Problems of the rheology of structured oil Текст научной статьи по специальности «Физика»

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AZ9RBAYCAN KIMYA JURNALI № 3 2016

YffK 622.692.4

PROBLEMS OF THE RHEOLOGY OF STRUCTURED OIL

G.LKelbaliyev, M.R.Manafov

M.Nagiyev Institute of Catalysis and Inorganic Chemistry NAS of Azerbaijan

mmanafov@gmail.com Received 17.05.2016

The problems of oil rheology of the disperse systems, accompanied by a change in environment, the physical properties of the particles and structure formation are subject to the analysis. The models of coagulation of asphaltenes and calculating the size of nanoaggregates are offered. The conditions of the decay of the structure are considered and rheological models of filtering oil disperse systems according to Maxwell's equations and models change of viscosity and mobility are suggested. The results are compared with available experimental data.

Keywords: oil disperse systems, non-newtonian flow, viscoelastic skeleton, coagulation structure, filtering.

Introduction

Aggregative and unstable oil disperse systems are characterized by intermittency of the environment caused by the continuous structure formation and the change of the physical properties of the particles [1, 2], i.e., changing the volume and the particle size of the as-phaltenes as a result of their interaction, collisions, coagulation and fragmentation at their certain concentrations in a confined space. The relationship between the structure and viscosity of the oil disperse systems, as well as their non-newtonian flow characteristics are explained by change of structure as a result of occurrence (coagulation) and the destruction of aggregates

particles of asphaltenes. Oil structured disperse systems containing crystals of high-molecular paraffin, resins and asphaltene particles and other solid particles form the chain or take shape of the continuous network (frame) between itself and the structure of the porous medium in the limiting case at very low speeds of laminar flow or in the absence of the flow. Serial coagulation or agglomeration of individual nanoparticles of, asphaltenes (1 nm) by virtue of Van der Waal's forces, to nanoparticles and nanoaggregates clusters eventually form a viscoelastic skeleton, giving certain rheological properties of non-newtonian fluids [3] (Figure 1) to oil.

й о

о

SxMT1

Fig. 1. Aggregation of particles of asphaltenes in oils: I - individual molecules and particles; II -nanoaggregates; III - nanoaggregates clusters; IV - unstable suspension; V - viscoelastic skeleton; VI - stable emulsion with toluene.

2-4

100 100

Particle size, nm

Nanoparticles of asphaltenes are dispersed in oil, thereby forming nanocolloidal system, which as a result of aggregation at small velocity gradients or pressure passes into unstable suspension of nanoaggregates of asphalt-tenes solids in a continuous fluid. In further stages, nanoaggregates are shaped into clusters of nanoaggregates and eventually the visco-elastic skeleton undergoing aggregation.

The basis of the rheological model based on the following assumptions [4, 5]:

• in the structured oil system, there are na-noaggregates caused by collision, coagulation and aggregation of asphaltene particles through diffusion in laminar and turbulent shear flow and sedimentation (gravity coagulation); formed floccules of asphaltenes may precipitate on the surface forming enough thick layer of deposits on the walls of the collector pores and flow lines; moreover, the pressure drop as a function of temperature, can lead to the detachment of particles of precipitated asphalttenes at intensive hashing or turbulent flow;

• nanoaggregates proceed as independent units of flow before the collision with other similar units or particles of asphaltenes; by colliding among each other, nanoaggregates band in clusters of nanoaggregates and then create a viscoelastic skeleton with the maximum high viscosity and loose coagulation structure; the maximum size of the nanoaggregates skeleton is defined by the sizes of channels (pores, tubing) through which the stream flows;

• nanoaggregates are able to rotate in a gradient field and rupture under lengthened hydrodynamic forces, which depend on the gradient of the pressure or flow rate;

• linear dimensions of nanoaggregates are in the range of isolated particle size of asphaltene to the maximum size of the cluster or the skeleton;

• in the limiting case of an infinite speed, all units collapse to separate particles on condition that lim (t0/t)^ 0, therefore the current

of disperse system approaches to the Newtonian;

• in the presence of aromatic hydrocarbons asphaltenes dissolve well, by not allowing the structure formation, i.e. formations of clusters and viscoelastic skeleton. In addition, the solubility of the asphaltenes impact on the presence of other compounds contained in oil, such as tar and gums.

Oil disperse systems are characterized by thixotropic properties, i.e. with a decrease of stress or pressure the process is reversed, that means dispersion system due to aggregation of the particles is structured with the formation of the nanoaggregates and skeleton. When increasing stress is applied, destruction of the skeleton structure, nanoaggregates clusters and aggregates themselves takes place whereas the structured dispersed system transforms into the normal liquid with dispersed inclusions. Thus, rheological lines of thixotropic fluids form a characteristic hysteresis loop (Figure 2).

Fig. 2. Formation of coagulation structures.

It should be noted that the formation of the structured system depends on the content (by volume) of the particles in the oil, an interval and value of interaction forces between the particles, the probability of their collision and coagulation structure of the generating aggregate is important factor as for aggregation of particles is an important condition. Oil dispersions may also create aggregates with solid walls of pipes and pores of the porous layer, as well as with other solid particles contained in the oil. Sedimentation of asphaltenes particle ( pas = 1200 kg/m3 )

or nanoaggregates in the oil medium changes range of sizes in the volume flow.

The aim of this study is development of rheological model of the structured oil systems.

Coagulation of the particles and the formation of aggregates

Coagulation of particles of asphaltene in the oil volume is carried out by their transfer due to the molecular diffusion in a laminar flow and turbulent diffusion in a turbulent flow. The main principle of coagulation research is that one motionless particle is defined in the sphere of radius 7?-(l.5-2.0)a. Moreover, it is assumed that any particle crossing this sphere will most probably be collided and coagulated with the allocated particle. Taking into account this condition, by solving the equation of mass transfer for laminar flow in the works [6, 7] suggested expression for the particle flux, or the frequency of collisions q(a) = 8xDN0a (where D = kBT / (3tcvca) - the molecular diffusion coefficient), and in the works [8-10] for the turbulent flow:

( \

ш(a)« f-R I exp

-C

-R a

,5/3

À > À„

(1)

o( a ) = СохФо

f \m -r

VVc У

exp

-C

02

i \1/2 (Vc-R ) aP

À < Àn

(2)

For small Weber's numbers or for solid non-deformable particles of small size, the

exponential component tends to unity and the expressions are simplified to the form in these expressions

ш

( a )<

ш(a ) = Со1Фо —

À > Àn

À < Àn

(3a)

(3b)

However, given the degree of particles entrainment with pulsating medium for turbulent diffusion coefficient of the particles can be written as follows: DTP « p2pDT, where p2p - the

degree of particle entrainment with turbulent flow, depending on the particle size, and with their growth, it can be assumed that p2p ^ 0 . For asphaltene particles whose size

reaches 1 nm can be put p2 = 1, whereby as-

phaltenes particles are completely transferred by turbulent vortexes Dw « DT . More broadly, in

work [11], on the basis of the available experimental studies there were suggested empirical formulas for determining the diffusion coefficient of the particles depending on the dynamic flow rate and deposition rate, and so on, where it is possible successfully to use the software package of "OptimMe" [12, 13].

Equation (1) experimentally confirmed in the works [14, 15]. The change in mass of non-deformable nanoaggregates is determined as

dm , n.

— = (m»-m )ш

dt

(4)

The solution of this equation is represented in the form

m = m [ 1 — exp (—ш t )] .

(5)

Putting nanoaggregates spherical shape and

к

having in mind that m = — a the size of nanoag-

6

gregates, taking into account (2), define as

a„ = a„

1 - exp

1/2 Y

-C0 Фо

VVc У

1/3

(6)

For laminar flow aggregate formation is described by equation of the form

a = a

,[l- exp (~8kDN0a0t)] . (7)

As can be seen from Figure 1, the dimensions of nanoaggregates vary a = 8-10 nm

and the maximum frame size is limited by the presence of the walls pore or tubes. With the increasing of volume fraction of asphaltene particles increase the frequency of collisions

between them. The relaxation time for turbulent

a!am

1/2

flow is defined by expression iR=(yJs^) and laminar flow xR = 3vc/(8kTN0 ) - that contributes to the rapid achievement of the finite size of the unit aggregate. With the increase in oil viscosity as for laminar and turbulent flow, the frequency of collisions of particles of asphaltenes decreases, which inhibits formation rate of nanoaggregates (Figure 3).

t/ZR

Fig. 3. Resizing of nanoaggregates over time depending on the content of asphaltene particles in oil: 1 - 9=0.05, 2 - 0.1, 3 - 0.2, 4 - 0.3.

Deformation and fracture of structure

The aggregates which are formed as a result of coagulation and aggregation contain set of minute particles linked among themselves and have a loose structure, although their density increases towards the center. Due to the presence of voids within the aggregates, they can not be stable and the resulting increase of the external load in hydrodynamic field is broken down to the individual particles. The density of aggregates is much lower than the density of the asphaltenes particles, although they behave as a single particle with appropriate dimensions. As the size of the cluster units or viscoelastic frame their state becomes less stable as a result of reducing the density (Figure 4). Using the experimental data [16], we obtain

P 0 433

^ = 0.011 + 0433 .

Pd

a

To improve the rheological properties of the structured oil disperse systems, it is necessary

to ensure mechanical failure of viscoelastic asphaltenes skeleton under the impact of external forces (velocity gradient or pressure). The main deformation types of the carcass or clusters nanoaggregates leading to changes in its size and shape are: compression, tension, bending and torsion.

In the process of elastic deformation, asphaltenes particles in the frame, they are slightly shifted relative to each other, whereas the greater is the distance between the particles, the greater the force of interaction between particles. After removal of the external load on the frame under the impact of these forces, the particles return to their original position, thereby the structure distortion disappears. Following the plastic deformation, the particles move over long distances in the structure, the frame is stretched and under heavy loads (velocity gradient or pressure in the pores) association between the clusters and particles break off.

Pag/Pd

Fig. 4. Dependence of density of structure of a skeleton on its sizes

(a point - experiment [14]).

This displacement becomes irreversible with increasing of load, which leads to the destruction of the carcass. Elastoplastic deformation at achievement of high tension x>x can

complete with dispersion of system of bounded particles to the individual particles. As a result, the current of the structured disperse system passes into the usual current of the Newtonian liquid. Destruction of frame leads primarily to the significant reduction in viscosity and increase the mobility of the disperse system.

Rheological equation for structured

oils

For structured oil systems Darcy's filtration law deviates from the classical form, and can be written in a non-linear form [17, 18]

v=-4 1 .

r y t J ox

(8)

If t»t0 this expression turns into the

usual Darcy's equation for unstructured oil. The rheological equation of Maxwell viscoelastic fluid is written in the form [19]

dx

X —+ t = nj t = 0, t = t0, y = 0. (9) at

Here X = /G - Maxwell relaxation time, G - shear modulus of elasticity, y = dy/d/-

shear rate, z - shear stress, y- shear gradient, t(1 - shear stress limit or liquid limit. If x < x0, then y = 0. The solution of equation (9) has the form

G t ln(i-r|cy) = lni0--i = lnT0-- (10)

It is evident that the value of t/X characterizes deformation of a viscoelastic frame in time and depends on a gradient of the velocity or pressure, that can be in approach this dependence can be presented as t/ X =

= t y/We = / [gradP / (gradP)n ], (where We=A,y

- Weissenberg number). Analysis of experimental data on [20] of filtration non-newtonian oils, by analogy with (10), allowing a semi-empirical equation for the viscoelastic rheological frame in the form

ln t = ln t„ - a

grad P ( §rad P )o

(11)

Obviously, the exponent n is determined depending on the temperature, the layer properties and other parameters of the oil field. For most structured oils can be accepted n = 6. The proposed rheological model (11) differs by the structure from the known models, although, it has similarity to Bingham model in some ins-

—\n

tances of proximity. Figure 5 shows the dependence of the filtration rate on the pressure gradient using experimental data [20]. As follows from this figure, the portion of 0A is an area corresponding to the condition that t < t0 i.e. the presence of stable viscoelastic frame. The portion AB is an area corresponding to the condition t > t0 for the destruction of the frame down to the individual particles of asphaltenes. At the point B the frame completely collapses when t = t , where t - the limit stress

of frame fracture. Filtration rate equation (8) represented by the following formula

V = K (T ) (1 - exp (-«! (T) ( z / z0 )6)) X, (12)

where z=gradP, z0=(gradP)0, (grad P) =

t = t„

= (grad P)Q=1.4285-10-4+ , K2 =y. - oil

mobility, n=6, a1=0.0445exp(-0.0262J), K1= Kx = 3.01-10-5 exp (0.0182471). It should be noted that grad P corresponds to tension of initiation of a fracture of the frame in point A t = th > t0 and the tension, corresponding to complete destruction of the frame in dependence on the temperature at point B can be

defined as grad P

t = t,

= 0.005 + 0.596/ T

(Figure 5).

The change in the effective viscosity of the abnormal oil from pressure gradient based on experimental data is determined by the empirical formula

*

exp(-30z6)

(13)

where r0, r«, - the initial and final dynamic viscosity of the oil (t>>t0) . In Figure 6 expression (13) is compared with the experimental data at T=240C [20].

As follows from Figure 6, at low flow rates the effective viscosity of the anomalous oil depends on the sheer rate or pressure gradient, and when t0 < t < tp the effective viscosity

decreases from the maximum value to the minimum and then stabilized.

Dependence of mobility of abnormal oil on pressure gradient at a temperature T=240C taking into account (13) and calculated by the expression

7/ * 0.0310

k/r = . (14)

r ( grad P )

V106, cm/s

5.0

4.0 /

3 0 / 3

/j

20 / /

/ /+ o/

ID / y

"R \ ■ 1

u^hf ^^

1 (non am 6 W grad P, kgs (cm"2 m_1)

Fig. 5. Changing the structured oil filtration rates for different tempera-

tures: 1 - T = 240C, 2 - T = 500C, 3 - T = 800C.

i)\ сП

Fig. 6. Dependence of viscosity on the pressure gradient.

dent on porosity of oil layer.

Using the experimental data of work [21] it is possible to obtain the following dependence of the permeability coefficient on average porosity of the layer

k-103 = 0.40 + 0.46s, mkm2,

where s - layer porosity, %.

It should be noted that given in the literature experimental data on dependence of permeability coefficient on porosity of layer have a large spread. However, the trend growth rate of permeability coefficient with increasing porosity of the layer is observed in all studies.

Analysis and discussion of results

The above-stated problems rheology of structured oils is an important step in the process of filtering the oil through porous media. The presence of asphaltenes in oil which create nanoaggregates clusters, nanoaggregates and ultimately the viscoelastic frame by coagulation and aggregation of the particles significantly affect the hydrodynamics filtering oil in the porous layer. The proposed equation (5)-(7) allow us to estimate changes in the size and weight of nanoaggregates in time on the basis of molecular and turbulent diffusion of particles of asphaltenes. And with the increasing size

The given formulas (12)-(14) are suitable for calculation of filtration process of oil in porous layer of different fields, and for different fields of oil their viscosity and permeability coefficient changes, that have a significant impact on their mobility.

The presence of asphaltenes in oil complicates its filtration in a porous layer due to their deposition on the walls of the pores and tubes until complete occlusion. This fact has a significant impact on the porosity of the layer, the mobility of the oil, the sheer stress, the structure of rheological model, thereby shifting the start and end of the destruction of the structure. With increasing thickness of asphal-tenes at the surface pores, reduces porosity and layer permeability, which leads to a decrease in oil mobility.

It is important to note that in the processes of filtration medium porosity plays an important role, the destruction of the structure occurs first in the pores of large dimensions, and then with increasing pressure gradient - in the pores of small size. Therefore, it is possible to put that mobility of oil or coefficient of permeability, and also depend on porosity of oil layer.

Consequently, we can assume that the mobility of the oil or the permeability coefficient, and the tension zh and zp is also depen-

loose structure is created, the density of which decreases with increasing the size of the unit (Figure 4). At a sufficiently high external load, connection between the particles are broken down to the individual particles, and the current of the structured oil goes into the usual current of Newtonian oil.

Conclusions

Models of a filtration (8) and (12) and the rheological model (11) and (13) based on solving Maxwell's equations for viscoelastic fluid are offered. Expressions for estimation of the effective viscosity of oil (13) and its mobility depending on temperature are offered (14).

Nomenclature:

a - particle size; a , a - current and maximum size of the unit; a0 - the initial size of the particles; C, Ci, C, C2 - coefficients determined from the experimental data; D - the molecular diffusion coefficient; DT - turbulent diffusion coefficient of the liquid; D - the coefficient of turbulent diffusion of particles; kB - the Boltz-mann constant; k - permeability coefficient; m, mm - the current and final weight of the unit; N - the number of particles per unit volume; P - pressure; T - temperature; V - filtration rate; a0 - coefficient; s - porosity layer; sR - the specific energy dissipation per unit volume; 9 -the volume fraction of the particles; X, X0 - the current and the Kolmogorov scale of turbulent fluctuations; ^ - the degree of entrainment of particles pulsing environment; vc - the kinematic viscosity of the medium; pd - the density of the particles; p - density of the medium; p - the density of the aggregate; p^ - density of as-

phaltenes; a - surface tension; ra - the frequency of collisions between particles; tr - relaxation time; z0 - elastic limit; z - tension corresponding to limit destruction; - effective dynamic viscosity of non-newtonian oil; ^ - maximum dynamic viscosity of oil.

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STRUKTURLA§MI§ NEFTLORiN REOLOGiYASININ PROBLEMLORi

Q.LKalbaliyev, M.RManafov

Maqalada dispers mühitin halinin, hissaciklarin fiziki xassalarinin dayi§masi va strukturla§ma ila mü§aiyat olunan neftli dispers sistemlarin reologiyasinin problemlari analiz edilir. Asfaltenlarin hissaciklarinin koaqulyasiyasi va nanoaqreqatlann ölgülarinin hesablanmasi ügün modellar taklif olunmu§dur. Strukturun dagilmasi ¡jartlarina baxilmi§ va Maksvell tanliyi nazara alinmaqla neftli dispers sistemlarin filtrasiyasinin reoloji modellari va özlülük va mütaharrikliyin dayi§masini tasvir edan modellar taklif olunmu§dur. Modellar asasinda alinmi§ naticalar, tacrübi naticalar ila müqayisali §akilda taqdim edilmi§dir.

Agar sözlar: neftli dispers sistemhr, qeyri-nyuton axin, özlü elastik qsfss, koaqulyasiya strukturu, filtrasiya.

ПРОБЛЕМЫ РЕОЛОГИИ СТРУКТУРИРОВАННЫХ НЕФТЕЙ

Г.И.Келбалиев, М.Р.Манафов

Анализируются проблемы реологии нефтяных дисперсных систем, сопровождающихся изменением состояния дисперсной среды, физических свойств частиц и структурообразованием. Предложены модели коагуляции частиц асфальтенов и расчета размеров наноагрегатов. Рассматриваются условия разрушения структуры и предложены реологические модели фильтрации нефтяных дисперсных систем с учетом уравнения Максвелла и модели изменения вязкости и подвижности. Результаты сравниваются с имеющимися экспериментальными данными.

Ключевые слова: нефтяные дисперсные системы, неньютоновское течение, вязкоупругий каркас, коагуля-ционная структура, фильтрация.