Effects of Capillary Pressure on Multiphase Flow during CO 2 Injection in Saline Aquifer

This paper focused on supercritical CO2 injection into saline aquifer, in particular its capillarity’s effects on the plume migration, reservoir pressure alteration and CO2 flux density. The numerical method used to solve the incompressible two-phase flow equations is based on the mimetic method, which conserves the mass and fluxes simultaneously. The investigation showed that exclusion of capillarity can greatly underestimate the CO2 plume migration and resulted in distinctive reservoir pressure distribution. It is found that capillarity showed no significant effect on the flux intensity of CO2.


Introduction
Reduction of CO2 emission can be achieved through carbon capture and its subsequent geological storage (CCS) [1][2][3].Saline aquifer has been the main focus of CCS due to its wide availability and potential storage capacity of 1000Gt [3].This paper briefly discussed the two phase flow equation starting from the Darcy's law and limit the scope to horizontal two incompressible phases.The objective of current study is to study the effects of capillary pressure on the saturation migration, pressure and flux intensity of CO2 after 300 days of injection.

CO2 Sequestration in Geological Sites
CO2 has been identified as the most important greenhouse gas (GHG) which is responsible for global warming [4].Approximately 24Gt of CO2 emitted from human activities annually, an amount that exceeds the capacity of natural systems to absorb them [5][6].Carbon capture and geological storage is a promising technology that reduces GHG emission into the atmosphere [7][8], and one of the major potential geological storage is the saline aquifers [5,8].According to [3], the estimated global storage a jionseanpau@gmail.comb william.paokings@petronas.com.mypotential in saline aquifer is 1000Gt, thus providing the most substantial carbon dioxide storage capacity [9][10].

Two-Phase Flow
The storage of CO2 in sub-or supercritical state in geological media involves an active interaction amongst the solid matrix, country rock and two fluid phases [11].Mass conservation equation (also known as the continuity equation) relates the pressure p and the total (interstitial) velocity, .We obtain a first-order elliptic system which describes the incompressible flow in porous media by combining the Darcy's law and mass-conservation equation [12]., q p g z where v is the vector representing Darcy velocity, p is the pressure drop in the direction of flow, is the fluid viscosity and K denotes the permeability tensor.The capillary pressure, , is related to saturation of wetting fluid, as written in mathematical equation, Assuming incompressible flow, a two phase system, with one wetting and another non-wetting phase can be described as, , where, D U represents the density of phase D , D O denotes the mobility of phase D and w w f O O is the fractional flow term of wetting phase.

Discretization of Flow Equation
The notation used in this paragraph is in reference to [15].According to [15], in the mimetic difference method, local inner product M is the inverse of transmissibility matrix T. The Darcy's law is discretized based on each of the discrete cell as, , 1, , , represents the pressure taken at the centre of the faces of each discrete cell whereas p is the pressure taken at the centre of the cell.The flux and pressure drop, when written in tensor notation form, , Inner product M and transmissibility matrix T are related to one another to form a consistency condition necessarily to be obeyed through the calculation, , MNK = C NK = TC (6) Using hybridised mixed form of discretization scheme, we obtain a linear system that describes the continuity of flux and pressure across each cell and face [13].0 In the 3 3 u matrix on the left of Eq. 7, row one correspond to Darcy's law; row two is the mass conservation of cells, whereas row three is the continuity of fluxes of all cell faces.To solve the linear system of hybridized discretization method, we use Schur-Complement method and block-wise Gaussian elimination.The application of the methods yield the face pressure as, MATEC Web of Conferences 02001-p.2 The algebraic approximations for the 1 B matrix is obtained from mimetic method.

Methodology
Simulations on CO2 injection into brine solution are implemented using Matlab based on the final form of Eq. 7. Structured Cartesian grid with 60 60 5 u u dimensions have been set up, as in Fig. 1 to study the effects of capillary pressure, which the properties are listed in Table 1.

Residual CO2 Saturation
Residual water saturation

Result and Discussion
The injection well is located in the centre of the x-y plane of the grid generated whereas the production well is located at the far end of the other corner, as shown in Fig. 1.The boundary of the grid is set to be no flow condition.The results with and without capillary pressure are compared and discussed.
Capillary effects will govern the motion of the fluid phase that enters a porous medium initially occupied by the other phase of fluid.The capillary effects is not only accounted by the capillary pressure but also the relative permeability.Referring to Fig. 2, neglecting the capillary force has shown distinctive areas of different CO2 saturation, with saturation about 1 from the well centre to 0 as the location goes further from the injection well.This means that the propagation of CO2 in the aquifer is underestimated if we neglect the effect of capillary pressure.This causes distinctive saturation difference along the distance from injection well.Contradictory, when we include the effects of capillary pressure in the flow of CO2, the saturation of CO2 within the area of study is about 0.4 to 0.6 after 300 days.From here, capillary pressure will accelerate the migration of CO2 plume at the early time injection as discussed in [14].
The CO2 pressure distribution after 300 days of injection show variation when we compare the case with and without capillary effects in Fig 3 .The pressure distribution is about the same for both cases but the pattern of distribution varies.Without capillary pressure, a higher pressure distribution is found around the injection well whereas with capillary effect, the reservoir pressure is more evenly distributed throughout the area.There is not much different in the flux intensity of CO2 after 300 days of injection.In short, capillary pressure affect the saturation and pressure distribution of CO2 after some time of injection, but it show insignificant effect on flux intensity of CO2.

Conclusion
The study of CO2 migration in saline aquifer is important as saline aquifer serve as the highest capacity geological storage media for carbon capture and storage (CCS).CCS is identified as one of the promising technology to reduce GHG.In predicting the flow of CO2 in the saline aquifer, capillary effect significant parameter at the beginning of injection.This research showed that the exclusion of capillary pressure will underestimate CO2 plume migration.The distribution of CO2 pressure after 300 days of injection with capillary pressure is more even.However, the effect of capillary pressure on flux intensity of CO2 is minor.This research can be further enhanced by including the effect of geochemical evolution during CO2 injection in saline aquifer, particularly the precipitation of salt due to water evaporation.
By solving for face pressures, cell pressures and fluxes can be obtained by back substitution, Lp = q + Fπ, Bu = Cp -Dπ