Management Engineering - Fundamental of energy technologies

Completed notes of the course

Complete course

1 FUNDAMENTALS OF ENERGY TECHNOLOGIES This course is intended to study thermodynamic and electrochemistry: Thermodynamic is the branch of physic that studies systems characterized by heat and work energy transfers (conventional power cycles). Electrochemistry is the branch of physic that analyses systems undergoing electrochemical reactions and it studies the interaction between electrical energy and chemical change (batteries, fuel cells). An electrochemical reaction is a reaction involving the production or the consumption of one electrode. The main difference between the two branches that we are going to study is that in a thermodynamic system a combustion occurs, while this doesn’t happen in electrochemistry. The study of these two branches will also be done in terms of off-design and degradation, since all energy technologies work in off-design system: All systems have an operating conditions (best condition in which the system can work) but for most of the time the system works in off-design, that is, when the efficiency of the system is reduced and degradation occurs. Worldwide energy consumption: As we can expect, the share of renewables is minor compared to others (such as fossil ones), indeed, we have new emerging technologies, however, there is also the need to keep in mind that 85% of energy consumption is based on fossil fuels, which, as thermodynamics explains are converted through a combustion process in heat. The share of the different consumptions is divided into the different areas of the world. As for the Eu, the energy consumption of renewables is accounted for the 10%, while their use for electricity is accounted for the 30%. The situation in Italy is similar to other European countries, starting from 2009 we did not have an increase in the consumption of energy, this is related mainly to two aspects: 1) Increase in energy efficiency: If we are more efficient we consume less; 2) Economical crisis: That is, no further development of industries In terms of renewables, the shares are limited and starting from 2008/2010 we had a strong increase in the production of renewables thanks to governmental incentives. As a matter of fact, the trend for renewables is increasing but we are close to a saturation point, caused by the fact that renewables are intermittent (we cannot expect to have energy from solar panels if there is no sun) and because of storage problems. The most of the consumption is related to fossil fuels (thermodynamic). 2 Introduction to thermodynamic and electrochemical systems Thermodynamic system: A thermodynamic system identifies the subject of the analysis, it is the quantity of matter that we study, interacting with the surroundings by exchanging three components: 1) Mass 2) Work: Mechanical energy transfer; it is not a property and depends on the path ( production; 3) Heat transfers: Thermal energy transfer; it is not a property and depends on the path (Not a property means that if we want to evaluate e.g. the work exchange during the process we need to know the starting point, the final point and also the part followed) Surroundings: everything external to the system. Systems: There are different types of systems which are going to be studied in thermodynamics: a) SIMPLE SYSTEM: Which means no internal boundaries. b) COMPOSED SYSTEM: System composed of internal boundaries; it is composed of different systems (such as thermodynamic cycles), which can exchange between them mass, work and heat. c) ISOLATED SYSTEM: System that does not have an interaction with the surroundings; A, B and C can exchange between them but not with the surroundings. Boundary: (Mass) impermeable / porous (Work) rigid / movable (Heat) adiabatic / diathermic 3 Thermodynamic properties: 1) Intensive properties: Properties who do no depend on the size of the system and are defined only if the system is at equilibrium. - T (temperature, K): potential related to heat transfer - P (pressure, Pa): potential related to work transfer It states that these two properties are potential related to heat and work transfer, which means that they have the possibility to transfer work and heat. 2) Extensive properties (specific properties if divided by m o n): - m (mass, kg): Mass - n (moles, mol): Number of moles, it expresses the quantity of particles inside a system - V (volume, m3 ): System volume - Ec (kinetic energy, J): Energy related to macroscopic system velocity; it is a system property - Ep (potential energy, J): Energy related to an elevation relative to the surface of the earth; it is a system property - U (internal energy, J): Kinetic energy related to the microscopic component of the matter; it is a system property Remember: When we talk about “properties” of the system, it means that they are characteristics and they depend on some aspects. Temperature: In thermodynamic the temperature scale that is used is Kelvin, the point of reference that can be used is 273.16K (0°C) which is the triple point of water. The other scale for temperature is the Celsius scale, where the ice point at atmospheric pressure is 0°C and the steam point at atmospheric pressure is 100°C. Energy: Energy is usually identified with work and we can say that energy can be measure in Joules, calories and Kilowatt per hours. Power: The is expressed in Wh. Difference between Joules and Kilowatt: Joules are expressing the energy to complete a certain activity, while Wh are expressing the rate between the amount of energy taken to complete an activity and the amount of time needed. An important aspect that has to be stated is that the work per unit time (Watt) can also be obtained by the voltage difference (V) multiplied by the current (A=ampere) and not only by the movement of a kilogram of mass with a given velocity. In thermodynamic cycle we can produce work through the first case (with the movement of a mass), in electrochemical systems, we can provide work through a device that has got no velocity but with a flow of current. 4 Pressure: Thermodynamic equilibrium: To better explain this, we will make an example: We have a wall, outside we have 30°C and inside 5°C: There will be a temperature difference, which means that I have a potential difference and for sure I will have an heat flask, which is always following a decreasing potential. This is a system not at equilibrium since temperature is not constant. A system can be in equilibrium just in a case like this: In the case in which we have 30°C is constant, however, we do not have any potential difference and any energy exchange. Even if we are in a situation in which we are not exactly at equilibrium, even a system like this: We can say that we are at equilibrium, because if we divide this system into smaller systems and we consider that the green area is composed of two subsystems, they have the same temperature. This condition is not a condition of equilibrium, but it is a condition of mutual equilibrium. [Heat flask: an insulating flask that has double walls, usually of silvered glass, with an evacuated space between them. It is used for maintaining substances at high or low temperatures] Local equilibrium: a system at non-equilibrium state can be divided in small sub-systems, that can be considered at equilibrium state. Equilibrium state: a system is at equilibrium state when a condition of balance is maintained by an equality of opposing potentials. In thermodynamic, equilibrium is obtained when intensive properties – temperature and pressure – are homogeneous. 5 Two systems are at mutual equilibrium if characterized by the same T and p. A system can be considered at equilibrium if composed by sub-systems at mutual equilibrium. The condition of equilibrium is important also for internal reversible processes. Internal reversible processes (IRP): The IRP is a SLOW process which passes through equilibrium state, it is very slow: In each point of the slow process we can define the equilibrium and also T and P. =n a normal and realistic condition we don’t have =RP, but it is an important process because we can always define the conditions (T and P) in order to use it as a benchmark, since it is the best condition we could have to compare others. The IRP is the best. FIRST AND SECOND LAW OF THERMODYNAMICS: The purpose of thermodynamic is that of analyzing systems; in order to do so, we have different instruments: 1. MASS BALANCE: Considering a thermodynamic system, the first instrument to analyze it can be by looking at its mass conservation. In a generic system, the principle of mass conservation states that all the mass flowing inside the system is equal to the one flowing outside plus an accumulation term. The accumulation term is the derivate of the mass with respect to time, which expresses the variation in time of the mass: In our case we will always consider a steady state situation. A steady state situation occurs when the mass variation with respect to time is equal to 0; that is, in steady state condition the aggregated term is equal to 0: Considering a simplified system (steady state) the mass going inside is equal to the one going out, for this reason, the MASS FLOW RATE (the mass balance) is expressed as follow: The mass flow rate is equal to the density of the fluid flowing (p)* the velocity of that fluid (w) * the area (A); the latter is The area is the one depicted in red: The mass flow rate is constant while the volumetric one is not: IRP (or quasi-equilibrium process) is a quasi-equilibrium process where the departure from thermodynamic equilibrium is at most infinitesimal. All states through which the system passes in a quasi-equilibrium process may be considered equilibrium states. Because non-equilibrium effects are inevitably present during actual processes, systems of engineering interest can at best approach, but never realize, a quasi-equilibrium process. 6 The volumetric flow rate can change between inlet and outlet. 2. ENERGY and ENTHALPY BALANCE – first law of thermodynamic: A generic power based system is a system in which we have a flow rate going inside (m in), a flow rate going outside (m out) and work and heat exchange with the environment, as a matter of fact, we have L (work) going inside and outside and the same for the heat (Q). The conservation is always the same: the quantity going inside are equal to the quantity going outside plus the aggregated term. =n the case of energy balance, the mass that goes inside is multiplied by a coefficient, which is called “e”. This coefficient expresses the specific energy of the fluid and it has three components: 1) Internal energy (u): Function of the temperature 2) Potential energy (e p): Function of the elevation with respect to the ground 3) Kinetic energy (e c) The internal energy is a number, we can calculate it, it is already known according to the property of the fluid. The same for the potential energy, which is the function of the elevation and the kinetic is the function of the velocity. The energy exchange with the environment can derive by two main dimensions: work and heat. In this case the system exchanges mechanical power, that is, the work over time and heat over time; for this reason: This is because the balance is expressed in terms of power. 7 We will now analyze the energy balance by looking at different systems: a) CLOSED SYSTEM: The closed system is a system that cannot exchange mass. Let’s imagine that we are now going to provide heat to the closed system and inside there is a gas: =f we provide heat to the gas we have an expansion, which means work goes outside (we could also have heat going outside). The work going outside is given by the combustion of a fuel which introduces in the system a given amount of heat such that it is possible to produce work (that is, electricity). → Once heat is introduced, from time t 0 we move to time t 1. Moving from the first function to the second one, we are doing the integral of the power in time: Integral: As the “e”: We have said before that it is equal to the sum of internal, potential and kinetic energy, however, the mass inside the closed system has a velocity compared to the environment that is equal to 0, so the kinetic energy of the mass inside is equal to 0 and the same holds for the potential energy. So the specific energy is equal just to the internal one, since I neglect the other two components. → we have then the mass multiplied by the internal energy, that is, U (the internal energy of the system). The first law of thermodynamic states that in a closed system the variation of internal energy is equal to the heat going inside minus the work going outside. The net work done by a closed system (useful work done by a closed system) during an internal reversible process (IRP) is generated by the introduction of an expansion, that is, the variation in volume (dV). Of course, the variation in volume has to be greater than 0, then, it has to be positive in order to create work. L out is equal to the integral of pressure multiplied by volume variation (if the volume variation is negative then the work would not go outside and remain inside). 8 b) OPEN SYSTEM: As we can see from the picture, the is mass going inside and outside, while heat goes inside and work goes outside. We assume steady state condition, so where the derivative with respect to time is equal to 0, for this reason the accumulation term is 0: If we substitute the expression of specific energy, the result is as follow: Note than “m” has not in or out written since the mass flow in an open system is the same, m in=m out. As we can see from the function before, L* out is not net work L out is not the net work, this is because there is a mass flow that has to be created by energy, that is, in order to have a mass flow we need to induce a velocity. By neglecting kinetic and potential energy (just for theoretical aspects), we need to introduce ENTHALPY. Enthalpy is given by internal energy summed with pressure and specific volume: The energy balance is equal to the one for close system but the difference is that in open ones we have to use enthalpy and not internal energy. Enthalpy is of high importance in order to have the net work of an open system. As a matter of fact, by looking at the integral form here: The specific form: We can see that L is the net work, that means that in order to have net work we need to use the enthalpy instead of the internal energy. While in a close system we need volume variation to produce work, in an open system we need pressure variation, which has to be NEGATIVE: As we can see, the pressure variation has to be negative in order to have a positive work. 9 c) CYCLIC PROCESS: A cyclic process is a sequence of transformation that can be composed by open and closed system. We start from a point (condition) with a fluid and we continuously exchange heat and work; the processes end in the same place (point). The energy balance is of a cyclic process is: The energy exchanged with the environment going inside the system is equal to the one going outside. Also in this case we neglect “m*e” because the flow rate going inside is equal to the one going outside, since the initial point and the final one are the same. Energy balance is important since we need to quantify starting from a given amount of fuel (heat) which is the amount of KW of electricity we can obtain. However, energy balance does not include any information about the quality of the process; as a matter of fact, we can have an internal combustion engine with different efficiencies, that is, two different combustion engines can give the same amount of work but the process might be efficient on one side and inefficient on the other side if we look at the energy balance. → The energy balance is really quantitative, it doesn’t measure the efficiency. 10 3. ENTROPY BALANCE – second law of thermodynamic: Second law of thermodynamic: In order to introduce the second law of thermodynamics, we need to start from the origin, which is the Clausius statement: Let’s imagine that we have two bodies in contact, one with low temperature and the second one with a hot temperature, the heat CANNOT move from lower temperature to higher temperature, the only possibility is to move from hot to low temperature. Let’s impose in the middle the energy balance: If we look at the volume we can say that the heat going inside is equal to the one going outside. if we impose the energy balance, it does not provide information about the quality and about the possibility of the process; as a matter of fact, if we only take energy balance into consideration, the process looks possible. → In order to provide info about quality and possibility we need the second law which is the entropy balance. In other words, this means that if we want to move heat from a low temperature body to a high temperature one, we need to use WORK. The Kelvin-Planck statement defines that the efficiency of the system cannot be 100%, if we apply the energy balance to a system like this: The process looks possible. In practice we know that this is not possible, work and heat are not the same since if we want to produce work starting from heat, we will produce it, but at the same time we produce a given amount of heat released from the environment: The heat represents the consequence of an internal combustion engine, for which the generation of Qc is inevitable. It is impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from a cooler to a hotter body. 11 Kelvin-Planck statement: =n order to better understand this, let’s explain the difference between energy balance and entropy: In an IRP, the mechanical work done by a system has a function where the integral of an intensive property (P) is multiplied by an extensive one (V); for this reason, we will do the dame for heat. At the end, the heat going inside the system is equal to the integral of temperature which is the intensive property defined just at equilibrium. Remember that this expression is right only in internal reversible process, this is because just in IRP temperature is defined. To sum up: - The intensive property is T (temperature) - The extensive property is S (entropy): Entropy is a property and it expresses the level of order or disorder inside the system. If, for example, we have a closed system with a gas, this can be ordered or not ordered, which means that if the gas is low the entropy is low, if heat is introduced then we increase the level of disorder in the system even if gas is low and, thus, entropy increases. If the entropy variation is positive, the heat stays inside; if the S (entropy) is lower than 0, the heat is going outside. It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of energy by work to its surroundings while receiving energy by heat transfer from a single thermal reservoir. Y = intensive X = extensive 12 In order to better explain entropy, we will introduce three cases: 1) CASE I – SPONTANEOUS PROCESS: In this case we have a thermal reservoir at constant temperature (a body that keeps the temperature constant even if there is a heat exchange). As we can imagine, heat flows from the body at high temperature to the body at low temperature. If we impose the entropy balance to this system and the temperature is constant: Considering the definition of heat and the fact that temperature is constant, we can say that the variation of entropy of the hot reservoir is equal to: The same holds for the cold reservoir: What happens to the entropy balance in this case? The entropy balance for an isolated system is always the same, the overall entropy variation of the system given by the generation of entropy is equal to the entropy variation of all the subsystems inside the control volume. If we assume that Qh=Qc, that is, all the heat is transferred to Qc and they are the same, this also means that: Th>Tc If we substitute these two functions: But we also know that Th is greater than Tc and also temperature is always greater than 0, so this means: -∆Sh is lower than ∆Sc, since Th is greater than Tc. The overall entropy variation then is positive: Once the heat moves from the hot to the cold body, this process cannot do the opposite. For a spontaneous process which is not reversible, the generation of entropy is always greater than 0. 13 2) CASE II – NOT-SPONTANEOUS PROCESS: In this case the heat moves from the cold to the hot body (case which before we said it was not possible): Let’s imagine Q moves from Tc to Th: We have the same assumptions as before, we just change the direction of heat. Since the entropy variation is Q/T, ∆Sh is now positive due to the fact that the heat goes inside the subsystem: While the opposite happens for ∆Sc since the heat goes outside: With the same assumption of before, Th>Tc still holds. The point is that Th is always greater than Tc, but now ∆Sh is a positive number, so in this situation we will have that ∆Sh positive and ∆Sc is negative. The absolute value of the variation of entropy is greater compared to ∆Sh, in other terms, the absolute value is the same as before, but now ∆Sc is greater but negative. The overall variation is the sum of the entropy variation of the subsystems: Which means that the generation of entropy is lower than 0. If we impose the entropy balance to a process that is not possible, the generation to entropy is lower than 0. 14 3) CASE III – REVERSIBLE PROCESS: In this case Th and Tc are equal, since the heat can go from one body to the other and can also do the opposite, that is, a reversible process is enacted. If Tc is equal to Tc, the two entropy variation are equal, and the generation of entropy is equal to 0. There is a continuous exchange of heat in order to keep the temperature constant. For this reason, the generation of entropy is equal to 0 in a process that is reversible: Let’s imagine these two bodies in contact, let’s imagine that for a while the heat goes from A to B, but since the temperature needs to be the same, it will flow again from B to A: there is a continuous exchange of heat in order to keep temperature constant. However, in real life, once the heat moves from one body to the other, reversibility is not possible: If we have a process that is possible, the generation of entropy is greater than 0; this process would be possible and irreversible. Once the heat moves from the hot to the cold body it is not possible to reverse the heat, or we can reverse it using work (not spontaneous process). TO SUM UP: a) Spontaneous process: S gen >0 b) Not-spontaneous process (not Clausius): S gen