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INJECTION POWER CYCLEAPPLIED IN OTEC POWER PLANTS
Author:
P.Eng. Marijo Miljkovic
PIN: 0203974500203
October, 2015
Asia Clean Energy Summit – RE Asia Conference 201527-28 October 2015, Singapore
INTRODUCTION OCEAN THERMAL ENERGY CONVERSION
Oceans cover more than 70% of Earth's surface, making them the world’s largest solar collectors.
The sun's heat warms the surface water a lot more than the deep ocean water, and this temperature difference creates thermal energy.
In the existing Rankine cycle OTEC system, the ocean's warm surface water vaporizes a working fluid, which has a low – boiling point (e.g. Ammonia - R717 or R32) flowing through a heat exchanger (evaporator). The vapor expands at moderate pressures and turns a turbine connected to a generator that produces electricity. The vapor is then condensed in another heat exchanger (condenser) using the ocean's cold deep water.
Figure 1. Schematic diagram of a Rankine Cycle applied in an OTEC system.
Figure 2. Chart for a Rankine Cycle applied in an OTEC system.
Initial assumptions for the calculation of a real Rankine Power Cycle (RPC) with irreversible processes (i.e. with friction):
- Heat source temperature: TSO = 25°C - Heat sink temperature: TSI = 5°C - Evaporating temperature in an evaporator: TE = 20 ̊C- Condensing temperature in a condenser: TC = 10 ̊C
Table 1. States of the working fluid R32 and its parameters for a real Rankine PowerCycle.
Useful technical work done by the OTEC system:
lt = lt3-4 + lt1-2 = h3 – h4 + h1 – h2 = 9.24 kJ/kg (1)
Heat absorbed by the OTEC system:
qIn = q2-3 = h3 – h2 = 298.16 kJ/kg (2)
Efficiency of the Rankine Cycle OTEC system:
ηRPC = lt / qIn = 0.03099 (3)
A maximal pressure difference in a Rankine Cycle OTEC system:
ΔpRPC = p3 – p4 = 3.67 bar (4)
CONVENTIONAL THERMAL COMPRESSORS (INJECTORS)
Figure 3. Layout of the Conventional Thermal Compressor (Injector / Ejector)
Description of the operation of a thermal compressor (ejector / injector): In thermal compressors a high heat potential (enthalpy) of the motive stream of fluid is utilized to increase the pressure of a low heat potential suction stream of fluid (at the outlet of a turbine) in order to reach medium (condensing) pressure.
In other words, a hot and high pressure motive fluid enters the nozzle of an injector, where it expands and its velocity and kinetic energy increase (its enthalpy decreases), as well as its pressure is reduced to the low suction pressure. Then a motive stream of vapor withdraws the cold suction stream of vapor and they are mixed in the mixing chamber of the injector. Then the mixture of vapors enters the diffuser where it is compressed to the medium (condensing) pressure and its velocity and kinetic energy decrease (its enthalpy increases).
The 1st Law of Thermodynamics for the processes (expansion and compression) in a thermal compressor (injector, ejector) states that the change in the heat potential energy (enthalpy) and the change in kinetic energy of an isolated system is equal to the amount of heat transferred into the system and the amount of technical work done by the system on its surroundings.
q + lt = hA – h3 + 1/2·(vA2 – v3
2) (5)
where:q = 0 ……….….quantity of heat exchanged with its surroundings lt = 0 ……….…. quantity of technical work done by the system on
its surroundingshi ……..……… enthalpy (heat potential) [kJ/kg]
vi ……………. velocity [m/s]
i = {1,2,3,4,5,A,B,C,D,E,…} ….. states of the refrigerant
h3 + v32/2 = hA + vA
2/2 = EHP + EK = ETot = Const (6)
Also, the Law of Conservation of Energy states that the total energy of an isolated system is constant. Therefore, energy cannot be created or destroyed. It can only be converted from one form to another.
The equations that determinate the state of the mixture after mixing of two vapor streams (motive and suction) in the mixing chamber and with respect to the Law of Conservation of Energy:
hC · (m3 + m5) = h3 · m3 + h5 · m5 (7)
sC · (m3 + m5) = s3 · m3 + s5 · m5 (8)
where:mi …...... mass fluid flow (kg/s)si …….. entropy [kJ/(kg·K)]pi ……. pressure [bar] ti …….. temperature [°C]
THERMAL COMPRESSOR WITH INTERNAL COOLING
Figure 4. Layout of the Injector With Internal Cooling With A High Density Fluid Injected Into A Mixing Chamber.
Efficiency of the conventional injector is less than 35%. The main reason of low efficiency of a thermal compressor is the increase of entropy of the mixture of vapors. The friction between fluid particles (molecules) and between them and the walls of a thermal compressor causes losses in kinetic energy (entropy generation). So the heat potential energy (enthalpy) of a motive stream of fluid is mainly used to increase the entropy of mixture instead of its pressure. Actually increasing the enthalpy of a suction stream of fluid is not a goal. So, in order to increase its pressure in an efficient manner, a high density fluid can be injected into the fluid mixture. In this way, the compression of the mixture in a mixing chamber takes place simultaneously with mixing with a high density fluid. So the kinetic energy of both streams, in the first place, is used for increasing the pressure of the secondary mixture, while reducing the entropy of the primary mixture, as well as rising the entropy of the secondary cooling stream (with high density fluid). In this way, the compression of the secondary mixture is intensified. Finally, this results in the increase of the overall efficiency of an injector.Actually, a part of liquid from the secondary cooling stream evaporates and cools the secondary mixture. In other words, the entropy generated by friction can not be destroyed, but it is only transferred from the primary mixture to the secondary cooling stream.
INJECTION POWER CYCLEAPPLIED IN OTEC POWER PLANT
The initial assumptions for the calculation of a real Injection Power Cycle (IPC) with the injection of a high density fluid into a mixing chamber and with all irreversible processes (i.e. with friction):
- Heat source temperature: TSO = 25°C - Heat sink temperature: TSI = 5°C - Evaporating temperature in an evaporator: TE = 20 ̊C- Condensing temperature in a condenser: TC = 10 ̊C - A high density fluid of state E=1 is injected into the mixing chamber of an injector. It expands in the nozzle to the state D.- The compression of a mixture in a diffuser takes place simultaneously with the mixing with a high density fluid injected into a mixing chamber. The final state of the second mixture (m3+m5+mE) is CIII.
Figure 5. Schematic diagram of the Injection Power Cycle (IPC) applied in an OTEC power plant.
Figure 6. Chart for the real Injection Power Cycle with internal cooling with a high density fluid injected into a mixing chamber of an injector.
Description of the Injection Power Cycle with internal cooling with a high density fluid injected into a mixing chamber of an injector
After the liquid working fluid (8.82m) leaves the condenser (point 1), it is divided into two streams. The first one (0.89m) enters the nozzle of an Injector (the cooling stream) and it is injected into the mixing chamber. The other medium pressure stream (7.94m) enters the pump which increases its pressure to 14.74 bar. Then the liquid working fluid enters evaporator (state 2) where it evaporates. After that the hot and high pressure stream of vapor (state 3) is split into two streams. The first one (6.94m) enters the nozzle of an injector (the motive stream) and it is injected into the mixing chamber. The other hot and high pressure stream (1.00m) expands in the turbine. Then such cold and low pressure stream is mixed with hot and high pressure stream in a thermal compressor in order to raise the pressure of a cold suction stream to the condensing medium pressure (state CIII). After that, the mixture enters the condenser where it is condensed.
The equations that determinate the state of a mixture with respect to the Law of Conservation of Energy:
hCIII · (mE + m3 + m5) = h3 · m3 + h5 · m5 + hE · mE (9)
The equations that determinate the states of a fluid with respect to The 1st Law of Thermodynamics :
h3 + v32/2 = hA + vA
2/2 (10)
hE + vE2/2 = hD + vD
2/2 (11)
From the equations (9) - (11), as well as for the flow ratio:
kI = mA/m5 = 6.93620 (12)
kII = mD/(mA + m5) = 0.11167 (13)
we get the following values:
hCIII = (kI · h3 + h5 + hE · kII · (kI + 1))/((kI + 1) · (kII + 1)) = 477.92 kJ/kg (14)
sCIII = (kI · s3 + s5 + sE · kII · (kI + 1))/((kI + 1) · (kII + 1)) = 1.9812 kJ/(kg·K) (15)
Table 2. States of the working fluid R32 and its parameters for the Injection PowerCycle with the injection of a high density fluid into a mixing chamber.
Useful technical work done by the OTEC system :
ltIPC = lt3-5 + (kI + 1) · lt1-2 = 72.34 kJ/kg (16)
The heat absorbed by the OTEC system:
qInIPC = (kI+1) · q2-3 = 2,366.26 kJ/kg (17)
The heat rejected by the OTEC system:
qout = ktot · qCIII-1 = (kI + 1) · (kII + 1) · qCIII-1 = 2,293.91 kJ/kg (18)
Efficiency of the mixing and compression process:
ηmix = 1 – hE · kII · (kI + 1) / (kI · vA2/2 + kII · (kI + 1) · vD
2/2) = 0.60 (19)
Efficiency of the Injection Power Cycle OTEC system:
ηIPC = ltIPC / qInIPC = 0.03057 (20)
A maximal pressure difference in the Injection Power Cycle OTEC system:
ΔpRPC = p3 – p5 = 13.49 bar (21)
CONCLUSION
Firstly, a thermal compressor (injector, ejector) applied in a power cycle allows extension of expansion of a working fluid. Therefore, the unique feature of the Injection Power Cycle (IPC) is that the maximal temperature difference of the working fluid in a power cycle is greater than the temperature difference between a heat source and a heat sink. This results in an increase of pressure drop of working fluid during its expansion.The IPC is, actually, a replacement for the Absorption Power Cycle, but it can be applied at lower temperature and a smaller temperature difference between a heat source and a heat sink.Furthermore, the OTEC power can be used to produce energy carriers such as Hydrogen (stored in HYDRNOL: Organic Liquid Storage), which can be shipped to areas not close to OTEC resources. This could be fuel for thermal power plants, as well as for internal combustion vehicles, such as gas turbines and reciprocating engines.
The ability to store and transport hydrogen within a liquid carrier at standard (room) temperature and atmospheric pressure provides many advantages over current hydrogen storage methods. The need for large, heavy storage tanks is eliminated. Major changes in the fueling infrastructure of the world are avoided. The risk for explosion is minimized since the hydrogen is stored within a molecule and not in its elemental form. Furthermore, it is less flammable than gasoline or diesel. Also, HYDRANOL is cost effective when compared to traditional (fossil) fuels.
Secondly, I believe that I just opened a new page in High Velocity Fluid Thermodynamics.
Thermal compressors have the following advantages compared to the mechanical ones:
1. They operate with two-phase flow.2. They operate with mixing of several streams of fluid.3. They allow the conversion of heat potential energy of fluid into kinetic energy of fluid.4. They allow the conversion of kinetic energy of fluid into work (needed for compression) and heat potential energy of fluid.
Table 3. Comparison of the Efficiency of Thermodynamic Cycles
By introducing of low entropy fluid for cooling the mixture, the entropy of the primary mixture (of motive and suction stream) is decreasing. Also, according to the Law of Conservation of Energy, the entropy of cooling stream is rising. In this way, the increase in entropy of mixture during its compression is prevented. This combined with the possibility of converting the kinetic energy of a high-velocity fluid into work (needed for compression), will allow us to discover new designs of thermal compressor, which will have even greater efficiency. Finally, this will bring the efficiency of the Injection Power Cycle even closer to the efficiency of the Ideal Carnot Cycle.
Thank you,
Author:
P.Eng. Marijo MiljkovicPIN: 0203974500203
