Isenthalps

To reduce the work of compression in this cycle a two-stage or dualpressure process may be usedwhereby the pressure is reduced by two successive isenthalpic expansions. Since the isothermal work of compression is approximately proportional to the logarithm of the pressure ratio, and the Joule-Tnomson cooling is roughly proportional to... 

In a work-producing expansion, the temperature of the process fluid is always reduced hence, coohng does not depend on being below the inversion temperature prior to expansion. Additionally, the work-producing expansion results in a larger amount of coohng than in an isenthalpic expansion over the same pressure difference. 

It is not uncommon to utilize both the isentropic and isenthalpic expansions in a cycle. This is done to avoid the technical difficumes associated with the formation of liquid in the expander. The Claude or expansion engine cycle is an example of a combination of these meth-... 

Jotile-Thomson Valves The principal function of a J-T valve is to obtain isenthalpic coohng of the gas flowing through the valve. These valves generally are needle-type valves modified for cryogenic operation. They are an important component in most refrigeration systems, particularly in the last stage of the liquefac tion process. Joule-Thomson valves also offer an attractive alternative to turboexpanders for small-scale gas-recovery applications. 

Since pipe flow is more nearly isenthalpic, the flash fraction x is found from an enthalpy balance between the stagnation point and a point z downstream. Accounting for changes in potential energy, kinetic energy, and heat added or removed from the pipe Q, x is given by ... 

The process of reducing gas pressure with an expander is an isen-tropic process, which is able to recover both the energy from the gas pressure and also the gas temperature. A conventional gas regulator station is an isenthalpic process, which only reduces pressure. As a result, an expander system produces much lower gas temperatures downstream compared to a pressure regulator operating under the same pressure conditions. 

Isothermal—constant temperature Isometric—constant volume Isobaric—constant pressure Isentropic—constant entropy Isenthalpic—constant enthalpy... 

A Mollier Diagram is useful for the expansion of a specific gas/vapor or multicomponent vapor fluid. See Figure 12-91 for comparison of (1) constant enthalpy (Joule-Thompson effect), isenthalpic, and (2) isentropic (constant entropy), which provides the colder temperature. Note that the expander indicated on the figure is somewhere between isenthalpic and isentropic or polytropic. See Figure 12-92. ... 

Thus, the Joule-Thomson expansion is an isenthalpic process. 

Figure 3.6 shows how pressure and temperature are related for a series of isenthalpic (Joule-Thomson) expansions. For example, if we start at the... 

Since the Joule-Thomson process is isenthalpic, the slope of each line can be represented as (dT/dp)lf. This quantity is referred to as the Joule Thomson coefficient, pj j.. Thus1... 

Figure 5.15(b) shows that the final expansion stage occurs in a turbine, rather than in an isenthalpic Joule-Thomson orifice. It has a higher thermodynamic efficiency than that of the Joule-Thomson but is more complex and expensive. 

Isenthalpic Nature. As the Joule-Thomson experiment is carried out adiabati-cally, we can write... 

However, it does not follow from this fact alone that AH also is zero, because the process involves a change in pressure. Nevertheless, it can be shown that the process is an isenthalpic one that is, AH is zero. 

Thus, we have proved that the Joule-Thomson experiment is isenthalpic as well as adiabatic. 

Joule-Thomson Coefficient. Knowing that a process is isenthalpic, we can formulate the Joule-Thomson effect quantitatively. 

Figure 5.9 The Joule-Thompson cycle (Linde cycle). The gas is first compressed and then cooled in a heat exchanger, before it passes through a throttle valve where it undergoes an isenthalpic Joule-Thomson expansion, producing some liquid. The cooled gas is separated from the liquid and returned to the compressor via the heat exchanger.

The liquid flow from the stage immediately above is treated in the same way, except that the calculation is slightly different if the stage above is a condenser. At statement 40, the entire feed of components to the stage is added up in flfees and the data necessary to calculate an isenthalpic flash on the stage is complete. 

In either procedure, the enthalpy of the streams resulting from the first flash is calculated as qout. At statement 80, the enthalpy of the streams resulting from the second flash is calculated as toth. In addition the enthalpy of the streams of the first flash at the temperature of the second flash is calculated as sensh. The temperature of the first flash is called T, the temperature of the second flash is called ti. In the same way the vapor phases resulting from the two flashes are flv and flvi. In the ordinary case flvi would not equal flv, nor would ti equal t. These differences are then used to predict temperature and flow amounts at the solution to the isenthalpic flash, totcp is the amount of energy which must be added to the system to raise the temperature by 1°F. and is calculated by (toth — qout) /(t1 — t). Similarly the amount of energy added to produce one more mole of vapor (and hence one less mole of liquid) is TOTMCP = (toth — qout) /(flvi — flv). SENSCP is the amount of sensible heat which would have to be added to raise the temperature 1°F. if no vaporization or condensation occurred in changing from t to ti. 

The predicted change in temperature, delt, to be added to t is then (qin — qout) /totcp, and the predicted vapor change, delvs, to be added to flv, is (qin — qout) /totmcp. These corrections, since they are linear, only solve the isenthalpic flash approximately. As convergence is approached, however, the amount of correction to t and flv becomes smaller and smaller, and linear corrections suffice. The isenthalpic flash could of course be solved as exactly as one desired, but the authors have found the partial solution and linear extrapolation used here to be quite satisfactory for the purposes of this program. 

This can be evaluated using the Omega method, if applicable (see Annex 8) or other HEM model (see Annex 4). The Omega method can be used to obtain G and the exit choke pressure, PE for the upstream pipe. An isenthalpic flash calculation can then be performed from the stagnation pressure at the start of the pipe to the choke pressure, PE, in order to evaluate the mass fraction of vapour, x, at the pipe exit. If the flow is not choked, then the term (PE - Pa) becomes zero. 

This relationship makes use of properties at a pressure, PtI which is lower than that in the upstream vessel. It is suggested151 that Pt is taken to be 80 or 90% of P0 (90% if there is little friction) and that an isenthalpic flash routine (within, a computerised package for evaluating multi-component physical properties) is used to find the two-phase specific volume v, at Pt. Woodward161 gives examples of the use of this approach. 

No enthalpy change occurs. An isenthalpic. sdepressurisation is irreversible. It is common to. assume that, the pressure drop across the pressure discontinuity at a choke is isenthalpic. 

In the period 1852-62, J. P. Joule and W. Thomson (later Lord Kelvin) perfected a clever method for measuring the isenthalpic property (dT/dP)Ih which has come to be called the Joule-Thomson coefficient, symbolized /xJT ... 

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