2. Exergy Analysis of STHE P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Formalization of Thermo-economics…..

3. Shell and Tube as a Thermal System In most cases, heat exchangers are designed for one of two cases: fixed thermal duty or fixed heat exchanger area with specified flow rates.

4. Availability & Exergy Availability at the original state : The potential for achieving the maximum possible work by the mass. Exergy : Flow Availability: The maximum reversible work per unit mass flow without the additional heat transfers is the flow availability or exergy. e is the physical exergy. For liquids, the physical exergy can be obtained, when assuming a constant specific heat capacity, as where v is the specific volume determined at temperature T 0.

5. The Exergy Destruction Rate : A Measure of Running Cost The entropy generation lowers the overall exergy level of a thermal system. Identify the regions in space where this occurs (the locations that have entropy generation). The exergy destruction is identical to the term, irreversibility. The exergy destruction rate for the control volume of an adiabatic heat exchanger in steady state is calculated from the difference between the incoming and outgoing exergy flows

6. Formulation of Objective Functions Type 1 : Objective function : Fixed Thermal Duty Type 2 : Objective function : – Fixed Heat Transfer Area

7. Objective function : Fixed Thermal Duty In the case of design with fixed thermal duty, consider the effect of varying the baffle spacing, baffle cut etc., while keeping the heat transfer rate constant at any prescribed value. At the fixed heat transfer rate, by reducing the baffle spacing, baffle cut etc., the heat transfer area, and also the capital cost, of the exchanger is decreased because the shell side heat transfer coefficient is increased. On the other hand, this generally means higher total exergy destruction, due to more pressure drop which leads to larger costs associated with the exergy destruction.

8. Thus, there may exist an optimum baffle spacing, baffle cut etc., that minimizes the total annual cost. In this case, the objective function can be expressed as Where t op is the period of operation per year, c ex is the unit cost of the exergy, E D is the rate of exergy destruction, a 1 is the capital recovery factor and C HEX is the capital cost of the heat exchanger. Consider a heat exchanger without baffles as a reference case.

9. Objective functions – Fixed Heat Transfer Area In the case of fixed heat transfer area, in comparison to the baffle free shell, the baffle arrangement will lead to a reduction in the monetary flow rates associated with the exergy destruction. The advantage of baffling is the considerable reduction it offers in the total cost associated with exergy destruction. Nevertheless, the increase in total cost because of the requirement for additional baffling comes as a disadvantage. Thus, there may exist an optimum baffle spacing that maximizes the amount of net saving associated with the exergy. The effect of the baffle arrangement on total annual cost may be calculated by taking the difference between the costs associated with the exergy profit and the baffle costs.

10. In this case, the objective function can be expressed as where S ex is the net exergy saving, t op is the period of operation per year, C ex is the unit cost of exergy, P ex is the net exergy profit caused by baffling, a f is the capital recovery factor and C B is the capital cost of the baffle arrangement.

11. An Alternative Approach …. Profit due to Baffling …..

12. Profit due to Baffling In the case of the baffle free shell, a significant reduction occurs in the pressure component of exergy destruction because of the fact that the pressure drop is invariably much lower than that of the baffled shell. On the otherhand, a decrease in the heat transfer coefficient of the shell side occurs, which considerably increases the thermal component of exergy destruction. This leads to an increase in the total exergy destruction rate in comparison to the case of the baffled shell. However, due to the baffle arrangement on the shell side, it is often possible to take advantage of the total exergy destruction in comparison to the case of the baffle free shell.

13. It is apparent that the exergy destruction difference between the baffled and baffle free shell varies considerably with baffle spacing and baffle cut. An exergy profit is calculated by taking the exergy destruction difference between the cases of baffle free and baffled heat exchangers as follows: where P ex is the net exergy profit, E D, Baffle free is the exergy destruction rate of the baffle free exchanger and E D, Baffle is the exergy destruction rate of the baffled exchanger.

14. Effect of Baffle Spacing on Energy Profits

15. Selection of Cost Functions

16. Capital Cost of STHE Several different correlations regarding cost estimations of shell and tube heat exchangers can be found in the relevant literature. In general, the total cost of the heat exchanger is directly proportional to heat transfer area and hence a strong function of baffling. The capital cost of a shell and tube exchanger for steel-steel material can be estimated by using the Hall Method where A is the heat exchanger area required for a given duty.

17. Baffling Cost The baffling cost is also considered as a significant cost for cost analysis. This cost for a piece of equipment consists of three major components: weight of material, labor hours and labor costs. Labor hours significantly depend on the drilling of the raw baffle material and are strongly affected by the variation of the number of tubes. The baffle cost may be calculated by the following expressions:

18. where C M is the cost of raw baffle material and C D is the drilling cost of the baffle arrangement. Material cost and drilling cost may be expressed simply as where c M is the price of material, N b is the number of baffles, n is the number of tubes, D s is the shell diameter,  b is the baffle thickness,  St is the material density, c L is the labor costs and t D is the drilling labor per unit hole depth.

19. Effect of Baffle Spacing on Total Cost

20. Cost Vs Experience Min. Total Cost based Baffle Spacing

21. Minimum cost Design : Chart -1

22. Minimum cost Design : Chart -2

23. Minimum cost Design : Chart -3

24. Minimum cost Design : Chart - 4

25. Performance of Minimum Cost Design

26. Limitations of STHE Optimization Optimization is possible only if following parameters are uniform through out the HX. Tube spacing, layout, diameter…. Baffle type, spacing, cut …. All the clearances….. Most popular applications of STHE are required to be designed with non-uniform parameters.

27. Closed Feed Water Heaters A closed feedwater heater is a shell-and-tube heat exchanger that warms up feedwater or condensate by means of steam or condensate. It is used in almost all power plants with steam turbines. Purpose : Closed feedwater heaters are used in a regenerative feedwater cycle to increase thermal efficiency and thus provide fuel savings. An economic evaluation will be made to determine the number of stages of feedwater heating to be incorporated into the cycle. Condensing type steam turbine units often have both low pressure heaters (suction side of the boiler feed pumps) and high pressure heaters (on the discharge side of the feed pumps).