**2. Formation of disordered coagulation structures and aggregates in oils**

The flow of oil disperse systems is accompanied by various physical phenomena of hydrodynamic interaction, and collision, resulting in the formation of coagulation structures and aggregates, in which energy dissipation plays an important role. Hydrodynamic interaction of particles among itself is observed at their high concentrations when the distance between the particles allows them to collide: *l*≈80*a*<sup>3</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffi *ρd=Cm* p . The probability of a particle collision is determined by many factors: the number of particles itself per unit volume, their shape and properties, the properties of the medium, the flow velocity, and temperature, on which important parameters such as diffusion coefficient and viscosity depend. In viscous fluid flow, the dissipative function is determined as

$$\eta\_D = 2\eta\_C \left(\frac{\partial V\_x}{\partial \mathbf{x}}\right) + 2\eta\_C \left(\frac{\partial V\_y}{\partial \mathbf{y}}\right)^2 + \eta\_C \left(\frac{\partial V\_x}{\partial \mathbf{y}} + \frac{\partial V\_y}{\partial \mathbf{x}}\right)^2 \tag{1}$$

The energy dissipated in the volume of the liquid is expressed by the formula

$$-\frac{dE}{dt} = \int \frac{\eta\_C}{2} \left(\frac{\partial V\_1}{\partial \mathbf{x}\_1} + \frac{\partial V\_k}{\partial \mathbf{x}\_i}\right)^2 dv\tag{2}$$

Energy dissipation per unit mass of flow is defined as follows

$$\varepsilon\_{R} = -\frac{dE}{dtdm} = \frac{\eta\_{C}}{2} \left(\frac{\partial V\_{1}}{\partial \mathbf{x}\_{r}} + \frac{\partial V\_{k}}{\partial \mathbf{x}\_{i}}\right)^{2} \tag{3}$$

(where)

*dm* ¼ *ρCdυ*

For non-Newtonian oils, expression (Eq. (3)) will be written as

$$\varepsilon\_{R} = -\frac{dE}{dtdm} = k\_{0} \left(\frac{\partial V\_{1}}{\partial \mathbf{x}\_{r}} + \frac{\partial V\_{k}}{\partial \mathbf{x}\_{i}}\right)^{n+1} \tag{4}$$

where *<sup>k</sup>*<sup>0</sup> <sup>¼</sup> *<sup>η</sup><sup>C</sup>* 2 *∂V ∂y <sup>n</sup>*�<sup>1</sup> – consistency coefficient. In the one-dimensional case for viscoplastic oil flow, by applying expression (Eq. (4)), we have

$$
\varepsilon\_{\mathbb{R}} = k\_0 \dot{\mathbf{y}}^{n+1} \tag{5}
$$

Coagulation structures are formed by intermolecular bonds between the particles, moreover if liquid interlayers remain between the particles, then the thickness of these interlayers significantly affects the strength of the coagulation structure. Aggregate-unstable oil systems are characterized by the inconstancy of the medium due to continuous structuring and changes in the physical properties of the particles, i.e. changes in volume and size of asphaltene particles caused by their interaction, collision, coagulation, and crushing at a certain concentration in an enclosed volume [16]. The connection between the structure and viscosity of oil dispersal systems as well as the features of their non-Newtonian flow is explained by a change in structure resulting from the emergence and collapse of aggregates from asphaltene particles in the presence of resins. Oil structured systems containing high molecular paraffin crystals, resins, and asphaltene particles at very low laminar flow velocities or in absence of flow form a chain or in the extreme case a continuous grid (frame) between itself and the structure of the porous medium. **Figure 1** shows the formation of a framework of asphaltene particles contained in oil [5, 9].

In [17] it is noted that real oil disperse systems are classified by activation energies into two structural groups differing by the nature of intermolecular interaction of particles in an oil disperse medium. These groups are distinguished from each other by their asphaltene and resin content and, they can be classified into immobile with low asphaltene content, and, interacting with high asphaltene content. **Figure 2** illustrates the characteristic changes in activation energies for the two groups.

A large amount of asphalt-resin substances in the oil reduces the activation energy and creates more favorable conditions for the formation of coagulation structures. The change in mass of non-deformable nanoaggregates is defined as

$$\begin{aligned} \frac{dm}{dt} &= (m\_{\infty} - m)\alpha\\ t &= 0, m = m\_0 \end{aligned} \tag{6}$$

where *ω* is the frequency of particle collision.

#### **Figure 1.**

*Asphaltene particle aggregation in oils: I- single molecules and particles; II- nanoaggregates; III- clusters of nanoaggregates; IV- unstable suspension; V- viscoelastic framework; VI- stable emulsion with toluene.*

**Figure 2.** *Dependence of activation energy on asphaltene content for the stationary group (I) and the interacting group (II).*

The solution to this equation will be represented as

$$m = m\_{\Leftrightarrow} - (m\_0 - m\_{\Leftrightarrow}) \exp\left(at\right) \tag{7}$$

If assume that *m*<sup>∞</sup> > > *m*0, we will get

$$m = m\_{\Leftrightarrow} [1 - \exp\left(-at\right)] \tag{8}$$

where *m*∞- is the limiting steady mass of the aggregate, *m*<sup>0</sup> - is the initial mass of the aggregate.

Assuming the spherical shape of nanoaggregates and imagine that, *<sup>m</sup>* <sup>¼</sup> *<sup>π</sup>* <sup>6</sup> *a*3*ρ*, the size of the nano-aggregates, will be defined the following form, considering (Eq. (7)),

$$a\_{\rm g} = a\_{\rm g\infty} \left[ 1 - \exp\left( -\mathcal{C}\_0 \phi\_0 \left( \frac{\varepsilon\_R}{\nu\_c} \right)^{1/2} t \right) \right]^{1/3} \tag{9}$$

For laminar flow, the formation of aggregates is expressed by an equation of the form.

$$a\_{\mathfrak{g}} = a\_{\mathfrak{g}^{\rm iso}}[1 - \exp\left(-8\pi DN\_0 a\_0 t\right)] \tag{10}$$

According to **Figure 3**, the size of the nano-aggregates fluctuates in range and the maximum size of the framework is limited by the presence of pore or tube walls. The frequency of collisions between asphaltenes increases as the rises of volume fraction of asphaltene particles. The relaxation time for turbulent flow is defined by the expression *τ<sup>R</sup>* ¼ ð Þ *νC=ε<sup>R</sup>* <sup>1</sup>*=*<sup>2</sup> and for laminar flow *<sup>τ</sup><sup>R</sup>* <sup>¼</sup> <sup>3</sup>*νC=*ð Þ <sup>8</sup>*kTN*<sup>0</sup> , which leads to a rapid reaching of the final aggregate size. With increasing oil viscosity, for both laminar and turbulent flows, the collision frequency of asphaltene particles decreases, which inhibits the rate of nanoaggregate formation.

Maxwell's rheological equation for a viscoelastic fluid in substantive derivatives is written as 3½ �

$$\begin{aligned} \lambda \left( \frac{\partial \tau}{\partial t} + U \frac{\partial \tau}{\partial \boldsymbol{\gamma}} \right) + \tau &= \eta\_c \bullet \boldsymbol{\gamma} \\ t = \mathbf{0}, \boldsymbol{\tau} = \tau\_0, \boldsymbol{\tau} \boldsymbol{\gamma} = \mathbf{0} \end{aligned} \tag{11}$$

**Figure 3.** *Variation of nano-aggregate size over time depending on the content of asphaltene particles in the oil:* 1 � *φ* ¼ 0*:*05; 2 � 0*:*1; 3 � 0*:*2; 4 � 0*:*3*:.*

A special form of equation (Eq. (11)), is given in the following form

$$
\lambda \left( \frac{\partial \tau}{\partial t} + U \frac{\partial \tau}{\partial \mathbf{y}} \right) + \tau = \mathbf{0} \tag{12}
$$

The solution of Eq. (12) can be represented as

$$
\pi = \mathsf{C}\_{\mathsf{U}} f(\mathsf{y} - \mathsf{U}t) \exp\left(-\mathsf{y}\boldsymbol{\zeta}\right) \tag{13}
$$

Substituting this solution into (Eq. (13)) we obtain the identity. Here *λ* ¼ *<sup>η</sup><sup>c</sup>=<sup>G</sup>* - is the relaxation time by Maxwell, *U* - is the rate of displacement of the deformation front, *f y*ð Þ � *Ut* - is the function defining the deformation displacement front in the framework, *y*- is the coordinate, *G*- is the modulus of shear elasticity, *γ*\_ ¼ *dγ=dt* - is the rate of shift, *y*- is the shifting gradient, *τ*<sup>0</sup> - is the ultimate shift stress or the yield stress.

Moreover, if *τ* ≤*τ*0, then *γ*\_ ¼ 0. The complete solution of equation (Eq. (13)) will be

$$
\pi = \mathcal{C}\_{\mathsf{U}} f(\mathsf{y} - \mathsf{U}t) \exp\left(-\mathsf{r}\zeta\_{\mathsf{k}}\right) \mathsf{r}\_{\mathsf{0}} \tag{14}
$$

Otherwise, the equation can be represented in logarithmic form

$$
\ln \tau = \ln \tau\_0 - \nu\_\lambda + \ln \left( C\_\mathbf{U} f(\mathbf{y} - Ut) \right),
\tau\_0 = \eta\_c \dot{\gamma} \tag{15}
$$

Obviously, the value *t=λ* in equation (Eq. (15)) characterizes the deformation of the viscoelastic framework in time and depends on the velocity or pressure gradient. In approximation, this dependence can be presented as *<sup>t</sup> =<sup>λ</sup>* ¼ *tγ*\_*=Wef gradP=*ð Þ *gradP* <sup>0</sup> *<sup>n</sup>* , (where *We* <sup>¼</sup> *λγ*\_) is the Weissenberg number).

As can be seen from **Figure 1**, the reduction in asphalt-resin content while dissolving them in aromatic hydrocarbons inhibits the formation of various disordered structures.

## **3. Mechanism and kinetics of dissolution of asphalt-resinous substances in aromatic hydrocarbons**

The presence of asphalt-resin compounds in high-viscosity oil, in heavy oil products (tar, bitumen), and in waste oil water has a negative effect on oil extraction, transport, treatment, and refining processes. Due to their high adhesion and cohesion capacity, asphalt-resin compounds adhere and precipitate on equipment surfaces, forming deposits of a certain thickness. In refining processes at high temperatures, asphalt-resin substances form heavier remains (coke) which deposit on the surface of water droplets in oil emulsions, and form adsorption layers which complicate the coalescence and aggregation of water droplets, thereby inhibiting the stratification and separation of the oil–water system. The presence of asphaltenes in oil determines its rheological properties through the formation of coagulation structures nanoaggregates, nanoaggregate clusters, and eventually a viscoelastic framework, which worsens the rheological properties of the fluid and complicates oil filtration in the porous reservoir, its production, and transport. As noted above, the usage of different reagents prevents the formation of certain structures in the oil volume,

which leads to a decrease in its effective viscosity and an improvement in rheological properties. According to the work, asphalt-resin substances are very soluble in hexane and aromatic hydrocarbons (gasoline, toluene, xylene) and poorly soluble in alcohols and esters.

The problem of dissolving asphaltenes is an important one for improving the rheological properties of oil and for processes of cleaning waste oil water from asphaltresin compounds by liquid-phase extraction.

Along with asphalt-resinous substances, crude oil contains some by-products: format the ion water, solid phase, and other impurities that also affect the rheological properties of the oil. Usually, the formation water in an oil volume is in a dispersed form, that is, in other words, the form of droplets, which under different flow conditions can form coagulation structures (flocculus) that significantly affect rheological properties. The separation of water from oil, or a significant reduction in the water content of oil, also has a positive effect on the rheological properties of the last.

The present section will be considered only improving the rheological properties of the crude oil by partial dissolution of asphalt-resinous substances in aromatic hydrocarbon. Experimental studies have shown that the best characteristics of mixability and solubility in heavy oil asphaltenes have been obtained with aromatic solvents and solvent mixtures at different temperatures. It has been discovered that temperature and solvent properties are the physical parameters that most affect the dissolution phenomenon of asphaltenes in oil. The aromatic hydrocarbon content is a key chemical property of solvent blends that improves their solubility properties. Works, [17–20] presented the degree of asphaltene deposition depending on the toluene content for different oilfields.

It has been noted that the degree of asphaltene deposition using a solution of 65–69% normal heptane and toluene decreases to 30–35% (wt.). In works [21–23], is offered a model of the kinetics of asphaltene-resin substances dissolution in hexane and in a mix of hexane and benzene for the Russian oils.

The presented model has an empirical character, although satisfactorily describes the experimental data

$$a = 1 - \exp\left(-kt^{\pi}\right) \tag{16}$$

where *α* - dissolution degree, *k* - dissolution rate constant, *n*- index of degree *n* ¼ 0*:*5 � 1*:*05. Moreover, the kinetics of the process is not built on the phenomena of mass transfer under certain flow conditions, but is regarded simply as a heterogeneous process.

In work [22] for the convenience of determining the kinetic parameters, the exponential model is decomposed into a McLaren series, which reduces the non-linear model to a two-parameter Langmuir model. Many experimental data and kinetic curves of dissolution of asphaltenes in aromatic hydrocarbons are given in [21–23].

The most widespread model of particle dissolution kinetics is the membrane model, according to which in each phase there are fixed or moving laminar boundary layers directly adjacent to the particle boundary, in which the transport is carried out by molecular diffusion. Therefore, there is a scheme for a stationary unit particle in which the whole boundary layer is considered as an area where turbulent pulsations do not excite, and the variation of the solute concentration is characterized by a linear dependence. Unlike laminar flow, in turbulent flow the buffer sublayer plays this role. At intensive mixing in the apparatus, due to the appearance of developed isotropic turbulence, the kinetic curves may differ from the linear dependence, because of the

complex distribution profile of the turbulent diffusion coefficient and flow velocity in the boundary layer. Dissolution of asphaltene particles belongs to mass-exchange processes and, depending on the hydrodynamic flow regime, is characterized by different mechanisms. Especially, in the fixed-film model, there is a thin boundary diffusion layer at the interface, in which the entire concentration gradient of the substance is concentrated, and the transfer through this layer is carried out only by molecular diffusion. The turbulent boundary layer model describes the mass transfer between a fixed boundary and a turbulent fluid flow with a complex turbulent diffusion coefficient profile. According to this model, the concentration of substance in the flow is constant and in the turbulent sublayer gradually decreases as it approaches the buffer sublayer, where the turbulence gradually attenuates, passing into laminar mode. Usually, the diffusive boundary layer are taking into account: a) the nature of fluid flow and convective transport of substance; b) molecular and convective diffusion in the transverse and tangential direction; c) the absence of a pronounced border between sublayers. The process of dissolution of asphaltene-resin substances in aromatic hydrocarbons is characterized by nonstationary behavior, in connection with which the models of mass transfer differ significantly according to the nature of the hydrodynamic flow around the particle. In particular, at laminar flow around the particle, the diffusion flux of dissolved substance per unit time from the surface of asphaltene particles can be defined by the following expression (23).

$$J = \sqrt{\frac{3}{\pi} \left(\frac{3D\_M U}{2R}\right)^{1/2}} \Delta C, \, \_0\lambda \ge \lambda\_0 \tag{17}$$

In isotropic turbulent viscous streamline, with some assumptions, the same flow is defined as.

$$J = \sqrt{\frac{3}{\pi}} \left(\frac{\varepsilon\_R}{\nu\_C}\right)^{1/4} (UR)^{1/2} \Delta C, \lambda < \lambda\_0 \tag{18}$$

Here Δ*C* ¼ *C*<sup>0</sup> � *C*<sup>1</sup> - driving force of the dissolution process, *C*0,*C*1- concentration of dissolved substance far from the particle surface and on the surface, *DM*coefficient of molecular diffusion, *U*- flow velocity, *ε<sup>R</sup>* - dissipation of turbulent flow energy in the unit of mass, *R* - particle radius, *νc*- viscosity of the medium, *α* coefficient. Both solutions were obtained at boundary conditions:

$$r \to \infty, \mathcal{C} = \mathcal{C}\_0; r = R, \mathcal{C} = \mathcal{C}\_1$$

As follows from equation (Eq. (16)), the flow of asphaltene mass from the particle surface is directly proportional to the dissipation of turbulent flow energy and inversely proportional to toluene viscosity, ð Þ¼ *<sup>ε</sup>R=ν<sup>c</sup> <sup>k</sup>*<sup>0</sup> \_ *<sup>γ</sup><sup>n</sup>*þ<sup>1</sup>*=ν<sup>C</sup>* � � i.e., at high viscosity values corresponding to low temperatures, the dissolution rate decreases and, similarly, at high rotation frequencies corresponding to high energy dissipation values, the dissolution rate increases.

It should be noted that the main requirement for dissolution of particles is the condition of equality of diffusive and convective fluxes on the surface of the boundary layer

$$\left| -D\_{\epsilon \overline{\mathcal{H}}} \frac{\partial \mathcal{C}}{\partial r} \right| r = \delta = \beta (\mathcal{C} - \mathcal{C}^\*) \tag{19}$$

where *r*- is the coordinate in the thickness of the interfacial layer, *C*- is the concentration of the absorbed substance, *C*<sup>∗</sup> - is the equilibrium concentration, *δ*- is the thickness of the interfacial layer, which is proportional to *δ* � ð Þ *αDM=V*<sup>0</sup> <sup>1</sup>*=*<sup>2</sup> where *V*0- is the streamline velocity at the particle surface, *β*- is the mass transfer coefficient, *DE*- is the effective diffusion coefficient.

The effective coefficient of diffusion is defined as the sum of molecular *DM* and turbulent *DE* diffusion *DE*, with molecular diffusion dominating in the viscous sublayer as it approaches the surface of the dissolving particle, and with sufficient distance from the surface, turbulent diffusion *DT* ≫ *DM*.

The coefficient of turbulent diffusion is a function not only of the physical characteristics of the medium, but also the turbulent characteristics of the flow and the transverse coordinate. According to the statistical theory of turbulent diffusion, the value of mean square displacement of particles of dissolved medium from initial position in radial direction, is defined by dependence

$$r^{-2} = 2D\_M \Delta t \tag{20}$$

The dissolution of asphalt-resin substances in toluene depends on the nature and properties of the particle and the solvent.

It can be assumed that the dissolution process is determined by softening of the upper layers of asphaltene particles as a result of diffusion penetration of the solvent into the near-surface layers. In this aspect, expression (Eq. (19)) is the basic condition for dissolution of asphaltene particles. It should be mentioned that in mixing devices the level of turbulence of flow in the apparatus is determined by the rotation frequency of the stirrer. Usually, at sufficiently high rotational speeds, achieved isotropic turbulence, which dampens as it approaches the surface of the particle. The mass flow from the unit surface of asphaltene particles is determined by Eq. (E18), where the dissipation specific energy is proportional to *<sup>ε</sup><sup>R</sup>* � *<sup>n</sup>*<sup>3</sup> 0*d*2 , *n*0, *d*- rotation frequency and diameter of the mixer. Hence, the dissolution process intensifies with increasing frequency of rotation. In isotropic turbulent flow, the turbulent diffusion coefficient included in equation (Eq. (19)) depends on the dissipation energy and viscosity of the medium

$$D\_T \sim \left(\frac{\varepsilon\_R}{\nu\_0}\right)^{1/2} \sim \left(n\_0^{3/2} d\right) / v\_c \tag{21}$$

In order to study the kinetics of asphalt-resin substances dissolution process in toluene experimental studies were carried out in stirrers in the temperature range 20–60<sup>0</sup> С for 60 min at stirrer speed 1000–1200 min�<sup>1</sup> . Asphalt-resinous substances were extracted by additional evaporation of bituminous tar fraction with density 1280kq/m<sup>3</sup> , with asphaltene content of 14.28% and paraffin content of 7.15% from Azerbaijan oils mixture.

The dissolution mechanism of asphalt-resin substances in aromatic solvents is based on three stages: a) diffusive transfer of solvent to the surface of asphaltene particles; b) physical dissolution of surface layers at certain temperatures; and b) diffusive transfer of dissolution products to the volume through the boundary layer. Experimental studies on dissolution of asphalt-resin substances in toluene are presented in **Table 1**. It should be noted that with the increase of stirrer rotation frequency, the process of asphalt-resin substances dissolution in toluene is intensified


#### **Table 1.**

*Dependence of asphalt-resin solubility on time at different temperatures.*

to a certain limit and is improved by increasing the intensity of turbulent flow, turbulent diffusion and mass transfer coefficients. On the other hand, an increase in turbulence intensity leads to the growth of a number of collisions and turbulent diffusion of asphaltene particles, which may contribute to the development of their coagulation processes. At low turbulence intensity, the disperse system tends to structure formation, with visco-elastic rheological properties manifested.

Experimental studies show that at low temperatures the dissolution of asphaltresinous substances is incomplete *<sup>T</sup>* <sup>¼</sup> <sup>25</sup><sup>0</sup>*C*- at �72% and at *<sup>T</sup>* <sup>¼</sup> <sup>40</sup><sup>0</sup>*C*-84%.

Using condition (Eq. (19)) and replacing the variables in expression (E20) *dr* <sup>¼</sup> <sup>2</sup>*Deff* � �<sup>1</sup>*=*<sup>2</sup> *t* �1*=*<sup>2</sup>*dt*, write the expression as follows

$$\begin{aligned} \frac{\partial \mathbf{C}}{\partial t} &= -K(\mathbf{C} - \mathbf{C}^\*) \\\\ \mathbf{C}(t)|t=\mathbf{0} &= \mathbf{C}\_0 \end{aligned} \tag{22}$$

here *<sup>K</sup>* <sup>¼</sup> <sup>2</sup> *Deff t* � �<sup>1</sup>*=*<sup>2</sup> *β* - coefficient of mass transfer for the dissolution process, *C*<sup>0</sup> initial concentration of asphaltenes in toluene, *C t*ð Þ- concentration of dissolved asphaltene-resin substances in toluene. Expression (E22) is an equation for the kinetics of the mass-exchange diffusion process of dissolution. For the non-stationary process of dissolution, at the value of the coefficient *K*, depending on time, the solution of equation (Eq. (22)) will be presented as

$$\mathbf{C}(t) = \mathbf{C}^\* - (\mathbf{C}^\* - \mathbf{C}\_0) \exp\left(-\int\_0^t \mathbf{K}(t)dt\right) \tag{23}$$

For pure solvent, this equation is simplified to

*Applied Problems in the Rheology of Structured Non-Newtonian Oils DOI: http://dx.doi.org/10.5772/intechopen.105948*

$$\mathbf{C}(t) = \mathbf{C}^\* \left( \mathbf{1} - \exp\left(\int\_0^t \mathbf{K}(t)dt\right) \right) \tag{24}$$

Using experimental studies and expression (E23), can be placed.

 $K(t) = K\_0 t^{-1/2}, K\_0 = \left(\bigvee\_{\text{Diff}} \right)^{1/2} \beta$  and  $\mathbf{C}^\*(T) = \mathbf{57.33} + \mathbf{0.77}^0 \mathbf{C}$ .

Using the above-mentioned expressions for the dissolution of a single particle from expression (Eq. (24)) we will obtain dependencies, and ultimately the equation for the dissolution of asphalt-resinous substances in toluene will be given as

$$\mathbf{C}(t) = \mathbf{C}^\* \left( \mathbf{1} - \exp\left(-at^{1/2}\right) \right) \tag{25}$$

where *α* ¼ 2*K*0.

For the "collective" dissolution of more particles, should be used the effective time-averaged value of the mass transfer coefficient

$$\begin{aligned} \label{eq:1} \int\_{P} \beta dt\\ \beta\_E = \frac{\begin{array}{c} 0\\ \end{array}}{T\_P} = \beta \frac{t}{T\_P} \end{aligned} \tag{26}$$

where *TP* - is the complete dissolution time of the particles. As follow from the **Table 1** the time for the complete dissolution of asphaltene particles is about 50–60 min. Considering this expression, the solution (Eq. (26)) will be

$$\mathbf{C}(t) = \mathbf{C}^\* \left( \mathbf{1} - \exp\left(-a t^{3/2}\right) \right) \tag{27}$$

where *α* ¼ <sup>2</sup>*K*<sup>0</sup>*=*<sup>3</sup>*TP*. The results of experimental studies and calculated values according to formula (Eq. (27)) for different temperatures are shown in **Figure 2**.

#### **Figure 4.**

*Kinetic curves of dissolution of asphaltene-resin substances in toluene at temperatures equal to: 1-*20<sup>0</sup>*С; 2-* 400*С; 3-* 600*С. The straight lines correspond to the linear kinetics of asphaltene dissolution in toluene at temperatures equal to:*1<sup>0</sup> *–*200*С;* 2<sup>0</sup> *–*400*С;* 3<sup>0</sup> *–*600*С.*

Practical calculations show that in the indicated range the temperature changes insignificantly *α* ¼ 0*:*025 � 0*:*030. Eq. 23 adequately describes experimental data on the dissolution of asphalt-resinous substances in toluene. **Figure 4** shows the areas corresponding to the approximate direct dependence of asphalt-resin dissolution kinetics in the form of the equation *C t*ðÞ¼ *K T*ð Þ*t*.

For a straight line dependence, the dissolution constant can be approximated by an expression depending on the temperature

$$
\ln K = -\frac{752.087}{T} - 0.8507\tag{28}
$$

with a correlation coefficient equal to *<sup>r</sup>*<sup>2</sup> <sup>¼</sup> <sup>0</sup>*:*992. In this dependence *<sup>T</sup>*- is the absolute temperature. As **Figure 4** shows, the linear correlation of the direct solubility is only observed at *t*≤ 20 min. and within the viscous sublayer of the entire boundary layer volume.
