In this work, we present a kinetic simulation model for gas hydrates in porous media using the Operator-Based Linearization (OBL) technique. The OBL approach introduces algebraic operators that represent the physical terms in the mass and energy balance equations. Operators are calculated only in supporting points comprising the discretized parameter space, and operator values and partial derivatives for linear system assembly are readily obtained through (multi-)linear interpolation. Taking advantage of this setup, the implementation of advanced thermodynamic models for hydrate formation and dissociation under kinetic assumptions is simplified. We test the assumptions for thermodynamic modelling by analysing the Gibbs energy surfaces of the fluid and hydrate phases and demonstrate that, in the limit, the thermodynamic equilibrium for both kinetic and equilibrium reaction models is equivalent. We compare the simulation results with the published experimental results for CH₄-hydrates and extend the assessment to a CO₂-hydrate formation experiment in a semi-batch, constant-pressure configuration. The model reproduces the main pressure–temperature transients and hydrate evolution for both CH₄- and CO₂-systems. We demonstrate applicability at core scale for hydrate formation and, at field scale, for gas production from CH₄-hydrates by thermal stimulation and depressurization. The interaction of thermal-compositional phenomena (phase changes, adiabatic expansion, kinetic rates, and reaction enthalpy) gives rise to highly nonlinear physics that an appropriate OBL discretization resolves. Overall, the patterns of hydrate formation and dissociation are highly sensitive to the kinetic-rate inputs; hence, the appropriate choice of the reaction model remains a key consideration from both physical and numerical perspectives.

Physics-Informed Neural Networks (PINNs) gains attentions as a promising approach for applying deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, due to the challenging regions within the solutions of 'stiff' PDEs, e.g., shock front of CO₂ immiscible flooding, adaptive methods are essential to ensure the neural network accurately addresses these issues. In this work, we introduce a novel method for adaptively training PINNs, named Self-Adaptive PINNs (SA-PINNs). This approach employs fully trainable adaptation weights that are applied individually to each training point. Consequently, the neural network autonomously identifies challenging regions of the solution space and focuses its learning efforts on these areas. This method is hereby used to simulate a two-phase immiscible flooding in a low-permeability oil reservoir, with considering gas dissolution and the threshold pressure gradient of oil phase in low-permeability oil reservoirs, i.e., modified Buckley-Leverett (B-L) problem. The model is capable of generating a precise physical solution, accurately capturing both shock and rarefaction waves under the specified initial and boundary conditions, though the introduction of complicated physics increases the nonlinearity of the governing PDEs. The self-adaptive mechanism modifies the behavior of the deep neural network by simultaneously minimizing the losses and maximizing the weights. It, thus, can effectively capture the non-linear characteristics of the solution, thereby overcoming the existing limitations of PINNs. In these numerical experiments, the SA-PINNs demonstrated superior performance compared to other state-of-the-art PINN algorithms in terms of L2 error. Moreover, it was also achieved with a reduced number of training epochs. SA-PINNs can effectively model the dynamics of complex physical systems by optimizing network parameters to minimize the residuals of the PDEs.

A consistent thermodynamic model based on a combination of the Peng-Robinson equation of state for gas components with an activity model for the aqueous phase is utilized in this study to accurately evaluate the performance of geologic CO₂ storage in saline aquifers. To account for thermal effects, the phase enthalpy and conductivity are derived with consideration of CO₂ dissolution in brines. Several conceptual numerical setups with variations in parameters and physics are constructed to investigate the enhanced CO₂ dissolution in saline aquifers. In addition, a realistic geological structure is considered to evaluate the potential for storing CO₂ at the field scale. Our simulation results show that the presence of a capillary transition zone (CTZ) can significantly reduce the onset time and enhance the dissolution rate. The temperature has a crucial effect on the dissolution trapping compared to isothermal assumptions. Thermal conduction and convection suspend the onset of mass convection, while the final mass flux is augmented. Heat conduction smears out the temperature difference between rocks and fluids, thus suppressing thermal fingering. We demonstrate that the dissolution trapping in realistic 3D aquifers can be significantly different from their 2D analogues. The field-scale simulation results show that the dissolution rate increases sharply once the convection dominates the CO₂ migration which corresponds to a reduction of residual trapping. Besides, a high-resolution 3D model is required for accurately resolving the enhanced CO₂ dissolution in realistic heterogeneous reservoirs. An efficient multi-scale framework for an accurate evaluation of CO₂ trapping is proposed for this purpose.

Foam injection is one efficient way to mitigate gravity segregation during CO2 injection into porous media. The effect of gravity segregation on foam propagation in heterogeneous porous media is not yet fully resolved. To assess CO2 foam transport for enhanced oil recovery (EOR) and for CO2 storage processes in heterogeneous reservoirs, an accurate prediction of foam behavior is essential. In this study, we investigate the effect of heterogeneity on gravity segregation in the presence of foam. For nonlinear analysis, we use an extension of an Operator-Based Linearization (OBL) approach proposed recently. The OBL approach helps to reduce the nonlinearity of complex physical problems by transforming the discretized nonlinear conservation equations into a quasi-linear form based on state-dependent physical operators. The state-dependent operators are approximated by discrete representation on a uniform mesh in parameter space. In our study, foam in porous media is described using an implicit-Texture (IT) foam model with two flow regimes. We first validate the numerical accuracy of the foam simulation with OBL by comparing segregation length using the IT foam model with Newtonian rheology to analytical solutions. Next, the foam-model parameters are fit to foam-quality scan data for four sandstone formations ranging in permeability by an order of magnitude using a least-squares optimization approach. We then construct several hypothetical models containing two communicating layers with different permeability and thickness ratios to examine foam s effect on gravity segregation. The numerical results of the segregation length in homogeneous domains show good agreement with analytical solutions, except in a transition zone beneath the override zone which is not included in the analytical model. Through fractional-flow theory, we find that the transition zone is not a numerical artefact, but caused by low gas relative-mobility during the transient displacement process. Permeability affects both the mobility reduction of wet foam in the low-quality regime and the limiting capillary pressure at which foam collapses. Thus the segregation length varies with permeability and foam strength. In two-layer models, the thickness of the top layer plays an important role in the ultimate segregation length. A thin top layer does not affect segregation in the bottom layer, while a thicker top layer dominates the segregation length, with less influence of the bottom layer.

Foam injection is a promising enhanced-oil-recovery (EOR) technology that significantly improves the sweep efficiency of gas injection. Simulation of foam/oil displacement in reservoirs is an expensive process for conventional simulation because of the strongly nonlinear physics, such as multiphase flow and transport with oil/foam interactions. In this work, an operator-based linearization (OBL) approach, combined with the representation of foam by an implicit-texture (IT) model with two flow regimes, is extended for the simulation of the foam EOR process. The OBL approach improves the efficiency of the highly nonlinear foam-simulation problem by transforming the discretized nonlinear conservation equations into a quasilinear form using state-dependent operators. The state-dependent operators are approximated by discrete representation on a uniform mesh in parameter space. The numerical-simulation results are validated by using three-phase fractional-flow theory for foam/oil flow. Starting with an initial guess depending on the fitting of steady-state experimental data with oil, the OBL foam model is regressed to experimental observations using a gradient-optimization technique. A series of numerical validation studies is performed to investigate the accuracy of the proposed approach. The numerical model shows good agreement with analytical solutions at different conditions and with different foam parameters. With finer grids, the resolution of the simulation is better, but at the cost of more expensive computations. The foam-quality scan is accurately fitted to steady-state experimental data, except in the low-quality regime. In this regime, the used IT foam model cannot capture the upward-tilting pressure gradient (or apparent viscosity) contours. 1D and 3D simulation results clearly demonstrate two stages of foam propagation from inlet to outlet, as seen in the computed-tomography (CT) coreflood experiments: weak foam displaces most of the oil, followed by a propagation of stronger foam at lower oil saturation. OBL is a direct method to reduce nonlinearity in complex physical problems, which can significantly improve computational performance. Taking its accuracy and efficiency into account, the data-driven OBL-based approach could serve as a platform for efficient numerical upscaling to field-scale applications.

CO₂-foam injection is a promising technology for reducing gas mobility and increasing trapping within the swept region in deep brine aquifers. In this work, a consistent thermodynamic model based on a combination of the Peng-Robinson equation of state (PR EOS) for gas components with an activity model for the aqueous phase is implemented to accurately describe the complex phase-behavior of the CO₂-brine system. The phase-behavior module is combined with the representation of foam by an implicit-texture (IT) model with two flow regimes. This combination can accurately capture the complicated dynamics of miscible CO₂ foam at various stages of the sequestration process. The Operator-Based Linearization (OBL) approach is applied to improve the efficiency of the highly nonlinear CO₂-foam problem by transforming the discretized nonlinear conservation equations into a quasi-linear form based on state-dependent operators. We first validate our simulation results for enhanced CO₂ dissolution in a small domain with and without the presence of a capillary transition zone (CTZ). Then a 3D unstructured reservoir is used to examine CO₂-foam behavior and its effects on CO₂ storage. Simulation studies show good agreement with analytical solutions in both cases with and without CTZ. Besides, the presence of a CTZ enhances the CO₂ dissolution rate in brine. Foam simulations show that foams can reduce gas mobility effectively by trapping gas bubbles and inhibit CO₂ from migrating upward in the presence of gravity, which in turn improves the sweep efficiency and opens the unswept region for CO₂ storage. In the long run (post-injection), with the increasing effects of dissolution, the mechanism of residual trapping, due to the presence of foam, may not be significant. This work suggests a possible strategy to develop an efficient CO₂ storage technology.

It is very important to quantitatively analyze steam chamber expanding and bottom water invading during steam flooding. Firstly, a novel method was established to identify the moment of water invading based on the energy conservation law. Then, a series of experiments were carried out to research the effect of steam flooding through 3D physical simulation and oil-component analysis. The results showed that water invading was recognized through the inflection point of tangent slope of temperature vs. time. Steam mainly migrated in upper layer and hot water moved downwards into bottom layer. The four stages of steam flooding were corresponding to the growth processes of steam chamber, such as expanding, advancing, channeling and overriding. The ultimate oil recovery factor was only 36.00%. The shape of water coning deformed from a triangle to a trapezoid. Finally, the dimensionless volume of water coning was about 32.29%. During steam flooding, the content of oil components gradually changed due to the effect of distillation. The content of light hydrocarbon was higher at the front of steam chamber. However, heavy components mainly occupied the swept zone of steam flooding. The results are important in exploitation practice aiming at heavy oil reservoirs with bottom water.

Alternative to CPU computing architectures, such as GPU, continue to evolve increasing the gap in peak memory bandwidth achievable on a conventional workstation or laptop. Such architectures are attractive for reservoir simulation, which performance is generally bounded by system memory bandwidth. However, to harvest the benefit of a new architecture, the source code must be inevitably rewritten, sometimes almost completely. One of the biggest challenges here is to refactor the Jacobian assembly which typically involves large volumes of code and complex data processing. We demonstrate an effective and general way to simplify the linearization stage extracting complex physics-related computations from the main simulation loop and leaving only an algebraic multi-linear interpolation kernel instead. In this work, we provide the detailed description of simulation performance benefits from execution of the entire nonlinear loop on the GPU platform. We evaluate the computational performance of Delft Advanced Research Terra Simulator (DARTS) for various energy transition subsurface applications of practical interest on both CPU and GPU platforms, comparing particular workflow phases including Jacobian assembly and linear system solution with both stages of the Constraint Pressure Residual preconditioner.

Geological storage of CO2 is a crucial emerging technology to reduce anthropogenic greenhouse gas emissions. Due to the buoyant characteristic of injected gas and the complex geology of subsurface reservoirs, most injected CO2 either rapidly migrates to the top of the reservoir or fingers through high-permeability layers due to instability in the convection-dominated displacement. Both of these phenomena reduce the storage capacity of subsurface media. CO2-foam injection is a promising technology for reducing gas mobility and increasing trapping within the swept region in deep brine aquifers. A consistent thermodynamic model based on a combination of a classic cubic equation of state (EOS) for gas components with an activity model for the aqueous phase has been implemented to describe the phase behavior of the CO2-brine system with impurities. This phase-behavior module is combined with representation of foam by an implicit-texture (IT) model with two flow regimes. This combination can accurately capture the complicated dynamics of miscible CO2 foam at various stages of the sequestration process. The Operator-Based Linearization (OBL) approach is applied to reduce the nonlinearity of the CO2-foam problem by transforming the discretized conservation equations into space-dependent and statedependent operators. Surfactant-alternating-gas (SAG) injection is applied to overcome injectivity problems related to pressure build-up in the near-well region. In this study, a 3D large-scale heterogeneous reservoir is used to examine CO2-foam behaviour and its effects on CO2 storage. Simulation studies show foams can reduce gas mobility effectively by trapping gas bubbles and inhibit CO2 from migrating upward in the presence of gravity, which in turn improves remarkably the sweep efficiency and opens the unswept region for CO2 storage. We also study how surfactant injection and forming of foam affect enhanced dissolution of CO2 at various thermodynamic conditions. This work provides a possible strategy to develop robust and efficient CO2 storage technology.

Steam channeling, one serious problem in the process of steam flooding in heavy oil reservoir, decreases the sweep efficiency of steam to cause a lower oil recovery. Viscosity reducer and nitrogen foam, two effective methods to improve oil recovery with different mechanism, present a satisfactory result after steam flooding. In this article, a 2D visualized device was introduced to investigate the synergistic development effect of two different chemical additives and intuitively study their flowing characteristic in porous media, as well as macroscopic and microscopic mechanism of improving heavy oil recovery by chemical additives after steam flooding. The results showed that the fingering phenomenon was generated obviously in the process of steam flooding, which restricted the swept area of steam. Due to decreasing oil-water interface tension, O/W emulsion with lower viscosity was formed to enhance the oil flow capacity and polish up the displacement efficiency of steam after injecting viscosity reducer. And the synergistic effect of viscosity reducer & foaming agent was more conductive to improve displacement efficiency of steam, with 4.3% of oil recovery higher than purely viscosity reducer assisting steam flooding in this process. Microscopic results indicated that thermal foams can be trapped in the porous media to improve injection profile effectively and displace the residual oil caused by steam flooding. The ultimate oil recovery of synergistic development is 65.6%, 11.0% higher than one additive (viscosity reducer). This article can provide reference for the study of thermochemistry assisted steam flooding in heavy oil reservoir.