Thermodynamic Concepts Efficiencies of alternative secondary cycles

Organic Rankine Cycle (is working with an organic compound like isopentan)

The Rankine-cycle (a thermodynamic and cyclic process which is called after the Scottish Ingenieur William John Macquorn Rankine) The four changes of states The Rankine-Cycle is being divided into four parts. One is starting with the hot steam which flows from the steamer towards the turbine. 1 to 2: adiabatic expansion of the steam in the turbine (ideal case: isentropic process) 2 to 3: isobatic und isothermal condensation of the steam which is cooled by cold water 3 to 4: adiabatic (ideal: isentropic) increase of pression by a pump. 4 to 1: isobatic delivery of heat in the steamer, so the water is being heatet up to the boiling point, then evaporates and finally becomes overheated.

The Kalina-process In difference to ORC: a two compound mixture of ammonia and water is used in the Kalina-process. Optimal fitting of the working medium ammonia and water on the thermodynamic properties of the heat source. In opposition to the ORC-process no isothermal evaporation or isothermal condensation takes place by the use of the ideal two components mixture. Thus the enclosed area of the cyclic process is becoming larger and repre- sents the useful work. Therefore the efficiency is improved.

Advantages and disadvantages of the Kalina-process Advantages of the Kalina-Process: Non-isothermal evaporation and condensation, therefore approximation to the ideal line of heat source and heat sink, smaller losses than the ORC- process. Improvement of thermal efficiency by enlargement of the enclosed area from the cyclic process Water of 90°C may already be used as a heat source to generate electric energy. To reach this conditions, it is not needed to dig very deep into the solid rock. Disadvantages: Solutions of ammonia tend to be corrosive against common steel. Large areas for heat transitions are necessary.

Geothermal power plants with a Kalina cycle Geothermal power plant at Húsavík (Iceland)

Azeotropic mixtures are boiling isothermally like pure compounds their boiling point stays in a higher or deeper point than the boiling point of the pure compounds. Example Water-Ethanol

The mixture Water-Ammonia has no azeotropic point

The ideal heat pump the ideal cogeneration engine The ideal heat pump or cogeneration engine is exploiting the complete efficiency of Carnot. The Carnot process consists of two isothermal and two iso-entropic changes of states, which form a rectangle in the T-S-diagram, which represents the optimum work. The Carnot process is working with an ideal gas, which doesn‘t know neither a condensation nor an evaporation. The Carnot process is a purely theoretical process.

Carnot: an ideal cyclic process p-V-diagram vs T-S-diagram

Steam a real working medium Evaporation heat 2250 kJ/kg Entropy s in kJ/K)

Steam as a working medium in a power plant The rectangle of Carnot is cut off by the boiling line of water up to the critical point. Thus the amount of useful energy is diminishing by using steam instead of an ideal gas. Even the use of other real gases may only partially fulfil the ideal conditions of Carnot.

Lifetime of a geothermal power plant Lifetime of a geothermal power plant is limited by cooling the rock during the working period. This cooling is assumed to decrease the temperature of the rock by 30 K. A cylindrical volume with radius of 2 km and hight of 2 km is assumed to function as a heat collector, which cooles down 30 K through the technical lifetime.

Lifetime of a geothermal power plant Heat flow through the solid rock is around 0.07 W/m 2. This cannot avoid cooling because of heat discharge by geothermal use. A temperature decrease of about 30 K by an enclosed volume of 25 km 3 leads to a heat output of 1.5*10 15 kJ. Heat discharge of 1 GW leads to a lifetime of geothermal use of around 48 years.

Geothermal calculations I Enclosed volume for geothermal use: V=  r 2  h = km 3, (r = h = 2km) Heat content of the enclosed volume  Q = Cp  V  T = 1.5  kJ, Cp = 2  10 6 J/(m 3  K),  T = 30K Expected lifetime (undistorted case):  t =  Q/P = 48 years, P th = 1 GW

Geothermal calculations II Heat flow through solid rock becomes up to 27 times faster if cooling of the enclosed volume takes place. So the heat flow reaches around 1.88 W/m 2 by cooling of 30 K. Thermal diffusion leads to a 10 % larger enclosed volume, thus one obtains km 3 instead of km 3. Expected lifetime reaches now 56 years.

Geothermal calculations III Formulas: