Case study:

You are tasked with planning and designing a $50$ MW geothermal power plant.

A schematic of a geothermal plant is shown in Figure $1.$ A geothermal power plant uses the thermal energy of the hot rocks below the earth's surface to heat the working fluid. Boreholes are drilled into the earth's surface to reach the hot rocks. Next, a suitable working fluid is pumped through the boreholes and is heated at high pressure by a heat exchanger $("$boiler$")$ near the hot rocks below the ground level. Finally, the heated working fluid is passed through a power cycle of choice to generate electricity.

Figure $1$: Geothermal powe, pur.

The ambient temperature at the ground level, T$\_($C$)$ is $30^($@$)$C$.$ The temperature beneath the surface

increases at a rate of $25^($@$)$C$//$km of depth into the lithosphere. You would like the maximum

temperature of your cycle, T$\_($H$),$ to be at least $200^($@$)$C$.$

a$.$ Determine the depth, H $,$ in km $,$ of drilling needed to reach a T$\_($H$)$ of $200^($@$)$C$.(2$pts$)$

b$.$ Calculate the maximum thermal efficiency that your power plant can achieve. $(3$ pts$)$

You have decided to use a Rankine cycle to design the power cycle for your geothermal plant.

Your next task will be to make a decision on the working fluid for the power cycle. Three fluids

are being considered namely:

Water

Ammonia

R$22$

For each fluid, the boiler's operating pressure should be such that the vapor quality at the turbine

exit is at least $88\%.$ Assume the turbine and pump are isentropic$,$ and the working fluid is heated

to a temperature of T$\_($H$)$ at the boiler exit.

c$.$ Determine the operating pressure in the boiler of the cycle for each fluid $(10$ pts $)$

d$.$ Determine the state of the fluid at the turbine inlet and draw the T$-$s diagram of the power

cycle for each of the working fluids. $(5$ pts $)$

e$.$ Calculate the thermal efficiencies provided by each fluid $(20$ pts $)$

f$.$ Evaluate the mass of working fluid required for each fluid to generate a power of $50$ MW $.$

$(5$ pts$)$

g$.$ Compare the densities of the working fluids at the turbine inlet and outlet and comment on

how the densities and total volume of the working fluids at these locations may affect your

decision in selecting a working fluid. $(5$ pts $)$

ALREADY SOLVED A and B$,$ Need C through end, We're supposed to use Thermostate.github.io program to get all of the required info for the questions