Application of CO2-water-rock reaction transport simulation in NPs-CO2 flooding and storage


 As a hot issue in geological engineering, CO2 flooding and sequestration still face many challenges. Injection of nanoparticles into CO2 can improve the injectability and effective reserves of CO2. However, the migration law of the mixed fluid of CO2 and nanoparticles (NPs-CO2) in the reservoir under the condition of chemical reaction is still unclear. Based on chemical reaction kinetics, a mass transfer model of NPs-CO2 nanofluid in reservoir is established by combining the micro-pore structure change of porous media under CO2-water-rock reactions condition and the migration law of NPs-CO2 fluid. The geochemical reaction process between CO2 and reservoir and the influence of heterogeneity caused by rock microstructure on the miscibility and migration of NPs-CO2 brine fluid are simulated. The results show that the CO2-water-rock reaction increases the heterogeneity of reservoir, and the porosity and permeability are rising as a whole; the increase of reservoir heterogeneity caused by chemical reaction can makes the migration of NPs-CO2 selective. The local accumulation of NPs-CO2 in the unconnected pores will weaken the original oil displacement efficiency to some extent; in the process of CO2 sequestration, the density difference between NPs-CO2 and formation water can not only promote the miscibility of NPs-CO2-brine fluid, but also inhibit the acid fluid under buoyancy. The upward diffusion is moved to the cover layer to prevent the chemical reaction of the rocks in the cap layer, so as ensuring the permanent storage of greenhouse gases.

CO2-water-rock reactions have been considered in the above studies. However, the common calcite, feldspar, 59 quartz, and clay minerals in reservoir can react with CO2 in a complex way (Ahmad et  For the percolation process including the chemical reactions of heterogeneous porous media, the flow 78 pattern is determined by the density difference between the mixed fluids, the reaction rate of the fluid and the 79 change of the porous media porosity. That is to say, after NPs-CO2-brine injection into the formation, the solvent 80 moves to the lower part of the reservoir, and dissolution or precipitation reactions occur between solvent and 81 formation rock particles, resulting in the porosity and permeability of the reservoir changes. The injected fluid 82 is easier to flow down driven by the density difference, when the fluid flows from the area with large 83 permeability to the area with small permeability, there is a small disturbance at the front edge, and the amplitude 84 of the disturbance will increase with time, forming an unstable flow pattern of reactive and transport (Chadam 85 et al. 1986;Chadam et al. 1991), and the rock matrix are further dissolved, these three processes promote and 86 couple with each other, which further increases the instability at the interface. 87

Chemical reaction kinetics 88
When ions migrate to the surface of minerals, they react with minerals, dissolve to form free ions, or 89 precipitate to form secondary minerals. According to the chemical kinetics law, for a series of solid-liquid 90 surface reactions, the mineral reaction rate can be expressed as follows (Bethke 1996): 91 mn , Where， mn ζ is the amount of reactions； R β is the velocity of reactions, mol/L·s -1 ；A is the reactive surface Where,  is porosity; l  is the density of liquid, kg/m 3 ; ux (uz) is the velocity along x-axis(z-axis), m/s; t is 107 time, s.
Where, k is permeability, m 2 ;  is the viscosity, Where, Ci is the concentration of material i mol/m 3 ; D is diffusion coefficient, m 2 /s;

Initial and boundary conditions 130
The initial saturation of NPs-CO2 solution in the reservoir was set to 0, only considering the inflow of 131 fluid. The whole reaction process was carried out in a closed environment without mass exchange. The 132 concentration of ions in the initial formation water was evenly distributed in the grid, they changed with the 133 time of chemical reaction, which was subject to the chemical rate equation of water-rock reaction. 134

Changes of rock microscopic physical properties 138
According to the chemical equilibrium equation, the change quantity of a certain mineral quality 139 participating in chemical reaction in reservoir rock can be obtained: 140 Where, m is the quality of a substance participating in a chemical reaction, g; M is the molar mass of the mineral 142 component, mol/g; V is the molar volume of the mineral component, mol/cm 3 ; n is the amount of mineral 143 substance participating in the chemical reaction, mol. 144 There are many kinds of minerals in the reservoir rock that have chemical reaction at the same time, the 145 pore volume reduction of various minerals participating in chemical reaction in the reservoir rock can be 146 superposed and simplified as follows: 147 The change of matrix permeability of a single rock reference unit can be calculated by the change of 149 porosity. The change of permeability with porosity is calculated according to Carman-Kozeny formula (Xu et  (1). There was no adsorption on the surface of the reservoir; 167 (2). The chemical reactions all take place under isothermal condition; 168 (3). The minerals in the reservoir are evenly distributed, and the physical properties conform to their initial 169 porosity and permeability; 170 (4). The inhibition of convection caused by the consumption of CO2 in chemical reactions is ignored; 171 (5). The nano particles are uniformly dispersed in CO2, which will not agglomerate or precipitate due to 172 the consumption of CO2 in chemical reactions.

Change of each mineral content 181
The chemical reaction process was shown in Table 2  The porosity range changed from 2.40% to 21.58% after 10 years of injection (Fig.3a), from 3.34% to 22.20% 218 after 40 years (Fig.3b), from 4.55% to 23.50% after 70 years (Fig.3c), and from 6.43% to 25.84% after 100 219 years (Fig.3d). However, the physical properties of the reservoir are improved, the average porosity increased 220 from 12% to 16%, indicating that the dissolution reaction played an important role after CO2 injection. 221 The permeability of reservoir can be regarded as the concentrated expression of reservoir heterogeneity. 222 Therefore, in order to describe the change process of reservoir heterogeneity more intuitively, in the study of 223 formation rock permeability, the injection layer section at Y(700m)-Z(90m) section is taken as the research 224 object (Fig.4). The change rule of permeability at different reservoir locations was directly proportional to porosity. The 231 permeability range changed between 0.02~0.22mD after 10 years of injection (Fig.5a), between 0.04~0.23mD 232 after 40 years (Fig.5b), 0.05~ 0.25mD after 70 years (Fig.5c), and from 0.07~0.27mD after 100 years (Fig.5d). 233 The average permeability increased from 0.013 mD to 0.017 mD. As the density of NPs-CO2 is slightly higher than the formation water. After injection (Fig.8), it moved 248 downward under the action of gravity overcoming buoyancy and spread along the horizontal direction. Because 249 of the density difference of miscible fluid, the miscible interface did not move forward as a flat interface under 250 the action of gravity, but developed into a fingerlike shape, namely, Rayleigh Taylor instability. With the 251 increasing mixing of NPs-CO2-brine, the density difference at the front edge was decreasing, which weakened 252 the downward movement of fluid front interface. This phenomenon of slowing down CO2 fingering can achieve 253 the expected stable displacement of CO2. However, with the development of chemical reaction, the pore 254 structure of reservoir rock changes, and the dissolved solid part is more likely to form a fluid flow channel. This 255 effect and the Rayleigh Taylor instability caused by density difference superimposed, which further leads to the 256 instability of the interface. 257

Velocity of flow 258
In order to reduce the iteration times and internal degrees of freedom, a 500 × 1000 μm rectangle near the 259 injection point (x = 0 ~ 500 μm, z = 0 ~ 1000 μm) is selected as the research object. The rock matrix of rock 260 before reaction was assumed to be uniformly distributed, the porosity difference before and after the reaction 261 was calculated, and the data (i.e. the secondary minerals formed by precipitation reaction) at the position with 262 the difference less than 0 is eliminated (Figure 9) (1) The primary mineral composition of the reservoir is the key factor affecting the CO2-water-rock 290 reaction. The micro mechanism of the reaction and the change of pore structure directly affect the overall 291 efficiency of CO2 flooding and storage. The simulated formation rock dissolution reaction and precipitation 292 reaction are carried out at the same time, and three kinds of secondary minerals are generated in the first 30 293 years of simulation. With the extension of chemical reaction time, the sedimentation rate gradually increases, 294 but the average porosity and permeability show an overall upward trend, indicating that the mineral dissolution 295 amount is always greater than the precipitation amount, and the reservoir physical properties are improved. 296 (2) In the process of oil displacement, the change of rock microstructure caused by CO2-water-rock 297 reaction will have a negative impact on fluid migration. The location of secondary mineral precipitation will 298 narrow the fluid migration channel, and then block up. The corrosion pit will cause the local accumulation of 299 solute, making the fluid migration rate close to 0, resulting in the failure of NPs-CO2 mixed fluid to achieve the 300 expected oil displacement efficiency. 301 (3) In the process of storage, the enhancement of reservoir heterogeneity caused by chemical reaction and 302 the improvement of physical properties can improve the local velocity fluctuation and miscibility degree of 303 nanofluids, and by increasing the density of mixed fluids, most acidic fluids are located at the bottom of the 304 reservoir and diffuse along the horizontal direction, which is more conducive to the safe storage of CO2. 305

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A 307
In the Lorentz curve drawn, the actual cumulative permeability distribution curve is between AC and BC, 308 showing a convex curve L. The more the curve L deviates from AC, the more serious the heterogeneity is.

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The specific calculation method is as follows (Li 2006).