Available energy flows

In this section we focus our attention on two particular examples, the photodissociation of H2O2 and the photodissociation of H2O via the BlA state. In the first case, the extent of rotational excitation is moderate, i.e., only a few percent of the total available energy flow into rotation. The dissociation of H20(S), on the other hand, represents an example of extremely strong rotational excitation. 

The problem must be set up such that the objective function and the Lagrange constraint equations are functions of the state and decision variables (Equations 4 and 5). A major deviation from the procedure outlined by Tribus and El-Sayed (5) is in the selection of the Lagrange constraint equations and state variables. The added complexity of having steam as the working fluid (compared to an ideal gas in the gas turbine optimization performed by Tribus and El-Sayed) makes it impractical to select state variables that correspond to available-energy flows. Consequently, this requirement was relaxed entirely. This gives the designer the opportunity to use any variable as a state variable,... 

In the application of this method to a Rankine cycle cogeneration system, generalized costing equations for the major components have been developed. Also, the utility of the method was extended by relaxing the rule that each state variable (and hence each Lagrange constraint) must correspond to an available-energy flow. The applicability was further extended by the introduction of numerical techniques necessary for the purpose of evaluating partial derivatives of steam table data. 

Figure 2. Simple distillation system for the separation of a 45%-55% benzene-toluene feed into 92% benzene distillate and a 95% toluene bottoms product. Available-energy flows and destructions are given in 10° Btu/hr.

If Q represents the energy supplied at a temperature Tq to a steady-state or cyclic "heat engine" (Figure 2), it follows rrom an available energy balance that the net rate of available energy flowing from the cycle in the form of shaft work can at most be equal to the thermal available energy supplied to the cycle i.e.,... 

Evaluation of Available Energy Transport Expressions. Available energy transport relations are seen to be products of thermostatic properties with commodity currents. Given the commodity currents, the available energy transports can then be evaluated by determining the thermostatic properties, using traditional thermochemical property evaluation techniques. References (6) and (7) present convenient relationships for practical evaluation of available energy flows for several important cases. 

How the tools are organized into a methodology for process evaluation via available energy will be illustrated in this paper with the help of a very simplified coal-fired boiler, often found in textbooks on thermodynamics. It will be used to demonstrate the calculation of available energy flows, losses and consumptions. 

A detailed available energy analysis was carried out in reference (13) on a modem 300-MW coal-burning power plant. The available energy flows calculated in that analysis are presented in Figure 7. Corresponding energy flows sure included in psuren-theses for comparison. 

Figure 6. Available energy flow diagram for coal-fired boiler problem...

If the practitioner is willing to forego the information given by the absolute values of available energy flows, but would be satisfied with the evaluation of available energy consumptions only, then... 

On this basis, a cost or value of the available energy flows at the various junctures within the system can be determined (iteratively). Then if, for example, a particular component needs to deliver some specified output, knowing the unit cost of the availability supplied to the component, the component and its operating conditions can be selected (or designed) so that the total costs—of availability supplied thereto and of capital costs thereof, (etc.)—can be minimized. Typical parameters (decision variables) of a component which can be adjusted in order to attain the optimum system are efficiency, operating pressure and temperature, speed, and so on and so forth. 

Figure 1. Skeleton schematic of 1960 system available-energy flows (megawatts). Also shown are the unit costs of the steam and electricity outputs based on the equality method and sunk capital costs.

Af a(j,j is the additional boiler fuel required when the heater is ou of service, cB is the unit cost of steam in the i - 1 bleed line, and cp is the unit cost of boiler fuel (coal). These available-energy flows are calculated in the usual manner and are given in Table II and reference (6). The unit costs are obtained with exactly the same techniques discussed by Reistad and Gaggioli (2)—by applying money balances to each component (boiler, high-pressure turbine,. . . ) of the system of interest to get the dollar flows and then by the subsequent division of the appropriate available-energy flows to obtain the unit costs. 

In this example, a subtle advantage of second law analysis has come to light. Any available energy flow or consumption can properly be expressed directly in kW (hp), which often tends to improve one s "feel" for what is actually happening. In contrast, it is usually inappropriate to express certain kinds of energy flows or losses in dimensional units normally reserved for work or electricity.)... 

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