# FossilFuelBoiler ## 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. ![ThermoSysPro.MultiFluids.Boilers.FossilFuelBoiler.svg](./icons/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 - 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.