Clusters can form and grow from a supersaturated vapor by successive reactions in which molecules (or “monomers”) of the vapor collide with the cluster and stick. In general, these reactions are reversible. The net forward rate of each of these reactions is termed the “nucleation current” of clusters of the size formed by the reaction. If a steady-state cluster size distribution exists, then the nucleation currents for clusters of all sizes are identical and can be equated to the steady-state (or “stationary”) nucleation rate. In that case, one can derive a closed-form expression for the nucleation rate in terms of a summation over clusters of all sizes up to some arbitrarily large size. The key terms in this summation are the forward rate constants and the Gibbs free energies of cluster formation from the monomer vapor. Evaluating the summation requires size-dependent values of these terms. For saturation ratios that lie within the condensation–evaporation regime, the free energy of cluster formation has a maximum at the critical cluster size. The nucleation theorem relates this size to the dependence of the nucleation rate on saturation ratio.

The compositional module in the MATLAB Reservoir Simulation Toolbox (MRST) implements two different formulations of a three-phase compositional system that consists of a pair of multicomponent phases and an optional immisicible phase. In petroleum engineering, the aqueous phase is taken to be immiscible and the hydrocarbon liquid and vapor phases are governed by an equation of state (EoS). The overall composition formulation uses pressure and overall mole fractions as primary variables, whereas the natural variable formulation relies on solving for phase mole fractions and phase saturations simultaneously. Thermodynamic behavior is modeled using $K$-values or a (standard) cubic EoS. In the chapter, you will learn about the model equations, choice of primary variables, and numerical strategies for solving the thermodynamic problem, alone or coupled to the flow equations. We discuss details of the implementation, which builds upon the object-oriented, automatic differentiation (AD-OO) framework and utilizes state functions and generic model classes for increased modularity. We also present a few relatively simple simulation examples to illustrate typical behavior and teach you how to set up simulation cases yourself.