The Rankine Cycle
Consider the Bull Run Fossil Plant as a simple, Rankine Cycle, thermal plant: Water is heated to steam in a boiler using coal. The steam then spins a turbine which is linked to a generator to produce power. The steam is then condensed back into water in a cooling tower (condenser) before being pumped back to the boiler.
According to the TVA website, and wikipedia, the boiler here operates at 3650 psig and 1000° F. For this calculation, assume the condenser pressure is 2.9 psig, the turbine has an isentropic efficiency of 86%, the pump is adiabatic and isentropic (reasonable for steady flow, reversible process in incompressible fluids) and that the water is saturated liquid at the pump inlet. The power output for the plant is 950 MW. By making some additional assumptions such as negligible pressure drop or heat loss through process piping, the total efficiency of the plant can now be calculated, as can the steam flow rate and coal consumption. To find this geocache you will need to work through these calculations using the guide below.
Calculations
Step 1: Thermal Properties Table
At each point in the Rankine cycle, the working fluid is at a different state which can be expressed by its pressure, temperature and phase.
| State | Temperature T [F] | Pressure P [psig] | Phase | Specific Enthalpy h [BTU/lbm] | Specific Entropy s [BTU/lbm/R] |
|---|---|---|---|---|---|
| 1 | 2.9 | Saturated liquid | |||
| 2 | 3650 | ||||
| 3 | 1000 | 3650 | |||
| 4 | 2.9 | ||||
| 4S* | 2.9 |
To complete this calculation you will need a little understanding of how to determine the properties of steam, As you proceed through the calculations, fill out the table above as needed to keep tabs on the properties at each state. In order to arrive at a consistent result, use the calculators from the Department of Energy website to compute state properties for the steam (Note: You could use your own sourced steam tables, but may end up with slightly different values depending on the source). You will also want to familiarize yourself with phase diagrams, specifically the T-S diagram.
Step 2: Pump States
Look up the specific enthalpy and specific volume for state 1. h1= BTU/lbm
v1= Ft^3/lbm
Calculate the specific work of the pump assuming kinetic energy and potential energy effects are negligible (Be careful about unit conversion here) . wpump= BTU/lbm
Knowing the work of the pump and h1, calculate the specific enthalpy at state 2. h2= BTU/lbm
Step 3: Ideal Turbine States
An ideal turbine maintains constant entropy, thus by looking up the specific entropy at State 3, you can find out the specific entropy at State 4S. s3 = s4S = BTU/lbm/R
Knowing the pressure at 4S, check the saturation properties at this pressure and note that it is in the saturation curve. Then calculate the quality (x) of the steam at State 4S, x4S= .
Now that the quality of state 4S is known, the specific enthalpy can be calculated, h4S= .
Step 4: Real Turbine State
Since the real turbine has an 86% isentropic efficiency, the specific enthalpy of the steam at the turbines exit can now be computed realizing that the work output of the turbine is simply the difference between the specific enthalpy before and after: h4= .
With the specific enthalpy and pressure of state 4 known, the steam properties can be determined. Determine what phase the steam exiting the turbine is in, and what the temperature is: T4= .
Note that at this point, if the steam is in the saturation curve, you could also compute the quality now. This is important to know since turbines last longer if the steam coming out of them is higher quality since there is less water condensing on the blades.
Step 5: Net efficiency
With the specific enthalpy known at each state, the net efficiency of the plant can be computed and is equal to the specific work output of the turbine minus the specific work input of the pump divided by the specific heat input to the boiler. Yeesh, that's a lot of specifics! Net efficiency NET= %.
Step 6: Steam/water flow rate
Based on a power output of the plant of 950MW, and assuming no generator efficiency losses the mass flow rate through the closed loop system can be calculated. ṁ= klb/hr. (watch unit conversions here).
Step 7: Required Coal
Assuming that the coal being used has an energy density of 10300 BTU/lb, and the boiler efficiency is 88%, compute the amount of coal required per day to maintain 950MW power output: Coal Consumption = Short-Ton/day.
Note that the wikipedia page states that Bull Run Fossil Plant consumes 7,300 tons/day. How does this differ from the value computed above and what does this say about the actual plant versus our model? As you can see, we've only touched the tip of the ice-berg when it comes to designing a power plant.
Getting the geocache coordinates
So now that you've beaten your brain over BTUs and thrashed the thermodynamics to shreds, it is time to get down to the serious business of finding the geocache, GC59T9E. Use your answers above to fill out the table below. The coords should pop right out.
| 1st digit of NET efficiency | |
| 3rd digit of s3 | |
| 1st two digits to the right of the decimal for v1 | |
| 2nd digit of NET efficiency | |
| 2nd digit of h4s | |
| 2nd digit of wpump + 4th digit of h1 | |
| 1st digit of ṁ | |
| 2nd digit of s3 | |
| 2nd digit of h2 | |
| 2nd digit of ṁ times the 2nd digit of consumption of coal | |
| 2nd digit of consumption of coal + 3rd digit of h4S | |
| 3rd digit of h4 plus 2 | |
| 1st digit of h4s |
No comments:
Post a Comment