A Modeling Approach for Solid Solutions: Application to Phase Behavior of Wax-Containing Systems Over Wide Pressure Ranges

PORRAS GIRALDO, ANDRÉS FELIPE; RODRIGUEZ REARTES, SABRINA BELÉN; ZABALOY, MARCELO SANTIAGO

Conferencia; The 21st International Conference on Petroleum Phase Behavior and Fouling; 2021

ExxonMobil

Solids of varying nature, such as waxes, asphaltenes or hydrates, bring important economic losses in the gas and petroleum industries, due to unwanted solid precipitation in, e.g., pipelines and production facilities. Well known available options for modeling wax precipitation either assume that one or more solid phases each made of a pure component can precipitate (multi-solid approach, MSA), or that only one multicomponent solid phase (solid solution approach, SSA) can be formed1. Using as starting point the ideas in ref.2 and ref.3, it can be shown that, for multicomponent systems, imposing on the model precipitation in pure state is strictly inconsistent. Such inconsistency happens within the universe of the model and it rules out the choice of the MSA as a valid alternative, despite the widespread use it may have. On the other hand, the alternative of allowing the model to produce at most a single multicomponent solid phase (SSA) is only consistent if the solid solution is set to be ideal or if the non-ideal model adopted for the solid phase has an intrinsic impossibility of phase split in solid state (e.g., Wilson)4. Otherwise, the proper application of stability analysis and subsequent calculation of the true phase equilibrium (minimization of overall Gibbs energy) will establish the valid number of solid phases present at equilibrium (which may be greater than 1), and their compositions4. The word ?valid? in the previous sentence applies to the model, irrespective of the degree of agreement between model and experimental data. For systems for which it is experimentally known that solid phases are practically made of pure components, the MSA and the SSA become, in a way, reconciled, if the SSA computation results show that for any solid phase the concentration of one of the components is very high, being the concentration of every other component very low. Solid solutions are frequently modeled through activity coefficient models, in which the fugacity of a component in a solid phase is obtained from the product of the component activity coefficient, the component mole fraction and the fugacity of the pure component in solid state at the same temperature (T) and pressure (P) of the solid solution5. This was the choice, e.g., in ref.4, and it implies a zero molar volume change on mixing for the solid solution. The modeling approach of ref.6 (which we here identify as SSA*) is free from such restriction, and it is quite analogous in nature to the equation of state (EOS) approach for fluid phases. In the SSA* the solid solution is characterized by pure component parameters and by interaction parameters in solid state. In this work, we use an EOS for the fluid phases and the SSA* for the solid phases, to compute the phase behavior of binary systems containing waxes. The tangent plane distance (tpd) analysis7 is used to test the stability of the calculated phase equilibria. Both, fluid and solid trial phases are considered in the tpd analysis. The level of agreement between experimental data from the literature and the particular form of the SSA* used here show a good potential for the SSA*. In cases where the T and P conditions and the asymmetry of the binary system would imply the expectation of a solid phase made of a pure component, the SSA* consistently predicts a very high concentration of such component in the solid phase. Finally, the SSA* makes possible to predict solid-solid equilibrium regions and homogeneous solid regions in computed isopleths