which takes into account the effect of changing volume. In Equation 2-44,
ci (SI unit: mol/m
3) is the species molar concentration,
Vr (SI unit: m
3) denotes the reactor volume, and
Ri (SI unit: mol/(m
3·s)) is the species rate expression.
In Equation 2-45,
Cp,i (SI unit: J/(mol·K)) is the species molar heat capacity,
T (SI unit: K) is the temperature, and
p (SI unit: Pa) the pressure. On the right-hand side,
Q (SI unit: J/s) is the heat due to chemical reaction, and
Qext (SI unit: J/s) denotes heat added to the system. The heat of reaction is:
where Hj (SI unit: J/mol) is the enthalpy of reaction, and
rj (SI unit: mol/(m
3·s)) the reaction rate.
For an ideal reacting gas, the energy balance is given by Equation 2-45. For an incompressible and ideally mixed reacting liquid, the energy balance is given by
Equation 2-46.
In Equation 2-47,
cf,m (SI unit: mol/m
3) is the species molar concentration of the associated feed inlet stream
vf,m (SI unit: m
3/s)
. Vr (SI unit: m
3) denotes the reactor volume and is a function of time.
In Equation 2-48,
vp (SI unit: m
3/s) denotes the volumetric production rate. It is given by
Equation 2-49 for ideally mixed liquids and by
Equation 2-50 for ideal gases.
where νij is the stoichiometric coefficient of species
i in reaction
j,
Mi (SI unit: kg/mol) denotes the species molecular weight,
ρi (SI unit: kg/m
3) the species density, and
Ri (SI unit: mol/(m
3·s)) is the reaction rate of species
i.
where Fi (SI unit: mol/s) is the species molar flow,
V (SI unit: m
3) is the reactor volume, and
Ri (SI unit: mol/(m
3·s)) denotes the species rate expression.
In order to evaluate the rate expressions Ri, which are functions of the species concentrations, the physics interface calculates:
where v (SI unit: m
3/s) is the volumetric flow rate.
where Mi (SI unit: kg/mol) denotes the species molecular weight and
ρi (SI unit: kg/m
3) the species density
where p (SI unit: Pa) is the constant pressure.
Equation 2-60 is similar to the energy balance for the batch reactors (
Equation 2-46), but with a reactor volume dependence instead of a time dependence.