Uncertainty in fault seal parameters : implications for CO 2 column height retention and storage capacity in geological CO 2 storage projects

Faults can act as barriers to fluid flow in sedimentary basins, hindering the migration of buoyant fluids in the subsurface, trapping them in reservoirs and facilitating the build-up of vertical fluid columns. The maximum height of these columns is reliant on the retention potential of the sealing fault with regards to the trapped fluid. Several different approaches for the calculation of maximum supported column height exist for hydrocarbon systems. Here, we translate these approaches to the trapping of carbon dioxide by faults and asses the impact of uncertainties in i) the wettability properties of the fault rock, 15 ii) fault rock composition, and iii) reservoir depth, on retention potential. In similarity to hydrocarbon systems, uncertainties associated with the wettability of a CO2-brine-fault rock system for a given reservoir have less of an impact on column heights than uncertainties of fault rock composition. However, the wettability of the carbon dioxide system is highly sensitive to depth, with a large variation in possible column height predicted at 1000m and 2000m depth, the likely depth range for carbon storage sites. In contrast to hydrocarbon systems higher phyllosilicate entrainment into the fault rock may reduce the amount of carbon 20 dioxide that can be securely retained. Our results show that if approaches developed for fault seal in hydrocarbon systems are translated, without modification, to carbon dioxide systems the capacity of carbon storage sites will be inaccurate, and the predicted security of storage sites erroneous.

Abstract.Faults can act as barriers to fluid flow in sedimentary basins, hindering the migration of buoyant fluids in the subsurface, trapping them in reservoirs, and facilitating the build-up of vertical fluid columns.The maximum height of these columns is reliant on the retention potential of the sealing fault with regards to the trapped fluid.Several different approaches for the calculation of maximum supported column height exist for hydrocarbon systems.Here, we translate these approaches to the trapping of carbon dioxide by faults and assess the impact of uncertainties in (i) the wettability properties of the fault rock, (ii) fault rock composition, and (iii) reservoir depth on retention potential.As with hydrocarbon systems, uncertainties associated with the wettability of a CO 2 -brine-fault rock system for a given reservoir have less of an impact on column heights than uncertainties of fault rock composition.In contrast to hydrocarbon systems, higher phyllosilicate entrainment into the fault rock may reduce the amount of carbon dioxide that can be securely retained due a preferred CO 2 wettability of clay minerals.The wettability of the carbon dioxide system is highly sensitive to depth, with a large variation in possible column height predicted at 1000 and 2000 m of depth, which is the likely depth range for carbon storage sites.Our results show that if approaches developed for fault seals in hydrocarbon systems are translated, without modification, to carbon dioxide systems the capacity of carbon storage sites will be inaccurate and the predicted security of storage sites erroneous.

Introduction
Carbon capture and storage (CCS) is one of the key technologies to mitigate the emission of anthropogenic carbon dioxide (CO 2 ) to the atmosphere (IPCC, 2005;Benson and Cole, 2008;Haszeldine, 2009;Aminu et al., 2017).Fault seal behaviour will impact geological CO 2 storage security and storage capacity calculations.For the successful widespread implementation of CCS, the long-term security of storage sites is vital and the fate of injected CO 2 needs to be understood.Faults are of major importance as potential fluid pathways for both the vertical and lateral migration of fluids in the subsurface (Bjørlykke, 1993;Sibson, 1994;Bense et al., 2013).Assessing whether a fault forms a lateral flow barrier or baffle for CO 2 is crucial to assessing the efficiency and safety of subsurface carbon storage, as faults are ubiquitous in sedimentary basins, which are the most likely CO 2 storage reservoirs, and will naturally occur close to or within storage complexes.The scale and distribution of faults depend on the type of sedimentary basin and its geological history.In particular, faults that are below the resolution of seismic surveys cannot be avoided (Maerten et al., 2006;Le Gallo, 2016).Indeed, faults occur at many of the first industrial and pilotscale CO 2 storage sites located in sedimentary basins (e.g.In Salah, Algeria, Mathieson et al., 2010;Snøvhit, Norway, Chiaramonte et al., 2011;Ketzin, Germany, Martens et al., 2012;Otway, Australia, Hortle et al., 2013).
Faults influence the flow and migration of fluids in three basic ways: (i) they can modify flow paths by juxtaposing stratigraphically distinct permeable and impermeable units against each other (Fig. 1a; Allan, 1989).(ii) The petrophysical properties of fault rocks can impede cross-fault flow between permeable units (Fig. 1b; Yielding et al., 1997;Aydin and Eyal, 2002;van der Zee and Urai, 2005), and (iii) faults can provide fault-parallel flow through fracture networks in otherwise impermeable rocks linking separate permeable units (Fig. 1c; Eichhubl et al., 2009;Dockrill and Shipton, 2010).Mechanism (i) assumes no (or minimal) permeability change in the fault zone, whereas mechanisms (ii) and (iii) require permeability reduction and increase respectively.For CO 2 storage sites the latter two mechanisms are of particular interest and are considered here.It is worth noting that these permeability changes are temporal and dynamic, and fault reactivation (Barton et al., 1995;Wiprut and Zoback, 2000) should be an important consideration in CO 2 storage projects.
Whether a fault is sealing or non-sealing is dependent on the structure and composition of the rock volume affected by faulting and the mechanics of faulting (Caine et al., 1996;Aydin, 2000;Annunziatellis et al., 2008;Faulkner et al., 2010).Caine et al. (1996) describe fault zones in siliciclastic rocks defined by a fault slip surface and core and an associated damage zone, and they considered the changes in the permeability of a fault in this context.Fault damage zones and the fault cores are interpreted as having contrasting mechanical and hydraulic properties, with the fault core often being rich in phyllosilicates, which typically have low permeability, while open fractures in the damage zone can have a substantially higher permeability than the host rock (Caine et al., 1996;Faulkner and Rutter, 2001;Guglielmi et al., 2008;Cappa, 2009).Models for fault zone characterization have evolved and describe fault zones with single high-strain cores (Chester and Logan, 1986) and containing several cores (Faulkner et al., 2003), with cores and slip surfaces at the edge of the fault zone and in the middle.Perhaps to think of it simply, one model does not fit all and the heterogeneities in natural fault systems and rocks result in unique fault geometries and evolutions, albeit with similarities and semipredictable processes.
When a fluid lighter than the pore-filling brine, such as hydrocarbons or CO 2 , is introduced into a reservoir, it will naturally migrate upwards due to the buoyancy effect until it encounters a flow barrier such as a cap rock or a fault.The fluid will accumulate underneath the flow barrier until capillary breakthrough or, less frequently, induced fracturing occurs due to the increase in pressure within the reservoir.The maximum vertical extent of the fluid underneath the seal before seal failure, often referred to as column height, is controlled by the fluid flow properties of the seal with regards to the fluid (Wiprut and Zoback, 2002).In the hydrocarbon industry, column heights are routinely calculated as they estimate the maximum amount of oil or gas that could be accumulated within a prospect (Downey, 1984).As the fluid flow properties of the seal may vary spatially, some uncertainty is associ- ated with column heights, in particular when faults with their associated heterogeneities form reservoir-bounding seals.In the context of CO 2 storage, column heights represent the maximum amount of CO 2 that could be stored within a reservoir before migration out of the reservoir.
Evidence from outcrop studies indicates that faults play an important role for the migration of CO 2 in the subsurface.Both fault-parallel migration of CO 2 in fault damage zones (Annunziatellis et al., 2008;Gilfillan et al., 2011;Kampman et al., 2012;Burnside et al., 2013;Keating et al., 2013Keating et al., , 2014;;Frery et al., 2015;Jung et al., 2015;Skurtveit et al., 2017; Figure 2. Injection of CO 2 into a faulted geological formation where the fault is sealing.The buoyancy of CO 2 creates a pressure difference at the seal and fault displayed on a pressure-depth plot for the point of the diagram labelled A-A'.Bond et al., 2017;Miocic et al., 2019) and across-fault migration have been reported (Shipton et al., 2004;Dockrill and Shipton, 2010).Studies of natural analogues for CO 2 storage sites have shown that if naturally occurring CO 2 reservoirs fail to retain column heights of CO 2 in the subsurface, this is almost exclusively due to fault leakage (Miocic et al., 2016;Roberts et al., 2017).
In this contribution we review the main methods used to predict hydrocarbon column heights for fault-bound reservoirs as applied to hydrocarbons.Placing these into a CO 2 context, we consider the implications of the assumptions used and their applicability for CO 2 storage.Stochastic simulations are used to test the impact of CO 2 -specific uncertainties on different fault seal algorithms and how these affect the predicted CO 2 column height.The results highlight the fact that fault seal parameters are poorly constrained for CO 2 and can significantly change the predicted CO 2 storage volume in fault-bounded reservoirs.Importantly, our results suggest that increasing amounts of phyllosilicates within the fault core, normally associated with increasing fault impermeability, may not necessarily increase the CO 2 column height within a reservoir.
2 Predicting fault seals for hydrocarbons and implications for CO 2 storage As they are less dense than the pore-filling brine, hydrocarbons (HCs) migrate to the top of a reservoir where they accumulate underneath a seal.The buoyancy of HCs creates a pressure difference of P at the seal-reservoir interface that is proportional to the hydrocarbon plume or column height (h) and the difference in mass density between brine (ρ w ) and HC (ρ hc ): where g is the gravitational constant, and the density of HCs is dependent on the phase (gas or oil) and the in situ pressure and temperature conditions.The trapping of HCs within rocks is controlled by capillary forces: the interfacial tension (IFT) between HCs and the brine, the wettability of the rock-mineral surface (wetting or contact angle, θ) with respect to HCs, and the structure (size) of the pore system.Capillary pressure (P c ), the pressure difference that occurs at the interface of HCs and brine, is commonly expressed as where P hc is the pressure of the HC, P brine is the pressure of the brine, and r is the pore-throat radius.P c is inversely proportional to the pore-throat radius, and thus fine-grained rocks with small pores exhibit larger P c and act as flow barriers to migrating HCs, leading to the accumulation of fluids underneath fine-grained seal rocks.
For HCs the wettability parameters IFT and θ vary with depth, and particularly large changes occur between surface conditions and conditions found at depths of 1000 m.IFT of oil increases from around 25 mN m −1 at very shallow conditions to around 40 mN m −1 for conditions commonly found in reservoirs at 2.5 km of depth (Yielding et al., 2010).For methane IFT is around 70 mN m −1 at surface conditions and decreases to 40 mN m −1 at subsurface conditions (Firoozabadi and Ramey, 1988;Watts, 1987).The contact angle for HCs is commonly reported as 0 • (Vavra et al., 1992), simplifying Eq. (2) as the cosine of 0 • is 1.However, for other fluids such as CO 2 , the wettability parameters IFT and θ are even more pressure and temperature dependent.
Due to the heterogeneous nature of rocks the size of pores within the sealing rock (fault rock or cap rock) varies to a certain degree, and thus two capillary pressures can be defined.The first is the capillary entry pressure (P e ), which controls the initial intrusion of the non-wetting fluid into the low-permeability rock and is controlled by the radius of the largest pore throat that is in contact with the reservoir rock.The second, which is of greater interest for column height calculations, is the capillary threshold pressure (P th ), sometimes called the capillary breakthrough pressure, at which the wetting phase in the low-permeability rock is displaced to such an extent that the percolation threshold is exceeded and a continuous flow path of the non-wetting phase forms across the pore network.The capillary threshold pressure is controlled by the smallest pore throat along the flow path, and thus P e < P th applies.Seal failure occurs when buoyancy pressure is larger than capillary breakthrough pressure and the maximum supported column height follows from Eqs. ( 1) and ( 2): www.solid-earth.net/10/951/2019/Solid Earth, 10, 951-967, 2019 The ability of fault-bound reservoirs to retain significant column heights thus depends on the fault rock composition, which controls the pore-throat size (r), and the wettability parameters (IFT, θ ).The composition and type of fault rocks in siliciclastic rocks are mainly influenced by (i) the composition of the wall rocks that are slipping past each other at the fault, in particular their content of fine-grained phyllosilicate clay minerals, (ii) the stress conditions at the time of faulting, and (iii) the maximum temperature that occurred in the fault zone after faulting (Yielding et al., 2010).
In clay-poor sequences (i.e.clean sandstones with less than 15 % clay), the dominant fault rock types are disaggregation zones and cataclasites (Fisher and Knipe, 1998;Sperrevik et al., 2002).Disaggregation zones form during fault slip at low confining stress during early burial and constitute grain reorganization without grain fracturing.Thus, they tend to have similar hydraulic properties as their host sandstones and do not form flow barriers (Fisher and Knipe, 2001).At deeper burial (typically > 1 km) and higher confining stresses, cataclastic processes are more significant and the resulting fractured grain fragments block the pore space, resulting in higher P th and in permeabilities on average 1 to 2 orders of magnitude lower than the host rock (Fisher and Knipe, 2001).Additionally, quartz cementation can further lower permeabilities in both disaggregation zones and cataclasites if they are subjected to post-deformation temperatures of > 90 • C, which equates to > 3 km burial depths at typical geothermal gradients (Fisher et al., 2000).
In sequences with intermediate clay content (15 %-40 % phyllosilicate), fault rocks are formed by a deformationinduced mixing of generally unfractured quartz grains and clay matrix.The resulting texture creates a fault rock with a texture termed clay-matrix gouge or phyllosilicate framework fault rock (Fisher and Knipe, 1998).Due to the clay content these fault rocks generally have high P th and low permeabilities (Gibson, 1998).
In sequences dominated by clay or shale beds (> 40 % phyllosilicate), clay-and shale-rich smears can be formed on the fault plane (Weber et al., 1978).Such smears occur during ductile deformation at depths at which the beds are not strongly consolidated and are often wedge-shaped, with the thickest smear adjacent to the source bed (Aydin and Eyal, 2002;Vrolijk et al., 2016).If faulting occurs at deeper burial depths at which the beds are lithified, shale smears can be generated by abrasional rather than ductile processes.In such cases thin shale coatings of more or less constant thickness are formed along the fault plane (Lindsay et al., 1993).Gaps within the clay and shale smears can occur at any point (Childs et al., 2007), lowering the hydrocarbon sealing capacity of the fault rock significantly.
As direct information on fault rock composition is very rare for subsurface cases, several algorithms have been developed in the past decades to estimate the probable fault rock composition at each point of the fault surface (Weber et al., 1978;Fulljames et al., 1997;Lindsay et al., 1993).The widely used shale gouge ratio (SGR) algorithm takes the average clay content of beds that slipped past any point (based on fault throw) (Yielding et al., 1997): SGR can be used as an estimate of fault rock composition; with high SGRs (> 40 %-50 %) the fault rock is assumed to be dominated by clay smears, while low SGRs (< 15 %-20 %) indicate that the fault rock is likely to be disaggregation zones or cataclasites (Yielding et al., 2010).The SGR algorithm, similar to other algorithms like the shale smear factor (Lindsay et al., 1993), the clay smear potential (Fulljames et al., 1997), and the probabilistic shale smear factor (Childs et al., 2007), which all use a combination of throw and clay bed distribution or thickness to predict the effects of clay smears, does not consider the detailed fault rock distribution and fault zone complexity observed on outcrops or at the centimetre and sub-centimetre scale (Faulkner et al., 2010;Schmatz et al., 2010).It has, however, been successfully used during the last 2 decades to predict hydrocarbon fault seals in the subsurface (Manzocchi et al., 2010;Yielding, 2012).Two different approaches to link SGR and fault rock composition estimation with fault seal prediction parameters such as capillary threshold pressure have been developed over the years: (1) using known sealing faults to constrain relationships between SGR and HC column height and/or across fault pressure differences (Bretan et al., 2003;Yielding et al., 2010) and (2) measuring the capillary threshold pressures and clay content of micro-faults and correlating these with SGR, assuming that SGR is equivalent to the clay content of the fault rock (Sperrevik et al., 2002).The first approach has been fine-tuned with datasets from sedimentary basins around the world, while equations linking capillary pressure and clay content in the second approach are derived from best-fit relationships of samples mainly from the North Sea.
with C = 0.5 for burial depths of less than 3 km, C = 0.25 for burial depths of 3.0-3.5 km, and C = 0 for burial depths greater than 3.5 km.
(for burial depths of less than 3 km) for burial depths of more than 3.5 km P thS is the Hg-air fault rock threshold pressure and k f the fault rock permeability: where z max is the maximum burial depth and z f is the depth at the time of faulting.These three algorithms (Eqs.5-9) are widely applied to predict fault seals.In combination with Eq. ( 3) they can be used to calculate maximum fluid-column heights.While the Bretan et al. (2003) algorithm (Eq.5) assumes an exponential correlation between the fault rock clay content (FRCC) and the capillary threshold pressure, Yielding's (2012) algorithm (Eqs.6 and 7) is based on the assumption of a linear correlation between these variables.The Sperrevik et al. (2002) (Eqs.8 and 9) algorithm also assumes an exponential relationship but tends to predict lower capillary threshold pressures than the Bretan et al. (2003) algorithm (Fig. 3).Note that reported capillary pressures are typically measured in Hg-air-rock systems, which are often used to experimentally derive capillary pressures.In order to convert them to fluid-brine-rock systems, the following equation is used: where P is capillary pressure, IFT interfacial tension, and θ contact angle; indices indicate the fluid system.This equation highlights the fact that uncertainties of the wettability parameters can strongly influence capillary breakthrough pressures derived from mercury injection experiments (Heath et al., 2012;Lahann et al., 2014;Busch and Amann-Hildenbrand, 2013).Thus, the results of the three algorithms are not necessarily directly comparable.Here we apply these equations (Eqs.5-10) to a CO 2 storage framework to test their veracity and analyse the revealed associated uncertainties.
3 Fault seal algorithms for CO 2 In contrast to the HC-brine-rock system, the wettability of the CO 2 -brine-rock system is strongly controlled by temperature, pressure, and mineralogy (Iglauer et al., 2015b;Zhou et al., 2017).As a result, a fault seal that supports a certain hydrocarbon column height may not necessarily support a similar amount of CO 2 (Naylor et al., 2011).This highlights the need to have a good understanding of the CO 2 wettability in the subsurface in order to establish the security of carbon storage sites.
The IFT of the CO 2 -brine system is temperature, pressure, and salinity dependent.It decreases from ∼ 72 to 25 mN m −1 as pressure increases from atmospheric to 6.4 MPa and plateaus at around 25 ± 5 mN m −1 for supercritical CO 2 conditions and deionized water (Kvamme et al., 2007;Chiquet et al., 2007;Espinoza and Santamarina, 2010).High salinity levels, as often found in the brine filling deep saline formations, can increase the interfacial tension by up to 10 mN m −1 (Espinoza and Santamarina, 2010;Saraji et al., 2014).Additionally, CO 2 dissolved in the brine may decrease IFT (Nomeli and Riaz, 2017), as may impurities such as CH 4 or SO 2 (Ren et al., 2000;Saraji et al., 2014).Thus, for the conditions most likely for storage reservoirs -supercritical CO 2 at depths greater than 1200 m with saline brine (Miocic et al., 2016) -CO 2 -brine IFT will be of the order of 35 ± 5 mN m −1 (Fig. 4), similar to the range recently illustrated by Iglauer (2018).
The contact angle formed by the CO 2 -brine interface on mineral surfaces varies strongly and is dependent on pressure and temperature conditions, mineral type, the presence of organic matter, and the wetting phase (Sarmadivaleh et al., 2015;Espinoza and Santamarina, 2017).On water-wet minerals, the contact angle (θ ) is about 40 • on amorphous silica and calcite surfaces, θ ∼ 40 to 85 • on mica, θ ∼ 50 to 120 • on coal, and θ ∼ 8 to 30 • on organic shale surfaces, while on oil-wet amorphous silica θ ∼ 85 to 95 • (Chi et al., 1988;Chiquet et al., 2007;Chalbaud et al., 2009;Espinoza andSantamarina, 2010, 2017;Iglauer et al., 2015b;Arif et al., 2016;Guiltinan et al., 2017).With pressure rising from   2) with a pore-throat diameter of 100 nm, a typical value for organic-poor shales (Dong et al., 2017), and a CO 2 density of 630 kg m −3 , correlating to a depth of about 1500 m. rock composition (FRC) described on commonly used fault seal algorithms when applied to CO 2 , we run stochastic models in which the input parameters follow probability distributions (i.e. have uncertainties associated).We use a Markov chain Monte Carlo (MCMO) approach, which samples the probability distributions of input parameters (Gilks et al., 1996), to statistically analyse the effect of uncertainties in wettability and fault rock clay content (based on SGR) on the amount of CO 2 that can be securely stored in a fault-bound reservoir.The input parameters, which are all treated as independent, are derived from the published data described: empirical values from Iglauer (2018) 2014).These parameters follow a normal distribution described by the mean and the standard deviation (σ ) as seen in Table 1 and are randomly sampled 20 000 times for each model run.Capillary threshold pressures for fault seals are calculated by using Eqs.( 5) to (9) (the algorithms by Bretan et al., 2003, Yielding, 2010, and Sperrevik et al., 2002); these are then converted to the CO 2 -brine system using Eq. ( 10), and subsequently column heights are calculated assuming a pore-throat size of 100 nm (Eq.3).Note that Eqs. ( 5) to (7) result in maximum column heights (or minimal wettability), while Eqs.( 8)-( 9) give an average column height.The resulting column heights also follow a probability distribution (Table 2).
Two theoretical cases are modelled: reservoir A is located at 1000 m of depth with a temperature of 45 • C, a pressure of 10.2 MPa, and a resultant CO 2 density of 515 Kg m −3 .
Table 1.Table listing the input parameters for the MCMO modelling.Reservoir A and B refer to the two theoretical reservoirs described in the text, the approach refers to the algorithm used (see text), and the model indicates whether uncertainties in wettability parameters (Wet), fault rock composition (FRC), and/or combined uncertainties (Comb) are modelled.IFT is the interfacial tension (mN m −1 ), CA the contact angle, SGR the shale gouge ratio as a parameter for fault rock composition, and PTS the pore-throat size in nanometres; σ is the standard deviation and describes the shape of the input normal distribution.Iglauer (2018).For models in which the approaches by Bretan et al. (2003) and Yielding (2010) are used, these correspond to the mean least wettability.For each of the reservoirs 27 models were run with 20 000 iterations each, 9 models for each of the approaches that link SGR to fault rock threshold pressure (Eqs.5 to 9).Of these nine models three simulate varying uncertainties in CA and IFT of the fault rock (models Wet1 to Wet3), three have varying uncertainties in FRC (models FRC1 to FRC3), and three models calculate column heights based on uncertainties of FRC and fault rock wettability (models Comb1 to Comb3).Five additional models investigate the impact FRC (and associated uncertainties) and the size of the pore throat have on supported column heights for reservoir A using Eq. ( 3).Model nos.55 to 57 simulate a quartz-rich fault rock (95 % of IFT within 38 ± 2 mN m −1 , 95 % of CA within 40 ± 5 • ), a quartz-phyllosilicate mixture (95 % of IFT within 38 ± 2 mN m −1 , 95 % of CA within 60 ± 5 • ), and a phyllosilicaterich fault rock (95 % of IFT within 35 ± 2 mN m −1 , 95 % of CA within 75 ± 5 • ) with pore-throat sizes of 100 ± 10 nm (95 % interval).Model nos.58 and 59 adopt pore-throat sizes reported by Gibson (1998) for outcrop and core samples of fault zones: the pore-throat diameters of the quartzphyllosilicate mixture of model no.58 are intermediate (95 % within 50±5 nm), and for the phyllosilicate-rich fault rock of model no.57 they are low (95 % within 10 ± 1 nm).

Model
The results of the MCMO models highlight the differences between the three approaches that link FRC to fault rock threshold pressure with the approach of Sperrevik et al. (2002), generally resulting in lower column heights than the approaches of Bretan et al. (2003) and Yielding (2012) for both reservoir A and B (Table 2, Figs. 5 and 6).Uncertainties in the wettability of fault rocks (CA, IFT) have less of an impact on the supported column height distributions than uncertainties in FRC.
For reservoir A, the models which are used to investigate the impact of uncertainties in wettability (Wet1-Wet3) have column heights ranging from 14.8 ± 0.9 to 14.6 ± 3.6 m (after Sperrevik et al., 2002), from 73 ± 4 to 72 ± 18 m (after Bretan et al., 2003), and from 111 ± 6 to 110 ± 27 m (after Yielding, 2012).Models which simulate uncertainties in FRC in the same reservoir have column heights ranging from 16 ± 7 m, from 74 ± 14 to 95 ± 80 m, and from 111 ± 14 to 111 ± 55 m for the three different approaches, respectively.Models which combine the uncertainties of fault rock wettability and FRC (Comb1-Comb3) have an even wider spread in column height distributions (Fig. 5c, f, i).For reservoir B, all models show a similar pattern to those of reservoir A (Fig. 6); however, the mean supported column heights are only about 60 % of those for reservoir A due to the differences in fault rock wettability parameters (Tables 1, 2).This illustrates the fact that conditions in deeper reservoirs may lead to lower column heights.
The results of models 55 to 59 (Fig. 7) illustrate the impact of both pore-throat size and FRC on the supported column height.For conditions similar to reservoir A, a quartzrich fault rock with a pore-throat size of 100 nm (model 55) can support a column height of 118 ± 13 m, while a mixture of quartz and phyllosilicates with the same pore-throat size (model 56) is likely to support 77±10 m, and a phyllosilicaterich fault rock (model 57) can support a column height of 40 ± 8 m.For a smaller pore-throat size of 50 nm a mixture of quartz and phyllosilicates (model 58) can support a column height of 153±20 m, and a phyllosilicate-rich fault rock with a pore-throat size of 10 nm can on average support a column height of 398 ± 78 m.Note that the tails of the model distributions increase from model 55 to model 59.Based on the change in pore-throat sizes alone, the column heights of model 59 should be 1 order of magnitude larger than those of model 55.  (a, d, g) The impact of uncertainties in fault rock wettability, (b, e, h) the impact of uncertainties in fault rock clay content (SGR), and (c, f, i) the impact of combined uncertainties on column heights.Each row uses a different approach to link fault rock composition to threshold pressure.Uncertainty increases from dark-to light-coloured models (Table 1).For all models N = 20 000.
www.solid-earth.net/10/951/2019/Solid Earth, 10, 951-967, 2019 Figure 6.Density distribution of column heights of models for reservoir B (models 28 to 54).(a, d, g) The impact of uncertainties in fault rock wettability, (b, e, h) the impact of uncertainties in fault rock clay content (SGR), and (c, f, i) the impact of combined uncertainties on column heights.Each row uses a different approach to link fault rock composition to threshold pressure.Uncertainty increases from dark-to light-coloured models (Table 1).For all models N = 20 000.If the pore size decreases with increasing phyllosilicate content, the column height increases with increasing phyllosilicate content.However, the increase in column heights is significantly less than the 1 order of magnitude expected due to the change in pore-throat size.This is due to CO 2 wettability depending on fault rock composition, which results in phyllosilicate-rich fault rocks supporting a lower column than quartz-rich fault rocks with a similar pore throat.Column height is calculated using Eq. ( 3) and a CO 2 density of 515 kg m −3 (as reservoir A).For all five models N = 20 000.

Discussion
The results of the stochastic modelling illustrate that even small uncertainties in fault seal parameters can introduce significant variations and spread in the amount of CO 2 predicted to be securely stored within a fault-bound siliciclastic reservoir.In particular, uncertainties in fault rock composition result in a wider range of possible column heights when compared to uncertainties of CO 2 -brine-rock wetta-bility.The outcomes also illustrate large differences between the algorithms used to calculate column heights.Additionally, phyllosilicate-rich fault rocks can support lower CO 2 column heights than quartz-rich fault rocks if a constant pore-throat radius is assumed.The use of SGR as a proxy for fault rock composition, as in our study, is widely accepted and commonly applied for hydrocarbon reservoirs (Fristad et al., 1997;Lyon et al., 2005).The algorithm linking SGR to fault zone threshold pressure and column height is a critical step in fault seal studies, and our results show that different algorithms (Eqs.5-9) predict different CO 2 column heights.This is in line with other works comparing the three algorithms (Bretan, 2016) and is due to the sensitivity of the Sperrevik algorithm to geological history (faulting depth and maximum burial).The algorithm has been developed from samples of North Sea cores from depths ranging from 2000 to 4500 m.The approaches by Bretan et al. (2003) and Yielding (2012) are both used to calculate the maximum threshold pressure, and the approach by Sperrevik et al. (2002) gives an average threshold pressure.Thus, when used for a carbon storage capacity assessment, the column heights calculated with the algorithms of Bretan et al. (2003) and Yielding (2012) would illustrate the maximum potential storage capacity, while the column heights resulting from the Sperrevik et al. (2002) algorithm would likely represent average capacities.
The high impact of SGR on column heights is predictable as SGR is a proxy for the amount of phyllosilicates incorporated into the fault rock, and our results are in line with other work which highlights the fact that good prediction of fault rock composition is crucial for hydrocarbon column height prediction (Fisher and Knipe, 2001;Yielding et al., 2010).When SGR is used for predicting fault seals in a hydrocarbon context, higher SGR values coincide with higher contained column heights, as high-SGR-value fault rocks have a higher phyllosilicate content (and hence smaller pore-throat radii).Our results show that for a CO 2 fluid the decrease in pore-throat size due to a higher phyllosilicate content results in lower column heights than anticipated.The fact that for constant pore-throat sizes phyllosilicate-rich fault rocks can only support lower column heights than quartz-rich fault rocks (Fig. 7) highlights the difference between the wettability of the CO 2 -brine-rock system and the wettability of the HC-brine-rock system at subsurface conditions.Phyllosilicate minerals have contact angles of up to 85 • , while quartz has a contact angle around 40 • (Espinoza and Santamarina, 2017;Iglauer et al., 2015a).Increasing the content of phyllosilicates in the fault rock (increasing FRCC and SGR) effectively increases the contact angle, which directly reduces the capillary threshold pressure as the cosine of the contact angles approaches zero (Eq.2).This indicates that an increase in phyllosilicates in the fault rock may not increase the amount CO 2 that can be retained by the fault to the same degree as for hydrocarbons.This calls into question whether algorithms such as SGR, which assume that higher phyllosilicate content in fault gouges equal higher sealing properties, can be used to effectively predict CO 2 fault seals.We suggest that introducing pore-throat sizes into fault seal algorithms may result in more reasonable column height predictions for CO 2 systems.
The results of our stochastic models also illustrate the impact of depth on the wettability of the CO 2 -brine-rock system, with the deeper faulted reservoir scenario (at a depth of 1800 m) holding significantly lower column heights than the shallower reservoir (depth of 1000 m).This is in contrast to fault seals for hydrocarbons for which faults can retain higher fluid columns for similar SGR values in deeper reservoirs (Yielding, 2012).The influence of pressure on the sealing capacity of fault rocks for CO 2 has direct implications for the selection of carbon storage sites, with shallow reservoirs being able to retain a higher column of CO 2 than deeper reser-voirs (Fig. 8).Note that minimum CO 2 storage site depths are around 1000 m and are governed by the CO 2 state and density (Miocic et al., 2016).
Non-sealing faults are often undesired in a hydrocarbon exploration context, but this is not necessarily true in the case of carbon storage sites.Here, sealing faults may actually reduce the amount of CO 2 that can be safely stored within a reservoir as the lateral migration of the CO 2 plume is hindered and pressure build-up may occur (Chiaramonte et al., 2015;Vilarrasa et al., 2017).If fault rocks that are sealing for hydrocarbons are not necessarily sealing for CO 2 , as the results of our study suggest, faulted abandoned hydrocarbon reservoirs could form good carbon storage sites as long as no vertical migration of CO 2 along the fault occurs.

Conclusions
Fault seal modelling is associated with significant uncertainties arising from the limited subsurface data, resolution of seismic data, faulting mechanics and fault zone structure, spatial and temporal variations, and overall limitations of the scalability of observations.Nonetheless, several models to estimate the sealing properties of faults have been developed and successfully used to predict hydrocarbon column heights.However, for the fault seal modelling of CO 2 reservoirs the wettability of the CO 2 -brine-rock system introduces additional uncertainties and reduces the amount of CO 2 that can be securely stored within a reservoir compared to hydrocarbons.
In this study uncertainties in fault rock composition, as well as uncertainties of how CO 2 fluid-rock wettability properties of the reservoir change with depth, have a stronger impact on CO 2 column heights than uncertainties in wettability.Importantly, a higher phyllosilicate content within the fault rock at a given pore-throat size, which is commonly assumed to increase the threshold pressure, may reduce the threshold pressure due to increased CO 2 -wetting behaviour with such minerals.In particular, deep reservoirs and high pressures seem to lead to lower column heights when compared to the equivalent predicted hydrocarbon column height.
To ensure CO 2 storage security, appropriate site characterization for storage sites is critical.Faults of all scales must be identified and their seal potential modelled with a range of uncertainties, including the fault rock composition and wettability.During storage operations fault seal potential predictions could be refined by high-resolution monitoring and the development of databases similar to those used (Bretan et al., 2003;Yielding et al., 2010) to predicted hydrocarbon column heights.While fault seals may impact storage capacities, it should be kept in mind that lateral migration through non-sealing faults can increase storage capacity.

Figure 1 .
Figure 1.Impact of faults on plume migration in a CO 2 storage site.(a) Juxtaposition of the permeable storage formation and impermeable cap rocks generating a juxtaposition seal.(b) Impermeable fault rocks impede fluid flow within the storage formation (fault rock seal).(c) Fault-parallel, vertical migration through fracture networks bypasses the cap rock.

Figure 3 .
Figure3.Plot of SGR content of fault rocks and the resulting column heights for the algorithms ofBretan et al. (2003),Sperrevik et al. (2002), andYielding (2012) for different fluid types for a reservoir at a depth of 1000 m.Assumes contact angles of 50 • for CO 2 and 0 • for methane and oil, with interfacial tensions of 38 mN m −1 for the CO 2 -brine-rock system, 60 mN m −1 for the methane-brine-rock system, and 30 mN m −1 for the oil-brine-rock system.Fluid densities are 515 kg m −3 for CO 2 , 75 kg m −3 for methane, 800 kg m −3 for oil, and 1035 kg m −3 for brine.

Figure 4 .
Figure 4.Figure showing the influence of contact angle (θ ) and interfacial tension (IFT) on supported CO 2 column height.Black lines are contours at 50 m intervals.The full range of IFT and θ shown here has been reported for CO 2 -brine-rock systems; the dashed rectangle indicates conditions likely for geological storage.Column height calculated using Eqs.(1) and (2) with a pore-throat diameter of 100 nm, a typical value for organic-poor shales(Dong et al., 2017), and a CO 2 density of 630 kg m −3 , correlating to a depth of about 1500 m.

Figure 5 .
Figure5.Density distribution of column heights of models for reservoir A (models 1 to 27).(a, d, g) The impact of uncertainties in fault rock wettability, (b, e, h) the impact of uncertainties in fault rock clay content (SGR), and (c, f, i) the impact of combined uncertainties on column heights.Each row uses a different approach to link fault rock composition to threshold pressure.Uncertainty increases from dark-to light-coloured models (Table1).For all models N = 20 000.

Figure 7 .
Figure7.The density distribution of column heights of models 55 to 59 illustrates the role of fault rock composition and porethroat size on supported column heights.If the pore-throat size is the same, phyllosilicate-rich fault rocks can only support low column heights compared to quartz-rich fault rocks.If the pore size decreases with increasing phyllosilicate content, the column height increases with increasing phyllosilicate content.However, the increase in column heights is significantly less than the 1 order of magnitude expected due to the change in pore-throat size.This is due to CO 2 wettability depending on fault rock composition, which results in phyllosilicate-rich fault rocks supporting a lower column than quartz-rich fault rocks with a similar pore throat.Column height is calculated using Eq.(3) and a CO 2 density of 515 kg m −3 (as reservoir A).For all five models N = 20 000.

Figure 8 .
Figure 8. Supported column heights of a fault with a phyllosilicate-rich fault rock (SGR = 40) depending on the depth of the fault and the trapped fluid.For CO 2 the column height decreases with depth (after an optimum at ∼ 1000 m of depth), while methane column heights increase with depth.Based on depth-wettability relationships for CO 2 by Iglauer (2018).

Table 1 .
Continued.C, a pressure of 18.36 MPa, and a resultant CO 2 density of 617 Kg m −3 .Both reservoirs have a brine density of 1035 Kg m −3 , a maximum burial depth of 2000 m, and a faulting depth of 1500 m.The normal distributions of the input parameters (FRC (SGR) and wettability of the fault rock (CA, IFT)) for the MCMO modelling are listed in Table1.IFTs of 38 and 34 mN m −1 and CAs of 50 and 70 • are used as mean wettability for the MCMO models of reservoir A and reservoir B, respectively, based on the IFT-depth and CAdepth relationships of www.solid-earth.net/10/951/2019/Solid Earth, 10, 951-967, 2019

Table 2 .
Table showing the results of the MCMO models defined in Table 1.