Plug Flow Reactor#
A plug flow reactor (PFR) represents a one-dimensional steady-state flow in a channel.
Perpendicular to the flow direction, the gas is assumed to be homogenous.
In the axial direction
In addition, the interior surface of the reactor may consist of one or more catalytically active surfaces where heterogeneous reactions occur.
Plug-flow reactors are often used to simulate emission formation and catalytic processes.
A plug flow reactor is defined by the state variables:
, the density of the fluid phase (in kg/m3) , the velocity of the fluid phase (in m/s) , the pressure (in Pa) , the temperature (in K) , the mass fractions for each fluid phase species (dimensionless) , the coverage of each surface species on each surface (dimensionless)
The reactor geometry is defined by the length
The governing equations for a PFR are a system of differential-algebraic equations,
which depend on the spatial derivatives of some but not all of the state variables. The
plug flow reactor model in Cantera is implemented by class FlowReactor and
available in Python as the FlowReactor
class.
Equation of State#
The fluid satisfies the ideal gas law:
where
Mass Conservation#
The net rate per unit cross sectional area at which fluid phase species are generated by reactions on the walls can be defined as
where
Momentum Conservation in the Axial Direction#
Energy Equation#
where
Gas Phase Species Equations#
Surface Phase Species Equations#
Because the PFR is modeled as steady state, net rate of production for each surface species must be zero.
To satisfy the constraint that the total surface coverage is 1, the conservation equation for the first surface species on each surface is replaced by this constraint:
Without this constraint, the solver could find the trivial, non-physical solution
Integrating the PFR Equations#
Because diffusion is neglected, downstream parts of the reactor have no influence on upstream parts. Therefore, PFRs can be integrated as initial value problems, starting from the composition at the inlet. Some care is required to determine initial values for the algebraic variables (the surface species coverages) and the time derivatives for the differential variables (the other state variables) that are consistent with the governing equations.
To do this, we first solve the steady-state problem for each surface, holding the fluid
phase composition, temperature, and pressure fixed at the inlet values to determine the
values of