Flow of non-newtonian fluids in porous media

Rheologica Acta, 1985

An analysis is presented for the flow of polymer solutions through a tube having a periodically varying diameter; this geometry is often used to represent a porous medium. It is found that if the stretch rate is assumed constant, the stress depends not only upon the Deborah number, but also on the ratio of the maximum to the minimum diameter. If the latter dimensionless group is not too large, no shear thickening is predicted to arise irrespective of the value of the Deborah number. These results explain the observed lack of superposition of curves of the product of the friction factor with the Reynolds number plotted against the Deborah number when different porous media are used. In addition, they also, in a qualitative sense, explain the experimentally observed maxima in the plots of the relative pressure drop as a function of the deformation rate.

AIChE Journal, 1966

This paper describes a preliminary study of the linear flow of a non-Newtonian fluid, a water solution of Dextran (a polysaccharide), in porous media. A modification of Darcy's law, which uses capillary rheology data, is developed to describe non-Newtonian flow in underground reservoirs. The generalization, in effect, replaces the porous media with a capillary of equivalent radius proportional to the square root of the ratio of permeability to porosity. The constant of proportionality a . should be independent of permeability and porosity for a given type of rock. This has been partially confirmed experimentally. In principle, a capillary rheogram and a single core test permit evaluation of ao. Then non-Newtonian flow can be predicted in this type of rock regardless of porosity, permeability, or flow rate. p ( a R ) = (2L)/(4Q) (mR8)

We study the mobilization and subsequent flow in a porous medium of a fluid with a yield stress, modeled as a Bingham plastic. We use single-capillary expressions for the mobilization and flow in a pore-throat, and a pore-network model that accounts for distributed yield-9 stress thresholds. First, we extend the statistical physics method of invasion percolation with memory, which models lattice problems with thresholds, to incorporate dynamic effects due to the viscous friction following the onset of mobilization. Macroscopic relations between 11 the applied pressure gradient and the flow rate for single-phase flow are proposed as a function of the pore-network microstructure and the configuration of the flowing phase. Then, the algorithm is applied to model the displacement of a Bingham plastic by a Newtonian 13 fluid in a porous medium. The results find application to a number of industrial processes including the recovery of oil from oil reservoirs and the flow of foam in porous media.

Transport in Porous Media, 2010

A thermomechanical theory for multiphase transport in unsaturated swelling porous media is developed on the basis of Hybrid Mixture Theory (saturated systems can also be modeled as a special case of this general theory). The aim is to comprehensively and non-empirically describe the effect of viscoelastic deformation on fluid transport (and vice versa) for swelling porous materials. Three phases are considered in the system: the swelling solid matrix s, liquid l, and air a. The Coleman–Noll procedure is used to obtain the restrictions on the form of the constitutive equations. The form of Darcy’s law for the fluid phase, which takes into account both Fickian and non-Fickian transport, is slightly different from the forms obtained by other researchers though all the terms have been included. When the fluid phases interact with the swelling solid porous matrix, deformation occurs. Viscoelastic large deformation of the solid matrix is investigated. A simple form of differential-integral equation is obtained for the fluid transport under isothermal conditions, which can be coupled with the deformation of the solid matrix to solve for transport in an unsaturated system. The modeling theory thus developed, which involves two-way coupling of the viscoelastic solid deformation and fluid transport, can be applied to study the processing of biopolymers, for example, soaking of foodstuffs and stress-crack predictions. Moreover, extension and modification of this modeling theory can be applied to study a vast variety of problems, such as drying of gels, consolidation of clays, drug delivery, and absorption of liquids in diapers.

International Journal of Heat and Fluid Flow, 2009

In this article, the extensional flow and viscosity and the converging-diverging geometry were examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shearthinning, elasticity and thixotropic time-dependency, was used for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm, originally proposed by Philippe Tardy, that employs this model to simulate steadystate time-dependent flow was implemented in a non-Newtonian flow simulation code using pore-scale modeling and the initial results were analyzed. The findings are encouraging for further future development.

2014

One of the most important criteria for evaluating chemical enhanced oil recovery (EOR) processes that use polymers is its rheological behaviour which in turn account for other physical effects of adsorption and resistance factors during polymer-formation rock interactions. However, complete knowledge of behaviour of polymer solution in porous media has not yet been fully gained. A computational fluid dynamics (CFD) simulations implemented in COMSOL Multiphysics is used to simulate a 1-D single- phase, non-elastic xanthan gum flow in geometries approximating formation pore throats. Simulation results show the degree of solution viscosity degradation at different inlet pressures and shear rates at varying pore constriction diameters. Results also show that numerical techniques can predict the performances of polymer solution applications in actual field operational conditions and aid in design and interpretation of laboratory tests.

1993

Constant Rate (100 cm/sec) Immiscible Displacement for n=0.35 and K=6.20 Psec '_-1 (Ca=0.333 and Np=174.8) at Four Different Time Steps (a) 30 (b) 60 (c) 90 (d) 120. 44 Constant Rate (0.01 cm/sec) Immiscible Displacement for n=0.35 and K=6.20 Psec n-1 (Ca=3.33 × 10-4 and Np=0.0174) at Four Different Time Steps (a) 120

E3S Web of Conferences, 2020

Injecting fluid into a porous material can cause deformation of the pore structure. This hydro-mechanically coupled (i.e., poromechanical) phenomenon plays an essential role in many geological and biological operations across a wide range of scales, from geologic carbon storage, enhanced oil recovery and hydraulic fracturing to the transport of fluids through living cells and tissues, and to fuel cells. In this study, we conducted an experimental and numerical investigation of the hydro-mechanical coupling during fluid flows in porous media at the fundamental pore-scale. First, experimental demonstrations were undertaken to ascertain the effect of the hydro-mechanical coupling for two-phase fluid flows in either deformable or non-deformable porous media. Next, a hydro-mechanically coupled pore network model (HM-PNM) was employed to test a various range of influential parameters. The HM-PNM results were consistent with the experimental observations, including the advancing patterns o...

The multiphase flow in porous media is a topic of various big complexities for a long time in the field of fluid mechanics. This is a subject of important technical applications, most probably in oil recovery from petroleum reservoirs and also in others. The single phase fluid flow through a porous medium is generally defined by Darcy's law. In the petroleum industry and in other technical applications, the transport phenomenon is modeled by postulating a multiphase analysis of the Darcy's law. In this analysis, the distinct pressures are defined for each phase with the difference and well known as capillary pressure. That is determined by the interfacial tension, geometry of micro pore and the chemistry of the surface related to the solid medium. In regarding flow rates, the relative permeability is defined that gives the relationship between the volume flow rate of each fluid and the pressure gradient. In the present paper, there is an analysis about the mathematical laws and equations for the slightly compressible flow and rock and the analysis and important results have been founded. The analysis show that velocity of fluid related to any phase is inversely proportional to the viscosity of the fluid. The capillary pressure of the capillary tube is inversely proportional to the radius of tube and increases with increasing values of the surface tension of the fluid. It also varies inversely with the radii of curvature for the interface of the fluid. The pressure exerted by the fluid varies positively with its velocity and varies inversely with the absolute permeability of the porous medium.

Frontiers in Physics

Improving the displacement efficiency of capillary entrapments in porous media by adding high molecular weight polymers to the invading phase has various industrial applications, from enhanced oil recovery to soil remediation. Apart from an increased viscosity contrast compared to regular water flooding, the flow of viscoelastic polymer solutions exhibits unstable flow behavior even at small Reynolds numbers, which can lead to an additional displacement mechanism of the capillary entrapments. In this work, we employ a microfluidic approach to unravel the underlying physics and mechanism of this enhanced pore scale displacement. To this end, we show that the major complex topological flow features in a typical porous medium can be mimicked by a flow geometry consisting of a single capillary entrapment connected to two symmetric serpentine channels. This design excludes the effect of viscous stresses and allows direct focus on displacement processes driven solely by elastic stresses. ...