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Diffusion of CO₂ in water and in hydrocarbons in is increasingly recognized as an important part of transport of species in both improved oil recovery and CO₂ sequestration. There are very little data at the conditions of the subsurface for both pressure and temperature. Theoretical modeling and predictions, especially for CO₂-H₂O mixtures, may not be also reliable.

There is only a handful of data points for Fickian diffusion coefficients in three-component mixtures in hydrocarbon mixtures. There is only one set of data points for thermal diffusion coefficients in ternary mixtures to the best of our knowledge.  The main goal of the project in the second year has been to employ the laser beam deflection apparatus provided by Professor J. Sengers from the University of Maryland for measuring both Fickian diffusion and thermal diffusion coefficients in binary and ternary mixtures. There has been no report of the use of optical technique in diffusion measurement of ternary mixtures.

In the second year of the project after making various effort to use the existing beam deflection apparatus we decided to design and build a new diffusion cell to allow high accuracy in measurements. We also developed a new model for calculation of Fickian diffusion coefficients in water-CO₂ mixtures.

In the following, we will discuss the new cell design and the results from it, and then move on to the theoretical work.

Figure 1 shows a schematic view of the new cell for the laser beam deflection apparatus. The cell is composed of a quartz glass ring sandwiched between two solid copper plates. The cell is leveled by adjusting the nuts on which the cell sits. The spacing between the copper plates is 6.8 mm. Another design allows a spacing of about 3.0 mm. The later can reach stationary state in time about 1/3 of the former. 

Fig. 1- Schematics of the new laser beam cell.

Temperature control on the copper plates is achieved through a PID system which controls the output of the power supplies, each one connected to thermofoil heaters attached to the plates. There are two thermofoil heaters attached to each plate. In order to prevent parasitic heating from erasing the temperature gradient applied across the sample, the cell is placed in a cold environment regulated by a thermostat. The temperature gradient in each plate is around 2 mK per length of the plate. In our setup for a temperature gradient of about 1.6 K/cm across the sample, the temperature on the top plate reaches to within 1% of the desired set point. The temperature stabilizes in 3-4 minutes and fluctuates about 4 mK of the set point temperature of the top plate. The lower plate's temperature is fixed.

The most important parameter which sets the accuracy and reliability of diffusion measurements is the stability of the laser beam. Figure 2 shows the fluctuations in the recorded stability of the laser beam at a distance of about 50 cm from the outlet window.

Fig. 2- Fluctuations of the recorded laser beam at a distance of 50 cm from the cell outlet.

The temperatures of the top and bottom plates were set at 298 K. The standard deviation of the fluctuations is around 0.35 microns. Such low variations are superior to other measurements in the literature and allow diffusion measurements, both Fickain and thermal diffusion coefficients, with high accuracy.   We have measured Fickian and thermal diffusion coefficients of equimolar mixtures of hexane and toluene. The results produce reported values in the literature. The stationary beam deflection is around 0.215 mm from the time a stationary temperature gradient is established. We are now in the process of measuring diffusion coefficients of two similar normal alkanes nC₉ and nC₁₀ to examine the extreme accuracy of the new design.

The circular cell used in this work allows high pressure modification once we complete atmospheric pressure measurements.

On the theoretical side, we have developed a model to accurately calculate infinite dilution Fickian diffusion coefficients of CO₂ in H₂O, and of H₂O in CO₂ both in the vapor phase and in the liquid state. Figure 3 compares our calculations with measured data in the literature for the infinite dilution Fickian diffusion coefficients. The data and the theory cover the vapor and liquid states. Infinite dilution diffusion coefficients are required for the prediction of concentrated mixtures. Our model allows calculations in vapor and liquid states in a unified approach. Non-ideality in the vapor and liquid states are accounted by a cubic equation of state combined a model for association. We also account for cross association between water and CO₂ molecules.  In the process of model development we have gathered all the data in the literature. The model is expected to cover subsurface conditions considered for CO₂ sequestration.

Fig. 3- Comparison of the computed and measured infinite dilution diffusion coefficients of CO₂-water mixtures in vapor and liquid regions.