Impact of capillary hysteresis and trapping on vertically integrated models for CO2 storage

Vertically integrated models are frequently applied to study subsurface flow related to CO₂ storage scenarios in saline aquifers. In this paper, we study the impact of capillary-pressure hysteresis and CO₂ trapping on the integrated constitutive parameter functions. Our results show that for the initial drainage and a subsequent imbibition, trapping is the dominant contributor to hysteresis in integrated models. We also find that for advective processes like injection and plume migration in a sloped aquifer the correct treatment of the hysteretic nature of the capillary fringe is likely of secondary importance. However, for diffusive/dispersive processes such as a redistribution of the CO₂ plume due to buoyancy and capillary forces, the hysteretic nature of the capillary fringe may significantly impact the final distribution of the fluids and the timescale of the redistribution.     

Influence of capillary-pressure models on CO2 solubility trapping

The typical shape of a capillary-pressure curve is either convex (e.g., Brooks–Corey model) or S-shaped (e.g., van Genuchten model). It is not universally agreed which model reflects natural rocks better. The difference between the two models lies in the representation of the capillary entry pressure. This difference does not lead to significantly different simulation results for modeling CO₂ sequestration in aquifers without considering CO₂ dissolution. However, we observe that the van-Genuchten-type capillary-pressure model accelerates CO₂ solubility trapping significantly compared with the Brooks–Corey-type model. We also show that the simulation results are very sensitive to the slope of the van-Genuchten-type curve around the entry-pressure region. For the representative examples we study, the differences can be so large as to have complete dissolution of the CO₂ plume versus persistence of over 50% of the plume over a 5000-year period.The cause of such sensitivity to the capillary-pressure model is studied. Particularly, we focus on how the entry pressure is represented in each model. We examine the mass-transfer processes under gravity-capillary equilibrium, molecular diffusion, convective mixing, and in the presence of small-scale heterogeneities. Laboratory measurement of capillary-pressure curves and some important implementation issues of capillary-pressure models in numerical simulators are also discussed. Most CO₂ sequestration simulations in the literature employ one of the two capillary-pressure models. It is important to recognize that these two representations lead to very different predictions of long-term CO₂ sequestration.     

Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradp_c in combination with a chord-slope technique must be utilized.     

Co-sequestration of SO2 with supercritical CO2 in carbonates: An experimental study of capillary trapping,relative permeability,and capillary pressure

In this study we performed three categories of steady- and unsteady-state core-flooding experiments to investigate capillary trapping, relative permeability, and capillary pressure, in a scCO₂ + SO₂/brine/limestone system at elevated temperature and pressure conditions, i.e., 60 °C and 19.16 MPa. We used a Madison limestone core sample acquired from the Rock Springs Uplift in southwest Wyoming. We carried out two sets of steady-state drainage-imbibition relative permeability experiments with different initial brine saturations to study hysteresis. We found that the final scCO₂ + SO₂ drainage relative permeability was very low, i.e., 0.04. We also observed a rapid reduction in the scCO₂-rich phase imbibition relative permeability curve, which resulted in a high residual trapping. The results showed that between 62.8% and more than 76% of the initial scCO₂ + SO₂ at the end of drainage was trapped by capillary trapping mechanism (trapping efficiency). We found that at higher initial brine saturations, the trapping efficiency was higher. The maximum initial and residual scCO₂-rich phase saturations at the end of primary drainage and imbibition were 0.525 and 0.329, respectively. Each drainage-imbibition cycle was followed by a dissolution process to re-establish S_w = 1. The dissolution brine relative permeabilities for both cycles were also obtained. We characterized the scCO₂ + SO₂/brine capillary pressure hysteresis behavior through unsteady-state primary drainage, imbibition, and secondary drainage experiments. We observed negative imbibition capillary pressure curve indicative of possible wettability alteration throughout the experiments due to contact with scCO₂ + SO₂/brine fluid system. The trapping results were compared to those reported in literature for other carbonate core samples. We noticed slightly more residual trapping in our sample, which might be attributed to heterogeneity, different viscosity ratio, and pore-space topologies. The impact of dynamic effects, i.e., high brine flow rate imbibition tests, on trapping of the scCO₂-rich phase was also explored. We performed two imbibition experiments with relatively high brine flow rates. The residual scCO₂ saturation dropped to 0.291 and 0.262 at the end of the first and second imbibition tests, i.e., 11.5% and 20.4%, respectively, compared to 0.329 under capillary-dominated regime.     

Similarity solution for capillary redistribution of two phases in a porous medium with a single discontinuity

In this paper we consider one-dimensional capillary redistribution of two immiscible and incompressible fluids in a porous medium with a single discontinuity. We study a special time-dependent solution, a similarity solution, which is found when the initial saturation is discontinuous at the same point as the permeability and porosity, and is constant elsewhere. The similarity solution can be used to validate numerical algorithms describing two-phase flow in porous media with discontinuous heterogeneities. We discuss the construction of the similarity solution, in which we pay special attention to the interface conditions at the discontinuity, both for media with positive and zero entry pressure. Moreover, we discuss some qualitative properties of the solution, and outline a numerical procedure to determine its graph. Examples are given for the Brooks-Corey and Van Genuchten model. We also consider similarity solutions for unsaturated water flow, which is a limit case of two-phase flow for negligible nonwetting phase viscosity.     

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.     

The influence of capillarity in numerical modeling of organic liquid redistribution in two-phase systems

Numerical experiments are performed to explore the influence of model assumptions and parameters on the prediction of two-phase flow during long-term NAPL redistribution. Sensitivity of numerical solutions to grid resolution and the use of alternative fitting functions for capillary retention data are examined. Due to the inclusion of capillary entrapment, numerical solutions in one- and two-dimensions are strongly dependent on grid resolution. Solution convergence tests based upon spreading behavior reveal that nodal spacings as small as one-fifth to one-tenth of the displacement pressure head may be required to obtain reasonable convergence in some simulations. Solutions employing the Brooks and Corey and van Genuchten functional forms are found to yield different solution behavior. These differences are attributed to the representation of capillary pressure below the entry pressure. Brooks and Corey solutions exhibited greater spreading, less inclination to penetrate semi-permeable layers, and poorer spatial convergence behavior.     

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.     

Capillary pressure for the sand–CO2–water system under various pressure conditions. Application to CO2 sequestration

Accurate modeling of storage of carbon dioxide (CO₂) in heterogeneous aquifers requires experiments of the capillary pressure as function of temperature and pressure. We present a method with which static drainage and imbibition capillary pressures can be measured continuously as a function of saturation at various temperature (T) and pressure (P) conditions. The measurements are carried out at (T, P) conditions of practical interest. Static conditions can be assumed as small injection rates are applied. The capillary pressure curves are obtained for the unconsolidated sand–distilled water–CO₂ system. The experimental results show a decrease of drainage and imbibition capillary pressure for increasing CO₂ pressures and pronounced dissolution rate effects for gaseous CO₂. Significant capillary pressure fluctuations and negative values during imbibition are observed at near critical conditions. The measurement procedure is validated by a numerical model that simulates the experiments.     

Parameter equivalence for the Gardner and van Genuchten soil hydraulic conductivity functions for steady vertical flow with inclusions

The analytic element method is well suited for the Gardner hydraulic conductivity function, but is limited in describing real soils. Therefore, parameter equivalence between the van Genuchten and Gardner hydraulic conductivity functions is explored for the case of steady vertical flow through a homogeneous medium with a single inclusion, i.e., a binary soil. The inclusion has different hydraulic parameters than the background medium. Equivalence is established using three methods: (1) effective capillary drive; (2) capillary length; (3) and a least-squares optimization method that aims to fit a Gardner function to a corresponding van Genuchten function by minimizing the difference in log conductivity over a specified pressure range. Comparisons between hydraulic models are made based on scatterplots of pressure head and the vertical Darcian flux obtained using a finite-element numerical solution with both constitutive relations. For applicability of an equivalent Gardner function over a broad range of pressure heads, the crossover pressure must be maintained between the two parametric functions. The crossover pressure is defined as the pressure in which the hydraulic conductivity of the inclusion is equal to the background. It can be shown that a hybrid methodology of preserving the crossover pressure exactly and using the effective capillary drive will result in hydraulic parameters that are easily obtained and provide good agreement between the conductivity functions of the GR model to the VG model.     

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.     

CO2 storage in the high Arctic: efficient modelling of pre‐stack depth‐migrated seismic sections for survey planning

The sequestration of CO₂ in subsurface reservoirs constitutes an immediate counter‐measure to reduce anthropogenic emissions of CO₂, now recognized by international scientific panels to be the single most critical factor driving the observed global climatic warming. To ensure and verify the safe geological containment of CO₂ underground, monitoring of the CO₂ site is critical. In the high Arctic, environmental considerations are paramount and human impact through, for instance, active seismic surveys, has to be minimized. Efficient seismic modelling is a powerful tool to test the detectability and imaging capability prior to acquisition and thus improve the characterization of CO₂ storage sites, taking both geological setting and seismic acquisition set‐up into account. The unique method presented here avoids the costly generation of large synthetic data sets by employing point spread functions to directly generate pre‐stack depth‐migrated seismic images. We test both a local‐target approach using an analytical filter assuming an average velocity and a full‐field approach accounting for the spatial variability of point spread functions. We assume a hypothetical CO₂ plume emplaced in a sloping aquifer inspired by the conditions found at the University of Svalbard CO₂ lab close to Longyearbyen, Svalbard, Norway, constituting an unconventional reservoir–cap rock system. Using the local‐target approach, we find that even the low‐to‐moderate values of porosity (5%–18%) measured in the reservoir should be sufficient to induce significant change in seismic response when CO₂ is injected. The sensitivity of the seismic response to changes in CO₂ saturation, however, is limited once a relatively low saturation threshold of 5% is exceeded. Depending on the illumination angle provided by the seismic survey, the quality of the images of five hypothetical CO₂ plumes of varying volume differs depending on the steepness of their flanks. When comparing the resolution of two orthogonal 2D surveys to a 3D survey, we discover that the images of the 2D surveys contain significant artefacts, the CO₂‐brine contact is misplaced and an additional reflector is introduced due to the projection of the point spread function of the unresolvable plane onto the imaging plane. All of these could easily lead to a misinterpretation of the behaviour of the injected CO₂. Our workflow allows for testing the influence of geological heterogeneities in the target aquifer (igneous intrusions, faults, pervasive fracture networks) by utilizing increasingly complex and more realistic geological models as input as more information on the subsurface becomes available.     

Petrophysical characterization of porous media starting from micro-tomographic images

A quasi-static scheme based on pore space spatial statistics is presented to simulate pore-scale two-phase capillary-dominant displacement processes. The algorithm is coupled with computational fluid dynamics in order to evaluate saturation functions. Wettability heterogeneity in partial and fractional/mixed-wet media is implemented using a contact angle map. The simulation process is pixel-wised and performed directly on binary images. Bypassing and snap-off are tackled as non-wetting phase trapping mechanisms. Post-processing results include residual saturations, effective permeability and capillary pressure curves for drainage and imbibition scenarios. The primary advantages of the proposed workflow are eliminating pore space skeletisation/ discretization, superior time efficiency and minimal numerical drawbacks when compared to other direct or network-based simulation techniques.     

Unsaturated hydraulic properties of xerophilous mosses: towards implementation of moss covered soils in hydrological models

Evaporation from mosses and lichens can form a major component of the water balance, especially in ecosystems where mosses and lichens often grow abundantly, such as tundra, deserts and bogs. To facilitate moss representation in hydrological models, we parameterized the unsaturated hydraulic properties of mosses and lichens such that the capillary water flow through moss and lichen material during evaporation could be assessed. We derived the Mualem‐van Genuchten parameters of the drying retention and the hydraulic conductivity functions of four xerophilous moss species and one lichen species. The shape parameters of the retention functions (2.17 < n < 2.35 and 0.08 < α < 0.13 cm^?1) ranged between values that are typical for sandy loam and loamy sand. The shapes of the hydraulic conductivity functions of moss and lichen species diverged from those of mineral soils, because of strong negative pore‐connectivity parameters (?2.840 < l < ?2.175) and low hydraulic conductivities at slightly negative pressure heads (0.016 < K₀ < 0.280 cm/d). These K₀ values are surprisingly low, considering that mosses are very porous. However, during evaporation, large pores and voids were air filled and did not participate in capillary water flow. Small K₀ values cause mosses and lichens to be conservative with water during wet conditions, thus tempering evaporation compared to mineral soils. On the other hand, under dry conditions, mosses and lichens are able to maintain a moisture supply from the soil, leading to a higher evaporation rate than mineral soils. Hence, the modulating effect of mosses on evaporation possibly differs between wet and dry climates. Copyright © 2013 John Wiley & Sons, Ltd.     

Thorough wetting and drainage of a peat lysimeter in a climate change scenario

A peat deposit (Zennare basin, Venice coastland, Italy) was monitored in previous field studies to investigate the hydrological response of organic soil to meteorological dynamics. Field tests and modelling predictions highlighted the risk of the complete loss of this peat layer during the next 50 years, due to oxidation enhanced by the increased frequency of warmer periods. Unfortunately, despite the considerable impacts that are expected to affect peat bogs (in this area and worldwide), only a few experimental studies have been carried out to assess the hydrologic response of peat to severe water scarcity. Because of that, an undisturbed 0.7 m³ peat monolith was collected, transferred to the laboratory and instrumented. The total weight (representative of the water content dynamics of the peat monolith as a whole), and two vertical profiles of matric potentials and water content were monitored in controlled water-scarce conditions. After an extended air-drying period, the monolith was used as an undisturbed peat lysimeter and a complete cycle of wetting and drainage was performed. Supplementary measurements of matric potential ψ and water content θ were collected by testing peat subsamples on a suction table apparatus. A set of water retention curves was determined in a range of matric potentials broader (ψ down to −7 m) than the current natural conditions in the field (minimum ψ = −1 m). While water content at saturation showed values similar to those in the original natural conditions (θ ≅ 0.8), a remarkable loss of water holding capacity (even for low potentials) has been highlighted, especially in deep layers that are now permanently below the water table. The retention curves changed shape and values, with a more pronounced hysteresis visible in an increasing distance between wetting and drying data. Hydraulic non-equilibrium between the water content and water potential could be a possible cause and it is worth modelling in future studies. The parameters of the van Genuchten retention curves were obtained for the wetting and the drying phases.     

Hydraulic properties of peat soils along a bulk density gradient—A meta study

Our understanding of hydraulic properties of peat soils is limited compared with that of mineral substrates. In this study, we aimed to deduce possible alterations of hydraulic properties of peat soils following degradation resulting from peat drainage and aeration. A data set of peat hydraulic properties (188 soil water retention curves [SWRCs], 71 unsaturated hydraulic conductivity curves [UHCs], and 256 saturated hydraulic conductivity [K_s] values) was assembled from the literature; the obtained data originated from peat samples with an organic matter (OM) content ranging from 23 to 97 wt% (weight percent; and according variation in bulk density) representing various degrees of peat degradation. The Mualem‐van Genuchten model was employed to describe the SWRCs and UHCs. The results show that the hydraulic parameters of peat soils vary over a wide range confirming the pronounced diversity of peat. Peat decomposition significantly modifies all hydraulic parameters. A bulk density of approximately 0.2 g cm^?3 was identified as a critical threshold point; above and below this value, macroporosity and hydraulic parameters follow different functions with bulk density. Pedotransfer functions based on physical peat properties (e.g., bulk density and soil depth) separately computed for bog and fen peat have significantly lower mean square errors than functions obtained from the complete data set, which indicates that not only the status of peat decomposition but also the peat‐forming plants have a large effect on hydraulic properties. The SWRCs of samples with a bulk density of less than 0.2 g cm^?3 could be grouped into two to five classes for each peat type (botanical composition). The remaining SWRCs originating from samples with a bulk density of larger than 0.2 g cm^?3 could be classified into one group. The Mualem‐van Genuchten parameter values of α can be used to estimate K_s if no K_s data are available. In conclusion, the derived pedotransfer functions provide a solid instrument to derive hydraulic parameter values from easily measurable quantities; however, additional research is required to reduce uncertainty.     

Volcanic CO2 flux measurement at Campi Flegrei by tunable diode laser absorption spectroscopy

Near-infrared room temperature tunable diode lasers (TDL) have recently found increased usage in atmospheric chemistry and air monitoring research, but applications in volcanology are still limited to a few examples. Here, we explored the potential of a commercial infrared laser unit (GasFinder 2.0 from Boreal Laser Ltd) for measurement of volcanic CO₂ mixing ratios, and ultimately for estimating the volcanic CO₂ flux. Our field tests were conducted at Campi Flegrei near Pozzuoli, Southern Italy, where the GasFinder was used during three campaigns in October 2012, January 2013 and May 2013 to repeatedly measure the path-integrated mixing ratios of CO₂ along cross sections of the atmospheric plumes of two major fumarolic fields (Solfatara and Pisciarelli). By using a tomographic post-processing routine, we resolved, for each of the two fields, the contour maps of CO₂ mixing ratios in the atmosphere, from the integration of which (and after multiplication by the plumes’ transport speeds) the CO₂ fluxes were finally obtained. We evaluate a total CO₂ output from the Campi Flegrei fumaroles of ～490 Mg/day, in line with independent estimates based on in situ (Multi-GAS) observations. We conclude that TDL technique may enable CO₂ flux quantification at other volcanoes worldwide.     

Pore-scale contact angle measurements at reservoir conditions using X-ray microtomography

Contact angle is a principal control of the flow of multiple fluid phases through porous media; however its measurement on other than flat surfaces remains a challenge. A new method is presented for the measurement of the contact angle between immiscible fluids at the pore scale at reservoir conditions (10 MPa and 50 °C) inside a quarry limestone through the use of X-ray microtomography. It is applied to a super-critical CO₂–brine–carbonate system by resampling the micro-CT data onto planes orthogonal to the contact lines, allowing for vectors to be traced along the grain surface and the CO₂–brine interface. A distribution of contact angles ranging from 35° to 55° is observed, indicating that the CO₂–brine–carbonate system is weakly water-wet. This range of contact angles can be understood as the result of contact angle hysteresis and surface heterogeneity on a range of length scales. Surface heterogeneity is examined by comparison of micro-CT results with optical thin sections and SEM images.