FossilFuelBoiler

FossilFuelBoiler#

ThermoSysPro Version 4.2#

This component model is documented in Sect. 7.2 of the ThermoSysPro book.

Fossil fuel boiler#

The boiler is the most complex subsystem of a power plant.
It is split into a pair of interacting circuits: the water/steam circuit and the flue gases circuit.
There are different components present in flue gases and water/steam circuits: boiler furnace with membrane water-walls, heat exchangers, drums, headers, volumes, mixers, splitters, and valves.

Modelica component model#

The equations mentioned below are implemented in the component FossilFuelBoiler, located in the MultiFluids.Boilers sub-library.
The component has 5 connectors:

  • Cws1: water/steam flow at the inlet,

  • Cws2: water/steam flow at the outlet,

  • Cair: air at the inlet,

  • Cfuel: fuel at the inlet,

  • Cfg: flue gases at the outlet.

ThermoSysPro.MultiFluids.Boilers.FossilFuelBoiler.svg

Nomenclature#

Symbol

Description

Unit

Definition

Modelica name

\( c_{p, f} \)

Fuel specific heat capacity

\( \mathrm{J/kg/K} \)

Cpcomb

\(E_x \)

Dry air stoichiometry necessary for 1kg fuel combustion

-

Proportion of oxygen in the air at the inlet required to burn 1kg of fuel

-

\(E_{X,a} \)

Excess air

\(\% \)

\( 100 \cdot \left( \frac{\dot{m}_a \cdot (1 - X_{h_2O, a})}{\dot{m}_f \cdot E_X} - 1 \right) \)

exc_air

\( h_{a, i} \)

Air specific enthalpy at the inlet

\(\mathrm{J/kg} \)

Hea

\(\tilde{h}_{a, r} \)

Air reference specific enthalpy

\(\mathrm{J/kg} \)

\(2501569 \cdot X_{h_2O, a} \)

Hrair

\( h_{f} \)

Fuel specific enthalpy at the inlet

\(\mathrm{J/kg} \)

\(c_{p, f} \cdot (T_f - 273.16) \)

Hcomb

\( \tilde{h}_{f, r} \)

Fuel reference specific enthalpy

\(\mathrm{J/kg} \)

0

Hrcomb

\( h_{g} \)

Flue gases specific enthalpy after combustion

\(\mathrm{J/kg} \)

Hf

\( h_{g, o} \)

Flue gases specific enthalpy at the outlet

\(\mathrm{J/kg} \)

Hsf

\( \tilde{h}_{g, r} \)

Flue gases reference specific enthalpy

\(\mathrm{J/kg} \)

\(2501569 \cdot X_{h_2O, g} \)

Hrfum

\( h_{ws, i} \)

Water/steam specific enthalpy at the inlet

\(\mathrm{J/kg} \)

Hee

\( h_{ws, o} \)

Water/steam specific enthalpy at the outlet

\(\mathrm{J/kg} \)

Hse

LHV

Fuel lower heating value

\(\mathrm{J/kg} \)

Cfuel.LHV

\(\dot{m}_a \)

Air mass flow rate

\(\mathrm{kg/s} \)

Qea

\(\dot{m}_f \)

Fuel mass flow rate

\(\mathrm{kg/s} \)

Qcomb

\(\dot{m}_g \)

Flue gases mass flow rate

\(\mathrm{kg/s} \)

Qsf

\(\dot{m}_{ws} \)

Water/steam mass flow rate

\(\mathrm{kg/s} \)

Qe

\( M_C \)

Carbon atomic mass

\(\mathrm{kg/kmol} \)

12.01115

amC

\( M_H \)

Hydrogen atomic mass

\(\mathrm{kg/kmol} \)

1.00797

amH

\( M_O \)

Oxygen atomic mass

\(\mathrm{kg/kmol} \)

15.9994

amO

\( M_S \)

Sulfur atomic mass

\(\mathrm{kg/kmol} \)

32.064

amS

\( M_{CO_2} \)

\(CO_2\) molar mass

\(\mathrm{kg/kmol} \)

\(M_C + 2 \cdot M_O \)

amCO2

\( M_{H_2O} \)

\(H_2O\) molar mass

\(\mathrm{kg/kmol} \)

\(M_O + 2 \cdot M_H \)

amH2O

\( M_{SO_2} \)

\(SO_2\) molar mass

\(\mathrm{kg/kmol} \)

\(M_S + 2 \cdot M_O \)

amSO2

\( P_{g,i} \)

Air pressure at the inlet

\(\mathrm{Pa} \)

Pea

\( P_{g,o} \)

Flue gases pressure at the outlet

\(\mathrm{Pa} \)

Psf

\( P_{ws,i} \)

Water/steam pressure at the inlet

\(\mathrm{Pa} \)

Pee

\( P_{ws,o} \)

Water/steam pressure at the outlet

\(\mathrm{Pa} \)

Pse

\( T_{a,i} \)

Air temperature at the inlet

\(\mathrm{K} \)

Tea

\( T_{f} \)

Fuel temperature at the inlet

\(\mathrm{K} \)

Tcomb

\( T_{g,o} \)

Flue gases temperature at the outlet

\(\mathrm{K} \)

Cfg.T

\( T_{g} \)

Flue gases temperature after combustion

\(\mathrm{K} \)

Tf

\( W_l \)

Thermal losses

\(\mathrm{W} \)

Wloss

\( X_{C,f} \)

Carbon mass fraction in the fuel

\(\mathrm{-} \)

XCcomb

\( X_{H,f} \)

Hydrogen mass fraction in the fuel

\(\mathrm{-} \)

XHcomb

\( X_{O,f} \)

Oxygen mass fraction in the fuel

\(\mathrm{-} \)

XOcomb

\( X_{S,f} \)

Sulfur mass fraction in the fuel

\(\mathrm{-} \)

XScomb

\( X_{CO_2,a} \)

\( CO_2 \) mass fraction in the air at the inlet

\(\mathrm{-} \)

XeaCO2

\( X_{CO_2,g} \)

\( CO_2 \) mass fraction in the flue gases

\(\mathrm{-} \)

XsfCO2

\( X_{H_2O,a} \)

\( H_2O \) mass fraction in the air at the inlet

\(\mathrm{-} \)

XeaH2O

\( X_{H_2O,g} \)

\( H_2O \) mass fraction in the flue gases

\(\mathrm{-} \)

XsfH2O

\( X_{O_2,a} \)

\( O_2 \) mass fraction in the air at the inlet

\(\mathrm{-} \)

XeaO2

\( X_{O_2,g} \)

\( O_2 \) mass fraction in the flue gases

\(\mathrm{-} \)

XsfO2

\( \eta \)

Boiler efficiency \( 0 < \eta \le 1 \)

\(\mathrm{-} \)

Net thermal power at the outlet divided by the total thermal power at the inlet

eta_boil

\( \eta_c \)

Combustion efficiency \( 0 < \eta_c \le 1 \)

\(\mathrm{-} \)

Burnt fuel mass divided by the input fuel mass

etacomb

\( \Lambda_g \)

Flue gases pressure loss coefficient

\(\mathrm{m}^{-4} \)

Kf

\( \Lambda_{ws} \)

Water/steam pressure loss coefficient

\(\mathrm{m}^{-4} \)

Ke

\( \rho_g \)

Flue gases density

\(\mathrm{kg/m}^3 \)

rhof

\( \rho_{ws} \)

Water/steam density

\(\mathrm{kg/m}^3 \)

rhoe

Governing equations#

The FossilFuelBoiler model is based on the energy and momentum balance equations.
This set of equations must be completed by the state equations involving \( h_{a,i}, \, h_{g,o}, \, T_g, \, \rho_g \; \text{and} \; \rho_{ws} \).

Mass balance equation for the flue gases#

  • Validity domain:

    \( \forall \dot{m}_g \, , \dot{m}_a \; \text{and} \; \dot{m}_f \)

  • Mathematical formulation:

\[\dot{m}_g = \dot{m}_a + \dot{m}_f \]

  • Comments:

Flue gases result from the combustion of fuel with air. If the combustion is not perfect (i.e. \( \eta_c < 1 \) ), there is unburnt fuel in the exhaust flue gases.

Energy balance equation for the flue gases#

  • Validity domain:

    \( \forall \dot{m}_a \, , \dot{m}_f \; \text{and} \; \dot{m}_g>0 \)

  • Mathematical formulation:

\[ \dot{m}_g \cdot h_g = \dot{m}_a \cdot h_{a,i} + \dot{m}_f \cdot (h_f + \eta_c \cdot LHV) - W_l \]

  • Comments:

This equation is used to compute the flue gases specific enthalpy after combustion \( h_g \).
The combustion efficiency \(\eta_c \) and the fuel lower heating value LHV are model inputs.
The specific enthalpies \( h_f \) and \( h_{a,i} \) are computed using properties tables from the known temperatures \(T_f \) and \(T_{a,i} \).

Power exchanged in the boiler between flue gases and water/steam circuits#

  • Validity domain:

    \( \forall \dot{m}_g \, , \dot{m}_a \, , \dot{m}_f \; \text{and} \;\ \dot{m}_{ws} \neq 0 \)

  • Mathematical formulation:

\[ \dot{m}_a \cdot h_{a,i} + \dot{m}_f \cdot (h_f + \eta_c \cdot LHV) - W_l - \dot{m}_g \cdot h_{g,o} = \dot{m}_{ws} \cdot (h_{ws,o} - h_{ws,i}) \]

  • Comments:

This equation computes the water/steam specific enthalpy at the outlet \( h_{ws,o} \).

Boiler efficiency#

  • Validity domain:

\( \dot{m}_a > 0 \; \text{and} \;\ \dot{m}_f > 0 \)

  • Mathematical formulation:

\[ \eta = 100 \cdot \frac{\dot{m}_{ws} \cdot (h_{ws,o} - h_{ws,i})}{ \dot{m}_a \cdot h_{a,i} + \dot{m}_f \cdot (h_f + LHV)} \]

  • Comments:

Another possible definition for the efficiency only takes into account the fuel LHV:

\[ \eta = 100 \cdot \frac{\dot{m}_{ws} \cdot (h_{ws,o} - h_{ws,i})}{\dot{m}_f \cdot LHV} \]

Momentum balance equation for the flue gases#

  • Validity domain:

\( \forall \dot{m}_f \)

  • Mathematical formulation:

\[ P_{f,o} = P_{f,i} - \Lambda_f \cdot \frac{\dot{m}_f \cdot |\dot{m}_f|}{\rho_f} \]

  • Comments:

Momentum balance equation for the water/steam#

  • Validity domain:

\( \dot{m}_a > 0 \; \text{and} \;\ \dot{m}_f > 0 \)

  • Mathematical formulation:

\[ P_{w,o} = P_{w,i} - \Lambda_{ws} \cdot \frac{\dot{m}_{ws} \cdot |\dot{m}_{ws}|}{\rho_{ws}} \]

  • Comments:

Dry air stoichiometry for the combustion of 1 kg fuel#

  • Validity domain:

\( X_{H_20,a} < 1 \; \text{and} \;\ X_{O_2,a} > 0 \)

  • Mathematical formulation:

\[ E_X = M_O \cdot \frac{\frac{2 \cdot X_{C,f}}{M_C} + \frac{X_{H,f}}{2 \cdot M_H} + \frac{2 \cdot X_{S,f}}{M_S} - \frac{X_{O,f}}{M_O}}{\frac{X_{0_2,a}}{1 - X_{H_2O,a}}} \]

  • Comments:

This formulation arises from the chemical reactions considered in the combustion:

\( C + O_2 \longrightarrow CO_2 \)

\( H + \frac{1}{4} 0_2 \longrightarrow H_2O \)

\( S + O_2 \longrightarrow SO_2 \)

\( CO_2 \) mass fraction in the flue gases#

  • Validity domain:

\( \dot{m}_g \neq 0 \)

  • Mathematical formulation:

\[ X_{CO_2,g} = \frac{\dot{m}_a}{\dot{m}_g} \cdot X_{CO_2,a} + \frac{\dot{m}_f}{\dot{m}_g} \cdot X_{C,f} \cdot \frac{M_{CO_2}}{M_C} \]

  • Comments:

This formulation arises from the chemical reaction considered in the combustion:

\[ C + O_2 \longrightarrow CO_2 \]

\( H_2O \) mass fraction in the flue gases#

  • Validity domain:

\( \dot{m}_g \neq 0 \)

  • Mathematical formulation:

\[ X_{H_2O,g} = \frac{\dot{m}_a}{\dot{m}_g} \cdot X_{H_2O,a} + \frac{\dot{m}_f}{\dot{m}_g} \cdot X_{H,f} \cdot \frac{M_{H_2O}}{2 \cdot M_H} \]

  • Comments:

This formulation arises from the chemical reaction considered in the combustion:

\[ H + \frac{1}{4} O_2 \longrightarrow H_2O \]

\( O_2 \) mass fraction in the flue gases#

  • Validity domain:

\( \dot{m}_g \neq 0 \)

  • Mathematical formulation:

\[ X_{O_2,g} = \frac{\dot{m}_a}{\dot{m}_g} \cdot X_{O_2,a} - M_O \cdot \frac{\dot{m}_f}{\dot{m}_g} \cdot \left( \frac{2 \cdot X_{HC,f}}{M_C} + \frac{X_{H,f}}{2 \cdot M_H} + \frac{2 \cdot X_{S,f}}{M_S} \right) + \frac{\dot{m}_f}{\dot{m}_g} \cdot X_{O,f} \]

  • Comments:

This formulation arises from the three chemical reactions mentioned in the dry air stoichiometry equation.

\( SO_2 \) mass fraction in the flue gases#

  • Validity domain:

\( \dot{m}_g \neq 0 \)

  • Mathematical formulation:

\[ X_{SO_2,g} = \frac{\dot{m}_a}{\dot{m}_g} \cdot X_{SO_2,a} + \frac{\dot{m}_f}{\dot{m}_g} \cdot X_{S,f} \cdot \frac{M_{SO_2}}{M_S}\]

  • Comments:

This formulation arises from the three chemical reactions mentioned in the dry air stoichiometry equation.

References#

Contents