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# Ocean thermal energy conversion

Ocean thermal energy conversion is a way to generate electricity using the temperature difference of seawater at different depths. See also renewable energy and heat engine for general additional info.

Nearly all energy produced by humans originates from a cyclic heat engine. A heat engine is placed between a high temperature reservoir and a low temperature reservoir. As heat flows from one to the other, the engine extracts some of the heat in the form of work.

The oceans, which constitute some 70% of the earth's surface area, contain enormous thermal reservoirs that vary in temperature. They are a huge storage unit of the solar input. This, if economically tapped on a large scale, could be a solution to some of the human population's energy problems. The energy extraction potential is one or two orders of magnitude higher than other ocean energy options.

OTEC utilizes the temperature difference that exists between the surface waters heated by the sun and the colder deep (up to 1000 mts) waters to run a heat engine. This source and sink provides a temperature difference of 20°C in ocean areas within 20° of the equator. Such a small temperature difference makes energy extraction difficult and expensive. Hence typically OTEC systems have an overall efficiency of only 1-3%

 Contents

## Variation of ocean temperature with depth

The total insolation received by the oceans = (5.457 × 1018 MJ/year) × 0.7 = 1.9 × 1018 MJ/year. (taking an average clearness index of 0.5)

Only some 15% of this energy is absorbed. But this 15% is still huge enough.

We can use Lambert's law to quantify the solar energy absorption by water,

$-\frac{dI(y)}{dy}=\mu I$

Where, y is the depth of water, I is intensity and μ is the absorption coefficient. Solving the above differential equation,

I(y) = I0exp( - μy)

The absorption coefficicent μ may range from 0.05 m−1 for very clear fresh water to 0.5 m-1 for very salty water.

Since the intensity falls exponentially with depth y, the absorption is concentrated at the top layers. Typically in the tropics the surface temperature values are in excess of 25°C, while 1 km below the temperature is about 10°C. Contrary to the usual cooking pot situation of heat supplied from the bottom surface, the warmer (and hence lighter) waters at the top means that there are no thermal convection currents. Due to the very low temperature gradients, heat transfer by conduction is too low to cause any significant change to the scenario either. So with neither of the major mechanisms of heat transfer operating, the top layers remain hot and the lower layers remain cold. Thus its is like an essentially infinite heat source and an essentially infinite heat sink between a separation of ~1000mts that has been set up naturally for us to run heat engines. This temperature difference varies with latitude and season, with the maximum at the tropical, subtropical and equatorial waters. Hence in general tropics are the best choice for setting up OTEC systems.

## Types of OTEC systems

OTEC systems can be classified as two types based on the thermodynamic cycle (1) Closed cycle and (2) Open cycle.

### The open/Claude cycle

In this scheme, warm surface water at around 27°C is admitted into an evaporator in which the pressure is maintained at a value slightly below the saturation pressure.

Water entering the evaporator is therefore superheated.

h1 = hf

Where hf is enthalpy of water liquid water at the inlet temperature, T1.

This temporarily superheated water undergoes volume boiling as opposed to pool boiling in conventional boilers where the heating surface is in contact. Thus the water partially flashes to steam with a two phase equilibrium prevailing. Suppose that the pressure inside the evaporator is maintained at the saturation pressure of water at T2. This process being iso-enthalpic,

h2 = h1 = hf + x2hfg

Here, x2 is the fraction of water by mass that has vaporized. The warm water mass flow rate per unit turbine mass flow rate is 1/x2.

The low pressure in the evaporator is maintained by a vacuum pump that also removes the dissolved non condensable gases from the evaporator. The evaporator now contains a mixture of water and steam of very low quality. The steam is separated from the water as saturated vapour. The remaining water is saturated and is discharged back to the ocean in the open cycle. The steam we have extracted in the process is a very low pressure, very high specific volume working fluid. It expands in a special low pressure turbine.

h3 = hg

Here, hg corresponds to T2. For an ideal adiabatic reversible turbine,

s5,s = s3 = sf + x5,ssfg

The above equation corresponds to the temperature at the exhaust of the turbine, T5. x5,s is the mass fraction of vapour at point 5.

The enthalpy at T5 is,

h5,s = hf + x5,shfg

This enthalpy is lower. The adiabatic reversible turbine work = h3-h5,s.

Actual turbine work wT = (h3-h5,s) × polytropic efficiency

$h_{5}=h_{3}-\ \mathrm{actual}\ \mathrm{work}$

The condenser temperature and pressure are lower. Since the turbine exhaust will be discharged back into the ocean anyway, a direct contact condenser is used. Thus the exhaust is mixed with cold water from the deep cold water pipe which results in a near saturated water.That water is now discharged back to the ocean.

h6=hf, at T5. T7 is the temperature of the exhaust mixed with cold sea water, as the vapour content now is negligible,

$h_{7}\approx h_{f}\,\ at\ T_{7}$

There are the temperature differences between stages. One between warm surface water and working steam, one between exhaust steam and cooling water and one between cooling water reaching the condenser and deep water. These represent external irreversibilities that reduce the overall temperature difference.

The cold water flow rate per unit turbine mass flow rate,

$\dot{m_{c}=\frac{h_{5}-\ h_{6}}{h_{6}-\ h_{7}}}$

Turbine mass flow rate, $\dot{M_{T}}=\frac{\mathrm{Turbine}\ \mathrm{work}\ \mathrm{required}}{w_{T}}$

Warm water mass flow rate, $\dot{M_{w}}=\dot{M_{T}\dot{m_{w}}}$

Cold water mass flow rate $\dot{\dot{M_{c}}=\dot{M_{T}m_{C}}}$

### The closed/Anderson cycle

In this cycle, QH is the heat transferred in the evaporator from the warm sea water to the working fluid. The working fluid exits from the evaporator as a gas near its dew point.

The high-pressure, high-temperature gas then is expanded in the turbine to yield turbine work, wT. The working fluid is slightly superheated at the turbine exit and the turbine typically has an efficiency of 90% based on reversible, adiabatic expansion.

From the turbine exit, the working fluid enters the condenser where it rejects heat, -QC, to the cold sea water. The condensate is then compressed to the highest pressure in the cycle, requiring condensate pump work, wC. Thus, the Anderson closed cycle is a Rankine-type cycle similar to the conventional power plant steam cycle except that in the Anderson cycle the working fluid is never superheated more than a few degrees Fahrenheit. It is realized that owing to viscous effects there must be working fluid pressure drops in both the evaporator and the condenser. These pressure drops, which are dependent on the types of heat exchangers used, must be considered in final design calculations but are ignored here to simplify the analysis. Thus, the parasitic condensate pump work, wC, computed here will be lower than if the heat exchanger pressure drops were included. The major additional parasitic energy requirements in the OTEC plant are the cold water pump work, wCT, and the warm water pump work, wHT. Denoting all other parasitic energy requirements by wA, the net work from the OTEC plant, wNP is

wNP = wT + wC + wCT + wHT + wA

The thermodynamic cycle undergone by the working fluid can be analyzed without detailed consideration of the parasitic energy requirements. From the first law of thermodynamics, the energy balance for the working fluid as the system is

wN = QH + QC

where wN = wT + wC is the net work for the thermodynamic cycle. For the special idealized case in which there is no working fluid pressure drop in the heat exchangers,

 QH = ∫ THds H

and

 QC = ∫ TCds C

so that the net thermodynamic cycle work becomes

 wN = ∫ THds + ∫ TCds H C

Subcooled liquid enters the evaporator. Due to the heat exchange with warm sea water, evaporation takes place and usually superheated vapor leaves the evaporator. This vapor drives the turbine and 2-phase mixture enters the condenser. Usually, the subcooled liquid leaves the condenser and finally, this liquid is pumped to the evaporator completing a cycle.

#### Working fluids

Various fluids have been proposed over the past decades to be used in closed OTEC cycle. A popular choice is ammonia which has superior transport properties, easy availability, and low cost. Ammonia, however, is toxic and flammable. Fluorinated carbons viz. CFCs and HCFCs would have been a better choice had it not been for their contribution to ozone layer depletion. Hydrocarbons too are good candidates. But they are highly inflammable. The power plant size is dependent upon the vapor pressure of the working fluid. For fluids with high vapor pressure, the size of the turbine and heat exchangers decreases while the wall thickness of the pipe and heat exchangers should increase to endure high pressure especially on the evaporator side.

### Technical difficulties

#### Degradation of heat exchanger performance by dissolved gases

A very important technical issue pertaining to the Claude cycle is the performance of direct contact heat exchangers operating at typical OTEC boundary conditions. Many early Claude cycle designs used a surface condenser since their performance is well understood. However direct contact condensers offer significant advantages. As the warm sea water rises in the intake pipes, the pressure decreases to the point where gas begins to evolve. If a significant amount of gas comes out of the solution, designing a gas trap before the direct contact heat exchangers may be justified. Experiments simulating conditions in the warm water intake pipe indicated about 30% of the dissolved gas evolve in the top 8.5 mts of the tube. The tradeoff between pre-deareation of the sea water and expulsion of all the non condensable gases from the condenser is dependent on the gas evolutiuon dynamics, deareator efficiency, head loss, vent compressor efficiency and parasitic power. Experimental results have indicated that vertical spout condensers performs some 30% better than the falling jet types.

#### Improper sealing

The evaporator, turbine, and condenser operate in partial vacuum ranging from 3 percent to 1 percent atmospheric pressure. This poses a number of practical concerns that must be addressed. First, the system must be carefully sealed to prevent in-leakage of atmospheric air that can severely degrade or shut down operation. Second, the specific volume of the low-pressure steam is very large compared to that of the pressurized working fluid used in the case of a closed cycle OTEC. This means that components must have large flow areas to ensure that steam velocities do not attain excessively high values.

#### Parasitic power consumption by exhaust compressor

An approach for reducing the exhaust compressor parasitic power is as follows. After most of the steam has been condensed by spout condensers, the non condensable gas steam mixture is passed through a counter current region which increases the gas-steam reaction by a factor of 5. The result is an 80% reduction in the exhaust pumping power requirements.

## Other benefits

Exhaust from an Open cycle OTEC plant is once distilled. Hence the spin off benefit of desalinating seawater adds to their commercial viability.

Also, deeper water contains valuable nutrients, which OTEC can collect.