Design Rankine Cycle: $40K Budget, Calculate Payback Time

[emilynb]

Homework Statement

I have a project for a class of mine that asks me to design a rankine cycle to produce electricity from a lake using temperature differences between the water and the atmosphere.

I have a budget that I must stick with ($40,000), a defined effeciency for the pump (50%) and turbine (80%), obviously I am restrained by the temperatures of the water and air at the lake I use, and I am also given the thermal resistance for the water and air side of the heat exchanger (0.01 m²K/W for the water side and 0.05 m²K/W for the air side). Then I must calculate the payback time assuming that I can sell the electricity at $0.03/kWh. My goal is to produce max power output.

Any suggestions on where/how/what numbers to start with the calculations would be greatly appreciated. Also, where would be a good place to look to determine approximately how much it would cost to build such a machine?

Homework Equations

Pump (1-2) - isentropic compression: -w_in = v(P₂ - P₁)

Boiler (2-3) - constant pressure heat addition: q_in = h₃ - h₂

Turbine (3-4) - Isentropic Expansion: w_out = h₃ - h₄

Condenser (4-1) - constant pressure heat rejection: q_out = h₄ - h₁

The Attempt at a Solution

I have the machine set up, but I am having troubles figuring out how to get started with my calculations in order to make the machine be reasonable/justifiable and workable. So far, what I have is pumping water up from a lake, using it to boil the working fluid in a boiler, expanding it through a turbine which will power the generator to produce electricity, then going back through a condenser and starting all over again. For the working fluid, I am considering using organic fluids - propane, ammonia, R-123, etc.

 

[Q_Goest]

Don't know this is going to help much because the problem is very loosely defined. Do you have much time to work on this project?

If I were doing this, I'd want to use a thermophysical properties database for the working fluid. NIST REFPROP works great, and probably has all the fluids you might want to use. Check it out here: http://www.nist.gov/srd/nist23.htm

You might ask your prof to see if there's a copy you can use. Many of the colleges have them.

If you can't use this kind of database, you'll certainly need to find tables. Look in your library for data on the thermophysical properties of the fluids you're interested in using.

Break the system down into 4 parts as you show. Work in, Work out, Heat in, Heat out.

Do you know how to determine these, including the efficiency factors? I see you've written the equations, but those for the pump and turbine don't include efficiency. Do you know how to do that?

Set up a spreadsheet, computer program, or just a chart with enthalpy at the various points. You need to be able to calculate the change in enthalpy due to heat or work added/removed. You also need to determine the two pressures you'd like to work between. That pretty much sets up the entire cycle. You also need the ambient temperatures though (water and air) to determine if it's reasonable to gain/reject heat at the various points in the cycle.

Regarding the thermal resistance, that just forces the size (surface area) of your heat exchangers. Determine that after you've got the basic cycle down. Neglect to start.

Regarding cost, I'm surprised they'd ask that, but they often do. The right way to do it is do a cost estimate. Spec equipment, get quotes, determine costs for labor, non-recurring engineering, etc... not easy. When I did these in school, I made a lot of those costs up because you really can't be expected to obtain good costs as a student.