(535f) Experimental and Numerical Simulation of Rayleigh-Taylor Convection with Interfacial Mass Transfer Enhancement

ABSTRACT:

The process of
CO₂ absorbed into an aqueous solution of NaHCO₃ and Na₂CO₃,
which called the Solvay method, is frequently applied for producing refined NaHCO₃
in chemical industry. During dissolution of CO₂ into liquid phase, a
kind of hydrodynamical instabilities appears in the liquid phase beneath gas-liquid
interface, and the dissolution rate of CO₂ increases meanwhile. A reason
of the hydrodynamical phenomenon is gravitational convection called the Rayleigh-Taylor
convection (RTC), which is caused by a denser CO₂-rich liquid
overlying a more buoyant one. The RTC is a kind of buoyancy-driven convection, and
the phenomena related to the RTC are widespread in chemical engineering and geological
storage of CO₂.

In this work, the
absorption of CO₂ into water is implemented in experiment to
investigate the process of RTC with mass transfer rate enhancement. At first, the
experimental set-up that consists of gas-liquid mass transfer analogous system
and coupled PIV/LIF data measuring system is established. The liquid storage cell that is made of optical glass
has internal dimensions of 100 mm by 100 mm by 3 mm. The coupled PIV/LIF data
measuring system includes a Nd:YAG laser device, two CCD cameras, and a synchronizer.
The laser device purchased from Beamtech Optronics Co., Ltd. emits a laser with
wavelength of 532 nm and maximum pulse energy of 200 mJ. Both cameras that purchased
from LaVision company (Germany) have resolutions of 1376 by 1040 pixels. The resolution
is sufficient to quantify the concentration and velocity fields as a result of the
obtained real size of 0.09 mm for every pixel. Then the relationship between the
fluorescence intensity in solution and its containing CO₂ concentration
is calibrated. The fluorescer of sodium fluorescein solution with concentration
of 40 mg/L is prepared using the degassed ultrapure water, and one half the
solution is saturated with CO₂ in experimental conditions. Several
solutions with different content of CO₂ are obtained by mixing the pre-saturated
CO₂ solution with the fresh solution in different proportions. One
part of each CO₂ solution is titrated by NaOH solution (0.01 mol/L) to
measure the CO₂ concentration by the titrimetric method. Another
part of each solution is excited by the 532 nm laser to record the gray level of
the solution by LIF CCD camera according to the fluorescence intensity of the fluorescer.
To reduce the operator bias in the calibration process, 50 consecutive images for
every solution are recorded and processed to quantify the concentration of CO₂
that is averaged from three-parallel titration results. At last, the
dissolved CO₂ concentration in liquid can be obtained with the help of
the previous calibrated curves. According to the obtained concentration and velocity
information in the RTC process, the effect of fluid hydrodynamics and concentration
distributions on the progress of convective fingers can be analyzed.

In order to present
the convective finger structures more clearly, a computational domain of three-dimensional
(3D) geometry is modeled in accordance with the experimental device. 3D
simulation adds a degree of freedom in the gap direction and thus characterize
the convective structure more visually. The properties of the fluid mixture,
such as viscosity, diffusion coefficient of CO₂, are assumed to be independent
of concentrations because of small content of CO₂ in water. The Boussinesq
approximation is also validated in this limited content. Therefore, the nonlinear
governing equations that describe the diffusion-convection process of CO₂
absorption into water are numerically solved. The up-boundary interfacial
condition is determined according to the assumption that the gas-liquid
interface is in a non-equilibrium state right after two fluid contact, which is
different from the condition that the up boundary keeps at saturation state reported
in literature. Besides, some small random disturbances in concentration were
imposed on the gas-liquid interface to stimulate the onset of the density-driven
instability. The independency of solution to mesh is verified according to the onset
time of convection in different mesh scenarios.

Some qualitative
comparisons between experimental and numerical results are investigated to verify
the effectiveness of numerical simulation. The convective fingers obtained from
numerical simulation have 3D features in its shape and concentration
distribution as shown in Fig. 1.

Fig. 1. 3D concentration contours of CO₂
at (a) 40 s, (b) 120 s, (c) 200 s, and (d) 400 s.

In order to implement
comparison between numerical and experimental results, the information of convective
fingers in a plane where 0.0005 m away from the liquid cell center is sliced in
3D simulation considering the width of planer laser of about 1 mm in the
experiment. The comparisons of concentration contours at various time from numerical
and experimental outcomes are implemented, which is given in Fig. 2.

Fig. 2. Comparisons of concentration contours from experiment (a ~ d)
at 40 s, 90 s, 200 s, 400 s and from numerical calculation (A ~ D) at 40 s, 120
s, 200 s, 400 s.

At the moment of
40 s, the process of molecular diffusion dominates the absorption of CO₂,
and the mass boundary layer keeps steady both from the calculation and experiment.
After the convection, the convective structures from two approaches are similar
as well both in shape and fingers width. The onset time (t_c) for
convection and critical wavelength (l_c) of convection fingers
are selected to verify the availability of numerical simulation. The observed t_c
from experimental and numerical are 80 s and 107.8 s, respectively. The values
of l_c calculated from the experimental and numerical
concentration contours are 3.67 mm and 3.23 mm. The near values of t_c,
l_c and the similar convective fingers from numerical calculation
to experiment prove the validity of 3D numerical method for the RTC in this
work.

Furthermore, the dissolved flux of CO₂ is calculated according
to the instantaneous accumulated CO₂ in the liquid, and the
gas-liquid interfacial mass transfer coefficient thus can be determined based
on the dissolved flux through the interface. The liquid-side interfacial mass
transfer coefficient (k_L) is assumed to represent the overall
one because the mass transfer resistances concentrate on the liquid side.

Fig. 3. Interfacial mass transfer coefficient during the dissolution
of CO₂.

Fig. 3 presents
the obtained variation curves of k_L versus time during the CO₂
absorption. The mass transfer process in the diffusion period can be described
by the Higbie penetration theory. The value of k_L increases suddenly
after the onset of convection because the convective fingers entrain some fluid
with high CO₂ concentration into bulk liquid. The interaction of
fingers with their neighbors results in the decreases of mass gradients in liquid
and thus the dissolved flux and mass transfer coefficients. After a brief
descent stage, the constant flux period appears due to the formation of complex
downwelling fingers as a consequence of the finger merging and coarsening. The average
value of k_L in the constant convective flux period is about 6.4E⁻⁶
m/s, which is close to the calculated value from experiment of about 4.2E⁻⁶
m/s.

Some discoveries
deserve to be concluded finally in this work. The designed experimental device
that combines the PIV and LIF technique for recording the velocity and concentration
information in the CO₂ absorption process can be applied to other specific
experiment. 3D numerical simulation for similar computational geometry to the experimental
device with non-equilibrium gas-liquid interfacial boundary assumption presents
accurate results to the experiment according to the qualitative and quantitative
comparisons. The obtained evolution of velocity and concentration during the
RTC process reveals the principle for enhancing CO₂ dissolution rate
by interaction between fluid flow and mass transfer. The principles may be helpful
for further improving the absorption rate of CO₂ into liquid in
interfacial mass transfer in engineering.