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2.3. Permeation Flux
The presence of impurities would also affect CO2 injection. Here we discuss their physical effects (no chemical reactions involved) on the injection first. We have discussed the IFT for CO2 mixtures earlier, which could affect the relative permeability of the CO2 in two-phase flow. In particular, the presence of N2, O2 and Ar in the high-impurity oxyfuel CO2 may increase the IFT and lead to a lower relative permeability. As two-phase flow also depends on a number of other factors, a quantitative evaluation of the effects of impurities requires additional information. However, for the single-phase flow of injected CO2, the effects may be analyzed in terms of an expression based on Darcy’s Law, for the permeation flux O2:
where is the mass flow per unit area, ρ is the density of injected stream, k is rock permeability, Δ is the gradient operator, p is the pressure, and μ is the viscosity of the fluid. As the impurities lower the density of the CO2 stream, the mass flux will decrease for the same pressure drop. However, the impurities also affect the viscosity of the injected fluid. When the viscosity of the impure CO2 stream is lower than the viscosity of pure CO2, the flux would increase, hence the decrease in density may be compensated by a corresponding decrease in viscosity. The density and viscosity are functions of temperature and pressure. The permeability and pressure gradient vary case by case. However, for an estimation of the impurity effects under the same permeability and pressure drop conditions, one may use the following relation which is a consequence of Equation 2.16:
where and are the mass flow per unit area for CO2 in the mixture and in its pure state, respectively. ρ0 and μ0 are the density and viscosity of pure CO2, respectively. This expression represents a normalized permeation flux, and should be able to provide a measure of the relative injectivity of the impure CO2 stream. To evaluate the temperature and pressure dependence of this permeability, knowledge of the viscosity is needed. The calculation of viscosity for high-pressure gas mixtures is less certain, especially in the supercritical region. The viscosity can be quite sensitive to pressure at relatively low temperature. Various methods exist but we could not find reported data to verify calculated results for CO2 mixtures evaluated. Since the impurity effects are more important for high impurity levels, we only discuss the high-impurity case. The viscosities of pure CO2 and impure CO2 shown in Figure 2.10 are calculated using the TRAPP method (Huber and Hanley, 1996; Poling et al., 2001). Whereas the accuracy of the numerical values is not certain, the pattern of the predicted pressure dependence looks plausible. The mixture is seen to have considerably lower viscosity than pure CO2 at high pressures. At 5 MPa, the lowest pressure for the evaluation, the viscosity of the mixture is slightly higher. This is not unreasonable given the fact that the viscosities of N2, O2 and Ar are all higher than the viscosity of CO2 at ambient pressure. The pressure dependence of the normalized permeation flux, based on the calculated viscosities, is shown in Figure 2.11. As a trend it can be seen that the injectivity of the impure CO2 with about 15% N2/O2/Ar is lower than that of pure CO2 by more than 15 percent at lower pressures, but reaches the same level as pure CO2 after a transition range of pressure. This pressure range is likely related to the minimum of the relative density of CO2. This will be discussed later on.
As has been discussed, the viscosity of supercritical CO2 is lowered by the impurities N2, O2 and Ar. Consequently, the effect of increased volume on the permeation flux is partly offset. Thus, the overall physical effect of the impurities on the permeation flux would be less important than on the storage capacity. When the impurity level is lower, the effect on CO2 permeation flux or injectivity would be smaller still.
Figure 2.10. Calculated viscosity for 330 K. The symbols represent calculated values and the curves are trend lines.
Figure 2.11. Normalized permeation flux for the high-impurity CO2 stream (5.8% N2 + 4.7% O2 + 4.47% Ar) from oxyfuel combustion at 330 K.