Diffusion coefficients of CO2 in hydrocarbon fluids are important properties in relation to modeling the process of dissolution of injected CO2 in crude oil during either miscible displacement for enhanced oil recovery or CO2 sequestration in depleted oilfields. In these applications, diffusion coefficients are required at reservoir conditions of temperature and pressure and, to date, few such data have been reported in the literature. In this work, we have measured the diffusion coefficients of CO2 in several liquid hydrocarbons at pressures up to 69 MPa and temperatures up to 423 K. The results have been correlated in terms of both a generalized Stokes-Einstein model and a rough-hard-sphere model. The latter provides a means of predicting CO2 diffusion coefficients in normal alkanes as a function of temperature, density and carbon number.
The measurements were carried out by the Taylor dispersion method in an apparatus that has been described previously in detail [1, 2]. The diffusion column was a coiled Hastelloy tube of length 4.5 m and internal radius 0.54 mm. This was housed in a thermostatic oil bath and the hydrocarbon liquid was delivered as various constant flow rates from a high-pressure syringe pump. The outflow from the diffusion column passed through a short section of small-bore capillary, which served to reduce the pressure, into a refractive index detector operating at near-ambient pressure. Small aliquots of the same liquid hydrocarbon, partially-saturated with CO2, were prepared in a pressure vessel and were introduced into the flowing hydrocarbon upstream of the diffusion column by means of a chromatographic injection valve. After passing through the diffusion column, the solute concentration was determined as a function of time since injection from the refractive-index signal, and analyzed according to the Taylor-Aris theory  to determine the mutual diffusion coefficient for CO2 in the hydrocarbon at effectively infinite dilution. Measurements were carried out for CO2 in hexane, heptane, octane, decane, dodecane, hexadecane, cyclohexane, squalane and toluene at temperatures between (298 and 423) K with pressures between (1 and 69) MPa.
The Stokes-Einstein equation relates the diffusion coefficient D of a dilute solute to the viscosity η of the solvent as follows:
D = kBT/(4πaη), (1)
where kB is Boltzmann's constant, and a is the hydrodynamic radius of the solute molecule. In aqueous solutions of CO2, a was found to be a function of temperature but to be essentially independent of pressure at temperatures well below the critical temperature of water. This reflects the nearly incompressible nature of water under those conditions. In the present work, pressure is an important variable and it was found empirically that the hydrodynamic radius in equation (1) was strongly dependent upon both temperature and pressure. However, for the light hydrocarbons, a could be correlated well as a function of the liquid density only. Unfortunately, this was not the case for heavier and more complex liquids such as squalane.
The rough-hard-sphere theory [4, 5] provides a more well-founded approach in which the diffusion coefficient is represented as a linear function of the molar volume Vm as follows:
D = β(Vm - VD)√T, (2)
where VD is the molar volume at which diffusion ceases. In this work, we find that the experimental data for each hydrocarbon system conform to equation (2) to within a few percent and that, for the normal alkanes, a universal correlation emerges for D as a function of temperature, molar volume and carbon number.
Valuable new experimental data have been determined and, based on these, a predictive model has been developed for CO2 diffusion in normal alkanes as a function of temperature, molar volume and carbon number.
1. C. Secuianu, G. C. Maitland, J. P. M. Trusler, W. A. Wakeham, J. Chem. Eng. Data 56 (2011), 4840-4848.
2. S. P. Cadogan, G. C. Maitland, J. P. M. Trusler, J. Chem. Eng. Data, 59 (2014) 519-525.
3. Aris, R., Proc. R. Soc. London, Ser. A 235 (1956) 67-77.
4. Chandler, D., J. Chem. Phys. 62 (1975) 1358-1363.
5. Matthews, M. A., Ackerman, A., J. Chem. Phys. 87 (1987) 2285-2291.
We gratefully acknowledge the funding of QCCSRC provided jointly by Qatar Petroleum, Shell, and the Qatar Science and Technology Park, and their permission to publish this research.
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