Effective rates of coalescence in oil-water dispersions under constant
shear

Meenakshi Mazumdar, Aniruddh
Singh Jammoria and Shantanu Roy*

Department of Chemical Engineering,
Indian Institute of Technology - Delhi, New Delhi- 110016, India.

(meen.iitd@gmail.com, aniruddhjammoria@gmail.com, *roys@chemical.iitd.ac.in)

Keywords: coalescence, simple shear, crude
oil-water emulsion, population balance equation

Introduction

Emulsions
are thermodynamically unstable systems where one of the two liquid phases is
dispersed as small droplets into the other. However, many emulsions have
significant lifetimes owing to the stabilization forces that govern their
formation and preservation (due to the presence of surfactants). The stability of emulsions may be
useful in certain applications where it is required by design. Whereas, in
others stability may pose severe problems where the objective is to destabilise
the emulsion into its constituent phases, such as in the upstream oil sector.
There, processes like enhanced oil recovery (EOR) produce highly stable crude
oil water-emulsions. Stability of such emulsions pose
an enormous challenge in destabilizing and meeting refinery standards for
further processing of the crude oil. A related problem is one of oil spills,
where the sub-surface oil is a stabilized emulsion and large volumes of such
spills have lifetimes over several weeks, sometimes longer. Natural surfactants
like asphaltenes present in crude oil, and indeed heavy crudes, worsen this
problem. Owing to the huge volumes involved in such applications and the
narrow range of drop sizes, adding chemicals such as de-emulsifiers or passing
the emulsion through an electric field are becoming economically unviable
options for destabilization. Typically, the industry standard is to destabilize
these emulsions using low shear, by passing the two-phase mixture through a
so-called ?coalescer? [1].

The design of industrial coalescers
is almost impossible from first principles. This is due to limited
understanding of coalescence in shear field. Also, as crude oil feedstocks are getting heavier and thus more viscous,
efficient operation of coalescers becomes even more challenging. As coalescence
leads to destabilization, fundamental understanding of coalescence and its
kinetics is key to such applications. Addressing the phenomena of coalescence
at droplet scale and associating it to a large scale industrial coalescer is
challenging due to the multi-scale nature of the phenomena involved. Thus, both
the physical models, as well as the probing experimental methods, must address
this problem involving a spectrum of length and time scales. It is known that
under low to moderate shear rates, emulsions can be destabilized by action of
shear [2], [3]. This contribution focuses on quantifying the volumetric
coalescence rates as a function of shear rate, while maintaining physical and
interfacial properties of a system that mimic a crude oil-water emulsion. The
quantification of the volumetric coalescence rates will be done by matching
experimental and simulation results in the form of transient evolution of drop
size distribution (DSD).

Experimental: Setup and Key Results

The system used in our experiments is a
surfactant?stabilized, buoyant emulsion of synthetic oil and water. Experiments
were designed to understand the effect of shear rate, viscosity ratio and
dispersed phase holdups on coalescence kinetics. Care was taken to target high
dispersed phase holdups (up to 40%) with a narrow initial DSD (0-10μm) as
is the case in industrial coalescers [4]. While the motivation for this work
was destabilization of crude oil-water emulsions, in our study we focused on
viscosity ratios which span much wider than what may find in the former (which
will obviously depend on the source and nature of the crude).

                                   
(a)                                                                   
(b)

Figure 1. Couette flow apparatus (a) 3D isometric view (b) 2D front view
with specifications

The emulsion was prepared in a
homogenizer. It was then subjected to constant shear in a batch cylindrical
Couette apparatus (Figure
1a & b). Samples were withdrawn from the sampling ports and a diluent
solution was used to effectively ?freeze? further coalescence. DSD of samples
was then examined under a microscope by capturing images and processing them
digitally. Repeating this procedure at different fixed shear rates as a
function of time, results in time variation (?effective kinetics?) of the
coalescence process.

Figure 2(a-d) shows the evolution
of drops sizes for a 20% dispersed phase emulsion it is clearly seen that as
time proceeds large drops become dominant. 

Figure
2. Images showing evolution of DSD for 20% dispersed phase holdup at different
times of shearing (a) initial at 0 hours (b) after 1 hour (c) after 2 hours (d)
after 3hours.

Shearing generated bimodal
distributions at lower holdups and three modes were observed at higher holdups.
Figure 3(a) shows the evolution of a unimodal initial distribution to bimodal
distribution. For all holdups, increasing shear rates showed faster kinetics of
coalescence until initial hours of shearing. However, the kinetics slowed down
with time. An interesting
observation is noted in case of 40%holdup. As shown in Figure 3(b), three
distinct peaks are seen within half an hour of shearing for 40% dispersed phase
(DP) holdup at 10s^-1 shear rate. A 40% holdup results in increased
number density of droplets, thereby increasing the initial rate of coalescence.
This enhanced rate of coalescence causes three drop sizes to dominate the
system. As time proceeds, the second peak merges into the third while the first
peak diminishes. This results in a broader DSD. The reason for such a behavior
is presence of large number density of droplets under the first mode.This is believed to have led to a higher probability
of collision and coalescence between droplets under first and second mode.

                                   
(a)                                                                   
(b)

Figure
3. (a) Evolution of DSD at a shear rate of 10 s^-1 and 10% holdup (b)
Evolution of DSD at a shear rate of 10 s^-1 and 40% holdup. Points
are experimental data and lines are fitted curves.

In summary, it is inferred that
unimodal initial DSD results in a bi- and tri-modal DSD depending on the shear
rate employed (recall that a single shear rate is ensured by design of the
Couette apparatus by fixing RPM of the motor) and the DP holdup.

To rationalize observations made in
the experiments, it is necessary to examine the statistics of drainage time,
interaction time and other less relevant time scales that dominate draining of
thin film between two drops. Broadly, it can be argued that large number
density of oil droplets signifies higher collision frequency (due to more
interaction between droplets) and higher shear rates signify larger collision
forces (due to increased interaction time). The evolution of DSDs as a function
of shear rate and volume fraction of DP is rationalized in this backdrop. Since
measurements at the length scale of thin films is outside the scope of current
research, a Population Balance Model is used to connect the film-scale physics
(through the appropriate ?coalescence kernel?) with the macro-scale shear
induced DSD evolution.

Modeling

Two numerical schemes are used to
solve the population balance equation (PBE): method of individual volumes (MIV)
and method of classes (MOC). In order to check the sensitivity of the code,
simulation results are compared with available analytical solution [5].
Although both methods are able to predict evolution in DSD (Figure 4), the method of classes produces
marginally more accurate results at greater computational expense. Anyhow, for
analytically solvable PBE problems (for simple kernels), figures such as Figure 4 establish the correctness of the
code.

Figure 4. Comparison of number density distribution
for constant kernel [3]. (IV represents MIV and C represents MOC, with the
numbers following them represents the discretization of the Droplet Radius
axis.)

Numerical simulations using MOC was
carried out with Smoluchowski?s [6] coagulation
kernel and coalescence efficiency values empirically obtained [3]. One sees (Figure 5) qualitatively similar evolution
patterns, as observed in experiments (Figure 3), even though one does not see the bimodality (and possible
multi-modality) seen in all the experimental cases. Evolution patterns and time
scales are within the measured range. A fairly good agreement is obtained
between the experiments [3] and the simulations as shown in Figure 5.

The final submission will discuss
more about the experimental validation of the model and the use of different
kernels to rationalize the experimental observations.

Figure 5. Comparison of experimental and simulated
volume distributions (data from [3]).

References:

[1]    
Wines, H. T., 2003. ?High Efficiency Coalescers
Increase On-Line Process Analyzer Sensor Reliability.? Analysis Division
48th Annual Spring Symposium. Calgary, Alberta Canada, April 27-30.

[2]     Mishra, V., Kresta,
S. M., Masliyah, J.H., ?Self-Preservation of the Drop
Size Distribution

Function
and Variation in the Stability Ratio for Rapid Coalescence of a Polydisperse

Emulsion
in a Simple Shear Field.? Journal of Colloid and Interface Science 197,
57?67,

         
1998.

[3]      
Nandi, A., Mehra, A., and Khakhar,  D.V.,   2006. ?Coalescence in a surfactant-less emulsion
under simple Shear Flow?. AIChE Journal,
52, 885-894.

 [4]
    Abdurahman, N.H., Azhari, N.H., and Yunus, Y.M.,
2013. ?Formulation and evaluation of water-continuous emulsion of heavy crude
oil prepared for pipeline transportation?. International Journal of
Engineering Science and Innovative Technology, 2, 170-179.

[5]
    Scott W., 1968. ?Analytic
Studies of Cloud Droplet Coalescence I?. Journal of the Atmospheric Sciences,
25(1), 54 - 65.

[6]
    Smoluchowski M. 1917. ?Versucheinermathematischentheorie
der koagulationskinetikkolloiderlosungen?. Zeitschrift fur PhysikalischeChemie,
92, 129 - 135.