the constant may absorb some of the deficiencies in the model. Although other models avoid direct incorporation of empirical constants, use of empirical relationships is necessary to obtain specific-estimates of scrubber collec tion efficiency. One of the areas of greatest uncertainty is the estimation of droplet size. 

In extreme cases, very high pressure waves are encountered in which the time to achieve peak pressure may be less than one nanosecond. Study of solids under the influence of these high pressure shock waves can be the source of information on high pressure equations of states of solids within the framework of specific assumptions, and of mechanical, physical, and chemical properties under unusually high pressure. 

According to the aim of the present chapter, let us focus our attention on the academic-theoretical approach. It should be mentioned that in the study of surface reaction processes one frequently has to deal with fairly complex systems. Since the handling of such systems imposes severe problems, the standard procedure is to rationalize their study. The academic approach starts from simplified systems and a reduced number of plausible assumptions, and the goal is to achieve a general solution. The knowledge and understanding of these solutions allows us to undertake specific topics and more complex problems. 

It is important to note that most molecules are not rigid but may prefer a distrinct structure and the conformation of a molecule strongly depends on its specific environment. Hence, the crystal structure of a drug does not have to correspond to the receptor bound conformation. Also, a conformation in solution depends on the nature of the solvent and measuring conditions, and may change when the molecule is bound to the receptor [4]. In addition, different receptors or receptor subtypes can bind the same drug in different conformations. It is a general assumption and observation, but by far not a strict condition, that the conformation in aqueous solution is similar to the bound conformation and is a better representation of the bioactive conformation than an X-ray structure of the isolated molecule in the crystalline state. 

The approach introduced by E. A. Guggenheim and employed by H. S. Harned, G. Akerlof, and other authors, especially for a mixture of two electrolytes, is based on the Br0nsted assumption of specific ion interactions in a dilute solution of two electrolytes with constant overall concentration, the interaction between ions with charges of the same sign is non-specific for the type of ion, while interaction between ions with opposite charges is specific. 

From the beginning of 14C studies, bone was burdened with a marginal status as a sample type. It was missing from the list of sample materials which Libby initially recommended [10]. He and other researchers discouraged its use for the reason that the carbon content and specifically the organic carbon content, was low even in relatively recent bone and because it was a very porous structure potentially subject to chemical alteration and presumably to contamination. It was concluded that bone would systematically violate the third assumption of the 14C method as listed in Table 1. (It should be noted that "burned bone" was highly recommended. However, the sample material was the carbonized hair, skin, and other tissue rather than the bone matrix itself.)... 

In simple cases, you can start with the assumption that every type identified in the specification model will be implemented directly as a separate class for large components you may go through a recursive step of subcomponent partition and specification. We determine intended responsibilities of each class and then build interaction diagrams to design their interactions to realize the specified behaviors. 

Reasonable assumptions on specific surface area for aluminum oxides are 10 m2 g-1 we may further assume 10 4 surface sites g1 and a concentration of 1 g/e.Thus,... 

Analytical model, assumptions and practical implications, 52-57 Analytical performance, correlation chromatography, 108 Analytical process, steps of, 7 Aroclors, isomer-specific analysis of, application of SIMCA, 195-232 Atomic absorption spectrometry, determination of iron in water, 116... 

---