Steam reheating is an important feature in steam-power plants. The main objective of reheat is to increase the power output and, under certain conditions, the thermal efficiency of the plant, thus improving plant performance. There is a wide range over which reheat pressures can be varied. Hence, for every set of steam conditions, an optimum value of reheat pressure exists that will yield an optimum steam turbine-boiler reheat-cycle. Second-law analysis was considered for optimizing conventional plants. [5 and 6] provided a second-law analysis for the optimization of cogeneration steam plants. Some constraints exist and present a limiting factor for the range of choice of reheat pressures. [7] analyzed the influence of reheat temperature and pressure on regeneration-cycle performance. Their results indicated that the most economical gain would occur when the reheat temperature increases no more than 30 K from the saturation temperature corresponding to the steam pressure from a high-pressure turbine-exhaust. Silvestri et al. concluded that both first- and second-reheat pressures can be varied over an appreciable range only with a limited effect on the heat rate. Equipment designs and operating concerns that place limits on reheat-pressure selection were also noted in both studies.

Recent studies indicate the importance of reheat temperature control and numerical modeling of reheat regenerative furnaces. The most recent analyses indicate the possibility of attaining high plant-efficiencies, over 45%, as a result of using efficient steam turbines, even reaching 67% with multiple Rankine topping cycles. However, improving the performance of existing plant configurations through optimization of reheat pressures remains a desirable objective for the next decade or so.

The present paper is an extension of a previous paper by Habib et al. which applied first-and second-law analysis for optimizing the reheat pressures of non-regenerative power plants. The analysis in the present paper is extended to include feedwater heating in the plant.

The layout of the thermal-power plant considered in the present work is shown in Fig. 1. The plant utilizes the reheat regeneration-cycle and comprises a boiler with two reheats, multistage turbines, a condenser and open-type feed-water heaters.

The thermal power plant can be divided into two main units, the steam generator which consists of the furnace and the heat exchanger unit and the turbine cycle which consists of the high-pressure turbine, intermediate-pressure turbine, low-pressure turbine, condenser and feed-water heaters.

The exergy destruction in the steam generator can be calculated as described in the following paragraphs.

The exergy destruction in the furnace occurs as exergy losses from the boiler in the exhaust gases, thermo-mechanical loss and chemical loss.

The contours of the first-law thermal efficiency are shown in Fig. 2. The figure indicates a maximum efficiency close to high reheat-pressure P₁ of 25% of the boiler pressure and at low reheat-pressure P₂ of 4.4% of the boiler pressure. The diagonal of the figure with P₂=P₁ presents the single reheat case. For this case, the maximum efficiency is almost 0.357. Thus the improvement in ?_I due to incorporating the second reheat is approximately 0.02 or 5.6%. The contours provide a spectrum for the selection of optimum thermodynamic reheat-level for a specific application. For the same improvement in efficiency, a selection of reheat pressures is available to suit different temperatures at the inlet to the boiler. These temperatures are usually limited by the boiler design. It is anticipated that low temperatures at the inlet to the reheaters at the second reheat-pressure will result in a high temperature at the exit of the low-pressure turbine.

The second-law efficiencies of the plant, steam generator and turbine cycle are shown in Fig. 3, Fig. 3 and Fig. 3 respectively. Fig. 3(a) indicates an improvement of.0261 or 6.3% in the second-law efficiency due to incorporating the second reheat pressure. Compared with Fig. 2, Fig. 3(a) indicates that the maximum second-law efficiency occurs at the same location as the maximum of the first-law efficiency. Comparison of the three Fig. 3, Fig. 3 and Fig. 3 indicates different optimum conditions of reheat pressures for the plant, the steam generator and the cycle. The optimum steam generator efficiency occurs at P₂=56% and P₁=20% of the boiler pressure. Corresponding values for the cycle are 12.6 and 2.8%. The figure also indicates that the steam generator efficiency is more sensitive to changes in P₂ than in P₁. Cycle efficiency is more sensitive to P₁ than P₂.

At high values of reheat pressures, the temperature difference through which heat is transferred from hot gases to the steam is lower and therefore irreversibilities are expected to be lower. The irreversibility rates in the steam generator are shown in Fig. 4 and Fig. 5. It is indicated by Fig. 4(a) that the minimum irreversibility rates occur at P₂=56.2% and P₁=20% of the boiler pressure. The irreversibility in the steam generator is more sensitive to changes in P₂ than in P₁. The irreversibility losses in the steam generator are due to availability destruction in the furnace and boiler heat-exchanger sections. The irreversibilities in these two sections are shown in Fig. 4 and Fig. 4. These figures indicate that the heat-transfer irreversibility losses are more than 3 times greater than the furnace irreversibility losses. The furnace irreversibility losses are due to availability destruction as thermo-mechaincal, chemical and exergy destruction in stack gases. These are presented in Fig. 5 and Fig. 5.

The irreversibilities in the cycle and its components are shown in Fig. 6, Fig. 7, Fig. 8 and Fig. 9. The cycle irreversibility losses are given in Fig. 6 and account for about 12% of the exergy input to the power plant. The cycle irreversibility losses are more sensitive to the low reheat-pressure P₁ than the high reheat-pressure P₂. The irreversibility losses occur at P₂=10% and P₁=2.5% of the boiler pressure. The irreversibility losses due to the cycle components, the condenser, the three turbines and the two feedwater heaters are given in Fig. 7, Fig. 8 and Fig. 9. The losses in these components at the optimum reheat pressures are 49, 7, 18, 11, 3 and 12%, respectively.

The choice of reheat pressures which may be available to the plant designer to achieve optimum efficiencies is limited by some specific constraints. These are the quality of the steam at exit of each turbine. A typical presentation of these constraints is given in Fig. 10 where the quality values at the exit of the high pressure turbine, x₁, and the intermediate pressure turbine, x₂, were kept above 1.0. In the case of the turbine preceding the condenser, the quality value x₃ was maintained above 0.9. Considering the constraints on quality at exit of each turbine, the choice of the two reheat pressures will be limited to the region bounded by x₁=1.0, x₂=1.0 and x₃=0.9 as indicated by Fig. 10.

A thermodynamic optimization procedure of reheat pressures for the reheat regeneration thermal-plant is presented. The results provide the different optimum low- and high-reheat pressures for each of the steam generator, turbine-cycle unit and the overall plant. It is concluded that the first and second law efficiency are more strongly influenced by the high reheat-pressure than the low reheat-pressure.