Pressure Buildup and Brine Migration During CO2 Storage in Multilayered Aquifers

Carbon dioxide injection into deep saline formations may induce large‐scale pressure increases and migration of native fluid. Local high‐conductivity features, such as improperly abandoned wells or conductive faults, could act as conduits for focused leakage of brine into shallow groundwater resources. Pressurized brine can also be pushed into overlying/underlying formations because of diffuse leakage through low‐permeability aquitards, which occur over large areas and may allow for effective pressure bleed‐off in the storage reservoirs. This study presents the application of a recently developed analytical solution for pressure buildup and leakage rates in a multilayered aquifer‐aquitard system with focused and diffuse brine leakage. The accuracy of this single‐phase analytical solution for estimating far‐field flow processes is verified by comparison with a numerical simulation study that considers the details of two‐phase flow. We then present several example applications for a hypothetical CO₂ injection scenario (without consideration of two‐phase flow) to demonstrate that the new solution is an efficient tool for analyzing regional pressure buildup in a multilayered system, as well as for gaining insights into the leakage processes of flow through aquitards, leaky wells, and/or leaky faults. This solution may be particularly useful when a large number of calculations needs to be performed, that is, for uncertainty quantification, for parameter estimation, or for the optimization of pressure‐management schemes.     

A coupled local–global upscaling approach for simulating flow in highly heterogeneous formations

A new technique for generating coarse scale models of highly heterogeneous subsurface formations is developed and applied. The method uses generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled properties (permeability or transmissibility). An iteration procedure assures consistency between the local and global calculations. Transport processes are simulated using a subgrid velocity reconstruction technique applied in conjunction with the local–global upscaling procedure. For highly heterogeneous (e.g., channelized) systems, the new method is shown to provide considerably more accurate coarse scale models for flow and transport, relative to reference fine scale results, than do existing local (and extended local) upscaling techniques. The applicability of the upscaled models for different global boundary conditions is also considered.     

Numerical modelling of stream–aquifer interaction: Quantifying the impact of transient streambed permeability and aquifer heterogeneity

Stream–aquifer interaction plays a vital role in the water cycle, and a proper study of this interaction is needed for understanding groundwater recharge, contaminants migration, and for managing surface water and groundwater resources. A model‐based investigation of a field experiment in a riparian zone of the Schwarzbach river, a tributary of the Rhine River in Germany, was conducted to understand stream–aquifer interaction under alternative gaining and losing streamflow conditions. An equivalent streambed permeability, estimated by inverting aquifer responses to flood waves, shows that streambed permeability increased during infiltration of stream water to aquifer and decreased during exfiltration. Aquifer permeability realizations generated by multiple‐point geostatistics exhibit a high degree of heterogeneity and anisotropy. A coupled surface water groundwater flow model was developed incorporating the time‐varying streambed permeability and heterogeneous aquifer permeability realizations. The model was able to reproduce varying pressure heads at two observation wells near the stream over a period of 55 days. A Monte Carlo analysis was also carried out to simulate groundwater flow, its age distribution, and the release of a hypothetical wastewater plume into the aquifer from the stream. Results of this uncertainty analysis suggest (a) stream–aquifer exchange flux during the infiltration periods was constrained by aquifer permeability; (b) during exfiltration, this flux was constrained by the reduced streambed permeability; (c) the effect of temporally variable streambed permeability and aquifer heterogeneity were found important to improve the accurate capture of the uncertainty; and (d) probabilistic infiltration paths in the aquifer reveal that such pathways and the associated prediction of the extent of the contaminant plume are highly dependent on aquifer heterogeneity.     

Upscaling of CO2 vertical migration through a periodic layered porous medium: The capillary-free and capillary-dominant cases

We present an upscaled model for the vertical migration of a CO₂ plume through a vertical column filled with a periodic layered porous medium. This model may describe the vertical migration of a CO₂ plume in a perfectly layered horizontal aquifer. Capillarity and buoyancy are taken into account and semi-explicit upscaled flux functions are proposed in the two following cases: (i) capillarity is the main driving force and (ii) buoyancy is the only driving force. In both cases, we show that the upscaled buoyant flux is a bell-shaped function of the saturation, as in the case of a homogeneous porous medium. In the capillary-dominant case, we show that the upscaled buoyant flux is the harmonic mean of the buoyant fluxes in each layer. The upscaled saturation is governed by the continuity of the capillary pressure at the interface between layers. In the capillary-free case, the upscaled buoyant flux and upscaled saturation are determined by the flux continuity condition at the interface. As the flux is not continuous over the entire range of saturation, the upscaled saturation is only defined where continuity is verified, i.e. in two saturation domains. As a consequence, the upscaled buoyant flux is described by a piecewise continuous function. Two analytical approximations of this flux are proposed and this capillary-free upscaled model is validated for two cases of heterogeneity. Upscaled and cell averaged saturations are in good agreement. Furthermore, the proposed analytical upscaled fluxes provide satisfactory approximations as long as the saturation set at the inlet of the column is in a range where analytical and numerical upscaled fluxes are close.     

Time-of-flight (TOF)-based two-phase upscaling for subsurface flow and transport

Subsurface formations are characterized by heterogeneity over multiple length scales, which can have a strong impact on flow and transport. In this paper, we present a new upscaling approach, based on time-of-flight (TOF), to generate upscaled two-phase flow functions. The method focuses on more accurate representations of local saturation boundary conditions, which are found to have a dominant impact (in comparison to the pressure boundary conditions) on the upscaled two-phase flow models. The TOF-based upscaling approach effectively incorporates single-phase flow and transport information into local upscaling calculations, accounting for the global flow effects on saturation, as well as the local variations due to subgrid heterogeneity. The method can be categorized into quasi-global upscaling techniques, as the global single-phase flow and transport information is incorporated in the local boundary conditions. The TOF-based two-phase upscaling can be readily integrated into any existing local two-phase upscaling framework, thus more flexible than local–global two-phase upscaling approaches developed recently. The method was applied to permeability fields with different correlation lengths and various fluid-mobility ratios. It was shown that the new method consistently outperforms existing local two-phase upscaling techniques, including recently developed methods with improved local boundary conditions (such as effective flux boundary conditions), and provides accurate coarse-scale models for both flow and transport.     

A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images

Fluid flow behavior in a porous medium is a function of the geometry and topology of its pore space. The construction of a three dimensional pore space model of a porous medium is therefore an important first step in characterizing the medium and predicting its flow properties. A stochastic technique for reconstruction of the 3D pore structure of unstructured random porous media from a 2D thin section training image is presented. The proposed technique relies on successive 2D multiple point statistics simulations coupled to a multi-scale conditioning data extraction procedure. The Single Normal Equation Simulation Algorithm (SNESIM), originally developed as a tool for reproduction of long-range, curvilinear features of geological structures, serves as the simulation engine. Various validating criteria such as marginal distributions of pore and grain, directional variograms, multiple-point connectivity curves, single phase effective permeability and two phase relative permeability calculations are used to analyze the results. The method is tested on a sample of Berea sandstone for which a 3D micro-CT scanning image is available. The results confirm that the equi-probable 3D realizations obtained preserve the typical patterns of the pore space that exist in thin sections, reproduce the long-range connectivities, capture the characteristics of anisotropy in both horizontal and vertical directions and have single and two phase flow characteristics consistent with those of the measured 3D micro-CT image.     

Hydrologic connectivity at the hillslope scale through intra-snowpack flow paths during snowmelt

The seasonal snowmelt period is a critical component of the hydrologic cycle for many mountainous areas. Changes in the timing and rate of snowmelt as a result of physical hydrologic flow paths, such as longitudinal intra-snowpack flow paths, can have strong implications on the partitioning of meltwater amongst streamflow, groundwater recharge, and soil moisture storage. However, intra-snowpack flow paths are highly spatially and temporally variable and thus difficult to observe. This study utilizes new methods to non-destructively observe spatio-temporal changes in the liquid water content of snow in combination with plot experiments to address the research question: What is the scale of influence that intra-snowpack flow paths have on the downslope movement of liquid water during snowmelt across an elevational gradient? This research took place in northern Colorado with study plots spanning from the rain-snow transition zone up to the high alpine. Results indicate an increasing scale of influence from intra-snowpack flow paths with elevation, showing higher hillslope connectivity producing larger intra-snowpack contributing areas for meltwater accumulation, quantified as the upslope contributing area required to produce observed changes in liquid water content from melt rate estimates. The total effective intra-snowpack contributing area of accumulating liquid water was found to be 17, 6, and 0 m² for the above tree line, near tree line, and below tree line plots, respectively. Dye tracer experiments show capillary and permeability barriers result in increased number and thickness of intra-snowpack flow paths at higher elevations. We additionally utilized aerial photogrammetry in combination with ground penetrating radar surveys to investigate the role of this hydrologic process at the small watershed scale. Results here indicate that intra-snowpack flow paths have influence beyond the plot scale, impacting the storage and transmission of liquid water within the snowpack at the small watershed scale.     

Flow time estimation with spatially variable hillslope velocity in ungauged basins

The automated spatial estimation of the hillslope runoff dynamics is used as a valuable tool for the estimation of the travel time distribution (flow time), a major factor for the hydrologic prediction in ungauged basins. In fact, while the flow time function is usually obtained by rescaling the flow paths with constant channel and hillslope velocities, in this work a spatially distributed kinematic component, as a function of terrain features and in particular slope and land use, is implemented and its influence on the hydrologic response is tested by means of the Width Function Instantaneous Unit Hydrograph (WFIUH) framework. Hillslope surface flow velocities are evaluated by applying different uniform flow formulas within an automated DEM-based (terrain analysis) algorithm. A comparison test of the performances of the Manning, Darcy, Maidment and Soil Conservation Service uniform flow equations is performed for several case studies in Italy pertaining to different climatic and geomorphic conditions. Results provide new insights for a better understanding of the flow time function also introducing a more parsimonious and physically-based calibration scheme of the WFIUH.     

Influence of geostatic stresses on permeability of jointed rock masses

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Real gas flow through heterogeneous porous media: theoretical aspects of upscaling

We consider the problem of upscaling transient real gas flow through heterogeneous bounded reservoirs. One of the commonly used methods for deriving effective permeabilities is based on stochastic averaging of nonlinear flow equations. Such an approach, however, would require rather restrictive assumptions about pressure-dependent coefficients. Instead, we use Kirchhoff transformation to linearize the governing stochastic equations prior to their averaging. The linearized problem is similar to that used in stochastic analysis of groundwater flow. We discuss the effects of temporal localization of the nonlocal averaged Darcy's law, as well as boundary effects, on the upscaled gas permeability. Extension of the results obtained by means of small perturbation analysis to highly heterogeneous porous formations is also discussed.     

Reactive transport upscaling at the Darcy scale: A new flow rate based approach raises the unsolved issue of porosity upscaling

This article demonstrates that permeability upscaling, which can require complex techniques, is not necessary to significantly decrease the CPU time in reactive transport modeling. CPU time depends more on the geochemistry than the flow calculation. Flow rate upscaling is proposed as an alternate method to permeability upscaling, which is more suited to time-consuming flow resolution. To apply this method, a finite volume approach is most convenient.Considering the equality of flow as the equivalence criterion, when the coarse grid overlays the fine grid, flow rate upscaling leads, by construction, to the exact results, whereas the accuracy of permeability upscaling methods often depends on specific conditions. Some focus is put on the limitations of a common permeability upscaling technique, the simplified renormalization. In stationary flow, the gain in CPU time is the same for both flow rate upscaling and permeability upscaling. In transient flow, flow rate upscaling is slightly less time-efficient but the ratio between both CPU times decreases when the geochemistry is more complex.Working with an accurate flow rate field in the upscaled case reveals that porosity upscaling is a surprisingly tricky issue. Solution mixing is induced and residence times can be significantly affected. These changes have potentially important consequences on reactive transport modeling. They are not specific to the flow rate upscaling method; they are a general issue. Some simplified cases, assuming a homogeneous mineralogy, are examined. At this stage, a simple heuristic method is proposed, which yields reliable results under particular conditions (high heterogeneity). Porosity upscaling remains an open research field.     

Comparison of relative permeability-saturation-pressure parametric models for infiltration and redistribution of a light nonaqueous-phase liquid in sandy porous media

To test and evaluate the ability of commonly used constitutive relations for multifluid flow predictions, results of numerical flow and transport simulations are compared to experimental data. Three quantitative experiments were conducted in 1-m-long vertical columns. The columns were filled with either a uniform sand, a sand with a broad particle-size distribution, or with a layered system where a layer of a course-textured uniform sand was placed in an otherwise finer-textured uniform sand. After establishing variably water-saturated conditions, a pulse of a light nonaqueous-phase liquid (LNAPL) was injected uniformly at a constant rate. Water and LNAPL saturations were measured as a function of time and elevation with a dual-energy gamma-radiation system. The infiltration and redistribution of the LNAPL were simulated with nonhysteretic and hysteretic parametric relative permeability-saturation-pressure (k-S-P) models. The models were calibrated using two-phase air-water retention data and an established scaling theory. The nonhysteretic Brooks-Corey k-S-P model, which utilizes the Burdine relative permeability model, yielded predictions that closely matched the experimental data. Use of the nonhysteretic and hysteretic k-S-P models, based on the van Genuchten S-P relations and k-S relations derived from the Mualem relative permeability model, did not agree as well with the experimental data as those obtained with the Brooks-Corey k-S-P model. Explanations for the differences in performance of the three tested parametric k-S-P models are proposed.     

An adaptive local–global multiscale finite volume element method for two-phase flow simulations

Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine scale permeability variations through the calculation of specialized coarse scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. This can be accomplished using global fine scale simulations, but this may be computationally expensive. In this paper an adaptive local–global technique, originally developed within the context of upscaling, is applied for the computation of multiscale basis functions. The procedure enables the efficient incorporation of approximate global information, determined via coarse scale simulations, into the multiscale basis functions. The resulting procedure is formulated as a finite volume element method and is applied for a number of single- and two-phase flow simulations of channelized two-dimensional systems. Both conforming and nonconforming procedures are considered. The level of accuracy of the resulting method is shown to be consistently higher than that of the standard finite volume element multiscale technique based on localized basis functions determined using linear pressure boundary conditions.     

Using hysteretic behaviour and hydrograph classification to identify hydrological function across the “hillslope–depression–stream” continuum in a karst catchment

In cockpit karst landscapes, fluxes from upland areas contribute large volumes of water to low-lying depressions and stream flow. Hydrograph hysteresis and similarity between monitoring sites is important for understanding the space–time variability of hydrologic responses across the “hillslope–depression–stream” continuum. In this study, the hysteretic feature of hydrographs was assessed by characterizing the loop-like relationships between responses at upstream sites relative to subsurface discharge at the outlet of a small karst catchment. A classification of hydrograph responses based on the multi-scale smoothing Kernel -derived distance classifies the hydrograph responses on the basis of similarities between hillslope and depression sites, and those at the catchment outlet. Results demonstrate that the temporal and spatial variability of hydrograph hysteresis and similarity between hillslope flow and outlet stream flow can be explained by the local heterogeneity of depression aquifer. Large depression storage deficits emerging in the highly heterogeneous aquifer produce strong hysteresis and multiple relationships of upstream hydrographs relative to the outlet subsurface discharge. In contrast, when depression storage deficits are filled during consecutive rainfall events, depression hydrographs at the high permeability sites are almost synchronous or exhibit a monotonous function with the hydrographs at the outlet. This reduced hydrograph hysteresis enhances preferential flow paths in fractured rocks and conduits that can accelerate the hillslope flow to the outlet. Therefore, classification of hydrograph similarities between any upstream sites and the catchment outlet can help to identify the dominant hydrological functions in the heterogeneous karst catchment.     

Satellite Observations of Plume-like Streaks in a Cloud Field in Canada

On the afternoon of 28 October 2013, plume-like streaks were detected by geostationary and polar orbiting satellites over eastern Ontario, Canada. These streaks were characterized by enhanced reflectivity in the visible bands and warmer brightness temperatures at 3.9 µm. These streaks were part of a low-level liquid water cloud layer. Due to the similarity of the streaks to plume-like features in marine stratocumulus caused by smoke from the stacks of ships, so-called ship tracks, a local source of emitted aerosols was suspected and subsequently identified as the burning of logging residue. This event provides further support for the ability of locally enhanced aerosol loading to alter microphysical characteristics of clouds. Ship tracks, pollution plumes from industrial burning, and pyro-cumulus are known examples of this type of interaction. In addition, the plume-like streaks could be used indirectly to identify the location of the source of the emitted particles.     

Pile response in submerged lateral spreads: Common pitfalls of numerical and physical modeling techniques

A three dimensional dynamic numerical methodology is developed and used to back-analyze experimental data on the seismic response of single piles in laterally spreading slopes. The aim of the paper is not to seek successful a-priori (Type A) predictions, but to explore the potential of currently available numerical techniques, and also to get feedback on modeling issues and assumptions which are not yet resolved in the international literature. It is illustrated that accurate simulation of the physical pile–soil interaction mechanisms is not a routine task, as it requires the incorporation of advanced numerical features, such as an effective stress constitutive soil model that can capture cyclic response and shear-induced dilation, interface elements to simulate the flow of liquefied ground around the pile and proper calibration of soil permeability to model excess pore pressure dissipation during shaking. In addition, the “conventional tied node” formulation, commonly used to simulate lateral boundary conditions during shaking, has to be modified in order to take into account the effects of the hydrostatic pore pressure surplus that is created at the down slope free field boundary of submerged slopes. A comparative analysis with the two different lateral boundary formulations reveals that “conventional tied nodes”, which also reflect the kinematic conditions imposed by laminar box containers in centrifuge and shaking table experiments, may underestimate seismic demands along the upper part of the pile foundation.     

Multi-level parameter structure identification for two-phase porous-media flow problems using flexible representations

We consider identification of absolute permeability (hydraulic conductivity) based on time series of pressure data in sparsely distributed wells for two-phase porous-media flow. For this problem, it is impossible to recover all details of the parameter function. On the other hand, a coarser, approximate recovery may be sufficient for many applications. We propose a novel solution approach, based on reparametrization, for such approximate identification of the parameter function. We use a nonlinear, composite representation, which is detached from the computational grid, allowing for a flexible representation of the parameter function at many resolution levels. This is utilized in a sequential multi-level estimation of the parameter function, starting at a coarse resolution, which is then gradually refined. The composite representation is designed to allow for smooth as well as sharp transitions between regions of nearly constant parameter value. Moreover, it facilitates the estimation also of the structure and smoothness of the parameter function itself. As a limiting case, the chosen representation is reduced to a zonation with implicit representation of the interior boundaries that is equivalent to a level-set representation. A motivation for the selected representation and the multi-level estimation is presented in terms of an analysis of sensitivity and nonlinearity. Numerical examples demonstrate identification of coarse-scale features of reference permeability distributions with varying degree of smoothness. Comparisons show how the multi-level strategy stabilize the identification and avoid local minima of the objective function compared to a single-level strategy.     

Dynamics of convective dissolution from a migrating current of carbon dioxide

During geologic storage of carbon dioxide (CO₂), trapping of the buoyant CO₂ after injection is essential in order to minimize the risk of leakage into shallower formations through a fracture or abandoned well. Models for the subsurface behavior of the CO₂ are useful for the design, implementation, and long-term monitoring of injection sites, but traditional reservoir-simulation tools are currently unable to resolve the impact of small-scale trapping processes on fluid flow at the scale of a geologic basin. Here, we study the impact of solubility trapping from convective dissolution on the up-dip migration of a buoyant gravity current in a sloping aquifer. To do so, we conduct high-resolution numerical simulations of the gravity current that forms from a pair of miscible analogue fluids. Our simulations fully resolve the dense, sinking fingers that drive the convective dissolution process. We analyze the dynamics of the dissolution flux along the moving CO₂–brine interface, including its decay as dissolved buoyant fluid accumulates beneath the buoyant current. We show that the dynamics of the dissolution flux and the macroscopic features of the migrating current can be captured with an upscaled sharp-interface model.     

Flow based oversampling technique for multiscale finite element methods

Oversampling techniques are often used in porous media simulations to achieve high accuracy in multiscale simulations. These methods reduce the effect of artificial boundary conditions that are imposed in computing local quantities, such as upscaled permeabilities or basis functions. In the problems without scale separation and strong non-local effects, the oversampling region is taken to be the entire domain. The basis functions are computed using single-phase flow solutions which are further used in dynamic two-phase simulations. The standard oversampling approaches employ generic global boundary conditions which are not associated with actual flow boundary conditions. In this paper, we propose a flow based oversampling method where the actual two-phase flow boundary conditions are used in constructing oversampling auxiliary functions. Our numerical results show that the flow based oversampling approach is several times more accurate than the standard oversampling method. We provide partial theoretical explanation for these numerical observations.     

Effective macroscopic transport parameters between parallel plates with constant concentration boundaries

A macroscopic transport model is developed, following the Taylor shear dispersion analysis procedure, for a 2D laminar shear flow between parallel plates possessing a constant specified concentration. This idealized geometry models flow with contaminant dissolution at pore-scale in a contaminant source zone and flow in a rock fracture with dissolving walls. We upscale a macroscopic transient transport model with effective transport coefficients of mean velocity, macroscopic dispersion, and first-order mass transfer rate. To validate the macroscopic model the mean concentration, covariance, and wall concentration gradient are compared to the results of numerical simulations of the advection–diffusion equation and the Graetz solution. Results indicate that in the presence of local-scale variations and constant concentration boundaries, the upscaled mean velocity and macrodispersion coefficient differ from those of the Taylor–Aris dispersion, and the mass transfer flux described by the first-order mass transfer model is larger than the diffusive mass flux from the constant wall. In addition, the upscaled first-order mass transfer coefficient in the macroscopic model depends only on the plate gap and diffusion coefficient. Therefore, the upscaled first-order mass transfer coefficient is independent of the mean velocity and travel distance, leading to a constant pore-scale Sherwood number of 12. By contrast, the effective Sherwood number determined by the diffusive mass flux is a function of the Peclet number for small Peclet number, and approaches a constant of 10.3 for large Peclet number.