Value of Steam for Producing Useful Shaft Work

A comprehensive accounting system for the value of steam energy must evaluate the opportunities for generating prime power as well as for providing for heat transfer. A look at a simple pressure-reducing valve (PRV) demonstrates the inadequacy of any type of simple cost per Btu ratio.

The expansion of steam by throttling it through a valve is referred to as adiabatic expansion. Since no work is performed and there is no change in kinetic or potential energy, the entering enthalpy equals the leaving enthalpy. If, for example, 1,000 lbm (454 kg) of steam at 475 psig and 700°F (33.8 bar and 371°C), which has an enthalpy of 1,357 Btu/lbm (3,156 kJ/kg), is expanded to atmospheric pressure through a PRV, the resulting steam at 0 psig and 646°F (101 kPa and 341°C) would also have an enthalpy of 1,357 Btu/lbm (3,156 kJ/kg). Using enthalpy as the sole measurement of value, this steam, after undergoing a 100% efficient expansion, would have the same economic value as in its prior state.

However, there is still an important loss. The theoretical maximum amount of work that could be extracted from the steam in its original state is approximately 204 hp (152 kW). After adiabatic expansion through the PRV, this is reduced to about 126 hp (94 kW). This results in a 38% loss of ability to do theoretical work.

Both levels of work production are, however, unrealistic. In fact, it is practically impossible for steam to do work starting at 0 psig (101 kPa). From a theoretical maximum shaft work-producing level of availability, the adiabatic expansion is only 62% efficient. Actually, it would likely be 0% efficient, as no shaft work would be done after the expansion. In many respects, the PRV, efficient as it seems, is a major source of loss in the economic value of steam.

In addition to the loss of ability to do work resulting from the combustion of fuel in a boiler, the approach temperature between the flame and the steam temperature is also a loss of work potential. Ironically, viewed from the standpoint of enthalpy, most of the potential work loss from steam turbine power generation is in the condenser because most of the heat is lost at that stage. However, at that point, the majority of the work-producing potential of the steam has already been used.

This points out the critical difference between heat loss and loss of work potential. The steam turbine allows for the production of prime power with a relatively minor reduction in enthalpy. To determine the economic value of steam, its full potential for producing useful shaft work and providing thermal energy transfer must be identified with respect to all aspects of the "task at hand" and compared with all of the alternatives for providing the same values.

The process of determining value includes the efficiency of alternative equipment and the cost of energy to power that alternative equipment during any given hour. Given the tremendous real-world differences in energy costs, the relative value of the shaft work of steam may be as much as 10 or even 50 times greater during one hour than another.

Sometimes it will be most economical to produce every last unit of power possible from high-pressure steam in a steam turbine. Sometimes it will be most economical to use the same pressure steam in a topping cycle. And, sometimes, when compared with off-peak electric rates, steam will be most economically used solely for the purpose of thermal energy transfer.

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