(175j) A Thermodyanimc-Based Approach to Predict Solid-Liquid Interfacial Tension : Molecular Dynamics Simulation

Low salinity water (LSW) flooding has been
considered by the oil industries in recent years as an augmented-water flood
technique, which presents a substantial potential to improve the oil recovery
factor. Although the LSW flooding technology was initially applied in sandstone
reservoirs, the positive effects were also observed in those of the carbonate
type. In sandstone reservoirs, low salinity water with less multivalent ions is
usually employed, while sea water with more potential-determining ions such as
Ca²⁺, Mg²⁺ and SO4²⁻ is generally
injected into carbonate reservoirs. Rock wettability defines the
tendency of the fluid (e.g. water) to spread or absorb by the solid surface of
rock grains in the presence of the other immiscible fluid (e.g. oil). When the
liquid droplet contacts with the solid surface, there is a competition between
the surface adhesion force at the solid/liquid interface and intermolecular
cohesion force inside the liquid droplet. The competition results in a
mechanical equilibrium where a balance is established between three interfacial
tensions: the liquid/vapor surface tension, the solid/vapor surface tension and
the solid/liquid interfacial tension. The contact angle at the liquid solid
surface is usually measured during special core analysis (SCAL) in the
laboratory and its numerical value characterizes the spreading tendency of the
fluid over the rock surface. Young (1805) model has been used widely to relate
the contact angle. The estimation of solid/liquid surface tension is the most
challenging part of the prediction of contact angle and wettability
characteristic of the rock. Although experimental procedures have been applied
to measure the surface tension, more reliable computer simulations have also
been developed to offer the possibility of measuring solid/liquid surface
tension. In
this work, we employ a thermodynamic-based approach in evaluating the change in
the free energy from a perturbation in the area of a system. This method is used
for the efficient determination of the interfacial (surface) tension from a
single simulation. The approach can be applied to molecules interacting through
continuous or discontinuous potentials, planar to highly non-planar molecules,
and to mixtures over a wide range of temperature.

 A reference
model of calcite/liquid (water or oil) was built where calcite has 12, 12, 12,
atomic layers in x-,y-, and z-directions respectively.
A second system was developed where numbers of layers were changed compared to
the reference state as 13, 12, 11 in x-,y-, and
z-directions, respectively, increasing the surface area (x- and y- ) by one
layer and decreasing the number of layers in z-direction.  Next, a third system was built with a
decrease in the surface area compared to the reference state as 11,12,13 in x-,y-, and z-directions, respectively, and increased in the
z-direction accordingly.  The total numbers
of molecules in each forward and backward state were 1716; hence, 6 molecules
from each surface of the reference state were removed to keep the number of
molecules in the three states the same. 
In all of the three states, the liquid (water or oil) was stacked on the
calcite surface and the surface changed accordingly.  The same procedures were applied for
water/oil system to obtain the liquid-liquid interfacial tension.  The calculated interfacial tensions of
calcite-water, calcite-oil and water-oil were then fit into Laplace-
YoungÕs equation to predict theta as shown in figure 1.