Dissolved CO2 Increases Breakthrough Porosity in Natural Porous

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Dissolved CO2 increases breakthrough porosity in natural porous materials Yi Yang, Stefan Bruns, Susan Louise Svane Stipp, and Henning Osholm Sørensen Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b02157 • Publication Date (Web): 16 Jun 2017 Downloaded from http://pubs.acs.org on June 18, 2017

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Environmental Science & Technology

Dissolved CO2 increases breakthrough porosity in natural porous materials Yi Yang*1, Stefan Bruns1, Susan Louise Svane Stipp1 and Henning Osholm Sørensen1 1

Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-

2100 Copenhagen, Denmark

*[email protected]; Tel: +45 9161 4575; Fax: +45 3532 0219

ACS Paragon Plus Environment


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ABSTRACT

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When reactive fluids flow through a dissolving porous medium, conductive channels form, leading to

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fluid breakthrough. This phenomenon is caused by the reactive infiltration instability and is important in

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geologic carbon storage where the dissolution of CO2 in flowing water increases fluid acidity. Using

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numerical simulations with high resolution digital models of North Sea chalk, we show that the

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breakthrough porosity is an important indicator of dissolution pattern. Dissolution patterns reflect the

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balance between the demand and supply of cumulative surface. The demand is determined by the

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reactive fluid composition while the supply relies on the flow field and the rock’s microstructure. We

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tested three model scenarios and found that aqueous CO2 dissolves porous media homogeneously,

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leading to large breakthrough porosity. In contrast, solutions without CO2 develop elongated convective

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channels known as wormholes, with low breakthrough porosity. These different patterns are explained

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by the different apparent solubility of calcite in free drift systems. Our results indicate that CO2 increases

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the reactive subvolume of porous media and reduces the amount of solid residual before reactive fluid

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can be fully channelized. Consequently, dissolved CO2 may enhance contaminant mobilisation near

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injection wellbores, undermine the mechanical sustainability of formation rocks and increase the

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likelihood of buoyance driven leakage through carbonate rich caprocks.

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Introduction

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A great challenge in predicting the consequences of geologic carbon storage (GCS) is to quantify the

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interaction between flowing reactive fluids and geologic formations as a function of time.1-8 Making

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progress in this direction requires considering a GCS reservoir as a constantly evolving flow system, that

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is subject to geochemical and geomechanical instabilities.9, 10 The reactive infiltration instability (RII) is

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the morphological instability of a migrating dissolution front resulting from heterogeneities in

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petrophysical properties. RII controls the microstructural evolution of rock in response to an imposed

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flow field and is the key to the self-organization of fluid flow through natural porous materials.11-17

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Identifying the trigger of this instability, as well as the chemical reactions leading to the morphological

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development,18, 19 is especially important for predicting the evolution of the sealing integrity of caprock

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and the geomechanical deformation susceptibility of reservoir structures as host rocks are eroded away.

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The morphological evolution of porous media caused by the reactive infiltration instability can be

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described qualitatively using dissolution patterns (homogeneous, ramified, channelized etc.;20-22 also

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Figure 1), or quantitatively, using breakthrough porosity, ϕc, the macroscopic porosity of a sample when

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fluid creates a penetrating channel.20, 23, 24 Given a sample size, the breakthrough porosity is an indicator

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of dissolution pattern. A large ϕc is typically associated with a uniformly dissolving morphology while a

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small ϕc indicates the formation of fingering channels. Breakthrough porosity can also be qualitatively

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related to the mechanical stability of a sample after fluid penetration. A large ϕc means little solid is left

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behind and the porous microstructure is mechanically weak, and vice versa. These features of

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breakthrough porosity motivated the use this parameter to describe the dynamic process of

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microstructure development. Worth mentioning is that the breakthrough porosity of an evolving porous

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medium is different from the solute breakthrough curve in a steady state flow field. The former


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describes microstructural evolution while the latter characterises the transport within a static geometry

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and can be effectively computed using streamline tracing.25

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A strong coupling between mineral dissolution rate and rock permeability is essential for a dynamic

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process involving RII. Coupling can be decomposed into 3 aspects of sensitivity.21, 26 First, the sensitivity

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of the flow field to rock microstructure determines how the reactants and products of the water-rock

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interactions are conveyed in a flow field so the chemical system remains far from equilibrium.27-30 This

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sensitivity can be affected by variables such as the geometry and the texture of the pore surfaces,31-35

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the properties of the fluids and their interactions during flow,36-38 as well as the body forces exerted by,

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e.g. gravitational or electrostatic fields.39 Second, the sensitivity of the reaction rates to fluid

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composition, which determines the spatial variations of chemical conversion (i.e. the extent of chemical

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reaction, which is characterised by the relative amount of reactant converted to product).40 This

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sensitivity is often complicated by the intrinsic mineral heterogeneity in natural porous media,41-44 and

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by the large number of aqueous species involved in the reactions.45, 46 Finally, the sensitivity of the rock

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microstructure to chemical conversion closes the loop of the positive feedback leading to RII. 47 This

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sensitivity reflects the density, molar mass and the solubility of the dissolving or precipitating minerals.

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If any of the three sensitivities becomes zero, the infiltration instability vanishes and the self-

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organization of the porous structure ceases.13, 48, 49


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Figure 1. A qualitative demonstration of the dissolution front instability in a 2D domain. The instability

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determines the morphology of the dissolving porous medium. Yellow indicates the dissolving front. (a)

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Stable dissolution front: mineral dissolution always takes place at the same distance from the injection

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point. (b) – (d): increasingly unstable dissolution fronts, where the distance between the injection point

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and the dissolution front varies considerably. The same amount of reactive fluid was injected in each

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simulation and snapshots were taken after the same reaction time. Greater instability leads to a higher

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likelihood of channel formation (wormholing).

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thus affects all three types of sensitivity. For example, buoyant gaseous or supercritical CO2 might

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induce Rayleigh-Taylor instability,50 influencing the spreading of the reactive aqueous phase and mixing

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of the fluids.51 Dissolution of CO2 in water changes many aspects of the kinetics of the water-rock

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interactions. Mineral dissolution rates increase because of lower pH and a stronger contribution from

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carbonic and bicarbonate species through surface complexation.52, 53 The apparent order of reaction,

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i.e., the sensitivity of reaction rate to reactant concentration, decreases because of the buffering effect

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of dissolved CO2 as a weak acid.33 Apparent mineral solubility can also be affected by modified ion

Introducing CO2 into a natural porous formation changes many of the factors that control behaviour,


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activity and buffered pH. Increased solubility is a thermodynamic driving force for the dissolution

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reactions. It can change the relative stability of the secondary phases and as a result, the sensitivity of

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the solid architecture to the extent of reaction.7, 8, 54, 55 Finally, the impact of CO2 depends on how the

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gas is introduced.56, 57 Direct injection,58 surface mixing59 and wellbore mixing4, 60 all yield distinct

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pressures and solution compositions.

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The dynamics of dissolving microstructures and consequently, the CO2 effect on the breakthrough

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properties of natural porous materials remain poorly understood for three reasons. First, structural

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heterogeneities (e.g., spatial variations in porosity and permeability) can be viewed as perturbations for

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reaction front migration. These perturbations are amplified by infiltration instability. Thus, in a series of

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experiments, the initial microstructure must be identical for meaningful comparison of results, but this is

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not possible in experiments with real materials.19, 31, 32 Second, there are few numerical models currently

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available that can directly account for the pore scale heterogeneities that cause the instabilities that are

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important for simulations to be valid.61-63 Recent advances in X-ray imaging, however, have made it

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possible to create models using actual images from natural samples and use them to numerically

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simulate microstructure evolution in 2.5D64 or even in 3D.65, 66 Such an operation usually requires

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binarisation (segmentation) of the image data because of the limited applicability of governing

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equations that are derived from first principles. For example, Navier-Stokes equations cannot be applied

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directly for a mixed system of solid and fluids.67, 68 Such “hard segmentation” loses a large portion of the

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information contained in each pixel, which can erase the important heterogeneities that trigger the

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unstable migration of the dissolution front.69, 70 This loss of detail is especially significant when the

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imaging resolution is not sufficient to fully resolve the grains and pores in very fine grained materials,

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such as chalk. Finally, simulating microstructure evolution is a free boundary problem of partial

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differential equations and often requires prohibitive computational resources, even with binarised

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geometry.14, 48


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In this study, we used a model that reflects the submicrometre scale heterogeneities that are present in

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real samples to study the influence of dissolved CO2 on the microstructure evolution of natural porous

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materials. We focus on the geochemical aspect of the comparison, i.e. CO2 is considered an aqueous

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species that modifies the dissolution rate and the apparent solubility of calcite but does not affect the

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physical properties of fluid. In three model scenarios, we tested the effect of reactive fluids with three

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different compositions, as they flowed through the simulation domain. We used high resolution X-ray

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tomography images (25, 50 and 100 nm voxel size) to characterise the microstructure in natural chalk

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samples. Chalk was chosen as a rapidly dissolving model material. It is the dominant bedrock in

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northwest Europe, often hosting oil and gas reservoirs that have been considered for GCS. After

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computing voxel specific porosities from the 32 bit images, the greyscale datasets were implemented

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directly into numerical simulations. The simulations allowed us to differentiate between the effects of

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the initial microstructure and solution composition and to investigate their effects on microstructure

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evolution. The simulated spatial and temporal evolution of rock properties (porosity, permeability and

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surface area) provided insight into the interplay between breakthrough porosity, wormholing and

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aqueous CO2 concentrations.

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Methods and Materials

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Three chalk pieces from the Hod formation, drilled from different locations in the North Sea Basin, were

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imaged with X-ray holotomography at 29.49 keV at ID22 at the European Synchrotron Research Facility

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(ESRF).61 The 3D microstructure was reconstructed from 1999 radiographs at 25, 50 and 100 nm voxel

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resolution and processed as described by Bruns et al.70 Post reconstruction image processing included

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ring artefact removal by the method developed by Jha et al.,71 followed by iterative nonlocal means

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denoising66 and sharpening using the image deconvolution of Wang et al.72 Greyscale intensities of the

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voxels were then converted to localized porosity values using linear interpolation between the void

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phase and the carbonate phase, as identified by fitting a Gaussian mixture model.67

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The greyscale data were then imported into numerical simulations using a previously developed reactor

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network model.26 The model describes each voxel as a combination of 7 ideal reactors, i.e. each dataset

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is modelled as a network of continuously stirred tank reactors (CSTRs) interconnected by plug flow

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reactors (PFRs).40 The volume, permeability and specific surface area of each reactor were assigned

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according to the voxel size and porosity of neighbouring voxels. Hydraulic pressure drops only in the

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PFRs. Darcy flow was solved to obtain the flow field. The extent of the dissolution reaction in each

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reactor was calculated by solving the performance equations (Eqs S3-7) for all reactors in the network

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simultaneously. The microstructure was evolved in each time step by applying mass balance to update

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voxel porosity (Eqs S8-9). Equations used in the model are summarised in the SI. A comprehensive

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sensitivity analysis of the parameters used in the model has been presented in the context of entropy

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production patterns.73 More information can be found in Yang et al.26, 74 The simulation domains in this

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study are randomly chosen subvolumes of three tomographic datasets of the chalk pieces. Each

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subvolume (“sample”) consisted of 1003 32-bit voxels, corresponding to 15.625 µm3, 125.00 µm3 and

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1000.0 µm3 for the three levels of resolution. A constant flow velocity, 50 µm/s, was imposed at the


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fluid inlet and outlet. This flowrate is selected so that 1) the residence time of the fluid corresponds to a

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reactive region comparable to the size of the simulation domain and that 2) Darcy’s law is applicable on

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the voxel level.

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For each of the 40 randomly chosen samples (15 samples each from the 25 nm/pixel and 100 nm/pixel

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datasets and 10 samples from the 50 nm/pixel dataset), we developed 3 model scenarios and simulated

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the microstructural evolution with and without dissolved CO2. This led to 6 conditions (Table 1) and 240

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instances of simulation (Table S2). Scenario I represents the ambient conditions where MilliQ water,

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equilibrated with 1 bar CO2, percolated through the porous material at room temperature. In Scenario

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II, concentrated CO2 was premixed with seawater at ambient temperature and then injected into a

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porous material at intermediate CO2 partial pressure. This procedure is similar to the method used in

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the CarbFix project in Hellisheidi, Iceland.60 Scenario III represents a direct injection into deep

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formations where the supercritical CO2 mixes with brine under reservoir conditions and then migrates

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away from the injection wellbore. This scenario is most relevant to the state-of-the art practices for

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sedimentary basins. The combination of temperature (100 oC) and pressure (250 bar) used in this

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scenario are representative of that of a North Sea chalk reservoir.75 In the systems without CO2, we used

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hydrochloric acid to adjust the initial pH of the solutions. Doing so allows the solution pairs in each

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scenario to have the same pH and thus a comparable calcite dissolution rate at the fluid entrance. The

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physical differences between the solutions, e.g. the variations of fluid viscosity or solute diffusivity

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stemming from the elevated aqueous concentration of CO2, were not accounted for in our simulations.

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We used the rate of entropy production from fluid friction over the entire sample, SP (nJ K-1 s-1), to

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identify a breakthrough event. SP quantifies the pressure drop in 3D,

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S P = − ∫∫∫ ( Q ⋅∇ P ) dV T V

,

(1)


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where V indicates an integration over the entire sample, Q represents the volumetric flow rate (m3 s-1),

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P, the pressure (Pa) and T, the temperature (K). When porous media are dissolved by reactive fluids, the

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evolution of entropy production depends on the initial microstructure, the rate(s) of the dissolution

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reaction(s) and the flow rate. In addition to the breakthrough porosity, we also recorded the number of

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pore volumes required before breakthrough (# of PV, i.e., the total volume of percolated fluid divided by

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the initial pore volume of a sample), whenever an SP inflection could be identified. If a sample dissolved

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homogeneously, the breakthrough porosity was reported as the difference between its initial porosity

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and 1. The # of PV is not reported for these cases.

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Speciation calculations for the three model scenarios (ambient, premixing and direct injection; details in

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Table 1) were made with PHREEQC (Version 3) using the llnl database.76, 77 For the composition of

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seawater in Scenario II, we used data from Nordstrom et al.78 The Peng-Robinson equation of state was

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used to calculate fugacity coefficients.79 For the aqueous species concentrations in Scenarios II and III,

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we used the B-dot equation, an extension of the Debye-Hückel model.80 We used the rate law for calcite

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dissolution from Pokrovsky et al.52, 53 to approximate chalk dissolution rates. Surface speciation was

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determined from aqueous speciation results in a closed, free drift compartment, where the aqueous Ca

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concentration served as the master variable for determining both pH and the saturation index of calcite.

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The rates were then determined and compiled in Figure S1.

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Table 1. The model scenarios.78


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Results and Discussion

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Figure 2 shows two patterns of SP evolution: a wormhole pattern, where channels form in the porous

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medium, and a homogeneous pattern, where the whole domain dissolves evenly. During wormhole

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growth, SP drops rapidly one or more times, representing necking in regions with high porosity, i.e.,

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small breakthrough of fluid. Necking events are represented by local SP’ minima, the first derivative of SP

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with respect to time, and can thus be identified by inflection points (Figure 2a). Because of the structural

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heterogeneity of natural porous media, the critical porosity at which necking occurs, as well as the

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frequency of its occurrence, differs for each sample even with the same solution composition. In this

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study, we refer to the porosity at the global minimum of SP’ as the breakthrough porosity (ϕc, green

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arrow in Fig. 2a). This choice does not imply the uniqueness of the necking event during percolation.

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Figure 2d shows cross sections of a wormhole sample before and after breakthrough and the

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corresponding spatial patterns of entropy generation. Formation of flow paths with higher permeability

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lead to bypassing fluid from the less porous regions. After breakthrough, the macroscopic entropy

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production is solely determined by the significant pressure drop at the necks of pores (e.g., ϕa = 0.50).


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Figure 2.

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developing porous structures. Evolution of SP in isothermal (a) wormhole and (b) homogeneously

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dissolving systems. SP’ and SP’’ are first and second derivatives of SP with respect to percolation time. We

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used the inflection point at the global minimum of SP’ to represent the occurrence of breakthrough (e.g.,

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ϕc in a). When ϕc > 1, no inflection exists and the medium dissolves homogeneously. (c to e) Cross

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sections of porosity (ϕ) and entropy production rate (T⋅SP) from 3D simulations using GeoID 1832 (Table

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S2). Fluid flows from left to right. (c) The initial geometry. (d) A wormhole system following on from

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(c), before (ϕa = 0.30) and after (ϕa = 0.50) breakthrough. (e) A homogeneous dissolution system,

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following on from (c), at the same reaction progression (ϕb = 0.30 and ϕb = 0.50).

Typical temporal and spatial patterns of entropy generation, Sp, from fluid friction in


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Figure 2b shows a temporal pattern of SP where no abrupt pressure drop can be observed before the

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depletion of solid material. This pattern indicates a homogeneous dissolution where SP’ increases

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monotonically. The spatial patterns in Figure 2e reveal that the morphology change is not strongly

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dependent on flow direction, i.e. the entire sample behaves as a homogeneous medium, despite its

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geometric complexity, and in different regions, porosity decreases at similar rates. Because of the

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absence of a favoured flow path, no significant fluid focusing occurs.

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Figure 3 shows results of 240 simulations. In 74% of all the simulations, compared to solutions with

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hydrochloric acid, dissolved CO2 led to greater breakthrough porosity, but the conditions under which

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CO2 entered the system had an influence. For atmospheric CO2 pressure (Scenario I), the breakthrough

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porosity was higher than the HCl control in 83% of the cases. In the premixing scenario (II), 78% of the

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breakthrough with dissolved CO2 took place at a greater porosity. The percentage decreased to 63% in

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the direct inject scenario (III), where CO2 mixed with saline water under reservoir conditions. In all

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systems, fluids with CO2 required fewer pore volumes (# of PV) to breakthrough than the CO2 free

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systems. This difference in # of PV was between one and two orders of magnitude and depended only

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weakly on the initial porosity (ϕ0).

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The homogeneous boundaries (dashed lines in Fig. 3) are lines marking the difference between the

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initial porosity and a porosity of 1 (complete dissolution). They were determined from mass balance

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and decreased linearly with ϕ0. Symbols that fall on these lines represent cases where the structures

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dissolved homogeneously, i.e. where the initial geometric complexity of the simulation domain does not

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affect the position of the symbols. In these cases, the system evolution was not sensitive to the initial

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heterogeneities so could be considered more stable and predictable. The # of PV is inversely

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proportional to the initial porosity because less fluid is needed for breakthrough in a more porous

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material.


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In Figure 3, it is interesting to note that no significant resolution dependence is observed. The resolution

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of tomography typically affects the characterisation of porosity and surface area.61 However, our model

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uses greyscale tomographic data. The greyscale images preserve the local material density information

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because the X-ray absorption is averaged in each voxel, even when the resolution is low. Consequently,

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our simulations are not subject to the resolution dependence of porosity characterisation.70 Imaging

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resolution does affect surface area characterisation. However, the resolution difference (e.g., 25 nm vs

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100 nm) does not yield significantly different specific surface area values for chalk,70 especially within

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our fairly small simulation domains. On a similar note, our simulations have not accounted for either

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chemical heterogeneity or any variation of effective diffusivity within a domain. These limitations may

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contribute to the uncertainty of simulation results, but not to a significant extent given the small domain

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sizes. Another limitation of the current model is that it does not account for mineral precipitation, which

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may significantly affect breakthrough behaviours. A mathematical scheme considering both mineral

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dissolution and precipitation in evolving microstructures in imposed flow fields is a focus of our future

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works.


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Figure 3. Breakthrough porosity and the corresponding number of pore volumes of fluid (# of PV, red

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symbols). ∆ϕc (blue) represents the difference between the breakthrough porosity (ϕc) and the initial

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porosity (ϕ0) of a sample. All samples are cubes and consist of 1 million voxels. The open symbols show


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results with CO2 and the filled symbols represent CO2 free systems. The shape of the symbols represents

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the voxel size: square: 100 nm; triangle: 50 nm and circle: 25 nm. The grey dashed line near the top of

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each figure marks the homogeneous boundary, which corresponds to cases where no inflection of SP is

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observed before solid depletion (i.e., the sample dissolves homogeneously throughout the percolation).

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For points on this boundary, the number of PVs is not shown because of the difficulty in defining

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breakthrough. (a) Ambient conditions, CO2 in ultrapure water (Scenario I). (b) Premixing conditions, CO2

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dissolved in seawater (Scenario II). (c) Direct injection conditions, CO2 dissolved in saline water under

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reservoir conditions (Scenario III).

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Both the differences in the breakthrough porosity (∆ϕc) and the number of pore volumes (# of PV) can

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be explained by the observed dissolution patterns. Given the same initial sample microstructure, the

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dissolution pattern is determined by distribution of reactants in the medium. Figure 4 shows the

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decrease of fluid reactivity (measured by reaction rate and pH) as a function of cumulative surface (CS),

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‫׬‬଴ ೝ೐ೞ ܵܵ‫ݐ݀ ∙ ܣ‬, in the 3 model scenarios. ߬௥௘௦ represents the residence time of the fluid in the porous

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medium (s), and SSA, the specific surface area (m-1). The physical significance of CS is the overall surface

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area that the fluid “sees” as it travels through a sample. Therefore, the curves represent the chemical

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history of an isolated fluid parcel, an imaginary unit of flowing fluid, travelling along a streamline. Here

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we assume that the parcel only interacts with the solid along the streamline and does not exchange

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mass with other fluid parcels. As solid dissolves, pH and the saturation index (SI) in the fluid parcel

266

increase. Both effects slow the reaction. The reaction front along the streamline is the position at which

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the reactivity of the fluid parcel drops to a very small value (e.g. 10-6 mol/m2/s in Figure 4). This

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definition suggests the equivalent effect of the residence time and that of the surface area in

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determining the reaction front.

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In general, a dissolution pattern reflects a demand-supply relation for cumulative surface. When the

271

demand is high and the supply is low, a porous medium dissolves homogeneously. In contrast,

ఛ


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wormholes form when the demand is low and the supply is high. The demand is determined by the

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chemical properties of the reactive fluid, while the supply is affected by both the available geometric

274

surface area and the fluid residence time. Although specific surface area (SSA) depends exclusively on

275

the sample microstructure, the residence time (߬௥௘௦ ) depends on both the microstructure and the fluid

276

flow rate. Consequently, different dissolution patterns can coexist in a system. This is because the

277

patterns reflect the competition between the reaction front and the cumulative surface within a region

278

of interest (ROI). Given the same solution conditions, one observes a homogeneous dissolution pattern

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when the fluid leaves the ROI without depleting reactivity. This is typical for fluids with a high apparent

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mineral solubility, i.e. a high demand for CS. The reaction front of such a fluid appears only when

281

residence time is sufficiently long or when the specific surface area is large. If, in contrast, the reaction

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front is reached well before the fluid leaves the ROI, wormholes appear. The residence time can be

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increased by using a lower flow rate or by making the sample larger (i.e., a large ROI). For example,

284

Figure S2 shows that with an ROI 5 times longer in the flow direction, flow rate change alone can affect

285

the observed dissolution pattern.

286

Given sample size (i.e., ROI) and flow rate, the CS supply of a sample is fixed, and distinct dissolution

287

patterns are most likely to occur when the ROI contains only one of the two reaction fronts. This is

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demonstrated by the green shaded areas in Figure 4. These areas are left bounded by the dissolution

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front of systems without CO2 and right bounded by those with dissolved CO2. This difference between

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the positions of the dissolution fronts, defined by the apparent solubility of the solutions, is the most

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important geochemical difference between the solutions in each pair. It provides a straightforward

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explanation for the impacts of different infiltrating fluids on dissolution patterns, i.e. why the same

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domain dissolves differently with and without CO2. If the CS of a sample falls to the left of the shaded

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areas, the supply is always less than the demand and the sample dissolves homogeneously. If the CS falls

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to the right of the shaded areas, the supply is always greater than the demand and therefore wormholes


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appear regardless of whether CO2 is present. The fluid velocity in this study (50 µm/s) produced

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distributions of CS that overlapped with these shaded areas. Therefore, the widths of the shaded

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regimes explain the percentages of patterns observed in the model scenarios. In the ambient scenario

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(I), the reaction fronts with and without CO2 are farthest from each other (the shaded area is widest in

300

Figure 4a). Without CO2, the ROI is larger than the reactive volume and the wormhole pattern appears.

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With dissolved CO2, the opposite is true. As a result, in 33 of the 40 comparisons (83%), breakthrough

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porosity was higher for systems with CO2 than without. In contrast, the two reaction fronts were very

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similar in the direct injection scenario (III, Figure 4c). Only 63% of the simulated cases (25/40) showed

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that dissolved CO2 increased the breakthrough porosity compared to the cases without CO2. The

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distance between the two reaction fronts is intermediate in the premixing scenario (Figure 4b) and so is

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the percentage (78%) of increased ϕc in the presence of CO2.


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Figure 4. Decrease of calcite dissolution rate (solid lines) with cumulative surface area (‫׬‬଴ ೝ೐ೞ ܵܵ‫) ݐ݀ ∙ ܣ‬

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in a free drift system. The integral represents the overall surface area that an isolated parcel of reactive

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fluid experiences before leaving the sample. If a sample has a greater cumulative surface, it is more likely

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to show wormhole patterns (and vice versa). Shaded regimes are bounded by the dissolution fronts of the

312

two fluid compositions (with vs. without CO2). Also shown is the evolution of pH (dashed lines). (a)

ఛ


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313

Ambient conditions (Scenario I). (b) Premixing conditions (Scenario II). (c) Direct injection conditions

314 315

(Scenario III).

316

A wormhole pattern lowers the breakthrough porosity because of fluid focusing. Similarly, more

317

effective use of geometric surface on the pore scale for the dissolution reaction explains why systems

318

with dissolved CO2 need less fluid to breakthrough. Both phenomena are demonstrated in Figure 5,

319

where a case study of microstructural evolution in Scenario I is presented. The initial geometry for both

320

simulations is shown in Figure S3. The two systems start with the same percolative entropy production

321

rate because of their identical initial geometry. The isothermal SP for the system with CO2 decreases

322

gradually, indicating a homogeneous dissolution pattern. In contrast, the system without CO2 showed a

323

sharp decrease in SP near ϕ = 0.4, suggesting significant necking of pores, typical of wormhole growth. SP

324

without CO2 dropped below that with CO2 after an overall porosity of 0.45, which suggests bypassing

325

flow through a fully developed wormhole. The pressure drop after this point is determined by the shape

326

of the channel rather than the amount of solid in the pores. Also shown in Figure 5a is the evolution of

327

reactive surface area (RSA). Although the two systems start with exactly the same geometric surface

328

area, their RSA differs by almost one order of magnitude because of the rapid depletion of fluid

329

reactivity in the CO2-free system. The initial increase in RSA is characteristic of a system with infiltration

330

instability. The decrease of RSA is caused by the depletion of solid material. Although RSA in both cases

331

evolve with similar trends, the absolute difference increases with time, contributing to the difference in

332

# of PV at breakthrough.


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333 334

Figure 5. A case study of CO2 effect on microstructure evolution (simulations uid-3813 vs. uid-96443).

335

(a) Evolution of isothermal entropy generation rate (T⋅SP) and reactive surface area (RSA) with overall

336

porosity as an indicator of reaction progress. (b) Distribution of residence time multiplied by specific

337

reactive surface area (SRSA) in the context of calcite dissolution rates in Scenario I. The same shaded

338

regime is shown here, as in Figure 4a. The blue bars show the density function of fluid with CO2 and the

339

red bars, without. Also shown are microstructures, cross sections (10 ൈ 10 µm ) of pH and of reactive

340 341

surface distribution for percolation (c) with and (d) without CO2.

2


22

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342

Figures 5b to d compare the evolution of microstructure in the presence and absence of CO2. In Figure

343

5b the CS for the complete flow field is approximated by the product of specific reactive surface area

344

(SRSA, m2/m3) and residence time distribution (RTD, giving the probability density of fluid parcels with

345

residence time, τ). The same shaded regime in Figure 4a is shown. Both distributions fall entirely into

346

the regime between the two reaction fronts. As a result, the dissolution front with CO2 cannot be

347

observed in the simulation domain because it is beyond the sample size (blue bars). In contrast, the

348

dissolution front without CO2 is fully contained in the domain. This is because the sample provides

349

approximately 10 times more cumulative surface required to reach the front (the maximum distance

350

from the injection point to where the dissolution rate drops to zero, the red bars). The development of

351

the distribution at different overall porosities (ϕ = 0.3, 0.4 and 0.5) can be decomposed into two parts.

352

The morphing of their shapes reflects the redistribution of fluid as the micropore evolves. The lower

353

bound of the distribution represents the flow pathways with minimum flow resistance. As the sample

354

dissolves, the mean residence time shifts to the left, indicating the tendency of the fluid to focus in the

355

more permeable pathways. Fluid focusing during wormhole development is directly reflected in the

356

standard deviations. With CO2, the standard deviation of the cumulative surface increases from 1.4 ×

357

104 s/m for ϕ = 0.3 to 1.6 × 104 s/m for ϕ = 0.5, suggesting more uniform fluid distribution. In contrast,

358

without CO2, cumulative surface area decreased from 1.0 × 104 s/m to 6.5 × 103 s/m for the same

359

overall porosity. Therefore, much less geometric surface in the pores is in contact with reactive solution

360

during wormhole growth (e.g., spatial distribution of RSA in Figures 5c and d). The development of

361

reactive surface determines the horizontal shifting of the distribution. With dissolved CO2, the

362

maximum of RSA appears after an overall porosity of 0.5, thus increasing the mean of the distribution. In

363

contrast, the overall RSA in the CO2 free system decreases after an overall porosity of 0.35, shifting the

364

entire distribution of cumulative surface leftward.


23


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365

The spatial distributions of pH in Figure 5c and 5d provide a pore scale interpretation for the stabilised

366

migration of dissolution front on the macroscale. pH is an indicator of calcite dissolution rate. In this

367

case, both solutions started with the same rate at the fluid entrance (on the left of the cross sections,

368

corresponding to a pH of 3.91). Figure 5d shows that in a CO2-free system this rate drops much faster

369

than the rate in a CO2-buffered system, i.e. the reaction rate in the absence of CO2 is very sensitive to

370

the extent of reaction and can drop from the initial value to zero within a few voxels. This sensitivity is

371

an important in forming the loop of positive feedback leading to infiltration instability. In addition, the

372

buffering effect of dissolved CO2 also increases the area of the geometric surface that has access to

373

reactive fluid (in Fig. 5d most geometric surface is in contact with highly saturated fluid with pH greater

374

than 7). Overall, this combined effect of rate sensitivity and surface area in the presence of CO2 results

375

in breakthrough with significantly fewer PVs in all cases, even though the breakthrough porosity has

376

been increased in 74% of the cases.

377

The CO2 effect on breakthrough porosity has several implications. Mineral dissolution serves as a trigger

378

for many water-rock interactions. In GCS, dissolution provides cations for carbon mineralization and at

379

the same time, it initiates microstructure evolution that determines the mechanical strength of the

380

formation. Greater instability in the dissolution front, often associated with wormhole development, is

381

favoured when geomechanical stability is desirable. This is because lower breakthrough porosity leads

382

to flow structures that dissipate injected fluid effectively, without removing a substantial portion of solid

383

that serves as mechanical support. Our results show that dissolved CO2 has adverse effects as it

384

stabilises the migration of dissolution front. This stabilisation is reflected in an increased demand for the

385

cumulative surface in order to form wormholes. When the size of a sample is fixed, so is the supply of

386

cumulative surface. The increased demand therefore makes fluid penetration through wormholing less

387

likely. Also, the wide spread of fluid reactivity during homogeneous dissolution may increase the chance

388

of contaminant mobilisation near injection wellbores. This likelihood is related to an increased region of


24

Page 25 of 33


389

disintegrating carbonates during acidic fluid injection. In addition to sedimentary basins, the other

390

geologic settings suitable for GCS may also contain carbonates, especially in the sealing structures. Our

391

results suggest that the fractures cemented by carbonates are subject to geochemical alterations and

392

may serve as active flow pathways for CO2 leakage. The presence of CO2 may enhance the opening of

393

these pathways and dramatically shorten the time for fluid breakthrough. Furthermore, we have shown

394

that the tomography-based greyscale approach is a powerful tool to assemble geochemical and

395

microstructural knowledge in studying evolving systems. Similar approaches may be useful in other GCS

396

scenarios and in subsurface applications.

397


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Page 26 of 33

398

ASSOCIATED CONTENT

399

Supporting Information. Reactor network model details. Calcite dissolution rate based on 3 published

400

rate laws, for the 3 model scenarios. Cross sections of simulations showing the coexistence of different

401

dissolution patterns within one sample at various flow rates. The initial geometry upon which the case

402

study presented in Figure 5 was based. Tabulated results for all simulations. This material is available

403

free of charge via the Internet at http://pubs.acs.org.

404

AUTHOR INFORMATION

405

Corresponding Author

406

* [email protected]

407

Author Contributions

408

YY designed the research and conducted the simulations. SB processed the tomography data.

409

HOS and SLSS advised during the research. All authors contributed to writing the paper.

410

ACKNOWLEDGMENTS

411

We thank Heikki Suhonen at the ID22 beamline at ESRF (The European Synchrotron Radiation Facility)

412

for technical support. We are grateful to F. Engstrøm from Maersk Oil and Gas A/S for providing the

413

sample. We deeply appreciates K. Dideriksen and three anonymous reviewers’ careful review of the

414

manuscript and for the thoughtful comments. Funding for this project was provided by the Innovation

415

Fund Denmark, through the CINEMA project, the Innovation Fund Denmark and Maersk Oil and Gas A/S,

416

through the P3 project as well as the European Commission, Horizon 2020 Research and Innovation

417

Programme under the Marie Sklodowska-Curie Grant Agreement No 653241 for the Postdoctoral

418

Fellowship to YY. We thank the Danish Council for Independent Research for support for synchrotron

419

experiments through DANSCATT.


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TOC

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