Reactors and Reactor Networks#

In Cantera, a reactor network represents a set of one or more homogeneous reactors and reacting surfaces that may be connected to each other and to the environment through devices representing mass flow, heat transfer, and moving walls. The system is generally unsteady – that is, all states are functions of time. In particular, transient state changes due to chemical reactions are possible.

Homogeneous Reactor Types and Governing Equations#

A Cantera reactor represents the simplest form of a chemically reacting system. It corresponds to an extensive thermodynamic control volume \(V\), in which all state variables are homogeneously distributed. By default, these reactors are closed (no inlets or outlets) and have adiabatic, chemically-inert walls. These properties may all be changed by adding components such as walls, surfaces, mass flow controllers, and valves, as described below.

The specific governing equations defining Cantera’s reactor models are derived and described below. These models represent different combinations of whether pressure or volume are held constant, whether they support any equation of state or are specialized for ideal gas mixtures, and whether mass fractions or moles of each species are used as the state variables representing the composition.

Control Volume Reactor: A reactor where the volume is prescribed by the motion of the reactor’s walls.
Constant Pressure Reactor: A reactor where the pressure is held constant.
Ideal Gas Control Volume Reactor: A reactor where the volume is prescribed by the motion of the reactor’s walls, specialized for ideal gas mixtures.
Ideal Gas Constant Pressure Reactor: A reactor where the pressure is held constant, specialized for ideal gas mixtures.
Control Volume Mole Reactor: A reactor where the volume is prescribed by the motion of the reactor’s walls, with the composition stored in moles.
Constant Pressure Mole Reactor: A reactor where the pressure is held constant and the composition is stored in moles.
Ideal Gas Control Volume Mole Reactor: A reactor where the volume is prescribed by the motion of the reactor’s walls, specialized for ideal gas mixtures and with the composition stored in moles.
Ideal Gas Constant Pressure Mole Reactor: A reactor where the pressure is held constant, specialized for ideal gas mixtures and with the composition stored in moles.

Plug Flow Reactors#

A plug flow reactor (PFR) represents a steady-state flow in a channel. The fluid is considered to be homogeneous perpendicular to the flow direction, while the state of the gas is allowed to change in the axial direction. However, all diffusion processes are neglected.

These assumptions result in a system of equations that is similar to those used to model homogeneous reactors, with the time variable replaced by the axial coordinate. Because of this mathematical similarity, PFRs are also solved by Cantera’s reactor network model. However, they can only be simulated alone, and not part of a network containing time-dependent reactors.

Plug Flow Reactor: A reactor modeling one-dimensional steady-state flow in a channel that may contain catalytically active surfaces where heterogeneous reactions occur.

Reactor Interactions#

Reactors can interact with each other and the surrounding environment in multiple ways. Mass can flow from one reactor into another can be incorporated, heat can be transferred, and the walls between reactors can move. In addition, reactions can occur on surfaces within a reactor. The models used to establish these interconnections are described in the following sections:

All of these interactions can vary as a function of time or system state. For example, heat transfer can be described as a function of the temperature difference between the reactor and the environment, or wall movement can be modeled as depending on the pressure difference. Interactions of the reactor with the environment are defined using the following models:

Reservoirs: Reservoirs are used to represent constant conditions defining the inlets, outlets, and surroundings of a reactor network.
Flow Devices: Flow devices are used to define mass transfer between two reactors, or between reactors and the surrounding environment as defined by a reservoir.
Walls: Walls between reactors are used to allow heat transfer between reactors. By moving the walls of the reactor, its volume can be changed and expansion or compression work can be done by or on the reactor.
Reacting Surfaces: Reactions may occur on the surfaces of a reactor. These reactions may include both catalytic reactions and reactions resulting in net mass transfer between the surface and the fluid.

Reactor Networks#

While reactors by themselves define the governing equations, the time integration is performed by assembling reactors into a reactor network. A reactor network is therefore necessary even if only a single reactor is considered.

Cantera uses the CVODES and IDAS solvers from the SUNDIALS package to integrate the governing equations for the reactor network, which are a system of stiff ODEs or DAEs.

Preconditioning#

Some of Cantera’s reactor formulations (specifically, the Ideal Gas Control Volume Mole Reactor and the Ideal Gas Constant Pressure Mole Reactor) provide implementations of a sparse, approximate Jacobian matrix, which can be used by ReactorNet to generate a preconditioner and use a sparse, iterative linear solver within CVODES. This sparse, preconditioned method can significantly accelerate integration for reactors containing many species. A derivation of the derivative terms and benchmarks demonstrating the achievable performance gains can be found in Walker et al. [2023]. An example demonstrating the use of this feature can be found in preconditioned_integration.py.