ESRL Module 9. Optimal Design Cogeneration Systems

Transcription

1 ESRL Module 9. Optimal Design Cogeneration Systems repared by F. Carl Knopf, Chemical Engineering Department, Louisiana State University Documentation Module Use Expected Learning Outcomes/Objectives Upon completion of the module, students will be able to: -Optimal Design Cogeneration.pdf -6 Examples files -2 Combustion Library dlls -2 Student Assignment - Capstone Design - Economics Course - Special opics Course - Laboratory Course (1) Explain the impact of variable loading on power plant operation and profitability. (2) Develop and explain an optimum design in the presence of variable inputs and multiple outputs. You should complete, or least understand the concepts, in Modules 1 and 4 before trying Module 9. Cogeneration systems can take a variety of configurations ranging from a simple diesel engine with a water jacket for heat recovery to combined cycle systems with gas turbines, heat recovery steam generators (HRSG), and steam turbines with multiple extraction points. Cogeneration system design needs to account for both daily and seasonal variations in the electrical and steam demands of a process or plant or site. Within established daily or seasonal demands, short-term steam or electrical demand may often exceed (or fall below) expected levels. A qualifying cogeneration facility can purchase or sell electricity, in either an open or a regulated electric market. he potential profit from the sale of electricity can be a factor in the construction and sizing of a cogeneration facility. he sale of surplus steam can also be a factor in the sizing of the cogeneration facility. Generally the sale of surplus steam is not regulated. Before we examine cogeneration system design we do need to caution that even in the most straightforward case, where electrical and steam demands are known and relatively constant, fluctuation in cogeneration fuel costs (for example the cost of natural gas) can quickly move a cogeneration project from being economically viable to nonviable. For example, many industrial natural gas fuel based cogeneration projects are economically viable with natural gas prices in the $4 - $6/MM Btu range. However, as natural gas prices rise above $6, the fuel mix for utility companies, which generally includes coal, natural gas, hydroelectric and perhaps nuclear, allows the sale of electricity at a price which eliminates many of the advantages for cogeneration. his $6 benchmark will certainly move upwards if CO2 sequestration from coal fired power plants becomes a reality. he design of an optimal cogeneration system requires minimizing total costs. otal costs include capital equipment, installation costs, and operating costs including fuel purchase and maintenance costs, and the cost of (or profit from) supplemental electricity. he design requires selection of cogeneration configuration and equipment as well as the determination of processing conditions. Equipment selection must address which type and size of units to use, for example a gas turbine or steam turbine or both. Equipment must be configured, for example in some cases parallel units 1

2 may be better at matching processing needs than a single larger unit; parallel units allow increased reliability or the ability to cycle units for widely varying loads. Often the best cogeneration system design is one which targets the base power and base heat requirements of the site. Additional electricity can be purchased and additional steam production can be realized by supplemental firing of the HRSG. In this module we explore the optimal economic design of cogeneration systems. he optimal design problem begins by first selecting the cogeneration configuration that matches the site utility needs and then assembling material and energy balances for the chosen cogeneration configuration. hese material and energy balance performance equations provide needed flow rates, temperatures and pressures which are used to size and then the cost equipment. Often fuel cost, as determined from the fuel flow rate, is the dominate cost component for the cogeneration system. Economic Optimization of a Cogeneration System he CGAM roblem A problem to allow comparison of different methods of thermoeconomic optimization and analysis for cogeneration system design was developed by A. Valero, M. Lozano, L. Serra, G. satsaronis, J. isa, C. Frangopoulos, and M. Von Spakovsky, CGAM roblem: Definition and Conventional Solution (1994). he CGAM cogeneration flowsheet is shown in the Figure 1. We are asked to determine the optimal equipment sizing and design parameters (,, flow rates, etc) which minimize total system costs for fixed base line loads of 30 MW of electricity and lbm/s of saturated steam at 290 psia. 2

3 6 Gas (Fuel + Air) Air reheater 2 Air 3 F fuel R bar 1 Air Air Compressor Combustion Chamber 4 Gas & ower urbine 5 Net ower 30 MW 6 Exhaust Gas Stack reheat or Economizer Evaporator 7 20 bar HRSG 8 Water R 9 Steam 8 8 Figure 1 Cogeneration System with Air reheat and HRSG F steam 874 R bar lb s Here we show the process for the economic optimization of the cogeneration system in Figure 1. his configuration is very similar to the LSU cogeneration system which we detailed in our Ideal Gas (Module 1) and Real Gas (Module 4) Cogeneration erformance Modules. In the LSU system an air cooler as opposed to an air heater is used. But we did account for the design and performance equations of Figure 1 with the air preheater in roblem 1 of both Module 1 and Module 4. All of these performance calculations are independent of the cost equations that are used to determine the optimal design. For the nonlinear optimization employed here, equipment costs are approximated as continuous functions and expressed in terms of the design variables. Recall that any independent variable can be changed in our Excel-based performance calculations and values will be determined for dependent variables we will utilize this for system costing and optimization. he independent variables in our cogeneration system formulation, which impact 3

4 the economic optimization, will be referred to as design variables in our economic optimization as these design variables are changed, the system cost changes. As part of the example and problem solution files in Modules 1 and 4 we determined the cost of cogeneration system. We did not optimize the cost, but we did see as the design variables are changed the system cost changes. he Objective Function Cogeneration System Capital and Operating Costs (Valero et al., 1994a) he objective function accounts for capital and operating costs which are minimized by varying the design variables. he total cost rate including fuel, equipment and maintenance, ($/s), can be found as ϕ 3600 (1) where: is the fuel cost per energy unit (based on the fuel lower heating value LHV); is the fuel flow rate (lb/s); i indexes the five equipment items: air compressor, combustion chamber, gas and power turbine, air preheater, and HRSG; Zi, is the purchase cost of the i th component ($) (see ables 1 and 2); CRF, is the annual capital recovery factor (CRF =18.2%); N is the number of hours of plant operation per year (N = 8000 hr and 3600 s/hr); and is the maintenance factor ( = 1.06). For the cogeneration system, the fuel and equipment costs are being brought to an equivalent $/s basis through the capital recovery factor (see the Levelized Economics discussion in Module 3). For cogeneration systems fuel costs often dominate. Here = $4.2204/MMBtu based on the LHV of the methane fuel. Do recall that natural gas is actually priced on the higher heating value of the fuel which is ~110% the LHV. herefore fuel costs in this problem would be ~ $4.60 natural gas which would be ~ $4.60/ MM Btu or ~ $4.60/mSCF (1000 Standard Cubic Feet). able 1: Cost Equations urchase Cost (Valero et al., 1994) Component Capital Investment Costs ($) Air compressor Combustion chamber Gas and power turbine ln 1 ln 1 & 4

5 Air preheater HRSG.... In able 1, C ij are cost coefficients (see able 2);, is the overall heat transfer coefficient in the air preheater, and, is the log mean temperature difference in the specified heat recovery unit. able 2: Cost Coefficients for the cogeneration components (Valero et al., 1994). Field Units SI Units Air compressor = $/(lb/s) = 39.5 $/(kg/s) = 0.9 = 0.9 Combustion chamber = $/(lb/s) = 25.6 $/(kg/s) = = = 0.01 (1/R) = 0.018(1/K) = 26.4 = 26.4 Gas and power turbine = $/(lb/s) = $/(kg/s) = 0.92 = 0.92 = 0.02 (1/R) = 0.036(1/K) = 54.4 = 54.4 Air preheater = 2290 $/(m 1.2 ) = 2290 $/(m 1.2 ) = = HRSG = $/(Btu/(s R)) 0.8 = 3650 $/(kw/k) 0.8 = $/(lb/s) = $/(kg/s) = 254.8$/(lb/s) 1.2 = 658 $/(kg/s) 1.2 In the costing equation, the use of the log-mean temperature difference in the air preheater and HRSG represents a temperature driving force at each end of the heat exchanger given by,, 5

6 ,, For the HRSG economizer and evaporator, temperatures have been defined in both the Ideal Gas and Real Gas Cogeneration erformance Modules. Example 1 Design problem component costing Determine the purchase cost of the air compressor component of the gas turbine system if = 230 lb/s, = 0.84, = bar and = 9 bar. Solution: ln $1,335, Equipment purchase costs will be multiplied by the capital recovery factor to bring costs to a yearly basis and then converted to a per second basis. Fuel and maintenance costs are included to form the system costs on a $/s basis. Optimization Variable Selection and Solution Strategy he nonlinear programming solution approach to the design problem consists of minimizing the capital and operational costs (given by equation 1) while delivering 30 MW of electricity and lbm/s of saturated steam at 290 psia. he objective function is minimized by varying the independent design variables. We can walk through the optimization process by recalling our performance equation developments of both the Ideal Gas and Real Gas Cogeneration erformance Modules. For the ideal gas optimization formulation we use for the independent design variables: the air flow rate, ; ; the air compressor efficiency, ; ; ; the gas and power turbine efficiency, & ; and, for the HRSG values for and. he system dependent design variables (,,,, etc.) are calculated as functions of these independent design variables and known system parameters including, pressure drops, fuel LHV, etc. (see able 4, below). he real gas optimization formulation, follows the ideal gas 6

7 formulation with one change, the fuel flow rate, rather than will be used as an independent variable. he inlet air temperature and pressure to the compressor are fixed at ambient conditions. he optimization program will select values for, and, and as we have seen in Example 1 a cost for the air compressor can be determined. A value for will be selected and from and the known pressure drop in the air preheater, all conditions at point 3 will be known. As is increased in value, the cost of the air-preheater will increase but the fuel flow rate (and fuel cost) needed to bring the combustion products to will decrease. he power turbine efficiency, & will impact the delivered power. Values for and will control the amount of steam raised and the cost of the HRSG. his economic design optimization problem does require comment. We have discussed in both the Ideal Gas and Real Gas Cogeneration erformance Modules that values for and should be selected based on fuel type and expected exhaust gas inlet temperature to the evaporator. Values for and are not generally considered design optimization variables. We will solve the optimization problem with constraints added to keep and at appropriate values or simply fix values for and and solve the remaining optimization problem. A larger problem is that this optimal system design assumes continuous variables, for example the efficiency of the air compressor can take on any value. he optimization problem here should be viewed as a framework for helping to select among several alternative cogeneration systems, or possible system configurations, or help identify needed ranges in operating conditions. rocess Constraints he inlet air temperature and pressure to the compressor are fixed at ambient conditions. And the cogeneration system must generate 30 MW of electricity and lb/s of saturated steam at 290 psia. he power and steam requirements will necessitate the use of at least two constraints in the formulation, here are other processing conditions or limitations which may need to be imposed on the design solution depending on the problem formulation and the initial guess used. For example, materials of construction impose certain practical limits on the inlet temperature to the gas and power turbine. Similarly concerns exist for the compression ratio in the air compressor. he form of the cost expression for the air compressor and the gas and power turbine require that < 0.90 and that & < 0.92; a practical lower limit on efficiency for each of these units is 75%. During the optimization process temperature cross-over in the air preheater heat exchanger may occur but this can be avoided by temperature constraints 10 and 7

8 10 ; here a minimum 10 R approach temperature is being used. he exhaust gas temperature at the stack,, should be > ~ R when using methane or natural gas fuel in order to avoid acid condensation. Allowable values will increase as the sulfur content of the fuel increases. able 3 summarizes possible constraints which may need to be added to the optimization model to obtain a reasonable solution. able 3 ossible Constraints for the CGAM Cogeneration Design roblem 4 < 75% < < 90% 75% < & < 92% > R (250 F) I Economic Design Optimization of the CGAM roblem Ideal Gas he cogeneration system in Figure 1 consists of an air compressor, air preheater, combustion chamber, gas and power generating turbine and HRSG. We developed material and energy balances for these operations in the Ideal Gas Cogeneration erformance Module (and roblem 1 of Module 1) for use in the Excel-based optimal design solution. In this section both the air feed and the combustion products are taken as ideal gas with known heat capacity. In addition both and will be taken as know values. With fixed in value, water and steam properties are fixed in the HRSG. In Section II (below) real gas and water / steam properties from our combustion library (SI+) will be used allowing for variable steam properties within the HRSG. Species and physical properties available in SI+ have been discussed in Module 4 (Real Gas erformance Module) and they are listed in the able of Function Names.pdf provided in this module. Air reheater Equations (AH): Energy from the exhaust gas leaving the power turbine is used to heat the compressed air that will enter the combustion chamber. With adiabatic heat exchange, (2),, (3), (4), 8

9 where the. he pressure drop on each side of the air preheater can be found as, 1, (5) 1, (6) CGAM roblem hysical roperties able 4 provides physical properties for the air, exhaust gas, and fuel and known system parameters. Steam physical properties are found from steam tables. able 4: hysical roperties, Design arameters and Constants Field Units SI Units, R, bar K, bar , , ,,,, 0.05, 0.05, , 0.05, R 1.64 K 27 R 15 K 874, ,

10 536.7, he pinch and approach temperature difference and the condensate return temperature deserve comment. As we discussed in the Ideal Gas Cogeneration erformance Module, the HRSG design case requires specification of pinch and approach temperature differences. Here we have set the pinch temperature difference at = 3 R and the approach temperature difference = 27 R; both values are taken from the CGAM problem optimal solution (Valero, 1994a). he = 3 R value is questionable and this value will be changed in Example 2. Recall from our discussions of the Ideal Gas and Real Gas Cogeneration erformance Modules that typical values for and with methane fuel in gas turbines are both ~15R. Also in Figure 1, the condensate return temperature, = R used in this problem is very low. should be kept as high as possible. oo low of a temperature for may necessitate use of special materials of construction in the economizer. Example 2 Original CGAM design problem ideal gas working fluid Solve the original CGAM problem as shown in Figure 1 with system costs provided in able 1 and 2 and with physical properties in able 4. Here we provide a solution template to this problem Example 2a.xls. he reader is encouraged to use this template as the starting point for obtaining the solution to this problem. In this template we have provided named variables and the design variables are indicated on the Excel sheet. In this template we have also provided the objective function the total cost equation, which combines fuel and all equipment costs. Solution: A good initial guess is an important step in any optimization process. his is especially true for this problem which shows several local minima. he independent design variables, which will be varied during the optimization process, are shown on the Excel sheet in the column named Variables. o start: assume air enters the compressor at 230 lb/sec; the efficiency of the air compressor = 0.84; the air pressure at the exit of the air compressor = 9.0; the combustion chamber inlet temperature = 1625 R; the turbine inlet temperature = 2650 R; and, the efficiency of the power turbine = With the provided initial guess, the remaining dependent variables in the solution template can be determined using the equations we have developed in the Ideal Gas Cogeneration erformance Module. When assembling the material and energy balance equations avoid using the flow rate of the product gas in the balance equations, instead use which will help avoid a circular reference error from Excel. We also caution that depending on the initial guess used, constraints as provided in able 3 may be required. wo constraints, and will be required in all formulations. he independent design variables can be varied by Solver and the optimal solution for the cogeneration design determined. he solution is provided in Example 2b.xls and shown in Figure 2. 10

11 F fuel 3.615lb / s lb / s R bar R bar R bar lb / s R bar kw R bar 30 MW lb s R lb s R bar 20 bar lb s 874 R bar lb s R bar Btu/s Btu/s Figure 2 Solution CGAM problem, ideal gas, = 3 R and = 27 R he optimal cogeneration system cost, while meeting the requirements of 30 MW net power and lb/s of saturated steam at 20 bar, is found as $0.3697/s. he results found in the Excel solution file are also summarized in able 5 (below). 11

12 Before we leave Example 2 it is instructive to see how sensitive the solution is to the starting guess. From the solution in Excel file (also Figure 2) set: the air mass flow rate to 226 lb/s; = 8.4; = 1650 R; and, = 2670 R, and run Excel Solver. A new solution with a lower optimal cost of $0.3690/s should be found. he multiple optimums in this problem are, in part, due to the form of the equipment costing equations. Example 3 Original CGAM design problem with = 15 R and = 15 R. In Example 2 we solved the original CGAM problem. Here we used = 3 R and = 27 R; both these values are taken from the CGAM problem optimal solution (Valero, 1994a). For Example 3 let us solve the CGAM problem with the pinch temperature difference fixed at = 15 R and the approach temperature difference also fixed at = 15 R; both these values are typical of methane fired gas turbine / HRSG design calculations. Solution: We allowed for the possibility of variable and values in our formulation of Example 2. We will need to change the enthalpy value for water to reflect = 15 R. Here, =, = Btu/lb. With the same starting guess as used in Example 2, the solution to Example 3 is provided in Example 3.xls. Here the optimal cogeneration system cost, while again meeting the requirements of 30 MW net power and lb/s of saturated steam at 20 bar, is found as $0.3709/s. Key results are summarized in able 5. In this design problem the impact of and selection on the total cost rate is relatively small; the difference in the total cost rate for the two examples is ~ $34,650/year. For both examples, fuel costs dominate the total cost rate. he importance of and selection occurs in off-design operation of the HRSG. II he CGAM Cogeneration Design roblem - Real hysical roperties We want to reexamine the CGAM problem to see the impact of rigorous physical properties on the optimal system design. In Section I (above) we used ideal gas properties, for the power-side, and real steam properties in the HRSG when solving the optimal design problem. However, to find steam properties we had to specify prior to solving the performance equations for the HRSG. With SI+ (see the able of Function Names.pdf provided in this module) providing rigorous gas and steam properties we will no longer need to fix or prior to design optimization, however, values for these independent design variables may need to be constrained. Example 4 CGAM design problem real fluid solution Solve the original CGAM problem as developed in Example 2, using real gas properties. Solution: he optimal solution is provided Example 4.xls and shown below in Figure 3. As we discussed in Example 2 a good initial guess is an important step in the optimization process. he independent design variables, which will be varied during the optimization process, are shown on the Excel sheet in the column named Variables. o start: assume air enters the compressor at 230 lb/sec (design variable); the efficiency of the air compressor = 0.84 (design variable); the air pressure at the exit of the air compressor = 9.0 (design variable); the combustion chamber inlet 12

13 temperature = 1625 R (design variable); the mass flow of fuel to the combustion chamber is 3.6 lb/sec (design variable); and, the efficiency of the air compressor = 0.87 (design variable). With our combustion library it is more convenient to the fuel mass flow rate, as opposed to, as an independent design variable. We also set the pinch temperature difference at = 3 R and the approach temperature difference = 27 R. We will solve the design problem with variable and in Example 6. With the provided initial guess, the remaining dependent variables can be determined using the equations developed in Real Gas Cogeneration erformance Module (Module 4) and information from ables 1, 2 and 4. When assembling the material and energy balance equations again avoid using the flow rate of the product gas in the balance equations, instead use which will help avoid a circular reference error from Excel. 13

14 F fuel lb / s lb / s R bar R bar R bar lb / s R bar kw R bar 30 MW lb / s R bar lb/ s R bar lb/ s R 20 bar F steam lb / s 874 R 20 bar Btu / s Btu / s Figure 3 Solution CGAM problem, real fluid properties, Δ = 3 R and Δ = 27 R Here the optimal cogeneration system cost (fuel + equipment), while meeting the requirements of 30 MW net power and lb/s of saturated steam at 20 bar, is found as $0.355/s. he results found in Figure 3 are summarized in able 5. 14

15 Example 5 CGAM design problem real fluid solution = 15 R and = 15 In Example 4 we solved the original CGAM problem using real fluid properties and using Δ = 3 R and Δ = 27 R. For Example 5 solve the CGAM problem using real fluid properties and with a more realistic values Δ = 15 R and Δ = 15 R. Solution: We allowed for the possibility of varying Δ and Δ values in our formulation of Example 4. With the same starting guess as used in Example 4, the solution to Example 5 is provided in Example 5.xls. Here the optimal cogeneration system cost (fuel + equipment), while again meeting the requirements of 30 MW net power and lb/s of saturated steam at 20 bar, is found as $0.3563/s. Key results are again summarized in able 5. Example 6 CGAM design problem real fluid solution variable Δ and Δ Finally we solve the CGAM problem using real fluid properties and allowing Δ and Δ to both be independent design variables in the optimization process. Here we can use the same starting guess as our two previous examples, plus the starting guesses for Δ = 15 R and Δ = 15 R. We do need to provide lower bound constraints on both Δ and Δ ; here we use Δ 10 and Δ 10. Solution: he solution to Example 6 is provided in Example 6.xls. You will find that at the optimal solution, Δ and Δ both reach their lower bound of 10.0 R. Here the optimal cogeneration system cost, while again meeting the requirements of 30 MW net power and lb/s of saturated steam at 20 bar, is found as $0.3549/s. Key results are summarized in able 5, but this design would not be recommended as the exhaust gas temperature from the HRSG is o R this temperature is of concern as acid condensation may occur at values below ~710 o R with methane fuel. able 5 Optimal solutions to the GCAM design problem Variable / Cost Example 2 Ideal gas Example 3 Ideal gas Example 4 Real fluid Example 5 Real fluid Example 6 Real fluid lb/s lb/s lb/s lb/s lb/s η bar bar bar bar bar R R R R R lb/s lb/s lb/s lb/s lb/s η & Δ 3.0 R 15.0 R 3.0 R 15.0 R 10.0 R Δ 27.0 R 15.0 R 27.0 R 15.0 R 10.0 R R R R R R kw kw kw kw kw 15

16 & kw kw kw kw kw & 3000 kw 3000 kw 3000 kw 3000 kw 3000 kw lb/s lb/s lb/s lb/s lb/s ransferred Btu/s Btu/s Btu/s Btu/s Btu/s ransferred Btu/s Btu/s Btu/s Btu/s Btu/s Cost Air Compressor 1,571,619 $ 1,571,689 $ 1,153,588 $ 1,139,670 $ 1,174,642 $ Cost Comb Chamber 121,348 $ 122,295 $ 140,132 $ 143,485 $ 140,617 $ Cost G& urbine 2,691,912 $ 2,617,611 $ 2,181,144 $ 2,192,872 $ 2,224,209 $ Cost Air reheater 848,751 $ 835,130 $ 743,419 $ 732,636 $ 743,006 $ Cost of the HRSG 992,817 $ 991,430 $ 996,707 $ 994,351 $ 1,076,375 $ Equipment Cost Rate $/s $/s $/s $/s $/s Fuel Cost Rate $/s $/s $/s $/s $/s otal Cost Rate $/s $/s $/s $/s $/s In able 5 for all examples, fuel costs dominate the total cost rate. It is interesting to note that within ideal gas solutions (Examples 2 and 3) and real gas solutions (Examples 4 6) the selection of and did not greatly impact the total cost rate. However, there is significant difference in the total cost rate when and are common and ideal gas and real gas solutions are compared (Example 2 and 4) and (Example 3 and 5). For example, when comparing the total cost rate of Example.2 (ideal gas formulation) and Example.4 (real gas formulation) a difference of $ 421,881/ year occurs. his cost savings is almost equally split between fuel costs and equipment costs. Before we leave our discussion of the results in able 5, we want to again emphasize that, this optimization problem and our developed solutions should be viewed as a framework for helping to select among several alternative cogeneration systems, or possible system configurations, or help identify needed ranges in operating conditions. In closing, cogeneration system design includes consideration of the system configuration (equipment type and number) and determination of the optimal size and operating conditions in order to minimize costs. In this module equipment costs were approximated as continuous functions and costs (capital + operating) were minimized for a given cogeneration configuration with fixed process utility demands. Excel was shown an ideal solution platform for this cogeneration design problem as Excel provides both optimization routines and sheet function capabilities. Sheet functions allow inclusion of rigorous physical properties providing more accurate system design and performance calculations. Sheet functions also allow calculation of all system variables when one or more design variables are changed this is ideal for design optimization, evaluation of control strategies, or improved operability of cogeneration facilities. We also used sheet functions, combined with numerical methods, to determine temperature profiles in the HRSG tubes and at the HRSG walls. he equipment costs provided in the CGAM problem provide a starting point for cost estimates (1994 dollars) for many significant cogeneration equipment items. hese included individual costs for: the air compressor; combustion chamber; gas and power turbine; the air preheater heat exchanger; and, both the economizer and evaporator sections of the heat recovery steam generator. Cogeneration systems often include additional equipment items including: a main boiler; auxiliary 16

17 boilers; feedwater heat exchanger; back pressure steam turbine; absorptive chiller; compression chiller; as well as a capital investment to allow connection to the grid for the sale of excess power or the import of power. Additional costing expressions for utility systems can be found in: Woods et al. (1979); Manninen and Zhu (1999); and Rodriguez (2003). Acknowledgements his work was completed as part of the National Science Foundation hase II grants: NSF Award Integrating a Cogeneration Facility into Engineering Education (September ); and NSF Award Collaborative roposal: Energy Sustainability Remote Laboratory (September ). References Manninen, J., and X.X. Zhu. Optimal gas turbine integration to the process industries. Ind. Eng. Chem. Res. 38: (1999). Rogriguez, M. Combined Heat and ower echnologies Applied Studies of Options including Microturbines, M.S. hesis, echnische Universitat Wien, November (2003). Valero, A., M.A. Lozano, L. Serra, G. satsaronis, J. isa, C. Frangopoulos, and M. von Spakovsky. CGAM problem: definition and conventional solution. Energy he International Journal. 20(3): (1994). Woods, D.R., S.J. Anderson, and S.L. Norman. Evaluation of capital cost data: offsite utilities (supply). Canadian Journal of Chemical Engineering. 57(5): (1979). You are responsible for roblem 1. Student Assignments roblem 1. he cogeneration system presented in the CGAM problem (solved above) is very similar to the cogeneration system at LSU shown in Figure 1. Determine the optimal equipment sizing and design parameters (,, flow rates, etc) which minimize total system costs for the LSU system using real fluid properties. You will need to replace the air preheater (Figure 1) with an air cooler (Figure 1). Some of the parameters in the costing equations of ables 1 and 2 will need to be adjusted for the LSU system (Figure 1). For the air cooler use:., C41 = 2290 $/(m 1.2 ) and assume = =

18 R bar R bar R 20 bar 8 F steam R 20 bar Figure 1 Cogeneration ower Cycle with Air Chiller and HRSG Student Assignments - Laboratory Course 18

19 You must complete the Student Assignment (above) before attempting this laboratory course student assignment. his assignment does not have a single correct answer. Laboratory Course Student Assignment Go to the web site or and access operational data from the LSU cogeneration facility found in the folder Cogeneration Operational Data. Determine base line loads, typical loads, and peak loads for the system. o help you get started, I have found LSU has: a.) a peak load of 35 MW of electricity and 150,000 lbm/hr of saturated steam at 150 psia. b.) a typical summer load of 28 MW of electricity and 46,000 lbm/hr of 150 psia steam. a typical winter load of 28 MW of electricity and 125,000 lbm/hr of 150 psia steam. c.) a baseline load of 19 MW of electricity and 40,000 lbm/hr of 150 psia steam. Use your solution to roblem 1 of this module to help determine if the LSU cogeneration system should have been designed for baseline or a typical peak load or something in between. Is the LSU current system optimal? Of course you will need to account for the amount of time these loads occur. Also be sure to evaluate the cost of natural gas and cost of purchased electricity on your solution. As these values change the optimal design will move that is why I indicated this assignment does not have a single correct answer. 19