Termoeconomía y optimización energética

Temario 1. Introducción 2. Revisión de termodinámica 3. La exergía 4. Determinación de exergía 5. Balances y Álgebra lineal 6. El coste exergético 7. Análisis termoeconómico 8. Optimización termoeconómica 9. Integración energética

Fronteras de análisis Ambiente Entorno Sistema System: an identifiable collection of matter whose behaviour is the subject of study. A specified region that can be separated from everything else by a well – defined surface (system boundary). Boundary Surroundings: everything outside the boundary.

Tipos de sistemas m m Q m Q Q W W W Abierto Cerrado Aislado Closed system: no flow matter across the system, but heat and power flows are alloyed. Isolated system: if no changes in the surroundings produce no changes in the system The terms Heat and work refer to interactions in which energy is transferred. Work: work is done by a system on its surroundings if the sole effect on everything external to the system could have been the raising of a mass. The symbol W is used to denote work. Heat: The symbol Q denotes Heat.

Estado de un sistema Sistema Estado: Condición de un sistema definida por el conjunto de sus propiedades. Property: any measurable characteristic of a system whose value depends on the condition of the system, on the state, but not in the history of the system Thermodynamic state: condition of the system which is described fully by its observable properties. The condition of a system at any instant of time. The state determines the properties of the system. Simple compressible Substance: One for which the only reversible work mode is volume change (pdV work). A wide range of industrially important gases and liquids are satisfactory modelled as simple compressible substances. For a simple compressible substance of fixed composition, the number of independent thermostatic properties is Two (state principle). Propiedades: Características macroscópicas de un sistema a las que puede asignarse un valor en un instante dado sin un conocimiento previo de la historia del sistema: masa, vol, energía, presión, temperatura.

Propiedades del sistema y notación Cantidad de materia Aditivas específicas (/masa) molares (/cantidad de sustancia) Intensivas Extensivas Minúsculas p T Mayúsculas V M U H S B Property: any measurable characteristic of a system whose value depends on the condition of the system, on the state, but not in the history of the system Intensive properties are independent of the size or extent of the system. Pressure, Temperature. Extensive properties depend on the size or extent of the system. Volume, mass, energy. Specific property. When an extensive property is reported on a unit mass or a unit mole (molar) Mole. Quantity of substance having a mass numerically equal to its molecular weight. Notación: Por unidad de tiempo (con un punto encima) Por unidad de masa (minúsculas) Por cantidad de sustancia (con una tilde encima)

Tipos de transformaciones h p v Among the different processes or transformations it’s usual to see the following ones. Isochoric, Isobaric, Isothermal in which the system volume, pressure or temperature remain constant. Also the adiabatic transformation is a usual one, but in this case no heat exchange is allowed (Q=0). The important difference is that Heat is not a property. Isocórica Isoterma Isobara Isoentálpica Isoentrópica Adiabática

Equilibrio vs Estado Permanente Intercambio de: Propiedades intensivas Calor Trabajo Materia Equilibrio termodinámico Constante Estado permanente Between the Themodynamic Equilibrium and the Steady State exists a fundamental difference. Although in both of them the intensive properties remain constant, in the former no mass or energy exchange is allowed.

Principios de la termodinámica 0 - Temperatura Equilibrio térmico Balances 1 - Energía Conservación energía Energía = 0 Exergía < 0 2 - Entropía Entropía dSi  0 Entropía >0 Zeroth Law.- (Principle of thermal equilibrium). If two systems A and B are in equilibrium with system C when in thermal contact with C, then they are in equilibrium with each other. Basis of temperature measurement: Thermometer. Hotness and Coldness of an object Fist Law.- General energy conservation law. Energy is not created or destructed it’s only transformed. Input Energy minus Output Energy = Energy accumulation. Second Law.- Clausius postulate: Thermal energy cannot, of itself, pass from a lower to a higher temperature. Kelvin-Planck statement: a PMM2 (perpetual motion machine of the second kind) is impossible. A PMM2 is a heat engine that delivers net positive work, while experiencing a heat interaction with a single system in a stable equilibrium state. Real heat engines efficiency is invariable less than 100 % (Carnot efficiency). 3 – Entropía Absoluta S = 0 a T= 0 K

1er principio termodinámica Energía entrante = Energía saliente + Energía acumulada U W Q mgz Fist Law.- General energy conservation law. Energy is not created or destructed it’s only transformed. Input Energy minus Output Energy = Energy accumulation. Entalphy. h = u + p·v Let’s figure an open system in a steady state, with a mass input in 1 and a mass output in 2. Let’s think an ideal piston in A1 that in a determined time passes to A1’, and A2 to A2’. v1 & v2 specific volume´s at T1,p1 & T2,p2. The laws in thermodynamics deal with interactions between systems. For a control mass these interactions may be divided into two classes: work interactions and heat interactions. Work: work is done by a system on its surroundings if the sole effect on everything external to the system could have been the raising of a mass. The symbol W is used to denote work.

Ej. Balance Energía Humos Calor Sonidos Pérdidas Energía Equipo Trabajo  = We/Wt < 1 Pérdidas

Ej. Balance Energía Orion LT500EC  = We/Wt < 1 Humos Gasolina 325 g/kWhe 5900 We  = We/Wt < 1 Humos Orion LT500EC

2º Principio termodinámica Kelvin-Planck: Es imposible la existencia de una máquina cíclica que realice trabajo sin más que tomar calor de un sólo foco Qf T frío T caliente Qc W=Qc-Qf Q W C implica K-P K-P implica C Q T frío T caliente Q T frío T caliente W The second law is required to establish the difference in quality between mechanical and thermal energy and to indicate the directions of spontaneous processes. Entropy is a measure of the “unavailability” of internal energy. The entropy generation may be caused by a heat interchange with the environment or by internal production. Gibbs equation: TdS = dU + P dV (for a simple compressible substance of a state of equilibrium, any two suitable independent properties can be used to determine a third property: U = U (S,V); dU= (dU/dS)v.dS+(dU/dV)s.dV; where T= (dU/dS)v and P = -(dU/dV)s k = Bolzmann constant  = Themodynamic probability (Physical measure of the system randomness/disorder). Clausius: Es imposible la existencia de una máquina que haga pasar calor de un cuerpo frío a otro más caliente sin consumir trabajo

2º ppio Reversible vs Irreversible Un proceso es reversible si el sistema y todas las partes de su entorno pueden devolverse exactamente a sus estados iniciales después de que el proceso haya tenido lugar Transferencia de calor a través de una diferencia finita de temperaturas Expansión libre de un gas o líquido a una presión más baja Reacción química espontánea Mezcla espontánea de sustancias diferentes Rozamiento (deslizamiento y viscosidad) Electricidad a través resistencia Histéresis Deformación inelástica Cogido de Moran UNED. Pág 198 Todos los procesos reales son irreversibles Entonces, ¿qué interés tienen los procesos ideales?

2º ppio: Formulación matemática Ambiente Interna The second law is required to establish the difference in quality between mechanical and thermal energy and to indicate the directions of spontaneous processes. Entropy is a measure of the “unavailability” of internal energy. The entropy generation may be caused by a heat interchange with the environment or by internal production. Gibbs equation: TdS = dU + P dV (for a simple compressible substance of a state of equilibrium, any two suitable independent properties can be used to determine a third property: U = U (S,V); dU= (dU/dS)v.dS+(dU/dV)s.dV; where T= (dU/dS)v and P = -(dU/dV)s k = Bolzmann constant  = Themodynamic probability (Physical measure of the system randomness/disorder). Aproximación estadística:

Reversibilidad e irreversibilidad Proceso Real Irreversibilidad Proceso Ideal Reversibilidad A process is said to be reversible if it is possible for its effects to be eradicated in the sense that there is some way by which both the system and its surroundings can be exactly restored to their respective initial states. A process is irreversible if there is no way to undo it. The condition for reversibility of a process is that: The system passes through a series of equilibrium states, i.e. the process is performed quasi-statically, and Dissipative phenomena are absent from the system. Only Greater than 0 in an adiabatic process. Only = 0 in a reversible and adiabatic process. Reversible: increase of entropy without generation. The entropy comes from the heat absorbed from the environment. Adiabático

Balances Materia: Entrante – Saliente – Acumulada = 0 Energía: Entrante – Saliente – Acumulada = 0 Entropía: Entrante – Saliente – Acumulada = Generada Exergía: Entrante – Saliente – Acumulada = Destruida