GENG4405 2019 - Assignment 2, Part 3
Part 3 of the Assignment: What is optimal pressure?
As previously mentioned, the steam enters the separator as a two-phase fluid. After separation,
the saturated liquid is reinjected to the reservoir and the saturated vapor is run through a turbine
and then condensed.
As you may remember, the power output of a turbine is dependent on the enthalpy change of the
steam running through the turbine and the mass flowrate of the steam
Since in the case of our geothermal reservoir the steam comes in as a saturated vapor, its
enthalpy is a function of the saturation pressure. The enthalpy leaving the turbine is a function of
the condenser pressure (which is in turn a function of the cooling water temperature and
temperature difference across the condenser).
The mass flowrate is also connected to the pressure. The reservoir itself is at near hydrostatic
pressure (and the pressure in the reservoir will likely decrease over time if the water is taken out
faster than it can recharge). Hydrostatic pressure would imply that under no-flow the water level
in the well would just reach the surface, where it would be at atmospheric pressure. To get water
to flow, a pump is placed down in the well to boost the pressure in the region of the well above
the pump. By controlling the pressure in the separator, the overall pressure drop between the
reservoir and the turbine inlet can be adjusted. This controls the mass flowrate of water entering
the well.
Therefore, the power output of the turbine can be optimized by adjusting the pressure of the
steam coming in (which will affect both the flowrate and the enthalpy change).
A 1700-meter-deep well has been drilled into the reservoir. You may assume hydrostatic
pressure. I am making the assumption that you can calculate/estimate the pressure; be sure to
state your own assumptions. The water in the reservoir may be assumed to be saturated liquid.
For our purposes the process of bringing the geothermal fluid to the surface and introducing it to
the separator may be approximated as isenthalpic (another assumption). You may assume the
pressure in the condenser is 10 kPa. The turbine has an isentropic efficiency of 0.85.
Your team has been given the task of finding the pressure which will maximize the power output
of the turbine. A test has been conducted linking the flowrate in the well to the pressure of the
separator. That test data is included in this document. Steam tables will be provided on LMS.
Separator Pressure in MPa Mass Flowrate in kg/s
Suggestion: Create polynomial functions for flowrate as a function pressure as well as for the
enthalpy of saturated liquid water and the enthalpy and entropy of saturated water vapor. This
does not have to be done in MATLAB and is not a part of the assignment question.
Assignment Questions:
1. (5%) Write MATLAB code that calculates the enthalpy of the saturated liquid based on
your estimate for the water pressure at the bottom of the 1700 meter deep well. Then
uses that value for enthalpy to calculate both the quality of the steam in the separator as a
function of the separator pressure and the mass flowrate of water entering the separator as
a function of separator pressure.
2. (5%) Write MATLAB code that calculates the mass flowrate of steam into the turbine
(the quality of the steam in the separator multiplied by the total mass flowrate of fluid)
3. (5%) Write MATLAB code that calculates the specific enthalpy change in the turbine and
multiplies that value times the mass flowrate of steam entering the turbine to get the total
power output of the turbine.
4. (10%) Using one of the optimization methods discussed in the lectures, write MATLAB
code to maximize the power output of the turbine by varying the pressure in the
separator. In your report be sure to state what the maximum power output was found to
be and the corresponding pressure as well as some statement about the accuracy/tolerance
used.

1. Geothermal fluid, approximated as pure water, enters the well from the reservoir as
(approximately) a saturated liquid at hydrostatic pressure.
2. The water moves up the well, through the surface pipework and into the separator.
This is approximated as an isenthalpic expansion to the pressure of the separator.
3. The fluid splits into two phases and the saturated vapor is sent to the turbine.
4. The saturated vapor passes through the turbine and exits at the condenser pressure.
Had it expanded isentropically, it would have reached point 4s, instead it reaches
point 4. The enthalpy change between points 3 and 4 is 85% (the isentropic
efficiency) of the enthalpy change between points 3 and 4s.

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