Fuel and oxidant flow rates for fuel cell testing and sizing the reactant Mass Flow Controllers is linearly related to the electrical current production. The equation, which is based on Farady’s Law, is:
Flow Rate = (Gas Stoichiometry Constant)(Current in Amps)(Number of Cells in Stack)(Stoichiometry Ratio).
The Gas Stoichiometry Constant, in standard cubic centimeters per min (sccm) or standard liters per minute (SLM), is the mass consumption rate of the gas required to sustain 1 Amp of current at standard state conditions. The Gas Stoichiometry Constants are: hydrogen (H2) = 7 sccm; O2 = 3.5 sccm; and Air = 16.7 sccm for standard state defined at 0 oC and 1 atmosphere.
The Stoichiometry Ratio is the ratio of the actual mass flow rate to the mass consumption rate. Typical Stoichiometry Ratios are 1.1 to 1.5 for H2 and 2 or more for Air, although there are cases where much higher values are used (e.g., when performing electrode kinetics and catalysis studies where it is desirable that mass transport effects are negligible).
Sample calculation: a 25 cm2 single cell operating on H2 and Air will generate about 1 Amp/cm2 or 25 Amps. (Higher current density up to ~ 2 Amp/cm2 can be realized when using O2 instead of air).
Using the above equation, the required H2 mass flow rate = (7 sccm/A/cell)(25 A)(1 cell)(1.0) = 175 sccm (@ Stoichiometry Ratio = 1).
Generally it is a good idea to provision for running Stoichiometry Ratio of 3 or 4 (delivering to the fuel cell 3 to 4 times the amount of reactant than is required by the chemical reactions) which modifies the equation to: (7)(25)(1)(4) = 700 sccm (@ stoich ratio = 4). The nearest standard MFC size is 1000 sccm (1 SLM).
Cathode flow requirement when using Air is = (16.7 sccm/A/cell)(25 A)(1 cell)(4) = 1670 sccm (@ stoich ratio = 4). The nearest standard MFC size is 2000 sccm (2 SLM).