Fix definition of elemental mole fraction

include/cantera/thermo/Phase.h

@@ -541,12 +541,16 @@ class Phase
     //! Elemental mole fraction of element m
     /*!
      *  The elemental mole fraction \f$Z_{\mathrm{mole},m}\f$ of element \f$m\f$
-     *  is defined as
+     *  is the number of atoms of element *m* divided by the total number of
+     *  atoms. It is defined as:
+     *
      *  \f[
-     *      Z_{\mathrm{mole},m} = \sum_k \frac{a_{m,k}}{\sum_j a_{j,k}} X_k
+     *      Z_{\mathrm{mole},m} = \frac{\sum_k a_{m,k} X_k}
+     *                                 {\sum_k \sum_j a_{j,k} X_k}
      *  \f]
      *  with \f$a_{m,k}\f$ being the number of atoms of element \f$m\f$ in
-     *  species \f$k\f$and \f$X_k\f$ the mole fraction of species \f$k\f$.
+     *  species \f$k\f$, \f$\sum_j\f$ being a sum over all elements, and
+     *  \f$X_k\f$ being the mole fraction of species \f$k\f$.
      *
      *  @param[in] m Index of the element within the phase. If m is outside the
      *               valid range, an exception will be thrown.

interfaces/cython/cantera/test/test_thermo.py

@@ -65,15 +65,31 @@ def test_elemental_mole_fraction(self):
 
         mO = self.phase.element_index('O')
         self.assertEqual(Zo, self.phase.elemental_mole_fraction(mO))
-        self.assertNear(Zo, 0.5/3 + 0.5)
-        self.assertNear(Zh, 0.5*2/3)
+        self.assertNear(Zo, (0.5 + 1) / (0.5*3 + 0.5*2))
+        self.assertNear(Zh, (2*0.5) / (0.5*3 + 0.5*2))
         self.assertEqual(Zar, 0.0)
 
         with self.assertRaises(ValueError):
             self.phase.elemental_mole_fraction('C')
         with self.assertRaises(ValueError):
             self.phase.elemental_mole_fraction(5)
 
+    def test_elemental_mass_mole_fraction(self):
+        # expected relationship between elmental mass and mole fractions
+        comps = ['H2O:0.5, O2:0.5', 'H2:0.1, O2:0.4, H2O2:0.3, AR:0.2',
+                 'O2:0.1, H2:0.9']
+        for comp in comps:
+            self.phase.X = comp
+
+            denom = sum(self.phase.elemental_mole_fraction(i)
+                        * self.phase.atomic_weight(i)
+                        for i in range(self.phase.n_elements))
+
+            for i in range(self.phase.n_elements):
+                self.assertNear(self.phase.elemental_mass_fraction(i),
+                                self.phase.elemental_mole_fraction(i)
+                                * self.phase.atomic_weight(i) / denom)
+
     def test_weights(self):
         atomic_weights = self.phase.atomic_weights
         molecular_weights = self.phase.molecular_weights

interfaces/cython/cantera/thermo.pyx

@@ -542,13 +542,15 @@ cdef class ThermoPhase(_SolutionBase):
     def elemental_mole_fraction(self, m):
         r"""
         Get the elemental mole fraction :math:`Z_{\mathrm{mole},m}` of element
-        :math:`m` as defined by:
+        :math:`m` (the number of atoms of element m divided by the total number
+        of atoms) as defined by:
 
-        .. math:: Z_{\mathrm{mole},m} = \sum_k \frac{a_{m,k}}{\sum_j a_{j,k}} X_k
+        .. math:: Z_{\mathrm{mole},m} = \frac{\sum_k a_{m,k} X_k}
+                                             {\sum_k \sum_j a_{j,k} X_k}
 
         with :math:`a_{m,k}` being the number of atoms of element :math:`m` in
-        species :math:`k` and :math:`X_k` the mole fraction of species
-        :math:`k`.
+        species :math:`k`, :math:`\sum_j` being a sum over all elements, and
+        :math:`X_k` being the mole fraction of species :math:`k`.
 
         :param m:
             Base element, may be specified by name or by index.

src/thermo/Phase.cpp

@@ -643,15 +643,19 @@ doublereal Phase::elementalMassFraction(const size_t m) const
 doublereal Phase::elementalMoleFraction(const size_t m) const
 {
     checkElementIndex(m);
-    doublereal Z_n = 0.0;
-    for (size_t k = 0; k != m_kk; ++k) {
-        double nTotalAtoms = 0;
-        for (size_t l = 0; l != m_mm; ++l) {
-            nTotalAtoms += nAtoms(k, l);
+    double denom = 0;
+    for (size_t k = 0; k < m_kk; k++) {
+        double atoms = 0;
+        for (size_t j = 0; j < nElements(); j++) {
+            atoms += nAtoms(k, j);
         }
-        Z_n += nAtoms(k, m) / nTotalAtoms * moleFraction(k);
+        denom += atoms * moleFraction(k);
+    }
+    doublereal numerator = 0.0;
+    for (size_t k = 0; k != m_kk; ++k) {
+        numerator += nAtoms(k, m) * moleFraction(k);
     }
-    return Z_n;
+    return numerator / denom;
 }
 
 doublereal Phase::molarDensity() const