Ideal isothermal

Detailed Modeling Results. The results of a series of detailed calculations for an ideal isothermal plug-flow Langmuir system are summarized in Figure 15. The soHd lines show the form of the theoretical breakthrough curves for adsorption and desorption, calculated from the following set of model equations and expressed in terms of the dimensionless variables T, and P ... 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

Steady-state reactors with ideal flow pattern. In an ideal isothermal tubular pZi/g-yZovv reactor (PFR) there is no axial mixing and there are no radial concentration or velocity gradients (see also Section 5.4.3). The tubular PFR can be operated as an integral reactor or as a differential reactor. The terms integral and differential concern the observed conversions and yields. The differential mode of reactor operation can be achieved by using a shallow bed of catalyst particles. The mass-balance equation (see Table 5.4-3) can then be replaced with finite differences ... 

The gas-phase dehydrogenation of benzene to diphenyl (D) and further to triphenyl (T) is conducted in an ideal isothermal tubular reactor. The aim is to maximize the production of D and to minimize the formation of T. Two parallel, gas-phase reactions occur at atmospheric pressure... 

This example models the dynamic behaviour of an non-ideal isothermal tubular reactor in order to predict the variation of concentration, with respect to both axial distance along the reactor and flow time. Non-ideal flow in the reactor is represented by the axial dispersion flow model. The analysis is based on a simple, isothermal first-order reaction. 

Ideal isothermal packed catalytic tubular reactors, 25 286-287 Ideal isothermal tubular reactors,... 

Fig. 6.10 shows idealized isotherms (at constant pH) for cation binding to an oxide surface. In the case of cation binding, onto a solid hydrous oxide, a metal hydroxide may precipitate and may form at the surface prior to their formation in bulk solution and thus contribute to the total apparent "sorption". The contribution of surface precipitation to the overall sorption increases as the sorbate/sorbent ratio is increased. At very high ratios, surface precipitation may become the dominant "apparent" sorption mechanism. Isotherms showing reversals as shown by e have been observed in studies of phosphate sorption by calcite (Freeman and Rowell, 1981). 

Energy is needed to eompress gases. The compression work depends on the thermodynamic compression process. The ideal isothermal compression cannot be realized. Even more energy is needed to compact hydrogen by liquefaction. Low density and extremely low boiling point of hydrogen increases the energy cost of compression or hquefaction. 

Compression of hydrogen consumes energy depending on the thermodynamic process. The ideal isothermal compression requires the least amount of energy (just compression work) and the adiabatic process requires the maximum amount of energy. The compression energy W depends on the initial pressure p and the final pressure pf, the initial volume V and the adiabatic coefficient y ... 

Most common non-ideal isotherms semi-quantitatively describe lateral interactions through an exponential term in coverage [47]... 

Contaminations are also responsible for the second difference between real and ideal isotherms. At 7rc the isotherm is not perfectly horizontal but slightly tilted, in particular at elevated temperatures. Contaminations are expelled from the liquid condensed phase. Thus, when more and more of the monolayer goes into the liquid condensed phase, contaminations are enriched in the remaining liquid expanded phase. This reduces the two-dimensional... 

The only heat-flow rate discussed so far has been the heat flow through the reactor jacket (ijFlow in Fig- 8.1). For the general case of an isothermal reaction, the main heat-flowrates that have to be considered in a reaction calorimeter are shown in Fig. 8.2 and will be discussed next. In this discussion, ideal isothermal control of the reaction temperature, %, will be assumed [4]. Consequently, no heat accumulation terms of the reaction mixture and the reactor inserts are shown in Fig. 8.2. However, this underlying assumption does not hold for all applications and apparatuses. 

On the basis of the Saam-Cole-Findenegg approach, we are now able to revise the ideal isotherm for capillary condensation. A more realistic isotherm for the physisorption of a vapour in an assemblage of uniform cylindrical mesopores is shown in Figure 7.5. Here, C represents the limit of metastability of the multilayer (of thickness fc) and M the point at which the three phases (multilayer, condensate and gas) all coexist. Along MC the multilayer and gas are in metastable equilibrium. 

Idealized moisture isotherms are presented in this article for substances that sorb moisture in discrete stages (e.g., crystalline materials capable of forming a hydrates) and for substances that do not interact with water in discrete stages. These idealized isotherms form a basis for the discussion of deviations and unexpected effects of moisture sorption that can influence the physical or chemical properties of the solid. 

An ideal isothermal single-phase batch reactor in which a general reaction network takes place nas the following general material balance equation ... 

Semibatch Reactor (SBR) In semibatch operation, a gas of limited solubility or a liquid reactant may be fed in gradually as it is used up. An ideal isothermal single-phase semibatch reactor in which a general reaction network takes place has the following general material balance equation ... 

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