**Abstract**

This study is devoted to the rheology of oil emulsions, accompanied by both the formation and destruction of the structure. The presence of particles of a dispersed phase in an oil emulsion, including asphaltenes and resins, determines the formation of coagulation structures as a result of interaction and collision of particles. In this regard, to study the formation of coagulation structures, analytical solutions to the mass transfer equations are proposed, based on which the coalescence and fragmentation frequencies of the droplets are determined. Models and analytical solutions of the equation for the thinning of an interfacial film between droplets with their coalescence in the volume of an oil emulsion are proposed taking into account the Marangoni effect and the effect of asphaltene content. The thickness of the adsorbed layer on the droplet surface was estimated. Many empirical and semiempirical formulas have been proposed for determining the dependence of viscosity on the content of water and asphalt-resinous substances in oil. Based on the solution of the Fokker-Planck equation, the evolution of the distribution function of droplets in time and size in an oil emulsion is studied.

**Keywords:** oil emulsion, rheology, coalescence, deformation, breaking, asphaltenes, drop, viscosity, Marangoni effect, distribution function

#### **1. Introduction**

The separation processes of oil emulsions are an important stage for the preparation and purification of crude oil from water, mineral salts and various related impurities, asphalt-resinous substances, and paraffins contained in oil. The processes of separation of oil emulsions, the purpose of which is to completely reduce their aggregative and kinetic stability, are carried out in various ways: in gravitational (settling systems and other modifications); in centrifugal, electric, and magnetic fields [1–4]; as well as using filtering through solid and liquid layers, using microwave and membrane technology [5, 6].

Oil emulsions contain water droplets of a sufficiently large size, in connection with which, in most practical applications, high-capacity separation processes use settling systems, and at small sizes and droplet concentrations, using a constant electric field and membrane technologies or combined methods to achieve high degree of purification.

Experimental and theoretical studies indicate a very complex, in disperse composition (separation) and in the flowing physical phenomena (coalescence, deformation, crushing), the structure of the intermediate layer. Many works have been devoted to theoretical and experimental studies of the mechanism of the formation of stabilization and destruction of oil emulsions as heterogeneous media [2, 4]; although many problems associated with the phenomena occur at the oil–water interface, the coalescence and fragmentation of water droplets, separation, and deposition have not been resolved correctly. Oil emulsions are polydisperse media with droplet sizes of 1–150 microns, although coarse (150–1000 microns) and colloidal (0.001–1 microns) particles are found in them. Such a size dispersion has a significant effect on the mechanism of structure formation, structural destruction, separation, and precipitation of droplets in oil emulsions. The mechanism of destruction and coalescence of droplets in oil emulsions can be divided into the following stages [7, 8]:

a. Convergence and collision of droplets of different sizes with the formation of an interfacial film. It should be noted that droplet transfer in a polydisperse medium is determined mainly by hydrodynamic conditions and flow turbulence. Under conditions of isotropic turbulence, the collision frequency of droplets depends on the specific dissipation of the energy of the turbulent flow and the properties of the medium and the dispersed phase [9–12]. As a result of the collision and fixation of two drops with sizes *a*<sup>1</sup> and *a*2, an interfacial film of circular cross section is formed, the radius of which can be determined in the form [13]

$$R\_K = \left[\frac{3\pi}{4}P\_m(k\_1 + k\_2)a\_r\right]^{1/3} \tag{1}$$

The rheology of oil emulsions is associated with the presence of coagulation phenomena of dispersed particles in the presence of asphalt-resinous substances, accompanied in most cases by structure formation. The rheological properties of oil emulsions largely depend on the state of aggregation (solid phase, droplets, gas bubbles) and the properties of the dispersion medium. However, the presence of a dispersed phase can significantly change these properties under the influence of adhesion forces between particles of a dispersed phase and their interaction with a dispersion medium. In free-dispersed systems, particles of a dispersed phase are not interconnected and are able to independently move in a dispersion medium. In connected dispersed systems, particles of the dispersed phase form continuous spatial networks (structures); they lose their ability to transitional movement, maintaining only oscillatory movements. Unstable disperse systems provide structure formation in the system, up to the formation of aggregates and a skeleton, which can negatively affect the structural state (viscosity, fluidity), changing rheological properties, as well as to obtain precipitation during phase separation, treatment of industrial emissions, wastewater, etc. Aggregate stability characterizes the ability of a dispersed system to maintain a uniform distribution of particles of a dispersed phase over the volume of a dispersed medium without their interaction, providing conditions for the stability of the medium to phase separation. The loss of aggregative stability in concentrated emulsions is associated with coagulation of particles and their enlargement and can manifest itself in the formation of a bulk structure in which the dispersion medium is evenly distributed, thereby changing the rheological properties of the medium. The aggregate stability of dispersed systems with respect to coagulation is determined by the coagulation rate, which, in addition to the intensity of Brownian and hydrodynamic motion and the number of collisions, depends on the properties of the surface layers surrounding the particles. A deeper coagulation process leads to the destruction of the interlayers of the medium and direct contact of the particles, resulting in the formation of rigid coagulation structures and aggregates of particles, or their complete merging in the

*Rheology of Structured Oil Emulsion*

*DOI: http://dx.doi.org/10.5772/intechopen.92770*

case of a liquid and gaseous dispersed phase (coalescence) (**Figure 1**).

increase in the structural viscosity of the medium.

coalescence and fragmentation of the droplets.

*Scheme of coagulation and formation of aggregates of particles of various structures.*

**Figure 1.**

**203**

The formation of coagulation structures and aggregates in the flow volume significantly affects the physical properties of oil emulsions associated with a sharp

deformation, and crushing of droplets in a turbulent flow and the formation of coagulation structures associated with this; (b) the effect of asphalt-resinous substances on the formation of adsorption films and the structural viscosity of emulsions; (c) issues related to thinning and tearing of an interfacial film; and (d) the evolution of the droplet size and time distribution functions, taking into account

Based on this, the aim of this work is to study (a) the phenomena of coalescence,

where *Pm* is the maximum compressive pressure, *k*1, *k*<sup>2</sup> are the elastic coefficients of two drops, *ar* ¼ *<sup>a</sup>*1*a*<sup>2</sup>*=*ð Þ *<sup>a</sup>*1þ*a*<sup>2</sup> is the average size of the drops, and *a*1, *a*<sup>2</sup> are the diameters of two drops. In [14], the expression for the hydrodynamic compression pressure in a turbulent flow is defined as

$$P\_m = \pi a\_r^2 \rho\_C \overline{U}^2 \tag{2}$$


An equally important factor affecting the efficiency of separation of oil emulsions is the conditions of thinning, tearing of the interfacial film [7], and the coalescence rate associated with the destruction of the adsorbed film on the surface of the droplets with the participation of demulsifiers.

#### *Rheology of Structured Oil Emulsion DOI: http://dx.doi.org/10.5772/intechopen.92770*

deformation, crushing), the structure of the intermediate layer. Many works have been devoted to theoretical and experimental studies of the mechanism of the formation of stabilization and destruction of oil emulsions as heterogeneous media [2, 4]; although many problems associated with the phenomena occur at the oil–water interface, the coalescence and fragmentation of water droplets, separation, and deposition have not been resolved correctly. Oil emulsions are polydisperse media with droplet sizes of 1–150 microns, although coarse (150–1000 microns) and colloidal (0.001–1 microns) particles are found in them. Such a size dispersion has a significant effect on the mechanism of structure formation, structural destruction, separation, and precipitation of droplets in oil emulsions. The mechanism of destruction and coalescence of droplets in oil emulsions can be divided into the following stages [7, 8]:

*Nano- and Microencapsulation - Techniques and Applications*

a. Convergence and collision of droplets of different sizes with the formation of an interfacial film. It should be noted that droplet transfer in a polydisperse medium is determined mainly by hydrodynamic conditions and flow

turbulence. Under conditions of isotropic turbulence, the collision frequency of droplets depends on the specific dissipation of the energy of the turbulent flow and the properties of the medium and the dispersed phase [9–12]. As a result of the collision and fixation of two drops with sizes *a*<sup>1</sup> and *a*2, an interfacial film of circular cross section is formed, the radius of which can be

> *Pm*ð Þ *k*<sup>1</sup> þ *k*<sup>2</sup> *ar* <sup>1</sup>*=*<sup>3</sup>

*a*1, *a*<sup>2</sup> are the diameters of two drops. In [14], the expression for the hydro-

*<sup>r</sup>ρCU* !<sup>2</sup>

ð Þ *<sup>a</sup>*1þ*a*<sup>2</sup> is the average size of the drops, and

where *Pm* is the maximum compressive pressure, *k*1, *k*<sup>2</sup> are the elastic

*=*

dynamic compression pressure in a turbulent flow is defined as

*Pm* <sup>¼</sup> *<sup>π</sup> <sup>a</sup>*<sup>2</sup>

b. The deformation and destruction of adsorption shells at the oil–water interface in the flow volume at certain temperatures (60–70<sup>0</sup>*C*) and

c. Thinning and rupture of the interfacial film, followed by coalescence and coarsening of the droplets. The rupture of the interfacial film contributes to the coalescence of smaller droplets into larger ones. It is important to note that as a result of the transport of the oil emulsion in the pipes, the droplet crushing rate is much higher than the coalescence rate, as a result of which the oil emulsion is characterized by a large dispersion of droplet size and

d. Precipitation of droplets and separation of the dispersed phase as a

An equally important factor affecting the efficiency of separation of oil emulsions is the conditions of thinning, tearing of the interfacial film [7], and the coalescence rate associated with the destruction of the adsorbed film on the surface

(1)

(2)

determined in the form [13]

coefficients of two drops, *ar* ¼ *<sup>a</sup>*1*a*<sup>2</sup>

polydispersity of the medium.

continuous phase (separation).

of the droplets with the participation of demulsifiers.

pressures.

**202**

*RK* <sup>¼</sup> <sup>3</sup>*<sup>π</sup>* 4

The rheology of oil emulsions is associated with the presence of coagulation phenomena of dispersed particles in the presence of asphalt-resinous substances, accompanied in most cases by structure formation. The rheological properties of oil emulsions largely depend on the state of aggregation (solid phase, droplets, gas bubbles) and the properties of the dispersion medium. However, the presence of a dispersed phase can significantly change these properties under the influence of adhesion forces between particles of a dispersed phase and their interaction with a dispersion medium. In free-dispersed systems, particles of a dispersed phase are not interconnected and are able to independently move in a dispersion medium. In connected dispersed systems, particles of the dispersed phase form continuous spatial networks (structures); they lose their ability to transitional movement, maintaining only oscillatory movements. Unstable disperse systems provide structure formation in the system, up to the formation of aggregates and a skeleton, which can negatively affect the structural state (viscosity, fluidity), changing rheological properties, as well as to obtain precipitation during phase separation, treatment of industrial emissions, wastewater, etc. Aggregate stability characterizes the ability of a dispersed system to maintain a uniform distribution of particles of a dispersed phase over the volume of a dispersed medium without their interaction, providing conditions for the stability of the medium to phase separation. The loss of aggregative stability in concentrated emulsions is associated with coagulation of particles and their enlargement and can manifest itself in the formation of a bulk structure in which the dispersion medium is evenly distributed, thereby changing the rheological properties of the medium. The aggregate stability of dispersed systems with respect to coagulation is determined by the coagulation rate, which, in addition to the intensity of Brownian and hydrodynamic motion and the number of collisions, depends on the properties of the surface layers surrounding the particles. A deeper coagulation process leads to the destruction of the interlayers of the medium and direct contact of the particles, resulting in the formation of rigid coagulation structures and aggregates of particles, or their complete merging in the case of a liquid and gaseous dispersed phase (coalescence) (**Figure 1**).

The formation of coagulation structures and aggregates in the flow volume significantly affects the physical properties of oil emulsions associated with a sharp increase in the structural viscosity of the medium.

Based on this, the aim of this work is to study (a) the phenomena of coalescence, deformation, and crushing of droplets in a turbulent flow and the formation of coagulation structures associated with this; (b) the effect of asphalt-resinous substances on the formation of adsorption films and the structural viscosity of emulsions; (c) issues related to thinning and tearing of an interfacial film; and (d) the evolution of the droplet size and time distribution functions, taking into account coalescence and fragmentation of the droplets.
