Experimental study of the features of filtration of non-Newtonian oils in a porous medium

. The current state of development of deposits with high-viscosity oils is characterized by a low value of the achieved oil recovery with a high water cut in the produced wells. However, ways to improve the implemented development systems in order to increase the recovery factor in conditions of high water cut in well production, especially in the late stage of operation requires further research. Therefore, this research intended to investigate features of filtration of non-Newtonian oils in a porous medium. Oil fields with a complex geological structure have been discovered in many oil and gas regions of the world. These fields are characterized by a small oil-saturated thickness of the reservoirs, low reservoir properties, high viscosity of reservoir oil and heterogeneity of productive horizons. To study the filtration process, a specially designed installation was used. Clearly, the main elements are a column (core holder) with a water jacket, an oil tank, a thermostat and a high-pressure air tank (compressor). A research experiment was undertaken in two oil fields, which are X and Y. The results of physicochemical properties of oil field X showed that the density was 0.878g/cm 3 , followed by sulfur content (1.51%), pitches (21.89), asphaltenes was 4.19, and paraffin was 5.18.


Introduction
In recent years, oil fields with a complex geological structure have been discovered in many oil and gas regions of the world.These fields are characterized by a small oilsaturated thickness of the reservoirs, low reservoir properties, high viscosity of reservoir oil and heterogeneity of productive horizons [1,2].In addition, the depth of occurrence of promising structures and the cost of geological exploration are growing.Under these conditions, one of the ways to increase oil production is to increase the recovery factor of geological oil reserves (GOR) remaining in the developed fields.This task is especially relevant for fields with high-viscosity oils [3]. the achieved recovery factor values at such facilities are two or more times lower than at fields with low-viscosity oils.Given that at present the main technology for the development of oil deposits is associated with the displacement of oil by water, it is important to increase the efficiency of this process by using various solutions [4,5].
Noteworthy, the experience of many years of development of oil fields in Uzbekistan, as well as studies abroad, show that the complications that arise in the process of oil production and significant losses of oil in the reservoir are largely related to the properties of the produced oils [6].
The non-Newtonian nature of oils, due to the presence of paraffin-asphaltene -resinous substances in the system, is of particular importance in the process of their extraction and the application of methods to increase the oil recovery factor.At present, a large theoretical and experimental material has been accumulated on the study of the structural-mechanical properties and features of the flow of non-Newtonian oils [1][2][3][4][5][6][7].Studies have shown that during the development of wells that have discovered deposits of heavy, high-viscosity oils, complications arise associated with the difficulty of lifting oil to the surface.A high content of asphaltene -resinous substances causes the manifestation of initial pressure gradients and relaxation processes in the oil-reservoir system during filtration, large pressure losses in wellhead communications and oil flow rates [8][9][10] leads to a significant reduction in oil recovery.
A.H. Mirzazhanzade, G.I. Barenblatt, Yu.P. Zheltov, R.S. Gurbanov, A.T. Gorbunov, V.M. Sanatir, Sh.A. Abaydulin, Yu.N.Baydyukov, V.E.Gubin made a significant contribution to the development of studies of structural and mechanical properties, non-Newtonian systems, the development of deposits containing high-viscosity and heavy oils, the operation of wells producing such oil [1][2][3][4][5][6].The main principles for the development of high-viscosity oil fields are outlined in [11].A characteristic feature of the operation of wells producing heavy oils is also a sharp increase in water cut at the initial stage of development.The joint movement of high-viscosity oil and water in the bottomhole formation zone, along the wellbore and collection system leads to their mixing with the formation of stable and heavy emulsions [5,6,[9][10][11].The above characteristic features of heavy high-viscosity oils lead to a sharp decrease in the efficiency of field development and the retention of a significant part (up to 80-90%) of their geological reserves in productive strata.
As a result, the current state of development of deposits with high-viscosity oils is characterized by a low value of the achieved oil recovery with a high water cut in the produced wells.However, ways to improve the implemented development systems in order to increase the recovery factor in conditions of high water cut in well production, especially in the late stage of operation requires further research.Therefore, this research intended to investigate features of filtration of non-Newtonian oils in a porous medium.

Materials and methods
To study the filtration process, a specially designed installation was used (Fig. 1), the schematic diagram of which is shown in Fig. 1 and 2. Clearly, the main elements are a column (core holder) with a water jacket, an oil tank, a thermostat and a high-pressure air tank (compressor).A core holder with a water jacket made it possible to conduct research under isothermal conditions [2,3].The thermostatic liquid circulated according to the scheme thermostat-water jacket-thermostat.The pressure drop in the core holder was created with air from a cylinder (using a compressor).
A homogeneous porous medium was modeled with quartz sand of a certain fraction.To create low-permeable media, quartz sand was passed through a drum mill, where it was broken.Furthermore, the crushed sand was fractionated on sieves into separate fractions [11].The permeability coefficient varied depending on the grain diameters of the fraction.The smaller the particle diameter, the lower the permeability.Clearly, the core holder was filled with washed and dried sand and compacted to a certain porosity value.The determination of air permeability was carried out on the installation (Fig. 1).First, the installation was checked for tightness [10].Besides, measurement of rock permeability was carried out using a laboratory stand, the diagram of which is shown in fig. 2. The laboratory bench consists of a core holder imitating current tubes 500 (820, 790, 710) mm long and 60 mm in diameter.The core holder was filled with quartz sand with a grain diameter of 0.05 m 3 .The sand is pre-sifted on laboratory sieves to obtain the required dimensions.The laboratory stand consists of a compressor 2 for pumping liquid (oil, water) and gas with a maximum pressure set of 25 atm.Liquid and gas through the pipeline system 13 enters the core holder [10].To measure the flow of liquid and gas, the laboratory stand is equipped with a level gauge 12 and a gas meter 10.To determine the pressure at the inlet and outlet of the core holder, exemplary pressure gauges 8a and 8b were used, with a measurement limit of 0 to 1.6 MPa.
In addition, the laboratory stand was equipped with tanks for oil 11a, for water 11b, and a separator 9 for separating liquid (oil, water) and gas.To determine the permeability, a core holder filled with quartz sand (sand reservoir model) was taken.At the beginning and at the end of the core holder we install pressure gauges 8a and 8b.At the approach to the inlet of the core holder there is a valve 22; there is a valve 23 on the tube connected to the outlet.The experiment also requires: a measuring tank 14, a stopwatch and a compressor 2. The compressor pumps liquid (oil and water) through the piping system 13 from the tank 11a and 11b to the core holder.To measure the volume of pumped oil and water into the core holder, tanks 11a and 11b were connected to the level gauge 12.The volume of the released liquid from the linear model is preliminarily settled in the separator 9.The gas flow separated in the separator is measured using a gas meter 10, and the pumped liquid accumulates in a measuring tank 14.
Research was carried out using oil, water and gas.To determine the relative permeability of a core holder with a diameter of 60 mm and a length of 500 mm, oil poured into a container 11a, in a volume of 3.5 m 3 , water in a container 11b, in a volume of 3.5 m 3 .Furthermore, the compressor 2 were connected to the electric current.The compressor will work on the receiver to set the pressure up to the established norms (Pmax=25 atm), which was measured by the pressure gauge 2a.
Opening valves 15, 20 and 21, we begin to pass through gas core holder.We record time in a stopwatch.Some after the start of pumping, the pressure at the inlet and outlet of the core holder will change and then be established at the same level.The pumping process lasts until the pressure at the inlet p1 was established and output p2 was unchanged.Moreover, the pressure drop Δр was determined, where valves 15, 20 and 21 were closed.The volume of gas that was passed through the core holder enters the separator 9. We measure the volume of gas pumped through the core holder with a gas meter 10.After determining the absolute permeability of the core holder, we open the valves 15, 16, 17, 18, 19, 20 and 21 and begin to let the liquid (oil and water) through.The time was recorded in a stopwatch [9].Some after the start of pumping, the pressure at the inlet and outlet in the core holder will change and then be established at the same level.The pumping process lasts until the pressure at the inlet p1 was established and output p2 was unchanged.
The volume of the passed liquid entered the separator 9.In the separator, liquid and gas are separated.The volume of gas passed through the model was determined by the gas meter 10, the amount of liquid that has passed through the core holder in measuring container 14 [5][6][7]11].Now let's change the difference Δp (it's possible to do if you cover or open one or two valves 20 and 21).Let us carry out the same observations at the new steady pressure drop as in the first case.Having determined the flow rates of the liquid, we calculate the relative permeability of the core holder.The absolute permeability coefficient of the linear model was calculated by the formula: Where: ω -air consumption, cm 3 /sec; viscosity of air, cps L and F -respectively length and area core holder section Р а -atmosphere pressure.P1 and P2 -respectively, the pressure at the inlet and outlet in the core holder The filtration area is equal to: Permeability of the core holder was determined by the following formula:

𝐹𝛥𝑝
Where: µv and µn are the viscosities of water and oil, which are assumed to be known; L and F -respectively length and area core holder sections (which also known).The values of ωn and Δp were measured during the experiment.
The cross-sectional area of the core holder was: The relative permeability of the core holder was determined by the following formula: After determining the permeability, the column was saturated with oil.For saturation, the column was placed in a vertical position, and the saturation process was carried out at a high temperature and a low filtration rate [7].Clearly, these conditions were necessary for more complete saturation of the porous medium.After circulating oil in an amount equal to three times the pore volume, the column was ready for experiments.The experiment consisted in removing the relationship between flow rate and pressure drop during the flow of oil through a porous medium.Practically, the filtration was carried out as follows: the constant temperature of the oil and the column was maintained by a thermostat, Oil was supplied to the column from the tank using compressed air [4,5].Besides, the liquid flow rate was regulated by a flow regulator, and the pressure at the column inlet was recorded by a reference manometer.After some time, the movement of oil was stabilized.Then, oil for a certain period of time was taken.

Results and discussions
The study of oil filtration was carried out in a porous medium of different permeability and at different temperatures.A research experiment was undertaken in two oil fields, which are X and Y.The results of physicochemical properties of oil field X showed that the density was 0.878g/cm 3 , followed by sulfur content (1.51%), pitches (21.89), asphaltenes was 4.19, and paraffin was 5.18.It was reported that the density in the field Y was 0.968 g/cm 3 , sulfur content was 7.5-9.3%,asphaltenes was 4.9, resins was 72.9 and paraffin was 4.5.
The results depicted that the air permeability of the porous medium was 0.0409 µm 2 .It was observed that the oil filtration curves of the field X were rectilinear and proceed from the origin of coordinates (Fig. 3).This suggests that the filtration occurs in the region of the linear Darcy law.It was found that when there was an increase in temperature, an increase in the filtration flow rate of oil was occurred.Clearly, this was due to an increase in the mobility of oil, especially filtration coefficient by reducing the viscosity of oil.
Filtration of oil field X in low-permeability porous media was shown in Fig. 4., accordingly, the air permeability of the porous medium was 0.006 µm 2 .An analysis of the curves showed that at first the filtration proceeded according to a non-linear law.Furthermore, with an increase in the pressure gradient, the nonlinearity turned into a straight line.This non-linearity indicated that at small values of the pressure gradient, filtration was occurred in violation of Darcy's law.
Analyzing the filtration curves of oil field X at various permeabilities of the porous medium (Fig. 3 and 4), it can be seen that with a decrease in permeability, a nonlinearity begins to appear, which disappears with an increase in the pressure gradient.It was found that a high content of asphaltene-resinous substances and paraffins caused anomalous properties, such as non-equilibrium and relaxation properties, the manifestation of initial pressure gradients of produced oils.In fact, knowledge of these features is important for establishing the magnitude of reservoir pressures, hydrodynamic parameters of the reservoir and the oil recovery factor.To date, the influence of the viscoelastic properties of oil on filtration has not been fully studied.When filtering a homogeneous liquid, the equilibrium state between the filtration rate and the pressure gradient is reached instantly.When filtering viscoelastic oils, this assumption does not take place.To study the features of the filtration of high-viscosity oils in a porous medium, experimental studies were carried out on the filtration of oils from the Y field.The experimental studies were carried out on a column, where the porous medium was prepared from quartz sand with a permeability of 27.3 Darcy.
At the initial moment, a pressure drop was created, which was then maintained constant.During the experiment, the filtration flow was measured, which gradually decreased during the experiment until it reached a certain stationary value.After establishing the flow rate, the pressure was removed for several hours.Next, the same differential pressure was reapplied to restore flow.In this case, the flow rate after the drops turned out to be greater than before the flow was blocked, then the flow reached a steady state.This was due to the relaxation of oil particles.
The results of dependence measurement  = (∆)are shown in fig.5, where the removed dependence  = (∆)indicates the non-linear nature of the filtration, which must be taken into account when developing deposits.It was identified that the high content of asphaltene -resinous substances in the oil of the Y field caused anomalous properties and, especially, the manifestation of initial pressure gradients.Fig. 5 showed that oil filtration occurred after reaching a certain value of pressure drop ∆.Clearly, the value ∆ per unit length of the porous medium is called the initial pressure gradient.Table .1 shows the value of the initial pressure gradient ∆  , at various filtration temperatures.Due to the high content of resin in oil, these oils can have, in addition to viscosity and plasticity, also elasticity.As the temperature drops, the viscosity and ultimate shear stress (pressure gradient) increase rapidly, making it difficult for these oils to filter through reservoirs and pump through pipelines.To solve many scientific and technical problems associated with the stimulation of well development and operation, the Darcy filtration law was used, according to which the equilibrium state between the pressure gradient and flow rate is established instantly, an abrupt change in pressure corresponds to the same change in flow.
Subsequently, the filtration of viscous-plastic oils was studied and the generalized Darcy law was obtained.Back in 1953, a phenomenological theory of filtration of viscousplastic media in a porous medium was proposed: at|| >   = 0, and when|| ≤   = 0 where: ||is the initial (limiting) pressure gradient.
In filtration with a limiting pressure gradient, the well flow rate can be represented by the generalized Dupuis formula [6]: where: ∆ =   −  з is the pressure drop between circuits with radii   and   ; ∆ =    −  is the initial pressure drop, above which fluid flows into the well.
In [3], some non-stationary one-dimensional problems of filtration in the elastic regime are considered, assuming that the pressure gradient lags behind the filtration rate.Taking into account this nature of the dependence of the pressure gradient on the filtration rate, the generalized Darcy law was written, which in the linear case has the form [3]: where  is the pressure relaxation time.The physical meaning of equation ( 3), as indicated in [3], is that if a constant filtration rate is established  0 in a previously quiescent fluid, then the corresponding pressure gradient will not be established immediately, but gradually with some "delay": As can be seen from ( 4), the parameter  was characterized by the rate of establishment of a constant pressure gradient corresponding to a constant filtration rate  0 .In the above work, also using (3), based on the general assumptions of the theory of elastic regime [24], a differential equation for fluid filtration in a viscoelastic porous medium was derived: where  is the coefficient of piezoconductivity; -permeability; -porosity;   ,   are the compressibility factors of the fluid and formation, respectively.The work [4,5] discussed the delay in the onset of an equilibrium state between the pressure gradient and the filtration rate, which indicated that it was due to: 1) The inertia of the velocity and the delay of its value from the values of the pressure gradient; 2) Relaxation of pressure and delay of the value of the pressure gradient from the value of the filtration rate; 3) The complexity of the structure of the porous medium and the delay in the establishment of an equilibrium state and its micropores, and 4) delayed repacking of particles, changes in porosity and permeability.
In [4][5][6], equation (3) was generalized taking into account the delay in the filtration rate: where   is the filtration rate relaxation time.In this case, the differential equation of nonstationary filtration has the form: To describe one-dimensional filtration with an initial pressure gradient, A.Kh. Mirzajanzade introduced the generalized Darcy law: where is the filtration flow; viscosity; , , are the permeability, length, and cross section of the porous medium, respectively.

Conclusions
Experimental studies of the process of field X with a high content of asphaltene-resinous substances established the dependence of oil consumption on pressure drop.It is shown that in low-permeability, unlike high-permeability reservoirs, the beginning of filtration proceeds according to a nonlinear law, and with an increase in the pressure gradient, the nonlinearity turns into a straight line corresponding to the Darcy law.
The existence of the initial pressure gradient leads to the formation of stagnant zones and pillars inside the reservoir, which greatly affects the oil recovery factor.In addition, the presence of relaxation properties makes it necessary to consider the issue of optimal selection in terms of the minimum reduction in reservoir pressure.Note that when viscoelastic oil moves through a porous medium, an elastic stress arises, which leads to an increase in the effective viscosity in a porous medium compared to the movement in a pipe.As the temperature rises, the relaxation properties of oil weaken.Therefore, the difference in oil viscosities in a porous medium will decrease with increasing temperature.
It should be concluded that experimental studies were carried out on reservoir models within the range of permeability change from 6 to 40.9 Darcy.The permeability of the analyzed reservoirs varies from 150 to 450 millidarcies.
As can be seen from the results of the above experimental studies on the filtration properties of viscous and high-viscosity oils through a porous medium, with lowpermeability and high-permeability reservoir models, the question arises of choosing the optimal concentration and volume of the polymer solution for oil displacement.

Fig. 3 .
Fig. 3. Dependence of the flow rate on the pressure drop for oil field X during filtration in a porous medium with a permeability of 0.0409 µm 2

Fig. 4 .
Fig. 4. Dependence of oil flow rate on pressure drop for oil field X during filtration in a porous medium with a permeability of 0.006 µm 2

Fig. 5 .
Fig. 5.The dependence of the flow rate on the pressure drops during oil filtration of the Y field during filtration in a porous medium with a permeability of 27.3 Darcy.

Table 1 .
Values of the initial pressure gradient at various filtration temperatures.