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1

Viscoelastic effects under water-polymer flooding conditions of the fractured-porous reservoir

Pogrebnyak Volodymyr G., Shimanskii Volodymyr Y., Pogrebnyak Andriy V., Perkun Iryna V.

Nafta-Gaz

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2023

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R. 79, nr 7

455--463

EN

The work is devoted to the numerical simulation of the flow of simple and viscoelastic (polymer solution) fluids through a fracture by using polymer solutions for enhanced oil recovery from a reservoir. Polymer solutions have viscoelastic properties. Therefore, when polymer solution flows through the slot, we use the well-known Maxwell’s fluid model with the Jaumann derivative to evaluate deformation characteristics of the flow (stream functions, distributions of the longitudinal velocity gradient and normal stress) resulting in the manifestation of abnormal (compared with the behaviour of the ordinary fluid) effects. The case of slow flow is considered. In this case, the inertial terms can be neglected, the velocities, stresses, and stream functions can be written as the decomposition by Weisenberg number, and we can assume that the Weissenberg number is less than one. The determined regularities of viscoelastic (polymer solution) liquid behaviour with longitudinal velocity gradient and the elastic deformations effects manifested in this case have a decisive meaning in understanding the mechanism of anomalously high oil recovery capacity of a reservoir by using water-polymer flooding of the fractured-porous reservoir. Understanding the nature of the effects of elastic deformations under the conditions of water-polymer flooding of the fractured-porous reservoir enables hydrodynamic calculations of the optimal flow of the polymer solution. One of the main issues that need to be solved when developing the technology for increasing oil recovery from formations using polymer solutions is to determine the optimal flow regime in the fractured-porous reservoir. The calculation results verify the ideas obtained from the experimental solution of this problem concerning the strain-stress state of polymer macromolecules (liquid elements) during polymer flow in the inlet area of the fracture in the oil reservoir and confirm the possibility of using numerical analysis of convergent polymer flow for calculating longitudinal velocity gradients in the inlet area of the fracture and can also serve as additional substantiation of the proposed earlier mechanism for increasing oil recovery from reservoirs by using polymer solutions.

PL

Praca poświęcona jest symulacji numerycznej przepływu płynów prostych i lepkosprężystych (roztworów polimerowych) przez szczelinę z wykorzystaniem roztworów polimerowych w celu zwiększenia wydobycia ropy naftowej ze złoża. Dlatego, gdy roztwór polimeru przepływa przez szczelinę, używamy dobrze znanego modelu cieczy Maxwella z pochodną Jaumanna do oceny charakterystyk deformacji przepływu (funkcje strumienia, rozkład gradientu wzdłużnego prędkości i normalnego naprężenia), co skutkuje pojawieniem się nietypowych (w porównaniu z zachowaniem zwykłego płynu) efektów. Rozważany jest przypadek spowolnionego przepływu. W tym przypadku składowe inercyjne można pominąć, prędkości, naprężenia i funkcje strumienia można zapisać jako rozkład wg liczby Weisenberga i możemy założyć, że liczba Weissenberga jest mniejsza niż jeden. Określone prawidłowości lepkosprężystych właściwości cieczy (roztworu polimeru) z gradientem prędkości wzdłużnej, jak i przejawiające się w tym przypadku efekty odkształceń sprężystych, mają decydujące znaczenie dla zrozumienia mechanizmu anomalnie wysokiej wydajności wydobycia ropy naftowej ze złoża poprzez nawadnianie złoża szczelinowo-porowego cieczą wodno-polimerową. Zrozumienie natury efektów odkształceń sprężystych w warunkach nawadniania szczelinowo-porowatego złoża cieczą wodno-polimerową umożliwia przeprowadzenie obliczeń hydrodynamicznych optymalnego przepływu roztworu polimeru. Jednym z głównych zagadnień, które należy rozwiązać podczas opracowywania technologii zwiększania wydobycia ropy naftowej z formacji za pomocą roztworów polimerowych, jest określenie optymalnego reżimu przepływu w zbiorniku szczelinowo-porowym. Wyniki obliczeń weryfikują koncepcje uzyskane z eksperymentalnego rozwiązania tego problemu dotyczącego stanu naprężenia makrocząsteczek polimeru (elementów ciekłych) podczas przepływu polimeru w obszarze wlotowym szczeliny w zbiorniku ropy naftowej i potwierdzają możliwość zastosowania analizy numerycznej zbieżnego przepływu polimeru do obliczania gradientów prędkości wzdłużnej w obszarze wlotowym szczeliny, a także mogą służyć jako dodatkowe uzasadnienie proponowanego wcześniej mechanizmu zwiększania wydobycia ropy naftowej ze złóż za pomocą roztworów polimerowych.

2

Stability analysis and internal heating effect on oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation

Bhadauria B. S., Singh M. K., Singh A., Singh B. K., Kiran P.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 4

785--803

EN

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

3

Magneto-hydro dynamic flow and heat transfer of non-Newtonian power-law fluid over a non-linear stretching surface with viscous dissipation

Kishan N., Kavitha P.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

259--273

EN

A fluid flow and heat transfer analysis of an electrically conducting non-Newtonian power law fluid flowing over a non-linear stretching surface in the presence of a transverse magnetic field taking into consideration viscous dissipation effects is investigated. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. By using quasi-linearization techniques first linearize the non linear momentum equation is linearized and then the coupled ordinary differential equations are solved numerically by an implicit finite difference scheme. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, Eckert number, velocity exponent parameter, temperature exponent parameter, modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed.

4

Thermal instability of Walters' (model B') elastico-viscous compressible fluid in the presence of Hall current

Kumar S., Gupta D., Jaswal R., Rana G. C.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 3

61-72

EN

The thermal instability of a compressible elastico-viscous fluid is examined for viscoelastic polymeric solutions in the presence of uniform vertical magnetic field to include the Hall-current. These solutions are known as Walters' (model B') fluids and their rheology is approximated by the Walters' (model B') constitutive relations, proposed by WALTERS [12]. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the magnitude of the magnetic field and Hall current. The magnetic field is found to stabilize a certain wave number range of the unstable configuration. The Hall current has destabilizing and stabilizing effects on the system.

5

Stability of stratified elastico-viscous Rivlin-Ericksen rotating fluid in the presence of uniform horizontal magnetic field in porous medium

Kango S. K., Singh V.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 3

33-40

EN

The stability of stratified elastico-viscous Rivlin-Ericksen fluid in the presence of horizontal magnetic field and rotation in porous medium is considered. In contrast to the Newtonian fluids, the system is found to be unstable at stable stratification for low values of permeability or high values of kinematic viscoelasticity. Magnetic field is found to stabilize the small wavelength perturbations for unstable stratification. It has been found that the growth rate increases with the increase in kinematic viscosity and permeability, whereas it decreases with the increase in kinematic viscoelasticity.

6

Effect of Hall currents on thermal instability of compressible dusty viscoelastic fluid in porous medium

Kumar P.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 4

25-38

EN

The thermal instability of compressible Walters B' viscoelastic fluid in porous medium is considered to include the effects of Hall currents and suspended particles. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of magnetic field. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the system.

7

A mathematical theorem in double diffusive convection problem of viscoelastic fluid

Mohan H., Kumar P.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 4

49-61

EN

The present paper establishes mathematically that viscoelastic thermosolutal convection of Veronis type cannot manifest itself as oscillatory motion of growing amplitude in an initially bottom heavy configuration if the thermal Rayleigh number , the Lewis number , the Prandtl number and the viscoelastic parameter F satisfy the inequality. A similar mathematical theorem is also proved for Stern's type configuration.

8

Hall current effect on thermosolutal instability in a viscoelastic fluid flowing in a porous medium

Singh M.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 1

69-82

EN

The thermosolutal instability in a layer of an electrically conducting Oldroydian viscoelastic fluid in a porous medium is studied to include the effect of Hall current. For the case of stationary convection, the Oldroydian fluid behaves like an ordinary Newtonian fluid. The magnetic field and the stable solute gradient are found to have stabilizing effects whereas Hall currents and medium permeability are found to have destabilizing effects on the system. Graphs are plotted by giving numerical values to the parameters to depict the stability characteristics. The sufficient conditions for the non-existence of overstability are also obtained.

9

Simulation of the electrospinning process

Karra S., Srinivasa A. R.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 1

175-188

EN

The electrospinning process is modeled and the bending instability of a slender viscoelastic jet is simulated. This is accomplished by modifying the discrete bead model by Reneker et al. (2000). Specifically, the force due to surface tension is incorporated using the expression suggested by Kowalewski et al. (2005) (see Eq.(7)). The results obtained by the use of this modification seem to be in accord with the experimental observations reported in Reneker et al. (2000) (Fig.2). An attempt is also made to simulate the effect of a secondary electric field which could be used to control the electrospinning process and whipping instability. It is observed that the external secondary field considered here, unwinds the jet spirals, reduces the whipping instability and increases the tension in the fiber.

10

A theoretical study of the effect of a non-uniform heat source on heat transfer in a viscoelastic liquid flow over a stretching sheet

Nandeppanavar M. M., Abel M. S., Malipatil S.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 4

1039-1052

EN

A theoretical study of heat transfer in a visco-elastic liquid flow due to a stretching sheet in the presence of non-uniform heat generation / absorption is investigated. The stretching of the sheet is assumed to be proportional to the perpendicular distance from the slit. Two different temperature conditions are studied, viz., (i) the sheet with the prescribed surface temperature (PST) and (ii) the sheet with the prescribed wall heat flux (PHF). The non-linear boundary layer equations for momentum are converted into non-linear ordinary differential equations by means of a similarity transformation and the same is solved exactly. The heat transport equation with variable coefficients is transformed into a confluent hypergeometric differential equation and solved analytically. The effect of various parameters on the temperature distribution is presented graphically. Present results are compared with the existing theoretical data and found in good agreement with these results. The results have technological applications in liquid based systems involving stretchable materials.

11

Natural convection flows with variable viscosity, heat and mass diffusion along a vertical plate

Dimian M. F., Hadhoda M. K.

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 2

61-76

EN

The aim of this paper is a numerical study of laminar double diffusive free convection viscous flows adjacent to a vertical plate, taking into account the variation of the viscosity and double-diffusive heat and mass transfer with temperature. The governing conservation equations of mass, momentum, energy and chemical species are non-dimensionalized by using appropriate transformations. The resulting equations are solved numerically by using the fourth order Runge-Kutta integration scheme along with the Nachtsheim-Swiger shooting technique. It is noticed that both the velocity and concentration of air are increasing as the parameter Β 2, (the species diffusion parameter) increases, but an opposite effect for the velocity is observed at a certain distance far from the plate. It is also observed that the temperature decreases as the parameter Β 2 increases. The shearing stress at the plate, the local Nusselt number and the local Sherwood number are obtained. The friction coefficient at the plate, of heat and mass transfer at the plate, the momentum, thermal and concentration boundary layers thickness (δ, δ T, δ C) have been estimated for different values of α, Sc and N.

12

Pulsatile flow of electrically conducting non-Newtonian fluid and heat transfer through porous medium in a circular pipe

Eldabe N. T. M., Ghaly A. Y., El-hassan M., Oaf M. E.

Mechanics and Mechanical Engineering

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2001

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Vol. 5, nr 1

5-20

EN

The influence of elasticity and magnetic field on pulastile viscoelastic flow and heat transfer in a circular pipe is examined. By means of the perturbation method of the velocity and temperature fields, the analytical solution of the velocity and temperature are obtained in terms of Bessel and hypergeometric functions .The discharge and the rate of heat transfer are determined through the course of discussions.