ENERGY/EE 293B Final March 23 2020
180 minute open book exam, take-home
Answer all questions
 This is a take-home exam, and is subject to the Stanford Honor Code. You must work independently – the
answers you turn in must be completely your own work.
 Computers are allowed for calculation or reference look-up, but NOT for communication with other members of
the class (or anyone else).
 After the 3 hours of the exam are over, students are permitted an additional 30 minutes to scan or photograph
their manuscripts and upload to the Canvas website. Work on exam permitted from 08:30 until 11:30am.
Deadline for uploading is 12:00 noon.
 Please separate your answers to the three questions, and upload the files separately.
 If you encounter difficulties uploading to Canvas, just email your files to horne@stanford.edu
 If you have questions during the exam, you may phone the instructors:
o Roland Horne – (650)427-9049; Tony Kovscek – (650)619-9624; Jeff Rutherford (780)418-0939 (Canada)
or https://stanford.zoom.us/j/7868662979
Name: __________________________________ Honor Code observed: _______________________

1. Geothermal [40 points total]


2
Use the template Excel spreadsheet FInal2020Qu1-given.xlsm (which is based on Xsteam) to answer this question. Be
careful with the units of pressure – Xsteam uses bars, but this problem is posed in MPa. 0.1 MPa = 1.014 bar. Turn in the
completed Excel spreadsheet, together with any written workings you may have made on paper.
A hybrid steam/binary power plant uses the heat exchangers of the (downstream) binary plant in place of the condenser
of the (upstream) steam plant. The geothermal reservoir produces 500 kg/sec of saturated liquid water at 250°C, into
the separator at pressure p2 of 1 MPa. The steam turbine discharge is at a pressure p5 of 0.4 MPa. The steam turbine
discharge passes through the evaporator and preheater of the binary plant heat exchanger, and ultimately leaves as
liquid water at 65°C. Both steam and binary turbines have a (dry) efficiency of 0.85. Generator efficiencies are 1.00.
There is only a preheater and evaporator in the binary heat exchanger (no superheater). The binary working fluid is
pentane.
(a) In the Excel spreadsheet, fill the yellow boxes in the cycle table of the steam turbine, and use the results to
calculate the power output of the steam turbine, and the flow rate of steam into the steam turbine. [10 points]
(b) Make an energy balance of the heat exchanger (preheater and evaporator combined), to determine the flow
rate of the working fluid through the binary turbine. [5 points]
(c) Using the cycle table of the binary turbine, calculate the power output of the binary turbine. (The binary cycle
diagram is already completed for you – you don’t have to compute it.) [5 points]
(d) Compute the total geofluid consumption in kg per kWhr of electricity generated in the combined plant. (That is,
total kg of geofluid in, relative to total kWhr of electricity out.) [5 points]
(e) Compute the thermal efficiency of the combined plant. [5 points]
(f) Determine the optimal separator pressure (p2) that maximizes the electrical output of the combined plant.
(Consider the same flow rate of geothermal fluid at 500 kg/sec.) [10 points]
[Note: this kind of hybrid plant is deployed at Rotokawa in New Zealand, and Upper Mahiao in the Philippines. In
practice, the actual power plants are more complex than this simplified version, in that they also have binary turbines on
the water discharging from the separator.]