Exergy analysis aids boiler performance appraisal

Exergy analysis aids boiler performance appraisal

Even a rigorous energy balance can be enhanced by a detailed exergy account

By Manfred Fehr,

Chemical Engineering Department,

Federal University at Uberlandia, Brazil

The progressive refinement of industrial energy balances has led to the practice of exergy accounting. The division of energy into exergy and anergy is an accounting tool that assigns a value of quality to an available quantity of energy. This method`s use is now widespread and various books have covered the topic in some detail.

It can be argued that even a rigorous energy balance can benefit from an exergy analysis and yield a surprising quantity of information about a given heat-generating installation while pinpointing faults and other needed improvements.

Although the specific application outlined here is a utility boiler in the sugar industry, the exergy accounting method is quite universal. However, performing an exergy account analysis cannot be accomplished without a previous energy account, because both are compared because of the quality and amount of information each provides.

The boiler studied in this case is an integrated sugar cane processing unit and slaughter house. Sugar cane is transformed into anhydrous ethanol and bagasse, with stillage as a by-product. Part of the bagasse is burned in the utility boiler to make 2.2 MPa, 573 K superheated steam. The rest is hydrolyzed and used as cattle food. The boiler is the heart of the facility`s utility system. It supplies steam to a turbogenerator, to three turbine-driven cane dressing units and to a turbine-driven ammonia compressor. Exhaust steam from the turbines is condensed at 0.25 MPa in the heat exchanger`s evaporation and distillation units.

Data for bagasse is given in Table 1. The bagasse is blown horizontally into the combustion chamber by part of the preheated air. The rest of the air enters through the bottom of the chamber and flows upward to keep the fuel suspended. The ash falls through the grate and is periodically removed.

The boiler consists of the radiant transfer chamber, a convention section where water is preheated from 298 K to 368 K and the air preheater. Stack gases are vented at 490 K. The boiler operates at 30 cycles of concentration. Water feed rate is 27.854 t/h, and the yield is 1.68 tons of steam/tons of fuel. The boiler is rated at 22 MW. Water and steam operating data are given in Table 2.

This balance accompanies the combustion side temperature profile by determining the sensible heat flows as accurately as possible. The heat content of the flue gas stream, which is the sum of flow-rate products and heat capacity for all components, is evaluated at every point available.

The sensible heat given off in every part of the installation is compared to water side measurements in order to establish the losses. The sensible heat calculations are summarized in Table 3 and the energy balance is illustrated in Figure 1. Thermal effectiveness of the installation, defined as energy received by the water as a fraction of energy available at the burner is (19.509 + 0.213 + 2.278) / 38.490 = 0.571.

Every watt of heat flow is accounted for in this rigorous balance. There are no unknown losses. Exergy is the work potential in a stream, or the maximum work that the stream can deliver by coming to equilibrium with its surroundings. It is defined by the equation E = (H-Ho) – To (S-So).

The term To(S-So) represents the amount of entropy created in the surroundings which is not available for doing work. The exergy account for the boiler yields information on the use that is made of the work potential present in the energy source.

A sample calculation is presented in Table 4, and the complete exergy analysis appears in Figure 2. The principal insight gained from the exergy account is the limitation of energy conversion in the burner. Upon converting the chemical energy contained in the fuel to thermal energy contained in the flame, a great amount of exergy is lost. In order to preserve the exergy in this conversion, an infinite flame temperature “T” would have to be reached according to the equation E = DH (1-To/T).

Even with the theoretical flame temperature of 1,718 K, the exergy loss due to this conversion is 14.48 MW or 37.6 percent of fuel availability. Table 5 contains the corresponding calculations.

The energy balance shown in Figure 1 is as rigorous as practical. It leaves no unknown energy flows to be estimated and takes into account the variation of sensible heat capacity with temperature. This fact already illustrates the advantages of heat transfer at high temperatures. The flue gas gives off heat by two mechanisms: it lowers its temperature and its heat storage capacity. The inconvenience of this situation resides in the higher penalties incurred with heat losses. The thermal effectiveness is calculated as the fraction of available energy that is passed on to the water and steam. This information represents the main energy balance. Any improvements must be initiated from this point. Combustion losses of 22 percent are considered normal for this type of fuel and the heat losses in the various sections are within empirically admitted limits. The temperature potential existing between the stack gas and the preheated air is 67 K; anything lower is difficult to achieve. The energy balance suggests finding a client for stack gas heat at the 490 K level.

The exergy account in Figure 2 puts the quality of the various heat flows into perspective. This picture starts with the evaluation of possible energy conversion efficiency by combustion and information that the energy balance is unable to provide. In this case, only 63.2 percent of fuel energy is exergy, which changes the entire basis of the audit. The exergy account also testifies to the quality losses inherent in combustion inefficiency and heat transfer potential in the radiation section.

Due to the high temperature levels, the work potential of the loss streams from the burner and the radiation furnace are high. In general, all losses calculated from the exergy analysis are much higher than the corresponding losses calculated from the energy balance. Exergy is destroyed by the compulsory maintenance of heat transfer potentials in all sections.

The air preheater is a case in point. Its purpose is to recycle heat from the back to the front of the furnace. From the energy balance, the heat transferred from the flue gas to the air is the same as that taken by the air to the burner, namely 1.998 MW. The 0.155-MW loss identified by the energy balance may be attributed to heat transferred through the walls of the exchanger to the environment. Of the total heat supplied by the flue gas, 1.998/(1.998 + 0.155) = 92.8 percent is passed on to the air.

The exergy analysis tells a completely different story. Of the 0.933 MW of exergy that the flue gas leaves behind after passing through the exchanger, the air manages to retain only 0.330 MW, or 35.4 percent. The high exergy destruction is due primarily to the temperature gap of 67 K. This difference has to be overcome. It contributes nothing to the preservation of energy quality. The lost work may be calculated directly by the equation LW = QTo (1/Tcold-1/Thot) = 0.591 which is within 2 percent of the 0.603 value given by the exergy analysis.

The results of the analysis may be summarized in form of the quality preservation index. It simply divides the delivered product quality by the source quality. The boiler transferred 22.00 MW of energy to the steam cycle, of which 7.67 MW is exergy. This defines the delivered product quality as 7.67/22 = 0.349. The fuel supplies 38.490 MW of energy, of which 24.340 MW is exergy. The quality preservation index 0.349/0.632 = 0.552 divides the result of the exergy analysis by that of the energy balance (7.67/24.34)/(22.00/38.49) = 0.552.

The index thus could be called exergy /energy carry-over ratio. The value of the index is a consequence of the temperature profile in the installation. The delivered product quality is equal to 1-298/460 = 0.349 and the source quality to 1-298/811 = 0.632.

The energy quality in the source may be better preserved if the temperature level of heat transfer to the client (460 K) is raised.

In comparing exergy or work potential to the concept of ideal work, a difference of 2ToDS is found between the two. The work potential is a real quantity that subtracts from the enthalpy change, all entropy created in the surrounding area during an irreversible cooling operation.

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Manfred Fehr is a professor at Federal University, Uberlandia, Brazil. Fehr holds a bachelor`s degree from the University Laval, a master`s degree from the University of Alberta and a doctorate from the University Laval. He has published more than 50 papers on related and other topics and founded two local chapters of the Brazilian Society of Chemical Engineering.

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