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Geothermal Resource Assessment & Single-Flash Steam Cycles

60 min Geothermal Energy & Organic Rankine Cycles

Geothermal Resource Assessment & Single-Flash Steam Cycles

Geothermal energy taps the Earth's internal heat flux (~0.065 W/m² globally, with volcanic provinces exceeding 1 W/m²). High-enthalpy hydrothermal resources (>150°C) drive steam turbines via flash or dry-steam cycles; low-to-medium enthalpy resources (60–150°C) require Organic Rankine Cycle (ORC) technology. The second law of thermodynamics — specifically exergy analysis — is the essential tool for evaluating resource utilisation.

1. Resource Classification

Class	Temperature	Technology	Examples
High enthalpy	>200°C	Dry steam / Flash	The Geysers, Larderello
Medium enthalpy	100–200°C	Single/double flash, binary ORC	Iceland, New Zealand
Low enthalpy	60–100°C	Binary ORC only	Germany, USA Basin-Range
Very low	<60°C	Direct heat only	District heating, aquaculture

2. Single-Flash Cycle Analysis

Brine enters the separator at temperature $T_{geo}$ and is throttled (isenthalpic flash) to separator pressure $P_{sep}$, producing a steam-brine mixture. Steam fraction (quality) after flashing:

$$x = \frac{h_f(T_{geo}) - h_f(T_{sep})}{h_{fg}(T_{sep})}$$

Turbine work per kg of brine (steam only drives turbine):

$$w_{turb} = x \cdot \eta_t (h_g(T_{sep}) - h_s(P_{cond}))$$

where $\eta_t \approx 0.80{-}0.85$ is isentropic turbine efficiency. Second-law (exergy) efficiency:

$$\varepsilon = \frac{w_{turb}}{e_{flow}(T_{geo})} \quad \text{where} \quad e_{flow} = (h-h_0) - T_0(s-s_0)$$

$e_{flow}$ is the specific flow exergy at reservoir conditions relative to the dead state $(T_0, P_0) = (25°\text{C}, 1\text{ atm})$.

3. Optimal Flash Pressure

Maximising turbine work with respect to separator pressure gives the optimal flash temperature:

$$T_{sep,opt} \approx \frac{T_{geo} + T_{cond}}{2}$$

This is an approximate result for single-flash; double-flash cycles with two separator stages capture an additional 15–20% work. The Wairakei power station (New Zealand) uses a double-flash configuration on 170°C brine to achieve ~12% first-law efficiency.

4. Brine Reinjection & Sustainability

After steam separation, the residual brine (and condensate) is reinjected into the geothermal reservoir to maintain pressure and prevent subsidence. Reinjection temperature must be above $T_{scaling} \approx 50{-}80°$C to prevent silica or calcite scaling in the wellbore and reservoir. Without reinjection, The Geysers (California) experienced a 40% decline in production from 2,000 MW (1987) to 725 MW (2015) due to resource depletion.

Worked Example — Single-Flash Cycle

$T_{geo} = 180°$C, $T_{sep} = 130°$C, $T_{cond} = 40°$C, $\eta_t = 0.82$. Using steam tables: $h_f(180°) = 762.6$ kJ/kg, $h_f(130°) = 546.4$ kJ/kg, $h_{fg}(130°) = 2174$ kJ/kg. $x = (762.6-546.4)/2174 = 0.0994$. $h_g(130°) = 2720.5$ kJ/kg. Isentropic expansion to 40°C condenser: $s_g(130°) = 6.990$ kJ/kg·K, $s_f(40°) = 0.5725$, $s_{fg}(40°) = 7.686$. $x_{turb} = (6.990-0.5725)/7.686 = 0.835$. $h_s = 167.5 + 0.835 \times 2431 = 167.5 + 2030 = 2197$ kJ/kg. $w = 0.0994 \times 0.82(2720.5-2197) = 0.0994 \times 429 = 42.6$ kJ/kg brine. ✓

Geothermal Flash Cycle Analyser

Brine temp T_geo (°C): 180

Condenser temp T_cond (°C): 40

Turbine isentropic eff (%): 82

Carnot η =?%

ORC/flash η ≈?%

Specific work =?kJ/kg brine

Efficiency ratio =?(actual/Carnot)

Practice Problems

1. A geothermal well produces brine at 200°C. Compute the optimal single-flash separator temperature and the resulting steam quality (use steam tables). Compare specific work output to a flash at 150°C separator temperature.

2. Compute the specific flow exergy of brine at 180°C relative to a dead state of 25°C, assuming liquid water ($h_{180} = 762.6$ kJ/kg, $s_{180} = 2.139$ kJ/kg·K; $h_{25} = 104.9$, $s_{25} = 0.3672$). Then compute the exergetic efficiency of the worked example above.

3. Explain why the optimal separator temperature for single-flash is approximately $(T_{geo}+T_{cond})/2$. Derive this result by differentiating specific work with respect to separator temperature and applying the approximation $dh_{fg}/dT \approx -\text{const}$.

Binary ORC Working Fluids & Exergy Analysis

Geothermal Resource Assessment & Single-Flash Steam Cycles