Isothermal operation, definition

Vocabulary of Terms Used in Reactor Design. There are several terms that will be used extensively throughout the remainder of this text that deserve definition or comment. The concepts involved include steady-state and transient operation, heterogeneous and homogeneous reaction systems, adiabatic and isothermal operation, mean residence time, contacting and holding time, and space time and space velocity. Each of these concepts will be discussed in turn. 

The denominator in this efficiency definition quantifies all of the net thermal energy that is consumed in the process, either directly or indirectly. For a thermochemical process, the majority of the high-temperature heat from the reactor is supplied directly to the process as heat. For HTE, the majority of the high-temperature heat is supplied directly to the power cycle and indirectly to the HTE process as electrical work. Therefore, the summation in the denominator of Eq. (1) includes the direct nuclear process heat as well as the thermal equivalent of any electrically driven components such as pumps, compressors, HTE units, etc. The thermal equivalent of any electrical power consumed in the process is the power divided by the thermal efficiency of the power cycle. For an electrolysis process, the summation in the denominator of Eq. (1) includes the thermal equivalent of the primary electrical energy input to the electrolyser and the secondary contributions from smaller components such as pumps and compressors. In additional, any direct thermal inputs are also included. Direct thermal inputs include any net (not recuperated) heat required to heat the process streams up to the electrolyser operating temperature and any direct heating of the electrolyser itself required for isothermal operation. 

For the modeling of a reactor we need solutions of the equations of the balances of mass, energy, and impulse. For isothermal operation the energy balance is not needed. The impulse balance mostly only serves to calculate the pressure drop of a reactor. The definition of a suitable control space for balancing is important. In the simplest case, the variables - such as temperature and concentrations - are constant within the control space (stirred tank reactor). However, in many cases the system variables depend on the location, for example, in the axial direction in a tubular reactor. Then infinitesimal balances (differential equations) have to be solved to obtain integral data. 

In contrast to investigations with solid catalysts, where we can place the catalyst in a small and almost isothermal zone, we have to accept non-isothermal operation in the case of a homogeneous gas phase reaction. It is, therefore, required to determine the kinetic parameters by means of an effective reaction volume. VR efr is defined as the volume needed to reach the same conversion at a constant reference temperature T ef as under the non-isothermal conditions with an axial temperature Tx. Tref can be arbitrarily chosen, for example, the temperature at a fixed position in the middle of the tube. This definition leads to ... 

Where activated carbon is a potential treatment technology, the first evaluation step is generally to run simple isotherms to determine feasibility. Isotherms are based on batch treatment where impurities reach equilibrium on available carbon surface. While such tests provide an indication of the maximum amount of impurity a GAC can adsorb, it cannot give definite scale up data for a GAC operation due to several factors ... 

One should realize that adsorption isotherms are purely descriptions of macroscopic data and do not definitively prove a reaction mechanism. Mechanisms must be gleaned from molecular investigations (e.g., the use of spectroscopic techniques). Thus the conformity of experimental adsorption data to a particular isotherm does not indicate that this is a unique description of the experimental data, and that only adsorption is in operation. 

The primary definition is the thermod5mamlc one (sec. 1.2.3), according to which the tension is the force per unit length needed to expand the area by an infinitesimal amount, isothermally and reversibly. It is typical for thermodynamic definitions that they are based on processes that in principle can be Ccirried out, i.e. they involve operational quantities. When the expansion cannot be carried out isothermally and reversibly it is impossible to define the interfacial tension operationally. This is for instance the case with solids (sec. 1.2.24) but also with monolayers in which expansion involves energy dissipation as a result of the irreversible breaking of bonds. 

These expressions define the Isothermal reversible work done on the system after the enlargement the resulting Helmholtz or Gibbs energy resides in the interface. The definition y = (3U/9A)gy, is also operational, but virtually impracticable how can one enlarge an interface iso-entropically ... 

The terms and Q2 are, by definition, the quantity of heat transferred into the system isothermally at Tj temperature and heat transferred out of the system at T2 temperature, respectively, both operations being performed in reversible manner. 

That is, the ratio of the thermod5mamic temperatures of two heat reservoirs is equal, by definition, to the ratio of the absolute quantities of heat transferred in the isothermal steps of a Carnot cycle operating between these two temperatures. In principle, a measurement of qdqb during a Carnot cycle, combined with a defined value of the thermodynamic temperature of one of the heat reservoirs, can establish the thermodynamic temperature of the other heat reservoir. This defined value is provided by the triple point of H2O its thermod5mamic temperature is defined as exactly 273.16 kelvins (page 40). 

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