Unifying the framework of fluid dynamics and chemical reaction equilibrium for non-ideal systems in a numerical study

Fluid dynamics is a scientific field that has strong roots in theory. The transport equations are derived from conservation principles of mass, momentum and energy, and this is one of its major strengths. To ensure that the calculated fields are plausible, however, constitutive equations are required. These correlations include, but are not limited to, kinetic reaction rates. In the absence of such correlations, alternatives are of interest. One such alternative is the Differential Gibbs and Helmholtz reactors, which was coined by Solsvik et al. (2016). The reactor concept calculates the equilibrium composition by minimizing Gibbs (or Helmholtz) energy at every point in time and space, hence its name Differential Gibbs (or Helmholtz) reactor. The concept was tested for ideal gas and a simple packed bed reactor model, and the results agreed quite well for the fast kinetics of steam methane reforming. In this work, the concept was extended to other equations of state. For instance, the concept has been studied for more rigorous equations of state such as the virial equation of state and Soave-Redlich- Kwong. This affects both the reactor models as well as the thermodynamic equilibrium calculation, see for instance the Newton-Raphson blocks in the figure. As Gibbs energy is a function of the intensive variables temperature and pressure, this facilitates a point-discrete method such as those that belong to the family of spectral methods. Helmholtz energy, on the other hand, is a function of temperature and volume, and this facilitates the use of a volumetric method such as the finite volume method. Hence, there is a coupling between the thermodynamic energy function and the numerical scheme employed. This is explored further as two choices are available for the volume: one that can be calculated from the EOS, and one from the numerical grid cell. For multiphase systems, where mass transfer is important, the calculations are normally dependent on closure laws, e.g. Henry’s law. For complicated systems, or systems where correlations of this type are yet to be explored, a minimum Gibbs or Helmholtz approach is suitable. This shows that the Differential Gibbs or Helmholtz reactor model is also relevant here. The model considered suggests an approach for combining fluid flow with thermodynamic equilibrium. The thermodynamic part is a useful tool in the lack of constitutive equations while the fluid dynamic part retains the effects of fluid flow. As the minimum energy principle is versatile, the reactor concept has a wide area of application.