(146j) Diffusion Coefficients of Carbon Dioxide in Liquid Hydrocarbons at High Pressures: Experiment and Modeling

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.

2.
Experimental

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 [3] 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.

3.
Modelling

The Stokes-Einstein equation relates the diffusion coefficient D of a dilute solute to the
viscosity η of the solvent as follows:

                                                               D = k_BT/(4πaη),                                                 (1)

where k_B 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 V_m as follows:

                                                             D = β(V_m - V_D)√T,                                               (2)

where V_D 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.

4. Conclusions

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.

References

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.

Acknowledgment

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.