thermodynamics course that i have assignment.

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ME/NSE 312

Thermodynamics

Winter 2018

Project Description

Submitted as a single PDF to Canvas (GROUPS OF 2). No hard copy or emailed assignments

will be accepted. Late assignments will be accepted up to 24 hours after due date with a 50%

penalty. Projects from single individuals will earn at most 75% unless approved in writing prior

to submission. Projects with more than two students will not be accepted. Project must be

completed using Engineering Equation Solver.

DESCRIPTION: Geothermal power plants use the heat from the earth as the input to a heat

engine. In a binary cycle plant, water is pumped into the ground, heated, and returned to the

surface where it provides heat to a different working fluid in the power plant itself.

Your company is designing a power plant where the water from the geothermal well is returned

at 180°C. You and your colleagues have identified the cycle shown in Figure 1 as a promising

configuration. The cycle uses reheat and regeneration with multiple feedwater heaters. The cycle

uses toluene as the working fluid due to the low temperature of the heat source.

Figure 1 – Plant Schematic

The boiler pressure is Pb = 260 kPa. The water from the geothermal well is at Tg = 180°C. The

plant rejects heat to the ambient at TC = 30°C. The fluid is extracted at state 3 from turbine 1 at

Pext,1 = 120 kPa and fraction of the flow f1 is fed to the open feedwater heater 1. The fluid is

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subsequently extracted at state 4 from turbine 2 at Pext,2 = 50 kPa and reheated. The fluid is

finally extracted at state 6 from turbine 3 at Pext,3 = 20 kPa and the fraction of the flow f2 is fed to

open feedwater heater 2. The remainder of the flow passes through turbine 4 to the condenser.

Other assumptions:

 Isentropic efficiencies of each turbine ηt,1 = 0.85, ηt,2 = 0.86, ηt,3 = 0.88, ηt,4 = 0.89,

 Isentropic efficiencies of each pump ηp,1 = 0.65, ηp,2 = 0.67, ηp,3 = 0.69, ηt,4 = 0.89,

 Saturated liquid at exit of condenser, and feedwater heater 1 and 2

 T2 = Thf,in - ∆Tb where ∆Tb is 15 K for baseline condition (code as a variable)

 T5 = Thf,in - ∆Trh where ∆Trh is 10 K for baseline condition (code as a variable)

 T8 = TC + ∆Tc where ∆Tc = 5 K for baseline condition (code as a variable)

 The rate at which heat is extracted from the geothermal source is 2.5 MW (this is the sum

of heat transfer to the boiler and the reheater).

 Neglect pressure loss in all heat exchangers

Part 1 – Baseline Analysis

1. Determine each state associated with the cycle, following numbering in Figure 1. Use the

ARRAY table functionality in EES and print an array table showing T, P, s, h, x for each

state.

2. Plot state points on T-s diagram for Toluene.

3. Determine the maximum theoretical efficiency of the cycle.

4. Determine the actual thermal efficiency of the cycle.

5. Determine the mass flow rate of toluene passing through the boiler in kg/s.

6. Determine the net power produced by the cycle in MW.

7. Determine the rate of heat transfer through the condenser in MW.

8. Determine the effectiveness of the boiler and the condenser.

9. If electricity is sold at a rate of 0.055 $/kWhr, what is the total value of electricity

produced over a 10 year period (neglecting time value of money)?

Part 2 – Economic Analysis and Optimization of Plant

The heat transfer surface area required for the boiler and condenser are directly related to their

effectiveness. Your company has tested heat exchangers operating with toluene and developed

the following correlation for the surface area (A) as a function of the effectiveness (ε) and

toluene mass flow rate:

 ln 1HXA K m      

Where KHX = 170 m 2-s/kg is an empirical constant that is appropriate for both the boiler and

condenser. The cost of these heat exchangers scales linearly with their surface area according to:

HX Cost C A 

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Where CHX = 50 $/m 2 is the cost coefficient that is appropriate for both the boiler and condenser.

10. Using your answer from part 8, determine the area and cost for the baseline boiler and

condenser.

11. You have estimated that the capital cost of the balance of the plant is Costmech = $500 ×

103. What is the net profit that this plant would be made by building and operating the

plant (neglecting the time value of money)?

12. Plot the profit over a ten year period as a function of the approach temperature difference

for the boiler from 2 K < ∆Tb < 30 K and determine if an optimal temperature exists.

13. You are given freedom to vary ∆Tb and ∆Tc from

2 K to 30 K. Determine a set of

approach temperatures that maximizes plant profit over a ten year period.

Part 3 – Second Law Analysis of Plant

14. At baseline conditions, determine the rate of exergy destruction within the plant.

15. Plot the rate of exergy destruction, and boiler area as a function of the approach

temperature difference for the boiler from 2 K < ∆Tb < 30 K and determine if an optimal

temperature exists.

16. You are given freedom to vary ∆Tb and ∆Tc from

2 K to 30 K. Determine a set of

approach temperatures that minimizes exergy destruction.

SUBMISSION INSTRUCTIONS:

General:

 A cover sheet with names, email, date of submission and project title information.

 An executive summary limited to 500 words (double spaced, 12 pt. Times New Roman font with 1-inch margin). The narrative should be used to summarize your final results

and include detailed comments on the parametric trends observed in Parts 2 and 3.

Failure to discuss your results in a meaningful way will reduce your overall grade.

As Appendices:

Part 1

 Printout of EES array table of state point thermodynamic properties (T, P, h, s, x) for final

design results. You must use state points indicated in Fig. 1

 T-s diagram with state points located and labeled. You must use state points in Fig. 1.

 Summary sheet with numerical answers for #3-9 including proper units.

 Printout of EES solution window showing final results. All answers highlighted and no

unit errors detected.

 Printout of well commented EES code (equations window)

Part 2

 Summary of numerical answers for #10 and 11 including proper units.

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 Plots for #12 and #13 with well labeled axes, legends, etc., including units. (Plot trends

and optimized results should be discussed in narrative, above).

 Printout of well commented EES code (highlight changes from Part 1)

Part 3

 Summary of numerical answer for #14 a proper units.

 Plots for #15 and #16 with well labeled axes, legends, etc., including units (Plot trends

and optimized results should be discussed in narrative, above).

 Printout of well commented EES code (highlight changes from Part 1 and 2)

Note that completion of an item does not automatically result in a maximum score for

that item. For example, a number of things (accuracy, conciseness, thoroughness,

organization, neatness, completeness, communication, professionalism, relevance and

usefulness) contribute to the point value ultimately assigned.