Residual and Solubility trapping during Geological CO...

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2018

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1640

Residual and Solubility trappingduring Geological CO2 storage

Numerical and Experimental studies

MARIA RASMUSSON

ISSN 1651-6214ISBN 978-91-513-0257-7urn:nbn:se:uu:diva-343505

Dissertation presented at Uppsala University to be publicly examined in Hambergsalen,Geocentrum, Villavägen 16, Uppsala, Friday, 27 April 2018 at 13:00 for the degree of Doctorof Philosophy. The examination will be conducted in English. Faculty examiner: Dr JonathanEnnis-King (Commonwealth Scientific and Industrial Research Organization (CSIRO),Australia).

AbstractRasmusson, M. 2018. Residual and Solubility trapping during Geological CO2 storage.Numerical and Experimental studies. Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology 1640. 81 pp. Uppsala: ActaUniversitatis Upsaliensis. ISBN 978-91-513-0257-7.

Geological storage of carbon dioxide (CO2) in deep saline aquifers mitigates atmospheric releaseof greenhouse gases. To estimate storage capacity and evaluate storage safety, knowledge ofthe trapping mechanisms that retain CO2 within geological formations, and the factors affectingthese is fundamental. The objective of this thesis is to study residual and solubility trappingmechanisms (the latter enhanced by density-driven convective mixing), specifically in regardto their dependency on aquifer characteristics, and to investigate and develop methods forquantification of CO2 trapping in the field. The work includes implementation of existingnumerical simulators and inverse modeling, as well as the development of new models andexperimental methods for the study and quantification of CO2 trapping.

A comparison of well-test designs in regard to their abilities to estimate the in-situ residualgas saturation (that determines the residual trapping of CO2) is presented, as well as a novelindicator-tracer approach to obtain residual gas saturation conditions in a formation. Theresults can aid in the planning of well-tests for estimation of trapping potential during sitecharacterization.

Pore-network modeling simulations were conducted to study the effects of co-contaminantsulphur dioxide and formation thermodynamic and salinity conditions on residual CO2 trapping.

Furthermore, an analysis tool was developed and used to study the prerequisites for density-driven instability and convective mixing over broad geological storage conditions, including therelative influences of formation characteristics on factors controlling the convective process.The results show which conditions favour or disfavour residual and solubility trapping,knowledge useful for long-term predictions of the fate of injected CO2, and safety assessmentsduring site selection.

An optical experimental method, the refractive-light-transmission (RLT) technique, and ananalogue system design were developed for studying density-driven flow in porous media. Themethod exploits changes in light refraction to visualize convective flow, and incorporates acalibration procedure and an image post-processing scheme that enable quantification of soluteconcentration, density and viscosity within porous media. The experimental setup was used tostudy the dynamics of convective mixing, and to derive scaling laws for the onset time and massflux of convection.

Keywords: capillary trapping, CCS, convective flow, CO2, light transmission, SO2, well test

Maria Rasmusson, Department of Earth Sciences, LUVAL, Villav. 16, Uppsala University,SE-75236 Uppsala, Sweden.

© Maria Rasmusson 2018

ISSN 1651-6214ISBN 978-91-513-0257-7urn:nbn:se:uu:diva-343505 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-343505)

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Rasmusson, K., Rasmusson, M., Fagerlund, F., Bensabat, J.,

Tsang, Y., Niemi, A. (2014) Analysis of alternative push-pull-test-designs for determining in situ residual trapping of carbon dioxide. International journal of Greenhouse Gas Control, 27: 155-168. © Elsevier 2014, reprinted with permission.

II Rasmusson, M., Rasmusson, K., Fagerlund, F., Tsang, Y., Nie-mi, A. The impact of SO2 as a co-contaminant on the residual trapping of CO2 during geological storage. Submitted to Green-house Gases: Science and Technology.

III Rasmusson, M., Fagerlund, F., Tsang, Y., Rasmusson, K., Nie-

mi, A. (2015) Prerequisites for density-driven instabilities and convective mixing under broad geological CO2 storage condi-tions. Advances in Water Resources, 84: 136-151. © Elsevier 2015, reprinted with permission.

IV Rasmusson, M., Fagerlund, F., Rasmusson, K., Tsang, Y., Nie-

mi, A. (2017) Refractive-light-transmission technique applied to density-driven convective mixing in porous media with implica-tions for geological CO2 storage. Water Resources Research, 53, 8760-8780. © Wiley & Sons 2017, reprinted with permis-sion.

In the above listed Paper I, the author of this thesis contributed with half of the work on the; numerical modeling, analysis of results and first draft of the paper (the other half was made by Kristina Rasmusson). In Paper II the author conducted the numerical modeling, analyzed the results, and wrote the draft of the paper. In Paper III the author developed the analysis tool, conducted the analysis, processed the results, and wrote the draft of the pa-per. In Paper IV the author developed the concept of refractive-light-transmission technique, conducted the experiments, analyzed the results, and wrote the draft of the paper. The co-authors of Papers I, II, III and IV have

either contributed with data on field parameters, the development of the pore-network simulator used in Paper II, the bead-box construction used in the experiments in Paper IV, or participated in discussions on paper content, or contributed with advices on linguistic or analysis-interpretation improve-ments in manuscripts.

In addition, the author of this thesis has contributed to the following pa-

pers related to the thesis but not appended to it. Niemi, A., Bensabat, J., Fagerlund, F., Sauter, M., Ghergut, J., Licha, T., Fierz, T., Wiegand, G., Rasmusson, M., Rasmusson, K., Shtivelman, V., Gendler, M., and MUSTANG partners. (2012) Small-scale CO2 injection into a deep geological formation at Heletz, Israel. Energy Procedia, 23: 504-511. Rasmusson, K., Tsang, C.-F., Tsang, Y., Rasmusson, M., Pan, L., Fagerlund, F., Bensabat, J., Niemi, A. (2015) Distribution of injected CO2 in a stratified saline reservoir accounting for coupled wellbore-reservoir flow. Greenhouse Gases: Science and Technology, 5(4): 419-436. Rasmusson, K., Rasmusson, M., Tsang, Y., Niemi, A. (2016) A sim-ulation study of the effect of trapping model, geological heterogenei-ty and injection strategies on CO2 trapping. International journal of Greenhouse Gas Control, 52: 52-72. Rasmusson, K., Rasmusson, M., Tsang, Y., Benson, S., Hingerl, F., Fagerlund, F., Niemi, A. Residual trapping of carbon dioxide during geological storage - insight gained through a pore-network modeling approach. Submitted to International journal of Greenhouse Gas Control.

Furthermore, the author has contributed to several conference abstracts and deliverables within the MUSTANG project funded by the European Com-munity’s 7th Framework Programme (grant agreement number 227286), which are available on the project’s homepage www.co2mustang.eu.

Contents

1. Introduction ................................................................................................. 7 1.1 Background to geological CO2 storage ................................................ 7

The CO2-trapping mechanisms ......................................................... 8 1.2 Research objectives .............................................................................. 9

2. Theory ....................................................................................................... 10 2.1 Hydraulic processes & CO2 trapping mechanisms in porous media .. 10

2.1.1 Physical properties of fluids ....................................................... 10 2.1.2 Multiphase phenomena, flow & residual trapping ...................... 11 2.1.3 Interphase mass transfer, singlephase mass transport & solubility trapping ................................................................................ 12

Density-driven convective mixing .................................................. 14

3. Methods .................................................................................................... 19 3.1 Numerical & inverse modeling .......................................................... 19

3.1.1 The iTOUGH2 simulator ............................................................ 19 3.1.2 The Pore-Network simulator ...................................................... 23 3.1.3 An Analysis tool for determining prerequisites for convective mixing .................................................................................................. 25

3.2 Experimental method ......................................................................... 28 3.2.1 The Refractive-Light-Transmission Technique .......................... 29

4. Results & discussion ................................................................................. 34 4.1 Comparison of well-test designs for quantifying residual CO2 trapping in the field (PI) ........................................................................... 34 4.2 Impacts of SO2 co-contaminant & geological conditions on residual CO2 trapping (PII) ................................................................................... 43 4.3 Prerequisites for convective mixing under broad geological conditions (PIII) ...................................................................................... 47 4.4 Experimental study of convective mixing in porous media (PIV) ..... 55

5. Summary & Conclusions .......................................................................... 62

Acknowledgements ....................................................................................... 66

Sammanfattning ............................................................................................ 67

References ..................................................................................................... 71

Abbreviations

Br- BTC CO2

Bromide Break through curve Carbon dioxide

EOS Equation of state iTOUGH2

Kr

Name of numerical simulator (abbreviationof Inverse Transport Of Unsaturated Groundwater and Heat, version 2.0) Krypton

LT Light transmission PNM REV

Pore-Network Model Representative Elementary Volume

RLT Refractive Light Transmission SO2

Xe

Sulphur dioxide Xenon

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1. Introduction

1.1 Background to geological CO2 storage International agreements on reduction of atmospheric CO2 emissions have promoted the development and use of alternative renewable energy sources and greenhouse gas emission mitigation strategies. One such strategy is geo-logical CO2 capture and storage, which includes; 1) capturing CO2 from large anthropogenic point sources, such as oil refineries, fossil-fueled power plants, paper mills, cement factories and steel industry, 2) partly or com-pletely separating the CO2 from other process-related end emissions, and 3) compressing, transporting and injecting the CO2 at great depth into a geolog-ical formation (IPCC, 2005). Geological CO2 storage constitutes one of sev-eral means available to mitigate atmospheric CO2 emissions (Gale, 2004), and a “bridge technology”, required for a limited period of time of a few centuries during which fossil fuels are phased out and alternative energy sources are developed (McPherson, 2009).

Several types of geological reservoirs can be used for CO2 storage; de-pleted or almost depleted oil and gas reservoirs, unmineable coal seams, salt caverns and deep saline aquifers in sedimentary basins. However, the last type is of particular interest because of the wide geographical distribution and large global storage capacity of sedimentary basins (Koide et al., 1992; IPCC, 2005). Criteria for suitable CO2 storage formations were proposed by van der Meer (1992), Bachu et al. (1994) and Bachu (2003). Several factors affect the suitability (storage safety, capacity and efficiency) of a geological storage formation; initial formation pressure, stress, mineralogy, formation fluid chemistry, regional geothermal gradient, hydrodynamic flow regime, depth, thickness, porosity, permeability, geological heterogeneity and stratig-raphy, i.e., presence of fractures, faults or continuous thick cap rock with adequate sealing pressure (Bachu, 2002, 2003; Chadwick et al., 2008; Erl-ström et al., 2011). Suitable bedrocks for storage of CO2 are sedimentary rocks such as sandstones or carbonates characterized by relatively high po-rosity and permeability and few fractures (Bachu, 2003), while low permea-bility shales or anhydrites constitute suitable cap rocks (Bennion and Bachu, 2007).

Furthermore, CO2 storage safety, capacity and efficiency in deep saline aquifers depend on the interplay between geomechanical, thermal, hydraulic and geochemical processes that occur as injected CO2 migrates, dissolves in

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formation fluid, and reacts with formation bedrock. Hydraulic and geochem-ical processes, such as multiphase flow, interphase mass transfer and reac-tive mass transport trap CO2 in the formations.

The CO2-trapping mechanisms Injected CO2 is retained in deep saline aquifers by several mechanisms; physical, residual, adsorption, solubility and mineral trapping (IPCC, 2005). The trapping mechanisms occur on different time scales and exhibit different degrees of permanency. Adsorption trapping, especially important for stor-age in coal seams occurs as CO2 adsorbs onto the surface of minerals or or-ganic material (IPCC, 2005). Desorption can follow changes in pressure and temperature (Bachu and Celia, 2009). In the following the remaining trap-ping mechanisms are presented in order of increasing storage security. Phys-ical trapping of free phase buoyant CO2 includes structural trapping by an overlying low permeability cap rock, stratigraphic trapping by anticlines, non-transmissive faults or facies changes, and hydrodynamic trapping under the influence of a regional flow regime (Gunter et al., 2004). Local capillary trapping leads to the entrapment of free phase buoyant CO2 underneath het-erogeneity induced local capillary (entry) pressure barriers (Saadatpoor et al., 2009). Residual trapping or capillary trapping of CO2 occurs in pores through capillary snap-off of the CO2-rich phase at low saturations, which immobilizes CO2 in bubbles or ganglia (Ide et al., 2007). Residual trapping contributes significantly to the immobilization of CO2 on short time scales, before solubility and mineral trapping become the dominant trapping mechanisms (Kumar et al., 2005). Solubility trapping occurs as CO2 dis-solves in the formation fluid. Dissolved CO2 is in a reversible state as exso-lution can occur under depressurization following fracturing (McPherson, 2009). Dissolution through molecular diffusion is a relatively slow process. However, CO2 dissolution in formation fluid induces density changes in the fluid that can trigger density-driven convective flow and thus enhance the dissolution rate (Lindeberg and Wessel-Berg, 1997; Weir et al., 1996; Yang and Gu, 2006). Over long time scales, density-driven convective flow be-comes the dominant mechanism for CO2 solubility trapping (Ennis-King and Paterson, 2005). The dissolution of CO2 in formation fluid is dependent on pressure, salinity and temperature and leads to acidification of the formation water. In the presence of favourable rock mineralogy, pH-buffering occurs as the dissolution process proceeds and mineral precipitation of carbonate minerals follows (Gunter et al., 2004). Mineral trapping of CO2 is one of the most secure and permanent forms of trapping, but one that requires long time (Gunter et al., 2004; IPCC, 2005), immobilizing CO2 over a time scale of several tens of thousands of years (Kumar et al., 2005). A thorough under-standing of these mechanisms and ability to quantify CO2 trapping in the field is necessary in order to accurately predict the long-term fate of injected CO2 and assess storage safety, capacity and efficiency.

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1.2 Research objectives The overall objective of this thesis is to improve present knowledge of trap-ping mechanisms during geological storage of CO2, knowledge needed for accurate long-term prediction of the fate of injected CO2 as well as for stor-age capacity and safety assessment. The work focuses specifically on the residual and solubility trapping mechanisms of CO2 (the latter enhanced by density-driven convective mixing) during storage in deep saline aquifers in sedimentary basins. The influences of aquifer characteristics on CO2 trap-ping are investigated. In the work numerical modeling and experimental methods are used, including implementation of existing numerical simulators as well as the development of new models and experimental methods to study and quantify CO2 trapping on field, laboratory and pore scale.

The specific research objectives concerning residual trapping are:

to compare and develop well-test designs that can be used in the field during site characterization to estimate the in-situ residual CO2 gas saturation.

to investigate on the pore scale the relative influence of co-contaminant SO2 on residual CO2 trapping, compared to those of thermodynamic conditions and salinity.

The specific research objectives concerning solubility trapping are:

to develop an analysis tool and use this to investigate over broad

geological storage conditions the prerequisites for density-driven instability and convective mixing (enhancing the CO2 solubility trapping rate), as well as the trends in onset time and mass transfer of convection.

to develop an optical experimental method and system design for

studying solutally induced density-driven flow in porous media in the laboratory, as an analogue for CO2-induced convective mixing in geological reservoirs.

to use the experimental setup, to study the dynamics of density-

driven convective mixing, as well as to derive scaling laws for the onset time and mass transfer of convection, that improve the un-derstanding of the convective process.

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2. Theory

2.1 Hydraulic processes & CO2 trapping mechanisms in porous media During geological CO2 storage, deep saline aquifers constitute highly dy-namic non-isothermal multiphase systems in which hydraulic, thermal, me-chanical, and chemical processes are tightly coupled. Hydraulic processes such as multiphase flow, mass transfer, singlephase flow and reactive transport redistribute and trap injected CO2 within aquifers and thereby af-fect storage capacity, efficiency and safety.

2.1.1 Physical properties of fluids During storage in deep saline aquifers, the spread of CO2 depends on the properties of the injected CO2 and resident brine. In turn, thermophysical properties of fluids such as density, viscosity, fugacity, surface tension, compressibility, heat capacity, thermal conductivity and enthalpy depend on thermodynamic conditions and composition.

The thermodynamic conditions prevailing during injection and storage in the target formation determine whether the CO2 is in a liquid, gaseous, or supercritical state. Above the critical point, i.e., 31 ⁰C and 7.38 MPa, CO2 is in a supercritical state (Span and Wagner, 1996). Since supercritical CO2 is denser than gaseous CO2, storage of the former leads to more efficient stor-age (Chadwick et al., 2008). The increasing pressure and temperature with depth within a formation have counteracting effects on the CO2 density, which levels out with depth and reaches a maximum of ~850 kg/m3 (Bachu, 2003). In sedimentary basins, the temperature and pressure vary between 40-200 ⁰C and a few to several tens of mega pascals (Kaszuba and Janecky, 2009) depending on the regional geothermal gradient and pressure profile. In general, CO2 is expected to be in a supercritical state at depths below 800 meters (van der Meer, 1992).

Properties of fluids or mixtures of fluids can be estimated by using equa-tions of state, EOS, which are derived relationships between properties and state variables such as pressure and temperature. A review of existing EOS and transport property models for CO2 and CO2 mixtures was given by Li et al. (2011a) and Li et al. (2011b), respectively. The most commonly used equations of state for CO2 under geological storage conditions are those by

11

Peng and Robinson (1976), Redlich and Kwong (1949) and Span and Wag-ner (1996). Thermodynamics of CO2, as well as reactions and kinetics under geological storage conditions were reported in the work by Marini et al. (2007), while algorithms for formation fluid properties in sedimentary basins were reviewed by Adams and Bachu (2002). Fluid properties such as viscos-ity and density highly influence fluid flow, and therefore accurate estima-tions of these properties are necessary for predicting CO2 distribution within sedimentary basins. Han and McPherson (2009) further stressed the necessi-ty to quantify uncertainty in model predictions due to choice of EOS by studying the influence of choice of solubility model on the predicted dissolu-tion, migration pattern, and solubility trapping of CO2.

Furthermore, presence of impurities or co-contaminants (O2, N2, Ar, H2O, NOx, SOx, CO, H2S, H2, CH4) in CO2 emissions can affect the behaviour and transport properties of injected CO2-rich gas (IEAGHG, 2011).

2.1.2 Multiphase phenomena, flow & residual trapping A phase either liquid, gaseous or solid is defined as having a sharp identifia-ble outer boundary that separates it from surrounding phases (Pinder and Gray, 2008). As CO2 is injected and stored in a saline aquifer, the bedrock (solid phase), resident brine (aqueous phase) and CO2-rich phase compose the multiphase system. The injected CO2-rich phase is exposed to several types of forces within the aquifer; viscous, gravity and capillary forces.

During injection, the CO2 migration in the vicinity of the injection well is dominated by viscous forces. However, further away from the injection well and after CO2 injection has ceased the CO2 migration is dominated by gravi-ty forces. Under the influence of gravity, injected CO2 which under most thermodynamic conditions is of lower density than the resident brine mi-grates buoyantly upwards until reaching an impermeable cap rock. During the buoyant migration, CO2 from the tail of the rising CO2 plume becomes (following brine imbibition) residually trapped by capillary forces.

The capillary pressure, , is the pressure difference between the CO2-rich phase and the aqueous phase and depends on the aqueous phase saturation,

, and the geological medium. Several empirical - relations to be fitted to experimental data exist, among others the models by Brooks and Corey (1964) and van Genuchten (1980).

For drainage to occur, i.e., for the CO2-rich phase to invade an aqueous phase saturated pore, must exceed the capillary entry pressure, , de-fined by Eq. 1 (Bear, 1988)1:

∙ cos (1)

1 A circular pore cross section is assumed.

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In Eq. 1, is the interfacial tension, is the pore radius, and is the contact angle in the aqueous (wetting) phase. The interfacial tension, , arising due to forces acting on the interface between the CO2-rich and aqueous phase was studied under reservoir conditions by Chiquet et al. (2007a) and Chal-baud et al. (2006, 2009). The contact angle, , measured in a fluid2 conveys the wettability or preferential tendency of the fluid to wet the geological medium compared to another fluid. For < 90˚ the fluid is considered to be wetting (Bear, 1988). During geological storage, the CO2-rich phase is gen-erally considered to be non-wetting and the aqueous phase wetting, with the wettability partly dependent on the hydrophilicity of the bedrock (Chalbaud et al., 2009; Chiquet et al. 2007b). In Eq. 1 a receding contact angle, , is considered during drainage, and an advancing contact angle, , during im-bibition.

During imbibition, several pore scale mechanisms described in section 3.1.2 can occur as the aqueous phase reinvades pores and pore throats con-taining CO2-rich phase; piston-type displacements, snap-off, and cooperative pore body filling. The snap-off of CO2-rich (non-wetting) phase causes CO2 to become residually trapped as ganglia. Residual trapping has the potential to immobilize large fractions of injected CO2. In sandstones the residual gas saturations, , was quantified to be on average ~10-33% (Krevor et al., 2012).

The coexistence of multiple phases affects the flow of individual phases, and the relative permeability of a phase is consequently a function of satura-tion. Relative permeability relations were presented by e.g. Land (1968), and studied for CO2-brine systems by Bennion and Bachu (2008), Krevor et al. (2012) and Perrin et al. (2009). Because of several factors such as contact angle hysteresis, the ink bottle effect and entrapped non-wetting phase due to imbibition, both capillary pressure and relative permeability experience hys-teresis (Bear, 1988; Helmig, 1997). Relative permeability effects on flow are accounted for in the multiphase version of Darcy’s law given by Eq. 11 in section 3.1.1.

2.1.3 Interphase mass transfer, singlephase mass transport & solubility trapping During geological storage several interphase mass transfer processes occur between the CO2-rich phase and aqueous phase, such as dissolution of CO2 into the aqueous phase, and dissolution and evaporation of water into the CO2-rich phase. The dissolution of CO2 in resident brine, i.e., solubility trap-ping of CO2, constitutes an important trapping process and reduces leakage risks associated with buoyant free phase CO2. As CO2 dissolves, hydration

2 Angle measured between two lines intersecting in the point where the three phases meet; one line running along the fluid-fluid interface, the other running along the solid phase surface.

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of CO2 in the aqueous phase produces carbonic acid (H2CO3), and dissocia-tion into bicarbonate anions (HCO3

-) and carbonate anions (CO32-) leads to

acidification and ionic trapping (Marini, 2007). Depending on the mineralo-gy of the bedrock, pH-buffering can occur as a response to CO2 dissolution which enhances the CO2 solubility, or mineral trapping can occur through precipitation of secondary minerals (Rosenbauer et al., 2005).

The dissolution of CO2 into an aqueous phase is dependent on pressure, salinity (ionic strength and composition) and temperature, and was measured under different conditions by Kiepe et al. (2002), King (1992), Prutton and Savage (1945), Rumpf et al. (1994), and Wiebe and Gaddy (1939, 1940).

The solubility of CO2 in brine is proportionally dependent on pressure and inversely proportional to the salinity, i.e., ionic strength (Duan and Sun, 2003). The latter, so-called salting-out-effect limits the CO2 solubility at high ionic strengths (Gunter and Perkins, 1993). The temperature dependency of CO2 solubility in brine changes with pressure. For pressures <10 MPa, the solubility of CO2 in brine decreases with temperature. For higher pressures, the CO2 solubility decreases with temperature until reaching a pressure de-pendent minimum solubility point after which the solubility increases with temperature (Duan and Sun, 2003).

The mole fraction solubility of CO2, , in an aqueous phase can be es-timated with Eq. 2 (Marini, 2007):

, ∙ , ∙, ∙ , (2)

In Eq. 2, the subscripts and denote the CO2-rich (gaseous) phase and aqueous phase, respectively. Γ is the temperature, pressure and composi-tion dependent fugacity coefficient of CO2, is the molar fraction of CO2, is fugacity of CO2 at the standard state, is the total gas pressure, and is the temperature, pressure and composition dependent activity coefficient of CO2.

Several CO2 solubility models applicable to geological storage conditions were reviewed and compared by Zerai et al. (2009), among others the solu-bility models by Duan and Sun (2003), Duan et al. (2006), Spycher et al. (2003), and Spycher and Pruess (2005). The solubility model by Duan and Sun (2003) balances chemical potentials between phases to determine solu-bility; using the EOS by Duan et al. (1992) for calculating fugacity coeffi-cients of CO2, and the formulations by Pitzer (1973) and Pitzer et al. (1984) for calculating activity coefficients at specific ionic strengths, temperatures and pressures. In contrast, the solubility model by Spycher et al. (2003) uses equilibrium constants to estimate mutual solubility of CO2 and water be-tween phases; using a modified Redlich-Kwong equation for calculating fugacity coefficients. The solubility model by Spycher and Pruess (2005)

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based on the model by Spycher et al. (2003) additionally accounts for salt-ing-out-effects by using the formulation by Duan and Sun (2003) for calcu-lating activity coefficients.

The transport of dissolved CO2 can occur through several transport mech-anisms. In the presence of pressure gradients, solute transport is dominated by advection and dispersion, the latter dependent on geological heterogenei-ty. The advective mass transport depends on the solute concentration in the aqueous phase, and the Darcy velocity of the aqueous phase given by vector

in Eq. 3 (Bear, 1988):

∙ P ρ (3)

In Eq. 3, is the absolute permeability vector, is the dynamic viscosity, is the pressure, is the density, and is the vector of gravitational accelera-tion directed downward.

In the presence of concentration gradients, solute transport is affected by molecular diffusion. The diffusive mass flux, , depends on the effective diffusivity and the concentration gradient, , according to Fick’s law, Eq. 4 (Domenico and Schwartz, 1997):

(4)

As diffusion is a relatively slow transport process, concentration/density gradients can trigger density-driven instability and convective flow.

Density-driven convective mixing As CO2 trapped under a cap rock dissolves by molecular diffusion into the underlying aqueous phase, a diffusive boundary layer evolves in which den-sity changes are induced. Under geological storage conditions, increases in aqueous phase density generally occur, with some exceptions for certain thermodynamic and salinity conditions in warm basins (Lu et al., 2009). Density increases of up to 2-3% following CO2 dissolution in pure water, and ~1% in brine, were reported by Garcia (2001) and Pruess and Zhang (2008), respectively.

Depending on the aquifer conditions and characteristics, CO2-dissolution-induced density increases may produce density-driven instability that trig-gers convective flow (Lindeberg and Wessel-Berg, 1997; Weir et al., 1996). Density-driven convective flow redistributes dense CO2-saturated brine and less dense fresh brine within the aquifer, thereby enhancing the CO2 dissolu-tion rate beyond that of molecular diffusion and reducing the trapping time scale (Ennis-King and Paterson, 2003; Farajzadeh et al., 2007; Hassanzadeh et al., 2005; Yang and Gu, 2006). Over long time scales, density-driven con-vective mixing is the dominant mechanism for CO2 solubility trapping and

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thus affects the storage capacity (Ennis-King and Paterson, 2005; Lindeberg and Wessel-Berg, 1997).

The characteristic number, conveying the ratio between buoyancy and viscous forces in a homogeneous isotropic saturated porous media layer is the Rayleigh-Darcy number, , defined by Eq. 5 (Nield and Bejan, 2006):

∆ (5)

In Eq. 5, is the magnitude of gravitational acceleration, is the permeabil-ity, ∆ is the induced density change, is the dynamic viscosity, is the porosity, is the molecular diffusivity, and is the characteristic length e.g. the storage layer thickness. Using advection-diffusion scaling (Slim et al., 2013), i.e., the velocity scale3 ∆ ⁄ , the length scale4 ⁄ and the time scale5 ⁄ ; becomes the length-scale ratio ⁄ or the dimensionless layer thickness.

The precondition for density-driven instability in a system is identified by comparing the value of , obtained by using Eq. 5, against the value of a critical Rayleigh-Darcy number, , that depends on the initial and bounda-ry conditions of the system. Precondition for density-driven instability exists if the value of exceeds that of .

Several dynamic regimes of the convective process were identified (based on the dominating transport mechanism and dissolution rate) and studied experimentally (Backhaus et al., 2011; Neufeld et al., 2010; Slim et al., 2013) or numerically (Elenius and Johannsen, 2012; Slim, 2014; Hassanza-deh et al., 2007; Szulczewski et al., 2013; Zhang et al., 2011a) for different ranges of . For high values of , a constant-flux regime was identified (Backhaus et al., 2011; Hesse, 2008; Hidalgo et al., 2012; Neufeld et al., 2010; Pau et al., 2010; Pruess and Zhang, 2008; Slim, 2014). Emami-Meybodi et al. (2015) concluded that the convective process can be summa-rized in five well-established events or stages; the onset of density-driven instability, the onset of density-driven convection, an unsteady-flux peak, a constant-flux regime and convective shut-down. Slim (2014) numerically identified seven regimes; diffusive, linear-growth, flux-growth, merging (of convective fingers), reinitiation (of convective fingers), constant-flux and shut-down.

The critical onset time, , of density-driven instability, i.e., the time when instability initiates and starts to grow, can be estimated by using Eq. 6 (Ennis-King and Paterson, 2003):

3 The velocity of a fully saturated fluid parcel. 4 The length over which advection and diffusion balance. 5 The time for advection or diffusion over .

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∙∆

(6)

In Eq. 6, is a numerically derived constant with a reported value (Elenius and Johannsen, 2012; Elenius et al., 2012; Ennis-King and Paterson, 2005; Ennis-King et al., 2005; Hassanzadeh et al., 2006; Slim and Ramakrishnan, 2010; Riaz et al., 2006; Xu et al., 2006) that depends on the method of anal-ysis, initial conditions and stability criteria used (Hassanzadeh et al., 2007). The onset time, , of convection occurs later, as the dissolution flux grows and convective fingers become visible. The onset time of convection can be estimated by using Eq. 6 and a value of shown in Table 1. In numerical studies the onset time of convection strongly depends on the onset criteria and initial perturbation used (Bestehorn and Firoozabadi, 2012), which caus-es a spread in the reported value of (Emami-Meybodi et al., 2015).

Table 1. Numerically derived values of in Eq. 6 for the onset time of convection. Modified version of table published in Rasmusson et al. (2017a), reprinted with permission from Wiley & Sons.

-value Reference

845 Azin et al. (2013) 1,155.6, 1,411.5 Pruess and Zhang (2008) 1,200 Slim (2014) 1,000 - 5,000 Pau et al. (2010) 4,860 Elenius and Johannsen (2012) 5,400 Elenius et al. (2012)

During the flux-growth regime convective fingers grow and the dissolution flux increases until reaching a maximum value. For the following constant-flux regime, the steady convective flux, , is given by Eq. 7 (Slim et al., 2013):

∗ ∙

∆∙ (7)

In Eq. 7, ∗ is the dimensionless steady convective mass flux, and is the mass of solute per unit volume of saturated solution. Scaling laws of ∗ are shown in Table 2. Discrepancies between the scaling laws concerning the dependency of ∗ on exist. Reasons for these discrepancies, such as the type of experimental setup used (classic Rayleig-Darcy or analogue-fluid) and solute dependency of aqueous phase density (linear or non-monotonic) were discussed and analyzed by Emami-Meybodi et al. (2015) and Hidalgo et al. (2012). Furthermore, the duration of the convective regime was para-metrized by Slim (2014) as shown in Table 2.

17

As convective fingers approach the bottom of the system, concentration differences diminishes within the system and convective shut-down initiates (Slim, 2014).

Table 2. Scaling laws of F∗, in Eq. 7. Modified version of table published in Ras-musson et al. (2017a), reprinted with permission from Wiley & Sons. ∗

Method

Upper Boundary

Valid range

Reference

0.017 Num. Imperm. - Hesse (2008) 0.017-0.018 Num. Imperm. - Pau et al. (2010) 0.017a Num. Imperm. 102-5 104 Slim (2014) 0.02 Num. Imperm. - Elenius et al. (2012) 0.025

Num.

Semi-perm. (0.2)b

102-5 104

Slim (2014)

0.044

Num.

Semi-perm. (0.6)b

102-5 104

Slim (2014)

0.075 Num. Fully perm.c - Elenius et al. (2012) (0.12±0.03) . .

Exp. Num.

-

103-106

Neufeld et al. (2010)

(0.045±0.025) . .

Exp.

-

6 103-9 104

Backhaus et al. (2011)

(0.0794) .

Num.

Imperm.

103-8 103

Farajzadeh et al. (2013)

(0.037) . Exp. - 104-105 Tsai et al. (2013) a The duration of the convective regime ∗=0.017, is 1100 < t < 16 ∙ , where is the non-dimensional time, obtained by multiplying the dimensional time with ∆ ⁄ (Slim, 2014). b The relative permeability of the capillary transition zone. c Full exchange with the capillary transition zone. In a geological reservoir, double-diffusive convection can occur as the densi-ty gradient is influenced by both the concentration distribution and the re-gional geothermal gradient. Early studies of thermally induced convective currents in porous media were conducted by Horton and Rogers (1945) and Lapwood (1948). The thermal Rayleigh number can be calculated by using Eq. 5 and replacing the molecular diffusivity with the thermal diffusivity, , and the solutally induced density change with the density change, ∆ , in-duced by the geothermal gradient over the storage layer thickness . The ratio ∆ ∆⁄ is the so-called buoyancy ratio, and the system equiva-lent Rayleigh-Darcy number can be approximated by summing the solutal and thermal Rayleigh-Darcy numbers (Javaheri et al., 2010; Nield and Be-jan, 2006). The thermal contribution to instability was found to be negligible in comparison to the solutal contribution caused by CO2 dissolution (Ja-vaheri et al., 2010; Lindeberg and Wessel-Berg, 1997).

Several factors were identified to influence the convective mixing process in deep saline formations, including the formation inclination (Javaheri et al., 2009; Tsai et al., 2013), background flow and dispersion (Emami-Meybodi et al., 2015; Hassanzadeh et al., 2009), capillary transition zone between the

18

CO2-rich and aqueous phase (Elenius et al., 2012; Emami-Meybodi and Has-sanzadeh, 2015; Slim and Ramakrishnan, 2010), geochemistry (Ennis-King and Paterson, 2007; Ghesmat et al., 2011; Zhang et al. 2011a), permeability anisotropy (Ennis-King et al., 2005; Ennis-King and Paterson, 2005; Green and Ennis-King, 2014; Hong and Kim, 2008; Rapaka et al., 2009; Xu et al., 2006), and geological heterogeneity (Green and Ennis-King, 2010; Kong and Saar, 2013). As permeability heterogeneity increases in a system, the flow pattern during convective mixing changes from fingering to channeling and dispersive flow (Farajzadeh et al., 2011; Ranganathan et al., 2012; Chen et al., 2013).

19

3. Methods

3.1 Numerical & inverse modeling The following sections aim to give a short presentation of the numerical models used in this work, and the assumptions and governing equations up-on which they are based.

In section 3.1.1, the numerical model used for multicomponent, multi-phase flow simulations in Paper I, the iTOUGH2 simulator (Finsterle, 2007) with the EOS7C module (Oldenburg et al., 2004) is described. The inverse modeling capabilities of the iTOUGH2 simulator used in Paper I and Paper III are also described. Furthermore, accessibility to inverse modeling fea-tures for non-TOUGH models by linkage to the iTOUGH2 simulator (Fin-sterle, 2007) through the PEST protocol (Doherty, 2008; Finsterle and Zhang, 2011) exploited in Paper III is described.

In section 3.1.2, the Pore-Network simulator (Rasmusson, 2017) used in Paper II for simulations of pore scale mechanisms is described.

In section 3.1.3, the analysis tool developed in Paper III for determining prerequisites for density-driven instability and convective mixing is de-scribed.

3.1.1 The iTOUGH2 simulator For numerical simulations of multiphase flow in Paper I, the iTOUGH2 simulator (Finsterle, 2007) and EOS7C module (Oldenburg et al., 2004) were applied. The iTOUGH2 (inverse TOUGH2) simulator adds inverse modeling capabilities to the TOUGH2 simulator (Pruess et al., 1999).

The TOUGH2 (Transport Of Unsaturated Groundwater and Heat, version 2.0) general-purpose reservoir simulator (Pruess et al., 1999) developed at Lawrence Berkeley National Laboratory handles calculations of non-isothermal, multicomponent, multiphase flows in porous media. Depending on the application, the TOUGH2 simulator can be combined with one of several fluid property (EOS) modules.

For Paper I the EOS7C module (Oldenburg et al., 2004) was used. The module calculates thermophysical properties, partitioning, and transport in multiphase, multicomponent systems composed of water, brine, gas (mix-tures of CH4-CO2 or CH4-N2), gas tracer, methane and heat, under geological reservoir conditions. Thus, the EOS7C module was used in Paper I to ena-

20

ble simulations of well-tests incorporating gas tracers. For calculations of gaseous phase density and enthalpy the module employs the EOS by Peng and Robinson (1976), while viscosity is calculated based on the method by Chung et al. (1988). Component partitioning between aqueous and gaseous phases is determined by using partial molar volumes of Spycher et al. (2003) to calculate equilibrium constants for CO2, and for the other components by using SUPCRT92 (Johnson et al., 1992) and the slop98 database. The EOS7C module accounts for temperature and pressure dependency on aque-ous phase solubility, while salinity effects are neglected. Effects of dissolved gas components on aqueous phase density are also neglected.

For the TOUGH2 model (Pruess et al., 1999), the mass balance equation of a component, κ, or energy is given by Eq. 8:

M dV ∙ dΓ q dV (8)

In Eq. 8, the left-hand term represents the accumulation of mass or energy over a domain, V , which is balanced by the mass or heat flux over the do-main surface, Γ , (first right-hand term)6, and the contribution of sources and sinks in the domain, q, (second right-hand term). For mass balance of a component, κ, Eq. 8 can be expanded according to Eq. 9:

φ∑ S ρ X dV ∙ dΓ q dV (9)

In the left-hand term of Eq. 9, the mass of a component, κ, is calculated as a function of porosity, , saturation, S, density, , and mass fraction, X, summed over all phases, β, in the domain. In the first right-hand term of Eq. 9, the mass flux of a component, κ, over the domain surface is calculated as the sum of the advective mass flux, , (Eq. 10) and the mass flux caused by diffusion and hydrodynamic dispersion, .

∑ X (10)

In Eq. 10, the advective mass flux, , is calculated using a multiphase version of Darcy’s law given by Eq. 11. Here, is the absolute permeability, k is the relative permeability, is the density, is the viscosity, is the pressure gradient, and is the vector of gravitational acceleration.

k P ρ (11)

6 Here, represents the normal vector.

21

For energy balance, Eq. 8 can be expanded according to Eq. 12:

1 φ ρ C T ∑ S ρ u dV λ T ∑ h ∙

dΓ q dV (12)

In the left-hand term of Eq. 12, ρ is the grain density, C is the specific heat of rock, is the temperature, and u is the specific internal energy. In the first right-hand term of Eq. 12, the heat flux is calculated as the sum of conduc-tive and convective heat fluxes, where λ is the thermal conductivity, and h is the specific enthalpy. The value of λ was calculated as a function of liquid saturation, , dry heat conductivity, , and wet heat conductivity, , according to Eq. 13:

∙ (13)

The TOUGH2 model is written in FORTRAN and uses an integral finite

difference method to discretize space, and a first-order backward finite dif-ference to discretize time (Pruess et al., 1999).

The iTOUGH2 simulator (Finsterle, 2007) facilitates inverse modeling applications, among others local and global sensitivity analyses and parame-ter estimation. Local sensitivity analysis, applied in Paper I and Paper III produces sensitivity coefficients, i.e., ratios between (model output) variable changes and the (model input) parameter perturbations causing them. Thus, a high sensitivity corresponds to a large parameter influence on a variable. In Paper I, a high sensitivity was used as an indication of high information worth of an observation7, , for estimating a particular field parameter, . The relative influence (or worth) of observations of different types, unit or scales, was studied after scaling the sensitivity coefficients. Dimensionless sensitivity coefficients8 were obtained by multiplying the sensitivity coeffi-cients with the ratio of the anticipated parameter variation, , and the ob-servation standard deviation9, . In Paper I, scaled sensitivity coefficients were studied over time, and summed to determine the information worth of different data sets in concern to different field parameters. In Paper III, global sensitivity analysis was used to calculate sensitivity measures over parameter space and identify parameter-interaction effects. The Morris one-at-a-time (OAT) method (Morris, 1991) was applied. The method included partitioning of model input parameter ranges into intervals, and random sampling from these into sets of parameters. The sampled parameter values were then perturbed one at a time in random order, and changes in model

7 Simulated temperature, pressure or concentration response/measurement. 8 ⁄ ∙ ⁄ 9 Measurement error.

22

output variables were calculated. The calculations were repeated for multiple paths, i.e., multiple sets of parameter values and varying perturbation order of parameters. Based on the results from the calculations, a global sensitivity index, the mean elementary effect, , was obtained for each parameter over the parameter space. The absolute value of indicates how influential a parameter is, a high value indicating an influential parameter. The standard deviation, , of indicates the presence (a high value) or absence (a low value) of non-linearity and interaction-effects (Finsterle, 2007). Fur-thermore, the global sensitivity index uncertainty was calculated based on the number of paths, , used as .⁄ (Morris, 1991).

In Paper I, parameter estimation was used to compare the ability of dif-ferent single-well push-pull test sequences (with different sets of observa-tions) to estimate a certain field parameter. For the parameter estimation, parameter ranges, initial guesses of parameter values, and expected meas-urement errors of relevant field parameters were specified. The parameter estimation was conducted by minimizing the sum of squared weighted10 re-siduals (least squares) between observations, i.e., simulated responses, and synthetic field data11. The Levenberg-Marquardt minimization algorithm was used (Finsterle, 2007). The parameter value minimizing the least squares constituted the best-estimate, with uncertainties given by the ±standard devi-ation. In Paper I, the relative ability of different test sequences to estimate a certain field parameter was determined by comparison of estimation uncer-tainties.

The inverse modeling capabilities of iTOUGH2 can be made accessible to non-TOUGH2 models. This is possible through the PEST protocol (Doherty, 2008; Finsterle and Zhang, 2011) implemented in iTOUGH2, which enables the communication with an external model. Following minor coding, the iTOUGH2-PEST (Finsterle, 2011) architecture facilitates links between in-put and output parameters of an external model and iTOUGH2. This feature was exploited in Paper III, as the developed analysis tool was connected to iTOUGH2-PEST, and local as well as global (Morris one-at-a-time) sensitiv-ity analyses were conducted.

10 Weighted by the variance, i.e., squared measurement error of the observations. 11 Response from forward simulation with random noise (measurement errors) added.

23

3.1.2 The Pore-Network simulator

Pore-network modeling enables simulations of phase displacement and trap-ping mechanisms in void networks, consisting of pore bodies and pore throats. Thus, pore-network models constitute useful tools for studying re-sidual trapping which is controlled by several pore scale mechanisms. In Paper II, the Pore-Network Model (PNM) developed by Rasmusson (2017) was applied. The PNM written in FORTRAN, is a quasi-static, two-phase flow model that accounts for an aqueous phase and a CO2-rich phase. The PNM assumes laminar fluid flow and is applicable for conditions at which capillary forces dominate over viscous forces. In addition, the phases are assumed immiscible and incompressible. In the pore network, the pore bodies have either circular or square cross sections, while the pore throats have circular or equilateral triangular cross sections.

In Paper II, the pore network was calibrated to exhibit properties of sandstone. The calibration was conducted by manual adjustment of PNM input parameters until representative network properties (e.g. porosity, per-meability and tortuosity) were obtained. Input parameters varied were among others the mean coordination number12, distance between pore body centers, and fractions of pore throats and pore bodies with circular cross sections. The pore throat radii distribution reported by Sharqawy (2016) for Berea sandstone was used.

The lattice size of the pore network was varied and the representative el-ementary volume, REV, was identified. The number of pore-network reali-zations used (with similar statistical properties) was determined through analysis of the ensemble mean and standard deviation.

In Paper II, the PNM was used to simulate CO2 intrusion in brine-saturated networks, followed by brine imbibition. The left and right sides of the pore networks constituted in- and outflow-boundaries, respectively, while the top and bottom sides constituted no-flow boundaries. During CO2 intrusion, pore bodies at the inflow boundary were filled with CO2 and the spread of CO2 within the pore network was controlled by the entry pressures of the pore throats connected to the CO2 invaded pore bodies. The continu-ous spread at each pressure level, up to the highest entry pressure was evalu-ated.

The entry pressure, , of a pore throat with a circular cross section is giv-en by Eq. 1 in section 2.1.2 (using the receding contact angle, ), and for a pore throat with an equilateral triangular cross section by Eq. 14 (Øren et al.,1998; Patzek, 2001; Al-Futaisi and Patzek, 2003):

12 Network average number of connected pore throats to a pore body. Coordination numbers for individual pore bodies range between 0-26.

24

∙ cos ∙ 1 1∙ ∙∑ ∙

(14)

In Eq. 14, is the interfacial tension, is the pore throat radius, is the corner half angle(s), and is the shape factor of the cross section.

During imbibition, brine entered from the right side boundary. The brine invasion in the pore network was mainly controlled by pore body properties, and processes such as piston-type displacements and snap-off in throats and bodies, as well as cooperative pore body filling were accounted for.

Piston-type displacement, or the advancement of a main terminal arc me-niscus13 within a pore network occurs as a displacing phase gains space over another phase and thereby forces it towards the pore-network exit (Lenor-mand et al., 1983). For pore throats and bodies with circular cross sections, piston-type displacement was controlled by Eq. 1 in section 2.1.2 (and the advancing contact angle, ). For piston-type displacement in pore throats with triangular cross sections, calculations in accordance with Al-Futaisi and Patzek (2003) and Patzek (2001) were conducted.

Snap-off in pore throats or pore bodies occurs as films of wetting phase grow at the element corners until filling the center of the element and caus-ing disconnection, “snap-off”, of non-wetting phase. For pore throats with triangular cross sections, snap-off was calculated in accordance with the work by Al-Futaisi and Patzek (2003); accounting for the dependency of snap-off on parameters such as , the cross section radius, , and the reced-ing and advancing contact angle, and , respectively. No snap-off oc-curred in pore bodies with circular cross sections, while snap-off in pore bodies with square cross sections was controlled by Eq. 15, in accordance with Lenormand and Zarcone (1984):

,∙

(15)

Cooperative pore body filling can occur as a non-wetting phase occupies a pore body and one or several pore throats connected to it. The displacement process was simulated by the PNM by accounting for parameters such as the number of connected pore throats, the radius of the pore throats and pore body, , and in accordance with the work by Blunt (1997) and Patzek (2001). For further details on the PNM and the equations upon which it is based, the reader is referred to Paper II, Rasmusson (2017) and Rasmusson et al. (2017b).

13 Interface between non-wetting and wetting phase.

25

3.1.3 An Analysis tool for determining prerequisites for convective mixing In this section, the analysis tool developed in Paper III is described. The analysis tool was used to study prerequisites for density-driven instability and convective mixing in deep saline aquifers under broad geological CO2 storage conditions. The analysis tool enabled comprehensive calculations of the Rayleigh-Darcy number14, , onset time of instability, , (defined by Eq. 6, in section 2.1.3), and steady convective mass flux, , (defined by Eq. 7 in section 2.1.3).

The analysis tool coded in Matlab was developed to account for both the solutal contribution (from CO2 dissolution) and the thermal contribution (from the geothermal gradient) to density-driven instability, alternatively only the solutal contribution. Consequently, the analysis tool was construct-ed by several submodels according to Figure 1, accounting for CO2 solubility in brine, solutally and thermally induced density-change, brine viscosity, and molecular and thermal diffusivity under varying conditions. The analysis tool was applicable to a broad range of temperatures, 30-130˚C; pressures, 7.85-60 MPa; and salinities, 0-6 m NaCl (mol NaCl/kg H2O).

In Figure 1, the input parameters of the analysis tool are shown; the stor-age depth and surface temperature ( ), or alternatively, storage tempera-ture ( ) and pressure ( ). In addition, the salinity of the formation fluid, formation permeability ( ) and porosity ( ), storage layer thickness ( ), geothermal gradient ( ), magnitude of gravitational acceleration ( ), and a value of the constant ( ) in Eq. 6, were provided as input.

Figure 1. Schematic of the analysis tool, its overall structure, submodels, and work flow. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2015).

14 In Paper III, was approximated as the sum of thermal and solutal contributions,

, where ∆ ⁄ , and is defined by Eq. 5 in section 2.1.3.

26

For calculation of temperature, pressure and salinity dependent CO2 solu-bility in brine, , two solubility models were incorporated into the analysis tool. The solubility models by Duan and Sun (2003) and by Spycher and Pruess (2005) were used. The applicable temperature, pressure and salinity ranges of the solubility models differed slightly. Thus, by incorporating both solubility models the applicable range of the analysis tool was extended, and comparison within overlapping ranges was enabled.

For the calculations of solutally and thermally induced density changes in the aqueous phase, ∆ and ∆ , the density model (for CO2-H2O-NaCl solutions) by Li et al. (2011c) was used, which is based on the density model by Mao and Duan (2008) for aqueous NaCl solutions, and the work of Duan et al. (2008). However, in Paper III the pure water density was calculated using the thermodynamic formulation of IAPWS97 (Wagner et al., 2000). In addition, the volumetric Debye-Hückel limiting law slope was calculated by linearization of a dataset of tabulated values (Archer and Wang, 1990). The analysis tool calculated ∆ as the difference in density between the CO2 saturated and resident brine, while ∆ was calculated as the difference in density between the resident brine at the top and bottom of the storage layer.

For calculation of temperature, pressure and salinity dependent brine vis-cosity, the model by Mao and Duan (2009) was used.

The molecular diffusivity of CO2, , was estimated by applying the Wilke-Chang correlation (Wilke and Chang, 1955), given by Eq. 16:

. ⁄

. (16)

The correlation accounts for changes in temperature15, , and viscosity, , on the molecular diffusivity. In Eq. 16, is the molecular weight of water, is an empirical constant of the solvent (water) with a value of 2.6, and is the molar volume of the solute (CO2) with a value of 34.0 cm3/mol (Cussler, 2009; Wilke and Chang, 1955).

The thermal diffusivity, , was calculated as the ratio between the thermal conductivity of the medium, , and the fluid heat capacity, , according to Eq. 17:

⁄ (17)

In Eq. 17, the heat capacity, , and density, , of water were calculated based on the thermodynamic formulation of IAPWS97 (Wagner et al., 2000). was estimated with the empirical correction given by Eq. 18 (Som-erton, 1992; Tikhomirov, 1968): 15 is in Kelvin.

27

10 ∙ 293 ∙ 1.38 ∙ ∙ 1.8 10 . ∙ 1.28 ∙ . (18)

In Eq. 18, =1.5 W/(m K) was used, representative for sedimentary rocks (Lee and Deming, 1998).

The analysis tool used the calculated values of ∆ , ∆ , , , as well as the values of input parameters supplied to determine , , and . For calculations of , the seven scaling laws listed in Table 2 (on row three to nine)16 in section 2.1.3 were incorporated into the analysis tool.

In order to apply local and global sensitivity analyses the analysis tool was connected to the iTOUGH2 simulator (Finsterle, 2007), as described in section 3.1.1.

16 In the scaling laws was used.

28

3.2 Experimental method This section describes the optical experimental method and analogue system design developed in Paper IV to study convective mixing in porous media. The experimental method facilitates both qualitative and quantitative study of transport processes in porous media, while the analogue system design allows the processes to be studied in the laboratory under ranges of condi-tions applicable to the field.

Several types of optical measurement techniques exist for studying flow and transport processes in the laboratory; x-ray techniques for rigid systems such as core-samples or thick bead boxes, laser induced fluorescence tech-nique or reflection techniques (McNeil et al., 2006; Schincariol et al., 1993) for thin or moderately thin bead boxes up to several centimeters in thickness, and light-transmission techniques for thin transparent flow cells of millime-ters to a few centimeters in thickness (Catania et al., 2008). In common to all these methods is that they are non-intrusive and aid in the visualization and quantitative study of processes with relatively high spatial and temporal res-olution.

Because of difficulties associated with conducting experiments at reser-voir conditions, relatively few experimental studies of density-driven flow related to geological CO2 storage have been reported (Emami-Meybodi et al., 2015). PVT cell experiments for CO2-brine systems (Farajzadeh et al., 2007, 2009; Gholami et al., 2015; Khosrokhavar et al., 2014; Yang and Gu, 2006) enable easy quantification of mass-transfer rates under thermodynam-ic reservoir conditions, but they have limited ability to visualize the convec-tive flow pattern and dynamics. On the other hand, visualization experiments with CO2-water or analogue fluids in Hele-Shaw cells (Backhaus et al., 2011; Faisal et al., 2013, 2015; Kneafsey and Pruess, 2010, 2011; Slim et al., 2013) or bead packs (Agartan et al., 2015; MacMinn et al., 2012; MacMinn and Juanes, 2013; Neufeld et al., 2010) or combinations thereof (Nazari Moghaddam et al., 2012, 2015; Seyyedi et al., 2014; Tsai et al., 2013) are optimal for qualitative studies of the convective process (Emami-Meybodi et al., 2015), while the quantification of mass-transfer rate is less straight-forward.

Depending on the optical technique used in visualization experiments, the prerequisites and approaches for quantifying mass transfer have differed. Fluid cell experiments with analogue fluids utilizing the Schlieren technique (Khosrokhavar et al., 2014; Thomas et al., 2015) and shadowgraph (Back-haus et al., 2011; Tsai et al., 2013), exploit light intensity variations arising from changes in the index of refractive (caused by density/concentration gradients) to visualize the convective process. However, the shadowgraph was also used by Backhaus et al. (2011) and Tsai et al. (2013) to quantify mass flux based on interface movement. Light-transmission (LT) techniques

29

used in thin illuminated systems17 exploit light intensity variations caused by changes in light absorption and/or light refraction arising from solute (dye) or phase redistribution. For LT, pH-indicators were employed to study finger characteristics (Faisal et al., 2013, 2015; Kneafsey and Pruess, 2010), while quantification of concentration profiles or mass transfer was enabled by the use of dye (Neufeld et al., 2010) or naturally coloured solute (Slim et al., 2013), and the calibrated relationship between its concentration and the transmitted light (colour) intensity. Similarly, reflection technique was used by Agartan et al. (2015) to determine convective mass transfer based on the relationship between dye concentration and reflected light intensity.

In section 3.2.1, a LT technique and an experimental setup that differ from the previously mentioned are described. The so-called refractive-light-transmission technique utilizes changes in light refraction instead of light absorption to quantify concentration, thus rendering the use of dyes redun-dant. By exploiting light refraction for visualization, the new experimental method resembles the Schlieren and shadowgraph techniques. However, contrary to these, the new experimental method can be used to study flow and transport processes in porous media, and incorporates a calibration pro-cedure and image post-processing scheme that enable quantification of so-lute concentration as well as density and viscosity with high spatial and tem-poral resolution.

3.2.1 The Refractive-Light-Transmission Technique The refractive-light-transmission (RLT) technique captures variations in transmitted light intensity through a thin illuminated bead box packed with fluid-saturated translucent silica sand, variations caused by changes in the saturating fluid’s refractive index. Thus, the primary requirement for study-ing mass transport using RLT, is that the solute makes a detectable impact on the index of refraction of the fluid saturating the system. The intensity variations arising are relatively modest, and to better visualize solute spread image post-processing is required. Furthermore, quantification of solute con-centration is enabled by a calibration procedure that determines the relation-ship between transmitted light intensity and solute concentration.

Analogue system design & RLT

The use of an analogue system design allows for transport processes to be studied in the laboratory under conditions applicable to the field. In Paper IV, an analogue system design was used to study convective mixing under a wide range of conditions ( values). The analogue system design allowed by choice of solute, silica sand particle size (determining permeability, ,

17 Hele-Shaw cells, or thin bead boxes packed with glass beads or translucent silica sands.

30

and porosity, ,) and initial solute concentration (determining e.g. ∆ ) used, to duplicate a wide range of conditions and set the system to function as an analogue for density-driven convective flow systems found in nature.

In Paper IV, NaCl was used to induce density-driven convective mixing. The linear variation in the refractive index of the aqueous solution with the NaCl concentration (Jenkins, 1982) was exploited; an increase in NaCl con-centration corresponded to an increase in light transmission. Different condi-tions ( values) were obtained by varying the initial NaCl concentration in the system.

Experimental setup

The experimental setup, shown in Figure 2, consisted of a thin transparent bead box packed with water- or brine-saturated translucent silica sand, which was illuminated from behind by a LED light panel. Transmitted light intensi-ty was detected by a computer-controlled monochromatic charge-coupled device (CCD) camera.

Figure 2. Schematic of the a) experimental setup, b) bead box and salt holder, and c) experimental chamber. Reprinted with permission from Wiley & Sons, originally published in Rasmusson et al. (2017a).

The bead box (with a length of 30 cm, height of 20 cm, and width across the gap of 1 cm) was constructed by two long sides consisting of an outer Plexi-glass sheet and an inner glass sheet of 2 cm and 0.3 cm thickness, respective-

31

ly. The long sides were fixed to Teflon (PTFE) sheets constituting the bead box’s short sides and bottom. Inlets on the bottom and short sides of the bead box enabled fluid exchange in the system. The solute entered the system through a salt holder mounted on the top of the bead box. The holder con-sisted of a compartment for NaCl with a fine metal-mesh bottom through which dissolved NaCl could penetrate into the system. The LED light panel was mounted on a steel cooling plate to mitigate potential temperature in-creases. In addition, the experimental setup was enclosed within a dark chamber to ensure that only light transmitted through the bead box was cap-tured by the camera. Light scattering inside the chamber was minimized by the use of dark cloth draping.

Calibration procedure & Image post-processing

Concentration-intensity relationships were obtained on a pixel-by-pixel level by acquiring reference images at different solute concentrations, and con-ducting regression analysis on the concentration and light intensity data, as shown in Figure 3. Pixel-wise relationships were obtained on the form given by Eq. 19:

∙ (19)

In Eq. 19, is the light intensity, is the mass fraction of solute and and are pixel specific coefficients. The pixel-by-pixel calibration mitigat-ed experimental errors arising from non-uniform lighting and vignetting effects18.

The solute (NaCl) concentration of an aqueous solution not only influ-ences its refractive index, but also its density, , and viscosity, . Thus, for a concentration field measured at known thermodynamic conditions, the corre-sponding -, ∆ - and -fields were determined by applying equations of state19 during image post-processing, as shown in Figure 3.

Image post-processing was conducted with scripts programmed in Matlab. The subtraction of an initial reference image from a time series of images enabled visualization of the convective process. The resulting data on light intensity differences, ∆ , were used to study convective dynamics. The dissolved NaCl mass, , and mass flux, , over a domain with NP pixels were calculated by using Eq. 20 and Eq. 21, respectively, under the assump-tion of homogenous porosity, .

18 Reduction of an image’s brightness at its periphery compared to its centre. 19 Algorithms for NaCl solubility by Langer and Offermann (1982). EOS by Kestin et al. (1981) for and .

32

Figure 3. Schematic over the calibration procedure and image post-processing scheme. Reprinted with permission from Wiley & Sons, originally published in Rasmusson et al. (2017a).

In Eq. 20, is the total solute mass summed over the NP pixels of the stud-ied domain. is the area of a pixel , and is the width across the gap. The density ( ) and initial density ( ), were calculated as functions of tempera-ture ( ), pressure ( ), and solute mass fraction ( , ), alternatively, initial solute mass fraction ( , , ), in accordance to Kestin et al. (1981).

∑ , ∑ , , , , , , , ∙ ∙ ∙ (20)

In Eq. 21, the solute mass flux, , is defined as the change in mass between two images in a time-series of images, divided over the elapsed time be-tween the images and the cross-sectional superficial area ( ) of the salt holder.

⁄ (21)

The linear relationship between and enables studying the change in ∆ for a time-series of images as an intensity analogue for mass flux. Setting

=1, the unit of the analogue light intensity flux given by Eq. 22 is ∆ ∆ ∆

(22)

33

In Eq. 22, ∆ ∑ ∆ , ∑ , , , where is the number of the image in the time-series, 0 indicates the reference image, and is the acqui-sition-time of image .

34

4. Results & discussion

4.1 Comparison of well-test designs for quantifying residual CO2 trapping in the field (PI)

Residual trapping has been identified as an important CO2 trapping mecha-nism on short time scale during geological storage. Thus, quantification of the residual CO2 trapping potential during site characterization is of great importance for storage capacity estimation. This urges the development and comparison of well-test designs for estimating properties in the field, such as the in-situ residual gas (CO2) saturation, , that determines the residually trapped CO2. For this purpose, single-well injection-withdrawal tests also called push-pull tests can be used. In Paper I, three alternative single-well push-pull test sequences were presented, evaluated and compared for their ability to estimate in the field.

Simulations of test sequences were conducted using the numerical simula-tor iTOUGH2 (Finsterle, 2007) with the EOS7C module (Oldenburg et al., 2004), described together with its inverse modeling capabilities in section 3.1.1. The simulator allowed for the application of local sensitivity analysis to determine the relative worth of different data sets for estimation. In addition, parameter estimations using synthetic data from the test sequences were conducted, and the obtained estimation uncertainties of were com-pared, serving as measures of their abilities to quantify in the field. The added value of pressure measurements from a nearby passive observation well, located 40 m from the injection well, was also investigated.

The test sequences are shown in Figure 4-Figure 6. The test sequences in-cluded thermal, hydraulic, and tracer tests (except for test sequence 3, in which thermal tests were omitted), to exploit that affects thermal and hydraulic responses, as well as, the partitioning of dissolved gas tracers be-tween phases. In common to all three test sequences, was the repetition of thermal, hydraulic and tracer tests at different in-situ gas saturation condi-tions; fully water-saturated, gas-saturated, and residual gas saturation condi-tions. However, the approaches used to create these conditions differed be-tween the test designs. Simulated temperature, pressure and concentration responses (data sets) were later used to estimate . Acronyms used for data sets in Figure 4-Figure 6 are explained in each figure caption, respectively.

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Figure 4. Test sequence 1, after Zhang et al. (2011b). Acronyms refer to pressure (P), temperature (T), dissolved gas tracer (C) data sets from the injection well and a passive observation well (O). Numbers refer to their chronological order. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2014).

Test sequence 1, shown in Figure 4, was proposed by Zhang et al. (2011b)20. This test sequence starts with reference thermal, tracer and hy-draulic tests at fully water-saturated conditions. Thereafter, CO2 is injected to create in-situ gas-saturated conditions, and a thermal test is conducted. Afterwards, CO2-saturated water is injected to create residual gas saturation conditions in the formation around the injection well, followed by thermal, tracer and hydraulic tests. The partitioning (dissolved gas) tracers used in the tracer tests were Xenon (Xe) and Krypton (Kr).

Figure 5. Test sequence 2. Acronyms refer to pressure (P), temperature (T), dis-solved gas tracer (C) data sets from the injection well and a passive observation well (O). Numbers refer to chronological order. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2014).

In test sequence 2, shown in Figure 5, a different approach to create residual gas saturation conditions, compared to that used in test sequence 1 was pro-posed; an indicator tracer (bromide, Br-) is injected, followed by CO2 injec- 20 Modified injection rates compared to those in Zhang et al. (2011b) were used.

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tion, and withdrawal of formation fluid. Online-measurements of indicator tracer aid in determining when residual gas saturation conditions are estab-lished and withdrawal can cease. In Paper I, simulation results showed the establishment of residual gas saturation conditions around the injection well to coincide with the indicator tracer concentration approaching background level.

Figure 6. Test sequence 3. Acronyms refer to pressure (P), temperature (TX), dis-solved gas tracer (C) data sets from the injection well and a passive observation well (O). Numbers refer to their chronological order. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2014).

Test sequence 3, shown in Figure 6, differs from the previous ones in that no thermal tests (no heating events) are applied. The same approach as in test sequence 2, i.e., the indicator-tracer approach, is used to establish residual gas saturation conditions. However, contrary to the previous test sequences, in test sequence 3 no CO2-saturated water injection is used. Thus, after the last water injection (with dissolved gas tracers) semi-residual gas saturation conditions are established instead of residual gas saturation conditions. For further details on the test sequences, such as injection and pumping rates, see Paper I.

For the simulations, a homogenous isotropic two-dimensional radially symmetric model was used. The conceptual model consisted of a sandstone layer of 10.6 m thickness, with a 500 m radius, and properties representative of the MUSTANG project field experiment site at Heletz, Israel. The initial thermodynamic conditions 14.7 MPa and 67˚C were used, corresponding to a depth of 1600 m. Further details on model properties are given in Paper I.

In Figure 7–Figure 9, the simulated responses in temperature, pressure and dissolved gas tracer concentration break through curves, BTCs, for test sequences 1-3 at different values of are shown. The abbreviations used in the schematics on top of Figure 7–Figure 9 are: H (heating), Wtrc (water injection with dissolved gas tracer), WD (withdrawal), C (CO2 injection), CW (CO2-saturated water injection), CWtrc (CO2-saturated water injection

37

with dissolved gas tracer), and W+ ind. Trc (water injection with indicator tracer).

In Figure 7a, temperature responses for test sequence 1 are shown. The three major temperature increases (peaks) correspond to heating events dur-ing thermal tests. For thermal tests performed under fully gas-saturated and residual gas saturation conditions, temperature responses varied with the value of . -dependent temperature increases were observed during CO2 injection, while -dependent decreases (dips) in temperature were observed as CO2-saturated water injection ceased. As shown in Figure 7b, under fully gas-saturated and residual gas saturation conditions, pressure responses (in the injection well) during injection and withdrawal events de-pended on the value of . In Figure 7c, the dissolved gas tracer BTCs un-der residual gas saturation conditions are shown to vary in size and shape depending on the value, and the dissolved gas tracer used.

In Figure 8, similar trends in temperature and pressure responses, as well as dissolved gas tracer BTCs for test sequence 2 are shown. However, the alternative approach used to create residual gas saturation conditions (with-drawal and using an indicator tracer, instead of injecting CO2-saturated wa-ter) resulted in a -dependent pressure decrease instead of a pressure in-crease, as shown in Figure 8b. Furthermore, in test sequence 2 the indicator tracer BTC obtained a peak value of ⁄ ~2.5 (falling outside the plotted range in Figure 8c), i.e., an enrichment, caused by vaporization of water into the gaseous phase.

For test sequence 3, the temperature responses shown in Figure 9a dif-fered substantially from those of the other test sequences due to the exclu-sion of thermal tests. Despite absence of heating events, a -dependent temperature increase was detected during CO2 injection. Also the dissolved gas tracer BTCs shown in Figure 9c differed from those of the other test sequences; a higher relative concentration was observed in the second tracer test (during semi-residual conditions) than in the reference test, and no large differences between BTCs of Xe and Kr were observed. The higher relative concentration arose as residually trapped gas was dissolved by water injected during the last tracer and hydraulic tests, leading to enrichment of dissolved gas tracers in the aqueous phase.

As shown in Figure 7-Figure 9, during certain time periods the simulated temperature, pressure and dissolved gas tracer BTCs responses displayed high dependencies on the value of . Local sensitivity analyses, from which scaled sensitivity coefficients with time were obtained confirmed that data of high sensitivity or information worth to were sampled during these time periods (as described in section 3.1.1). In Figure 10, the summed scaled sensitivity coefficients for different data sets in regard to different field parameters are shown for test sequence 1-3.

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Figure 7. Simulated responses of a) temperature, b) pressure, and c) tracer BTC, for test sequence 1 at different . The schematic on top shows the different stages of the test sequence. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2014).

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40


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Figure 10. Data set sensitivity to different field parameters for a) test sequence 1, b) test sequence 2, and c) test sequence 3. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2014).

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In Figure 10, the field parameters are: the logarithm of permeability, log , porosity, Φ, residual liquid saturation, , residual gas saturation, , Brooks-Corey parameter lambda, , Brooks-Corey parameter entry pressure,

, dry heat conductivity, , wet heat conductivity, , the logarithm of pore compressibility, log , and the logarithm of inverse Henry’s constant for Xe, log H . The highest sensitivities to were exhibited by the pres-sure data sets (P4, P2, P3 A and P3 B) from the injection well and the con-centration data set from the second tracer test (C2). Relatively high sensitivi-ties to several of the field parameters were also exhibited by the pressure data sets from the passive observation well.

Parameter estimation was performed as described in section 3.1.1 for the cases shown in Table 3. Synthetic temperature, pressure and concentration data with measurement errors accounted for was used. The best-estimate of

and uncertainty (±standard deviation) obtained for each case are shown in Table 3. The estimation uncertainties of for the different cases were compared. Test sequence 1 and 2 estimated with a similar magnitude of uncertainty. However, test sequence 3 gave a larger uncertainty in estimates, due to the exclusion of thermal tests. For all test sequences, the estimation uncertainty decreased when pressure data sets from the observation well were included in the parameter estimation.

Table 3. Test sequences with data sets used for parameter estimation. The true value was 0.2. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2014).

Test sequence Data sets Best estimate,

1 T1, T2, T3, P1, P2, P3 A, P4, C1, C2 0.2001 ± 0.5 10-3

1 + passive obs. well

T1, T2, T3, P1, P2, P3 A, P4, C1, C2, PO1, PO2, PO3 A, PO4

0.2000 ± 0.4 10-3

2 T1, T2, T3, P1, P2, P3 B, P4, C1, C2 0.2003 ± 0.5 10-3 2 + passive obs. well

T1, T2, T3, P1, P2, P3 B, P4, C1, C2, PO1, PO2, PO3 B, PO4

0.2002 ± 0.4 10-3

3 without data set TX P1, P2, P3 B, P4, C1, C2 0.2001 ± 0.18 10-2 3 with data set TX TX, P1, P2, P3 B, P4, C1, C2 0.2004 ± 0.15 10-2 3 without data set TX + passive obs. Well

P1, P2, P3 B, P4, C1, C2, PO1, PO2, PO3 B, PO4

0.2003 ± 0.12 10-2

3 with data set TX + passive obs. Well

TX, P1, P2, P3 B, P4, C1, C2, PO1, PO2, PO3 B, PO4

0.2001 ± 0.14 10-2

Thus, since test sequence 1 and 2 estimated with a similar magnitude of uncertainty, the equipment and work resources available for creating in-situ residual gas saturation determine the choice of test sequence. Using the indi-cator-tracer approach proposed in this work requires less use of CO2-saturated water, but additional work with handling and measuring the indica-tor tracer.

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4.2 Impacts of SO2 co-contaminant & geological conditions on residual CO2 trapping (PII) Residual trapping has the potential to immobilize large amounts of CO2 over relatively short time, thereby affecting both storage capacity and safety. Knowledge of the impacts of different storage conditions on residual trap-ping is thus important for the assessment of CO2-trapping potential. One aspect of concern is the presence of co-contaminants in the injected CO2-rich phase. For power plants, which are the largest sources for CO2 emissions, sulphur dioxide (SO2) is one of the major co-pollutants to CO2. Removal techniques for eliminating co-contaminants exist. However, geological co-storage of CO2 and SO2 is considered an economically viable option (IPCC, 2005). Therefore, Paper II focused on determining the relative impact of SO2 co-contaminant on residual CO2 trapping in sandstone reservoir rock, compared to those of thermodynamic conditions and salinity.

In Paper II, the maximum residual gas saturation, , was studied for the scenarios listed in Table 4, which included varied SO2 content in the CO2-rich phase, brine salinity, reservoir temperature and storage depth.

Pore-network modeling was used in order to account for pore scale mech-anisms such as snap-off, cooperative pore body filling and piston-type dis-placement, described in section 3.1.2. The newly developed PNM by Ras-musson (2017) was applied, and pore networks were calibrated to exhibit properties of a generic sandstone with a permeability of ~500 mD, a porosity of ~0.20, and a mean coordination number of ~3.5. The lattice size of the pore networks was 20x20x20 (15 mm3). Figure 11 shows one of the 25 pore-network realizations used.

Table 4. Investigated cases.

Case #

Pressure [MPa]

Temperature [˚C]

Salinity [M]

SO2 content [wt%]

Study objective

1 20.8 60 1 0 base case 2 20.8 60 1 1 co-contaminant 3 20.8 60 1 6 co-contaminant 4 20.8 60 0.2 0 salinity 5 20.8 60 5 0 salinity 6 20.8 70 1 0 temperature 7 20.8 80 1 0 temperature 8 13.9 60 1 0 shallow deptha

9 27.7 100 1 0 deep storagea a Thermodynamic conditions expected at ~1300 m and ~2700 m depth, respectively, within a formation with a geothermal gradient of ~30˚C/km, surface temperature of ~20˚C, and hydro-static pressure gradient of ~10.5 MPa/km.

For the pore networks to exhibit wettability properties of sandstone for which quartz is the major component, experimentally measured values of the interfacial tension, , and receding and advancing contact angles, and ,

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by Saraji et al. (2014)21 were used as input parameters to the PNM simula-tions. Viscosities of brine, , and CO2, , were calculated using the EOS by Mao and Duan (2009) and Span and Wagner (1996), respectively.

Figure 11. Pore-network realization #1.

For the scenarios listed in Table 4, the PNM was used to simulate CO2 intru-sion in initially brine-saturated pore networks (all 25 realizations), followed by imbibition of brine.

The results of the PNM simulations are shown in Table 5 and Figure 12. The presence of SO2 (1-6 wt%) in the CO2-rich phase rendered median value increases in by 3.4-2.5%. Although the presence of SO2 in the CO2-rich phase strongly affected , the increases arose from decreases in (larg-est decrease for 1 wt% SO2), that reduced the relative occurrence of piston-type displacement events in throats and increased snap-off in throats.

Furthermore, decreased strongly with increasing salinity. As the salin-ity increased from 0.2 M to 1 M, and from 0.2 M to 5 M NaCl, the median value of decreased by 12.2% and 20.2%, respectively. Increases in both

and with increasing salinity resulted in higher relative occurrences of cooperative pore body filling and piston-type displacements events, which resulted in more CO2 being displaced out of the system during brine imbibi-tion. This, in combination with a reduced relative occurrence of snap-off in throats resulted in decreased .

21 For the CO2-brine-quartz system.

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Table 5. and relative occurrence of different pore scale mechanisms for the in-vestigated cases. Median values based on 25 realizations are shown.

Case #

[-]

Piston-type displ., throats

[%]

Piston-type displ., bodies

[%]

Snap-off, throats

[%]

Snap-off, bodies

[%]

Coop. pore body fill.

[%]

Total no. of events

1 0.37 35.8 29.6 30.2 0 4.4 8552 2 0.38 34.6 29.8 31.9 0 3.7 8424 3 0.38 34.9 29.8 31.6 0 3.7 8456 4 0.42 31.9 28.9 36.4 0 2.8 7881 5 0.34 42.0 27.3 22.4 0 8.3 8965 6 0.37 35.6 29.7 30.6 0 4.1 8530 7 0.39 34.2 29.7 32.7 0 3.4 8382 8 0.40 33.3 29.6 34.1 0 3.0 8191 9 0.38 34.5 29.9 32.0 0 3.6 8453

The results in Table 5 and Figure 12 indicate that increased with in-

creasing temperature, for the temperature range studied. Between 60ºC (case 1) and 70ºC (case 6) a small increase of 0.5% in the median value of was obtained. However, as temperature increased from 60ºC to 80ºC (case 7), a median value increase of 6.7% in was obtained. Both and decrease with increasing temperature. However, the large increase in at 80ºC was caused by the decrease in , which increased the relative occurrence of snap-off in throats, and reduced cooperative pore body filling and piston-type displacement events in throats.

Figure 12. The change in plotted against, a) the change in , and b) the change in for cases 2-9 compared to the base case (case 1) for all 25 pore-network reali-zations.

The results in Table 5 and Figure 12 further indicate that the median value of decreased by 6% for deep storage at high temperature and pressure (case 9) compared to shallow storage under moderate temperature and pres-sure conditions (case 8). This was caused by the higher value of at ther-modynamic conditions corresponding large depth, which reduced the relative

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occurrence of snap-off in throats, and increased the relative occurrence of cooperative pore body filling and piston-type displacement events.

The results show that presence of SO2 in the CO2-rich phase (at the con-centrations studied) can promote residual trapping of CO2 in sandstone res-ervoir rock. However, the influence on is limited compared to that of brine salinity, which is the most important factor to consider during storage site selection. Thermodynamic conditions, (dependent on the regional geo-thermal gradient and the storage depth) also have a relatively large influence on the amount of residually trapped CO2. The relative influence of brine salinity, thermodynamic conditions and co-contaminant SO2 on depend-ed predominantly on their influence on . For conditions rendering low values of , snap-off in throats was favoured and increased. Conse-quently, a strong negative trend between ∆ and ∆ is shown in Figure 12. Thus, although determines the breakthrough pressures for stratigraphic trapping, controls the residual trapping. Pore-network modeling and wet-tability measurements for CO2-brine-mineral systems relevant to a rock’s mineralogy could be used to estimate its residual CO2 trapping potential.

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4.3 Prerequisites for convective mixing under broad geological conditions (PIII) For geological CO2 storage in deep saline aquifers, solubility trapping is one of the most secure and important trapping mechanisms over large time scales. Dissolution of CO2 in formation brine leads to density changes of the aqueous phase that can trigger convective flow, and enhance the solubility trapping rate. Storage formation properties and conditions, affecting not least the CO2 solubility, determine the prerequisites for density-driven instability. Thus, understanding which conditions favour density-driven instability and convective mixing is important for storage site selection.

Therefore, in Paper III the prerequisites for density-driven instability and convective mixing under broad geological storage conditions were studied. The influences of temperature, pressure, salinity, permeability, as well as storage depth and basin type on trends in the onset of instability ( )22, onset time of instability ( ), and steady convective flux ( ) were studied. In addi-tion, the relative influence of different field characteristics was studied using local and global sensitivity analyses. From the results obtained, conditions favouring or hindering solubility trapping were identified.

To conduct the study, the analysis tool described in section 3.1.3 was de-veloped and used. The analysis tool accounted for impacts of thermodynam-ic and salinity conditions on the CO2 solubility in brine, solutally and ther-mally induced density change, viscosity, and molecular and thermal diffusiv-ity. Local and global sensitivity analyses were applied by connecting the analysis tool to iTOUGH2 (Finsterle, 2007), as described in section 3.1.1. Using the analysis tool, prerequisites for density-driven instability were stud-ied for wide ranges of temperatures (30-130 ˚C), pressures (7.85-60 MPa), and salinities of aqueous solutions (0-6 m NaCl).

Initially, trends in CO2 solubility, , and CO2-induced density change in the aqueous phase, ∆ , were studied. For the thermodynamic and salinity ranges studied, ∆ decreased with increasing temperature and salinity, and decreasing pressure. In general ∆ of a few tenths of a percentage to ~1% were found for the conditions studied, with a maximum value of ~2%. How-ever, under high temperature and salinity conditions, CO2-induced density decreases in the aqueous phase were found. Lu et al. (2009) identified the equal density temperature for which ∆ =0 to be 118 ˚C at 20 MPa and 4 m NaCl. However, for higher salinity (6 m NaCl) studied in Paper III, the equal density temperature decreased to 80 ˚C at 20 MPa, and decreased even more for lower pressures.

22 In Paper III, was approximated as the sum of thermal and solutal contributions,

, where ∆ ⁄ , while is defined by Eq. 5 in section 2.1.3.

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The trends in the ratio between ∆ and the thermally induced density change, ∆ , (induced by the geothermal gradient, T , over the storage layer thickness), as well as, the ratio ⁄ were studied over broad thermodynamic and salinity ranges, and for varying T . The ratios varied largely over the range of conditions studied. However, the direct thermal contribution (∆ ) to density-driven instability was generally small com-pared to the solutal contribution (∆ ), except at high salinities. The highest ratios were obtained for thermodynamic conditions corresponding to shallow depths. However, increased salinity, storage depth and value of T de-creased the ratios, and negative ratios were obtained for high salinity condi-tions.

Trends in values over broad thermodynamic, salinity and permeability ( ) conditions are shown in Figure 13. The solid red lines in Figure 13 dis-play the range: 13.8 < < 4π2, described in detail in Paper III. Pre-requisites for onset of instability exist for conditions rendering values exceeding this range. In Figure 13, the trends in are shown to follow the trends in ∆ ; decreasing with temperature and salinity and increasing with pressure. Thus, combinations of high temperature (≥80˚C), moderate-high salinity (≥4 m NaCl) and low (≤10-14 m2) disfavoured onset of insta-bility. At low , instability highly depended on thermodynamic and salinity conditions. For the broad range of conditions studied, varied from hun-dreds of thousands to close to zero (and even displayed negative values).

In Figure 14, trends in are shown for varying storage depth and salin-ity in a cold and a warm basin, respectively. The highest values were obtained for thermodynamic conditions corresponding to shallow storage depths of around 800 m. Furthermore, values were generally higher in the cold compared to the warm basin because of the lower temperatures in the cold basin, and thus larger ∆ . At high salinity, storage depth highly influenced the prerequisites for onset of instability, especially under warm basin conditions.

In Figure 15 the values for varying salinity under cold and warm basin conditions are shown. The values, based on the values in Figure 14, were calculated by using Eq. 6 in section 2.1.3 and =31 from Elenius et al. (2012)23. An increasing trend in with salinity and storage depth is shown in Figure 15. The influence of the storage depth increased with salinity. Fur-thermore, for a particular storage depth, was generally smaller under cold basin conditions than warm basin conditions.

In Paper III, the trends in were studied using the seven scaling laws listed in Table 2 (on row three to nine)24 in section 2.1.3, including -dependent and -independent scaling laws. An increase in with increas-ing depth was obtained from all scaling laws (at zero salinity). In Figure 16,

23 Corresponding to impermeable upper boundary conditions. 24 For the scaling laws was used.

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trends in based on the scaling law by Slim (2014)25 and the corresponding ∆ ⁄ ratio are shown for varying salinities, storage depths and different basin types.

Figure 13. for different temperature, pressure, salinity and permeability condi-tions. Columns show different permeability conditions. The coloured curves indicate different pressures: black – 7.85 MPa, green – 30 MPa, and blue – 60 MPa. The solid and dashed lines illustrate results based on the solubility models by Duan and Sun (2003) and Spycher and Pruess (2005), respectively. The solid red lines indicate the range: 13.8< <4π2. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2015).

25 See Table 2 (row three) in section 2.1.3.

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Figure 14. for (to the left) a cold basin with = 25 ˚C/km, and (to the right) a warm basin with =50 ˚C/km. =10 ˚C, =10-13 m2 and hydrostatic pres-sure was assumed. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2015).

Figure 15. for (to the left) a cold basin with = 25 ˚C/km, and (to the right) a warm basin with =50 ˚C/km. For both cases =10 ˚C and =10-13 m2. Re-printed with permission from Elsevier, originally published in Rasmusson et al. (2015).

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In Figure 16 a large influence of salinity on is shown, but also basin type ( ) exhibited an influence. The trends in followed those of ∆ ⁄ ; at low salinities (0-1 m NaCl) increasing with depth, at moderate salinities becoming more uniform, and at higher salinities decreasing with depth. Fig-ure 14 and Figure 16 indicate that the storage conditions rendering the high-est value do not necessarily render the highest .

Figure 16. To the left, the steady convective flux, , at different salinities and depths within a cold basin (black symbols) and a warm basin (magenta symbols) with = 25 ˚C/km and = 50 ˚C/km, respectively. =10 ˚C, =10-13 m2 and hydrostatic pressure was assumed. To the right, the corresponding ratio ∆ ⁄ . Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2015).

In Paper III, the influences of salinity, basin type ( ), and storage depth on the convective flux regime in concern to and its duration were studied (using the parametrization by Slim (2014) in Table 2, section 2.1.3). The combined effect of these factors highly affected and the approximate onset time and duration of the convective regime. Large storage depths and high salinities delayed the onset of convection, decreased and shortened the duration of the convective regime especially in warm basins.

In Paper III, the relative influence of field characteristics, i.e., different field properties and conditions on ,∆ , , , , , and the convec-tive regime duration was studied using local sensitivity analysis, and on using global sensitivity analysis. The sensitivity analyses are described in section 3.1.1, while the field parameters used in the analyses including their initial values or value ranges are shown in Table 6.

In Figure 17, the results of the local sensitivity analysis are shown. Alt-hough, all field parameters exhibited an influence on , was one of the

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most influential field parameters. The local sensitivity analysis also identi-fied the basin type ( ) to influence ∆ , , , and the convective regime duration.

Table 6. Parameters used in the sensitivity analyses. Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2015).

Analysis

[m2] Depth

[m]

[-]

[m]

[˚C/km] Salinity

[m NaCl] Local, initial valuea 1.0 10-13 1000 0.3

100 25 1

Global, rangeb

1.0 10-15-1.0 10-11

800-1800

0.1-0.4

10-100

25-50

0-6

a Initial parameter values were perturbed by 10% and centred finite differences were used. Sensitivity coefficients were scaled with the ratio of the parameter and variable variations, which were assumed to be 10% of their initial values. b Parameter ranges were partitioned into 11 equal intervals and 800 paths were used (=5600 simulations). In Fig 17, the most influential field parameters on (regardless of -dependency) were identified to be and salinity, although the basin type ( ) and storage depth also exhibited an influence. The most influential field parameters on were identified to be and , followed by salinity, basin type ( ) and storage depth. For the convective regime duration the most influential field parameters were identified to be , , and salinity.

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Figure 17. Scaled sensitivity coefficients displaying the relative influence of differ-ent field parameters on ,∆ , , , , , and the convective regime duration.

is based on the -independent scaling law by Slim (2014), while is based on the -dependent scaling law by Neufeld et al. (2010). Reprinted with permis-sion from Elsevier, originally published in Rasmusson et al. (2015).

In Figure 18, the results of the global sensitivity analysis (Morris OAT method, described in section 3.1.1) are shown. The field parameters identi-fied to exhibit the highest influences on (as shown by their large abso-lute mean values in Figure 18) were , salinity and . High SD EE val-ues convey non-linearity or interaction effects. A high influence of salinity on was identified over the salinity range studied. This high influence was not captured by local sensitivity analysis. Furthermore, all field parame-ters displayed statistically significant impacts on , as shown by their symbols falling below the dashed lines (standard error of the mean ) in Figure 18. Thus, it can be concluded that the geothermal gradient ( ) has a non-negligible effect on density-driven instability and convective mix-ing when accounting for both direct and indirect thermal effects.

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Figure 18. Mean EE showing the relative influence of different field parameters on

. The dashed lines mark the mean EE ± 2 ( .⁄ ). Reprinted with permission from Elsevier, originally published in Rasmusson et al. (2015).

The results in Paper III indicate that CO2 storage at shallow depths favours the onset of density-driven instability and short , while the optimal storage depth for rendering large depends on the salinity.

Furthermore, in Paper III proxy-equations for the so-called dynamic fac-tor (∆ ⁄ ) in Eq. 5 (section 2.1.3) were supplied, enabling easy estima-tions of site specific , which can serve as indicators for density-driven instability prerequisites during site selection.

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4.4 Experimental study of convective mixing in porous media (PIV) Density-driven flow is of interest to several areas of groundwater-science. For geological CO2 storage, dissolution of CO2 in the resident brine leads to density changes in the aqueous phase which can trigger convective flow, and thereby enhance the CO2 solubility trapping rate. Consequently, solubility trapping becomes one of the dominating trapping mechanisms on large time scales (IPCC, 2005). Understanding the dynamics of the convective-mixing process is therefore of great importance in order to predict CO2 solubility trapping in the field. Scaling laws (described in section 2.1.3) have also been derived for the parameters that determine the time scale and rate of CO2 solubility trapping, i.e., the onset time of convection, , and the mass flux of convection, . However, discrepancies between scaling laws exist both con-cerning equation form and values of constants (described in section 2.1.3). Therefore, Paper IV included the development of an experimental method and analogue system design for studying solutally induced density-driven flow in porous media in the laboratory, as an analogue for CO2-induced con-vective mixing during geological storage. The experimental setup was then used to qualitatively and quantitatively study convective mixing dynamics and derive scaling laws for and .

The developed experimental method was the refractive-light-transmission (RLT) technique, described together with the experimental setup in section 3.2.1. A computer-controlled monochromatic CCD camera was used to cap-ture images26 of the transmitted light intensity field of the experimental sys-tem with a resolution of 0.1404 mm/pixel (~0.0197 mm2/pixel), every 2-3 seconds during image acquisition.

The experimental system was calibrated (at concentrations of 0 wt%, 8 wt%, 16 wt% and 24 wt% NaCl), and pixel-wise relationships between the transmitted light intensity, , and NaCl concentration, , were obtained as described in section 3.2.1.

A classical Rayleigh-Darcy convective experiment setup was used, where the convective flow was initiated by solute dissolution from the top bounda-ry of the experimental system shown in Figure 2 (section 3.2.1). In the ana-logue system design (described in section 3.2.1) the solute used to represent CO2 and to trigger convection was NaCl, a solute with well-known impacts on aqueous phase density and viscosity. The initial NaCl concentration,

, , in the system was varied to obtained a range of conditions ( val-ues) under which the convective process was studied. The experiments con-ducted are shown in Table 7. The range of values studied corresponds to favourable conditions and is within the range of values studied previous-

26 16-bit grayscale, 2048 2048 pixel images, of class uint16, i.e., the captured light intensity can range from a value of 0 to 65535.

56

ly in analogue fluid experiments by Backhaus et al. (2011) and Neufeld et al. (2010), as shown in Table 2 (in section 2.1.3). The high values enabled the steady convective flux regime to be studied.

Table 7. Experiments conducted. The values of were calculated for =9.81 m/s2, =0.172 m, =0.32, and =2.5 10-10 m2. Reprinted with permission from Wiley &

Sons, originally published in Rasmusson et al. (2017a).

Exp. #

, [-]

∆ [%] a

∆ [kg/m3] a

[Pa·s] a,b

10-3 , [m2/s] c

10-9 [-] a 105

1 0 20.18 201.44 0.99 0.55 4.86 2 0 20.18 201.44 0.99 0.55 4.86 3 0 20.18 201.44 0.99 0.55 4.86 4 0.08 13.61 143.67 1.13 0.46 3.64 5 0.08 13.61 143.67 1.13 0.46 3.64 6 0.08 13.61 143.67 1.13 0.46 3.64 7 0.16 7.41 82.78 1.37 0.35 2.27 8 0.16 7.41 82.78 1.37 0.35 2.27 9 0.24 1.60 18.88 1.78 0.22 0.64

10 0.24 1.60 18.88 1.78 0.22 0.64 a Obtained for = 20.5˚C and =0.1 MPa. The values of were calculated using the EOS by Kestin et al. (1981) for the NaCl solubility determined by using the algorithms by Langer and Offermann (1982). b The values of were calculated using the EOS by Kestin et al. (1981). c The values of , ⁄ were obtained for = 20.5˚C and =0.1 MPa and =2.0, and accounting for the self-diffusion coefficient, , varying with , . The values of

were derived from a correlation obtained by multiple linear regression of the data on for =10°C to 40°C and up to 0.2451 presented by Ghaffari and Rahbar-

Kelishami (2013). The image post-processing procedure is displayed in Figure 3, section 3.2.1. Visualization of convective mixing was enabled using RLT and image post-processing, as shown in Figure 19a, were density-driven fingers are visible after subtraction of a reference image. The distribution of in Figure 19b was determined by the calibrated - relationships on the form giv-en by Eq. 19 in section 3.2.1. The corresponding distributions of , , and ∆ are shown in Figure 19c-e. These distributions were determined by using equations of state in the image-processing, as shown in Figure 3 (section 3.2.1). The distribution of shown in Figure 19f was determined by using Eq. 20 in section 3.2.1.

The dynamic regimes of the convective process were studied, specifically in regard to their temporal distribution. For this purpose the “intensity flux”, ∆ ⁄ , defined in Eq. 22 (section 3.2.1), was studied as an analogue to

mass flux. The critical onset time of convection, , and the temporal distri-bution of regimes27 were identified, as shown in Figure 20a.

27 In Figure 20a, the temporal distribution of regimes is marked with arrows and roman num-bers.

57

Figure 19. Post-processed images of experiment #1 at t=345.8 s, showing a) the ∆I, and b) the , and the corresponding c) , d) , e) ∆ , and f) . Reprinted with permission from Wiley & Sons, originally published in Rasmusson et al. (2017a). The convective process was initiated with (I) a slow diffusive regime. Thereafter (II) a convective flux-growth regime followed as visible fingers formed at and grew in size both laterally and vertically (giving rise to a rapid increase in ∆ ⁄ ), with relatively slow downwards movement. Thereafter (III) a constant-flux regime was identified during which fingers moved downwards in a steady pace, followed by (IV) a shut-down regime as fingers approached the bottom of the system. These regimes correspond well with those identified by Slim (2014) and described in section 2.1.3; diffu-sive, linear-growth, flux-growth, merging, reinitiation, constant-flux and shut-down. However, here the linear-growth regime is included in the diffu-sive regime and not separately identified, and merging and reinitiation occur during the flux-growth and constant-flux regimes.

58

Figure 20. The “intensity flux”, ∆ ⁄ , with time for experiment #1, calculated for each image, , (red dots) and for the marked domain (white dashed lines) in b)-e). Figures show, b) formation of density-driven fingering, c) growth of fingering during the convective flux-growth regime (II), d) fingering at the start of the con-stant-flux regime (III), e) fingers approaching the bottom of the bead box at the start of the shut-down regime (IV). Reprinted with permission from Wiley & Sons, origi-nally published in Rasmusson et al. (2017a).

In Figure 21, for the experiments is plotted against the 1⁄ ∙ ⁄ term of Eq. 6 in section 2.1.3. A linear relationship between and this term was expected with a slope given by the constant . However, the fitted rela-tionship, given by Eq. 23 (solid black line in Figure 21), indicates that for the

range studied, i.e., 6.4 104 < < 4.9 105, the value of followed the power-law relationship with = 0.8573 ± 0.0020:

59

Figure 21. The onset time of convection, , (symbols) plotted against the 1⁄ ∙

⁄ term of Eq. 6 in section 2.1.3. The fitted relationship, Eq. 23 (solid black line), with R2=0.9987 is shown. The inserted window shows ∗ plotted against and the fitted relationship ∗ ∆ ⁄ . (red solid line) with R2=0.7866. Reprinted with permission from Wiley & Sons, originally published in Rasmusson et al. (2017a).

. ∙ ∙ . ∙ (23)

This could possibly explain why the value of varies substantially between earlier theoretical/numerical studies listed in Table 1 (in addition to the rea-sons given in section 2.1.3). In the inserted window in Figure 21 the dimen-sionless onset time of convection, ∗, obtained by using the advection-diffusion scaling (described in section 2.1.3) is shown against . For vary-ing values of , a constant value of ∗ was expected. However, an increas-ing trend in ∗ with increasing was obtained. Furthermore, the fitted rela-tionship (red solid line) in the inserted window indicates a potential depend-ency of ∗ on ∆ , and . Eq. 23 indicates that decreases at a slower rate with increasing , and thereby renders longer at large compared to that predicted by the -scaling. The dependency of on in Eq. 23 indirectly implies a dependency of on , which is physically not straight-forward to explain for the characteristic length scale chosen28. However, is

28 The layer thickness.

60

probably dependent on at least one or several of the other variables of , such as ∆ , and , that were varied in the experiments. Thus, thermody-namic and salinity conditions affecting these parameters might have a larger influence on than predicted by the -scaling.

In Figure 22, the mean value of the convective mass flux29, , measured over the constant-flux regime is plotted against the ∆ ⁄ ∙ term of Eq. 7 (section 2.1.3) for the experiments. Thus, the slope of the plotted rela-tionship assumes the value of ∗. Previously derived scaling laws of ∗ listed in Table 2 (section 2.1.3) differ in -dependency.

Figure 22. The mass flux, , (symbols) plotted against the ∆ ⁄ ∙ term of Eq. 7 in section 2.1.3. The fitted relationships, -independent, Eq. 24, (solid line) and -dependent, Eq. 25, (dashed line) are shown, with R2=0.9118 and R2=0.9177, respectively. Reprinted with permission from Wiley & Sons, originally published in Rasmusson et al. (2017a).

Therefore, both a -independent scaling law, Eq. 24 (solid line), and a -dependent scaling law, Eq. 25 (dashed line), were fitted to the experimental data in Figure 22. For the range studied, i.e., 6.4 104 < < 4.9 105:

0.06024 0.0087 ∙∆∙ (24)

29 Measured for the domain (marked with white dashed lines) in Figure 19.

61

. . ∙

∆∙ (25)

The similar values of the coefficient of determination obtained for Eq. 24 and Eq. 25 (shown in Figure 22) indicate that ∗ for large appears to display both -dependent and -independent behaviour. The reason for this is that under conditions corresponding to large , the ∆ ⁄ ∙ term in common for both Eq. 24 and Eq. 25 has the largest influence on , while the . term in Eq. 25 with increasing for the range stud-ied approaches a value of ~0.06. Consequently for large , is captured by both -independent and -dependent scaling laws. This could explain the discrepancies in -dependency between reported scaling laws.

62

5. Summary & Conclusions

Geological storage of carbon dioxide (CO2) from large anthropogenic point sources is a mitigation strategy for atmospheric greenhouse gas emissions. Storage in deep saline aquifers in sedimentary basins is of particular interest because of the wide geographical distribution and estimated global storage capacity of sedimentary basins. The injected CO2 is retained within the for-mation by several mechanisms. In this thesis the focus of study was specifi-cally on the residual trapping (in Paper I and II) and solubility trapping (in Paper III and IV) mechanisms of CO2, the latter enhanced by density-driven convective mixing. The work incorporated numerical modeling and experi-mental methods, including implementation of existing numerical simulators as well as development of new models and experimental methods, which were used to study CO2 trapping on field, laboratory and pore scale. The overall objective of the work was to study residual and solubility trapping mechanisms, specifically in regard to their dependency on aquifer character-istics, and to investigate and develop quantification methods for CO2 trap-ping in the field.

In Paper I, multicomponent, multiphase numerical modeling and inverse modeling techniques were used to compare well-test designs in regard to their abilities to estimate the residual gas saturation that determines the re-sidually trapped CO2. In common to all test sequences was the repetition of thermal, hydraulic and tracer tests at different gas saturation conditions. However, the approaches used to create these conditions differed between the well-test designs as well as the data sets collected. A novel indicator-tracer approach was presented that can be used in the field to determine the establishment of in-situ residual gas saturation conditions. The findings of Paper I can aid in the planning of well-test designs for site characterization. Although, the focus of Paper I was on quantifying residual trapping, the well-test designs can also aid in determining in-situ formation properties affecting other trapping and migration processes of CO2, and thereby the storage capacity and suitability of a specific site.

In Paper II, pore-network modeling was used to study the effects of fac-tors such as co-contaminant sulphur dioxide (SO2) and varying formation thermodynamic and salinity conditions on the residual trapping of CO2. The results of Paper II demonstrated that co-contaminant SO2 (at the concentra-tions studied) has a limited effect on the residual CO2 trapping compared to thermodynamic and salinity conditions. However, the effect on the amount

63

of CO2 becoming residually trapped could be significant when large amounts of impure CO2 are stored. Furthermore, the thermodynamic and salinity con-ditions favouring residual trapping were identified. The results of Paper II revealed the formation fluid salinity to highly influence the residual trapping potential, and thus be of primary importance to consider during storage site selection. However, the temperature in the storage formation, i.e., the for-mation’s geothermal gradient, also impacts the residual CO2 trapping. Thus, storage at shallow depth, i.e., at moderate temperature and pressure, and at low salinity is most favourable for residual trapping of CO2.

Paper I and II displayed two different approaches for estimating residual CO2 trapping. Although exploiting different types of measurements obtained on different scales, both approaches combine measurements with numerical modeling in order to estimate the residual CO2 trapping potential.

In Paper III, an analysis tool was developed and used to study the pre-requisites for density-driven instability and convective mixing (enhancing the rate of CO2 solubility trapping) over broad geological storage conditions. The analysis tool accounted for effects of varying thermodynamic and salini-ty conditions on the CO2 solubility in brine, solutally induced density-change, brine viscosity, and molecular diffusivity, and thus enabled compre-hensive calculations and trend analysis of , the onset time of instability,

, and the steady convective mass flux, . The analysis tool was also able to account for the thermal contribution (from the geothermal gradient) to densi-ty-driven instability. Furthermore, inverse modeling was used to determine the relative influence of formation characteristics on factors controlling the process of density-driven instability and convective mixing. The results of Paper III indicated that shallow depth storage and low salinity conditions favour the onset of density-driven instability and short , while the optimal storage depth for large is salinity dependent. Furthermore, the geothermal gradient was found to have a non-negligible effect on density-driven insta-bility and convective mixing.

Based on the results of Paper II and III, it can be concluded that the con-ditions that were found to favour residual trapping also favour solubility trapping of CO2. Thus, for storage at high salinity conditions and large depth, for which both residual and solubility trapping (and consequently mineral trapping) are disfavoured, the physical trapping of CO2 becomes even more important.

In Paper IV, an optical experimental method, the so-called refractive-light-transmission (RLT) technique and an analogue system design were developed for studying solutally induced density-driven flow in porous me-dia. The use of the analogue system design allowed convective mixing to be studied in the laboratory under conditions ( values) applicable to geologi-cal CO2 storage. The experimental setup was used to study the onset time, , mass flux, , and dynamics of convective mixing, as well as, to derive scal-ing laws for both and that aid the understanding of the convective pro-

64

cess. The RLT technique described in section 3.2.1, exploits changes in aqueous phase refractive indices (within thin bead boxes packed with trans-lucent silica sand) caused by solute redistribution to visualize transport pro-cesses. The presented RLT technique resembles the Schlieren and Shadow-graph methods in utilizing changes in light refraction for visualization pur-pose. However, these methods are only applicable to fluid cells without a porous medium. Furthermore, in Paper IV a calibration procedure and an image post-processing scheme were implemented, which enabled the quanti-fication of solute concentration, density and viscosity fields within the exper-imental system. There are several advantages of using RLT (with the calibra-tion procedure and post-processing scheme) for studying mass transport processes, challenges typically encountered using light-transmission tech-niques, such as non-uniform lighting, vignetting and photobleaching of dye are mitigated or avoided. Furthermore, by avoiding the use of dye uncertain-ties associated with dye versus solute transport are removed. In Paper IV, the RLT technique was used to derive scaling laws, for and . For the scaling law of (Eq. 6, section 2.1.3), a constant value of was expected. However, the experimental data indicated to be dependent on at least one or several variables of , such as the solutally induced density change ∆ , diffusivity, , or viscosity, , which were varied in the study. Thus, the scal-ing law for obtained in Paper IV indicates that potentially decreases at a slower rate with increasing than previously thought. This could have implications for sites wit

h sloping formations where is a significant factor for long-term storage integrity. Furthermore, the result also implies that thermodynamic and salini-ty conditions (affecting parameters such as ∆ , and ) might have a larger influence on than previously thought. In Paper IV, the steady convective flux, , was studied in regard to its dependency on . As discussed in sec-tion 2.1.3, previously derived scaling laws listed in Table 2 vary in their dependency on . For the range of values studied in Paper IV, the di-mensionless convective flux, ∗, was found to display both -dependent and -independent behaviour. The reason for this was that for large , the

∆ ⁄ ∙ term (in Eq. 7, section 2.1.3) contributed the most to , while the value of ∗ for the derived -dependent scaling law (with in-creasing for the range studied) approached the value of the constant ∗ of the derived -independent scaling law. This finding potentially ex-

plains the discrepancies in -dependency between previously derived scal-ing laws of .

In future studies, RLT could be used to study convective mixing in heter-ogeneous systems. The RLT technique presented in Paper IV can also be used to study other types of mass transport processes in porous media, for example it could be used to study viscous processes. The only requirement of the solute used is that it makes a detectable impact on the index of refrac-tion of an aqueous phase.

65

The results of Paper I-IV give guidance on how to estimate the CO2 trapping potential during site characterization, and knowledge of which con-ditions favour or disfavour residual and solubility trapping. This knowledge can aid long-term predictions of the fate of injected CO2, and the safety as-sessments during storage site selection.

66

Acknowledgements

I would like to express my deepest gratitude to my main supervisor Assistant Professor Fritjof Fagerlund and my assistant supervisor Professor Auli Nie-mi at the Department of Earth Sciences at Uppsala University for giving me the opportunity to pursue a doctorate of technology in hydrology. I would also like to thank them for their support and scientific advices during the years of research work. I feel fortunate to the have been given the opportuni-ty to take part in large-scale international research projects that have permit-ted the collaboration with scientists from a broad range of research fields and given me insight into how research is conducted on the laboratory to field scale.

In addition, I would like to express my deepest gratitude and sincerely appreciation to co-author Yvonne Tsang for her valuable comments and advices during the research work. I would also like to thank co-authors Jacob Bensabat, and Kristina Rasmusson for their valuable contributions to the work done. I also thank my colleagues at the Department of Earth Sciences for their support and help.

Furthermore, I would like to thank the organizations that have provided the financial funding that enabled the research findings of this study; the European Community’s 7th Framework Programme through the MUS-TANG, PANACEA and CO2QUEST projects (grant agreement numbers 227286, 282900 and 309102) and the Swedish Research Council, VR (grant agreement number 2010-3657).

Finally I would like to thank my family for their support and help that I have received during the course of this work.

67

Sammanfattning

Geologisk lagring av koldioxid (CO2) från storskaliga antropogena punktkäl-lor är en strategi för att minska utsläpp av växthusgaser till atmosfären. Lag-ring i sedimentär berggrund och djupt belägna saltvattenakvifärer är av spe-ciellt intresse beroende på den vida geografiska utbredningen av sedimentär berggrund i världen och dess beräknade lagringskapacitet.

Injekterad CO2 fastläggs i berggrunden genom flera olika fastläggnings-mekanismer. I denna avhandling studerades kapillär fastläggning av CO2 (i artikel I och II) och fastläggning av CO2 genom lösning i formationsvatten (i artikel III och IV), den senare förstärkt genom densitetsdrivet (konvek-tivt) flöde. Avhandlingen omfattar såväl numerisk modellering som experi-mentellt arbete, och inkluderar implementering av redan etablerade nume-riska modeller, samt nyutveckling av numeriska analysmodeller och experi-mentella metoder, för att studera koldioxidlagring på fält-, laboratorie- och porskala. Avhandlingens övergripande syfte är att förbättra kunskapen om fastläggningsmekanismerna och utveckla metoder för att förutsäga och be-stämma potentialen för koldioxidlagring i fält, med hänsyn tagen till inver-kan av egenskaper hos berggrunden och förhållanden i saltvattenakvifären.

I artikel I användes numerisk modellering för simulering av multi-komponenttransport och flerfasflöde, samt inversmodellering för jämförelse av olika fälttest (testsekvenser) i avseende på deras förmågor att kvantifiera egenskaper hos berggrunden, så som kapillär CO2-mättnad vilken bestämmer mängden kapillärt bunden CO2 i berggrunden. Gemensamt för de studerade fälttesten var en upprepning av olika typer av test; termala, hydrauliska och spårämnestest, under olika förhållanden av CO2-mättnad i berggrunden. Det som skiljde fälttesten åt var tillvägagångssätten att skapa olika förhållanden av CO2-mättnad i berggrunden, samt det mätdata som samlades in. En ny metod (indikator-spårämnesmetod) presenterades som kan användas för att bestämma om förhållanden för kapillär CO2-mättnad föreligger i berggrun-den. Resultaten från artikel I kan användas i planeringsstadiet av fälttest som syftar till att karakterisera en geologisk formation inför geologisk lag-ring. Även om fokus i artikel I låg på kvantifiering av kapillärt bunden CO2, ger fälttesten information om flera olika egenskaper hos berggrunden som även påverkar andra fastläggningsmekanismer, samt spridningsprocesser och därmed lagringskapacitet och lämplighet för en specifik lagringsplats.

I artikel II användes pornätverksmodellering för att studera effekterna av kontaminering av svaveldioxid (SO2), samt olika termodynamiska och sali-

68

nitetsförhållanden på kapillärt bunden CO2. Resultatet i artikel II visade att kontaminering av SO2 (för de nivåer som undersöktes) har en begränsad effekt på mängden kapillärt bunden CO2, jämfört med inverkan av termody-namiska och salinitetsförhållanden. Effekten av SO2-kontaminering kan dock bli signifikant vid lagring av stora mängder kontaminerad CO2. Dessutom identifierades termodynamiska och salinitetsförhållanden som gynnar kapil-lär fastläggning av CO2. Resultaten i artikel II visade att saliniteten hos formationsvätskan på en lagringsplats har stor inverkan på dess potential för kapillär fastläggning, och är därmed av störst vikt att beakta vid beslut av lagringsplats. Dock har även temperaturen i berggrunden, styrd av den lokala geotermiska gradienten, en inverkan på den kapillära fastläggningen. Där-med kan slutsats dras att relativ ytlig lagring, d.v.s. vid moderata temperatur- och tryckförhållanden, och vid låg salinitet är mest gynnsam för kapillär fastläggning av CO2.

Artikel I och II visade på två olika tillvägagångssätt för att kvantifiera kapillär fastläggning av CO2. De två metoderna utnyttjar olika typer av mät-värden uppmätta på olika skalor, men båda kombinerar mätningar med nu-merisk modellering för att uppskatta potentialen för kapillär fastläggning av CO2.

I artikel III utvecklades en numerisk analysmodell för att studera förut-sättningarna för densitetsdriven instabilitet och konvektivt flöde (som på-skyndar fastläggning av CO2 genom lösning i formationsvatten) över vida geologiska, termodynamiska och salinitetsförhållanden. Analysmodellen tog hänsyn till inverkan av termodynamiska och salinitetsförhållanden på löslig-het av CO2 i formationsvatten, inducerade densitetsförändringar, viskositet hos formationsvatten, och diffusion, vilket möjliggjorde noggrann beräkning och trendanalys av , initieringstid för instabilitet, , och konvektivt mass-flöde, . Analysmodellen tog även hänsyn till den geotermiska gradientens inverkan på densitetsdriven instabilitet. Dessutom tillämpades inversmodel-lering för att fastställa den relativa påverkan som olika egenskaper och för-hållanden hos berggrunden har på faktorer som styr densitetsdriven instabili-tet och konvektivt flöde. Resultaten i artikel III indikerade att relativt ytlig lagring av CO2 i berggrund med formationsvatten av låg salinitet, ger gynn-samma förhållanden för uppkomst av densitetsdriven instabilitet och kortast initieringstid för instabilitet. Däremot är det optimala lagringsdjupet med avseende på (stort) beroende av formationsvattnets salinitet. Därutöver fastslogs att den geotermiska gradienten har en icke-försumbar påverkan på densitetdriven instabilitet och konvektivt flöde under geologisk CO2 lagring.

Utifrån resultaten i artikel II och III kan slutsats dras att de förhållanden som identifierades som gynnsamma för kapillär fastläggning även gynnar fastläggning av CO2 genom lösning i formationsvatten. Därmed kan även slutsats dras att för geologisk CO2-lagring vid hög salinitet och på stort djup, för vilket både kapillär fastläggning och fastläggning av CO2 genom lösning i formationsvatten (och därmed även som mineral) missgynnas, blir struktu-

69

rell (fysisk) fastläggning och förekomsten av geologiska lager med låg per-meabilitet ytterst viktig.

I artikel IV utvecklades en experimentell metod kallade “refractive-light-transmission” (RLT), och ett analogt experimentellt system för att studera densitetsdrivet flöde i porös media. Användning av det analoga systemet möjliggjorde att den konvektiva flödesprocessen kunde studeras i laborato-riet under förhållanden ( -värden) relevanta för geologisk CO2-lagring. Den experimentella metoden användes för att studera den konvektiva pro-cessens initieringstid, , massflöde, , och dynamiska regimer, samt för framtagandet av skalningslagar för både och , vilka ger förståelse för den konvektiva processen. RLT, beskriven i avsnitt 3.2.1, registrerar och utnytt-jar refraktionsvariationer30 inom en vätskelösning i ett tunt poröst system (här en tunn sandbox packad med genomlysbar, halvgenomskinlig kisel-sand), för att visualisera transportprocesser. Genom att utnyttja förändringar i ljusrefraktion för visualisering liknar RLT både Schlieren- och Shadowgraph-metoden, men till skillnad från dessa är RLT applicerbar i porös media. I artikel IV tillämpades även en kalibrerings- och bildbehand-lingsprocedur som möjliggjorde kvantifiering av löst masskoncentrations-, densitets- och viskositetsfält i systemet. Det finns flera fördelar med att an-vända RLT (med kalibrering och bildbehandling), utmaningar så som olik-formig belysning, linsvinjettering och fotoblekning som kan uppkomma vid användning av light-transmission, reduceras, korrigeras eller undviks. Dess-sutom, vid användning av RLT behöver inget färgämne tillsättas för att syn-liggöra och kvantifiera masstransport av ett löst ämne, vilket avlägsnar osä-kerheter associerade med färgämnes- kontra ämnestransport. I artikel IV tillämpades RLT för att härleda skalningslagar för och . Vid härledning av skalningslag för (Ekv. 6, avsnitt 2.1.3) förväntas ett konstant -värde erhållas, men istället indikerade experimentell data ett beroende hos -värdet på en eller flera variabler i , möjligen inducerad densitetsföränd-ring, ∆ , diffusion, , eller viskositet, , vilka varierades i studien. Därmed indikerade den härledda skalningslagen för att vid ökande minskar med lägre hastighet än tidigare ansett, d.v.s. längre är att förvänta vid höga . Detta kan ha stor inverkan för CO2 lagring i till exempel sluttande geologiska formationer där spelar en avgörande roll för lagringsintegrite-ten. Resultatet indikerar också att termodynamiska och salinitetsförhållanden (som påverkar ∆ , och ) därigenom kan ha en större inverkan på än tidigare ansett. I artikel IV studerades det konvektiva massflödet, , med avseende på dess -beroende eller -oberoende som för tidigare härledda skalningslagar, angivna i Tabell 2 i avsnitt 2.1.3, har varierat. För det -intervall som studerades i artikel IV uppvisade det dimensionslösa konvek-tiva massflödet, ∗, såväl -beroende som -oberoende beteende, d.v.s. skalningslagar för båda fallen kunde härledas med samma osäkerhet. Detta

30 Där refraktionsvariationerna uppkommer vid omfördelningen av ett löst ämne.

70

berodde på att vid höga -värden gav termen ∆ ⁄ ∙ (i Ekv. 7, avsnitt 2.1.3) det dominerade bidraget till , medan ∗-värdet för den här-ledda -beroende skalningslagen vid ökande närmade sig det konstanta ∗-värdet för den härledda -oberoende skalningslagen. Detta kan potenti-

ellt förklara skillnader mellan tidigare härledda skalningslagar för . För framtida studier skulle RLT kunna användas för att studera konvek-

tiva flöden i heterogena system. RLT skulle även kunna tillämpas för att studera andra typer av masstransportprocesser, till exempel skulle viskosi-tetsdrivna processer fördelaktigt kunna studeras med RLT. Det enda förbe-hållet är att det lösta ämne som används har en detekterbar inverkan på refr-aktionsindex hos den fas som mättar det porösa systemet.

Resultaten från artikel I-IV ger vägledning avseende hur CO2-fastläggningspotentialen kan uppskattas för en specifik lagringsplats, samt kunskap om under vilka förhållanden kapillär fastläggning och fastläggning genom lösning i formationsvatten gynnas, respektive, missgynnas. Dessa kunskaper kan vara till hjälp vid val av lagringsplats då den geologiska berggrundens lämplighet för lagring fastställs och riskanalys genomförs.

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