Vertical Equilibrium Models Research Articles

A hybrid multiscale framework coupling multilayer dynamic reconstruction and full-dimensional models for CO2 storage in deep saline aquifers

Numerical modeling of CO2 injection in the deep saline aquifer is computationally expensive due to the large spatial and temporal scales. To address the computational challenge, reduced-dimensional models (e.g., vertical equilibrium (VE) and dynamic reconstruction (DR) models) based on vertical integration of the full-dimensional governing equations have been developed. VE models assume rapid segregation of the injected and the resident fluids due to strong buoyancy. Conversely, DR models employ a multiscale framework that relaxes the VE assumption and captures the vertical dynamics of CO2 and brine by solving the vertical two-phase flow dynamics as one-dimensional fine-scale problems. Although DR models relax the VE assumption while maintaining much of the computational efficiency of VE models, they are thus far limited to homogeneous and layered heterogeneous formations. We present a novel hybrid framework that couples a multilayer dynamic reconstruction model and a full-dimensional model. The new hybrid framework allows simulation of CO2 injection in geological formations with local heterogeneities. It employs a full-dimensional model in local heterogeneous regions (where the full-dimensional model should be used for accuracy), while applying the dynamic reconstruction model in the rest of the domain. Numerical simulations of CO2 injection in three heterogeneous reservoirs show that the hybrid model maintains the accuracy of the conventional full-dimensional models with significantly reduced computational cost.

Vertically integrated dual-continuum models for CO2 injection in fractured geological formations

Various modeling approaches, including fully three-dimensional (3D) models and vertical-equilibrium (VE) models, have been used to study the large-scale storage of carbon dioxide (CO2) in deep saline aquifers. 3D models solve the governing flow equations in three spatial dimensions to simulate migration of CO2 and brine in the geological formation. VE models assume rapid and complete buoyant segregation of the two fluid phases, resulting in vertical pressure equilibrium and allowing closed-form integration of the governing equations in the vertical dimension. This reduction in dimensionality makes VE models computationally much more efficient, but the associated assumptions restrict the applicability of VE models to geological formations with moderate to high permeability. In the present work, we extend the VE models to simulate CO2 storage in fractured deep saline aquifers in the context of dual-continuum modeling, where fractures and rock matrix are treated as porous media continua with different permeability and porosity. The high permeability of fractures makes the VE model appropriate for the fracture domain, thereby leading to a VE dual-continuum model for the dual continua. The transfer of fluid mass between fractures and rock matrix is represented by a mass transfer function connecting the two continua, with a modified transfer function for the VE model based on vertical integration. Comparison of the new model with a 3D dual-continuum model shows that the new model provides comparable numerical results while being much more computationally efficient.

Multiresolution coupled vertical equilibrium model for fast flexible simulation of CO2 storage

CO2 capture and storage is an important technology for mitigating climate change. Design of efficient strategies for safe, long-term storage requires the capability to efficiently simulate processes taking place on very different temporal and spatial scales. The physical laws describing CO2 storage are the same as for hydrocarbon recovery, but the characteristic spatial and temporal scales are quite different. Petroleum reservoirs seldom extend more than tens of kilometers and have operational horizons spanning decades. Injected CO2 needs to be safely contained for hundreds or thousands of years, during which it can migrate hundreds or thousands of kilometers. Because of the vast scales involved, conventional 3D reservoir simulation quickly becomes computationally unfeasible. Large density difference between injected CO2 and resident brine means that vertical segregation will take place relatively quickly, and depth-integrated models assuming vertical equilibrium (VE) often represent a better strategy to simulate long-term migration of CO2 in large-scale aquifer systems. VE models have primarily been formulated for relatively simple rock formations and have not been coupled to 3D simulation in a uniform way. In particular, known VE simulations have not been applied to models of realistic geology in which many flow compartments may exist in-between impermeable layers. In this paper, we generalize the concept of VE models, formulated in terms of well-proven reservoir simulation technology, to complex aquifer systems with multiple layers and regions. We also introduce novel formulations for multi-layered VE models by use of both direct spill and diffuse leakage between individual layers. This new layered 3D model is then coupled to a state-of-the-art, 3D black-oil type model. The formulation of the full model is simple and exploits the fact that both models can be written in terms of generalized multiphase flow equations with particular choices of the relative permeabilities and capillary pressure functions. The resulting simulation framework is very versatile and can be used to simulate CO2 storage for any combination of 3D and VE-descriptions, thereby enabling the governing equations to be tailored to the local structure. We demonstrate the simplicity of the model formulation by extending the standard flow-solvers from the open-source Matlab Reservoir Simulation Toolbox (MRST), allowing immediate access to upscaling tools, complex well modeling, and visualization features. We demonstrate this capability on both conceptual and industry-grade models from a proposed storage formation in the North Sea. The current implementation assumes a sharp interface for the VE model, where the capillary forces do not lead to a capillary fringe. While the examples are taken specifically from CO2 storage applications, the framework itself is general and can be applied to many problems in which parts of the domain are dominated by gravity segregation. Such applications include gas storage and hydrocarbon recovery from gas reservoirs with local layering structure.

Vertical Equilibrium Flow Models with Fully Coupled Geomechanics for CO2 Storage Modeling, Using Precomputed Mechanical Response Functions

Vertical equilibrium (VE) models have proved to be attractive for simulation of CO2 storage scenarios. Their primary advantage is a substantial reduction in computational requirements compared to standard 3D simulation tools. In this work, we aim to include the effects of geomechanics on aquifer flow while preserving computational efficiency. When fluids are injected into a geological formation, changes in pore pressure leads to rock deformation, which influence the flow properties of the formation. To fully model this effect, a two way coupling between flow and mechanics equations is generally necessary, including the full under- and overburden. This leads to a computationally expensive system, thus reducing the computational advantage of using VE models. Within a linear poroelastic framework, the full effect of deformation on flow is captured through changes in volumetric strain, which can be precomputed for a given pressure basis at grid generation time and used directly in the flow equations during simulation. This allow us to model the full effect of geomechanics on aquifer flow while eliminating the need for solving the mechanics equations at simulation time. We demonstrate the approach on 2D and 3D examples, and compare with results obtained from a standard VE flow models and a model that includes the full poroelastic set of equations. Compared to the latter, we observe a significant computational benefit using our proposed approach. On the other hand, the impact of geomechanics appears to be primarily captured by a well-chosen rock compressibility coefficient, suggesting that a fully coupled model might not be required in many practical cases.

Vertically Integrated Dual-porosity and Dual-permeability Models for CO2 Sequestration in Fractured Geological Formation

Analysis of geological storage of carbon dioxide (CO2) in deep saline aquifers requires computationally efficient mathematical models to predict the pressure evolution and the injected CO2 plume migration. The subsurface system of CO2 injection into saline aquifers can be modeled as a two-phase flow system, with a non-wetting less dense (supercritical) CO2 phase and a denser brine as the wetting phase. For unfractured geological formations, one type of simplified model can be developed by integrating the three-dimensional governing equations in the vertical dimension. The vertically integrated models that assume buoyant segregation and vertical pressure equilibrium are referred to as vertical equilibrium (VE) models. VE models are computationally efficient owing to the dimension reduction from vertical integration, and have been extensively applied to field-scale modeling of CO2 injection, migration, and leakage in the past decade. For fractured geological formations, it is challenging to directly use vertically integrated models, because CO2 migration in fractured formations involves two different characteristic time scales due to significant contrast of permeability between the fractures and matrix. The high permeability of the fractures leads to fast buoyant segregation of CO2 and brine in the vertical direction within the fractures, while lower permeability of the matrix typically leads to much slower flow dynamics that involve longer time scales for segregation.In this paper, we use a dual-continuum approach to conceptualize the fractured geological formation, treating the fractures and the rock matrix blocks as overlapping continua, and develop vertically integrated models for CO2 injection in fractured geological formation. We use a VE model for the fracture domain and explore different model options for the matrix domain, including the classical dual-porosity model that treats the matrix as a source/sink term for the fracture as well as other more advanced models that explicitly account for the two-phase flow dynamics of the CO2 and brine in the matrix domain. We present the modeling framework and show preliminary model comparison results to demonstrate the applicability of the new models.

Categorization of Norwegian Continental Shelf Formations in Terms of Geological CO2 Storage Potentials

In the present study, we use data published alongside the Norwegian Petroleum Directorate (NPD) storage atlases to further investigate the storage capacity of 23 formations found in the Norwegian Continental Shelf. Our goal is to categorize the formations according to the main limiting factors for long-term geologic storage of CO2. We conduct the study by defining reasonable injection scenarios and running simulations on grids constructed from the NPD data, which also include the associated averaged rock properties. The use of vertical-equilibrium models allows us to rapidly run a large number of long-term simulations of injection and migration scenarios. The ability to run rapid simulations allows us to optimize injection rates using an adjoint-based nonlinear optimization algorithm. For a given number of wells and set of boundary conditions, we aim to optimize the amount of CO2 injected, subject to limits on long-term leakage and maximum allowed pressures. The outcome allows us to determine whether an aquifer is restricted mainly by long-time leakage across open boundaries, or global pressure buildup. We also provide figures for how much CO2 can be injected before the limitation is reached, subject to the working assumptions and demonstrate how changing these assumptions may influence the result. In particular, the assumed injection time and cost of leakage is discussed.We emphasize that through this study we wish to demonstrate a practical approach to the estimation of realizable storage capacity and illustrate how site-specific operational limitations influence the exploitable storage volume as compared with the initial storage estimates provided by NPD. As the study is based on large-scale averaged data under several simplifying assumptions, the realized storage capacity for each formation may well change if more detailed information, in particular on heterogeneity or more complex fluid-rock interactions, were to be taken into account. However, the use of simplified models to identify realizable storage capacity on the large scale allows us to quickly identify which formations may be best suited for a particular injection scenario.

On obtaining optimal well rates and placement for CO2 storage

Large-scale storage of CO2 in saline aquifers is considered an essential technology to mitigate CO2 emissions. Storage potential has mainly been estimated based on volumetrics or detailed simulations for specific injection scenarios. In practice, achievable storage capacity will depend on engineering, economical, and political restrictions and be limited by the length of the injection period, costs associated with potential CO2 leakage, pressure management, etc. We show how achievable storage volumes can be estimated and maximized using adjoint-based optimization and a hierarchy of simulation methods. In particular, vertical equilibrium models provide the simplest possible description of the flow dynamics during the injection and early post-injection period, while percolation type methods provide effective means for forecasting the long-term fate of CO2 during the later migration stages. We investigate the storage volumes that can be achieved for several formations found along the Norwegian Continental Shelf by optimizing well placement and injection rates, and using production wells for pressure management when necessary. Optimal strategies are obtained under various objectives and simple but realistic constraints, namely: penalization of CO2 leakage, minimization of well cost, and restriction of pressure buildup.

Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe

Geological carbon storage represents a new and substantial challenge for the subsurface geosciences. To increase understanding and make good engineering decisions, containment processes and large-scale storage operations must be simulated in a thousand year perspective. A hierarchy of models of increasing computational complexity for analysis and simulation of large-scale CO2 storage has been implemented as a separate module of the open-source Matlab Reservoir Simulation Toolbox (MRST). This paper describes a general family of two-scale models available in this module. The models consist of two-dimensional flow equations formulated in terms of effective quantities obtained from hydrostatic reconstructions of vertical pressure and saturation distributions. The corresponding formulation is fully implicit and is the first to give a mass-conservative treatment and include general (non-linearized) CO2 properties. In particular, the models account for compressibility, dissolution, and hysteresis effects in the fine-scale capillary and relative permeability functions and can be used to accurately and efficiently study the combined large-scale and long-term effects of structural, residual, and solubility trapping.

Multiphase modeling of geologic carbon sequestration in saline aquifers.

Geologic carbon sequestration (GCS) is being considered as a climate change mitigation option in many future energy scenarios. Mathematical modeling is routinely used to predict subsurface CO2 and resident brine migration for the design of injection operations, to demonstrate the permanence of CO2 storage, and to show that other subsurface resources will not be degraded. Many processes impact the migration of CO2 and brine, including multiphase flow dynamics, geochemistry, and geomechanics, along with the spatial distribution of parameters such as porosity and permeability. In this article, we review a set of multiphase modeling approaches with different levels of conceptual complexity that have been used to model GCS. Model complexity ranges from coupled multiprocess models to simplified vertical equilibrium (VE) models and macroscopic invasion percolation models. The goal of this article is to give a framework of conceptual model complexity, and to show the types of modeling approaches that have been used to address specific GCS questions. Application of the modeling approaches is shown using five ongoing or proposed CO2 injection sites. For the selected sites, the majority of GCS models follow a simplified multiphase approach, especially for questions related to injection and local-scale heterogeneity. Coupled multiprocess models are only applied in one case where geomechanics have a strong impact on the flow. Owing to their computational efficiency, VE models tend to be applied at large scales. A macroscopic invasion percolation approach was used to predict the CO2 migration at one site to examine details of CO2 migration under the caprock.

Vertically Averaged Equations with Variable Density for $$\hbox {CO}_2$$ CO 2 Flow in Porous Media

Carbon capture and storage has been proposed as a viable option to reduce $$\hbox {CO}_2$$ emissions. Geological storage of $$\hbox {CO}_2$$ where the gas is injected into geological formations for practically indefinite storage, is an integral part of this strategy. Mathematical models and numerical simulations are important tools to better understand the processes taking place underground during and after injection. Due to the very large spatial and temporal scales involved, commercial 3D-based simulators for the petroleum industry quickly become impractical for answering questions related to the long-term fate of injected $$\hbox {CO}_2$$ . There is an interest in developing simplified modeling tools that are effective for this type of problem. One approach investigated in recent years is the use of upscaled models based on the assumption of vertical equilibrium (VE). Under this assumption, the simulation problem is essentially reduced from 3D to 2D, allowing much larger models to be considered at the same computational cost. So far, most work on VE models for $$\hbox {CO}_2$$ storage has either assumed incompressible $$\hbox {CO}_2$$ or only permitted lateral variations in $$\hbox {CO}_2$$ density (semi-compressible). In the present work, we propose a way to fully include variable $$\hbox {CO}_2$$ density within the VE framework, making it possible to also model vertical density changes. We derive the fine-scale and upscaled equations involved and investigate the resulting effects. In addition, we compare incompressible, semi-compressible, and fully compressible $$\hbox {CO}_2$$ flow for some model scenarios, using an in-house, fully-implicit numerical code based on automatic differentiation, implemented using the MATLAB reservoir simulation toolkit.

Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs

AbstractIn this article, a two-layer vertical equilibrium model for the injection of carbon dioxide into a low-pressure porous reservoir containing methane and water is developed. The dependent variables solved for include pressure, temperature and $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathrm{CO}}_2$–${\mathrm{CH}}_4$ interface height. In contrast to previous two-layer vertical equilibrium models in this context, the compressibility of all material components is fully accounted for. Non-Darcy effects are also considered using the Forchheimer equation. The results show that, for a given injection scenario, as the initial pressure in the reservoir decreases, both the pressure buildup and temperature change increase. A comparison was conducted between a fully coupled non-isothermal numerical model and a simplified model where fluid properties are held constant with temperature. This simplified model was found to provide an excellent approximation when using the injection fluid temperature for calculating fluid properties, even when the injection fluid was as much as $\pm 15\, ^\circ \mathrm{C}$ of the initial reservoir temperature. The implications are that isothermal models can be expected to provide useful estimates of pressure buildup in this context. Despite the low viscosity of ${\mathrm{CO}}_2$ at the low pressures studied, non-Darcy effects were found to be of negligible concern throughout the sensitivity analysis undertaken. This is because the ${\mathrm{CO}}_2$ density is also low in this context. Based on these findings, simplified analytic solutions are derived, which accurately calculate both the pressure buildup and temperature decline during the injection period.

Application of Vertically-Integrated Models with Subscale Vertical Dynamics to Field Sites for CO2 Sequestration

Abstract To address the engineering questions on security issues of geological carbon sequestration (GCS), a broad range of computational models with different levels of complexity have been developed - from multiphase multicomponent fully coupled three-dimensional models to simplified analytical solutions. Within this wide range of models, a family of so-called vertical equilibrium (VE) models has been developed. These models assume that CO2 and brine have segregated due to buoyancy and reached a hydrostatic pressure distribution in the vertical direction. Such VE models are computationally efficient due to the dimensional reduction in the vertical, and accurate as long as the VE assumption is satisfied. However, a study comparing results from a VE model to results from a full three- dimensional model found that there are realistic conditions for which the VE assumption is not justified, especially for geological formations that have low vertical permeability, on the order of 10 milliDarcy or lower [1] . In an attempt to overcome the VE limitation of the vertically-integrated models, a new type of vertically-integrated model which relaxes the VE assumption while still using a vertically-integrated framework has been developed [2] . The new vertically-integrated model is cast into a multiscale framework, where the coarse scale is the horizontal domain and the fine scale is the vertical domain corresponding to the thickness of a geologic formation. This type of model maintains much of the computational advantages of the VE models, while allowing a much wider range of problem to be modelled. In this paper, we extend the model in [2] to include horizontally layered geologic heterogeneities and develop a new dynamic reconstruction model, which we refer to as a “multi-layer dynamic reconstruction” model. The model in [2] is called “single-layer dynamic reconstruction” model to distinguish the modelling approaches. We apply both dynamic reconstruction models to field injection sites, including a hypothetical injection scenario into the Mount Simon formation in the Illinois Basin, USA and the well-known industrial-scale injection into the Utsira formation at the Sleipner site in Norway. The modelling results show that the multi-layer dynamic reconstruction model is capable of dealing with horizontally layered heterogeneities and gives results that agree reasonably well with results from the full multi-dimensional model, although in geologic layers with high permeability the reconstruction algorithm is not able to fully capture the horizontal driving forces due to buoyancy. This could be important over long time scales for highly permeable geologic layers. The single- layer dynamic reconstruction model was shown be to the right model choice for homogeneous formations with relatively low permeability where it takes a long time for CO2 and brine to reach vertical equilibrium [2] . In this study, we found that for homogeneous formations with high permeability and steep capillary pressure curves, the single-layer dynamic reconstruction model gives results that are analogous to vertical equilibrium models, with the fast segregation dynamics requiring small time steps in the dynamic reconstruction algorithm. As such vertical equilibrium models are the appropriate choice for systems with high permeability, although we also note that the behaviour of the brine relative permeability curve at low brine saturations is an additional important consideration and must be included in the overall analysis.

Impact of Model Complexity on CO2 plume modeling at Sleipner

Abstract The goal of geologic carbon sequestration (GCS) is to store carbon dioxide (CO 2 ) in the subsurface for time periods on the order of thousands of years. Mathematical modeling is an important tool to predict the migration of both CO 2 and brine to ensure safe and permanent storage. Many modeling approaches with different levels of complexity have been applied to the problem of GCS ranging from simple analytic solutions to fully-coupled three-dimensional reservoir simulators. The choice of modeling approach is often a function of the spatial and temporal scales of the problem, reservoir properties, data availability, available computational resources, and the familiarity of the modeler with a specific modeling approach. In this study we apply a series of models with different levels of model complexity to the 9 th layer of the Utsira Formation. The list of modeling approaches includes (from least complex to most complex): numerical vertical-equilibrium model with sharp-interface, numerical vertical-equilibrium model with capillary transition zone, vertically-integrated model with dynamic vertical pressure and saturation reconstruction, and fully- coupled three-dimensional model. The model domain consists of a 3 x 6 km section of the 9 th layer, as described in the IEAGHG benchmark dataset. The layer thickness varies in space, ranging from 5 to 30 m, while porosity and permeability are close to constant at 0.36 and 1.8 Darcy, respectively. The models are all based on the same input data, and initial and boundary conditions are chosen in a way that ensures the different models are comparable. In addition, a simple box model is used for preliminary simulations. The models are compared based on the predicted CO 2 plume footprints and saturation cross-sections. The predicted CO 2 plumes are also compared to the actual CO 2 plume footprint from seismic surveys to determine the ability of the different models to predict the actual CO 2 plume footprint. The results show that vertical-equilibrium models are sufficient to model CO 2 migration in the 9 th layer of Sleipner, due to the formation's higher permeability and relatively thin capillary transition zone. None of the models used in this study was able to accurately predict the actual plume footprint; this suggests the modeling approaches used here are missing essential physics or that some parameters in the site model (e.g., topography of the caprock) are inaccurate.

Applicability of vertical-equilibrium and sharp-interface assumptions in CO2 sequestration modeling

Analysis of geological sequestration of carbon dioxide (CO2) requires mathematical models of different complexity to answer a range of practical questions. A family of vertically-integrated models of intermediate complexity can be derived by assuming that the strong buoyant drive in the system leads to vertical segregation of the injected CO2 and resident brine on a time scale that is fast enough to model the system as being stratified and in vertical-equilibrium. These models range from vertically-integrated numerical models which include capillary forces via mathematical reconstruction, to analytical models assuming a sharp-interface and homogeneous formation parameters. This paper investigates the limits of numerical vertical-equilibrium models and the more restricted vertical-equilibrium sharp-interface models via direct comparisons with a homogeneous three-dimensional model, exploring the impacts of injection rate, injection time, and formation characteristics. We use the commercial simulator ECLIPSE for the three-dimensional model. Our results demonstrate that the applicability of a vertically-integrated modeling approach to CO2 sequestration depends on the time scale of the vertical brine drainage within the plume, relative to the time scale of the simulation. The validity of the sharp-interface assumption is shown to depend on the spatial scale of the capillary forces, which drive the thickness of the capillary transition zone. A finite-capillary-transition-zone vertically-integrated numerical model with saturation reconstruction closely matches results from the three-dimensional model (ECLIPSE) including capillary pressure as long as the segregation time scales are respected. Overall, our results demonstrate that vertically-integrated and sharp-interface models are useful and accurate when applied within the appropriate length and time scales.

Numerical Simulation Studies of the Long-term Evolution of a CO2 Plume in a Saline Aquifer with a Sloping Caprock

We have used the TOUGH2-MP/ECO2N code to perform numerical simulation studies of the long-term behavior of CO2 stored in an aquifer with a sloping caprock. This problem is of great practical interest, and is very challenging due to the importance of multi-scale processes. We find that the mechanism of plume advance is different from what is seen in a forced immiscible displacement, such as gas injection into a water-saturated medium. Instead of pushing the water forward, the plume advances because the vertical pressure gradients within the plume are smaller than hydrostatic, causing the groundwater column to collapse ahead of the plume tip. Increased resistance to vertical flow of aqueous phase in anisotropic media leads to reduced speed of up-dip plume advancement. Vertical equilibrium models that ignore effects of vertical flow will overpredict the speed of plume advancement. The CO2 plume becomes thinner as it advances, but the speed of advancement remains constant over the entire simulation period of up to 400 years, with migration distances of more than 80 km. Our simulations include dissolution of CO2 into the aqueous phase and associated density increase, and molecular diffusion. However, no convection develops in the aqueous phase because it is suppressed by the relatively coarse (sub-) horizontal gridding required in a regional-scale model. A first crude sub-grid-scale model was developed to represent convective enhancement of CO2 dissolution. This process is found to greatly reduce the thickness of the CO2 plume, but, for the parameters used in our simulations, does not affect the speed of plume advancement.

Field-case simulation of CO2 -plume migration using vertical-equilibrium models

When injected in deep saline aquifers, CO2 moves radially away from the injection well and progressively higher in the formation because of buoyancy forces. Analyzes have shown that after the injection period, CO2 will potentially migrate over several kilometers in the horizontal direction but only tens of meters in the vertical direction, limited by the aquifer caprock [1, 2]. Because of the large horizontal plume dimensions, three-dimensional numerical simulations of the plume migration over long periods of time are computationally intensive. Thus, to get results within a reasonable time frame, one is typically forced to use coarse meshes and long time steps which result in inaccurate results because of numerical errors in resolving the plume tip. Given the large aspect ratio between the vertical and horizontal plume dimensions, it is reasonable to approximate the CO2 migration using vertically averaged models. Such models can, in many cases, be more accurate than coarse three-dimensional computations. In particular, models based on vertical equilibrium (VE) [3] are attractive to simulate the long-term fate of CO2 sequestered into deep saline aquifers. The reduced spatial dimensionality resulting from the vertical integration ensures that the computational performance of VE models exceeds the performance of standard three-dimensional models. Thus, VE models are suitable to study the long-time and large-scale behavior of plumes in real large-scale CO2-injection projects [4, 1, 2, 5]. We investigate the use of VE models to simulate CO2 migration in a real large-scale eld case based on data from the Sleipner site in the North Sea. We discuss the potential and limitations of VE models and show how VE models can be used to give reliable estimates of long-term CO2 migration. In particular, we focus on a VE formulation that incorporates the aquifer geometry and heterogeneity, and that considers the eects of hydrodynamic and residual trapping. We compare the results of VE simulations with standard reservoir simulation tools on test cases and discuss their advantages and limitations and show how, provided that certain conditions are met, they can be used to give reliable estimates of long-term CO2 migration.

Impact of Surfactant on Configuration of Petroleum Hydrocarbon Lens

A laboratory-scale physical model was constructed for visual observation of the basic 2-D flow characteristics of a gasoline spill through an unconfined aquifer and the subsequent treatment with a surfactant. The model consists of a parallel-plate glass tank (1 m×1 m×5 cm) packed with Ottawa sand. Gasoline was released from a point source in the vadose zone. As the specific gravity of gasoline is less than one (LNAPL), it pooled above the water saturated pores of the tension saturated region of water. Beyond the lens of gasoline, the height of the capillary fringe was reduced due to capillary pollution. The gasoline lens was then treated with an aqueous phase surfactant solution of 2% dodecyl benzene sulfonate (anionic) and 2% polyethoxylate nonyl phenol (nonionic). This surfactant solution reduced the interfacial tension between the gasoline and the aqueous phase by an order of magnitude. The surfactant solution was released from the same point source in the vadose zone as the gasoline. As a result, the location and geometry of the gasoline lens and the polluted capillary fringe were significantly altered. These changes were investigated using vertical equilibrium models, the capillary number, the buoyancy number and the total trapping number to evaluate the approach of pretreatment as a potential remediation strategy.

Experimental and Numerical Evaluation of LNAPL Lens and Polluted Capillary Fringe Thickness

The effective remediation of light non-aqueous-phase liquid (LNAPL) in the subsurface is dependent on predicting the location and geometry of the lens near the tension-saturated pores of the capillary fringe. The objective of this study was to evaluate both the thickness of a lens of light nonaqueous phase liquid spill in the subsurface and the subsequent alteration of the capillary fringe. Two-dimensional (2D) experiments were conducted in a parallel plate glass tank (1 m × 1 m × 5 cm) using Ottawa sand and gasoline. An equation for predicting the vertical thickness based on the displacement pressure in the lateral direction was developed. The model and previously published vertical equilibrium models for predicting the thickness of a lens were tested. The model equations were also used to evaluate changes in the capillary fringe due to capillary pollution. The results provide a means to better understand the behavior of light nonaqueous phase liquids in the subsurface.