Thermodynamics meets economics.

Thermodynamics Meets Economics

Cost optimization for complex energy-conversion systems (e.g., refineries or integrated gasification-combined-cycle power plants) or energy-intensive chemical plants is usually expensive and requires knowledge of engineering, science, and business. The

goal of optimization is to find the values of the system variables (the temperatures, pressures, and chemical composition of flow streams, equipment size, materials, etc.) that minimize the cost of the final products. This usually involves a trade-off between capital and operating (including fuel) costs for the entire system. Typical problems in the design and operation of energy systems have many solutions--sometimes an infinite number. Selecting the best solution among the entire set requires engineering judgments, intuition, and critical analysis.

In many cases a rigorous cost optimization for a complex energy system is not possible because some of the cost functions that are needed to express the capital cost of a component as a function of thermodynamic variables (temperatures, pressures, etc.) are either unavailable or inaccurate. But even in cases in which all the information is available and acceptably accurate, it is expensive and time-consuming to formulate and solve an optimization problem with an extremely large number of equations, constraints, and highly interdependent variables.

Computers and associated software now enable system designers and plant engineers to investigate alternatives with greater accuracy and detail than ever before. When there are many cases to consider, a computer strategy can improve the cost-effectiveness of the design and/or operation of an energy system.

Traditionally, design optimization includes the following steps. A detailed system configuration is developed first; material and energy balances are conducted for this configuration. Then product costs are estimated through an economic analysis. The third step includes development of a modified/new configuration that accounts for the corresponding material and energy balances. Subsequently the product costs for the new configuration are calculated. The last two steps are repeated several times.

Development of new process configurations is based, among other factors, on the experience and intuition of design engineers. Several decisions must be made with respect to thermodynamic variables. The final selection criterion, however, is economic. It is apparent that judiciously combining the thermodynamic and economic analyses is advantageous to the optimization process.

Energy-based variables are insufficient for this combination; we need to incorporate the second law of thermodynamics. The term thermo-economic analysis indicates that this methodology combines a second-law (exergy) analysis with an economic one; both are conducted at the system component level.

Why an Exergy Analysis?

A first-law (energy) analysis generally fails to identify energy waste or the effective use of fuels and resources. For instance, the first law does not recognize any waste in an adiabatic throttling process--one of the worst processes from the thermodynamic viewpoint.

The second law of thermodynamics shows that, in some energy carriers (e.g., enthalpy of a flow stream), a part of the energy is useless. Exergy is the part of energy that can be converted into any other form of energy. An exergy analysis, based on both the first and second laws of thermodynamics, calculates the useful energy associated with a thermodynamic system or with each flow stream in a process. It also identifies and evaluates the inefficiencies of an exergy system. This analysis shows that useful energy is destroyed during any step of an energy-conversion process, while the total energy remains constant. An exergy analysis is the only way to unmask the high irreversibilities in processes such as combustion, heat transfer, throttling, or mixing. The causes of irreversibilities or exergy destruction are located and quantified and the effects of inefficiencies in one component on the performance of other components is clearly illustrated. Thus, the interdependence of component inefficiencies and the effect of performance deviations from the design conditions can be easily demonstrated. For example, any change in the exergy destruction in the mixing device shown in Figure 1 will cause changes in the exergy destruction in the pump and throttling valve, assuming constant conditions for stream 5.

Exergy not only is an objective measure of the thermodynamic value of an energy carrier but also is related closely to the cost of the energy carrier, because users pay only for the useful part of energy. Consider two energy carriers that consist of the same material (e.g., water) and have the same pressure and the same total energy; one operates at a high temperature (superheated steam), and the other at a low temperature (saturated liquid water). The second carrier must have a larger mass. A thermal engineer would probably be willing to pay more for the first carrier than for the second one because the cost of the heat exchanger, where the thermal energy would be used, would be lower if the high-temperature energy carrier were used than if the low-temperature energy carrier provided the needed thermal energy. This example indicates that exergy, rather than mass or energy, should serve as a basis for assigning costs to energy carriers.

For the throttling valve shown in Figure 1, the first law of thermodynamics detects no losses in the process from state 3 to state 4. Thus, if we base the cost calculation on the energy content, the cost per unit of energy will be the same before and after the throttling valve, if the capital cost of the valve is ignored. The second law of thermodynamics, however, identifies exergy destruction during the throttling process and, with the aid of a cost balance, concludes that the cost per unit of exergy must be higher after the throttling process (state 4) than before it (state 3). An increase in the exergy destruction in the throttling valve (i.e., an increase in the pressure drop between 3 and 4) leads to an increase in the cost per unit of exergy between valve inlet and outlet and consequently between fuels and final products for the entire system (e.g., cost per unit of exergy between stream 5 and stream 3 in Figure 1). Thus, the second law sheds light on the cost formation process while the first law could lead to erroneous conclusions.

The operation of a pulverized-coal steam power plant offers a third example. If we assume a plant efficiency of 33.33 percent and exclude the contribution of the capital costs, then a unit of electricity will cost three times more than a unit of coal energy. The first law would indicate that the condenser is mainly responsible for this increase while the second law would correctly identify the boiler. The first law cannot reveal that the energy rejected to the condenser has an extremely low exergy content or that the exergy of the superheated steam entering the high-pressure turbine is approximately half of the coal exergy. That is, about 50 percent of the coal's useful energy is destroyed in the boiler alone. The values of the first-law and second-law efficiencies of the total plant would be close to equal because the exergy content for both electricity and coal is either identical or close to the corresponding energy content. The first law, however, gives a distorted picture of the losses and cost sources. Similar examples can be found in any energy system.

From the thermodynamic viewpoint, the unit exergy destruction in any component of a given plant has the same value. This is not true from the cost viewpoint. Exergy destruction of 1 Btu in the low-pressure steam turbine affects the cost of electricity more than exergy destruction of 1 Btu in the boiler of a steam power plant. Thus, the cost of unit exergy destruction in the boiler is lower than in the LP steam turbine. Similarly, as shown in Figure 2, a given amount of exergy destruction in group 7 costs the plant operating company more than the same amount of exergy destruction in group 2.

Thermoeconomic Analysis

In a thermoeconomic analysis, we calculate the exergy flow rate associated with each process stream, the exergy destruction in each system component, and the exergy (second-law) efficiency of each component. In addition to mass, energy, and exergy balances, cost balances are formulated for each system component by assigning cost to the exergy (and not to the energy) of each stream entering or exiting the component. The cost balance for the mixing device in Figure 1, for instance, shows that the cost per exergy unit of stream 5 depends on the cost per exergy unit of streams 2 and 4, the inefficiencies in the mixing device, and, if the system design is analyzed, the contribution of capital costs associated with the device. Similarly, the cost per exergy unit of stream 2 in the same figure depends on the cost of the electricity supplied to the pump, the cost per exergy unit of stream 1, the exergy destruction in the pump, and the pump capital cost contribution.

With the aid of cost balances and some auxiliary assumptions, the cost per unit of exergy for each process stream is calculated. Generally, this cost is known only for the raw fuels entering the total system (e.g., stream 1 in Figure 2), from their prices, and for the system product, if there is only one product. With a thermoeconomic analysis, the costs at intermediate junctures within the total system (streams 11-18 in Figure 2) and the costs of the products (streams 6 and 7) are calculated. Depending on the analysis objectives, market prices are assigned to the by-products (streams 8 and 9), or their costs are calculated in the thermoeconomic analysis.

After the cost of an exergy unit for each stream is calculated, simple algebraic relationships are used to figure the cost per exergy unit for the entering and exiting exergy flows of each system component and the cost of exergy destruction in each component.

Capital expenses, operating and maintenance costs, and fuel costs cause the increase in the cost of the exergy unit between raw fuels (stream 1 in Figure 2) and final products (streams 6 and 7). The capital expenses and operating and maintenance costs are considered to be capital costs. Assuming well-designed total system configurations, the contribution of the capital costs to the final product costs decreases with decreasing thermodynamic efficiency (increasing exergy destruction), whereas the fuel cost increases with decreasing efficiency (see Figure 3).

Conventional optimization techniques seek the optimum trade-off between capital costs and fuel costs for the entire system. Most thermoeconomic methods simplify the search for an optimum by making these trade-offs at the system component level. If the relationship between the capital costs and the thermodynamic efficiency of a component is known, then the thermoeconomic analysis calculates the optimal thermodynamic efficiency from the cost viewpoint.

If the capital costs are not known as a function of the thermodynamic efficiency, then for a given design configuration the capital cost is compared with the cost of exergy destruction for each component. This reveals whether it would be more cost-effective to reduce the capital cost at the expense of lower efficiency (higher cost of exergy destruction) or to increase both costs and efficiency.

Benefits of Thermoeconomics

The effectiveness of fighting costs in the design or operation of an energy system increases when we understand the real causes and sources of costs. A thermoeconomic analysis identifies these sources. This information, complemented by the engineer's intuition and judgment, helps reduce the product costs in energy systems. Decisions about the design, operation, and repair or replacement of equipment are facilitated. In addition, thermoeconomics provides an objective cost allocation to more than one product of the same process.

For instance, a thermoeconomic analysis of a cogeneration plant (which produces electricity and steam for heat) will provide the cost of steam and the cost of electricity separately. The cost ratio of steam to electricity calculated by the analysis does not have to be reflected in their selling prices, but the company that operates the plant should know the cost of each form of energy.

The analysis also shows how much raw fuel is required to produce each stream in the system. Finally, thermoeconomics helps management decide how to allocate research and development funds to improve plant components that contribute most significantly to the product costs.

It is true that many conclusions obtained by a thermoeconomic analysis could also be obtained through a number of conventional first-law analyses combined with economic analyses. The advantage of thermoeconomics is that it replaces an expensive and half-blind search for cost reduction with an objective, well-informed, and systematic search in which all of the components are properly identified and evaluated. The savings in both engineering and computer time are significant. Application of thermoeconomic analysis to new energy system concepts and complex installations (particularly those with several chemical reactions) should result in significant savings.