Newtonian Fluid In Porous Medium Research Articles

Analytical solution for chemical fluid injection into linear heterogeneous porous media based on the method of characteristics

Injection of Newtonian fluids in porous media to displace linearly another Newtonian fluid is described by the Buckley-Leverett (BL) fractional flow theory derived for incompressible, constant viscosity fluids at constant injection rate in a homogeneous and isotropic reservoir. Injection of non-Newtonian fluids can be addressed by modifying the fractional flow equation by considering the dependence of injected fluid viscosity with velocity, changes of residual oil saturation and chemical adsorption on rock. In this work, the BL fractional flow model is extended to describe injection of non-Newtonian fluids into a 1D linear heterogeneous formation accounting for fluid adsorption, permeability reduction, inaccessible pore volume, and presence of a denuded water bank developed over time ahead of non-Newtonian zone. Results from derived analytical solutions demonstrate fluids saturation and pressure drop across the formation, fluids production rate and cumulative volumes to be in close agreement with the ones from a commercial reservoir simulator.

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.

Traveling wave solutions of 3D fractionalized MHD Newtonian fluid in porous medium with heat transfer

In the present paper, we get exact solutions of Magnetohydrodynamic (MHD) of the fractionalized three-dimensional flow of Newtonian fluid with porous and heat transfer through the traveling wave parameter. The governing equations are produced dependent on established Navier-stokes equations which can be diminished to ordinary differential equation by wave parameter ξ=ax+by+nz+Utα/Γ(α+1). The new exact solutions are established for three various cases. In special cases the solution for Newtonian fluid with and without MHD and porous effects can also be found from the general solution by putting M+Φ→0 and solutions for simple Newtonian fluid can also be obtained by putting α→1 in general solutions. Finally, the effect of the parameter of interest on the stream motion, as well as difference among the Newtonian fluids is examined by 2D and 3D graphical interpretations.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Flow modelling of quasi-Newtonian fluids in two-scale fibrous fabrics

Permeability is the fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. In a previous work, the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and generalized Newtonian (shear-thinning) resins. In the linear case, only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as there are representative microscopic volumes in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, a large number of microscopic calculations must be carried out as the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. An original and efficient offline-online procedure was proposed for the solution of non-linear flow problems related to generalized Newtonian fluids in porous media. In this paper, this procedure is generalized to quasi-Newtonian fluids in order to evaluate the effect of extensional viscosity on the resulting upscaled permeability. This work constitutes a natural step forward in the definition of equivalent saturated permeabilities for linear and non-linear fluids.

An initial and boundary value problem of fractional Jeffreys’ fluid in a porous half space

In this paper, the fractional calculus approach is employed in the constitutive relationship of the fluid model and the Darcy’s law. The flow of the fractional Jeffreys’ fluid induced by the impulsive motion of a flat plate in a porous half space is studied in form of an initial and boundary value problem with fractional derivatives. Using the Laplace transform method, we obtain an exact solution of the model in term of Fox’s H-function. As a byproduct, the solutions of the analogous flow for the generalized second grade fluid, the fractional Maxwell fluid and the Newtonian fluid in the porous half space are also deduced. In addition, the influence of the material parameters and the fractional parameters on the fluid motion is investigated, as well as a comparison among the fractional Jeffreys’ fluid, the fractional Maxwell fluid and the Newtonian fluid in porous medium is also analyzed by graphical illustrations.

On Laminar Flow of Non-Newtonian Fluids in Porous Media

Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.

Synthesis and performance evaluation of a new kind of gel used as water shutoff agent

In this paper, a kind of modified cellulose as a raw material of a water-based gel is studied systematically. Its migration performance is good and its solution is Newtonian fluid in porous medium. And more importantly, a water-based gel is synthesized with modified cellulose, acrylamide, N,N′-methylene-bisacrylamide and persulphate. An appropriate formula of a gel is 0.8 wt% modified cellulose, 2 wt% acrylamide, 0.1 wt% cross-linking agent and 0.05 wt% initiator. The initial viscosity of this gelling solution is 72 mPa s and the gelation time is 15 h at 70 °C. After gelation, it is a strong gel and the elasticity is more outstanding than the viscosity. Its applied range in formation environment is the temperature of 60–90 °C, the salinity of 0–100 g/L and the pH value of 6–9. The experimental results show that the gel system can be better applied to conformance control of the heterogeneity reservoir.

Reliability of Convective Diffusion Process in Stenosis Blood Vessels

This paper presents a convective dominated reliable diffusion process in an axi-symmetric tube with a local constriction simulating a stenos artery considering the porosity effects. The investigations demonstrate the effects of wall shear stress and recirculation flow on the concentration distribution in the vessels lumen and on wall mass transfer keeping the porosity in view. The flow is governed by the incompressible Navier-Stokes equations for Newtonian fluid in porous medium. The convection diffusion equation has been used for the mass transport. The effect of porosity is examined on the velocity field and wall stress. The numerical solutions of the flow equations and the coupled mass transport equations have been obtained using a finite difference method. This paper explains the reliable effects of flow porosity on the mass transport.

A methodology for the derivation of non-Darcian models for the flow of generalized Newtonian fluids in porous media

A methodology is presented for the development of analytic models that can suitably describe the flow of generalized Newtonian fluids in porous media. First, the volume averaging technique is employed for the derivation of generalized non-Darcian models concerning the creeping flow of inelastic non-Newtonian fluids in porous media. Two macroscopic properties are involved in these models: the effective permeability and average viscosity. The approximate Rabinowitch–Mooney equation is used to obtain analytical solutions for the flow of Meter and mixed Meter-and-power law fluid models through a pore of arbitrary cross-sectional shape. The analytical solutions are integrated into numerical simulators of the one-phase flow of the foregoing fluids in two-dimensional pore networks. The effective medium theory (EMT) is coupled with pore network simulations in order to replace the disordered porous medium with an effective medium that is described by two anisotropic hydraulic conductances and two effective hydraulic pore radii. Finally, closed expressions are developed to relate the superficial flow velocity with the pressure gradient and the macroscopic properties with the effective hydraulic pore radii, rheological parameters and pressure gradient. The new flow models predict satisfactorily numerical simulations of the flow of non-linear fluids in theoretical pore networks, and experiments of the flow of non-Newtonian oils in two-dimensional artificial glass-etched pore networks. Any observed discrepancies are attributed to the use of a small number of pore structure parameters for the homogenization of the porous medium, as well as to uncertainties embedded into the estimated values of rheological parameters.

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.