In order to explain the nature of the research project, it is pertinent to previously expose a concept of current reality, this is that of Energy Management. It can mean different things to different people, but its current philosophy focuses on the judicious and effective use of energy to maximize energy yields and minimize economic costs. When studying energy resources, two aspects are considered: one, focused on their conservation and the economic savings that can be obtained from their use, and the other, aimed at the environment, with regard to their rational use and reduction of thermal and / or toxic effluents.
Cogeneration represents an energy concept that considers the coupling of two thermodynamic cycles where one of them works with the thermal waste of the other. In our specific case, we study the coupling between an internal combustion engine that drives an electricity generator on the one hand, and a lithium bromide and water absorption refrigeration equipment on the other, the latter operating with the thermal waste from the motor.
This Work is dedicated to the presentation of the fundamentals and tools of a theoretical nature that are necessary for the development and interpretation of the cogeneration model. It begins with the antecedents of cogeneration in order to understand its historical significance, then it seeks to understand the efficiency ratio of internal combustion engines as well as the electrical generators coupled to these combustion engines, the projected residual heat recovery equipment. by the engines, and finally the lithium bromide and water absorption cooling systems.
ANTECEDENTS OF COGENERATION.
Cogeneration is not a new process, its application dates from the early eighteenth century where its most representative form were the small mills installed inside a chimney.
In the mid-nineteenth century, Sadi Carnot's postulates (Reflections on the motive power of fire) stimulated actions to make the most of the waste steam from steam engines, where the recovery concept was basically for heating in the Industrial facilities. The last decade of the same century saw the birth of the electrical industry and the invention of internal combustion engines, which led to the expansion of the combined power and heat generation market.
Cogeneration within its evolution in the past was not due, as it is now, to the need to save energy, but to the purpose of ensuring the supply of electricity and heat, which in those years was insufficient and unreliable. Parallel to the use of turbines in electricity generation, alternative internal combustion machines (ICM) were also being developed, due to the growing need for smaller, versatile generation systems with lower initial investment. But the cogeneration in these engines was focused on the use of residual heat for heating the buildings, either by heating air or water.
At present, the use of waste heat is diversifying, creating combined cycles for the best use of primary energy, taking as an example the coupling of ICMs with absorption refrigeration cycles.
DESCRIPTION OF THE COGENERATION MODEL
Figure 1 graphically represents the cogeneration system under study. It can be seen that the system consists of the coupling of two cycles, one motor and another absorption cooling system, described by means of carnot diagrams.
Fig. 1 Scheme of the Cogeneration system
The link between the two cycles is performed by a heat recovery system that takes a fraction of the energy discarded by the engine, to thereby feed the generator of the refrigeration cycle.
In this way, according to what is presented in figure 1, the following equations are proposed that will serve as the basis for the development of the model:
Q ° f = m ° f. ΔHf "Thermal power of fuel consumed" (1)
W ° = ηt. Q ° f "Mechanical power" (2)
Ge ° = ηg. W ° = ηg. ηt. Q ° f "Electric Power" (3)
Q ° d = Q ° f - W ° "Power of thermal waste" (4)
From this set of equations, the efficiency of the combined cycle, η comb, in terms of the cooling power, Q ° r, and the electrical power, G ° e, is determined in relation to what is necessary to invest, this being the thermal power of the fuel delivered to the engine, Q ° f, is expressed as follows:
η comb = (Q ° r + G ° e) / Q ° f (5)
In our case, the η comb represents a power quality factor that will serve as a means of comparison between systems. This factor is very characteristic because it brings together two types of energy, one thermal and the other electrical, typical of the Cogeneration concept.
Figure 2 shows the circuit of the fluids that transport thermal energy to different parts of the system, this is nothing more than a mixture of water and additive. The heat recovery system referred to in figure 2, consists of two heat exchangers, one where the possible latent heat in the engine jacket is recovered and the other where the possible latent heat is recovered from the exhaust gases.
From Figures 1 and 2, it can be seen that to characterize the cogeneration cycle, as a whole, it is necessary to previously characterize the ICM, the heat exchangers, and the refrigeration cycle; these aspects to be developed below.
Fig. 2 Fluid Circuit of the Cogeneration system
THE INTERNAL COMBUSTION ENGINE
In our specific case, the engines to consider are reciprocating engines powered by natural gas as fuel, where the combustion of the air-fuel mixture starts with the spark of a spark plug.
- Theoretical Thermodynamic Cycle
The present work uses the Otto cycle as a representative thermodynamic cycle of a reciprocating engine, based on its affinity with natural gas as fuel for its operation. For the thermodynamic analysis of these motors, we start from the theoretical model or standard Otto Air cycle, represented in the PV diagram of figure 3, consisting of the following events:
Figure 3. Theoretical Otto cycle
The cycle begins at point "1" or lower dead center (PMI), and continues with an isentropic compression process "1-2", until it ends at top dead center (TDC) where heat is added at constant volume "2 -3 “, or spark ignition of the fuel that is inside the cylinders, generating its combustion and thus releasing the energy that the system consumes and uses in the process of isentropic expansion or power stroke, during which manifest positive work is done on the engine crankshaft. After the expansion, the exhaust or expulsion stroke of the post-combustion gases begins, during which most of the products are removed from the cylinder and heat is transferred to the medium.
This last consideration being (Heat transferred to the environment), where this work will pay special attention, in order to analyze the energy potential for use in other cycles with thermal requirements.
The thermal efficiency, h t, of the theoretical Otto cycle, is defined as the productive work (Desired effect) divided by the thermal energy delivered by the fuel (cost of said effect), but if we relate it according to its compression ratio it is gets:
η t = W ° / Q ° f = 1 - 1 / ŗ 1- k (6)
This allows us to deduce that the thermal efficiency of the theoretical Otto engine is constant in engines with the same compression ratio. In figure 4 such behavior is described and at the same time it is compared with the thermal efficiency of a real motor.
- Considerations of a real engine
Unlike the theoretical model of the Otto engine, the irreversible losses of thermal energy that characterize the real Otto engine are caused by the friction of the constitutive mechanisms of the engine, which force to generate losses due to heat transfer to cooling media and through exhausts. combustion. This makes it possible to indicate that the thermal efficiency of the actual Otto engine is variable depending on the operating circumstances of the engine.
The fact is relevant, that ideal and real engines show higher performance when the compression ratio increases, but the practical question of this ratio is of interest, as indicated below:
a) In a real engine, the compression ratio is limited by the temperature of state 2 (figure 3), if this temperature were high, the air-fuel mixture would spontaneously ignite at the wrong time.
b) If, under the same fuel mixture ratio, an increase in the compression ratio (see figure 5) promotes an increase in temperature and pressure at point 3 (figure 3), this leads to highly demanding engine designs characteristic of high temperatures and working pressures, as well as the importance of the engine cooling system and its losses of thermal energy through the engine jackets, in other words the increase in the compression ratio means that there is an increase in the area cylinder wall and its average temperature, in this sense, the greater the flow rates of the refrigerant to be used, but limited by the boiling point of the refrigerant, stability of the oil film on the cylinder wall and the properties of manufacturing materials.
Fig. 5 Effect of the mixing ratio and conditions T 3 and P 3
c) When considering the effect of the temperature T 4 or the temperature of the post-combustion gases, it is observed in figure 6 that said temperature T 4 decreases as the compression ratio increases, due to the great expansion of the gases in the cylinder during the exhaust process.
Fig. 6 Effect of the mixing ratio on the condition T 4
- Power Balance of a Motor
Cogeneration in internal combustion engines is considered two types of thermal waste: 1) thermal losses through the exhaust gases, 2) thermal losses through the cooling system, the rest of thermal losses are less relevant, due to their low quality energetic. Cogeneration not only considers residual thermal energy, but also the mechanical power generated by the engine, in other words, the ability of the system to convert the energy potential of the fuel into another manifestation of energy.
Starting from the energy balance in the motor (Figure 7), we obtain:
Q ° f = W ° + Q ° d (7)
Q ° d = Q ° f - W ° (8)
Considering equation 2, and substituting it in equation 8, we obtain:
Q ° d = Q ° f - W ° (9)
Q ° d = Q ° f - (ηt. Q ° f)
Q ° d = Q ° f. (1 - ηt) (10)
Fig. 7. Energy balance of an internal combustion engine
Continuing with figure 7, it is indicated that the total thermal waste is made up of the thermal powers to be delivered to the environment, by: the refrigerant in the shirts Q ° ac, the exhaust gases and other waste Q ° ge, among the which are mentioned: the engine lubrication system and engine radiation.
The equation holds that:
Q ° mc = Maximum power that it exchanges, if the exchange area were Infinite
Q ° mc = Cmin
From the definition of NUT 2, the equation that allows to calculate the transfer area A 2 is obtained, given the global thermal exchange coefficient U 2 between the jacket water and the working fluid, as follows:
A 2 = (NTU 2. C min) / U 2 (29)
ABSORPTION AIR CONDITIONING SYSTEM
As indicated in figure 2, the result of the recovery process of the thermal waste from the internal combustion engine contained in the working fluid, constitutes the thermal power recovered and brought to the generator of a lithium bromide absorption cooling system. and water.
This cooling system is the most suitable for environmental conditioning, because it uses water as a refrigerant and at the same time it is not a polluting fluid for the environment, its working pressures both in the generator and in the absorber are lower than atmospheric pressure and for this reason, the design specifications of this equipment are not demanding as those that can be provided by ammonia and water systems.
A lithium bromide and water absorption system uses low quality thermal energy to raise the pressure of the refrigerant in the generator, which in our case is water; and the necessary low pressure in the absorber is maintained by the use of another substance called an absorber, which is nothing more than a lithium bromide salt.
In figure 12, the different sections that make up a lithium bromide and water absorption refrigeration equipment are described, highlighting that both the generator and the absorber constitute the two key parts thereof; The generator represents the high pressure side and the absorber the low pressure side
The operation of the lithium bromide and water absorption refrigeration systems will depend on the power with which heat is delivered to the generator, Q ° go varying the power with which heat is extracted both by the condenser and by the absorber
Fig. 12 Typical BrLi and water absorption system
Energy balance in the absorption system
In Figure 13 it can be seen that, to carry out the energy balance in the cooling system, two important sources of thermal energy are observed, one is the thermal energy to be extracted from the ice water or Heat of the enclosure, Q ° r, and the other is the thermal energy required by the generator, Q ° g. On the other hand, the thermal energy to be extracted is appreciated, both by the condenser Q ° c and by the absorber Q ° ab.
Fig. 13 Energy balance of an absorption refrigeration system
Considering the postulate of the first law of Thermodynamics, we obtain:
Q ° g + Q ° r = Q ° c + Q ° ab, (30)
and on the other, considering the amount of water evaporated in the evaporator, it is defined: (king, 1984. p 179)
Q ° r = m ° e. h fg pa, (35)
In which it is fulfilled:
m ° e = mass flow rate of evaporated water in the evaporator
h fg pa = enthalpy of vaporization at absorber pressure
from the previous equation, it follows
m ° e = Q ° r / h fg pa = m ° ah. Cp ah. ∆T ah / h fg pa (36)
To determine the performance of the team absorption or performance, is defined as coefficient of performance, COP , the relationship between the heat absorbed by the evaporator and the transferred heat generator:
COP = Q ° r / Q ° g (37)
CHARACTERIZATION OF THE COGENERATION SYSTEM
Based on the equations developed above where they characterize the cogeneration system, it can be indicated that the mechanical power generated by the engine is a function of its Thermal Performance, already indicated in the equations 2 and 1, where:
W ° = ht. Q ° f = ht. m ° f. ΔHf, (38)
While the Mechanical power available in the shaft is used to generate electricity by coupling it to an Electric generator, as shown in figure 2 and quantified by equation 15; Therefore the electric power G ° e, is:
Gºe = Wº * hg = ht . hg. m ° f. ΔHf (39)
On the other hand, the waste heat Q ° d is related to the thermal performance of the motor as indicated in equations 2 and 4, as follows:
Q ° d = Q ° f - W ° = Q ° f - ηt. Q ° f = Q ° f. (1 - ht) (40)
In the waste heat recovery process, only a part or fraction, fr, it will be possible to take it and arrange it as a thermal source for a Q ° g refrigeration equipment, as indicated below:
Q ° g = Q d . fr (41)
Starting from equation 37, the refrigeration capacity Q ° r of the refrigeration equipment can be determined, where:
Q ° r = COP. Q ° g = COP. Q d . fr = COP. Q ° f. (1 - ht). fr
Qr = COP. (m ° f . ΔHf). (1 - ht). fr (42)
And from the above equation, you can know the mass flow of fuel m ° f consumed by the internal combustion engine:
m ° f = Q ° r / COP. ΔHf. (1 - ht). fr (43)
To calculate the performance of the combined cycle, h comb, it is from equation 6 already defined above, which sui generis indicates the performance of the combined cycle, which in our case is the Cogeneration system:
h comb = (G ° e + Q ° r) / Q ° f
h comb = + (44)
BIBLIOGRAPHIC REFERENCES
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