non-Newtonian Fluids In Porous Media Research Articles

Fractal permeability model for power-law fluids in embedded tree-like branching networks based on the fractional-derivative theory

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Convection heat and mass transfer of non-Newtonian fluids in porous media with Soret and Dufour effects using a two-sided space fractional derivative model

Non-Newtonian fluids within heterogeneous porous media may give rise to complex spatial energy and mass distributions owing to non-local mechanisms, the modeling of which remains unclear. This study investigates the natural convection heat and mass transfer of non-Newtonian fluids in porous media, considering the Soret and Dufour effects. A strongly coupled model is developed to quantify the coupled transport of energy and reactive pollutants with the non-Newtonian fluid. The constitutive equation for the non-Newtonian fluid is described by a two-sided Caputo type space fractional velocity gradient. The governing equation, with a symmetric diffusion term, is effectively solved using a stable and convergent shifted Grünwald–Letnikov formula. The influences of three important parameters, which are the average skin friction coefficient, the average Nusselt number, and the Sherwood number, on fluid heat and mass transfer are calculated and analyzed. Numerical results reveal a significant interaction between the fractional derivative and the buoyancy ratio number, both of which affect the average skin friction coefficient. Furthermore, the average Nusselt number increases with the Dufour number while decreasing with the average Sherwood number. These findings enhance our understandings of the dynamics of energy and mass co-transport in non-Newtonian fluids, particularly in relation to their constitutive equation featuring spatial non-local properties.

Blind zones in radiating dispersion at high Péclet number driven by non-Newtonian fluids in porous media

A wide range of environmental, energy, medical and biological processes rely on dispersive transport through complex media. Yet, because of the stagnant and opaque nature of the microscopic system, the role of disordered flow and structure in the dispersive transport of solutes remains poorly understood. Here, we use a circular porous microfluidic system to investigate the radial dispersion in porous media driven by non-Newtonian fluids with strong advection rate (or at high Péclet number) and low-to-moderate Reynolds numbers. We observe for the first time the presence of diffusion ‘blind zones’ in the microstructure for high solution injection velocities. More specifically, an in-depth analysis uncovers that the circumferential flow frame, coformed by obstacles and vortices especially the ‘twin-vortex’ with same rotation direction, is responsible for the diffusion ‘blind zones’ and transport heterogeneity. The vortices are induced by the coupling of microfluidics and porous structures, and correlated to inertial flow-induced instabilities. The trade-off between diffusion efficiency and quality/completeness with respect to the high Péclet number (or high inlet velocity) serves to enhance our comprehension of intricate fluid dynamics and affords a set of principles to aid a diverse range of practical implementations.

Correction: Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media

Correction: Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media

EFFECT ON INCLINED STRETCHING PLATE UNDER SLIP CONDITION DUE TO NON-NEWTONIAN FLUID IN POROUS MEDIUM FOR MAGNETOHYDRODYNAMIC FLOW OF UNSTEADY NATURE

An analytical probe is executed for evaluating the impact of unsteady flow pertaining to non-Newtonian fluid of magnetohydrodynamic nature on a stretching inclined porous plate, built in porous medium. Electrically conducting unsteady flow facing applied magnetic force with applied slip condition are the other factors utilized for the study of convective heat transfer. For converting governing equations to nonlinear differential equations, the similarity transformation method has been deployed. MATLAB was also used. Ordinary differential equations were solved numerically with the help of the Newton iterative method as well as the shooting method. Results for velocity and temperature were derived for a wide range of unsteady and other parameters including magnetic, source/sink, Grashof number, Prandtl number, Deborah number, and angle of inclination. Graphs and tables were used for compiling and computing values of skin friction and heat transfer rate. Results derived in the present analysis have been compared to those available in the previous literature, and parity has been formed to ascertain the accuracy of the current analytical exercise.

Effects of thermal radiation on Hiemenz slip flow and heat transfer of MHD non-Newtonian fluid in porous media due to permeable plate

This article is to presents a numerical study on effects of thermal radiation on stagnation point slip flow and heat transfer of MHD fluid through porous media due to permeable plate. The governing equations are P DE’s which are transformed into ODE’s by using similarity method. These ODE’s are numerically solved. It is observed that, the heat transfer rate increases with enhancing parametric values of Prandtl number. The results of the present work revels a good correlation with earlier published work. It is noted that temperature enhances as Casson parametric values enhanced. The velocity and temperature gradients are analyzed through graphs and tables. Based on the obtained scientific computations, it is claimed that the reported results can play a useful role in manufacturing processes and improvement in energy and heat resources. It is found that the effect of nonlinear thermal radiation stabilizes the thermal boundary layer growth.

Pore-scale hydrodynamics of non-Newtonian power-law fluids across a partially blocked porous medium in a confined channel

Transport of non-Newtonian fluids in porous media is pervasive in many natural and industrial applications. However, capturing the rheological behaviors of fluids by direct experimental techniques is challenging at the pore-scale. This paper outlines the pore-scale hydrodynamic interactions of non-Newtonian power-law fluids across a partially blocked porous medium in the laminar flow regime by computational fluid dynamics. The porous medium consists of an array of uniformly arranged square pillars. We explore the complex interplay of power-law rheology and Reynolds number on the microscopic flow field at the pore-scale. We capture the momentum transfer at the permeable interface between the porous and non-porous regions through stream-wise and span-wise velocity components and average volumetric flow rates at each pore-throat. Our results unveil a significant augmentation in stream-wise momentum by shear-thinning behavior and a diminution in momentum by shear-thickening behavior of the fluid through the porous medium. Further, the flow-leakage at the top interface purely depends on the combined effects of Reynolds number and power-law index. The channel pressure drop between the windward and leeward faces of the porous medium increases with the power-law index at low Reynolds number, while it decreases at high Reynolds number. Moreover, we provide a simple numerical framework to comprehend how the power-law behavior of the fluid dynamically regulates the flow field at the pore-scale.

Permeability and Mobility for Flows of Inelastic Non-Newtonian Fluids in Porous Media Based on the Energy Dissipation Rate

Permeability and Mobility for Flows of Inelastic Non-Newtonian Fluids in Porous Media Based on the Energy Dissipation Rate

Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media

Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media

Spatial fractional permeability and fractional thermal conductivity models of fractal porous medium

In order to describe the seepage and heat transfer problems of non-Newtonian fluids in porous media, a spatial fractional permeability model and a fractional thermal conductivity model for a fractal porous medium are developed based on the fractional non-Newtonian constitutive equation and the fractional generalized Fourier law. It is an innovative attempt to link fractional operators to the microstructure of pore porous media. The predictive capability of the proposed permeability and thermal conductivity model is verified by comparing with experimental data and the conventional capillary model, and the effects of fractal dimension, fractional parameters, and microstructural parameters on permeability and thermal conductivity are discussed. The results are as follows: (a) These two new models have higher accuracy than the conventional capillary model and reveal the relationship between the nonlocal memory and microstructural properties of complex fluids. (b) The permeability and thermal conductivity increase with increase in the fractional parameter α and radius ratio β and decrease with the increase in the fractal dimension (Dτ and Df) and microstructural parameters (length ratio γ, branching angle θ, and branching level m) of the porous medium. (c) When the radius ratio is larger than a certain value, the growth rate of permeability (β > 0.46) and thermal conductivity (β > 0.3) increases significantly, while the branch angle has the smallest influence on permeability and thermal conductivity, which can be ignored.

MHD flow, radiation heat and mass transfer of fractional Burgers' fluid in porous medium with chemical reaction

Non-Newtonian fluids such as asphalt are widely used in engineering field, but their application will also cause environmental pollution. This paper investigates the MHD flow of this kind of non-Newtonian fluid in porous media by using fractional Burgers' model. The effects of first-order chemical reaction, radiation effects and periodic oscillating boundary condition on fluid flow, heat and mass transfer are considered. The governing equations including a multi-term time fractional derivative are obtained by using the modified Darcy's law, fractional Fourier's law and fractional Fick's law. A convergent and stable L-algorithm, is established for governing equations. The influences of model parameters on the velocity, temperature and concentration distributions are analyzed. Numerical simulation results indicate that fractional derivative α and Darcy number Da have significant effect on velocity distribution. The momentum boundary layer becomes thinner remarkably with fractional derivative α. While the influence of Darcy number Da on the velocity performs conversely.

Enhanced thermal fingering in a shear-thinning fluid flow through porous media: Dynamic pore network modeling

Thermal-viscous fingering instability in porous media is a common phenomenon in nature as well as in many scientific problems and industrial applications. Despite the importance, however, thermal transport in flow of a non-Newtonian fluid in porous media and the resulting fingering has not been studied extensively, especially if the pore space is heterogeneous. In this paper, we propose a pore network model with full graphics processing unit-parallelized acceleration to simulate thermal transport in flow through three-dimensional unstructured pore networks at centimeter scale, containing millions of pores. A thermal Meter equation is proposed to model temperature- and shear stress-dependent rheology of the non-Newtonian fluids. After comparing the simulation results with an analytical solution for the location of the thermal front in a spatially uncorrelated pore network, thermal transport in flow of both Newtonian and non-Newtonian fluids is studied in the spatially uncorrelated and correlated pore networks over a range of injection flow rates. The simulations indicate that the injection flow rate, the shear-thinning rheology, and the morphological heterogeneity of the pore space all enhance thermal-viscous fingering instability in porous media, but with distinct patterns. In spatially correlated networks, the average temperature and apparent viscosity at the breakthrough point in flow of a shear-thinning fluid exhibit non-monotonic dependence on the injection flow rate. An analysis of the fractal dimension of thermal patterns at the breakthrough point supports the conclusion. The results highlight the importance of designing optimal flow conditions for application purposes.

3-D numerical simulation of sandstone matrix acidizing by non-Newtonian fluid

Matrix acidizing is a common technique to increase oil recovery in sandstone oil reservoirs. In the matrix acidizing process, reactive fluids are injected into the reservoir with the scope of dissolving and dispersing the rocks near the wellbore.In this study, the matrix acidizing of sandstone wells by a hydrochloric acid/hydrofluoric acid/additives mixture is described through mathematical modeling using the two-scale continuum model.The model developed in this study indicates the reactions and transport phenomena at pore and Darcy scales in 3-D radial flow. Due to using several additives during the acid injection process, the fluid phase has non-Newtonian behavior (shear-thinning). The effect of non-Newtonian fluid in porous media was investigated using a modified continuum model due to importance calculations in field scale. The Carreau-Yasuda constitutive equation has been used to modify the continuum model to consider the non-Newtonian fluid effects. In the proposed model, partial differential equations of reaction and diffusion at pore-scale, and simultaneously convection and dispersion phenomena at Darcy scale are solved using numerical methods. The finite volume and tri-diagonal matrix algorithm (TDMA) techniques were employed to gain a precise solution for the model and observe the dissolution pattern in different acidizing regimes and rheological properties. The effect of acid injection rate, dissolution rate constant and different reservoir properties, including permeability, porosity and heterogeneity on dissolution patterns, was investigated by considering non-Newtonian fluid effects, and concluded that acid having high shear-thinning behaviour (i. e., acid having low power-law index) seemed more promising for field operations because of deep penetration. The reservoir heterogeneity was defined by selecting a random local porosity distribution.It should be noted that the presented model can reproduce different types of acid/rock system (carbonate or sandstone reservoirs). Finally, the skin factor would be calculated to study the acidizing performance in the damaged zone. To solve the porosity evolution equation, couple pore and Darcy scales, and update the pore-scale parameters at each time step, the program was developed in FORTRAN by Parallel Processing and consisting of functions and routines. • Simultaneous numerical solution of Darcy, mass and pore equations in 3-dimension. • 3-D modeling of sandstone matrix acidizing by non-Newtonian fluid. • Pore volume to breakthrough and injection rate calculations in various conditions. • Consideration of power-law index (n) and viscosity effects in dissolution patterns. • Consideration of skin factor variation during the matrix acidizing.

Rheological effects on the acidizing process in carbonate reservoirs

In this work, we present a new formulation to study the flow of a reactive non-Newtonian fluid in porous media. The mathematical model consists of a two-scale continuum model that couples information from the pore scale to Darcy one. In the place of the traditional Darcy Law, we consider a complete linear momentum equation, based on the Continuum Theory of Mixtures. The upscaling is made by an interaction source term that corresponds to the flow resistance caused by the matrix inside the pores, which considers the non-newtonian nature of the fluid. Motivated by the often applied self diverting acids we analyze the rheological dependence on the local level of pH. Simulations are performed using the finite volume method with the OpenFOAM software. We investigate the influence of the Damköhler number and the power-law index over dissolution patterns and Pore Volume to Breakthrough (PVbt) curves. The results are compared with the corresponding Newtonian cases. The effect of both shear rate and pH on viscosity are also studied. We verify a significant dependency of the dissolution patterns and also in the optimum injection rate on the rheology of the fluid. More shear-thinning fluids lead to lower values of PVbt. Although the divergent acids were really able to find different paths for the breakthrough, higher times were needed for this achievement.

A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media

During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid.

Identifying the Optimal Path and Computing the Threshold Pressure for Flow of Bingham Fluids Through Heterogeneous Porous Media

Understanding flow of non-Newtonian fluids in porous media is critical to successful operation of several important processes, including polymer flooding, filtration, and food processing. In some cases, such as when a non-Newtonian fluid can be represented by the power-law model, simulation of its flow in a porous medium is a straightforward extension of that of Newtonian fluids. In other cases, such as flow of Bingham fluids, there is a minimum external threshold pressure below which there would be no macroscopic flow in the porous medium. Computing the threshold pressure is a difficult problem, however. We present a new algorithm for determining the threshold pressure for flow of a Bingham fluid through a porous medium, modeled by a pore-network (PN) model. The algorithm, the ant colony optimization (ACO), is described in detail and together with the PN model is used to determine the minimum pressure for flow of Bingham fluids in a heterogeneous porous medium, the Mt. Simon sandstone, whose PN and morphological properties were extracted from the sandstone’s image. To assess the accuracy and computational efficiency of the ACO algorithm, we also carry out the same computations with two previous methods, namely invasion percolation with memory (IPM) and the path of minimum pressure (PMP) algorithms. The IPM does not guarantee identification of the optimal flow path with the minimum threshold pressure, while the PMP algorithm provides an approximate, albeit accurate, solution of the problem. We also compare the computational complexity of the three methods. For large PNs, both the IPM and PMP are much less efficient than the ACO algorithm. Finally, we study the effect of the morphology of the pore space on the minimum threshold pressure.

Adomain computation of radiative-convective bi-directional stretching flow of a magnetic non-Newtonian fluid in porous media with homogeneous–heterogeneous reactions

In the present communication, the laminar, incompressible, hydromagnetic flow of an electrically conducting non-Newtonian (Sisko) fluid over a bi-directional stretching sheet in a porous medium is studied theoretically. Thermal radiation flux, homogeneous–heterogeneous chemical reactions and convective wall heating are included in the model. The resultant nonlinear ordinary differential equations with transformed boundary conditions via similarity transformation are then solved with the semi-analytical Adomain Decomposition Method (ADM). Validation with earlier studies is included for the nonradiative case. Extensive visualization of velocity, temperature and species concentration distributions for various emerging parameters is included. Increasing the magnetic field and inverse permeability parameter is observed to decelerate both the primary and secondary velocity magnitudes whereas they increase temperatures in the regime. Increasing sheet stretching ratio weakly accelerates the primary flow throughout the boundary layer whereas it more dramatically accelerates the secondary flow near sheet surface. Temperature is consistently reduced with increasing stretching sheet ratio whereas it is strongly enhanced with greater radiative parameter. With greater Sisko non-Newtonian power-law index the primary velocity and temperature are decreased whereas the secondary velocity is increased. Increasing both homogenous and heterogeneous chemical reaction parameters is found to weakly and more strongly, respectively, deplete concentration magnitudes whereas greater Schmidt number enhances them.

Qualification of New Methods for Measuring In Situ Rheology of Non-Newtonian Fluids in Porous Media.

Pressure drop (ΔP) versus volumetric injection rate (Q) data from linear core floods have typically been used to measure in situ rheology of non-Newtonian fluids in porous media. However, linear flow is characterized by steady-state conditions, in contrast to radial flow where both pressure and shear-forces have non-linear gradients. In this paper, we qualify recently developed methods for measuring in situ rheology in radial flow experiments, and then quantitatively investigate the robustness of these methods against pressure measurement error. Application of the new methods to experimental data also enabled accurate investigation of memory and rate effects during polymer flow through porous media. A radial polymer flow experiment using partially hydrolyzed polyacrylamide (HPAM) was performed on a Bentheimer sandstone disc where pressure ports distributed between a central injector and the perimeter production line enabled a detailed analysis of pressure variation with radial distance. It has been suggested that the observed shear-thinning behavior of HPAM solutions at low flux in porous media could be an experimental artifact due to the use of insufficiently accurate pressure transducers. Consequently, a generic simulation study was conducted where the level of pressure measurement error on in situ polymer rheology was quantitatively investigated. Results clearly demonstrate the robustness of the history match methods to pressure measurement error typical for radial flow experiments, where negligible deviations from the reference rheology was observed. It was not until the error level was increased to five-fold of typical conditions that significant deviation from the reference rheology emerged. Based on results from pore network modelling, Chauveteau (1981) demonstrated that polymer flow in porous media may at some rate be influenced by the prior history. In this paper, polymer memory effects could be evaluated at the Darcy scale by history matching the pressure drop between individual pressure ports and the producer as a function of injection rate (conventional method). Since the number of successive contraction events increases with radial distance, the polymer has a different pre-history at the various pressure ports. Rheology curves obtained from history matching the radial flow experiment were overlapping, which shows that there is no influence of geometry on in-situ rheology for the particular HPAM polymer investigated. In addition, the onset of shear-thickening was independent of volumetric injection rate in radial flow.

Effective Rheology of Bi-viscous Non-newtonian Fluids in Porous Media

We model the flow of a bi-viscous non-Newtonian fluid in a porous medium by a square lattice where the links obey a piece-wise linear constitutive equation. We find numerically that the flow regime where the network transitions from all links behaving according to the first linear part of the constitutive equation to all links behaving according to the second linear part of the constitutive equation, is characterized by a critical point. We measure two critical exponents associated with this critical point, one of the being the correlation length exponent. We find that both critical exponents depend on the parameters of the model.

Mathematical Simulation of local transfer for non-Newtonian uid in porous fabrics

Many processes in the polymer composite, textile, food, and pharmaceutical industries are associated with the flow of non-Newtonian fluids in porous media. This paper considers the mathematical model of a multi-scale process for the filtration of non-Newtonian fluid in periodic porous fabrics. The model should be based on a three-dimensional Navier-Stokes equation with non-Newtonian Carreau-Yasuda viscosity using the asymptotic averaging method. A numerical algorithm was developed for solving local problems of non-Newtonian fluids in periodic cells, and the distribution of velocity, pressure and non-Newtonian viscosity in a single pore was obtained. The algorithm for calculating the permeability tensor is developed, and the effects of fluid rheology are also highlighted.