# Alternative trends in development of thermal power plant cycles

May 7, 2011, 1:08 am
 Topics:

Using environmental thermal energy conversion for electricity production

The major conventional (non-nuclear) technologies of producing thermal and electrical energy at power plants, especially at thermal power stations (TPS), are based on burning carbon-containing fuel. As a result, it is the power units that are the major polluters of the air, and the source of dust, carbon dioxide (CO2), sulfur dioxide (SO2), nitrogen oxides (NOx), and heat discharge. In the last 30 years it has become possible to reduce the discharge of dust, SO2 and NOx through employment of dust collectors and gas traps, and improvements in the technologies of combustion and of steam production. However, it has been very difficult to lower the discharge of CO2 and heat, as those are incorporated in the very principle of thermal power production. The ideal way of solving the problem would be to completely give up burning carbon-containing fuel, such as coal, petroleum products, and other power resources of organic nature.

Let us examine more closely the technology of producing electric power by way of using the heat of the environment, which is considered to be the most promising from the point of view of reducing fuel consumption. To begin with, let us review the basic principles of physics and physical chemistry that make the foundations of said technology.

1. It has been established that one kilomol (kmol) of any gas occupies, at normal conditions: (Pn = 101.325 kPa; Tn = 288.15K) the volume of Vmn= 22.414 m3/kmol.
2. Vaporization and condensation are all examples of the first-order phase transition. The first-order phase transition (PT1) is characterized by changing the substance state at the point of transition. In transition from condensed to gaseous state or vice versa there takes place an abrupt change in the volume per kilomol of the substance, which is a regular trend with all substances. This also results in the release (in condensation) or gain (in boiling) of the substance energy content.

Let us consider some numerical examples borrowed from reference sources. While in the liquid state a kilomol of water has a volume of 0.018 cubic meters (m3), in the gaseous state, under normal conditions, it has a volume of 22.414 m3, that is, 1245 times greater. While in the liquid state a kilomol of nitrogen has a volume of 0.035 m3, in the gaseous state, under normal conditions, it has a volume of 22.414 m3, that is, 640 times greater. While in the liquid state a kilomol of carbonic dioxide has a volume of 0.040 m3, in the gaseous state, under normal conditions, it has a volume of 22.414 m3, that is, 561 times greater. While in the liquid state a kilomol of propane has a volume of 0.076 m3, in the gaseous state, under normal conditions, it has a volume of 22.414 m3, that is, 294 times greater.

3. From the equation of state for the ideal gas it follows:

(PnVn)/Tn = (PtVt)/Tt (1)

where Pn, Tn, and Vn are, respectively, the normal pressure (101.3 kPa, which is the annual average value of the atmospheric pressure at the sea level), the normal temperature (15 degrees Celsius, which is the annual average value of the temperature at the sea level), and the volume of one kilomol of substance in gaseous state; and Pt, Tt, and Vt are, respectively, the pressure, temperature, and volume of one kilomol of gas, such as steam at the temperature t.

When a kilomol of liquid is vaporized and the resulting gas is subsequently heated in a closed space, the relative rise in pressure will be proportional to the relative rise in temperature.

(Pt/Pn) = (22.414/Vt) x (Tt/Tn) (2)

This technological step carried out in steam superheater makes it possible to attain sufficiently high pressure values.

4. The turbine is driven by a gas flow with kinetic energy of:

Ek = (mv2)/2 (3)



The S. Carnot - R. Clausius Theorem: The efficiency of a heat engine reversibly operating by the Carnot cycle does not depend on the nature of the machine's working medium, but only depends on the temperatures of the heater and the cooler.

The above equation (3) is universal and holds true for any moving body. "Individuality" of the gas in the present case is only, if at all, manifested by its density, that is, by its mass per unit of volume. However, the density of the gas, its compressibility being taken into consideration, will be determined by the pressure as well.

5. The stored potential energy of the gas (accumulated energy) in the present case is determined by the pressure difference between the steam/gas superheater and the condenser, where the pressure depends on completeness of gas condensation, that is, the first-order phase transition from gaseous state to liquid state.

The Rankine cycle is characterized by use of phase transition liquid – gas and gas – liquid for a considerable change of pressure in a cycle due to considerable change of working medium volume (See Eq.2). In the widely known and commonly used Rankine cycle the water in a steam generator boils, resulting in pressure increase. The resulting steam is additionally heated in the superheater which raises its pressure still higher. In the condenser of the turbine the steam is condensed, which results in a drop of the pressure down to vacuum. The resulting pressure difference between the superheater and the condenser makes the steam rush with tremendous speed from the zone of high pressure to the zone of low pressure, rotating the turbine and producing power. Any substance experiencing the first-order phase transition (PT1), and turning from liquid to gaseous state and back, will behave in the same manner. For this reason authors of publications in Journal Applied Thermal Engineering continue to name cycles with use of carbonic acid, propane or nitrogen as Rankine cycle.

From the point of view of raising efficiency and improving ecological parameters of a thermal power station (TPS), the cycle employing, as a working body, a low-boiling substance, such as hydrogen, helium, nitrogen, oxygen, neon, carbon dioxide and the like, looks most promising. For the cycles employing these gases, most attractive is the fact that they boil at low temperatures. This means that there is no necessity to supply heat from the burning fuel to the gas generator, the apparatus where the PT1 occurs and the liquid turns to gaseous state, since the environment itself can be used as the heat source. For instance, we all remember that nitrogen boils at a temperature of -196 °Celsius or 77 Kelvin.

Let us estimate how much fuel can potentially be saved when using nitrogen in place of water to produce electric power. Boiling the liquid nitrogen (i.e., the heat for gas generation) shall in this case, be provided by employing the heat of environment, while superheating of the nitrogen to obtain higher pressure values shall be provided by burning conventional hydrocarbon fuels.

Table 1. Estimation of fuel consumption to raise the steam pressure at the input to the turbine.
Stage of
steam-turbine cycle
Initial temperature
(°Celsius)
Final temperature
(°Celsius)
Power consumption
(kJ/kg)
Relative fuel
consumption
Heating condensate
to boiling temperature
30 310 1277 0.38
Water boiling 310 310 1324 0.40
Steam superheating 310 530 726 0.22
TOTAL     3327 1.00

Let us assume that a thermal power station operating by the Rankine cycle and using water as a working medium has an efficiency of 41%. In operation, the TPS consumes 0.405 kilograms (kg) of equivalent fuel to produce 1 kilowatt-hour (kWh) of power. The equivalent fuel does not exist in the nature, it is used for comparative calculations. A heating value (calorific value) of equivalent fuel is accepted to be 7000 kcal/kg, or 29308 kJ/kg, or 12605 BTU/lb. We can create Table 1 assuming that consumption of fuel, at individual stages of steam pressure rising at the input of the turbine, is proportional to, respectively, the rise in the enthalpy of water being heated to boiling temperature, the specific heat of evaporation, and the rise in the enthalpy of superheated steam.

Now, let us replace water by nitrogen. Let us assume the heat capacity of steam, being a three-atom gas, to be 4R, and the heat capacity of nitrogen, being a two-atom gas, to be (7/2)R = 3.5R. To heat steam from 30 °Celsius to 530 °Celsius it is necessary to spend 894 kilojoules/kilogram (kJ/kg). To heat nitrogen from 30 °Celsius to 530 °Celsius it is necessary to spend h = 894x3.5/4 = 782 kJ/kg.

As has been illustrated above, water on evaporation increased in volume 1245 times, while nitrogen increased in volume only 640 times. To provide compatible conditions for calculation we shall assume that in the Rankine cycle that a double-sized mass of nitrogen, as compared with that of water, is used.

Table 2. Estimation of fuel consumption to raise the pressure of nitrogen at the input to the turbine.
Stage of turbine
cycle
Initial temperature
(°Celsius)
Final temperature
(°Celsius)
Power consumption
(kJ/kg)
Comment
Nitrogen boiling -196 -196   Heat of environment
Heating gaseous nitrogen -196 30   Heat of environment
Gas superheating 30 530 2 × 782 = 1564

In this way, by replacing water in the Rankine cycle by nitrogen while burning hydrocarbon fuel to superheated gaseous nitrogen to 530 °Celsius, it becomes possible to reduce fuel consumption 2.1 times, thus consuming 0.19 kilograms (kg) of equivalent fuel to produce 1 kilowatt-hours (kWh) of electric power. It is reasonable that the discharge of hazardous gases into the atmosphere will also be reduced 2.1 times.

Let us see if the proposed technology of producing electric power is not contradictory to the principal laws of thermodynamics. The First Law of Thermodynamics defines the principle of equivalence between heat and work that is the energy conservation law. Therefore the equation η = W/Gf can be formulated as follows: efficiency of a heat engine (as well as that of a power station) cannot exceed one. By reducing the specific consumption of conventional fuel 2.1 times it becomes possible to raise the efficiency of a thermal power plant up to 82%. In fact, the efficiency will be somewhat lower due to consumption of some power produced to provide for the operation of compressors to liquefy the nitrogen.

The Second Law of Thermodynamics, as formulated by Clausius, reads: there is no possible process in the course of which heat would spontaneously get transferred from colder bodies to bodies with higher temperature. Let us suppose that nitrogen is used in the thermodynamic cycle as a working medium. Since the boiling point of liquefied nitrogen is -196 °Celsius (77 Kelvin [K]), and the environment temperature can reach down to -50 °Celsius (223 K), in full conformity with the Second Law of Thermodynamics the heat of the environment (hot body) will spontaneously flow to the liquid nitrogen (cold body) thus providing its boiling.

The Second Law of Thermodynamics for the reversible Carnot cycle heat engine can be recorded as follows:

eta = frac{Thot - Tcold}{Thot}=1-frac{Tcold}{Thot} (4)

where Thot is the highest temperature reached in the cycle (temperature of the heat addition), and Tcold is the lowest temperature (in our case, the boiling temperature of nitrogen).

Let us make quite simple calculations in which we, naturally, will use the thermodynamic temperature scale:

• for the Rankine cycle, where water is used as working medium, η = 1 - 303/803 = 0.62;
• for the cycle where nitrogen is used as working medium, η = 77/803 = 0.90.

The nitrogen cycle, when in the steam generator (gas generator) liquid nitrogen is boiled in place of water, looks much more preferable from the point of view of thermodynamic efficiency. As we can see, the proposed technology of producing electric power does not contradict either the First or the Second Law of Thermodynamics.

The described technology of using environmental heat to make the working body boil has already been used for more than twenty years in the so-called thermocompressors (thermal pumps). These devices provide heat and hot water to houses and industrial buildings, drawing heat from the environment.

In April 2004 new data appeared dealing with employment of low-boiling substances as working media in producing electric power. The propane cycle makes it possible to utilize the heat of discharge flue gases by a conventional heat power station converting the heat into electric power.

In 2006 a solar energy powered Rankine cycle using supercritical carbon dioxide (CO2) for combined production of electricity and thermal energy was proposed. The proposed system consists of evacuated solar collectors, power-generating turbine, a high-temperature heat recovery system, a low-temperature heat recovery system, and a feed pump. The estimated power generation efficiency is 0.25 and heat recovery efficiency is 0.65.