From 28092621e4584852e6916976c4a3ea3ea54a13ad Mon Sep 17 00:00:00 2001
From: Ray Speth <speth@mit.edu>
Date: Fri, 15 Mar 2024 20:41:38 -0400
Subject: [PATCH] Migrate heating value example from Jupyter

---
 doc/sphinx/userguide/heating-value.md | 103 ++++++++++++++++++++++++++
 doc/sphinx/userguide/index.md         |   2 +
 2 files changed, 105 insertions(+)
 create mode 100644 doc/sphinx/userguide/heating-value.md

diff --git a/doc/sphinx/userguide/heating-value.md b/doc/sphinx/userguide/heating-value.md
new file mode 100644
index 000000000..d6f071833
--- /dev/null
+++ b/doc/sphinx/userguide/heating-value.md
@@ -0,0 +1,103 @@
+---
+file_format: mystnb
+kernelspec:
+  name: python3
+---
+
+```{py:currentmodule} cantera
+```
+
+# Calculating Heating Value of a Fuel
+
+This guide demonstrates how to use Cantera's thermodynamic data to calculate the lower
+[heating value](https://en.wikipedia.org/wiki/Heat_of_combustion) (LHV) and higher
+heating value (HHV) of methane and other fuels.
+
+## Heating value of Methane
+
+The complete reaction for heating methane is:
+
+$$\t{CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O}$$
+
+We compute the lower heating value (LHV) as the difference in enthalpy (per kg
+*mixture*) between reactants and products at constant temperature and pressure, divided
+by the mass fraction of fuel in the reactants.
+
+```{code-cell} python
+import cantera as ct
+gas = ct.Solution("gri30.yaml")
+
+# Set reactants state
+gas.TPX = 298, 101325, "CH4:1, O2:2"
+h1 = gas.enthalpy_mass
+Y_CH4 = gas["CH4"].Y[0]  # returns an array, of which we only want the first element
+
+# set state to complete combustion products without changing T or P
+gas.TPX = None, None, "CO2:1, H2O:2"
+h2 = gas.enthalpy_mass
+
+LHV = -(h2 - h1) / Y_CH4 / 1e6
+print(f"LHV = {LHV:.3f} MJ/kg")
+```
+
+The LHV is calculated assuming that water remains in the gas phase. However, more energy
+can be extracted from the mixture if this water is condensed. This value is the higher
+heating value (HHV).
+
+The ideal gas mixture model used here cannot calculate this contribution directly.
+However, Cantera also has a non-ideal equation of state which can be used to compute
+this contribution.
+
+```{code-cell} python
+water = ct.Water()
+# Set liquid water state, with vapor fraction x = 0
+water.TQ = 298, 0
+h_liquid = water.h
+# Set gaseous water state, with vapor fraction x = 1
+water.TQ = 298, 1
+h_gas = water.h
+
+# Calculate higher heating value
+Y_H2O = gas["H2O"].Y[0]
+HHV = -(h2 - h1 + (h_liquid - h_gas) * Y_H2O) / Y_CH4 / 1e6
+print(f"HHV = {HHV:.3f} MJ/kg")
+```
+
+## Generalizing to arbitrary species
+
+We can generalize this calculation by determining the composition of the products
+automatically rather than directly specifying the product composition. This can be done
+by computing the *elemental mole fractions* of the reactants mixture and noting that for
+complete combustion, all of the carbon ends up as $\t{CO_2}$, all of the hydrogen ends
+up as $\t{H_2O}$, and all of the nitrogen ends up as $\t{N_2}$. From this, we can
+compute the ratio of these species in the products.
+
+```{code-cell} python
+def heating_value(fuel):
+    """Returns the LHV and HHV for the specified fuel"""
+    gas.TP = 298, ct.one_atm
+    gas.set_equivalence_ratio(1.0, fuel, "O2:1.0")
+    h1 = gas.enthalpy_mass
+    Y_fuel = gas[fuel].Y[0]
+
+    # complete combustion products
+    X_products = {
+        "CO2": gas.elemental_mole_fraction("C"),
+        "H2O": 0.5 * gas.elemental_mole_fraction("H"),
+        "N2": 0.5 * gas.elemental_mole_fraction("N"),
+    }
+
+    gas.TPX = None, None, X_products
+    Y_H2O = gas["H2O"].Y[0]
+    h2 = gas.enthalpy_mass
+    LHV = -(h2 - h1) / Y_fuel / 1e6
+    HHV = -(h2 - h1 + (h_liquid - h_gas) * Y_H2O) / Y_fuel / 1e6
+    return LHV, HHV
+
+
+fuels = ["H2", "CH4", "C2H6", "C3H8", "NH3", "CH3OH"]
+print("fuel   LHV (MJ/kg)   HHV (MJ/kg)")
+for fuel in fuels:
+    LHV, HHV = heating_value(fuel)
+    print(f"{fuel:8s}   {LHV:7.3f}       {HHV:7.3f}")
+```
diff --git a/doc/sphinx/userguide/index.md b/doc/sphinx/userguide/index.md
index e8080c36a..acf6fc630 100644
--- a/doc/sphinx/userguide/index.md
+++ b/doc/sphinx/userguide/index.md
@@ -35,6 +35,7 @@ conditions, or calculating the voltage of a Lithium-ion battery as it is dischar
 
 ### Combustion Calculations
 - [](flame-temperature)
+- [](heating-value)
 
 ### Implementing Custom Models
 
@@ -70,6 +71,7 @@ input-errors
 legacy2yaml-tutorial
 
 flame-temperature
+heating-value
 
 extensible-reactor
 ```