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This study presents a comprehensive analysis of CO2 trapping mechanisms in subsurface reservoirs by integrating numerical reservoir simulations, geochemical modeling, and machine learning techniques to enhance the design and evaluation of carbon capture and storage (CCS) strategies. A two-dimensional reservoir model was developed to simulate CO2 injection dynamics under realistic geomechanical and geochemical conditions, incorporating four primary trapping mechanisms: residual, solubility, mineralization, and structural trapping. To improve computational efficiency without compromising accuracy, advanced machine learning models, including random forest, gradient boosting, and decision trees, were deployed as smart proxy models for rapid prediction of trapping behavior across multiple scenarios. Simulation outcomes highlight the critical role of hysteresis, aquifer dynamics, and producer well placement in enhancing CO2 trapping efficiency and maintaining long-term storage stability. To support the credibility of the model, a qualitative validation framework was implemented by comparing simulation results with benchmarked field studies and peer-reviewed numerical models. These comparisons confirm that the modeled mechanisms and trends align with established CCS behavior in real-world systems. Overall, the study demonstrates the value of combining traditional reservoir engineering with data-driven approaches to optimize CCS performance, offering scalable, reliable, and secure solutions for long-term carbon sequestration.

In this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng--Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory of thermodynamics and variational calculus to derive a generalized chemical equilibrium equation, which is mathematically a second-order elliptic partial differential equation (PDE) in molar density with a strongly nonlinear source term. To solve this PDE, we convert it to a time-dependent parabolic PDE with the main interest in its final steady state solution. A Lagrange multiplier is used to enforce mass conservation. The parabolic PDE is then solved by mixed finite element methods with a semi-implicit time marching scheme. Convex splitting of the energy functional is proposed to construct this time marching scheme, where the volume exclusion effect of an EOS is treated implicitly while the pairwise attraction effect of EOS is calculated explicitly. This scheme is proved to be unconditionally energy stable. Our proposed algorithm is able to solve successfully the spatially heterogeneous two-phase systems with the Peng--Robinson EOS in multiple spatial dimensions, the first time in the literature. Numerical examples are provided with realistic hydrocarbon components to illustrate the theory. Furthermore, our computational results are compared with laboratory experimental data and verified with the Young--Laplace equation with good agreement. This work sets the stage for a broad extension of efficient convex-splitting semi-implicit schemes for numerical simulation of phase field models with a realistic EOS in complex geometries of multiple spatial dimensions.

A large-eddy simulation (LES) of a gaseous hydrogen/liquid oxygen (GH2/LOX) single-injector rocket combustor is performed in this study. The Redlich–Kwong–Peng–Robinson (RK–PR) equation of state is used to simulate the real-gas effect under high-pressure conditions, and the steady laminar flamelet model (SLFM) is implemented to simulate fast chemistry, such as a H2/O2 reaction. From the numerical simulation, the characteristics of time-averaged flow and flame fields are obtained, and their relationship with the real-gas effect is investigated. It is possible to investigate unsteady flame features and the mixing mechanism of propellants in detail by examining multiple snapshots of the field contour. Another purpose of the study is to investigate the differences in flow and flame structures according to the variation in the turbulent Schmidt number. By comparing the simulation result with the natural OH* emission image and temperature profiles from experimental data, the appropriate range of the turbulent Schmidt number for the simulation is obtained. Furthermore, this paper suggests the usefulness and validity of the current research by quantitatively comparing (i.e., temperature profiles) numerical results with those of existing literature.

Experimental and theoretical techniques have been developed to quantify foamy oil behaviour of solvent-heavy oil systems at bubble level during a gas exsolution process. During constant composition expansion (CCE) tests, we artificially induced foamy oil dynamics for solvent-heavy oil systems by gradually reducing pressure and recorded the changed pressures and volumes in an isolated PVT setup at a given temperature. By discretizing gas bubbles on the basis of the classical nucleation theory, we theoretically integrated the population balance equation (PBE), Fick’s law, and the Peng–Robinson equation of state (PR EOS) to reproduce the experimental measurements. Pseudo-bubblepoint pressure for a given solvent-heavy oil system can be increased with either a lower pressure depletion rate or a higher temperature, during which gas bubble growth is facilitated with a reduction in viscosity and/or an increase in solvent concentration, but gas bubble nucleation and mitigation is hindered with an increase in solvent concentration. Compared to CO2, CH4 is found to yield stronger and more stable foamy oil, indicating that foamy oil is more stable with a larger amount of dispersed gas bubbles at lower temperatures. Using the PR EOS together with the modified alpha functions at Tr = 0.7 and Tr = 0.6, the absolute average relative deviation (AARD) is reduced from 4.58% to 2.24% with respect to the predicted pseudo-bubblepoint pressures.

In the present numerical study, implicit large eddy simulations (LES) of non-reacting multi-components mixing processes of cryogenic nitrogen and n-dodecane fuel injections under transcritical and supercritical conditions are carried out, using a modified reacting flow solver, originally available in the open source software OpenFOAM®. To this end, the Peng-Robinson (PR) cubic equation of state (EOS) is considered and the solver is modified to account for the real-fluid thermodynamics. At high pressure conditions, the variable transport properties such as dynamic viscosity and thermal conductivity are accurately computed using the Chung transport model. To deal with the multicomponent species mixing, molar averaged homogeneous classical mixing rules are used. For the velocity-pressure coupling, a PIMPLE based compressible algorithm is employed. For both cryogenic and non-cryogenic fuel injections, qualitative and quantitative analyses are performed, and the results show significant effects of the chamber pressure on the mixing processes and entrainment rates. The capability of the proposed numerical model to handle multicomponent species mixing with real-fluid thermophysical properties is demonstrated, in both supercritical and transcritical regimes.

The Density Gradient Theory (DGT) permits obtaining the surface tension by using an equation of state and the so-called influence parameter. Different correlations of the influence parameter versus temperature have been proposed, with the two-coefficient ones from Zuo and Stenby (full temperature range) and Miqueu et al. (valid for the lower temperature range) being widely used. Recently, Cachadiña et al. applied the DGT with the Peng-Robinson Equation of State to esters. They proposed a new two-coefficient correlation that uses a universal exponent related to the critical exponent associated with the dependence of coexistence densities on temperature near the critical point. When applied to n-alkanes, it is shown that the Cachadiña et al. correlation must be modified to improve the lower temperature range behavior. The proposed modification results in a three-coefficient correlation that includes the triple point temperature as an input parameter and incorporates the Zuo and Stenby and Miqueu et al. correlations as particular cases. Firstly, the correlation coefficients for each of the 32 n-alkanes considered are obtained by fitting the selected values for the surface tension obtained from different databases, books, and papers. The results obtained are comparable to other specific correlations reported in the literature. The overall mean absolute percentage deviation (OMAPD) between the selected and calculated data is just 0.79%. Secondly, a general correlation with three adjustable coefficients valid for all the n-alkanes is considered. Despite the OMAPD of 4.38% obtained, this correlation is discarded due to the high deviations found for methane. Finally, it is found that a new six-coefficient general correlation, including the radius of gyration as an input fluid parameter, leads to an OMAPD of 1.78% for the fluid set considered. The use of other fluid properties as an alternative to the radius of gyration is briefly discussed.

Interfacial tension (IFT) between two immiscible phases is a key parameter in various oil and gas industries, especially in enhanced oil recovery and Carbon dioxide capture and storage. There are several laboratory methods for measuring IFT, of which the pendant drop method is one of the most commonly used. This method can be used in both thermodynamic equilibrium and dynamic approaches. For a more complete study of IFT, dynamic pendant drop modeling can be used to investigate the process of component exchange between two phases to determine the mechanism of thermodynamic equilibrium. For this purpose, a novel computational algorithm is presented that calculates IFT under dynamic (non-thermodynamic equilibrium) conditions at different time intervals, where each time step is separately considered in equilibrium. Vapor–liquid equilibrium calculations were performed using the Peng–Robinson equation of state (PR-EOS), and the IFT was calculated using the Parachor model. The power parameter of the proposed Parachor model was also considered a matching parameter and was calculated using the fit of the model and the experimental data. Over time, the component exchange between oil and gas increases, thereby reducing the IFT. This decreasing process of IFT continues until it reaches a constant (thermodynamic equilibrium) value. In each time step, the exchangeable components between the two phases are calculated, and their transfer directions are determined. The results show that the component exchange rate between the two phases differed at any time. However, the process of intermediate component exchange between the two phases was intense at the beginning of the experiment, but gradually, as time passed and components were exchanged between the two phases, the component exchange rate decreased. This ultimately reduces the average molecular weight and viscosity of oil over time, which is one of the goals of injecting gas into oil reservoirs. Therefore, the proposed algorithm can determine the process of changes in the composition of oil and gas, as well as the properties of oil, to reach two-phase thermodynamic equilibrium. For the oil and gas composition used in this paper, the equilibrium IFT decreased by an average of approximately 31% compared to the first contact due to component exchange. The oil viscosity and molecular mass also decreased by an average of about 39% and 23%, respectively. These results justify the use of rich gas as an injection gas because of the increase in oil mobility during the gas injection process. Thus, the proposed algorithm can be effectively used in gas injection studies into oil reservoirs to accurately identify the mechanisms under different reservoir conditions.

A large eddy simulation (LES) and combustion instability analysis are performed using OpenFOAM for the multiple shear-coaxial injector combustor DLR-BKD (in German Deutsches Zentrum für Luft–Brennkammer D, German Aerospace Center–Combustion Chamber D), which is a laboratory-scale combustor operating in a real-gas environment. The Redlich–Kwong–Peng–Robinson equation of state and steady-laminar flamelet model are adopted in the simulation to accurately capture the real-gas combustion effects. Moreover, the stable combustion under the LP4 condition is numerically analyzed, and the characteristics of the combustion flow field are investigated. In the numerical simulation of the combustion instability, the instability is generated by artificially superimposing the 1st transverse standing wave solution on the stable combustion solution. To decompose the combustion instability mode, the dynamic mode decomposition method is applied. Several combustion instability modes are qualitatively and quantitatively identified through contour plots and graphs, and the sustenance process of the limit cycle is investigated.

In this paper, we investigate numerical solution of the diffuse interface model with Peng–Robinson equation of state, that describes real states of hydrocarbon fluids in the petroleum industry. Due to the strong nonlinearity of the source terms in this model, how to design appropriate time discretizations to preserve the energy dissipation law of the system at the discrete level is a major challenge. Based on the “Invariant Energy Quadratization” approach and the penalty formulation, we develop efficient first and second order time stepping schemes for solving the single-component two-phase fluid problem. In both schemes the resulted temporal semi-discretizations lead to linear systems with symmetric positive definite spatial operators at each time step. We rigorously prove their unconditional energy stabilities in the time discrete sense. Various numerical simulations in 2D and 3D spaces are also presented to validate accuracy and stability of the proposed linear schemes and to investigate physical reliability of the target model by comparisons with laboratory data.