Hydromechanical modelling to evaluate impact of fault structure on CO2 migration in stacked storage system

International Journal of Greenhouse Gas Control 93 (2020) 102886

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Hydromechanical modelling to evaluate impact of fault structure on CO2 migration in stacked storage system

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Muhammad Zulqarnain, Mehdi Zeidouni*, Richard G. Hughes Louisiana State University, Baton Rouge, LA, USA

ARTICLE INFO

ABSTRACT

Keywords: Fault heterogeneities Shale smear factor Local capillary trapping Fault leakage rates CO2 storage integrity

Faulting processes produce a complex fault damage zone (FDZ) having permeability variations over several orders of magnitude within a very short distance. In this study we use an example normal fault system from a depleted oil field in southern Louisiana with multiple stacked sand beds along the fault structure. Geostatistical techniques are used to introduce heterogeneities of several orders of magnitude over very short distances that honor the across- and along-fault architecture of the system. A total of 15 cases are simulated to account for the impact of a fragmented core, an intact core and a naturally fractured core on inter-sand leakage rates. The presented results show the complex nature of CO2 migration within the fault structure, where an interplay between overcoming the fault core’s high capillary entry pressure and stress propagation in the vertical direction dictates the leakage direction and rates. It is observed that hydromechanical evolution of fracture flow properties may result in significant leakage from the storage zone. In one case with small caprock thickness, a loss of 18% of the total injected mass is observed. The results presented highlight some unique features of representative fault related leakage in stacked sand systems and thus will be beneficial for storage integrity analysis in these systems.

1. Introduction Due to their potential to act as barriers and conduits to flow, faults are associated with some of the largest hydrocarbon accumulations in the US Gulf of Mexico. Faults can act as flow pathways allowing hydrocarbon migration from the source rock to the reservoir rock. Also, faults can act as barriers to flow and - in combination with other structural/stratigraphic traps - can inhibit the upward migration of hydrocarbons enabling the economic accumulation of the hydrocarbons in a reservoir. Therefore, the study of the behavior of faults to act as a barrier or fluid conduit becomes an essential element for the success of any long-term CO2 storage project. It has been observed in some hydrocarbon reservoirs that faults that were initially acting as barriers started acting as conduits when the pressure differential across the fault was increased due to hydrocarbon production (Molina and Zeidouni, 2018; Yielding et al., 1997). Therefore, fault-related fluid flow is essentially four dimensional in nature with the added dimension of time (Nicol et al., 2016). Due to the faulting process, the fault damage zones are the zones of highly fractured rock along the fault trace (central core), and extreme heterogeneities may exist in the fault damage zones over very small spatial distances (Choi et al., 2016; Nicol et al., 2016). Therefore, the study of fault structure and its role in fluid migration across the fault, laterally along the fault and vertically up along the ⁎

fault is an important element of the risk assessment process for potential CO2 storage formations with existing faults (Nicol et al., 2016). The sealing capability across a fault results from the sand/shale juxtaposition or by the creation of a very low permeability fault core in an originally highly permeable host rock (Cilona et al., 2015; Yielding et al., 1997). This process has resulted in reservoir compartmentalization for some of the hydrocarbon bearing formations (Fisher and Knipe, 2001). When acting as fluid conduits faults can transmit fluids laterally (along and/or across the fault) and vertically (Faulkner et al., 2010). The capacity of a fault to transmit fluids vertically results from its damage zone architecture along different sand/shale host intervals that it intersects, pore pressure distribution due to heterogeneities, available pressure gradients, interconnected network of fractures and the amount of injected fluids (Nicol et al., 2016). In a single sand interval alongfault permeability is generally orders of magnitudes larger than the across-fault permeability. However, for shale intervals intersected by a fault this may not be the case (Nicol et al., 2016). Some of the fractures in the FDZ of shale-host intervals may close while under stress, as shales have a tendency toward plastic deformation. Fault-related springs, natural hydrocarbon seeps, and leakage of CO2 from the earth’s mantle demonstrate the capability of faults to act as vertical fluid conduits (Jung et al., 2014). Therefore, investigating the implications of fault structure for fluid migration across, along, and up the fault is crucial in

Corresponding author. E-mail address: [email protected] (M. Zeidouni).

https://doi.org/10.1016/j.ijggc.2019.102886 Received 20 March 2019; Received in revised form 20 October 2019; Accepted 26 October 2019 1750-5836/ © 2019 Elsevier Ltd. All rights reserved.

International Journal of Greenhouse Gas Control 93 (2020) 102886

M. Zulqarnain, et al.

including host-zone lithology, host-zone permeability, shale smearing factor, nature of fractures, and deformation bands. In low porosity rocks, the fault permeability is generally controlled by fractures and their connectivity (Faulkner et al., 2010). While in high porosity host zones, the permeability is additionally altered by the presence of low permeability deformation bands. Therefore, the permeability of the damage zone in sand-host zones may be higher or lower than the host zone permeability depending on the conditions of the faulting process, strain localization and burial depth. The permeability of the FDZ in shale-host damage zones are generally higher than the original shalehost zone permeability before the faulting process. For high throw/bed thickness ratios, the intrusion of shale from adjacent shale beds (shale smear) may add another complexity resulting in permeability reduction for sand-host zones. Juxtaposition of a sand interval against a shale interval will also impact the permeability across the fault plane. Therefore, a fault generally presents highly anisotropic flow behavior impeding across-fault flow while facilitating along-fault flow (Bense et al., 2013). Shale smear factor and shale gouge ratio (Vrolijk et al., 2016; Yielding et al., 1997) are traditionally used to evaluate the across-fault flow potential. In Section 2, a representative fault damage configuration based on the throw to sand bed thickness ratio is presented, alongside the assignment of representative FDZ properties. Hydromechanical coupling and assignment of representative rock properties are presented in Section 2.1. In Section 2.2, a brief introduction of the model used for stress dependent FDZ permeability variations and assignment of representative properties is presented. In Section 3, simulations results for 15 cases are presented. Results of cases 1–5 are presented in Section 3.1. In these cases the low permeability core in sand-host FDZ is fragmented. The results for cases 6–10 with a continuous central low permeability core in sand-host FDZ are presented in Section 3.2. The results of hydromechanical coupling and stress dependent FDZ permeability alterations are presented in Section 3.3. Discussion and conclusions are presented in Sections 4 and 5 respectively.

Fig. 1. Simple conceptual diagram of the fault structure.

risk assessment of CO2 storage in a given site. A two-zone model approach can be used to idealize the complex fault damage zone internal structure, where a central thin core and surrounding damage zone are present as shown in Fig. 1. The central core is the result of highly localized straining and shearing, which generally consists of a number of slip surfaces and fault rocks such as gouges, cataclasites and breccias (Faulkner et al., 2010). The adjacent damage zones generally consist of secondary faults, fractures, veins and fault related folds. In high porosity sandstones, strain localization due to faulting can also create additional low permeability deformation bands in the damaged zone. Due to the rock properties, the thickness of the fault damage zone in sand-host intervals may be larger than the thickness in shale intervals, as the former is more susceptible to deform and fracture to accommodate stress changes. Therefore, the resulting fault zone structures depend on the burial depth, the host rock type (sand/shale), the tectonic environment (normal or reverse faulting) and the magnitude of displacement or throw and the cementation process. In low porosity rocks or under low confining stresses, the damage zone consists of dilatant fractures (Balsamo et al., 2012), while compaction bands or cataclastic deformation bands are developed in high porosity sandstones (Alikarami et al., 2013; Bense et al., 2013; Bond et al., 2017; Caine et al., 1996; Cilona et al., 2015; Torabi and Berg, 2011; Yielding et al., 1997). The damage zone permeability depends on a number of factors

2. Modelling fluid flow through the fault Based on general characteristics reported in the literature (Alikarami et al., 2013; Bense et al., 2013; Caine et al., 1996; Childs et al., 2009; Choi et al., 2016; Faulkner et al., 2010; Lindsay et al., 2009; Vrolijk et al., 2016), a representative fault damage zone (FDZ)

Fig. 2. Permeability distribution in a representative fault damage zone. (a) Entire model, (b) sands 3 and 4 with fragmented core and (c) sands 3 and 4 with intact core. 2

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Table 1 Geostatistical parameters used to generate different facies in the FDZ. Distance from core center (m)

0-11.5 11.5-22.9

Variogram Type

Exponential Exponential

Method

Nugget

Sequential Indicator Simulation Sequential Indicator Simulation

Table 2 Permeability assigned to different components of a fault’s structure. X-direction Permeability (md)

Reference

Sand host zone

611 2 × 10 0.0611 61.1 0.0611-611

Zulqarnain et al. (2017); Timur (1968) Mbia et al. (2014) Ballas et al. (2015) Fossen et al. (2015) Nicol et al. (2016)

0.00611-0.611

Nicol et al. (2016)

Shale host zone Fault core zone Compaction bands FDZ permeability in sand host zone FDZ permeability in shale host zone

−7

Across

Along

Up-fault

3.5 305

3.5 30.5

3.5 3.5

Dip Angle

Azimuth Angle

60 60

48 48

interval permeability (2 × 10−7 md) to accommodate the structural changes that take place during faulting processes which may enhance the permeability of these intervals (Nicol et al. (2016). The reported permeabilities are in the X-direction or perpendicular to the fault plane. In order to account for the permeability anisotropy caused by the geological depositional setting the permeability in the Zdirection or up fault is taken as 20% of the X-direction permeability. The burial depth to the top sand in the simulation model is 1358 m and that of the lower-most sand is 2252 m, shown in Fig. 2. Initial pressure in each sand/shale interval including the FDZ is based on the normal hydrostatic gradient 10.52 kPa/m (0.465 psi/ft) (Zulqarnain et al., 2017). Initially the sand and shale intervals are fully saturated with brine having bulk modulus of approximately 2.34 GPa. The density of formation brine and injected CO2 versus depth are shown in Fig. A1(a) in the Appendix A. The initial formation pressure and the lithopressure variation with depth are shown Fig. A1(b) in the Appendix A. The temperature variation with depth is shown in Fig. A1(c) in the appendix. The dissolution of CO2 into brine is modelled in these set of simulations. The salinity of formation brine was calculated from a well log for the lower-most sand interval to be 122,500 ppm. For upper sand intervals the same salinity value was used. The sands in the simulation model have a width of 30.5 m in the Ydirection with no-flow boundary condition. This makes sure that the injected CO2 is directed to the FDZ. A no-flow boundary condition is applied to all shale intervals in the outermost grid blocks in the X-direction. A no-flow boundary condition is also applied to the injection sand at the outermost grid block on the well side in the X-direction. There is also a no-flow boundary preventing downward flow from sand 1. All other boundaries act as open boundaries by the application of large volume grid blocks on the outer-most cells in each interval. An additional layer of cells is also created at sand tops and bottoms and on the sides of the FDZ in shale intervals in the X-direction to accommodate dilation/contraction that occurs during the hydromechanical modelling. The volume of these cells is increased to 100 times that of the adjacent cells inside the simulation model to handle the dilation/ contraction. These cells are assigned shale properties and are shown as hollow in Fig. 2. A rigid boundary condition is applied at the bottom of sand 1. The rock behavior was analyzed only in the elastic region, by specifying a very high value of cohesion in a Mohr-Coulomb model. The “host grid” option in CMG-GEM was used for the geomechanical grid. Under this option the geomechanics grid is constructed such that it exactly overlays the grid of the host fluid-flow simulator at initial conditions. Therefore the flow and geomechanical grids have the same initial dimensions in these simulations. As covered in detail in Section 3, 5 cases are initially modelled to investigate fluid flow in the fault with fragmented core. In case 1, the injector is located in the lower-most sand in the simulation model, designated as Sand 1 (Fig. 2). For cases 2, 3, 4 and 5 the injector is located in Sand 2, Sand 3, Sand 4 and Sand 5 respectively. A constant CO2 injection rate of 305 m3/day was specified for all cases, which, depending upon the pressure in the injection zone, translates to 21–25 tons/day. This is an equivalent rate based on the flux seen at the fault-section from a hypothetical well with 0.3 Mt/year injection rate, situated 214 m away from the fault. The injection well in the rectangular simulation setup is placed next to the FDZ to quickly expose the fault to injected CO2 to save simulation time by eliminating the need to

based on the representative characteristics of faults in a depleted oil field in south Louisiana is generated, shown in Fig. 2. The geostatistical technique and parameters used to create the representative FDZ are reported in Table 1. A commercially available software Petrel (Petrel, 2014) was used to generate the FDZ. In order to create a more heterogeneous zone around the core, two zones were defined as shown in Table 1. In this way a relatively higher damage localization in the FDZ was created around the core which decreases away from the core center. For the FDZ, a thickness to throw ratio of 1 is used (Childs et al., 2009) which results in a thickness of nearly 46 m for sand-host intervals, while for shalehost intervals the ratio is 0.5. A majority of the data observed by Childs et al. (2009) suggest even smaller values. As the focus of this study was on leakage rates, higher values are used as this will overestimate rather than underestimate flow through the FDZ especially in shale host intervals. An array of single grid cells in the center of the FDZ with dimension of 4.5 m perpendicular to the fault plane is treated as the fault core. This thickness is also consistent within the core thickness range observed by Childs et al. (2009), but is among the highest values they observed. The host zone permeability distributions for the sand- and shalehost zones are adopted from literature (Mbia et al., 2014; Timur, 1968; Zulqarnain et al., 2017). The damage zone and fault core permeabilities are also estimated from structure data reported in literature (Ballas et al., 2015; Fossen et al., 2015; Nicol et al., 2016) and shown in Table 2. It has been reported in the literature that for high porosity sandstones and for the burial depths considered in this study, cataclastic processes dominate deformation and as a result the FDZ permeability is typically 2–3 orders of magnitude below the host rock (Bense et al., 2013; Fisher and Knipe, 2001; Nicol et al., 2016). Therefore, we have introduced the 2–3 orders of magnitude in reductions of permeability of the FDZ in sand host intervals. In addition, the shale intrusion in sand intervals is represented as having four orders of magnitude reduction in comparison to the sand-host permeability. The resultant FDZ in the sand-host interval has permeability in the range of 0.0611–611 m d, and the FDZ in the shale-host interval has permeability values in the range of 0.00611–0.611 md. The faulting process may result in creation of fractures in low porosity shale intervals (Faulkner et al., 2010; Nicol et al., 2016) and sand from adjacent beds may also intrude into the shale intervals. Both of these processes enhance the permeability in the shale-host intervals. The FDZ permeability in the shale-host interval is assumed to be higher than the host

Rock Type

0.0001 0.0001

Anisotropy Range (m)

3

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Table 3 Sand and shale host thicknesses and fractions of cells with altered permeability. Sand No.

Sand Bed Thickness (m)

Lower Shale Bed Thickness (LSBT) (m)

Shale Smear Factor (SSF)

Throw/Sand-Bed-Thickness Ratio (TSTR)

Unaltered Facies Fraction

Across FDZ Weighted Geometric Mean Permeability (mD)

1 2 3 4 5

81 34 48 48 74

76 235 74 27 67

0.6 0.19 0.62 1.72 0.68

0.56 1.33 0.94 0.96 0.61

0.5 0.29 0.45 0.44 0.53

61.10 2.79 19.32 37.67 41.31

sandstone reported by Hart and Wang (1995). Therefore, we use the poroelastic properties of the Berea sandstone under confining pressure similar to the FDZ depth settings reported by Hart and Wang (1995). We treat the FDZ in all sand intervals as a single rock type with the same poroelastic properties, considering observations from the literature that these properties do not vary substantially (Hart and Wang, 1995) under the different confining pressures at different depths modelled in this study. Representative values for shale mechanical properties from literature (Xu et al., 2016) are used. Changes in rock porosity and hence permeability are computed from the coupling of fluid flow and geomechanical effects (Tran et al., 2004). Representative compressibility values from literature for sandstone (Newman, 1973) and shale (Davudov et al., 2018) are used. The values used for the base geomechanical properties are shown in Table 4. Four rock types were defined to represent sands, shales, fractures in sands and fractures in shales. The fractures in sand- and shale-host intervals were assigned the host-zone mechanical properties, although an option is available to assign a different set of mechanical properties to the fractures. The assigned mechanical properties are shown in Table 4. Two-way coupling is used, so that the porosity and permeability are updated at each time step in response to deformation from geomechanics.

Table 4 Parameters used for the base geomechanical properties. Parameter

Sand

Shale

Young’s Modulus (GPa) Poisson’s Ratio

20.68 0.23

34.99 0.4

model the CO2 flow inside the sand-host intervals. A schematic is shown in Fig. A2 in the Appendix A. The fluid fraction coming into the 30.5 m thick interval was estimated by using area ratios of the 30.5 m arc and the total circumference. A pressure constraint was also applied on the well bottomhole pressure to avoid the formation fracture pressure. This was taken as 0.8 of the absolute normal stress value. The pressure constraint for the five simulated sands are different due to their different burial depths. The absolute normal stress is based on an average porosity of 28%, a sandstone density of 2650 kg/m3, and a fluid hydrostatic pressure gradient of 10.52 kPa/m. When the pressure constraint is met, the injection rate is lowered to honor the pressure constraint. The sand bed thickness, shale bed thickness, shale smear factor, throw to sand bed thickness and cells with altered fraction are shown in Table 3. It has been reported in literature that sand host-FDZ thickness and the intensity of compaction band clusters increases with fault throw (Ballas et al., 2015; Bense et al., 2013; Fossen et al., 2015; Shipton and Cowie, 2001, 2003). For the current modeling setup, fault throw and FDZ thickness are assumed constant for all sand intervals. However, different degrees of damage would be expected due to different sand bed thicknesses even for a constant throw which is incorporated by using throw to sand-host interval bed-thickness ratio. Based on this ratio the permeability of a fraction of grid cells is reduced in the FDZ. A maximum of 70% altered cells corresponding to maximum throw/sandbed-thickness ratio (TSTR) value of 1.33 are assumed for Sand 2. For other sands the altered cell ratios are assigned by normalizing against the 70% fraction of Sand 2. In shale-host intervals, it is assumed that the structure in the FDZ is different than in the host zones due to faulting processes and therefore the FDZ has higher permeability than the host zone. The weighted geometric mean of the FDZ permeability in the shale-host zones are four orders of magnitude less than the unaltered permeability of the sand-host zones. The model used in simulation and the distribution of host and altered zone cells and their corresponding permeability for sands 3 and 4 are shown in Fig. 2. Host zone permeability is taken as reference to alter the permeabilities of cells in the FDZ. A Leverett J-function is used to scale the local capillary pressure and the reference capillary pressure used is shown in Fig. A3 in the Appendix A.

2.2. Stress-dependence of FDZ permeability (cases 11–15) In this work we use the Barton-Bandis (Barton et al., 1985) model to account for the stress dependent changes in fracture permeability. In this model the initial permeability of a dormant fracture, which is usually very small, is altered when a threshold effective normal stress differential value is reached. The effective normal stress is defined as the absolute normal stress minus the fluid pressure assuming Biot’s poroelastic constant equal to 1. The fracture opens up when this threshold is achieved. The fluid pressure or effective normal stress differential are specified alongside the resultant permeability variations in the initial simulation setup. The fracture permeability jumps from initially low values to a predefined maximum value when the pressure or effective normal stress differential threshold is met. Once the fracture is open, the subsequent permeability alteration is handled by the Barton-Bandis model, shown in Fig. 3. Point-A represents the effective normal stress level at the start of the injection process. The effective normal stress decreases as fluid pressure increases until the differential threshold stress (frs) is reached which is shown as point-B. At this effective normal stress the fracture permeability jumps from the initial value to the assigned opened fracture permeability (khf). If the effective normal stress remains below the stress level of point B, the fracture permeability remains at the constant level of khf. Once the effective normal stress increases beyond point B, the Barton-Bandis model dictates that fracture permeability variations follow the path CD in Fig. 3. The krcf value is the fracture closure permeability, which is one of the model inputs. It is specified to take into account the hysteretic nature of the fracture opening and closing process. Therefore a fracture that opens and then closes has a permeability that is higher than the initial fracture permeability before it was opened. In these sets of simulations, the fractures are introduced into the previously modelled fault structure alongside implementation of the hydromechanical coupling as described in Section 2.1. In this way, the

2.1. Hydromechanical coupling In coupled hydromechanical modelling, representative rock properties are assigned to the FDZ in the sand- and shale-host zones. Berea sandstone rock properties from the literature are used for the sand-host zone (Hart and Wang, 1995). Bauer et al. (2015) measured the fault damage zone mechanical properties for sandstones and they are very similar to the properties of unconfined measurements of Berea 4

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An initial effective permeability of 0.01 md is assigned to all fractures. These fractures open up when some threshold value of differential effective normal stress is encountered and their permeability increases to some predefined values by using the Barton-Bandis model (Barton et al., 1985), in the CMG-GEM compositional reservoir simulator (CMG-GEM, 2016). The assumed values of model parameter are shown in Table 5. The opened fracture permeability is based on the fracture spacing and grid cell size which can be much less than the intrinsic fracture permeability. For example, an effective fracture permeability of 5 md corresponds to an average intrinsic natural fracture permeability of nearly 5000 md (Bratton et al., 2006), based on the fracture spacing and fracture aperture size (3 mm) adopted for the simulation setup. The following formula is used to calculate the effective fracture permeability (kf ) based on intrinsic fracture intrinsic permeability (kf , int ), fracture width (wf ) and fracture spacing (l )

kf =

kf , int wf l

The values for threshold differential effective normal stress, permeabilities of fractures in the sand and shale in open and closed states are assumed values. Comparatively a higher permeability of the opened fractures in the FDZ in shale-host intervals is assumed to avoid numerical convergence problems. Further investigation is needed to relate the degree of fracturing, the quantification of fractures properties in sand and shale FDZ, and leakage rates.

Fig. 3. Barton-Bandis stress dependent fracture permeability model illustration (adopted from CMG-GEM (2016)).

impact of fractures can be determined through comparison with cases in which fractures and their hydromechanical effects are not modelled. Dual permeability formulations are used to model the presence of these natural fractures. Planer fractures parallel to the fault plane are overlaid in a pre-determined number of grid cells as only a fraction of the grid cells have fractures, as shown in Fig. 4(a–c). In the sand-host zone cells, fractures are overlaid on cells having one order of magnitude less permeability (61.1 md) than the original permeability (611 md), which are nearly 30% of the total number of cells. In the shale-host zones the fractures are introduced to blocks that have original permeability value of 0.0611 md. These blocks make up nearly 50% of the grid cells in the shale-host FDZ. This creates a distribution in which some fractures on a 2D plane seems discontinuous, but are interconnected in 3D, as shown in Fig. 4(c). The compressibility of the fractures is assumed to be the same as the host interval compressibility. Fractures are denser in the sand-host rock blocks with a spacing of 5 ft, while in the shale-host intervals the spacing is 10 ft in the horizontal direction. For consolidated sands and for sands with low porosity, excessive fracturing may happen in both the sand-host and the shale-host zones. The burial depth of sands in the area under investigation is not very deep and sand and shale zones have high porosity, therefore fractures are introduced into a fraction of the grid blocks.

3. Results The results are presented in three sections. The first five cases represent the injection into sands 1–5, and each sand has a different set of FDZ properties based on the sand-host zone thickness to fault throw ratio. In the first five cases a fragmented core is present in the sand-host intervals. In these cases, the hydromechanical coupling and fractures are ignored. In this way it is possible to quantify the impact of a continuous core and fractures when these cases are compared with cases 6–10 which have a continuous central core and cases 11–15 with a central continuous core and overlaid fractures. In next sub-section we present the results of these fifteen cases. 3.1. Cases 1–5: fragmented fault core without hydromechanical coupling (fluid only) As the degree of damage in the FDZ in sand beds is based on the throw-to-sand bed thickness ratio, the resulting FDZ in each case has a

Fig. 4. Gid blocks containing fractures and fracture spacing. FDZ in sand intervals have low fracture spacing implying more fractures in fault damage zone per grid block. 5

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Table 5 Parameters used in defining fracture properties in the Barton-Bandis model.

Initial intrinsic permeability (md) Initial effective permeability (md) Threshold differential effective normal stress (kPa) Opened effective fracture permeability (md) Closed effective fracture permeability (md)

Sand-host FDZ fractures

Shale-host FDZ fractures

10 0.01 689 2.5 0.25

10 0.01 1724 5 0.5

Fig. 5. (a) Temporal variations of well bottomhole pressure (WBHP), and (b) pressure contour plots corresponding to three time instants t1 = 0.6, t2 = 10 and t3 = 30 year.

variable degree of damage. Moreover these cases also differ due to different lengths of the FDZ in the caprock. The well bottomhole pressure variations for cases 1–5 are shown in Fig. 5(a) and (b). For all cases a constant injection rate was specified, but due to different depths, the pressure constraint for each case is different. Sand 1 is the deepest sand with the highest value of pressure constraint and Sand 5 is the shallowest with the lowest value. An interesting pattern in well bottomhole pressure behavior can be seen in Fig. 5(a). Just after the start of injection, a peak is observed in WBHP (Well Bottomhole Pressure). The magnitude of this peak corresponds to the flow resistance in the FDZ due to different throw to sand bed thickness ratios. Case-2 for Sand 2 has the highest throw to sand bed thickness ratio and therefore the FDZ offers more resistance to fluid moving in the lateral direction across the FDZ. Case-1 for Sand 1 has the lowest throw to sand bed thickness ratio and the FDZ presents less resistance to flow when it moves across the FDZ. This peak is the result of the local capillary pressure variations due to the different permeability distributions in each layer. As the CO2 starts migrating across the FDZ, the capillary pressure increases with an increase of CO2 saturation. As the FDZ in Case-2 has more cells with low permeability as compared to others, local capillary pressure scaling results in higher capillary entry pressure. Therefore, more differential pressure is needed to overcome this augmented capillary force. This higher differential pressure implies

higher peak pressures. The pressure contours on both sides of the FDZ for Case-2 at three time values are shown in Fig. 5(b). The differential pressure can be seen across the FDZ at time t1. Once pressure buildup is sufficient to overcome the capillary forces, the CO2 migrates across the FDZ and the pressure falls to a lower value. At time t2 another pressure buildup is noticed, but in this case as the WBHP constraint is met, the injection rate is altered and the pressure on the upstream side of the FDZ stops building up. If the constraint were not there, we could have seen another pressure buildup and release. As the injection rate is constrained to honor the WBHP-constraint the pressure slowly dissipates and towards the end of injection period at t3, the injection-generated fluid pressure perturbation increases as CO2 migrates along the sand beds across the FDZ. As Case-1 has the lowest throw to sand zone thickness ratio, its pressure constraint is not violated during the entire injection period due to its lower resistance to flow across the FDZ. Therefore, the CO2 migrates across the FDZ with the least resistance. The results for cases 3–5 fall in between those from Case-1 and Case-2. As discussed earlier, when the pressure constraint for a particular sand is met the injection rate is reduced to avoid the violation of this constraint. The injection rates for cases 1–5 are shown in Fig. 6(a). The CO2 saturation contour plots are also shown in Fig. 6(b). It can be seen from Fig. 6(b), that during the initial pressure buildup process, some

Fig. 6. (a) Injection rates for case 1–5, (b) CO2 saturation contour plots for case-2 at three instant of time. 6

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Fig. 7. (a) Instantaneous upward leakage rates for cases 1–5, (b) cumulative leaked/injected mass ratios for cases 1–5. Please note the secondary y-axis for case-3 in both (a) and (b).

fraction of injected CO2 has already migrated across the FDZ. We now look at the leakage rates for cases 1–5. It is to be noted that the injection well is located very close to the FDZ. Therefore, the injected CO2 either has to move across-along the fault or up-along the fault. The leakage mass reported in this study is upward leakage from the injection zone. Note that the pressure buildup, which represents the resistance to CO2 migrating across the FDZ is translated into leakage rates. With the exception of Case-3 in which inter-sand communication was established during the earlier stages of the injection period, Case-2 has both the highest pressure buildup and the highest leakage rate to upper sands amongst other cases, as shown in Fig. 7 (a). A slope change in leakage rate is observed with fluctuations in the WBHP. Case 3 has the highest leakage rates among the cases considered. Its high leakage rate is the result of pressure buildup and small caprock bed thickness. Due to comparatively small caprock thickness, inter-sand communication was established between Sand 3 and Sand 4. Therefore, inter-sand communication and pressure buildup results in leakage rates which are one order of magnitude higher than the up-fault leakage rates for other cases. Temporal behavior of leakage rates shown in Fig. 7(b) relates the ratio of the cumulative mass leaked to the cumulative mass injected at any instant of time. It can be observed that for the considered cases, only a fraction of the CO2 leaks in the upward direction and the majority migrates across the FDZ. The highest upward leakage is noted to be only 1.2% of the injected mass in Case-3. We now look at the saturation profile for cases 2, 3 and 4 at the end of the 30 year injection period. It can be observed that for Case-2 there has been no inter-sand communication through the injection period (Fig. 8(a)). Therefore, whatever leaked upward is contained within the inter-sand FDZ. For Case-3 an inter-sand communication is established

and the CO2 leaks to the upper sand zone (Fig. 8(b)). An interesting observation is that in each of the studied cases there is some CO2 that migrates downward as well. For Case-4 the downward migration is due to lower values of the inter-sand shale bed thickness between Sand 4 and Sand 3. Therefore, some amount of CO2 is observed in the lower Sand 3. In many scenarios, downward migration may not pose any major issues. However, for stacked oil and saline aquifers it may become necessary to monitor downward CO2 migration. The distribution of capillary pressure values at the end of the 30year injection period for cases 2 and 3 are shown in Fig. 9(a) and (b) respectively. For longer inter-sand shale bed thickness, leaking CO2 has to overcome the higher capillary pressure in order to escape from the injection zones. Therefore, only a fraction of the injected CO2 leaked to the shallower sand zones for the considered cases and the majority moved across the FDZ. For Case-2, the caprock has larger thickness as compared to Case-3. Therefore, the leaking CO2 has to overcome a longer section of low permeability FDZ in the caprock with higher capillary pressure. Inter-sand communication was not established in Case2 although this case had the highest observed pressure buildup. In the case of inter-sand communication, this high pressure buildup may have resulted in highest leakage to upper sand interval due to high pressure differential. In Case-3, due to a comparatively thinner caprock and associated FDZ, the leaking CO2 faces less resistance to moving upward and an inter-zonal exchange is established. Therefore, comparatively higher leakage is observed for Case-3 even though the pressure buildup is less than Case-2. A combination of pressure buildup and FDZ length in the caprock dictates the up-fault flow of CO2 for the studied cases.

Fig. 8. CO2 saturation plot at the end of 30 years injection period for cases 2, 3 and 4. 7

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Fig. 9. Capillary pressure distribution at the end of 30 years injection period for case2 and 3.

3.2. Cases 6–10: continuous fault central core with hydromechanical coupling In this set of models, a central continuous core is present in all of the sand-host zones. Due to the low permeability of the central core, which is four orders of magnitude less than the sand-host interval, the pressure constraint for all cases is met, shown in Fig. 10(a) as a straight line. Due to the higher pressures from the very early times, higher leakage rates are seen for all cases as compared to cases 1–5, despite comparatively smaller amounts of CO2 being injected in these cases. Only WBHP and cumulative leakage are reported for cases 6−10 as other trends are similar to cases 1–5. The well bottomhole pressure was constrained to not increase beyond 80% of the absolute normal stress, and injection rate was adjusted to honor that constraint. Therefore nominal changes in porosity and permeability were observed in this set of simulations.

Fig. 11. Temporal variations mass injection rate for cases.11–15.

3.3. Cases 11–15: continuous fault central core and fractures with hydromechanical coupling

respectively. Fluctuations in leakage rate can be observed for cases 11, 12, 14 and 15 in Fig. 12(a), while for Case-13 these fluctuations are nearly non-existent (Fig. 13(a)). An interesting observation is that the CO2 seemingly flows back into the injection zone, shown as negative leakage rates in Fig. 12(a). We will discuss Case-12 in detail noting that the other cases have very similar trends. The saturation and pressure distributions for Case-12 are shown in Fig. 12(c) and (d) at different time instances to assist in understanding this flow behavior. Pressure in the FDZ increases with the continued injection. The fractures in the FDZ start opening up when the threshold differential effective normal stress required for fracture opening is reached. Fracture opening and subsequent CO2 flow up the FDZ results in increased leakage rate until a peak is reached (at ∼4 years for Case-12). After the initial leakage peak for Case-12, the differential pressure

In this set of simulations, a set of natural fractures are incorporated into the fault damage zone in addition to the model setup for cases 6 to 10. Hydromechanical coupling in these cases facilitates investigating the impact of the presence of natural fractures in the fault damage zone on CO2 migration. Like cases 6–10 the WBHP is constrained from the very beginning, and as a result injection rates are lowered. The WBHP for cases 11–15 are nearly identical to those for cases 6–10, shown in Fig. 10(a). The injection rates for cases 11–15 are shown in Fig. 11. The instantaneous and cumulative leakages for cases 11, 12, 14, and15 are shown in Fig. 12 (a) and (b), respectively. In order to visualize the fluid movements, the CO2 saturation and fluid pressure contour plots for Case-12 are also shown in Fig. 12(c) and (d),

Fig. 10. Comparison of (a) WBHP and, (b) leakage rates for cases 6, 7, 8, 9 and 10. 8

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Fig. 12. (a) Instantaneous leakage rates for cases 11, 12, 14 and 15, (b) temporal variations of cumulative leaked to injected ratios for cases 11, 12, 14 and 15, (c) CO2 saturation contour plots for Case-12 at three instants of time t1 = 4, t2 = 14 and t3 = 30 year for Case-12, and (d) pressure contour at three instants of time t1 = 4, t2 = 14 and t3 = 30 year for Case-12.

Fig. 13. Leakage rates and contour plots for Case-13 (a) instantaneous leakage rates, (b) temporal variations of cumulative leaked to injected mass (c) CO2 saturation contour plots, (d) pressure contour at three instants of time t1, t2 and t3.

across the fault core results in migration of CO2 across the core. As a consequence, the upward leakage rate decreases as fluid takes the path of least resistance and preferentially flows across the core. As time passes, the pressure on the opposite side of the fault from the injection well also increases and the differential stress required to open the

fractures on that side of the fault is achieved. As a result, the fractures start opening up on the other side of the fault core as well. At this point, the pressure in the shale caprock FDZ is higher than the pressure in the sand FDZ beneath it across the core. This is the time at which downward flow is observed from the adjacent FDZ in the shale caprock to the 9

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sand interval on the other side of the core. Therefore, some amount of escaped CO2 flows back into the same sand interval but on the opposite side of the fault from the injection well, denoted as negative leakage rate. This behavior was not observed in earlier cases 1–10, where the fractures were not present. Therefore, this should be attributed to the process of pressure buildup and stress dependent fractures opening. The magnitude of downward flow decreases after CO2 breakthrough to the upper sand zone, also shown by the CO2 saturation distribution at t3 = 30 years in Fig. 12(c). It is expected that if the injection is continued beyond the 30 year injection period, the CO2 leakage rate will become positive again due to the pressure buildup in the sand interval across the core and on the opposite side of the injection well location. The temporal CO2 saturation and fluid pressure contour plots in Fig. 12(c) and (d), respectively depicts the extent of the CO2 and corresponding fluid pressure distributions. It can be observed that CO2 mostly flows across the FDZ and the corresponding fluid pressure builds up. Now, we look at the ratio of the cumulative leakage to cumulative injected, shown in Fig. 12(b). When compared with cases 6–10 in which fracture and hydromechanics were not modelled, some interesting comparisons can be made. Due to downward flow, comparatively lower cumulative leakage is observed for cases 12, 14 and 15, when compared with cases 7, 9 and 10 respectively. The only exception is Case-11, for which a higher leaked to injected ratio is observed when compared with Case-6. In cases 1, 6 and 11, which represent the injection into the lower-most sand interval in the simulation model, the bottom of the FDZ in this sand interval was treated as a no-flow boundary. If additional shale and sand intervals deeper than Sand 1 were to be modelled, the results should have been very similar to the ones observed in cases 12, 14 and 15. The maximum impact of fractures on the leakage rates is observed in Case-13. The instantaneous and cumulative leakage amounts for Case-13 are shown in Fig. 13(a) and (b), respectively. The CO2 saturation and fluid pressure contour plots are also shown at three time instances in Fig. 13(c) and (d), respectively. The downward flow is not observed for Case-13. For Case-13, unlike other cases, CO2 breaks through in the upper sand interval during the initial stages of the injection period and thus results in the highest leakage rates amongst the studied cases. This early breakthrough is mainly due to the short leakage interval in the shale caprock immediately above Sand 3. When compared with cases 12, 14 and 15, it is evident from the fluid pressure and CO2 saturation distributions that inter-sand fluid exchanges have not been established for these cases in the initial stages of the injection period. For Case-13, nearly 18% of the injected CO2 leaked to the upper sand interval, which suggests that the inter-sand link was established before flow across the core occurs. We now look at three cases namely 3, 8, and 13 to compare the impact of the presence of a fragmented core, an intact core, and an intact core with a naturally fractured FDZ, respectively. The ratio of the cumulative mass leaked to the cumulative mass injected for these cases is shown in Fig. 14. It can be observed that the presence of an intact core nearly doubles the cumulative leaked to injected mass ratio at the end of injection period. The flow resistance offered by the intact core in the injection interval results in higher pressure buildup. This pressure buildup is the main cause of higher observed leakage amount for Case-8 compared to Case-3. When the fractures are also present in the FDZ in the caprock along with the intact core (Case-13), the leakage to the upper sand interval is increased by more than four fold. Therefore, pressure buildup due to a low permeability intact core, short caprock interval, and fractures in the caprock FDZ result in substantial leakage. Now we select the cases 11 and 12 for qualitative result analysis. These two cases represent two extremes amongst the hydromechanically coupled cases (11 through 15). The weighted geometric mean permeability across the FDZ (see Table 2) are 61.10 and 2.79 md for cases 11 and 12, respectively while for other cases this value falls between these limits. This low mean permeability translates to

Fig. 14. Cumulative leaked/injected ratio for cases 3, 8 and 13, for the sand 3.

comparatively higher resistance to fluid flow in the FDZ for Case-12 compared to Case-11. The distribution of opened and non-opened fractures for Case-11 and Case-12 at the end of the injection period are shown in Fig. 15(a) and (b), respectively. The corresponding CO2 saturation distribution for these two cases are also shown in Fig. 15(c) and (d). It can be observed that for Case-11 with comparatively less resistance for across FDZ flow, only a small fraction of the fractures in the upper shale caprock are opened, shown by the yellow and orange colors in Fig. 15(a). For Case-12, most of the fractures in the entire FDZ between Sand 2 and Sand 1 are opened up, except a few that lie just on top of Sand 1. Looking at the CO2 saturation for Case-12, it can be observed that the permeability changes in the opened fractures have resulted in some downward propagation of CO2. However, the CO2 barely enters into the FDZ below the Sand 2 interval. The downward propagation of normal stress differential ceases once the CO2 link is established between Sand 2 and the upper Sand 3 interval. The saturation distribution in Fig. 15(d), shows CO2 leakage to the upper sand at the end of the injection period while this does not occur in Case-11. The results of cases 13 and 14 are discussed further to highlight the impact of shale caprock/bottom-rock thickness on leakage/migration rates. In the current modeling setup the smallest shale rock unit exists between sands 3 and 4. For Case-13 it is the caprock and for Case-14 it is the bottom rock. Due to relatively thin shale caprock and corresponding FDZ, the inter-sand fluid exchange for Case-13 was established during the early stages of the injection period. Therefore largest leakage rate was observed for this case. It can be observed in Fig. 16(a), that almost all of the fractures in the shale caprock FDZ are opened, and these also seems to be well-connected as well. Corresponding CO2 plume extent can be seen in Fig. 16(c), which depicts excessive CO2 leakage to the upper sand interval. For Case-14, we can observe from Fig. 16(b) that a number of fractures in the bottom shale-host FDZ are opened up during the injection phase. This results in comparatively more CO2 migration to the bottom sand interval than leaking to the upper sand interval, shown in Fig. 16(d). 4. Discussion Much of the existing literature about fault leakage potential deals with across fault flow (Alikarami et al., 2013; Bauer et al., 2015; Bense et al., 2013; Choi et al., 2016; Fisher and Knipe, 2001; Lindsay et al., 2009; Nicol et al., 2016; Yielding et al., 1997). An effort is needed to quantitatively categorize the up-fault structural changes for stacked sand systems for accurate up-fault leakage modelling. This work is an effort to address this gap. Values for the fracture opening stress and opened fracture permeability are assumed for fractures in the sand- and shale-host zones. These settings require further investigation in the form of sensitivity analysis to relate leakage rates to differential stress needed to open fractures and resultant fracture permeabilities in sand10

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Fig. 15. Distribution of opened and unopened fracture for cases 11 and 12 is shown at the end of the 30 year injection period in (a) and (b) respectively. In (c) and (d) corresponding CO2 saturation contour plots are shown for cases 11 and 12 respectively.

and shale-host zones. In addition, fault damage zone permeabilities are assumed for both the hanging and foot wall sections, while in reality they could be different, due to different geomechanical effects acting on each side. A representative fault damage zone configuration was created by honoring the fault displacement and sand interval thickness. A sensitivity analysis of these parametric variations and their impact on leakage rates is needed. For Case-2 a relatively high pressure buildup is noted during the very early stages of the injection period. This depends on the combination of injection rate and the fluid flow resistance in the FDZ. If either the injection rate is lowered or the flow resistance in the FDZ is decreased, this buildup could be less significant. It is expected that with lower injection rate, the appearance of the peak in pressure will be delayed and will be comparatively small, as fluid pressure will have some time to dissipate. As the focus of the study was on upward leakages to shallow sand intervals, only a limited number of grid cells was used in the along-fault Y-direction. In future works, this condition should be relaxed to extend the simulation model domain further in the Y-direction (along the fault plane). It is expected that extending the fault length in that direction while allowing higher permeability for along-fault flow would decrease the pressure buildup during the injection. It may happen that the formation fluids may preferentially move along the fault due to low flow resistance instead of moving across the fault. As a result, the arrival of the maximal injection pressure will likely be delayed. Simultaneously, this would engage a larger surface area of the fault plane into the potential for leakage. Incorporating the whole length of the fault plane is therefore important and merits further investigation. For the studied cases, a Barton-Bandis model was used to simulate

the evolution of fracture permeability. A more realistic approach would be to define the full geomechanical parameters of fractures and faults and model the fracture permeability evolution as a function of fracture mechanical failure and dilation. The across-fault permeability of the studied cases is larger than the vertical permeability (or up-fault permeability). This is why flow or fluid migration directions are largely across the fault. In nature, there might be different cases where vertical permeability (up-fault permeability) is greater than the horizontal permeability (across-fault). One such example could be a set of well-connected fractures in the vertical direction across multiple sand-shale intervals in a stacked sand system. For these cases substantial leakage can take place. The computational time substantially increases with incorporation of hydromechanics and conditional opening and closing of fractures. Numerical schemes also become unstable requiring reduced time steps to obtain convergence. 5. Conclusions Fault-related leakage from a stacked sand and normal fault system is modelled for a representative fault in a depleted oil field in south Louisiana. The key modelling results are:

• The mode of CO

•

2 transport is lateral flow i.e. only a small fraction of the injected CO2 leaks to upper zones. Thus, across fault flow is dominant as compared to up-fault flow in all of the cases. This is due to considering higher across-fault permeability in the study compared to the up-fault permeability in the fault damage zone in the shale caprock. It was observed that a combination of high pressure buildup, smaller

Fig. 16. Distribution of opened and unopened fracture for cases 13 and 14 is shown at the end of the 30 year injection period in (a) and (b) respectively. In (c) and (d) corresponding CO2 saturation contour plots are shown for cases 13 and 14 respectively. 11

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• •

upper shale interval thickness and existence of fractures in the FDZ in shale caprock results in substantial leakage rates. For the cases studied, the presence of fractures increased the leakage mass by up to 4.5 times the mass leaked when fractures were absent. CO2 may also migrate to deeper zones provided that the pressure buildup in the injection zone is high enough and a network of interconnected fractures exists. The presented results provide quantitative and qualitative measures of leakage rates though representative fault damage zones and are helpful in correlating fault structure features and flow rates. Thus will aid in storage site integrity analysis.

interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests. Acknowledgements The authors are thankful to funding from the U.S. Department of Energy, National Energy Technology Laboratory (NETL) under grant number DE-FE0031557, CFDA 81.089. We would like to thank Mikey Hannon from Indiana Geological and Water Survey for his constructive input on this work. We are also thankful to Computer Modelling Group and Schlumberger for providing the CMG-GEM and Petrel software packages.

Declaration of Competing Interest The authors declare that they have no known competing financial Appendix A .

Fig. A1. Parametric variations of (a) Density, (b) pressure, and (c) temperature used in the simulation models.

Fig. A2. Schematic showing the setup used to calculate the fraction of flow that will enter the 30.5 m wide FDZ simulated in this study.

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Fig. A3. Capillary pressure curve used for pure sand intervals with porosity and permeability of 0.29 and 611 respectively.

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