الدورة الثنائية

يُستخرج السائل الساخن الموجود في الخزان الحراري الأرضي (أو السائل الجيولوجي) إلى السطح عبر بئر ، بمساعدة مضخة عند الضرورة. على السطح، ينقل السائل الجيولوجي الساخن جزءًا من حرارته إلى الدورة الثانوية عبر مبادل حراري ، مما يؤدي إلى تبريده. ثم يُعاد حقن السائل الجيولوجي البارد في الخزان الحراري الأرضي عبر بئر منفصل، حيث يُعاد تسخينه. تُعتبر الدورة الأولية دورة "مفتوحة". ^{[ 1 ]}

Cold high-pressure working fluid is heated and vapourised in a heat exchanger by the hot geofluid. The hot high-pressure vapour is expanded in a turbine before being cooled and condensed in a condenser. To close the loop, the cold low-pressure liquid is repressurised via a feed pump. The secondary cycle is a closed cycle.

The two main secondary cycle configurations are organic Rankine cycles (ORC) or Kalina cycles, the main difference being the choice of working fluid; an organic fluid (commonly a hydrocarbon or refrigerant) or a water-ammonia mixture respectively.^[1]

The working fluid is evaporated at two different pressure levels, and thus temperatures. This improves efficiency by reducing exergetic losses in the primary heat exchanger by maintaining a closer match between the geofluid cooling curve and the working fluid heating curve.^[5]

Two secondary cycles are operated in tandem, each with a separate working fluid and boiling point. This improves efficiency by reducing the exergetic losses of the heat introduction process, by ensuring a closer match between the geofluid cooling curve and the working fluids' heating curves.^[6]

${\displaystyle {\dot {W}}_{\text{turbine}}={\dot {m}}_{\text{wf}}*\eta _{\text{turbine}}*(h_{1}-h_{\text{2s}})}$

• ${\displaystyle {\dot {W}}_{\text{turbine}}}$ is the rate of work done by the turbine, in kW
• ${\displaystyle {\dot {m}}_{\text{wf}}}$ is the mass flow rate of working fluid, in kg/s
• ${\displaystyle \eta _{\text{turbine}}}$ is the turbine efficiency, non-dimensional
• ${\displaystyle h_{1}}$ is the specific enthalpy of the working fluid at the turbine inlet, in kJ/kg
• ${\displaystyle h_{\text{2s}}}$ is the specific enthalpy of the working fluid at the turbine outlet, assuming isentropic expansion in the turbine, in kJ/kg

The equation below can be used to determine the condenser duty and mass flow rate of coolant required.

${\displaystyle {\dot {Q}}_{\text{condenser}}={\dot {m}}_{\text{wf}}*(h_{2}-h_{3})={\dot {m}}_{\text{coolant}}*(h_{y}-h_{x})}$

• ${\displaystyle {\dot {Q}}_{\text{condenser}}}$ is the rate of heat removed from the working fluid in the condenser, in kW
• ${\displaystyle h_{2}}$ and ${\displaystyle h_{3}}$ are the specific enthalpy of the working fluid at the condenser inlet and outlet respectively, in kJ/kg
• ${\displaystyle {\dot {m}}_{\text{coolant}}}$ is the mass flow rate of coolant, in kg/s
• ${\displaystyle h_{x}}$ and ${\displaystyle h_{y}}$ are the specific enthalpy of coolant at the condenser inlet and outlet respectively, in kJ/kg

${\displaystyle {\dot {W}}_{\text{pump}}={\dot {m}}_{\text{wf}}*(h_{\text{4s}}-h_{3})/\eta _{\text{pump}}}$

• ${\displaystyle {\dot {W}}_{\text{pump}}}$ is the rate of work done by the pump to repressurise the working fluid, in kW
• ${\displaystyle h_{\text{4s}}}$ is the specific enthalpy of the working fluid at the feed pump outlet, assuming isentropic compression, in kJ/kg
• ${\displaystyle h_{3}}$ is the specific enthalpy of the working fluid at the feed pump inlet, in kJ/kg
• ${\displaystyle \eta _{\text{pump}}}$ is the pump efficiency, non-dimensional

The equation below can be used to determine the primary heat exchanger duty and mass flow rate of geofluid required.

${\displaystyle {\dot {Q}}_{\text{PHX}}={\dot {m}}_{\text{wf}}*(h_{1}-h_{4})={\dot {m}}_{\text{geofluid}}*(h_{a}-h_{c})}$

• ${\displaystyle {\dot {Q}}_{\text{PHX}}}$ is the rate of heat added to the working fluid within the primary heat exchanger, kW
• ${\displaystyle h_{4}}$ is the specific enthalpy of the working fluid at the primary heat exchanger inlet, in kJ/kg
• ${\displaystyle {\dot {m}}_{\text{geofluid}}}$ is the mass flow rate of geofluid, in kg/s
• ${\displaystyle h_{a}}$ and ${\displaystyle h_{c}}$ are the specific enthalpy of the geofluid at the primary heat exchanger inlet and outlet respectively, in kJ/kg

The first law efficiency (from the first law of thermodynamics) is a measure of the conversion of the heat provided to the cycle into useful work. When accounting for real life losses and inefficiencies, real binary cycle geothermal plants have a first law efficiency of between 10 and 13%.^[1]

${\displaystyle \eta _{\text{I}}^{\text{th}}={\frac {{\dot {W}}_{\text{net}}}{{\dot {Q}}_{\text{PHE}}}}={\frac {{\dot {W}}_{\text{turbine}}-{\dot {W}}_{\text{pump}}}{{\dot {Q}}_{\text{PHE}}}}}$

The second law efficiency (from the second law of thermodynamics) is a measure of the utilisation of the ideally maximum work available and conversion into useful work.^[1]

${\displaystyle \eta _{\text{II}}^{\text{util}}={\frac {{\dot {W}}_{\text{net}}}{{\dot {E}}_{\text{geofluid}}}}={\frac {{\dot {W}}_{\text{turbine}}-{\dot {W}}_{\text{pump}}}{{\dot {m}}_{\text{geofluid}}*[(h_{a}-h_{0})-T_{0}*(s_{a}-s_{0})]}}}$

• ${\displaystyle {\dot {E}}_{\text{geofluid}}}$ is the exergy rate of geofluid, in kW.
• ${\displaystyle h_{0}}$, ${\displaystyle s_{0}}$ and ${\displaystyle T_{0}}$ are the specific enthalpy, in kJ/kg, the specific entropy, in kJ/kg/K and the absolute temperature, in K, of the geofluid at the local reference condition. This could be local ambient, wet-bulb or reinjection conditions.

• Olkaria III, Kenya^[8]
• Mammoth Lakes, California, United States^[9]
• Steamboat Springs (Nevada), United States^[10]
• Te Huka Power Station, New Zealand^[11]
• Kirchstockach (Munich), Germany^[12]
• Traunreut, Germany^[12]

• Husavik Power station
• Geothermie Unterhaching