Polytropic operation

In polytropic operation, the choice of the initial temperature and the temperature at which the cooling system is switched on are important for proper control of the reaction. If the cooling system is switched on too late, the temperature may overshoot the allowed maximum temperature. On the other hand, if it is switched on too early, the reaction will be too slow or may not mn to completion in a reasonable time. 

Compressors are rated in feet of compression head developed. This is the energy conveyed to a gas stream by a compressor. It is observed by the increase in gas pressure as the gas passes through the compressor. Centrifugal compressors more nearly follow polytropic operation and are widely used to handle large volumes of gas at pressure ranges of 0.5 to several hundred psi. 

The technical design is largely determined by the extent of heat generated or consumed by the reaction and by the type of temperature control used. We have to distinguish between the rare case of isothermal operation, polytropic operated cooled or heated reactors, and adiabatic operation (ideal insulated reactor, no heat exchange with the surrounding). For isothermal and adiabatic operation, no radial profiles of temperature will develop inside the reactor. 

Since most compressors operate along a polytropic path approaching the adiabatic, compressor calculations are generally based on the adiabatic cui ve. 

Polytropic. Sometimes the compression process has certain associated irreversibilities. The actual operation is therefore approaching adiabatic, but not quite. This "approximately adiabatic" operation is called polytropic. 

The usual centrifugal compressor is uncooled internally, and hence, operates with polytropic characteristics having n greater than k however, if the unit is internally cooled, then n will be greater than 1.0 but may be less than k. The inefficiencies caused by internal losses (friction, etc.) keep the operation from being truly adiabatic however, some compressions are close to this condition and may be used for approximations. 

Figures 12-65 and 12-65A give the relationship between polytropic and adiabatic efficiencies. The adiabatic efficiency can be calculated from operating data, and the polytropic efficiency can be read from the curves. For other cases, ep may be calculated from the preceding relation and the adiabatic efficiency may be determined from the curves. Figure 12-66 illustrates the relationships that may exist while evaluating a particular compressor design.

For a compression operation handling some condensable vapors, the temperature rise will be approximately 13°F. These values are considerably lower than for conventional polytropic compression. They are almost isothermal and demonstrate the contact cooling that takes place during compression. 

The centrifugal compressor, unless it is dirty or mechanically defective, has to operate on its curve. As the compressor discharge pressure increases, then Hp, the feet of polytropic head required, must also increase. Also, as can be seen from the compressor curve, the volume of gas compressed (ACFM) must decrease. When the volume of gas drops below a critical flow, the compressor will be backed up to its surge point. 

In order to ensure smooth control of the reaction, it must be started at a lower temperature, perhaps under adiabatic conditions, followed by a period with maximal cooling when the desired temperature level is reached. Therefore, batch reactions are often performed in the so-called polytropic mode of operation. 

Real compression processes operate between adiabatic and isothermal compression. Actual compression processes are polytropic processes. This is because the gas being compressed is not at constant entropy as in the adiabatic process, or at constant temperature as in the isothermal processes. Generally, compressors have performance characteristics that are analogous to those of pumps. Their performance curves relate flow capacity to head. The head developed by a fluid between states 1 and 2 can be derived from the general thermodynamic equation. 

The operative conditions suitable for air feeding section in H2FCS suggest that the air stream can be considered as ideal gas mixture. The relationship of polytropic compression for an ideal gas is ... 

As a consequence of equation (17.74) and the characteristic gas equation (3.2), the actual temperature ratio across a compressor section operating at a polytropic efficiency, rip, will be given by... 

The manufacturer will normally supply a set of curves for each compressor section (Figure 17.7), at the design speed with further curves at +/ — 10% or +/ — 20% speed. The surge line will be marked, indicating the region of unstable operation that must be avoided. The manufacturer should also specify the polytropic efficiency. 

Because of the affinity laws, however, the modeller need work with only the characteristic giving polytropic head vs. volume flow at the design point, which may be stored in the form of a curve of Qo vs. Hpo. Then for any off-design point, he may calculate the current polytropic head, H p, from the ratio of the inlet and outlet pressures and the inlet temperature using equation (17.85). Given the current operating speed, N, he may calculate the polytropic head at the design... 

The polytropic mode makes use of a thermal agent. The temperature profile inside the reactor can deviate more or less from the (ideal) constant temperature, depending on the rate of the heat transfer to the cooling agent. If the heat transfer is too low, a hot spot may occur, which in general is dangerous for operation. 

Reactions can be classified as reversible, irreversible, parallel, and consecutive. With regard to operating conditions they are isothermal at constant volume, isothermal at constant pressure, nonisothermal, adiabatic, and polytropic. Reactions are also classified according to the phases involved ... 

All calculations were made for a reactor operating at 200 bar and 150 °C under the assumption of isothermal conditions, since the adiabatic temperature difference under the given concentration conditions was only a few degrees and the reactor was operated in a polytropic mode. The target quantity was the conversion, which was calculated as a function of various reactor parameters. Some results of the simulation are described in the following. 

Here is supposed that gas in the bubble follows polytropic process with exponent X This equation was solved in linear approximation by operational method with the aim to analyze small amplitude, natural oscillations of the constant mass bubble in relaxing liquid. It was taken R = Rq + AR, AR/Ro 1, AR exp(ht) with h being the complex natural frequency. Logarithmic decrement. A, and dimensionless frequency, [t, of the oscillations are defined according to formulas... 

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