International Journal of Greenhouse Gas Control 78 (2018) 48–61 Contents lists available at ScienceDirect International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc Trapping of buoyancy-driven CO2 during imbibition ⁎ T Niels Bech , Peter Frykman Geological Survey of Denmark and Greenland (GEUS), Denmark A R T I C LE I N FO A B S T R A C T Keywords: Buoyancy driven CO2 Imbibition Residual trapping Capillary trapping CO2sequestration This paper presents a simulation study on the inﬂuence of rock heterogeneity on the distribution and magnitude of trapped CO2 resulting from a drainage/imbibition sequence in a saline aquifer with buoyant CO2. Four scenarios are studied, three simple 1D cases and a 2D case with heterogeneity derived from realistic architecture inspired by tidal sand deposits, having combined layering and crossbedding and sediment property contrasts. The four cases are examined in order to understand which underlying mechanisms are responsible for the results observed and therefore also which processes it is necessary to reﬂect in the simulation procedure. It is shown that it is important to take into account hysteresis in the capillary pressure. During the imbibition the capillary pressure decreases and the ability to capillary trap the CO2 is reduced and it may in some cases completely vanish. Thus, the capillary pressure hysteresis has a major impact on the amount of trapped CO2. If the imbibition curve has a threshold pressure the sealing power of the barrier is not completely lost, which leads to hyper-trapping, characterised by mobile CO2 being trapped with above end-point saturations. If the imbibition capillary pressure reaches zero, only local barriers constituting eﬀective seals are able to trap free and potentially mobile CO2 and the trapping mechanism is exactly the same as the one acting beneath the top seal. The neglection of capillary pressure hysteresis may result in a large overestimation of the amount of trapped CO2. 1. Introduction During CO2 injection in a saline aquifer the CO2 is typically trapped by the following mechanisms: • Structural trapping • Dissolution trapping • Residual trapping • Mineral trapping Over the last years, an additional trapping mechanism, local capillary trapping, has been examined Saadatpoor et al. (2010, 2011), Krevor et al. (2011); Behzadi et al. (2011); Behzadi and Alvarado (2012); Ren et al. (2014); Meckel et al. (2015); Krevor et al. (2015). The local capillary trapping is supposed to occur during buoyancy-driven migration of bulk phase CO2 within a saline aquifer exhibiting spatially varying properties such as permeability and capillary entry pressure. It closely corresponds to structural trapping at small scale under local seals with suﬃciently high capillary entry pressure which cannot be penetrated due to insuﬃcient column heights in the upwards migrating CO2. Saadatpoor et al. (2010, 2011) demonstrated by means of ﬁne scale ⁎ reservoir simulations that free, stagnant, but mobile (relative permeability > 0) CO2 may be trapped locally beneath capillary barriers. They have however, not taken into account capillary pressure hysteresis which they consider to have a small impact compared to hysteresis in the gas relative permeability. Krevor et al. (2011) have conducted experiments which demonstrate that “CO2 plumes can be immobilized behind capillary barriers as a continuous phase at saturations higher than would be possible as isolated ganglia”. Behzadi et al. (2011) and Behzadi and Alvarado (2012) conducted simulations which exhibit capillary trapping, but like Saadatpoor et al. (2010) they neglected capillary pressure hysteresis and the same assumption was used by Frykman et al. (2013), Ren et al. (2014) and Meckel et al. (2015). Frykman et al (2013) also ignored hysteresis by using the drainage curve also for the imbibition, and enthusiastically coined the term "hyper-trapping" for the mobile CO2 with above-endpoint saturations below the low-permeability barriers. Except for Saadatpoor et al. (2010), no reason is given for the neglection of the capillary pressure hysteresis. Altundas et al. (2011) show that the inclusion of capillary pressure hysteresis in the simulations reduces the migration rate of the CO2 plume. But, they consider a homogeneous and isotropic reservoir, so Corresponding author at: Geological Survey of Denmark and Greenland (GEUS), Øster Voldgade 10, Copenhagen K, DK-1350, Denmark. E-mail address: nbe@geus.dk (N. Bech). https://doi.org/10.1016/j.ijggc.2018.06.018 Received 6 July 2017; Received in revised form 31 May 2018; Accepted 20 June 2018 1750-5836/ © 2018 Elsevier Ltd. All rights reserved. International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman 2.1. Case I. 1D homogeneous case none of the phenomena described in the present paper appear here. Delshad et al. (2013) present ﬁeld scale simulations of CO2 sequestration in the Cranﬁeld reservoir in Mississippi. They demonstrate the importance of taking into account hysteresis in both capillary pressure and relative permeability, but it is not possible to see any local details of how the capillary pressure hysteresis aﬀects the trapping of CO2. Moreover, the simulated post injection period is rather short (less than 10 years). Mansour et al. (2013) investigate residual trapping of CO2 in a saline aquifer through analytical and numerical simulation methods using hysteresis in both relative permeability and capillary pressure. Their simulation cases are however, homogeneous and isotropic, so capillary trapping below local seals cannot occur. They appear to use the term “capillary trapping” synonymously with residual trapping. Gershenzon et al. (2014) describe the inﬂuence of small scale heterogeneity on CO2 trapping processes in saline aquifers. They compare simulation results obtained with and without capillary pressure hysteresis. The diﬀerence in CO2 saturation distribution is not large for the two cases, but that is probably due to the fact that the situation displayed is far from equilibrium which means that the various reservoir variables will still undergo signiﬁcant changes. It is evident that CO2 has started to escape upwards through the tight sand due to decreasing capillary pressure in the hysteresis case. Their approach does not allow a more precise analysis of the eﬀect of including or neglecting capillary pressure hysteresis. Gershenzon et al. (2017) have studied capillary trapping or pinning in heterogeneous ﬂuvial-type reservoirs. They consider the injection period only and conclude that capillary pressure has a negligible inﬂuence on the result, but increases the simulation time considerably. Zheming and Agarwal (2014) consider capillary pressure hysteresis in their numerical simulation of the Frio SAGCS pilot project, but there is no mention of its eﬀect. In a recent review by Krevor et al. (2015) it is concluded that “… a large body of theoretical, numerical and experimental research has led to a greatly increased understanding of capillary trapping during CO2 storage”. However, the conclusions are based on results either from simulations neglecting capillary pressure hysteresis or from observed post injection periods covering not more than 10 years where conditions are far from equilibrium. What is the situation after 50 or 100 years? The objective of the present work is to examine and illustrate in detail the mechanisms that determine the trapping of buoyancy driven CO2 in a strongly water wet aquifer. The study is focusing on the trapping processes after injection stop when the injected plume migrates and the buoyancy and capillary forces dominate. The amount of capillary and residual trapping is quantiﬁed for four simple, vertical scenarios. We consider only one injection cycle, i.e. constant injection for a certain time followed by an equilibration period where imbibition occurs as the CO2 plume is migrating upwards. The paper is organized as follows: In Section 2 we describe the four cases examined and Section 3 presents the results obtained. Section 4 contains a short summary of the work and the conclusions. The applied reservoir simulator is Eclipse 100, Schlumberger (2013). This case is the simplest possible and it is considered in order to see the equilibrium saturation in a completely homogeneous reservoir. The grid is deﬁned as follows: • Number of axial grid cells, n : 1 • Number of vertical grid cells, n : 160 • Axial grid cell size, Δx : 0.5 m • Lateral grid cell size, Δy : 0.5 m • Vertical grid cell size, Δz : 0.5 m • Absolute permeability, K : 800 mD • Porosity, φ : 0.35 • Pore volume multiplier in top cell : 500. • Pore volume multiplier in bottom cell: 500. x z In the top and bottom cells of the reservoir, grid cells number 1 and 160, respectively, pore volume multipliers are applied to give a pore volume enabling the two cells to serve as a CO2 source and sink, respectively and making sure that the entire reservoir section is ﬂooded by CO2. The saturation parameters are: • Irreducible water saturation, S : 0.121 • Critical CO saturation, S : 0. • Max. residual CO saturation to water, S • Capillary entry pressure, P : 0.012 bar wir 2 gc 2 grwmax : 0.352 ce The critical gas saturation is set to zero. Its value has no impact on the conclusions in this qualitative study. Hysteresis is applied in both relative gas permeabilty, krg,and capillary pressure, Pc, but not in the water phase. Two cases of capillary pressure hysteresis has been considered, one with a treshold pressure in the imbibition curve and one where the imbibition capillary pressure passes through zero (Kleppe et al. (1997); Skjaeveland et al. (1998); Bech et al. (2005)). The saturation functions are given in Figs. 2–4. Except for the bottom cell, the brine saturation in the reservoir is 100% initially. The bottom cell contains 40% CO2 and 60% CO2 saturated brine. These initial values make sure that the entire reservoir section is ﬂooded by CO2.The simulation continues until equilibrium is reached i.e., when both ﬂuids are stagnant. 2.2. Case II. 1D homogeneous case with a single tight layer This case is chosen in order to see how a tight layer inﬂuences the equilibrium saturation. Case II is identical to Case I, except that one of the cells contains low permeability rock type with properties: • Absolute permeability, K : 1 mD • Irreducible water saturation, S : 0.6 • Critical CO saturation, S : 0. • Max. residual CO saturation to water, S • Capillary entry pressure, P : 0.212 bar wir 2 gc 2 grwmax : 0.238 ce See also Figs. 2–4. The low permeability rock properties are given to cell 150 which is situated 5.25 m above the bottom. This is slightly above the entry height which means that the cell will be invaded by CO2. The entry height, hentry, of the tight rock is determined as follows: 2. Cases considered The cases considered are 1D or 2D, xz with heights 80 m and a porosity of 35%. In the top cell (nz = 1) and the bottom cell (nz = 160) pore volume multipliers are applied to give pore volumes enabling the two cells to serve as a CO2 source and sink, respectively. The four examples are shown schematically in Fig. 1. The initial pressure is 180 bars at a depth of 1800 m and the temperature is 66 °C. The reservoir ﬂuid is 25% concentration brine. In all cases hysteresis is modeled by means of Killoughs method (Killough, 1976). hentry = 49 Pce g (ρw −ρCO2 ) (1) ρCO2 ∼ 572 kg/m3 (2) ρw = 1177 kg/m3 (3) International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 1. Scematic illustration of geometries for the four cases. In the illustration of Case IV, the subsection is placed 20 m above the bottom of the reservoir. The two vertical boundaries are closed. Pce = 0.212 bar height of the CO2 column. When located higher in the reservoir the CO2 uptake will be larger. The subsection consists of a ﬁne-grid, 2D, x-z model for crossbedded shallow marine/tidal sands with eight sediment classes, ranging from high-permeable sand to low permeable material as thin layers, conf. red region in Fig. 1. The width of the heterogeneous subsection is 0.0875 m and the height is 0.4025 m, conf. Fig. 6. The total height of the reservoir is 80 m as in cases I to III, but the width is only 0.0875 m corresponding to the width of the subsection. Grid parameters are: (4) and hentry = 3.57 m (5) Here g is the acceleration of gravity, ρCO2 is the CO2 density and ρw is the density of brine. 2.3. Case III. 1D homogeneous case with two tight layers • Number of axial grid cells, n : 25 • Number of vertical grid cells, n : 141 with 115 in the subsection • Axial grid cell size, Δx : 0.0035 m • Lateral grid cell size, Δy : 0.5 m • Vertical grid cell size, Δz : 0.0035 m in subsection, up to 40 m outside depending on location of subsection. • Absolute permeability, K : 800 mD outside subsection, for subsection see Fig. 6. • Porosity, φ : 0.35 • Pore volume multiplier in top and bottom cells : See Table 1 What if the reservoir column contains two tight layers? This case is identical to Case II, except that both cell 75 (42.75 m above the bottom) and cell 150 (5.25 m above the bottom) contain the low permeability rock type, conf. Sec. 2.2. x z 2.4. Case IV. 2D case with heterogeneous subsection at diﬀerent heights above the reservoir bottom The purpose with this case is to examine the CO2 trapping in a more realistic geometry and evaluate the importance of the location of the subsection, i.e. its height above the bottom of the reservoir. When situated low in the reservoir CO2 penetration will be small due to a small The top of the subsection has been placed from 2 m to 60 m above Fig. 2. Relative permeability of water for two rock types with absolute permeability K = 800 mD and 1 mD respectively. Hysteresis is not considered in the water phase. 50 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 3. Relative permeability of CO2 for two rock types with absolute permeability K = 800 mD and 1 mD respectively. the bottom of the reservoir which is at a depth of 1880 m. The subsection height of 0.4025 m is gridded into 115 grid cells, leaving 26 cells with which to grid the homogeneous section of the reservoir which is outside of the subsection. The two reservoir sections above and below the subsection are both gridded with 13 cells. In the top and bottom cells of the reservoir pore volume multipliers are applied to give a pore volume equal to approximately 1.9 m3 enabling the two cells to serve as a CO2 source and sink, respectively. The subcases considered and their corresponding pore volume multipliers of top and bottom cells are given in Table 1. Fig. 5 shows examples of two subcases with the subsection placed 20 m and 40 m above the bottom of the reservoir, respectively. The eight rock types or sediment classes of the heterogeneous subsection have been assigned permeability properties and capillary pressure functions with absolute permeabilities ranging from 1 mD to 800 mD. The capillary pressure functions are linked to the permeability, and consistent endpoints for all functions are incorporated. The absolute permeability distribution is shown in Fig. 6. Examples of the saturation functions applied in the study are given in Figs. 7–9. Hysteresis is taken into account in both relative gas permeabilty, krg, and capillary pressure, Pc, but not in the water (Fig. 2). The imbibition capillary pressure in this case is assumed to equal zero at the residual gas saturation. Important saturation function parameters are given in Table 2. Table 1 Case IV. Subcases considered and correspondingpore volume multipliers of top and bottom cells. 60 M refers to the case where the top of the subsection is placed 60 m above the bottom of the reservoir. Subcase Δz1 (m) (Top cell) Δz141 (m) (Bottom cell) MULTPV1 (Top cell) MULTPV141 (Bottom cell) 60 M 40 M 20 M 15M 10M 7M 5M 4M 3M 2M 9.08 19.4 30.1 32.8 35.6 37.2 38.3 38.9 39.4 40.0 30.1 19.4 9.08 6.61 4.21 2.82 1.93 1.49 1.07 0.668 13.9 6.52 4.20 3.85 3.56 3.40 3.30 3.25 3.21 3.16 4.20 6.52 13.9 19.2 30.1 44.9 65.0 84.7 118 189 Except for the bottom layer the reservoir contains 100% brine initially. The bottom layer contains 40% CO2 and 60% CO2 saturated brine. The simulation continues untill equilibrium is reached. Fig. 4. Capillary pressure of CO2 for two rock types with absolute permeability K = 800 mD and 1 mD respectively. 51 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 5. Scematic illustration of gridding and relationship between depth, height and grid cell numbers for the two subcases 20 M and 40 M. 3. Results It is seen that the maximum attained drainage saturation occurs in the lowermost grid cell 159 and is equal to 0.368. It is clear that using Sgrwmax to estimate CO2 storage capacity will, in many cases, lead to a large overestimation of the residual CO2. It is also seen (cell 2, blue line) that the CO2 reaches the top after about 76 days. The results in Fig. 11 were obtained with no threshold pressure in the capillary imbibition curve. 3.1. Case I. Results for homogeneous case When the simulation starts the CO2 rises from the bottom layer and this continues until the saturation in the bottom layer becomes residual at 23.1%. The amount of CO2 which is not trapped in the reservoir section, cells 2–159, ends up in cell 1 at the very top. In Fig. 10 is shown the distribution of CO2 at equilibrium. All the cells, 2–159, contain residual CO2. Note, that all saturations are considerably below the maximum residual gas saturation which for rock type 8 is 0.352. This of course is due to the fact that no grid cell reaches the maximum drainage CO2 saturation, Sgrwmax, which is 0.879, and therefore by hysteresis is taken down to smaller values. It is noted, that the treatmemt of the imbibition capillary pressure has little inﬂuence on the results in this homogeneous case. The run without hysteresis in the capillary pressure diﬀers very little from the case with full hysteresis. This is because the ﬁnal CO2 saturation is determined solely by the relative permeabilities and equals Sgrw. Fig. 11 displays the CO2 saturation with time for three grid cells, cell 159 next to the bottom, the middle cell 80 and cell 2 next to the top cell. 3.2. Case II. Results for homogeneous case with tight cell This case is identical to Case I, except that cell 150, at depth 1874.8 m, contains the tight rock type 1 with a permeability of 1 mD. Fig. 12 shows the CO2 saturation as function of depth at equilibrium when all movable free CO2 has risen to the upper plenum (top cell no. 1). The corresponding capillary pressure is shown in Fig. 13 The picture is completely diﬀerent from Case I and considerably more complicated. Signiﬁcant amount of CO2 are stored below the tight cell 150 only. When there is no treshold pressure in the capillary imbibition curve all movable CO2 rises to the top of the reservoir because the sealing capacity of the tight layer 150 disappears when the capillary pressure becomes zero or negative. Thus only residual CO2 is left. When Fig. 6. Permeability distribution in the 2D subsection in case IV. For illustration purposes the true geometry as shown in A is portrayed with horizontal exaggeration of a factor 10 as in B in order to make comparisons easier throughout the paper. 52 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 7. Water relative permeability curves for four of the eight rock types. and Sgdr the maximum attained gas saturation during drainage. Now for cell 149 we have (conf. Fig. 14): the imbibition curve for the tight layer contains a threshold pressure the sealing power of the tight layer is not completely lost and some CO2 is capillary trapped below the tight layer. If hysteresis in the capillary pressure is neglected even more CO2 is simulated to be capillary trapped. Above cell 150 the CO2 saturations are zero although all the movable CO2 has risen from the lower plenum (bottom cell) to the upper plenum. Fig. 14 shows CO2 saturation with time for three grid cells above the tight cell, namely cells 149, 80 and 2. It is seen that the saturation rises to about 0.0029 and then drops to zero. A small residual CO2 saturation would have beeen expected according to the governing equations Schlumberger (2013): Sgrw = Sgc + C= Sgdr = 0.0029 (6) 1 1 − Sgrwmax −Sgc 1− Swir − Sgc (7) A = 1 + a(1 – Swir –Sgdr) Sgc = 0. (10) Sgrwmax = 0.352 (11) Swir = 0.121 (12) a = 0.1 (13) A = 1.09 (14) This gives Sgdr − Sgc A + C (Sgdr − Sgc ) (9) C = 1.70 (15) Sgrw = 0.0026 (16) But the simulation results say Sg = 0 at equilibrium. The gas relative permeability should be zero at Sg = Sgrw as it is for all grid cells below cell 49, but it is not. The value is of order 510−5 and it decreases with Sg towards zero. Anyway, the Region 2 gas saturations above the tight layer are negligible. The result is, that the amount of CO2 stored in Case II is reduced by a factor up to 8 compared to Case I, see Table 3. (8) where Sgrw is the residual gas saturation, Sgc the critical gas saturation Fig. 8. CO2 relative permeability functions for four of the eight rock types. 53 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 9. Capillary pressure curves for four of the eight rock types. is now a recognizable residual CO2 saturation of approximately 6% above the tight cell 150. For cell 149 we have now (conf. Fig. 16 and Eqs. (6)–(8)): Table 2 Absolute permeability, K, irreducible water saturation, Swir, maximum relative gas permeability, krg, maximum residual CO2 saturation, Sgrwmax, maximum capillary pressures and entry pressures for the eight rock types. Rock type K (mD) Swir krg (Swir) Sgrwmax(Swir) Pcmax (bar) Pce (bar) 1 2 3 4 5 6 7 8 1. 10. 50. 100. 200. 400. 600. 800. 0.600 0.435 0.320 0.270 0.220 0.171 0.142 0.121 0.050 0.248 0.386 0.446 0.506 0.565 0.600 0.625 0.238 0.288 0.315 0.326 0.335 0.344 0.349 0.352 43. 13.6 6.1 4.3 3.0 2.15 1.76 1.52 0.212 0.078 0.039 0.029 0.022 0.016 0.014 0.012 Sgdr = 0.074 (17) Sgc = 0. (18) Sgrwmax = 0.352 (19) Swir = 0.121 (20) a = 0.1 (21) A = 1.09 (22) This gives The very small saturations above the tight cell may be explained as follows: The velocity of the gas leaving cell 150 and entering cell 149 is much smaller than the velocity of the gas leaving further upwards because of the diﬀerence in permeability (1 mD vs. 800 mD). As a consequence, the gas saturation never builds up in cell 149. If the absolute permeability in the tight cell is 10 mD instead of 1 mD the CO2 distribution is as shown in Fig. 15. It is seen here, that there C = 1.70 (23) Sgrw = 0.061 (24) The simulation result for the gas saturation in cell 149 at equilibrium is 0.0616, so here we have conformance between analytical and simulation results. Fig. 10. Case I. Homogeneous case: CO2 saturation distribution at equilibrium as function of depth for diﬀerent descriptions of the imbibition capillary pressure. 54 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 11. Case I. Homogeneous case: CO2 saturation development with time for the grid cells 159, 80 and 2, respectively for the ﬁrst 100 days. Fig. 12. Case II: Homogeneous case with tight cell: CO2 saturation as function of depth at equilibrium for diﬀerent descriptions of the imbibition capillary pressure. Fig. 13. Case II: Homogeneous case with tight cell: Capillary pressure as function of depth at equilibrium for diﬀerent descriptions of the imbibition capillary pressure. In general, it is concluded that the maximum attained drainage saturation and thus the residual gas saturation in a given region, is reduced when a tighter region is located upstream. 3.3. Case III. Results for homogeneous case with two tight cells This case is identical to Case II, except that cell 75 at 1837.25 m like cell 150 contains the tight rock type 1. The CO2 saturations as function of depth at equilibrium when all movable free CO2 has risen to the 55 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 14. Case II. Homogeneous case with tight cell and Pc hysterese with no threshold pressure: CO2 saturation with time for the three grid cells 149, 80 and 2 above the tight cell 150. entry pressure in the tight layer of 0.21 bar. The entry height for the tight layer is computed as follows: Table 3 Comparison of amount of stored CO2 in Region 2 (cells 2–159) for Cases I, II and III. Case Case I : Homogeneous case, K = 800 mD With cap. press. hysteresis, no thrshld P With cap. press. hysteresis, thrshld P Without cap. press. hysteresis Case II: Homogeneous case with tight cell K = 1 mD in cell 150 With cap. press. hysteresis, no thrshld P With cap. press. hysteresis, thrshld P Without cap. press. hysteresis Case II: Homogeneous case with tight cell K = 1 mD in cell 150 K = 10 mD in cell 150 With cap. press. hysteresis, no thrshld P Case III: Homogeneous case with two tight cells K = 1 mD in cells 75 and 150 With cap. press. hysteresis, no thrshld P With cap. press. hysteresis, thrshld P Without cap. press. hysteresis Average CO2 saturation Free CO2 stored (sm3) 0.164 0.162 0.164 332 329 332 0.020 0.027 0.043 41.7 56.6 89.8 0.020 0.074 41.7 151 0.021 40.4 0.029 0.046 54.4 87.3 ρw = 1177 kg/m3 (25) ρCO2 ∼ 559 kg/m3 (26) The maximum capillary pressure in the tight layer during drainage is 0.28 bar, see Fig. 19 and the entry height is thus hentry = 28000 = 4.6 m g (ρw −ρCO2 ) (27) So, the height of the accumulated CO2 column below a tight layer corresponds to the layers entry height. In the case where the imbibition capillary pressure contains a threshold pressure a column of 1.5 m below the tight layer containes capillary trapped, mobile CO2. This column height is determined by the threshold pressure of the imbibition curve which is 0.1 bar, conf. Eq. (27) with 10,000 N/m2 instead of 28,000. The importance of taking into account the capillary pressure hysteresis is again realized by comparing to the result obtained without hysteresis in the capillary pressure (Figs. 17 and 18). It is seen (see also Table 3) that neglection of hysteresis in the capillary pressure results in a large overestimation of the amount of mobile free trapped CO2. upper plenum are shown in Fig. 17 for the diﬀerent descriptions of the imbibition capillary pressure. An additional column of CO2 is now formed below the tight cell 75. The column is 4.5 m high, corresponding to a column height which is able to overcome the capillary 3.4. Case IV. Results for subsection at diﬀerent heights above the reservoir bottom As mentioned in Chapter 2, the top of the subsection has been Fig. 15. Case II: Homogeneous case with tight cell and Pc hysterese with no threshold pressure: CO2 saturation with depth at equilibrium when the absolute permeability of the tight cell is 10 mD. 56 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 16. Case II. Homogeneous case with tight cell and Pc hysterese with no threshold pressure: CO2 saturation with time for the grid cell 149 when the absolute permeability of the tight cell is 10 mD. Fig. 17. Case III: Homogeneous case with two tight layers: CO2 saturation as function of depth at equilibrium for diﬀerent descriptions of the imbibition capillary pressure. Fig. 18. Case III: Homogeneous case with two tight layers: Saturations in CO2 column below uppermost tight layer as function of depth for diﬀerent descriptions of the imbibition capillary pressure. the subsection. This means that the height of the CO2 column, CO2HEIGHT, is equal to the depth of layer 141 minus the depth of layer 128, conf. Table 4 and Fig. 20. Fig. 21 shows the average gas saturation in the subsection as function the numerical height of the CO2 column, CO2HEIGHT (see also Table 4). It is seen, that the amount of stored CO2 increases initially with the height of the CO2 column, but the growth is drastically placed from 2 m to 60 m above the bottom of the reservoir in order to evaluate the importance of the height of the rising CO2 column. The total reservoir height is 80 m which is gridded in to 141 layers. The subsection height is gridded into 115 layers leaving 26 layers with which to grid the section of the reservoir which is outside of the subsection. 13 of the 26 layers are used to grid the height above the subsection and the remaining 13 layers are used to grid the height below 57 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 19. Case III: Homogeneous case with two tight layers: Capillary pressure in uppermost tight layer as function of time with (dashed line) and without (full line) threshold pressure in the capillary pressure. Fig. 24. When the height of the CO2 column is greater than 3.57 m the CO2 is able to penetrate even the tightest layer and all the mobile CO2 initially stored in the lower plenum escapes. Part of this CO2 is trapped in the subsection as dissolved and residual CO2. This is illustrated in Fig. 25 which gives the CO2 saturation distribution in the subsection at equilibrium when the maximum height of the underlying CO2 column, CO2HEIGHT, is 4.0 m. All the CO2 is residual, i.e. the relative permeability is zero everywhere. The CO2 left in the lower plenum is residual too, which means that all the originally mobile CO2 that has not been trapped in the subsection has passed through into the upper plenum storage. Fig. 26 depicts the ﬁnal CO2 saturation in the lower plenum as function of CO2HEIGHT. When CO2HEIGHT is larger than 3.57 m the ﬁnal saturation becomes residual equal to 0.231. Note (Fig. 25), that the upper approximately 14 layers of the subsection contain little or no CO2 although a lot of CO2 has passed though these layers. The small saturations occur above a tight layer (Fig. 23) and the reason for this was explained in connection with the Case II results in Section 3.2, as a result of limited supply from below and fast escape in the overlying permeable layers. Fig. 27 presents a more detailed picture of the CO2 saturation distribution and it can be seen that the CO2 saturation above the uppermost tight layer (Fig. 23) is very small. But, the saturations above lower situated tight layers are considerable, and that is because the distance to another tight layer above is much less than the required CO2 entry height of 3.57 m (Eq. (5)). So, the CO2 here is residual CO2 accumulated beneath the tight layers above. It is concluded, that if the imbibition capillary pressure is zero or negative at the residual CO2 saturation, potentially mobile CO2 can only Table 4 Results from the 10 simulations with diﬀerent CO2HEIGHT’s. Case DEPTH128 (m) DEPTH141 (m) CO2HEIGHT (m) RGSAT2 60 M 40 M 20 M 15M 10M 7M 5M 4M 3M 2M 1820.4 1840.4 1860.4 1865.4 1870.4 1873.4 1875.4 1876.4 1877.4 1878.6 1865.3 1870.7 1875.9 1877.1 1878.3 1879.0 1879.4 1879.7 1879.9 1880.2 44.9 30.3 15.5 11.7 7.9 5.6 4.0 3.3 2.5 1.6 0.265 0.264 0.263 0.262 0.259 0.253 0.243 0.208 0.200 0.183 RGSAT2 : Average CO2 saturation in subsection. DEPTHI : Depth of cell I. CO2HEIGHT : Height of the CO2 column = DEPTH141 - DEPTH128. reduced when the CO2HEIGHT becomes greater than about 10 m as Pc vs Sg gets steep (Fig. 9). In Fig. 22 is shown the CO2 saturation distribution in the subsection at equilibrium when the maximum height of the underlying CO2 column, CO2HEIGHT, is 1.6 m. It is seen, that all the CO2 is trapped below a tight layer around 0.15 m from the bottom of the subsection, conf. Fig. 23 which shows the absolute permeability. The tight layer has a capillary entry pressure of 0.212 bar and as shown in Eqs. (1) – (5) it requires a column height of at least 3.57 m for the CO2 to penetrate this layer. All the trapped CO2 is potentially mobile as the gas relative permeability is greater than zero, Fig. 20. Case IV: Height of CO2 column, CO2HEIGHT, as function of case number which equals the height of the subsection bottom above reservoir bottom. 58 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 21. Average gas saturation in the subsection as function the numerical height of the CO2 column, CO2HEIGHT. Fig. 22. CO2 saturation distribution in the subsection at equilibrium when the maximum height of the underlying CO2 column, CO2HEIGHT, is 1.6 m. Fig. 23. Permeability distribution in the subsection. trapped CO2. be trapped beneath layers which are not penetrated by CO2 at any time during the storage process, that is, completely tight seals. If the imbibition curve has a threshold pressure the sealing power of the barriers is reduced but not lost completely. In order to evaluate the importance of capillary hysteresis, case 40 M was run without hysteresis in the capillary pressure. The result is shown in Table 5. Again, it is observed that neglecting capillary pressure hysteresis results in a large over estimation of the amount of 4. Summary and conclusions The inﬂuence of rock heterogeneity on the distribution and magnitude of residual CO2 resulting from boyant CO2 gas has been examined by means of simple 1D and 2D examples in order to better understand the underlying mechanisms that are responsible for the 59 International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 24. CO2 relative permeability distribution in the subsection at equilibrium when the maximum height of the underlying CO2 column, CO2HEIGHT, is 1.6 m. Fig. 25. CO2 saturation distribution in the subsection at equilibrium when the maximum height of the underlying CO2 column, CO2HEIGHT, is 4.0 m. Fig. 26. Final CO2 saturation in lower plenum as function of CO2HEIGHT. • If the imbibition capillary pressure tends towards zero or negative results observed. The importance of taking into account capillary pressure hysteresis has been demonstrated. It is concluded that: • Hysteresis in the capillary pressure reduces a layers sealing power. • Neglection of the capillary pressure hysteresis in the simulation may result in a large overestimation of the amount of trapped CO2. In cases presented here the overprediction was larger than 100%. 60 values, only local barriers constituting eﬀective seals are able to trap free and potentially mobile CO2 and the trapping mechanism is exactly the same as the one acting beneath the top seal. If the imbibition capillary curve includes a threshold pressure, mobile CO2 can be trapped below low-permeable layers at above-endpoint values. This can be considered a new trapping mechanism International Journal of Greenhouse Gas Control 78 (2018) 48–61 N. Bech, P. Frykman Fig. 27. CO2 saturation distribution in the subsection at equilibrium when the maximum height of the underlying CO2 column, CO2HEIGHT, is 4.0 m. Conference and Exhibition. Dallas, Texas, U.S.A., 9-12 October 2005. Behzadi, H., Alvarado, V., 2012. Upscaling of upward CO2 migration in 2D system. Adv. Water Resour. 45, 46–54. Behzadi, H., Alvarado, V., Mallick, S., 2011. CO2 saturation, distribution and seismic response in two-dimensional permeability model. Environ. Sci. Technol. 45, 9435–9441. Delshad, M., Kong, X., Tavakoli, R., Hosseinio, S.A., Wheeler, M.F., 2013. Modeling and simulation of carbon sequestration at Cranﬁeld incorporating new physical models. Int. J. Greenh. Gas Control(March). 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Capillary heterogeneity trapping of CO2 in a sandstone rock at reservoir conditions. Geophys. Res. Lett. 38 (2011), L15401. Krevor, S., Blunt, M.J., Bensom, S.M., Pentland, C.H., Reynolds, C., Al-Menhali, A., Niu, B., 2015. Capillary trapping for geologic carbon dioxide storage – from pore scale physics to ﬁeld scale implications. Int. J. Greenh. Gas Control. https://doi.org/10. 1016/j.ijggc.2015.04.006. Mansour, S., Wessel-Berg, D., Kleppe, J., 2013. Investigating residual trapping mechanism in CO2 storage in the brine through analytical and numerical simulation methods. In: EAGE Annual Conference & Exhibition Incorporating SPE Europec. London, United Kingdom, 10–13 June 2013. Meckel, T.A., Bryant, S.L., Ganesh, P.R., 2015. Characterization and prediction of CO2 saturation resulting from modelling buoyant ﬂuid migration in 2D heterogeneous geologic fabrics. Int. J. Greenh. Gas Control 34 (2015), 85–96. Ren, B., Sun, Y., Bryant, S., 2014. Maximizing local capillary trapping during CO2 injection”, GHGT-12, Kyoto, Japan, 2014. Energy Procedia 63 (2014), 5562–5576. Saadatpoor, E., Bryant, S.L., Sepehrnoori, K., 2010. New trapping mechanism in carbon sequestration. Transp. Porous Media 82, 3–17. Saadatpoor, E., Bryant, S.L., Sepehrnoori, K., 2011. Eﬀect of upscaling hetero domain on CO2 trapping mechanisms”, GHGT-10, Amsterdam, Netherlands, 2010. Energy Procedia 4 (2011), 5066–5073. Schlumberger, 2013. Eclipse Reservoir Simulation Software”, 2013.2 Manuals. Skjaeveland, S.M., Siqveland, L.M., Kjosavik, A., Hammervold, W.L., Virnovsky, G.A., 1998. Capillary pressure correlation for mixed-wet reservoirs. In: 1998 SPE India Oil and Gas Conference and Exhibition. New Delhi, India, 10-12 February 1998. Zheming, Z., Agarwal, R.K., 2014. Numerical simulation of CO2 sequestration in large saline aquifers. In: Vaz Morgado, Claudia Rosario, Esteves, Victor Paulo Pecanha (Eds.), CO2 Sequestration and Valorization. Publisher: InTech. ISBN 978-953-511225-9, 470 pages, March 12, 2014. Table 5 Comparison of average CO2 saturation in subsection obtained with and without capillary pressure. Case Avg. CO2 saturation in Reg. 2 40 M with capillary hysteresis 40 M without capillary hysteresis 0.264 0.574 called hyper-trapping. • The maximum attained drainage saturation and thus the residual • • gas saturation in a given region, is reduced when a tighter region is located upstream and the distance to a possible tight zone downstream is greater than the entry height of that zone. In cases where the permeability contrast was 1 mD versus 800 mD there was practically no residual saturation at all in the high-permeability downstream region. This may lead to a considerable reduction of the total amount of trapped CO2. Using the maximum residual CO2 saturation to estimate CO2 storage capacity may lead to a large overestimation of the residual CO2. The amount of CO2 stored in a given subsection depends upon the height of the CO2 column accumulated beneath it or in other words, it depends upon the subsection’s location in the reservoir. In the present case the amount of CO2 stored did not increase much for heights greater than about 10 m. Acknowledgements This publication has been produced with support from the BIGCCS Centre, performed under the Norwegian research program Centres for Environment-friendly Energy Research (FME). The authors acknowledge the following partners for their contributions: Gassco, Shell, Statoil, TOTAL, ENGIE, and the Research Council of Norway. References Altundas, Y.B., Ramakrishnan, T.S., Chugunov, N., de Loubens, R., 2011. Retardation of CO2 caused by capillary pressure hysteresis: a new CO2 trapping mechanism. In: International Conference on CO2 Capture, Storage and Utilization. New Orleans, 1012 November 2010. SPE Journal December 2011. Bech, N., Frykman, P., Vejbæk, O.V., 2005. Modeling of initial saturation distributions in oil/water reservoirs in imbibition equilibrium. In: 2005 SPE Annual Technical 61

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