No abstract

Density functional theory (DFT) is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, etc. In this paper, we suggest a method for obtaining the equilibrium molecular fluid density in a nanopore using DFT without calculating the freeenergy variationVariation-Free Density Functional Theory (VF-DFT). This technique can be used to explore confined fluids with a complex type of interactions, additional constraints, and, to speed up calculations, which might be crucial in an inverse problem. The fluid density in VF-DFT approach is represented as a decomposition over a limited set of basis functions. We applied principal component analysis (PCA) to extract the basic patterns from the density function and take them into account in the construction of a set of basis functions. The decomposition coefficients of the fluid density by the basis were sought by stochastic optimization algorithms: genetic algorithm (GA) and particle swarm optimization (PSO), to minimize the free energy of the system. In this work, two different fluids were studied: nitrogen at a temperature of 77.4 K and argon 87.3 K, at a pore size of 3.6 nm, and the performance of optimization algorithms was compared. We also introduce the Hybrid Density Functional Theory (H-DFT) approach based on stochastic optimization methods and the classical Picard iteration method to find the equilibrium fluid density starting from the physically appropriate solution. The combination of Picard iteration and stochastic algorithms helps to significantly speed up the calculations of equilibrium density in the system without losing the quality of the solution, especially in cases with the high relative pressure and expressed layering structure.

Представлен гибридный алгоритм для решения совместных обратных задач, разработанный на основе стохастического алгоритма оптимизации sNES и техники построения Adjoint-градиента. Эффективность алгоритма проверена на задачах адаптации полей пористости и проницаемости по историческим данным разработки и по результатам трассерных исследований. Численно моделируется распространение пассивной примеси и течение флюида в пласте. Использование предложенного гибридного алгоритма позволило значительно снизить число вызовов симулятора для достижения сопоставимого качества адаптации.

The description of fluid mixtures molecular behavior is significant for various industry fields due to the complex composition of fluid found in nature. Statistical mechanics approaches use intermolecular interaction potential to predict fluids behavior on the molecular scale. The paper provides a comparative analysis of mixing rules applications for obtaining intermolecular interaction parameters of mixture components. These parameters are involved in the density functional theory equation of state for mixtures (Mixture DFT EoS) and characterize thermodynamic mixture properties in the bulk. The paper demonstrates that Mixture DFT EoS with proper intermolecular parameters agree well with experimental mixtures isotherms in bulk: Ar + N e, CO2 + CH4, CO2 + C2H6 and CH4 + C2H6. However, predictions of vapor-liquid equilibrium (VLE) experimental data for CO2 + C4H10 are not successful. Halgren HHG, Waldman -Hagler, and adaptive mixing rules that adjust on the experimental data from the literature are used for the first time to obtain intermolecular interaction parameters for the mixture DFT model. The results obtained provide a base for understanding how to validate the DFT fluid mixture model for calculating thermodynamic properties of fluid mixtures on a micro and macro scale.