**4. Rheology of structured non-Newtonian oils in gas lift method extraction**

The gas lift method is based on the principle of displacing oil from a reservoir by applying compressed gas (air) to its surface. Different schemes for the gas lift method are shown in **Figure 5**. High-pressure gas is injected into the annulus, which will lower the liquid level in the annulus and raise the level in the main pipe where the oil-gas mixture rises. When the liquid level drops to the lower end of the main pipe, the

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

compressed gas will begin to mix with the oil, resulting in a gas–liquid mixture of lower density and viscosity than the liquid coming from the reservoir, while the level in this liquid in the main pipe rises. The more gas is applied, the less dense the mixture will be and it will rise to a higher altitude. In a continuous gas injection into the well, the liquid (mixture) rises to the wellhead and pours to the surface, while a new portion of the liquid is constantly flowing from the reservoir into the well.

Despite the great advantages and disadvantages of the gas-lift method of oil extraction, significant attention is paid to improving the efficiency of this method of extraction of heavy oils, because the formation of gas–liquid mixture significantly affects the rheological properties, which is associated with a decrease in density and viscosity. In the case of a high-pressure gas supply at the gas–liquid interface, the gas is crushed into bubbles of a large range of sizes due to turbulization of the flow [24].

Research has shown that non-Newtonian oils have anomalous properties that are expressed primarily in the variability of their viscosity, their dependence on the effective shear stress, and the content of various dispersed particles (water droplets, gas bubbles, solid particles, asphalt-resinous substances). An increase in the content of high molecular weight compounds such as paraffin, resins, and asphaltenes in hydrocarbon liquids leads to the formation of spatial structural meshes and stable oil emulsions.

The composition of the oil and its various heavy fractions determine the structure of the rheological model. Currently, there are many rheological models, whose main tasks are to determine the dependence of shear stress on shear rate and identify a formula for calculating the effective viscosity of the medium. The rheological model does not reflect the essence of the process, but it is an important characteristic for evaluating the state of a complex medium.

Rheological properties of oil disperse systems are determined both by a high content of disperse particles (asphalt-resin compounds, water droplets, solids) in oil and by their ability to form different structures due to the physical interaction of particles between each other. Coagulation structures are formed by intermolecular links between particles, and if liquid interlayers remain between particles, the thickness of these interlayers significantly affects the strength of the coagulation structure. Aggregate-unstable oil systems are characterized by an unstable state of the medium due to continuous structuring and changes in the physical properties of the particles, i.e. changes in the volume and size of asphaltene particles due to their interaction, collision, coagulation and crushing at a certain concentration in a confined volume. The connection between the structure and viscosity of petroleum disperse 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 of asphaltene particles. The successive coagulation or agglomeration of individual asphaltene nanoparticles into nanoaggregates and into clusters of nanoaggregates eventually form a viscoelastic framework that gives oils certain rheological properties characteristic of non-Newtonian fluids.

The structural and mechanical stability of emulsion systems is related to the formation of adsorption layers at the oil–water and oil-gas interface on the surface of water droplets and gas bubbles, whose composition consists of asphaltenes, resins, paraffins, mineral salts and solids. Analysis of the composition of adsorption films on the surface of water droplets and gas bubbles in crude oil from various fields shows that the main stabilizers are asphaltenes and resins, which are composed of highmelting paraffins and inorganic mechanical impurities. The creation and formation of an adsorption layer on the surface of water droplets and gas bubbles with elastic and

viscous properties contribute to the stabilization of oil emulsions, which significantly affects the structure formation and rheological properties of the whole oil. The mechanism for the formation of adsorption layers on the surface is determined by the diffusive transfer of mass of substance (asphaltenes) from the volume of oil to the surface of water droplets and gas bubbles. The viscosity of oil with different water content increases up to a certain value of the water volume fraction, after which it decreases. Using experimental data, the effective viscosity of an oil emulsion can be determined using the formula

$$\frac{\eta - \eta\_W}{\eta - \eta\_W} = \left(1 + 2.5\phi + a\_0 \phi^2\right) \exp\left(-a\_1 \phi^2\right) \tag{29}$$

here *η*0, *η<sup>W</sup>* - is the viscosity of oil and water. As follows from expression (E28) at high water content we have *ϕ* ! 1, *η* ! *ηW*. **Figure 6** shows dependence of effective oil viscosity on water content calculated by formula (Eq. (29)) with coefficients *a*<sup>0</sup> ¼ 150, *a*<sup>1</sup> ¼ 4*:*88.

At low water concentrations in oil *φ* ≪ 0*:*1, expression (Eq. (29) can be simplified to the form: *η* ¼ *η*0ð Þ 1 þ 2*:*5*ϕ* . It should be noted that the coefficients of expression (Eq. (29)) *α*0, *α*<sup>1</sup> will depend on the nature and deposit of the oil.

The viscosity of oil is also significantly affected by its gas content. **Figure 7** shows a graph of the viscosity of oil. The viscosity of oil is plotted as a function of its gas content, with the viscosity of the oil/gas mixture *φ* ≪ 0*:*1 calculated according to the formula: *η* ¼ *η*0ð Þ 1 þ 2*:*5*ϕ* . At large gas concentrations in the oil, should be used an expression such as E29

$$\frac{\eta - \eta\_{\rm g}}{\eta\_0 - \eta\_{\rm g}} = \left(\mathbf{1} + 2.5\phi + b\_0 \phi^2\right) \exp\left(-b\_1 \phi^2\right) \tag{30}$$

Here *ηg*- viscosity of the gas contained in the oil, *b*0, *b*1- coefficients determined on the basis of experimental data.

Although many advantages and disadvantages of the gas lift method of oil extraction, considerable attention has been paid to improving the technical and economic performance of gas lift wells producing non-Newtonian oil.

In order to develop a rheological model in non-Newtonian oil extraction by gas lift method, laboratory research was carried out on an experimental setup, the scheme of which is shown in **Figure 8**.

**Figure 6.** *The viscosity of oil emulsion at different water concentrations.*

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

**Figure 7.** *Dependence of oil viscosity on low gas content for different oil.*

#### **Figure 8.**

*Scheme of experimental setup: 1- model of stratum (column with porous medium); 2- high-pressure capacity; 3 hand-operated press; 4-manifold; 5- fluid capacity; 6-thermostat; 7-model of gas–liquid-lift consisting of pipe d = 8. 10<sup>3</sup> m length 3,4 m, which is located inside the pipe d = 20.10<sup>3</sup> m length 3,5 m - 8; 9-gas cylinder; 10 pressure controller; 11-gas meter; 12- metering capacity; 13- model pressure gauge; 14- control valves.*

As tested liquids are used a model fluid consisting of transformer oil with a density of 820 kg/m<sup>3</sup> and viscosity of 3.8 mPa.s and tar oil with different percentages. It is known, that viscous liquid at the addition of high-molecular compounds of vacuum residue is transformed into a non-Newtonian system. After setting the lift operating mode, both the lift capacity and the gas meter readings are measured.

Analysis of the results of the experiments shows that at the same rate of pressure change in the porous medium and lifter, degassing of viscoelastic oil in the stratum is difficult due to the non-equilibrium of this process and the oil coming into the well

containing an increased amount of formation gas, which performs useful work when lifting the liquid. Lifting of viscoelastic oils excludes such phenomena as breakthrough and slippage of compressed gas, whose work is close to the moment of piston oil squeezing. The analysis of the experimental results shows that the viscoelastic properties of the lifted fluids can be used to improve the technological processes of oil production.

On a rotary viscometer, are investigated the rheological properties of non-Newtonian oils. As a model of non-Newtonian oil, a solution of vacuum residue in transformer oil was chosen (at different percentages) with shear rates in the range *γ*\_ ¼ 100 � 1300 s-1 and their corresponding values of shear tangential stress *τ* (**Table 2**).

It should be noted that the shear creeps deformation of oil media is many times greater than the elastic deformation. Rheological properties of dispersed oil media are determined by the movement of particles during volumetric change and, in particular, during structure formation, which is associated with different manifestations of rheological properties of non-Newtonian oils during shear and volumetric deformation. Shear deformation can progress over time at a decaying, constant, and progressing rate, while bulk deformation is obviously always at a decaying rate.

**a) The Bingham model**. Non-Newtonian fluids are primarily characterized by the fact that their character and flow patterns are predetermined by the particular


**Table 2.**

*Rheological fluid properties in different percentages (mixture of transformer oil and tar).*

influence of the velocity gradient on the shear resistance. The general equation is described by which the rheological curve for a non-Newtonian viscoplastic oil:

$$
\tau = \tau\_0 + k \left(\frac{dV}{dy}\right)^n = \tau\_0 + k \bullet \gamma^n \tag{31}
$$

here *τ*0- limit of fluidity, *γ*\_ ¼ *dV=dy* - gradient of velocity, *n* - index of degree. Let us consider characteristic features of non-Newtonian fluids: a) viscoplastic fluids, for which *n*<1, *τ*<sup>0</sup> ¼ 0. Examples of such fluids are polymer solutions, suspensions, and emulsions, including oil emulsions, oil sludge, and many oil products; b) dilatant fluids, for which *n*> 1, *τ*<sup>0</sup> ¼ 0.

Concentrated suspensions, pastes, etc. are examples of such fluids; c) Bingham fluids, which *n* ¼ 1, *τ*<sup>0</sup> > 0 and characterized by the fact that they can only flow at shear stress greater than the limit of fluidity *τ*0. In most cases, crude oil exhibits Bingham's rheological properties.

Using the experimental data in **Table 2**, the rheological model can be represented as

$$
\pi = \tau\_0(\phi) + \eta\_{\rm eff} \dot{\gamma} \tag{32}
$$

where *ϕ*- is the tar content of the transformer oil.

Using the experimental data in **Table 2**, the rheological model can be represented as

$$
\pi = \tau\_0(\phi) + \eta\_{\text{eff}} \dot{\gamma} \tag{33}
$$

where *ϕ*- is the tar content of the transformer oil.

**Figure 9** have been shown the experimental data and the calculated curve for model (Eq. (33)), using the expression *<sup>τ</sup>*<sup>0</sup> <sup>¼</sup> <sup>0</sup>*:*06*ϕ*<sup>1</sup>*:*8.

**b) Maxwell's model of a viscoelastic body**. By connecting elastic and viscous elements in the sequence, we reach the Maxwell model characterizing the equation of state:

$$
\dot{\mathbf{y}} = \frac{\mathbf{r}}{\eta} + \frac{\mathbf{r}}{\mathbf{G}} \tag{34}
$$

where *G*- is the modulus of shear elasticity of the studied liquid; *ηt*- is true viscosity.

To estimate the relaxation properties, the data were processed according to the method proposed in [25] and developed in [26, 27], the essence of which is to relate the shear tangential stress (*τ*) to the effective viscosity (*ηeff* ), in the form of a relation:

$$\frac{1}{\eta\_{\rm eff}^2} = \frac{1}{\eta\_t^2} + \frac{\tau^2}{4G^2 \eta\_t^2} \tag{35}$$

It should be emphasized that Eq. (E28) will hold if *η<sup>t</sup>* and *G* take constant values, i.e. provided that the system is linear. The dependence curves *τ* ¼ *f*ð Þ*γ*\_ have been recalculated in coordinates1*=η*<sup>2</sup> *eff* <sup>¼</sup> *<sup>f</sup> <sup>τ</sup>*<sup>2</sup> ð Þ (**Table 2**).

Based on the results of the calculation using the above formula, the dependence shown in **Figure 10** is shown. From the character of the curve, it is possible to estimate the interval of shear rates and also to identify the area of non-linearity.

#### **Figure 9.**

*Dependence of shear stress on shear rate at values ϕ equal to: 1–5%; 2–10%; 3–15%.*

#### **Figure 10.**

*Dependence* 1*=η*<sup>2</sup> *eff on τ*<sup>2</sup> *the solution transformer oil + tar at different temperatures oil + tar at different temperatures: 1-*300*С; 2-* 400*С; 3-* 500*С.*

The results of rotor viscometric tests for the solution (transformer oil + tar) at different temperatures show that the dependence sections which are parallel to the *τ*2, axis correspond to viscous fluid flow and are linear in nature.

The other part of the dependencies, which correspond to non-linear sections, expresses the manifestation of the viscoelastic properties of the fluid being tested.

As the oil moves towards the bottom of the well, the pressure in its volume drops and resulting in the gas release. Furthermore, in theoretical terms, have been determined changes in pressure over time and along the radius of the stratum.

Studies have shown that fluid movement in porous media takes the greatest velocity in the bottom hole zone, although the fluid gathers maximum velocity at the walls of the lifter. Calculations of pressure reduction rate, given when non-Newtonian fluid is lifted along the wellbore, showed that the rate of pressure change during lifting decreases. As follows from expression (Eq. (25)), the manifestation of inertial forces takes place in the bottom hole zone due to a change of velocity, mainly in direction, which leads to the increasing influence of abnormal oil properties [28] (**Figure 10**).

Analysis of the results of conducted experiments shows that at the same rate of pressure change in the porous medium and lifter, degassing of viscoelastic oil in the reservoir is difficult because of the non-equilibrium of this process. The oil flowing

into the well contains increased amounts of formation gas, which performs useful work in lifting the fluid. Therefore, the specific agent flow rate in wells producing viscoelastic oil is lower than in wells with conventional viscous oil.
