Expander efficiency

The turboexpander in combination with a compressor and a heat exchanger functions as a heat pump and is analyzed as follows In Fig. 29-44 consider the compressor and aftercooler as an isothermal compressor operating at To with an efficiency and assume the working fluid to be a perfect gas. Further, consider the removal of a quantity of heat by the tumoexpander at an average low temperature Ti-This requires that it dehver shaft work equal to Q. Now, make the reasonable assumption that one-tenth of the temperature drop in the expander is used for the temperature difference in the heat exchanger. If the expander efficiency is and this efficiency is mul-... 

The family of short curves in Fig. 29-45 shows the power efficiency of conventional refrigeration systems. The curves for the latter are taken from the Engineering Data Book, Gas Processors Suppliers Association, Tulsa, Oklahoma. The data refer to the evaporator temperature as the point at which refrigeration is removed. If the refrigeration is used to cool a stream over a temperature interval, the efficiency is obviously somewhat less. The short curves in Fig. 29-45 are for several refrigeration-temperature intervals. A comparison of these curves with the expander curve shows that the refrigeration power requirement by expansion compares favorably with mechanical refrigeration below 360° R (—100° F). The expander efficiency is favored by lower temperature at which heat is to be removed. 

For many years, turboexpanders have been used in cryogenic processing plants to provide low-temperature refrigeration. Power recovery has been of secondary importance. Expander efficiency determines the amount of refrigeration produced and, in gas process plants, the amount of product usually depends on the available refrigeration. Accordingly, there is a large premium on efficiency and, of course, on reliability. 

The control of leakage loss across die blades in a reaction expander is extremely important. Maintaining adequate clearance implies preventing mechanical rubs while at die same time minimizing die loss effect on expander efficiency. 

Figure 4-113. Effect of tip clearance (as a fraction of passage height) on expander efficiency.

The previous discussion of the velocity ratio parameter looked at the effect the available energy has on expander efficiency. The examples listed in Table 4-11 furdier illustrate diis effect. 

Fig ure 5-1. Typical expander efficiencies versus mass flow. 

The performance of a SOFC system with a Brayton-Rankine bottoming cycle for heat and fuel recovery has been calculated. Gas turbine compressor and expander efficiencies of 83% and 89% and a steam turbine efficiency of 90% have been assumed. 

First, it is instructive to examine the performance of a recuperated system that has only one compressor (i.e., remove the IC and C2 from Figure 8.2) and compare this to a simple cycle GT (i.e., also remove the recuperator from the diagram). Consider an isentropic compressor efficiency of 85%, isentropic turbine expander efficiency of 90%, recuperator effectiveness of 88% and no pressure losses. A fixed turbine inlet temperature of 1200 K will be assumed for various pressure ratios. This value is based on an assumed 1000 K SOFC inlet temperature, and a 200 K temperature rise from the SOFC inlet to the turbine inlet. The 200 K temperature increase from the cathode inlet to the turbine inlet is reasonable to assume given a cathode temperature difference across the cell of 150 K, and another 50 K temperature increase from anode exhaust combustion. Thus, 1200 K will be used as a base case for the turbine inlet temperature, and for sensitivity, values of 1100 and 1300 K will also be analyzed. 

Calculate actual enthalpy change using the expander efficiency. 

J5 An expander operates adiabatically with nitrogen entering at T, and P] with a molar flow rate ri. The exhaust pressure is P2, and the expander efficiency is q. Estimate the power output of the expander and the temperature of the exhaust stream for one of the following sets of operating conditions. 

Example 4.23 Analysis of the Claude process in liquefying natural gas We wish to partially liquefy natural gas in a Claude process shown in Figure 4.28. It is assumed that the natural gas is pure methane, which is compressed to 80 bar and precooled to 300 K. In the expander and throttle the methane is expanded to 1.325 bar. The methane after the first heat exchange at state 5 is at 80 bar and 250 K. Thirty percent of the first heat exchangers output is sent to the expander. Only 10% of the first heat exchange is liquefied. The expander efficiency is 0.8. Determine the work loss in the liquefaction section excluding compression and precooling. 

A significant improvement to the process outlined above was the use of an expansion engine. Typically, in ASUs turbo expanders are used. An ideal turbo expander is isentropic and reversible. Illustrated in Figure 3.9, air at -150°F (172 K) and 90 psia (620 kPa) is expanded to 20 psia (138 kPa). In an isentropic expansion A-B, the expansion follows the isentrope with a net change in enthalpy. In reality the expansion will not be reversible and will follow a curve similar to A-C. The actual enthalpy change divided by the isentropic enthalpy change is a measure of the expander efficiency. 

Fig, 4. Refrigeration effect vs. pressure ratio as a function of expander efficiency. 

Further examination of the expression for the refrigeration effect B indicates that for a fixed load return temperature, the refrigeration effect depends largely upon the heat exchanger AT and the expander efficiency ex. The relationship between refrigeration effect and compressor pressure ratio is shown in Fig. 3 for various AT s and for an expander efficiency ex = 0.65, and again in Fig, 4 for various expander efficiencies and for a cold end AT = 4°R. 

Influence of grid alloy composition on expander efficiency [22]... 

This chapter begins with a problem to find the expander outlet temperature when given the expander efficiency. The user will operate an expander operation in HYSYS to model the expansion process. At the end of this chapter, the user will determine the expander outlet temperature when given expansion efficiency or vice versa. 

The isentropic method is also applied to an expander. Eq. (15.7) is used for calculating the isentropic exit temperature, but taking into account possible condensation of the gas. Like the exit pressure, the exit temperature will be less than the inlet value. Then, the exit isentropic enthalpy is computed, from which Eq. (15.8) is used to calculate the power recovered, which will be a negative value. The effect of the expander efficiency is just the opposite of the compressor efficiency, as indicated by a revision of Eq. (15.9) for applicability to expanders ... 

The expander efficiency was calculated with aid of a polytropic expansion coefficient of 1.67, that is, an isotropic efficiency of 70%. A reversible process [22] is totally misleading for determining the potential of such a hybrid system. In addition, the mechanical and electrical transmission losses were evaluated with a transmission efficiency of 95%. 

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