What is Conversion reactor?
A reactor that takes reaction equations and the fraction of a reactant that reacts, and gives the outlet composition.
Without kinetic data you can still set up the mass and heat balances from a known or design conversion.
Decide that 40 % of the methane burns, and the oxygen used and the carbon dioxide and water formed follow.
Write the equation like CH4 + 2 O2 => CO2 + 2 H2O and give the key reactant and its conversion. Up to three reactions are applied from the top. Every equation's element balance is checked, and a conversion that would need more of a reactant than there is is refused. Heat: adiabatic, isothermal or a given duty.
The extent of reaction j follows from the key reactant's molar flow n_{\mathrm{key}}:
\xi_j = X_j\, n_{\mathrm{key}} / |\nu_{\mathrm{key},j}|
and every species changes by n_k \leftarrow n_k + \nu_{kj}\,\xi_j. Adiabatic: the outlet enthalpy equals the inlet's, and the temperature follows from it.
The conversion is an input, not a value derived from kinetics or equilibrium.