Question: the principle of geothermal power generation system is to use...
Question details
The principle of geothermal power generation system is to use heat from hot water extracted out of the ground and drive a turbine that converts the energy to electrical power for transmission to consumers (Figure 1). Design of geothermal power plants depends on the among of energy in the heat source. For low temperature geothermal well, a binary cycle power plant is used.
Figure 1: Schematic of a geothermal system
A binary cycle geothermal power plant uses heat exchanger to extract heat from lower temperature ground water to a turbine system which uses an organic compound with a low boiling point (Figure 2). The working fluid is vaporized in the heat exchanger and drives the turbine. The ground water after heat exchanger is then injected back into the ground to be reheated. The water and the working fluid are kept separated during the whole process, so there are little or no air emissions. The cooling tower component is to cool down the working fluid so it can be re-used in another thermal cycle.
Figure 2: Schematic of a binary geothermal system
Binary cycle turbine and cooling tower are commercially available systems so it is not necessary to design them. However, the heat extraction part is specific to individual geothermal wells. You are the system engineer responsible for designing heat extraction part of the system. More specifically, a system to pump ground water out to an heat exchanger as shown in Figure 3 is required to be designed.
Figure 3: Schematic of the ground water exchange system
If geothermal heat source has the following characteristics:
- Temperature of water at heat source = 90 ^{o}C
- Depth where hot water reservoir is tapped to (h_{1}) = 13 m
- Depth where cooled water injected point (h_{2}) = 10 m
- Distance between production well and injection well pipe locations (L_{1}) = 1 km
You are required to use one of the SSH pumps. The pump characteristics are given in Figure 4.
Figure 4: Pump characteristics curves
Which system parameter set would you recommend?
Formulae applicable to this question:
Pressure drop in a pipe is given by:
$\mathrm{\Delta}P={P}_{1}-{P}_{2}=\frac{128\mu LQ}{\pi {D}^{4}}$
where
- P_{1} = upstream fluid pressure (N/m^{2})
- P_{2} = downstream fluid pressure (N/m^{2})
- L = length of pipe section (m)
- Q = fluid mass flowrate (kg/s)
- $\rho $ = circle constant = 3.14159
- m = dynamic viscosity of water at operating temperature = 0.29
- D = internal diameter of the pipe
Pressure drop through pipe bend is given by:
$\mathrm{\Delta}P={P}_{1}-{P}_{2}=\frac{1}{2}{f}_{s}\rho {v}^{2}\frac{\pi {R}_{b}}{D}\frac{\theta}{{180}^{{}^{o}}}+\frac{1}{2}{k}_{b}\rho {v}^{2}$
where P_{1}, P_{2}, D and $\pi $ have the same meaning as before.
- R_{b} = bend radius
- v = velocity of fluid flow at the centre line of the bend.
- $\rho $ = the density of water (very heavily salted mineral water) (= 1,029 kg/m^{3})
- $\theta $ = the angle of circular segment of the bend sustained from the centre of bend in degrees
The pipe flow factor k_{b} depends on the angle of bend. To simplify the design, you have standardised to 90 degrees bends. The value of k_{b} can be interpolated from the following table:
R_{b}/D |
0.5 |
0.6 |
0.7 |
0.8 |
1.0 |
2.0 |
3.0 |
4.0 |
5.0 |
6.0 |
8.0 |
10.0 |
k_{b} |
0.85 |
0.68 |
0.56 |
0.48 |
0.39 |
0.34 |
0.18 |
0.16 |
0.15 |
0.14 |
0.13 |
0.13 |
Note: For R_{b}/D > 10.0, k_{b} = constant = 0.13.
The coefficient of pipe bend friction ${f}_{s}$ depends on Reynolds number Re. Reynolds number is given by:
$Re=\frac{\rho vD}{\mu}$
If Re < 2300, then it is laminar flow,
${f}_{s}=\frac{64}{Re}$
If Re > 4000, then it is turbulent flow,
$\frac{1}{\sqrt{{f}_{s}}}=-2{\mathrm{log}}_{10}(\frac{\u03f5}{3.7D}+\frac{2.51}{Re\sqrt{{f}_{s}}})$
Stainless steel will be used throughout the system. The pipe material roughness factor $\u03f5$ = 0.0015.
If 2300 < Re < 4000, then it is critical flow. Interpolate between laminar and turbulent flows using Re value.
The heat extracted H_{w} through the heat exchanger can be computed by the following relationship:
${H}_{w}=Q\rho {c}_{w}\mathrm{\Delta}{T}_{w}$
where
- H_{w} = Heat to be extracted by your system (= 50,000 W)
- Q = Volume of water flowing into the room coil (m^{3}/s)
- c_{w} = specific heat of water (J/kg/^{o}C) = 4,184 J/kg/^{o}C
- $\mathrm{\Delta}T={T}_{in}-{T}_{out}$
- $\rho $ = density of water as before
You can assume that the pressure drop across the heat exchanger is included in the 1 km long horizontal pipe line pressure drop.
Which system parameter set would you recommend?