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MEASUR-Tools-Suite v1.0.11
The MEASUR Tools Suite is a collection of industrial efficiency calculations written in C++ and with bindings for compilation to WebAssembly.
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This section documents the complete algorithm for determining available heat from solid and liquid fuels. The calculation includes normalization of fuel composition, enthalpy calculations for fuel and air inputs, stoichiometric analysis, flue gas component analysis, and all major loss mechanisms.
Final available heat percentage after all losses.
Available heat is the fraction of input fuel energy remaining for useful work after accounting for sensible heat in flue gas, ash losses, and unburned carbon losses.
\begin{equation}\label{eq:slfgm-available-heat} Q_{avail} = \frac{h_{in} - h_{fg} - h_{ash} - h_{carbon}}{HV_{fuel}}\end{equation}
| \(Q_{avail}\) | Available heat fraction \([\unit{ \unitless}]\) |
| \(h_{in}\) | Total input heat \([\unit{ \btu\per\pound}]\) |
| \(h_{fg}\) | Total sensible heat in flue gas \([\unit{ \btu\per\pound}]\) |
| \(h_{ash}\) | Heat loss due to ash \([\unit{ \btu\per\pound}]\) |
| \(h_{carbon}\) | Heat loss due to unburned carbon \([\unit{ \btu\per\pound}]\) |
| \(HV_{fuel}\) | Heating value of fuel \([\unit{ \btu\per\pound}]\) |
Total heat input from fuel, combustion air, and moisture.
Input heat includes the heating value of the fuel plus sensible heat contributions from elevated fuel temperature, preheated combustion air, and fuel moisture.
\begin{equation}\label{eq:slfgm-h-in} h_{in} = h_{fuel} + h_{combustion,air} + HV_{fuel} + h_{moisture}\end{equation}
| \(h_{in}\) | Total input heat \([\unit{ \btu\per\pound}]\) |
| \(h_{fuel}\) | Sensible heat in fuel \([\unit{ \btu\per\pound}]\) |
| \(h_{combustion,air}\) | Sensible heat in combustion air \([\unit{ \btu\per\pound}]\) |
| \(HV_{fuel}\) | Heating value of fuel \([\unit{ \btu\per\pound}]\) |
| \(h_{moisture}\) | Heat required for fuel moisture \([\unit{ \btu\per\pound}]\) |
Calculate heat content of each flue gas constituent.
For each component in the flue gas, calculate the sensible heat based on temperature rise and mass flow. Water vapor requires special treatment for latent heat of condensation.
\begin{equation}\label{eq:slfgm-h-sensible-co2} h_{CO_2} = m_{CO_2} \cdot \frac{Cp_{CO_2}}{MW_{CO_2}} \cdot (T_{fg} - T_{ref})\end{equation}
\begin{equation}\label{eq:slfgm-h-sensible-h2o} h_{H_2O} = m_{H_2O,fuel} \cdot (h_{sat} + \frac{Cp_{H_2O}}{MW_{H_2O}} \cdot (T_{fg} - T_{ref})) + m_{H_2O,air} \cdot (\frac{Cp_{H_2O}}{MW_{H_2O}} \cdot (T_{fg} - T_{ref}))\end{equation}
\begin{equation}\label{eq:slfgm-h-sensible-so2} h_{SO_2} = m_{SO_2} \cdot \frac{Cp_{SO_2}}{MW_{SO_2}} \cdot (T_{fg} - T_{ref})\end{equation}
\begin{equation}\label{eq:slfgm-h-sensible-o2} h_{O_2} = m_{O_2} \cdot \frac{Cp_{O_2}}{MW_{O_2}} \cdot (T_{fg} - T_{ref})\end{equation}
\begin{equation}\label{eq:slfgm-h-sensible-n2} h_{N_2} = m_{N_2} \cdot \frac{Cp_{N_2}}{MW_{N_2}} \cdot (T_{fg} - T_{ref})\end{equation}
\begin{equation}\label{eq:slfgm-h-fg} h_{fg} = h_{H_2O} + h_{CO_2} + h_{N_2} + h_{O_2} + h_{SO_2}\end{equation}
| \(h_{i}\) | Sensible heat of constituent i \([\unit{ \btu\per\pound}]\) |
| \(m_{i}\) | Mass of constituent i \([\unit{ \pound\per\poundFuel}]\) |
| \(Cp_{i}\) | Specific heat of constituent i - see Gas Constants \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(MW_{i}\) | Molecular weight of constituent i - see Gas Constants \([\unit{ \pound\per\lbmol}]\) |
| \(T_{fg}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(T_{ref}\) | Reference temperature (ambient) \([\unit{ \degreeFahrenheit}]\) |
| \(h_{sat}\) | Enthalpy of saturated steam \([\unit{ \btu\per\pound}]\) |
| \(m_{H_2O,fuel}\) | Water from fuel moisture and combustion \([\unit{ \pound\per\poundFuel}]\) |
| \(m_{H_2O,air}\) | Water from combustion air moisture \([\unit{ \pound\per\poundFuel}]\) |
| \(h_{fg}\) | Total sensible heat in flue gas \([\unit{ \btu\per\pound}]\) |
Calculate enthalpy at saturation for latent heat effects.
The enthalpy of saturated steam is needed to account for latent heat of condensation in the water vapor component of the flue gas.
\begin{equation}\label{eq:slfgm-h-sat} h_{sat} = 1096.7 \cdot (p_{H_2O} \cdot 29.926)^{0.013}\end{equation}
| \(h_{sat}\) | Enthalpy of saturated steam \([\unit{ \btu\per\pound}]\) |
| \(p_{H_2O}\) | Partial pressure of water vapor \([\unit{ \unitless}]\) |
| \(1096.7\) | Empirical correlation coefficient \([\unit{ \btu\per\pound}]\) |
| \(29.926\) | Atmospheric pressure in inches of mercury \([\unit{ \inchMercury}]\) |
| \(0.013\) | Empirical correlation exponent \([\unit{ \unitless}]\) |
Calculate mole fraction of water vapor in flue gas.
The partial pressure of water vapor is needed to determine saturation conditions for latent heat calculations. It is calculated from the volumetric fractions of all constituents using specific gravity ratios.
\begin{equation}\label{eq:slfgm-pp-h2o} p_{H_2O} = \frac{m_{H_2O}/0.047636}{m_{CO_2}/0.116367 + m_{H_2O}/0.047636 + m_{N_2}/0.074077 + m_{O_2}/0.084611 + m_{SO_2}/0.169381}\end{equation}
| \(p_{H_2O}\) | Partial pressure (mole fraction) of water vapor \([\unit{ \unitless}]\) |
| \(m_{i}\) | Mass of constituent i \([\unit{ \pound\per\poundFuel}]\) |
| \(0.047636\) | H2O specific weight - see Gas Constants \([\unit{ \pound\per\cubicFoot}]\) |
| \(0.116367\) | CO2 specific weight - see Gas Constants \([\unit{ \pound\per\cubicFoot}]\) |
| \(0.074077\) | N2 specific weight - see Gas Constants \([\unit{ \pound\per\cubicFoot}]\) |
| \(0.084611\) | O2 specific weight - see Gas Constants \([\unit{ \pound\per\cubicFoot}]\) |
| \(0.169381\) | SO2 specific weight - see Gas Constants \([\unit{ \pound\per\cubicFoot}]\) |
Account for moisture, unburned carbon, and ash losses.
Additional heat losses occur due to moisture evaporation, incomplete combustion leaving unburned carbon in ash, and sensible heat carried away by hot ash.
\begin{equation}\label{eq:slfgm-h-moisture} h_{moisture} = X_{moisture} \cdot (T_{fg} - T_{ref})\end{equation}
\begin{equation}\label{eq:slfgm-h-carbon} h_{carbon} = 14093.0 \cdot X_{unburned,carbon} \cdot (X_{ash}/x_{fuel})\end{equation}
\begin{equation}\label{eq:slfgm-h-ash} h_{ash} = (X_{ash}/x_{fuel}) \cdot 0.25 \cdot (1.8 \cdot T_{ash,discharge} + 32.0 - T_{ref})\end{equation}
| \(h_{moisture}\) | Heat loss due to moisture evaporation \([\unit{ \btu\per\pound}]\) |
| \(h_{carbon}\) | Heat loss due to unburned carbon \([\unit{ \btu\per\pound}]\) |
| \(h_{ash}\) | Heat loss due to ash sensible heat \([\unit{ \btu\per\pound}]\) |
| \(X_{moisture}\) | Moisture percent in fuel \([\unit{ \percent}]\) |
| \(X_{unburned,carbon}\) | Unburned carbon in ash \([\unit{ \percent}]\) |
| \(X_{ash}\) | Ash percent in fuel \([\unit{ \percent}]\) |
| \(x_{fuel}\) | Dry fuel fraction \([\unit{ \unitless}]\) |
| \(T_{fg}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(T_{ref}\) | Reference temperature (ambient) \([\unit{ \degreeFahrenheit}]\) |
| \(T_{ash,discharge}\) | Ash discharge temperature \([\unit{ \degreeFahrenheit}]\) |
| \(14093.0\) | Heating value of carbon \([\unit{ \btu\per\pound}]\) |
| \(0.25\) | Specific heat of ash \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(1.8\) | Fahrenheit to Celsius conversion factor \([\unit{ \unitless}]\) |
| \(32.0\) | Fahrenheit to Celsius offset \([\unit{ \degreeFahrenheit}]\) |
Calculate mass of each flue gas component and fuel heating value.
The mass of each combustion product is calculated from fuel composition and stoichiometry. The heating value is the sum of elemental contributions from carbon, hydrogen, and sulfur. See Gas Constants for stoichiometric constants.
\begin{equation}\label{eq:slfgm-m-co2} m_{CO_2} = x_C \cdot k_{C\to CO_2}\end{equation}
\begin{equation}\label{eq:slfgm-m-h2o} m_{H_2O} = x_H \cdot k_{H\to H_2O} + x_{moisture} + (M_{comb,air} \cdot M_{air,moisture}/100)\end{equation}
\begin{equation}\label{eq:slfgm-m-so2} m_{SO_2} = x_S \cdot k_{S\to SO_2}\end{equation}
\begin{equation}\label{eq:slfgm-m-o2} m_{O_2} = O2_{s,air} \cdot EA\end{equation}
\begin{equation}\label{eq:slfgm-m-n2} m_{N_2} = N2_{s,air} \cdot (1 + EA)\end{equation}
\begin{equation}\label{eq:slfgm-hv} HV_{fuel} = x_C \cdot k_{HV,C} + x_H \cdot k_{HV,H} + x_S \cdot k_{HV,S}\end{equation}
| \(m_{i}\) | Mass of constituent i per unit fuel \([\unit{ \pound\per\poundFuel}]\) |
| \(x_C\) | Carbon mass fraction in fuel \([\unit{ \unitless}]\) |
| \(x_H\) | Hydrogen mass fraction in fuel \([\unit{ \unitless}]\) |
| \(x_S\) | Sulfur mass fraction in fuel \([\unit{ \unitless}]\) |
| \(x_{moisture}\) | Moisture mass fraction in fuel \([\unit{ \unitless}]\) |
| \(k_{C\to CO_2}\) | Carbon to CO2 stoichiometric ratio - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(k_{H\to H_2O}\) | Hydrogen to H2O stoichiometric ratio - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(k_{S\to SO_2}\) | Sulfur to SO2 stoichiometric ratio - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(M_{comb,air}\) | Total combustion air \([\unit{ \pound\per\poundFuel}]\) |
| \(M_{air,moisture}\) | Moisture percent in combustion air \([\unit{ \percent}]\) |
| \(O2_{s,air}\) | Stoichiometric O2 required \([\unit{ \pound\per\poundFuel}]\) |
| \(N2_{s,air}\) | Stoichiometric N2 from air \([\unit{ \pound\per\poundFuel}]\) |
| \(EA\) | Excess air fraction \([\unit{ \unitless}]\) |
| \(HV_{fuel}\) | Heating value of fuel \([\unit{ \btu\per\pound}]\) |
| \(k_{HV,C}\) | Heating value of carbon \([\unit{ \btu\per\pound}]\) |
| \(k_{HV,H}\) | Heating value of hydrogen \([\unit{ \btu\per\pound}]\) |
| \(k_{HV,S}\) | Heating value of sulfur \([\unit{ \btu\per\pound}]\) |
| \(100\) | Percentage conversion factor \([\unit{ \unitless}]\) |
Calculate theoretical air requirements from fuel composition.
Stoichiometric air is the theoretical minimum air required for complete combustion. The calculation accounts for oxygen requirements of carbon, hydrogen, and sulfur, minus any oxygen present in the fuel. See Gas Constants for stoichiometric ratios.
\begin{equation}\label{eq:slfgm-stoich-air} O2_{s,air} = x_C \cdot k_{C\to O_2} + x_H \cdot k_{H\to O_2} + x_S \cdot k_{S\to O_2} - x_{O_2}\end{equation}
\begin{equation}\label{eq:slfgm-n2s-air} N2_{s,air} = O2_{s,air} \cdot k_{N_2/O_2}\end{equation}
\begin{equation}\label{eq:slfgm-ms-air} M_{s,air} = O2_{s,air} + N2_{s,air}\end{equation}
\begin{equation}\label{eq:slfgm-m-comb-air} M_{comb,air} = M_{s,air} \cdot (1 + EA)\end{equation}
| \(O2_{s,air}\) | Stoichiometric O2 required \([\unit{ \pound\per\poundFuel}]\) |
| \(N2_{s,air}\) | Stoichiometric N2 from air \([\unit{ \pound\per\poundFuel}]\) |
| \(M_{s,air}\) | Stoichiometric air \([\unit{ \pound\per\poundFuel}]\) |
| \(M_{comb,air}\) | Total combustion air \([\unit{ \pound\per\poundFuel}]\) |
| \(x_C\) | Carbon mass fraction in fuel \([\unit{ \unitless}]\) |
| \(x_H\) | Hydrogen mass fraction in fuel \([\unit{ \unitless}]\) |
| \(x_S\) | Sulfur mass fraction in fuel \([\unit{ \unitless}]\) |
| \(x_{O_2}\) | Oxygen mass fraction in fuel \([\unit{ \unitless}]\) |
| \(k_{C\to O_2}\) | Carbon to O2 stoichiometric ratio - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(k_{H\to O_2}\) | Hydrogen to O2 stoichiometric ratio - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(k_{S\to O_2}\) | Sulfur to O2 stoichiometric ratio - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(k_{N_2/O_2}\) | N2 to O2 ratio in air - see Gas Constants \([\unit{ \pound\per\pound}]\) |
| \(EA\) | Excess air fraction \([\unit{ \unitless}]\) |
Calculate sensible enthalpy of fuel and combustion air inputs.
When fuel or combustion air enters at temperatures above ambient, they contribute additional sensible heat to the system. The specific heat of combustion air varies with temperature.
\begin{equation}\label{eq:slfgm-h-fuel} h_{fuel} = C_{pfuel} \cdot (1 - x_{moisture}) \cdot (T_{fuel} - T_{amb})\end{equation}
\begin{equation}\label{eq:slfgm-cp-comb-air} C_{p,air} = a + b \cdot T_{comb}\end{equation}
\begin{equation}\label{eq:slfgm-h-comb-air} h_{comb,air} = M_{comb,air} \cdot C_{p,air} \cdot (T_{comb} - T_{amb}) / \rho_{air}\end{equation}
| \(h_{fuel}\) | Sensible enthalpy of fuel \([\unit{ \btu\per\pound}]\) |
| \(C_{pfuel}\) | Specific heat of fuel \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(x_{moisture}\) | Moisture fraction in fuel \([\unit{ \unitless}]\) |
| \(T_{fuel}\) | Fuel temperature \([\unit{ \degreeFahrenheit}]\) |
| \(T_{amb}\) | Ambient air temperature \([\unit{ \degreeFahrenheit}]\) |
| \(C_{p,air}\) | Specific heat of combustion air \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(a\) | Linear coefficient for air specific heat \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(b\) | Temperature coefficient for air specific heat \([\unit{ \btu\per\pound\degreeFahrenheit\squared}]\) |
| \(T_{comb}\) | Combustion air temperature \([\unit{ \degreeFahrenheit}]\) |
| \(h_{comb,air}\) | Sensible enthalpy of combustion air \([\unit{ \btu\per\pound}]\) |
| \(M_{comb,air}\) | Mass of combustion air \([\unit{ \pound\per\poundFuel}]\) |
| \(\rho_{air}\) | Density of air \([\unit{ \pound\per\cubicFoot}]\) |
Convert fuel analysis percentages to mass fractions.
Fuel composition is typically provided as percentages that may not sum to exactly 100%. Normalization ensures mass fractions sum to unity for stoichiometric calculations.
\begin{equation}\label{eq:slfgm-norm-fuel} x_i = \frac{X_i}{\sum_j X_j}\end{equation}
| \(x_i\) | Normalized mass fraction of constituent i \([\unit{ \unitless}]\) |
| \(X_i\) | Percent of constituent i in fuel \([\unit{ \percent}]\) |
1.9.8