Ocean Thermal Energy Converters

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4.1 Introduction

The most plentiful renewable energy source in our planet by far is solar radiation: 170,000 TW fall on Earth. Harvesting this energy is difficult because of its dilute and erratic nature. Large collecting areas and large storage capacities are needed, two requirements satisfied by the tropical oceans. Oceans cover 71% of Earth's surface. In the tropics, they absorb sunlight and the top layers heat up to some 25 C. Warm surface waters from the equatorial belt flow poleward melting both the arctic and the antarctic ice. The resulting cold waters return to the equator at great depth completing a huge planetary thermosyphon.

The power involved is enormous. For example, the Gulf Stream, has a flow rate of 2.2 x 1012 m3 day-1 of water, some 20 K warmer than the abyssal layers. A heat engine that uses this much water and that employs as a heat sink the cool ocean bottom would be handling a heat flow of ATcV, where AT is the temperature difference, c is the heat capacity of water (about 4 MJ m-3K-1) and V is the flow rate.t This amounts to 1.8 x 1020 J day-1 or 2100 TW. The whole world uses energy at the rate of only « 8 TW. These order of magnitude calculations are excessively optimistic in the sense that only a minuscule fraction of this available energy can be practically harnessed. Nevertheless, ocean thermal energy holds some promise as an auxiliary source of energy for use by humankind.

Figure 4.1 shows a typical temperature profile of a tropical ocean. For the first 50 m or so near the surface, turbulence maintains the temperature uniform at some 25 C. It then falls rapidly reaching 4 or 5 C in deep places.

Temperature (C)

Figure 4.1 Typical ocean temperature profile in the tropics.

Temperature (C)

Figure 4.1 Typical ocean temperature profile in the tropics.

t The expression flow rate is redundant. The word flow is defined as the volume of fluid flowing through a tube of any given section in a unit of time. (OED).

It is easier to find warm surface water than sufficiently cool abyssal waters which are not readily available in continental shelf regions. This limits the possible sitings of ocean thermal energy converters.

4.2 OTEC Configurations

Two basic configurations have been proposed for OTECs:

1. those using hydraulic turbines, and

2. those using vapor turbines.

The first uses the temperature difference between the surface and bottom waters to create a hydraulic head that drives a conventional water turbine. The advantages of this proposal include the absence of heat exchangers.

Consider a hemispherical canister as depicted in the left hand side of Figure 4.2. A long pipe admits cold water, while a short one admits warm water. The canister is evacuated so that, in the ideal case, only low-pressure water vapor occupies the volume above the liquid surface. In practice, gases dissolved in the ocean would also share this volume and must be removed. This configuration was proposed by Beck (1978).

At a temperature of 15 C, the pressure inside the canister is about 15 kPa (0.017 atmospheres). At this pressure, warm water at 25 C will boil and the resulting vapor will condense on the parts of the dome refrigerated by the cold water. The condensate runs off into the ocean, establishing a continuous flow of warm water into the canister. The incoming warm water drives a turbine from which useful power can be extracted. The equivalent hydraulic head is small and turbines of large dimensions would be required.

Wall chilled by cold water

Cold water pump

Wall chilled by cold water

Cold water pump

Boiling warm water

Double walled dome

Condensate

Cold water out

Condensate out

Surface chilled Partial by cold water vacuum^ 77^ Dome

Condensate level

Condensate out

Condensate level

Condensate out

* Cold water in

* Cold water in

Figure 4.2 Hydraulic OTECs.

To increase the hydraulic head, Zener and Fetkovich (1975) proposed the arrangement of Figure 4.2 (right). The warm surface water admitted to the partially evacuated dome starts boiling. The resulting vapor condenses on a funnel-like surface that seals one of the two concentric cylinders in the center of the dome. This cylinder receives cold water pumped from the ocean depths, which chills the steam-condensing surface. The collected condensed water subsequently flows into the central pipe creating a head that drives the turbine. The efficiency of the device is substantially enhanced by the foaming that aids in raising the liquid.

OTECs developed in the 1980s were of the vapor turbine type. They can use open cycles (Figures 4.3A and B), close cycles (Figure 4.3C) or hybrid cycles (Figure 4.3D). The open cycle avoids heat exchangers (or, if fresh water is desired, it requires only a single heat exchanger). However, the low pressure of the steam generated demands very large diameter turbines. This difficulty is overcome by using a close (or a hybrid) cycle with ammonia as a working fluid. Most work has been done on the close-cycle configuration, which is regarded as more economical. However, the costs of the two versions may turn out to be of comparable.

Non-condensibles

Power

Non-condensibles

Power

Degas-

Flash evaporator

Steam

Turbine

Con

ifier

Warm water

Cold water

Warm water

Non-condensibles

Warm water

Power

Cold water

Condenser

Non-condensibles

Power

Condenser

Degas-ifier

Flash evaporator

Steam

Turbine

^VvV

Warm water

Cold water

Warm water

Warm water

Cold water

Power

Power

Non-condensibles

Degas-ifier

Warm water

Non-condensibles

Degas-ifier

Warm water

Warm water

Flash evaporator

NH3 liquid

Con-> densate pump

NH3 gas

Con-> densate pump

Distilled water >-

NH3 gas

NH3 liquid

Pump

NH3 liquid

Con-

Cold water

NH3 gas

Turbine

Power

Cold water

Figure 4.3 OTEC configurations include the open-cycle type without distilled water production (A), the open-cycle type with distilled water recovery (B), the close-cycle (C), and the hybrid-cycle (D).

4.3 Turbines

A turbine generates mechanical energy from a difference in pressure. Usually, the state of the gas at the inlet and the pressure of the gas at the exhaust are specified.

Let pin and Tin be the pressure and the temperature at the inlet of the turbine and pout, Tout the corresponding quantities at the exhaust.

The output of the turbine is the mechanical work, W. The heat, Q, is exchanged with the environment by some means other than the circulating gases. Most practical turbines are sufficiently well insulated to be assumed adiabatic—that is, a condition in which Q = 0.

The inlet gas carries an enthalpy, Hin, into the turbine, while the exhaust removes Hout from the device. Conservation of energy requires that1"

Expressing the quantities on a per kilomole basis (quantities per kilomole are represented by lower case letters), we can write

because, under steady state conditions, Min = Mout = MIn a perfect gas, t hin - hout = cpdT- (3)

JTout

Assuming a constant specific heat, hin hout cp (Tin Tout), (4)

Exhaust

Tout, Pout

Figure 4.4 A turbine.

Exhaust

Tout, Pout

Figure 4.4 A turbine.

1 Provided there is no appreciable change in kinetic, potential, magnetic and other forms of energy.

The above equation looks similar to that which describes the behavior of a heat engine. However, the quantity, pcpTin, although having the dimensions of energy, is not the heat input to the device; rather it is the enthalpy input. For a given input state and a given exhaust pressure, the mechanical energy output increases with decreasing exhaust temperature. The lowest possible value of Tout is limited by the second law of thermodynamics that requires that the entropy of the exhaust gases be equal or larger than that of the inlet gases. The lowest exhaust temperature (highest output) is achieved by a turbine operating isentropically, one in which the entropy is not changed. Any deviation from this condition is due to irreversibilities (losses) in the device. These losses will generate heat and thus increase Tout.

Isentropic Processes

If there is no change in entropy in the gas that flows through the

turbine, then we have an isentropic process.

From the first law of thermodynamics:

dQ = dU + pdV

(7)

and from the second law:

dQ = TdS

(8)

TdS = dU + pdV

(9)

From the definition of enthalpy, H = U + pV,

dU = dH - Vdp - pdV

(10)

Hence,

TdS = dH - Vdp,

(H)

w<? dH Vri dS= — - —dp

(12)

But dH = cpdT and V/T = R/p, hence dT dp dS = c„--R—

T p

(13)

If the process is isentropic, then dS = 0, thus,

T p p

(14)

T V iJp

(15) (continues)

(continued)

And, finally, from the perfect gas law, pV7 = constant. (18)

Thus, the polytropic law derived for the case of adiabatic compression (see Chapter 2) applies to any isentropic process.

What is the exhaust temperature, Toutmin, in an isentropic turbine? Using the polytropic law,

PinVi7n = PoutVOut, (19)

Applying the perfect gas law, we can eliminate the volumes:

The energy delivered by the isentropic turbine is W = yCpTi

A turbine may be considered adiabatic in the sense that it does not exchange heat with the environment except through the flowing gas. However, it may exhibit internal losses that cause the exhaust temperature to be larger than that calculated from Equation 21.

The isentropic efficiency of a turbine is the ratio between the actual work produced by the turbine to the work it would produced if the input and output had the same entropy.

4.4 OTEC Efficiency

The Carnot efficiency of an OTEC is low due to the small temperature difference that drives it. OTECs must abstract a large quantity of heat from the warm surface waters and reject most of it to the cold bottom waters. They handle great volumes of water. How do such volumes compare with those handled by a hydroelectric plant of the same capacity?

Let the temperature difference between the warm and the cold water be AT = TH — TC. Prof. A. L. London of Stanford University has shown that the minimum water consumption occurs when the temperature difference across the turbine (in a close-cycle system) is AT/2, leaving the remaining AT/2 as the temperature drop across the two heat exchangers. If half of this is the drop across the warm water exchanger, and if V is the flow rate of warm water, then the power abstracted is jAT c V. The Carnot efficiency is AT/2TH. Assuming that the cold water flow is equal to that of the warm water, i.e., that VTOT = 2V, the power generated (with ideal turbines) is

161H

We took Th = 296 K. Notice that the power is proportional to AT2.

The power of a hydroelectric plant is

where S is the density of water (1000 kg/m3), g is the acceleration of gravity, and h is the height difference between the input and output water levels.

We ask now how large must Ah be for an hydroelectric plant to produce the same power as an OTEC that handles the same water flow.

AT 2c

An OTEC operating with 20 K temperature difference delivers the same power as a hydroelectric plant with identical flow rate and a (moderate) 34 m head. Thus, the volumes of water required by an OTEC are not exorbitant.

The above calculations are quite optimistic; they failed, for instance, to account for the considerable amount of energy required by the various pumps, especially the cold water pump. Nevertheless, the main problem with OTECs is not the large volume of water but rather one of heat transfer. Compared with fossil-fueled plants of the same capacity, the heat exchangers of an OTEC are enormous. Up to half the cost of a close-cycle OTEC is in the heat exchangers.

4.5 Example of OTEC Design

OTECs are not designed for minimum water consumption, but rather, for minimum cost. This alters the temperature distribution in the system. Figure 4.5 shows the temperatures in a Lockheed project. It is of the close-cycle type, using ammonia as the working fluid. The overall temperature difference is 18.46 K. The warm water flow rate is 341.6 m3/s.t It enters t To gain an idea of how much water is pumped, consider a 25 X 12 m competition swimming pool. The warm water pump of the Lockheed OTEC under discussion would be able to fill such a pool in less than 2 seconds!

the heat exchanger at 26.53 C and exits at 25.17 C, having been cooled by 1.36 K. This warm water delivers to the OTEC a total thermal power of

The ammonia at the turbine inlet is at 23.39 C while at the outlet it is at 11.11 C, which leads to a Carnot efficiency of

Electricity is produced at 90.2% of the Carnot efficiency. However a great deal of the generated power is used by the different pumps as illustrated in Table 4.1. In fact, in this example, 28% of the total power generated, is used internally just to run the system. In typical steam engines, pumps are mechanically coupled to the turbine, not electrically as in this OTEC.

Heat exchanger-to-turbine temp. drop

Temperature drop across warm water heat exchanger

25.17 C

Heat exchanger-to-turbine temp. drop

Turbine-to-heat exchanger temp. drop

Temperature drop ^ across cold water

25.17 C

8.07 C

heat exchanger

Figure 4.5 Temperatures in an OTEC designed by Lockheed.

Table 4.1

Internal Power Use in the Lockheed OTEC

Condensate pump (recirculates ammonia) 2.54 MW

Reflux pump (recirculates ammonia that failed to evaporate) 0.04 MW

Warm water pump 4.83 MW

Cold water pump 12.14 MW

TOTAL 19.55 MW

| MWt stands for thermal power, whereas MWe stands for electric power.

The main power consumer is the cold water pump not only because it handles the largest amount of water but also because it has to overcome the friction on the very long cold water pipe.

The electric power generated is

However, the electric power available at the output bus is only

Thus, the overall efficiency of this OTEC is

49.8

This 2.65% efficiency is what can be expected of any well designed OTEC.

The pressure of the ammonia at the inlet side of the turbine is 0.96 MPa (9.7 atmos) and, at the outlet, 0.64 MPa (6.5 atmos). An amount of heat equal to 1876.9 - 69.4 = 1807.5 MW must be rejected to the cold water by the heat exchanger. This is done by taking in 451.7 m3s-1 of water at 8.07 C and heating it up by 0.99 K to 9.06 C.

It is necessary to make the distance between the cold water outlet and the warm water inlet sufficiently large to avoid mixing. This gives the ocean currents opportunity to sweep the cold water away. In absence of currents, OTECs may have to move around "grazing" fresh warm water. Propulsive power for this grazing can easily be obtained from the reaction to the outlet water flow.

4.6 Heat Exchangers

The overall efficiency of an OTEC is small. The Lockheed OTEC of the example converts 1877 MWt into 49.8 MW of salable electricity—an efficiency of 2.6%. However, the "fuel" is completely free so the overall efficiency is of no crucial importance. What counts is the investment cost which greatly depends on the cost of the heat exchangers. The power transferred through a heat exchanger is

Ptherm jAATexb (31)

where 7 is the heat transfer coefficient of the exchanger, A is its area, and ATexb is the mean exchanger-to-boiler temperature difference.

Lockheed hoped to achieve a 7 = 2800 W m-2K-1. With a ATexb of approximately 2.5 K and a Ptherm of 1877 MW, the required area is about 270,000 m2—that is, over 500 x 500 m.

Even minor fouling will considerably lower the value of 7 and thus it is important to keep the heat exchanger surfaces clean and free from algae. It is possible to electrolyze a small fraction of the incoming water to liberate algae-killing chlorine.

Technically, the ideal material for OTEC heat exchangers seems to be titanium owing to its stability in sea water. Aluminum, being less expensive was also considered.

4.7 Siting

We saw that the economics of OTECs depend critically on AT. Consequently, a site must be found where a (comparatively) large AT is available. There is, in general, no difficulty in finding warm surface waters in tropical seas; the problem is to find cold water because this requires depths uncommon in the vicinity of land. For this reason, land based OTECs may be less common than those on floating platforms.

A large AT (some 17 K or more) is not the only siting requirement. Depth of a cold water layer at 6 C or less should be moderate, certainly less than 1000 m; otherwise the cost of the cold water pipe would become excessive. Anchoring problems would advice the placing of OTECs in regions where the total depth is less than some 1500 m. Surface currents should be moderate (less than 2 m/s).

Total ocean depth is, of course, of no importance if dynamically positioned OTECs are contemplated. This can be accomplished by taking advantage of the thrust generated by the sea water exhaust of the plant. As explained previously, if there are no currents, such thrusting may be necessary to keep the cooler exhaust water from mixing with the warm intake.

Another siting consideration is distance from the shore if one contemplates bringing in the generated electricity by means of electric cables. OTECs may be used as a self contained industrial complex operating as floating factories producing energy intensive materials. Ammonia, for instance, requires for its synthesis, only water, air and electricity and is almost the ideal product for OTEC manufacture. It is easier to ship the ammonia than to transmit electric power to shore. Once on shore, ammonia can be used as fertilizer or it can be converted back into energy by means of fuel cells (see Chapter 9).

One OTEC arrangement involves the use of only the cold ocean bottom water. Such water is first pumped through heat exchangers and then into shallow ponds, where it is heated by the sun. It can, in this manner,

4.10

reach temperatures well above those of the ocean, leading to larger Carnot efficiencies.

OTECs using solar heated ponds can be combined with mariculture. Deep ocean waters tend to be laden with nutrients and, when heated by the sun, will permit the flourishing of many species of microscopic algae. The algarich water flows into a second pond where filter feeding mollusks are raised. Oysters, clams, and scallops are produced. The larger of these animals are either kept for reproduction or sold in the market. The smaller ones are destroyed and thrown into a third pond where crustaceans (shrimps, lobsters, etc.) feed on them. The effluent of this pond should not be returned directly to the ocean because the animal waste in it is a source of pollution. A fourth and final pond is used to grow seaweed that clean up the water and serve as a source of agar or carrageen or, alternatively, as a feedstock for methane-producing digesters (see Chapter 13). The warm water from this pond is used to drive the OTEC.

References

Zener, C., and J. Fetkovich, Science, 189, 294, 1975.

4.11

PROBLEMS

4.1 An OTEC is to deliver 100 MW to the bus bar. Its warm water comes from a solar heated pond that is kept at 33 C. The water exhausted from the heat exchanger is returned to this same pond at a temperature of 31 C. (There is a slight heat loss in the pipes.) To reestablish the operating temperature, the pond must absorb heat from the sun. Assume an average (day and night) insolation of 250 W/m2 and an 80% absorption of solar energy by the water.

Cold water is pumped from the nearby abyss at a temperature of 8 C. Refer to the figure for further information on the temperatures involved.

The warm water looses 1.84 K in going through the heat exchanger, while the cold water has its temperature raised by 1.35 K in its exchanger.

Assume that 80% of the remaining temperature difference appears across the turbine and that the rest is equally distributed as temperature differentials between the colder side of the warm heat exchanger (whose secondary side acts as an evaporator) and the turbine inlet and between the warmer side of the cold heat exchanger (whose secondary side acts as a condenser) and the turbine outlet (ATet and ATtc, in the figure).

Internal power for pumping and other ends is 40 MW. The efficiency of the turbine-generator combination is 90%. Estimate the rates of flow of warm and cold water.

What is the required surface of the heating pond, assuming no evaporation?

If the residence time of the water in the pond is 3 days, what depth must it have have?

4.12

4.2 The Gulf Stream flows at a rate of 2.2 x 1012 m3/day. Its waters have a temperature of 25 C. Make a rough estimate of the area of the ocean that collects enough solar energy to permit this flow.

4.3 Assume that ammonia vaporizes in the evaporator of an OTEC at constant temperature (is this strictly true?). If the warm water enters the heat exchanger with a temperature ATI higher than that of the boiling ammonia and leaves with a AT2, what is the mean AT? To check your results: If AT1 = 4 K and AT2 = 2 K, then <AT>= 2.88 K.

4.4 A 1.2 GWe nuclear power plant is installed near a river whose waters are used for cooling. The efficiency of the system is 20%. This is the ratio of electric output to heat input.

Technical reasons require that the coolant water exit the heat exchangers at a temperature of 80 C. It is proposed to use the warm coolant water to drive an OTEC-like plant. Assume:

the river water is at 20 C, the OTEC efficiency is one half of the Carnot efficiency, half of the available AT is dropped across the turbine.

1. What is the flow rate of this water?

2. What is the maximum electric power that can be generated by such a plant?

4.5 An OTEC pumps 200 cubic meters of warm water per second through a heat exchanger in which the temperature drops by 1%. All the heat extracted is delivered to the ammonia boiler. The ammonia temperature at the turbine inlet is equal to the mean temperature of the water in the warm water heat exchanger minus 1 K. The condenser temperature is kept at 10 C by the cooling effect of 250 cubic meters per second of cold water. The efficiency of the turbine/generator system is 90%. 12 MW of the produced electricity is used for pumping.

What must the intake temperature of the warm water be, so that a total of 20 MW of electricity is available for sale?

What must the intake temperature be so that the OTEC produces only exactly the amount of power needed for pumping?

4.6 Consider an OTEC whose turbine/generator has 100% mechanical efficiency. In other words, the system operates at the Carnot efficiency. Input temperature to the turbine is TH and the output is at TC.

The input heat comes from a heat exchanger accepting water at THin and discharging it at a lower temperature, THout. The flow rate of warm water through this heat exchanger is VH.

4.13

The heat sink for the turbine is another heat exchanger taking in water at TCin and discharging it at a higher temperature, TCout. The flow rate of cold water through this heat exchanger is VC. Refer to the figure above.

Heat

Heat

All the heat extracted from the warm water by the heat exchanger is transferred to the input of the turbine. All the heat rejected by the turbine is absorbed by the cold water heat exchanger and removed. The following information is supplied:

Th is the mean of THin and THo TC is the mean of TCin and TCou VH = VC = V = 420 m3/s.

THout and TC0ut are not given.

Clearly, if THout is made equal to THin, no heat is extracted from the warm water, and the power output is zero. On the other hand, if THout is made equal to TCin, maximum power is extracted from the warm water but the output power is again zero because (as you are going to find out) the Carnot efficiency goes to zero.

Between these extremes, there must be a value of THout that maximizes power output. Determine this value and determine the value of THout that maximizes the Carnot efficiency.

4.14

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