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.

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During injection of supercritical CO2 into saline aquifers or depleted gas reservoirs, the complex interaction of CO2 and impurities with reservoir fluids plays a very important role and can significantly alternate the injectivity. Brine evaporation into the CO2-rich phase can lead to salt precipitation which will reduce the effective permeability of the porous rock. A tangible cooling of the near-wellbore region due to the Joule-Thomson effect can lead to hydrate formation which will reduce injectivity even more. Complex phase behavior of supercritical CO2 with brine and hydrocarbon components in highly heterogeneous porous media accompanied by all these phenomena will strongly affect pressure distribution which is in turn related to mechanical risks.

In this work, we present a unified simulation framework for modelling near-wellbore effects induced by supercritical CO2 injection developed in the Delft Advanced Research Terra Simulator (DARTS) platform. This framework uses the Operator-Based Linearization (OBL) technique for incorporating all complex physical phenomena in a fully coupled fully implicit manner. A general multicomponent multiphase flash based on a combination of classic cubic equations of state (e.g., Peng-Robinson) for hydrocarbon/CO2-rich phases and an activity model for the aqueous phase is implemented. Hydrate phase behavior is modelled using a modified Van der Waals-Platteeuw hydrate equation of state. Formation dry-out and salt precipitation are incorporated by using the Element Balance approach coupled with thermodynamics. Thermophysical property correlations relevant to the thermodynamic conditions of interest are implemented and validated against lab experiments.

We demonstrate that all important physical phenomena, such as the Joule-Thomson effect, hydrate formation and salt precipitation can be effectively captured by the OBL approach. We use several existing numerical benchmarks to validate the accuracy of the developed framework in the dynamic representation of all these effects. The interplay between these complex phenomena and reservoir heterogeneity is demonstrated in an unstructured heterogeneous near-wellbore reservoir model.@en

Polymer flooding is one efficient EOR technology by overcoming non-uniform and unstable displacement caused by water injection. Polymer flooding in reservoirs is a complicated process that involves strongly nonlinear physics, e.g., non-Newtonian rheology in porous media with retention and adsorption. In the presence of multi-scale heterogeneity, high-fidelity simulations are usually required to capture such nonlinear behavior, which is a time-consuming process for conventional reservoir modelling.

In this study, we extend an advanced linearization strategy, called the Operator-Based Linearization (OBL) approach, to simulate non-Newtonian polymer flooding with retention and adsorption mechanisms using the fully implicit method. A velocity-dependent viscosity multiplier compliments the operator form of governing equations to represent the non-Newtonian rheology of the high-molecular-compound polymer. The retention of polymer, reducing the porosity, is represented by a Langmuir-type adsorption model. Several simplified models have been used for validation of the developed numerical framework. The numerical results show good agreement with both the analytical solutions and the coreflood experimental data though some negligible discrepancies can be observed in simulation results.

A highly resolved near-well model is used to test the performance of polymer flooding in realistic reservoir conditions. Both shear-thinning and thickening regimes, depending on the injection velocity and polymer concentration, are recognized in the near-wellbore zone. The injected polymer concentration and brine salinity significantly affect the shear viscosity, and consequently, polymer injectivity. Polymer retention and adsorption have a substantial effect on the rate of polymer propagation through porous media. Overall, polymer flooding shows its advantages to mitigate water fingering in field-scale operations and improves the ultimate sweep of the reservoir. However, optimal injectivity is one essential factor that affects the performance of polymer flooding. The computational superiority of the proposed model allows us to optimize the parameters of polymer flooding in realistic reservoirs and operational settings.@en

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.

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Steam-assisted gravity drainage (SAGD) is one efficient and mature technology for recovering heavy oil and bitumen resources. The key underlying mechanism is the growth of the steam chamber after injecting steam. However, due to the complex geological environment, the thief zones exist and have a prejudicial effect on the development of the steam chamber, thus impacting the ultimate heavy-oil recovery. In this work, our objective is to investigate the effect of a top-water thief zone (i.e., water zone overlies the oil sand) on SAGD performance and further to understand the crucial mechanisms that control the heat loss during steam injection. A large-scale three-dimensional experimental apparatus is used to carry out the SAGD process with a top aquifer. Based on the similarity criterion, the field-scale model is transformed into a laboratory elemental model. To evaluate the SAGD performance quantitatively, the dynamic growth of the steam chamber is measured using the thermal detectors and the production data is recorded. The results show that the steam chamber exhibits three distinguished stages, that is, upward spread, lateral extension, and downward development in the presence of top-water zone. The bottom-water zone has less impact on the steam-chamber growth. The existence of a confined top-water zone, however, significantly affects SAGD performance, especially the lateral expansion of the steam chamber. The lateral propagation of the steam front is hindered by the top thief zone due to the heat exchange with the top water. Once the steam chamber reaches the boundary, the accumulation of energy in the water thief zone, in turn, can reduce the remaining oil saturation along the topwater-oil interface. This study provides us some key insights into the development of heavy oil resources with top thief zones when implementing SAGD technology.@en

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.

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Numerical simulation of coupled multiphase multicomponent flow and transport in porous media is a crucial tool for understanding and forecasting of complex industrial applications related to the subsurface. The discretized governing equations are highly nonlinear and usually need to be solved with Newton's method, which corresponds with high computational cost and complexity. With the presence of capillary and gravity forces, the nonlinearity of the problem is amplified even further, which usually leads to a higher numerical cost. A recently proposed operator-based linearization (OBL) approach effectively improves the performance of complex physical modeling by transforming the discretized nonlinear conservation equations into a quasilinear form according to state-dependent operators. These operators are approximated by means of a discrete representation on a uniform mesh in physical parameter space. Continuous representation is achieved through the multilinear interpolation. This approach provides a unique framework for the multifidelity representation of physics in general-purpose simulation. The applicability of the OBL approach was demonstrated for various energy subsurface applications with multiphase flow of mass and heat in the presence of buoyancy and diffusive forces. In this work, the OBL approach is extended for multiphase multicomponent systems with capillarity. Through the comparisons with a legacy commercial simulator using a set of benchmark tests, we demonstrate that the extended OBL scheme significantly improves the computational efficiency with the controlled accuracy of approximation and converges to the results of the conventional continuous approach with an increased resolution of parametrization.@en

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.

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Foam is an agglomeration of gas bubbles separated from each other by thin liquid films. Foam injection has been proved to be an efficient way to increase sweep efficiency in gas-injection enhanced-oil-recovery (EOR) processes or enlarge the storage space for trapping of CO2 in aquifers. Numerical simulation, an important tool developed by combining physics, mathematics, and computer programming, provides an efficient way to understand the complex fluid flow in subsurface reservoirs with applications to the evaluation of hydrocarbon recovery, energy efficiency, performance analysis, and various optimization problems. However, simulation of foam-related displacement in reservoirs is still an expensive process for conventional simulation due to the strongly nonlinear physics. In this dissertation, a newly developed numerical simulator, called Delft Advanced Research Terra Simulator (DARTS), is introduced to investigate the complicated flow behavior in porous media with the presence of foam.@en

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.

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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.

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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.

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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.

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