Fossil fuel boiler
## Copyright © EDF 2002 - 2026
## 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.
## 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
- El Hefni, Baligh and Bouskela, Daniel (2019). [Modeling and Simulation of Thermal Power Plants with ThermoSysPro](https://link.springer.com/book/10.1007/978-3-030-05105-1). Springer Nature Switzerland AG.
El Hefni, Baligh and Bouskela, Daniel (2019). [Modeling and Simulation of Thermal Power Plants with ThermoSysPro](https://link.springer.com/book/10.1007/978-3-030-05105-1), sect. 7.2. Springer Nature Switzerland AG.
Author Baligh El Hefni
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