International Journal of Greenhouse Gas Control 78 (2018) 135–147 Contents lists available at ScienceDirect International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc Local capillary trapping in carbon sequestration: Parametric study and implications for leakage assessment T Bo Ren Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 200 E. Dean Keeton St, Stop C0300, Austin, TX 78712, USA A R T I C LE I N FO A B S T R A C T Keywords: Local capillary trapping Carbon sequestration Buoyant ﬂow Leakage Residual trapping Local capillary trapping (LCT) is the trapping of CO2 by local capillary barriers. It occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer exhibiting spatially varying properties (permeability and capillary entry pressure). The beneﬁt of LCT, in the context of CO2 sequestration, is that local capillary trapped CO2 is not susceptible to leakage through failed seals. However, it is unclear how the petrophsyical/geological properties and ﬂow dynamics inﬂuence LCT. Thus, the objective of this work is to evaluate the degree to which potential local capillary traps are ﬁlled and quantify the extent of immobilization persisting after loss of seal integrity. This paper presents a systematic and thorough study of the inﬂuential parameters of LCT. Fine-scale capillary pressure ﬁelds are generated by using geostatistical permeability realizations and applying the Leverett j-function. Multiple factors are examined, including injection rate, anisotropy, formation dip, aquifer types, residual gas saturation, and capillary hysteresis. Leakage representative of wellbore failure is simulated, and LCT after leakage is evaluated and compared to other trapping mechanisms. The results show that local capillary traps in the near-well region can be fully ﬁlled during injection. Moreover, they remain ﬁlled after post-injection buoyancy-driven ﬂow ends. The ﬁlling eﬃciency of local capillary traps increases with the decrease in gravity number (ratio of buoyant force over viscous force). As a result, maximizing LCT in carbon sequestration in porous reservoirs may be achievable with the implementation of appropriate injection strategies. 1. Introduction CO2 sequestration in saline aquifers has been widely accepted as the promising and easily accessible way to reduce carbon emissions and global warming in this century (Bachu, 2008). In order for CO2 to be stored in a manner that is secure and environmentally acceptable, it is essential to understand the behavior and migration of CO2 in geologic formations under the eﬀects of complicated interplaying forces (namely buoyancy, capillary pressure, and viscous force), geologic characteristics, and operating conditions. Typically, CO2 can be trapped by the following mechanisms: stratigraphic/structural trapping (Gupta, 2011), dissolution trapping (Burton and Bryant, 2009), residual trapping (Pentland et al., 2008) and mineral trapping (Pruess et al., 2003). Among these mechanisms, dissolution, residual and mineral trapping are considered as the safest way of immobilizing CO2 in storage media. The remaining CO2 (as free gas), mostly in the stratigraphic and structural traps, is potentially mobile and most likely to escape from the storage media should leakage occur. Recently, a new trapping mechanism – local capillary trapping (LCT) – was proposed when considering the intrinsic heterogeneous capillary pressure of a given storage formation (Saadatpoor et al., 2010). LCT is a form of trapping where CO2 accumulates behind capillary barriers. It occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer exhibiting spatially varying properties (permeability and capillary entry pressure). Its beneﬁt, applied specially to CO2 sequestration, is that saturation of stored CO2 is larger than residual phase saturation (Saadatpoor et al., 2010). In addition, in case of leakage, CO2 in LCT does not escape from the storage formation even if seal systems are compromised (Saadatpoor et al., 2010). LCT is analogous to other well-known phenomena in the context of multiphase ﬂow through porous media. It is equivalent to the largescale “ﬁll and spill” process used in charging hydrocarbon reservoirs (Siddiqui and Lake, 1997). Additionally, it is analogous to pooling of non-aqueous phase liquid spilled onto soils (Van Valkenburg and Annable, 2002). Several mechanisms would create local capillary traps, such as grain size variation (e.g., ﬁning upward sequence), changes in depositional environments over time, and non-uniform/uneven diagenetic alteration. A number of studies (Saadatpoor et al., 2010; ; Trevisan et al., 2017a; Li and Benson, 2015) have been conducted to investigate the impact of LCT or capillary heterogeneity on CO2 movement and E-mail address: boren@utexas.edu. https://doi.org/10.1016/j.ijggc.2018.08.001 Received 15 May 2018; Received in revised form 19 July 2018; Accepted 1 August 2018 1750-5836/ © 2018 Elsevier Ltd. All rights reserved. International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren (2010). saturation distribution. Generally, these studies originate from two diﬀerent research considerations; theoretically, under the buoyancydominated ﬂow of CO2 in saline aquifers, buoyant force is comparable to capillary pressure, thus, capillary heterogeneity essentially inﬂuences CO2 movement. Experimentally, researchers found that it is difﬁcult to replicate two-dimensional (2D) and three-dimensional (3D) CO2 saturation proﬁles within cores when adopting a single capillary pressure curve for history matching. However, when appropriate scaling laws for capillary pressure are incorporated, the saturation proﬁles or ﬁelds can be better reproduced (Krause et al., 2011; Shi et al., 2011; Kong et al., 2014; Wei et al., 2014). Apart from LCT in cores, LCT has been studied in 2D bench-scale experiments when considering only buoyant ﬂow (Li and Benson, 2015; Sun, 2014) and when incorporating injection-period (Trevisan et al., 2017b). It is shown that CO2 buoyant ﬂow is greatly disrupted in the event of even slight heterogeneities, i.e., when the grain size becomes ﬁne, half of the size is enough to temporarily hinder buoyant ﬂow (Sun, 2014). All the above results provide important qualitative and quantitative insights on the role of capillary heterogeneity on CO2 ﬂow and distribution in storage aquifers. However, most of the researchers in this ﬁeld did not explore how LCT inﬂuences CO2 leakage, which is a signiﬁcant concern in geologic carbon sequestration (Tao, 2012). Additionally, previous work (Saadatpoor et al., 2010; Saadatpoor, 2012) indicates that 10–50% of local capillary traps get ﬁlled during the buoyancy-driven drainage process. However, the previous work (Saadatpoor et al., 2010) assumed a limiting-case initial distribution of CO2 in the storage formation. It remains to be determined whether more realistic distributions of saturation for buoyancy-driven CO2 migration, namely the distribution of CO2 at the end of injection, aﬀect the extent of LCT. In addition, it is valuable to examine the eﬀect of both ﬂuid/rock properties (e.g., residual phase saturation) and operating parameters (e.g., injection rates) on LCT. In this paper, a systematic numerical assessment of LCT is conducted to evaluate the fraction of potential local capillary traps ﬁlled as a function of primary controls while including both the injection and leakage periods. A series of two-dimensional synthetic domains are built and these domains are representative of typical storage formations. Diﬀerent factors are examined, including injection parameters and reservoir static properties. Particularly, a wide range of buoyancy numbers (i.e., ratio between buoyant force and viscous force) are considered. At the end of post-injection, a leak conduit is introduced along a wellbore to evaluate the eﬀect of LCT on storage security. The understanding thus obtained here will provide insights into post-injection leakage behaviors while the injection period is simulated realistically. 1/9.61 k ⎞ ϕ=⎛ ⎝ 7E + 7 ⎠ (1) Capillary entry pressure ﬁelds (Fig. 1c) are generated using the Leverett j-function [Leverett (1941), Eq. (2)]. In Eq. (2), pc is capillary pressure, σg/w is the interfacial tension between CO2 and brine water, θ is contact angle, k is permeability, φ is porosity. The detailed procedures of generating capillary entry pressure ﬁeld have been elaborated in (Saadatpoor et al., 2010). Table 1 summarizes the properties of the base geologic model. J (Sw ) = pc (Sw ) σg / w cos θ k ϕ (2) In this model (Fig. 1), the pore volume of cells in the right boundary is adjusted to mimic diﬀerent types of aquifers (i.e., an open aquifer and a closed aquifer). This is realized by using the keyword VOLMOD in CMG-GEM (2012). The magnitude of VOLMOD is chosen based on the magnitude of injected CO2 volume. An extremely large VOLMOD (1.0E + 7) is assigned to the right boundary cells to mimic an open boundary condition. This boundary is convenient because it prevents pressure buildup during injection. Alternatively, a small (1E + 4) VOLMOD is used to mimic a closed aquifer system, which enables us to study the eﬀect of pressure buildup on LCT. The above base storage model is varied in terms of permeability anisotropy, dip angle, and heterogeneity. Permeability ﬁelds are set to be anisotropic by considering the vertical component of permeability to be a tenth, hundredth, and thousandth of the horizontal component. Three formation dip angles (0, 5 and 25°) are examined; they represent horizontal, moderately-deviated, and highly-deviated formations, respectively. Diﬀerent horizontal auto-correlation lengths and standard deviations of permeability are also considered. Table 3 summarizes the settings of these parameters. Following the storage model, a leakage model is built (Fig. 2). The leakage conduit has a permeability of 10 Darcy (9.87 × 10−12 m2) and width of 2 ft (0.609 m). The lower formation in Fig. 2 is the same as the storage domain in Fig. 1. The properties of the upper formation is the same as described in Saadatpoor et al. (2010), and the main diﬀerence is the right boundary settings; previous work (Saadatpoor et al., 2010) employs a closed boundary (VOLMOD = 1), but here an open boundary condition is created through using a large VOLMOD (1E + 7). 2.2. Components and rock-ﬂuid properties Component properties are the same as those in previous work (Saadatpoor, 2012; Kumar et al., 2005) with CO2 dissolution in brine considered. Figs. 3 and 4 show the relative permeability curves and the capillary pressure curves, respectively. They are consistent with each other. The capillary pressure curves in Fig. 4 are assigned to the simulation cells with the arithmetic mean of permeability. The corresponding capillary pressure curves for other cells are scaled using Leverett j-function with the detailed procedures described in Saadatpoor et al. (2010). The hysteresis in both the relative permeability and capillary pressure curves are considered. The above settings mean that dissolution and residual trapping are modeled in simulations. However, our main interest is on LCT. Mineral trapping is not considered. 2. Approach The simulator used in the study, CMG-GEM (2012), is a multidimensional and equation-of-state compositional simulator. It can simulate all the important mechanisms controlling CO2 sequestration into saline aquifers. 2.1. Reservoir properties A series of 2D models are generated, and they are vertically oriented since LCT occurs during buoyant ﬂow. Fig. 1a shows the based model with the properties detailed in Table 1. Permeability ﬁelds (Fig. 1b) are generated using a fast Fourier transform technique (Jennings et al., 2000). The advantages of the method are speed and global conditioning, and it can be applied in any number of dimensions. Porosity is correlated with permeability by Eq. (1) (Holtz, 2002). In Eq. (1), the unit of permeability is mD. The initial reservoir pressure is 2265.6 psi (15.62 MPa) with a constant reservoir temperature of 140 °F (60 °C). The settings of other parameters are the same as Saadatpoor et al. 2.3. Injection and leakage simulation schemes A buoyancy number is introduced to describe the inﬂuence of buoyancy on CO2 migration; the number is a dimensionless ratio of buoyancy to viscous force that drives CO2 migration. Several deﬁnitions of the buoyancy number are possible. Here, the buoyancy number (Ngr) is deﬁned in following form (Shook et al., 1992): 136 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Fig. 1. A 2D aquifer model. Dotted lines in (a) represents cells with a large volume modiﬁer (1E + 7), which is used to create an open aquifer. Table 1 Properties of the base 2D synthetic model (corresponding to Fig. 1). Model parameters 2D Model size, ft (m) Grid block size, ft (m) Permeability frequency distribution Autocorrelation length λx, λz, ft (m) Arithmetic mean of permeability, mD (m2) Anisotropy of permeability ﬁeld Standard deviation of permeability, mD (m2) Arithmetic mean of porosity Arithmetic mean of capillary entry pressure, psi (MPa) Standard deviation of capillary entry pressure, psi (MPa) 400 (121.92) × 100 (30.48) 1 (0.30)×1 (0.30) lognormal 5 (1.52), 0 (0) 200 (1.97 × 10−13) isotropic 340 (3.36 × 10−13) 0.27 2.07 (1.43 × 10−2) 1.36 (9.37 × 10−3) Fig. 3. Relative permeability curves. Adapted from Saadatpoor (2012). Fig. 2. A 2D schematic aquifer leakage model. The schematic diagram is adapted from Saadatpoor (2012). Changes are made on the right boundary cells that are indicated by dotted lines. Ngr = Δρgk v H cos α uh μL (3) In the above, Δρ is the density diﬀerence between brine and CO2, g is gravitational acceleration, kv is the mean vertical permeability, H is perforation length, α is formation dip angle with respect to the horizontal direction, uh is the nominal horizontal ﬂux entering formations from wellbores, μ is CO2 viscosity, L is reservoir horizontal length. Under the reservoir condition (15.62 MPa, 60 °C), CO2 density is 618.7 kg/m3, brine density is 1024.6 kg/m3, and CO2 viscosity is 0.0486 cp. All terms, except for uh, in the above expression are ﬁxed for a given storage reservoir and well completion. uh varies with injection rate. Thus, Ngr is essentially a dimensionless injection rate (a reciprocal Fig. 4. Capillary pressure curves for the reference grid blocks. injection rate). Small values of Ngr (10−2) correspond to large injection rates, with correspondingly minimal inﬂuence of buoyancy on CO2 plume movement. For commercial scale injection rates, Ngr is small in the portion near the wellbore. This is the region of primary interest in this study. Table 2 shows injection rates used in this study. The injected amount is chosen to exactly ﬁll the pore volume (PV) of the domain excluding the right boundary cells. The amount is determined to be 190 tonnes (1 PV). The same mass is injected under 137 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren injection parameters, reservoir static properties, and rock/ﬂuid interaction parameters. The ﬁrst group consists of well injection rate (indicated by Ngr), injected volume (in multiples of pore volume or PV), and injection well type. The second group is comprised of permeability anisotropy (kv/kh), formation dip angle (α), horizontal auto-correlation length (λx), coeﬃcient of variation (Cv), and aquifer type (i.e., the closed or open aquifer). The third group parameters are residual gas saturation (Sgr), relative permeability hysteresis, and capillary pressure hysteresis. This work reports how these parameters aﬀect LCT spatial extent and mass fraction at the end of each process (i.e., injection, postinjection, and leakage). LCT mass fraction is deﬁned as the ratio of LCT mass over the total CO2 mass injected. The CO2 saturation associated with LCT is deﬁned in the range between residual gas saturation (Sgr) to 100%. In other words, CO2 in cells with gas saturation above residual are categorized as LCT. Table 2 Injection simulation scheme in 2D domains. Injector type Injection ratea, m3/s Flux entering formation from wellbore, m/s Injection duration, yr Ngr along wellboreb, (Eq. (3)) Dominant force Vertical 1.61 × 10−4 2.12 × 10−4 20 20 Vertical Vertical Vertical 1.61 × 10−3 1.61 × 10−2 1.61 × 10−1 2.12 × 10−3 2.12 × 10−2 2.12 × 10−1 2 0.2 0.02 2.0 0.2 0.02 Point Point 3.47 × 10−7 3.47 × 10−5 2.12 × 10−3 2.12 × 10−1 26 0.26 2.0 0.02 Buoyant force Transition Transition Viscous force Transition Viscous force a b At the surface condition. Ngr is calculated for isotropic permeability ﬁelds. 3. Results 3.1. Injection parameters 3.1.1. Eﬀect of injection rate on LCT Fig. 6 shows CO2 saturation ﬁelds at the end of injection under diﬀerent injection rates. The injection eliminates the transition zone (the zone between the bottom CO2 emplacement area and the top CO2 accumulation area) observed in Saadatpoor (2012) during buoyant ﬂow under an initial emplacement. This elimination occurs at least near the wellbore for an isotropic domain. In the following section of the anisotropy eﬀect, it is shown that such a transition zone occurs when using very anisotropic media. At a large injection rate (Ngr = 0.02), the immiscible displacement is “compact”; CO2 goes into most of the cells in the domain during injection. This compact displacement leads to a widespread residual gas trapping (cyan pixels in the right column of Fig. 6) during water imbibition into the tail edge of CO2 plume during the post-injection period. In addition, the residual phase trapping surrounds LCT. However, when a small injection rate is employed (Ngr = 20), CO2 mostly follows channels of auto-correlated larger-than-average permeability, and saturation distributions for the immiscible displacement are ramiﬁed. As injection rates decrease, buoyancy stands out as the main driving force and gravity segregation is pronounced. Notably, for the small injection rate (Ngr = 20), the injected CO2 ﬂows into the storage domain from only the upper portion of the perforated interval. This is because, for the lower portion, CO2 pressure along the wellbore is less than reservoir hydrostatic pressure, which prevents CO2 in the wellbore from ﬂowing into the reservoir. Such a phenomenon has also been observed in sandbox experiments (Trevisan et al., 2014). However, this phenomenon disappears as injection rate increases (Ngr = 0.02). This observation necessitates the optimization of perforation intervals when using diﬀerent injection rates (Kumar and Bryant, 2008). Obviously, among the four injection rates, the largest Ngr gives the least ﬁlling of local capillary traps in the domain. In other words, the ﬁlling eﬃciency of local capillary traps decreases as a transition from compact displacement to capillary channeling, i.e. as injection rates decrease. On the other hand, the ﬁlling of local capillary traps within the region invaded during injection is essentially the same for all injection rates. That is, if a region contains CO2 at the end of injection and that region corresponds to a local capillary trap, then, at steady state, that trap will contain locally trapped CO2 at a large saturation, regardless of buoyancy numbers during injection. This makes sense since LCT is an equilibrium phenomenon. In other words, while the buoyancy number strongly inﬂuences the fraction of the reservoir into which CO2 ﬂows during injection (essentially 100% at the smallest buoyancy number and falling to about 50% at the largest buoyancy number in the left column of Fig. 6), the migration that ﬁlls traps to a large saturation Fig. 5. A schematic illustration of injectors. (Upper) a vertical well is located in the left boundary with the perforation interval represented by small blue bars. (Lower) a point injector is located in the middle bottom of the domain, and the blue dot represent perforation intervals. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) diﬀerent injection rates, this yields injection periods shown in Table 2. For conﬁgurations of injectors, Fig. 5 shows a schematic illustration of well types, perforation lengths, and well locations. Two types of injector are examined: a vertical injector and a point injector. The purpose of using a point injector is to mimic injection from a horizontal well; the point injection could be considered a vertical slice of a horizontal injector. Well injection rates are calculated using both the CO2 ﬂux entering the formation from a wellbore (refer to Table 2) and the perforation length (same as the grid size for the point injection in Fig. 5b). The ﬂow simulation consists of three sequential processes: 1) an injection period; 2) a post-injection storage process; and 3) a leakage period. Injection and post-injection lasts for a total of 50 yrs. At the end of post-injection, a leak conduit along injectors is manually introduced with leakage lasting for another 50 yrs (refer to the aquifer leakage model in Fig. 2). Table 3 summarizes all cases studied with diﬀerent settings of conditions. In these cases, parameters are divided into three groups: 138 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Table 3 Summary of conditions for simulations. λx, m Cv Injection rate, m3/s Leak Injected volume, PV Injector type Right boundary condition kv/kh Formation dip angle Residual gas saturation Capillary pressure hysteresis Relative permeability hysteresis Figure 1.52 0.66 No 1 Vertical Open 1 0 0.29 No Yes 6 1.52 0.66 Yes 1 Vertical Open 1 0 0.29 No Yes 7 1.52 1.52 0.66 0.66 No No 0.1–1 1 Vertical Point Open Open 1 0.001, 1 0 0 0.29 0.29 No No Yes Yes 9 10 1.52 1.52 0.66 0.66 No No 1 1 Vertical Vertical Open Open 0.001–1 1 0 0, 5, 25 0.29 0.29 No No Yes Yes 11 12 60.96 0.66 No 1 Vertical Open 1 0 0.29 No Yes 13 60.96 0.66 Yes 1 Vertical Open 1 0 0.29 No Yes 14 1.52 1.52 1.52 1.52 1.52 0.66, 0.14 0.66 0.66 0.66 0.66 1.61 × 10−4 to 1.61 × 10−1 1.61 × 10−4 to 1.61 × 10−1 1.61 × 10−1 3.47 × 10−7, 3.47 × 10−5 1.61 × 10−2 1.61 × 10−4, 1.61 × 10−1 1.61 × 10−4 to 1.61 × 10−1 1.61 × 10−4 to 1.61 × 10−1 1.61 × 10−1 1.61 × 10−1 1.61 × 10−1 1.61 × 10−1 1.61 × 10−2, 1.61 × 10−1 No Yes NA NA NA 1 1 1 1 1 Vertical Vertical Vertical Vertical Vertical Open Open, closed Open Open Open 1 1 1 1 0.001, 1 0 0 0 0 0 0.29 0.29 0.18–0.44 0.29 0.29 No No No No Yes Yes Yes Yes No No 15 16, 17 18 19 20 occur after injection ends. Hence, the spatial distribution of LCT are independent of buoyancy number. Meanwhile, it is instructive to verify that the steady state post-injection CO2 distribution occupies local capillary traps. Take the largest injection rate (Ngr = 0.02, left column of Fig. 6) for example, CO2 displaces water in every cell of the domain by the end of injection because viscous forces are large throughout this 2D domain. Obviously, CO2 has invaded all the regions corresponding to local capillary traps. CO2 has also invaded all the regions corresponding to capillary barriers. This is to be expected: the deﬁnition of a barrier is with respect to capillary forces, not to viscous forces. None of cells have zero permeability, and thus when viscous pressure is suﬃcient to overcome capillary entry pressure, CO2 can and does invade the entire domain. The detailed structure of heterogeneous reservoir can still be detected in the ﬁneFig. 6. CO2 saturation ﬁelds at the end of injection (left column) and at the end of postinjection (right column) for decreasing injection rates from top to bottom. 190 tonnes (equivalent to 1 P V) of CO2 were injected. At the end of injection (left column), the CO2 mass staying in the storage domain was 148, 106, 92, and 58 tonnes from top to bottom. The diﬀerence between the injected CO2 masses and the remaining has entered the column of very large cells on the right side of the domain. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) 139 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren scale variation of saturation ﬁelds in the left column of Fig. 6. As an aside, this is the reason why the simulation of conventional hydrocarbon reservoir processes, in which ﬂow at commercial rates is driven by viscous forces, routinely ignores the heterogeneity of capillarity (Lake et al., 2014). In these cases, the solution, in terms of where injected and reservoir ﬂuids go, is dictated by the structure of a permeability ﬁeld, and this can be determined with suﬃcient accuracy by ignoring capillarity. However, for geologic CO2 sequestration, the onset of buoyancy-dominated migration and displacement is a crucial portion of a storage process. This buoyant behavior cannot be described correctly unless the heterogeneity of capillary pressure is explicitly included. The widespread ﬁlling of local capillary traps under the large rate case is similar to behaviors observed in the large-emplaced volume limit of the buoyancy-driven storage scenario (Saadatpoor, 2012). In the latter emplacement scenario, all the local capillary traps get ﬁlled as the rising CO2 forms a gas cap and then backﬁlls non-barrier regions downward from the reservoir seal. During the injection with large rates, viscous forces enable CO2 to ﬁll all the rock volume. In both cases, essentially all the traps are ﬁlled. The next step of the storage process, when injection ceases, is that the injected CO2 and the remaining native brine are free to rearrange themselves in response only to buoyant force. Since CO2 saturation in most of the cells is greater than its residual saturation, it can be expected signiﬁcant migration will occur. The right column of Fig. 6 conﬁrms this expectation and it demonstrates that CO2 with large saturation accumulate within local capillary traps - even when the saturation in the trap at the end of injection was a moderate value. To see this, note how many of the yellow/red pixels in the right column correspond to green pixels in the left column of Fig. 6. Evidently, postinjection migration enables CO2 to build to the drainage curve limit in local capillary traps. Meanwhile, in regions that are neither traps nor barriers, CO2 present at the end of injection migrates until it leaves residual saturation behind (cyan pixels). Thus, local capillary traps in the near-well region are ﬁlled during injection, and they remain ﬁlled after post-injection buoyancy-driven ﬂow ends. To examine the robustness of LCT in the case of leakage, a leaking conduit is introduced along the wellbore at the end of the post-injection period and then another 50 yrs of leakage modeling is conducted to look into the change of CO2 saturation inside LCT under buoyant ﬂow. CO2 saturation ﬁelds at the end of leakage are in Fig. 7. Most of the LCT (bright yellow pixels) remain in place. This demonstrates that local capillary trapped CO2 is stable and robust. What leaks from the formation is the CO2 in ﬂow paths that are connected to the leakage conduit. Fig. 7. CO2 saturation ﬁelds at the end of leakage for two extreme buoyancy numbers Ngr (0.02 and 20). The initial condition of leakage modeling corresponds to right column in Fig. 6. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) large injection rate (refer to Table 2), respectively. Fig. 9c and d show CO2 saturation in the anisotropic (kv/kh = 0.001) ﬁeld at the end of injection using the above two rates. Overall, as the decrease of the buoyancy number (either by increasing injection rate or by decreasing vertical permeability), capillary ﬁngering gets suppressed and displacement becomes compact. This is favorable to the ﬁlling of local capillary traps. Compared to the vertical injector scenario, point injector gives more dispersed CO2 ﬂow. This is because: when the vertical injector is used, CO2 ﬂow velocity across the 2D domain changes negligibly. This is because the CO2 ﬂow across-area in the 2D domain increases marginally (∼4×) as CO2 migrates away from the injector (see Fig. 6 as an example). However, for the point injector, the velocity is decreased as CO2 migrates away from the middle injection point. The resultant impact on CO2 ﬂow is similar to that of decreasing injection rates (refer to Fig. 6). Fig. 9e and f show CO2 saturation at the end of post-injection, which correspond to Fig. 9b and c. Injection well types do not alter the extent of LCT, whereas, they largely inﬂuence the ﬁlling of local capillary traps. 3.1.2. Eﬀect of injected volume on LCT Fig. 8 shows CO2 saturation ﬁelds at the end of the post-injection period. Obviously, as the injected CO2 volume increases, more local capillary traps become ﬁlled. The injected CO2 mass does not aﬀect the extent of LCT; the bright yellow pixels common in the four cases have the same spatial distribution. This again indicates that local capillary traps are intrinsic to capillary entry pressure ﬁelds. Similar to the behavior (refer to Fig. 6) observed at diﬀerent buoyancy numbers, Fig. 8 shows that CO2 occupies all the local capillary traps within the region swept by CO2. Thus, the essential question during injection is what fraction of the reservoir volume get invaded by the injected CO2. The gravity driven ﬂuid movement after injection ends enables CO2 to ﬁll local traps in the swept region to a large (∼0.8) saturation. 3.2. Reservoir static properties 3.1.3. Eﬀect of well types on LCT A vertical injector is used in the above analysis. In this section, a point injector is placed at the middle bottom of the domain, to mimic a vertical slice of horizontal injection. Fig. 9a and b show CO2 saturation in the isotropic (kv/kh = 1) ﬁeld at the end of injection for a small, and a 3.2.1. Eﬀect of anisotropy on LCT As stated earlier, injection of large quantities of CO2 eliminates transition zones in an isotropic formation, even when perforations are 140 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Fig. 8. CO2 saturation ﬁelds at the end of post-injection. Diﬀerent PV of CO2 were injected under a ﬁxed injection rate (Ngr = 0.02). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) This CO2 becomes the source CO2 zone for the post-injection buoyant ﬂow, during which, transition zones and gas caps are generated. The right column of Fig. 10 shows CO2 saturation at the end of post-injection, which conﬁrms the formation of transition zones. In the right column (at the end of post-injection) of Fig. 10, structures and distributions of LCT (bright yellow pixels) are similar in the ﬂooded areas common for four anisotropies. However, CO2 saturations are a little diﬀerent. The ﬁrst three ﬁelds have a higher CO2 saturation in local capillary traps than the highest anisotropic ﬁeld does. This is because the ﬁrst three have relatively large mass of CO2 left in the storage domain: as calculated for the left column of Fig. 10, the mass of CO2 staying in the storage domain were 106, 110, 97, and 69 tonnes, only in the bottom quarter of the domain. On the other hand, such transition zones are an important feature of CO2 migration from an initial emplacement of CO2 at the bottom of a storage domain (Saadatpoor, 2012). Therefore, it is important to determine if transition zones arise during long-term injection under other conditions. The condition most likely to lead to this situation is permeability anisotropy as shown in the eﬀect of well types on LCT. Here, kv/kh is set to be 0.1, 0.01, and 0.001 by decreasing vertical permeability. Fig. 10 shows the CO2 saturation ﬁelds at the end of injection. As kv/kh decreases (anisotropy increases), CO2 tends to ﬂow along the bottom of the domain. When kv/kh decreases to be 0.001, the injected CO2 is mainly restricted at the bottom at the end of injection. Fig. 9. CO2 saturation ﬁelds created through a point injector in the middle bottom of the domain. The upper row is CO2 saturation ﬁelds at the end of injection for the isotropic permeability ﬁeld using two diﬀerent injection rates (refer to Table 3). The middle row is CO2 saturation ﬁelds at the end of injection for the very anisotropic permeability ﬁeld using the same injection rates as the upper row. The lower row is CO2 saturation ﬁelds at the end of post-injection following CO2 distribution shown in the middle row. Anisotropy is increased by decreasing vertical permeability. Recall both injection rate and vertical permeability are considered in the deﬁnition of Ngr. 141 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Fig. 10. CO2 saturation ﬁelds at the end of injection (left column) and at the end of post-injection (right column). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) the inclined formation. This suggests, if small injection rates have to be employed (because of, e.g., small formation fracture pressure), it would be better to choose a horizontal saline aquifer to enhance LCT. respectively. In the transition zones (refer to the right column of Fig. 10), CO2 migrates along some of the ﬂow paths to reach the top seal but leaves a large gas saturation in the ﬂow path. Large CO2 saturations accumulate below the top seal but not uniformly. Notably, for the most anisotropic ﬁeld, almost half of the upper portion of the domain is uninvaded by CO2. Obviously, the local capillary traps in the portion are not ﬁlled. 3.2.3. Eﬀect of auto-correlation length on LCT Fig. 12 shows CO2 saturation at the end of injection and at the end of post-injection in the 2D domain with a large horizontal auto-correlation length of 60.96 m. Recall, the base case uses a horizontal autocorrelation length of 1.52 m. The large horizontal auto-correlation length enhances lateral migration of CO2, and gives rise to remarkable distribution patterns of CO2. For large injection rates, CO2 sweeps the whole domain and therefore, all the local capillary traps are ﬁlled. However, for small injection rates, auto-correlated structures with relatively small capillary entry pressure determine the CO2 preferential ﬂow paths, so large horizontal auto-correlation suppresses the upward migration of CO2. This is further reﬂected in Fig. 13 that shows CO2 saturation ﬁelds at the end of leakage. For the small injection rate, all the injected CO2 stays inside the storage formation, and no CO2 leaks out. However, for the large injection rate, both capillary barriers and ﬂow paths are ﬂooded. This causes some of CO2 to move toward the wellbore and subsequently escape from the storage formation. Through comparing Fig. 12 (λx = 60.96 m) to Fig. 6 (λx = 1.52 m), a large horizontal auto-correlation length yields: (1) widely extended LCT structures; (2) a large LCT mass fraction (it increased from 36% to 48 as λx increased from 1.52 to 60.96 m). Additionally, in the case of leakage, a large horizontal auto-correlation yields less leakage of CO2 along the wellbore (Fig. 13 vs. Fig. 7). This is because large horizontally auto-correlated ﬂow paths cause CO2 to migrate laterally, rather than upward. 3.2.2. Eﬀect of formation dip angle on LCT Fig. 11 shows CO2 saturation in formations with dip angles of 0°, 5°, and 25°. For each dip angle, both the smallest and largest injection rates (refer to Table 2) are employed. For the largest injection rate, the mass of CO2 staying in the storage domain (the 399 × 100 ft portion) at the end of post-injection for the three dip angles was 147.6, 147.73, and 148 tonnes, respectively. Whereas, for the smallest injection rate, the mass of CO2 remaining in the storage formation at the end of postinjection was 57.6, 48.6, and 25.8 tonnes, respectively. Thus, formation dip angle tends to have a greater impact on stored mass of CO2 inside a ﬁxed area under small injection rates (Ngr∼20). In a moderate dip (5°) formation, the structures of LCT are similar to those in the horizontal formation. However, when the formation becomes highly inclined (25°), LCT structures tend to be parallel to the formation inclination. Notably, when the injection rate is smaller for the highly-deviated formation, CO2 migration tends to be dominated by several of the capillary channels. For this scenario, obviously, most of the local capillary traps cannot be ﬂooded. The laterally extensive local capillary traps become convenient conduits for moving CO2 rapidly to the right boundary (Fig. 11). However, for the smallest injection rate (right column in Fig. 11); LCT ﬁlling eﬃciency in the horizontal formation is better than that in 142 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Fig. 11. CO2 saturation ﬁelds at the end of post-injection for the largest (left column) and smallest injection rate (right column). Recall the deﬁnition of Ngr includes the parameter of formation dip angle, so Ngr changes slightly with dip angles. The model vertical dimensions are visually compressed due to the incorporation of dip angle. All the models have the size of 121.92 m (along the dip direction) × 30.48 m (along the vertical direction). ft = 4.07 × 10−3 MPa/m). Hence, this is helpful to examine the robustness of LCT under viscous ﬂow. Under viscous ﬂow (Fig. 15b), the size of LCT (dispersed bright yellow) and magnitude of associated LCT saturations become small, as compared to the local capillary trapping under buoyant ﬂow of leakage (Fig. 15a). However, many small patches of local capillary trapping remain in the former case even after 50 yrs of leakage. Next, the mass of LCT in the storage domain is compared to residual and dissolution trapping. Fig. 16 shows the variation of trapped CO2 mass fraction along time (injection, post-injection, and leakage) for both closed and open aquifers. Many studies have examined the fraction change of CO2 in forms of residual phase trapping, dissolution trapping, and free states [e.g., Kumar et al. (2005), Doughty (2007), Taku Ide et al. (2007)]. Their analyses are restricted to the injection and postinjection periods. Whereas, this work focuses on the post-injection and leakage periods because LCT mainly takes the eﬀect on the safe storage of CO2 during these periods. During the post-injection period, LCT decreases while residual phase trapping increases: the former is converted into the latter as water imbibes into the trail of CO2 plume. During leakage, CO2 ﬂows toward to the leak point and then escapes from the formation in a short time period. After that, buoyant ﬂow approaches to a steady state, and the mass fraction of CO2 in diﬀerent forms keeps almost constant. LCT immobilizes more CO2 than dissolution trapping in the closed aquifer, while for the open aquifer, LCT can play as signiﬁcant role as residual phase trapping in storing CO2. It should be noted that those mass fractions are measured in a small (1.52 m) horizontally auto-correlated domain. They would change with horizontal auto-correlation length. Speciﬁcally, at the end of leakage, the LCT mass fraction was 0.37 for the open aquifer, and it was 0.15 in the closed aquifer. This indicates that viscous force compromises LCT during leakage, and LCT is sensitive to aquifer pressure. This ﬁnding is consistent with laboratory 3.2.4. Eﬀect of standard deviation of capillary entry pressure on LCT The above analysis demonstrates the spatial heterogeneity or autocorrelated structures of capillary entry pressure determines LCT amount and distribution. This part shows the eﬀect of another indicator of heterogeneity (i.e., standard deviation) on LCT. Fig. 14 shows CO2 saturation ﬁelds at the end of post-injection for capillary entry pressure ﬁelds with diﬀerent coeﬃcient of variations (Cv). Cv is the ratio of the standard deviation to the mean of capillary entry pressure. Larger Cv gives rise to a denser distribution of LCT (the yellow and red pixels). Quantiﬁcation shows the LCT volume fraction increased from 22 to 28% as Cv increased from 0.66 to 1.14. 3.2.5. Eﬀect of aquifer types on LCT All the above studies are limited to the eﬀect of buoyant force on LCT robustness in an open system where aquifer pressure has almost no change during the storage period; it increased by only 5 psi at the end of post-injection. However, pressure build-up would be encountered in a closed aquifer (Ehlig-Economides and Economides, 2010). Thus, during leakage, viscous ﬂow would be expected, which is driven by the relaxation of pressure build-up of a storage aquifer into the still hydrostatic pressure of an upper aquifer. The eﬀect of viscous ﬂow on LCT is examined through modelling leakage from a closed aquifer. The domain conﬁguration is the same as before except that a small VOLMOD (1.0E + 4) is employed to the right boundary cells. Meanwhile, the injected CO2 mass is kept at 190 tonnes (1 P V). Thus, the ﬁnite size of the domain is noticeable for the volume of CO2 injected, and consequently the ﬂuid pressure in the domain will increase during injection. At the moment of leakage or at the end of post-injection, the average pressure build-up relative to the original reservoir pressure was about 2000 psi (13.79 MPa). This gives rise to a pressure gradient (from the storage aquifer to the upper aquifer) around 10 psi/ft (0.23 MPa/m), which is much larger than buoyancy pressure gradient (0.18 psi/ 143 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Fig. 12. CO2 saturation ﬁelds at the end of injection (left column) and at the end of post-injection (right column). in terms of underlying mechanisms: the former trapping is resulted from the heterogeneity of capillary entry pressure at large or representative element volume scales, whereas, the latter is caused by snap-oﬀ (Roof, 1970) at pore-scales. experiments (Sun, 2014), in which locally trapped non-wetting phase remain intact when system pressure is hydrostatic, but when forcing imbibition occurs (driven by imposing a gradient in hydraulic potential in aqueous phase in the domain), much of the locally trapped phase is displaced. 3.3.3. Eﬀect of capillary hysteresis on LCT Fig. 19 shows CO2 saturation ﬁelds at the end of injection in the very anisotropic domain for cases without and with capillary hysteresis, respectively. In the compact displacement region, most of the CO2 inside local capillary traps have been displaced after considering capillary hysteresis. However, the remaining CO2 saturation after capillary imbibition was still around 0.4–0.5 (see scattered green pixels in Fig. 19b). Recall the residual gas saturation is 0.29, so the remaining CO2 saturation in LCT is still larger than residual gas saturation. The right open boundary condition creates “a very large aquifer”. This supplies enough water for the imbibition. Even after the complete imbibition, CO2 inside local capillary traps cannot be entirely displaced to the residual level even after 50 yrs of buoyant ﬂow. Moreover, in the transition zone, LCT keeps intact after considering capillary hysteresis. The yellow pixels (Fig. 19b) with high CO2 saturation are LCT. They are not compromised by capillary hysteresis, even if they are surrounded by water with high saturation. 3.3. Rock/ﬂuid interaction parameters 3.3.1. Eﬀect of residual gas saturation on LCT Recall the base case sets the residual gas saturation to be 0.29. Here, the residual gas saturation is changed from 0 to 0.44. This range is representative of sandstone/sand-packs (Iglauer et al., 2011). Fig. 17 shows the mass fraction of LCT, residual phase trapping, and dissolution trapping at both the end of post-injection and the end of leakage. These mass fractions change little during leakage, thus, curves almost overlap at the two measured times. As residual gas saturation increases, the LCT mass fraction decreases signiﬁcantly, and meanwhile, dissolution trapping decreases slightly. LCT and residual phase trapping compete with each other. 3.3.2. Eﬀect of relative permeability hysteresis on LCT Fig. 18a shows CO2 saturation ﬁelds with relative permeability hysteresis added (base case); the hysteresis is the reason for widespread residual gas (cyan color) inside the domain. Without hysteresis, residual phase trapping does not occur (Fig. 18b). However, LCT still occurs. In addition, its structures and saturation are similar to the case with hysteresis: the spatial distribution of high (∼0.8) CO2 saturation patches are similar in the two ﬁelds of Fig. 18. This means that the hysteresis in relative permeability has no eﬀect on LCT. Additionally, this observation indicates that LCT is diﬀerent from residual phase trapping 4. Discussion The spatial auto-correlated distribution of capillary entry pressure determines the extent of LCT. Such trapping determines the ﬁnal distribution of CO2 in a storage aquifer. Therefore, the amount of CO2 that is trapped locally changes with the spatial heterogeneity of capillary entry pressure. Speciﬁcally, the potential of LCT increases as a storage 144 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren analyses of spatial correlation eﬀects on capillary trapping of CO2 (Trevisan et al., 2015). For the capillary pressure hysteresis, our simulation results show that capillary hysteresis compromises LCT in compact displacement regions, rather than transition zones (Fig. 19). This is because the storage domain is connected to a large aquifer (recall the use of large volume modiﬁer for the boundary cells in the Approach Section). Aquifer water tends to move downward toward the compact region and imbibes into LCT. Thus, CO2 in the LCT are displaced. This is diﬀerent from Gershenzon et al. (2017b) which observed that capillary pressure hysteresis shows a negligible eﬀect. The reason behind this diﬀerence might be boundary conditions and capillary pressure magnitudes. The simulation results in this work show that LCT amounts are increased when decreasing Ngr. The decrease of Ngr can be realized through increasing injection rates (e.g., Fig. 6). This observed eﬀect of injection rate is consistent with Gershenzon et al. (2017b) that shows increasing injection rates enhances the amount of capillary pinned CO2. Speciﬁcally, this work shows that local capillary traps in near-well regions can be fully ﬁlled (CO2 invades all the traps and establishes a large saturation) during injection in an isotropic domain when the corresponding Ngr is less than 2. This region is named as a “compact displacement region” in the above. Moreover, local capillary traps remain ﬁlled after post-injection buoyancy driven ﬂow ends. The next question would be how large this “compact region” can be in a typical injection scenario in a 3D domain. Consider a vertical CO2 injector in an open aquifer, the aquifer thickness is 390 ft (118.87 m), and the vertical perforation interval is in the lower quarter part. CO2 is injected at the surface rate of 5.0E + 7 Scf/d (16.39 m3/s). The average vertical permeability is 20 mD (1.94 × 10−14 m2). The properties of brine and CO2 are the same as described above. The calculated radius of the compact region is around 60 ft. Therefore, such a “near-well region” is small for typical injection rates. For leakage modeling, a single leakage conduit along a wellbore is used to model the most probable leakage scenario of CO2 (Tao, 2012). Admittedly, LCT amount would be inﬂuenced by leakage settings, including the number of leakage points, leakage time, and the connection between leakage points and local capillary traps. Thus, the mass fraction of LCT calculated above would be changed as well. This work employs a simple way to estimate LCT. The cells in simulation models with CO2 saturation larger than residual phase saturation are considered as LCT. This approach to quantifying LCT is not accurate as some CO2 classiﬁed as LCT are structurally trapped in the locations just below the seal. However, the overestimation of LCT is relatively small in the cases examined. In the modeling eﬀorts, long (100 yrs) buoyant ﬂow simulations are run in order to i) enable CO2 to have enough time to charge local capillary traps; and ii) force the structurally-trapped CO2 to move laterally into the right boundary cells as much as possible. This minimizes the eﬀect of structural trapping on LCT. For example, through comparing the left uppermost ﬁeld of Fig. 6 to the upper ﬁeld of Fig. 7, it can be seen that structural trapping inﬂuences only a very small portion of the storage domain (i.e., the uppermost several layers). Alternatively, the bounds of LCT amounts Fig. 13. CO2 saturation ﬁelds after 50 yrs of leakage following the right column of Fig. 12. Two extreme buoyancy numbers (0.02 and 20) are shown in the ﬁgure. reservoir becomes heterogeneous (e.g., long horizontal auto-correlation length and large standard deviation of permeability; refer to Figs. 6, 12, and 14). The observation of the eﬀect of standard deviation on LCT is consistent with other studies (Gershenzon et al., 2015, 2017a,b), in which, the inﬂuence of small-scale ﬂuvial architecture on capillary pinning (it is essentially local capillary trapping) was systematically investigated. They showed that the amount of capillary pinning changes with (1) the volume portion of ﬁne grains to coarse grains changes the amount of capillary pinning; (2) the permeability and capillary pressure contrast between rock types. The observation of the eﬀect of autocorrelation length on LCT was also supported by the experimental Fig. 14. CO2 saturation ﬁelds at the end of post-injection for the capillary entry pressure ﬁelds with two coeﬃcients of variation (Cv). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) 145 International Journal of Greenhouse Gas Control 78 (2018) 135–147 B. Ren Fig. 15. CO2 saturation ﬁelds after 50 yrs of leakage modeling in an open aquifer (a) and in a closed aquifer (b). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) Fig. 17. Variation of CO2 mass fraction in diﬀerent forms with residual gas saturation. of LCT. This kind of system is mimicked by choosing a very large volume multiplier on the right boundary grid blocks and injecting the proper amount of CO2. LCT could be as signiﬁcant as residual gas trapping in immobilizing CO2 in the intermediate period of leakage from the open aquifer. This signiﬁcance is enhanced as aquifer heterogeneity become horizontally correlated in space. Thus, LCT would greatly enhance CO2 sequestration safety and reﬁne risk assessment framework. For the static reservoir parameters, the heterogeneity of permeability/capillary entry pressure ﬁelds essentially determines the LCT amount and structure. The injection parameters (i.e., injection rate and injected volume) inﬂuence only the ﬁlling eﬃciency of local capillary traps. This suggests that LCT can be maximized through manipulating injection strategies. The rock/ﬂuid interaction parameters (e.g., hysteresis in relative permeability and capillary pressure curves) aﬀect CO2 saturation in LCT, but not the spatial conﬁgurations of LCT. Overall, through compositional simulation, this work demonstrates that LCT is one of the most important trapping mechanisms during geological carbon sequestration in saline aquifers. Therefore, in the future CO2 sequestration projects, LCT should be considered during the design and optimization of trapping processes. Fig. 16. Variation of CO2 mass fraction stored by LCT, residual gas, and dissolution along with time. (a) is for a closed aquifer, (b) is for an open aquifer. could be estimated through analyzing the constitutive capillary pressure curves (Gershenzon et al., 2017b) or invoking reduced-physics modeling methods (Ren et al., 2018). 5. Summary and conclusions This work employs a commercial reservoir simulator CMG-GEM to study the inﬂuential parameters of local capillary trapping (LCT). These parameters are categorized into three groups: reservoir static parameters, injection parameters, and rock/ﬂuid interaction parameters. CO2 injection into heterogeneous 2D domains is simulated with two main objectives: i) to examine whether ﬂow rates (measured by gravity number) alter the extent of LCT; and ii) to determine whether an open system, generally encountered in sedimentary basins, alters the extent Acknowledgements The author would like to thank the sponsors of the Geological CO2 Storage Industrial Aﬃliates Project at The University of Texas at Austin. 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