Flow In Porous Systems Research Articles

Lucas-Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems.

Fluid flow in porous systems driven by capillary pressure is one of the most ubiquitous phenomena in nature and industry, including petroleum and hydraulic engineering as well as material and life sciences. The classical Lucas-Washburn (LW) equation and its modified forms were developed and have been applied extensively to elucidate the fundamental mechanisms underlying the basic statics and dynamics of the capillary-driven flow in porous systems. The LW equation assumes that fluids are incompressible Newton ones and that capillary channels all have the same radii. This kind of hypothesis is not true for many natural situations, however, where porous systems comprise complicated pore and capillary channel structures at microscales. The LW equation therefore often leads to inaccurate capillary imbibition predictions in such situations. Numerous studies have been conducted in recent years to develop and assess the modifications and extensions of the LW equation in various porous systems. Significant progresses in computational techniques have also been attained to further improve our understanding of imbibition dynamics. A state-of-the-art review is therefore needed to summarize the recent significant models and numerical simulation techniques as well as to discuss key ongoing research topics arising from various new engineering practices. The theoretical basis of the LW equation is first introduced in this review and recent progress in mathematical models is then summarized to demonstrate the modifications and extensions of this equation to various microchannels and porous media. These include capillary tubes with nonuniform and noncircular cross sections, discrete fractures, and capillary tubes that are not straight as well as heterogeneous porous media. Numerical studies on the LW equation are also reviewed, and comments on future works and research directions for LW-based capillary-driven flows in porous systems are listed.

Tailoring porous media for controllable capillary flow

HypothesisControl of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. Here we propose that the liquid flow by capillary penetration can be accurately adjusted by tuning the geometry of porous media. MethodologiesOn the basis of Darcy’s law, a general framework is proposed to facilitate the control of capillary flow in porous systems by tailoring the geometric shape of porous structures. A numerical simulation approach based on finite element method is also employed to validate the theoretical prediction. FindingsA basic capillary component with a tunable velocity gradient is designed according to the proposed framework. By using the basic component, two functional capillary elements, namely, (i) flow accelerator and (ii) flow resistor, are demonstrated. Then, multi-functional fluidic devices with controllable capillary flow are realized by assembling the designed capillary elements. All the theoretical designs are validated by numerical simulations. Finally, it is shown that the proposed concept can be extended to three-dimensional design of porous media.

An All Hydrophilic Fluid Diode for Unidirectional Flow in Porous Systems

AbstractA fluid diode that allows fluid flow in one direction but blocks fluid flow in the opposite direction has wide applications including oil recovery, drug delivery, and lab‐on‐a‐chip microfluidics. Many studies are conducted to facilitate directional liquid motion on the solid surface or across thin porous layers. However, the self‐driven one‐way flow inside porous systems still remains a significant challenge. Here, a novel all‐hydrophilic fluid diode (AHFD) made of porous materials with asymmetric pores is reported, which allows capillary flow in a chosen direction. The direction‐dependent flow process and the breakthrough pressure are experimentally and theoretically examined. The proposed AHFD can have many potential applications such as functional protective clothing, microfluidic valve, and oil–water separator, and the idea can be extended to develop other all lyophilic fluid diodes such as oleophilic diode.

Existence of convective threshold and its role on temperature in reactive flow through fractured rocks: a simulation study in 2D

A reactive fluid flowing through porous or fractured rocks causes changes in its porosity and permeability. Experimental studies on the effects of reactive flow in porous systems are normally confined to finite size rock samples in laboratories as actual field data is not sufficiently available. Such laboratory data and simulations based on them, may not always correctly predict or explain changes that take place in rock basins in geological time. In this study we simulate two cases- transient and steady. In a transient case, reactions occur as soon as a reactive fluid is injected into the rock, whereas in the steady case, reactions begin only after the injected fluid percolates through the sample length. The transient case is comparable to real rock basins, while the steady case mimics the situation in laboratory experiments. Variation of the hydrodynamic parameters such as porosity, permeability and surface area, and their inter-relationships at different temperatures, are discussed in both cases. We establish that for every temperature, there exists a threshold flux above which the two cases give similar results. Prediction of changes in rock property due to reactive flow in real situations can be made from laboratory experiments provided the flux is kept above this threshold value. When the fluid flux is kept above this threshold value, the porosity-permeability relation follows a power law behaviour. While the threshold flux is independent of temperature and channel width, the exponent of the power law is a slow decreasing function of temperature.

Capillary bundle model for gravitational flow of emulsion through granular media and experimental validation

Emulsion flow in porous systems is different from the flow of the individual phases, because there are different mechanisms that must be taken into account when modeling the movement of such liquids. In the literature, there are no mathematical models which take into account phenomena characterizing such flows. The development of such dependence would allow for substantial improvements on the assessment of contamination and facilitate the selection of appropriate methods of soil and groundwater remediation.In this paper a numerical model, describing the process of gravitational flow of the emulsion through the porous structures, has been developed. Using this model, it was possible to predict the flow rate of fluid through the bed, and changes in the emulsion structure. This model was based on the concept of capillary bundles and assumed conversion of granular deposit into a network of capillaries. The calculation results obtained using the proposed model were compared with the results of own experimental works and high accordance was achieved.

Microbial colonisation in heaps for mineral bioleaching and the influence of irrigation rate

Microbial colonisation is important for mineral dissolution in heap bioleaching of low grade ore. Colonisation studies to date have focused on the microbial attachment of single species to mineral concentrates in batch and flow systems. Hydrology and soil engineering studies suggest interaction between microbial colonisation and fluid flow in porous systems that result from solution-ore and microbe-mineral contacting (Wan et al., 1994; Yarwood et al., 2006).The effect of the irrigation rate on microbial colonisation was assessed using columns packed with acid agglomerated low grade copper-containing ore. Continuous flow, unsaturated, aerated bed reactors were inoculated by pulse irrigation with iron and sulphur oxidising mesophilic microorganisms (1012cells/ton ore), followed by operation at irrigation rates of 2, 6 and 18l/m2/h. A novel in-bed sampling technique allowed the extraction of ore samples from the bed during the leaching process. Novel insights regarding microbial growth, interstitial and weakly and strongly attached microbial populations were obtained.Bacterial adherence and cell number retained in the ore bed increased over the 32day leaching period. Average specific growth rates of ore-associated micro-organisms of 0.161±0.0045, 0.155±0.026 and 0.120 (± 0.00)1/h were obtained at 2, 6 and 18L/m2/h respectively. Faster colonisation occurred at lower irrigation rates. At higher irrigation rates, higher detachment and cell removal were apparent, based on PLS cell numbers. The interstitial cells from the stagnant fluid in the ore bed formed the dominant contribution to the microbial population within all the heap systems.

Physical and Numerical Coupling in Dual‐Continuum Modeling of Preferential Flow

Dual‐continuum models are useful for describing flow in porous systems with significant local pressure disequilibrium between slow moving water, contained in the porous matrix, and fast moving water in preferential pathways. The formation and intensity of preferential flow depends on the contrast between the hydraulic properties of the two flow domains as well as on the properties of their interface. In this study, we focused on both physical coupling of the flow domains through the mass transfer term and numerical coupling of the respective governing equations. The set of governing equations was alternatively solved using a sequentially coupled (SC) approach and a fully coupled (FC) approach. The SC approach was shown to be computationally more efficient for strongly developed preferential flow in systems with high interfacial resistance; however, it becomes numerically unstable for weak preferential flow associated with low interfacial resistance. The FC approach is a computationally more expensive yet numerically more robust alternative, capable of simulating a complete class of intermediate flow regimes ranging from strongly preferential flow in a dual‐continuum system to nonpreferential flow in a single‐continuum system. To illustrate the performance of the numerical coupling approaches in conjunction with the effect of different interfacial resistances, we present a simple example problem involving one‐dimensional near‐saturated flow in a vertical soil column.

Experimental investigation of trapped oil clusters in a water‐wet bead pack using X‐ray microtomography

Uncertainties in the quantification of transport properties associated with multiphase flow in porous systems often make the prediction of fluid residence and migration a difficult task. Movement and trapping of immiscible fluids in permeable formations depends upon a complex combination of fluid properties, rock properties, fluid‐solid interactions, and forcing conditions. This work consists of using X‐rays and visualization techniques to map the distribution of immiscible fluids, particularly trapped oil clusters, residing in a glass bead pack subject to different flow conditions. We analyze the effect of flowing conditions on the evolution of fluid microstructures using X‐ray microtomography. Spherical glass beads (0.425–0.600 mm in diameter), a water‐wet porous medium, were packed inside a specially designed core holder. High‐resolution imaging provides detailed mapping of pore structures resulting from bead packing, and characterization of fluid microstructures formed during sequential water and oil injections. We present spatial distribution of trapped oil clusters for the entire bead pack, as well as mechanistic explanations leading to the fluid configurations observed. We also present simple statistical analyses of blob size, shape, and surface area at the end of different fluid injection cycles. Trapped oil clusters appear in sizes that range from 5.923 × 10−5 mm3 to 3.119 × 103 mm3, where 0.01–0.50 mm3 clusters are most common. About 98% of the total trapped oil at the end of drainage and imbibition cycles corresponds to blobs that are smaller than 1 mm3. It is also shown that most blobs are larger than the mean pore size (0.03 mm3). The mean oil blob size is about 5 times larger than the average pore. A typical blob extends through various interconnected pores, exhibiting elongated of ramified shapes that include multiple voids and constrictions at the same time. The mean aspect ratio of these clusters is less than 2, and the surface area to volume ratio is constant for those larger than 0.1 mm3. Experimental methods and findings presented in this paper are expected to lead to powerful calibration mechanisms for multiphase flow models.

Unified lattice Boltzmann method for flow in multiscale porous media.

In this paper, we develop a unified lattice Boltzmann method for flow in multiscale porous media. This model not only can simulate flow in porous systems of various length scales but also can simulate flow in porous systems where multiple length scales coexist. Simulations of unidirectional steady flow through homogeneous and heterogeneous porous media both recover Darcy's law when the effects of inertial forces and Brinkman correction may be negligible. Direct use of this model on the usual computational nodes, with zero resistance on void spaces and infinite resistance on solid walls, gives results that agree well with analytical solutions. Simulations performed on a fractured porous system show that the method presented here gives very good overall permeability values for the whole fractured system. A series of simulations is performed on a simplified fractured system. The results indicate that, when the ratio of the permeability of the rock matrix to the fracture permeability calculated by the cubic law is less than 10(-4), the effects of the rock matrix flow are negligible, and the discrete-fracture models that ignore such flow are plausible. When the ratio is larger than 10(-4), the matrix flow has significant effects on the fractured system, and the assumption that the matrix is impermeable does not hold. Therefore, the use of the cubic law to calculate the fracture permeability may cause a significant error. It is also indicated that the larger the ratio of the width of the porous matrix to that of the fracture, the more significant is the error caused by using the cubic law.

Fluid flow in porous systems

Nuclear magnetic resonance (NMR) measurements of water velocity flowing through glass bead packs with a bead diameter of 10 mm have been made using the π echo-planar imaging (PEPI) sequence. These results indicate that for various flow rates the flow variance is proportional to the mean flow velocity in agreement with the Mansfield-Issa equation. The velocity distributions are approximately Gaussian. Investigation of the slopes of the variance vs. velocity curves as a function of slice thickness indicate some coherence effects in the connectivity of the glass bead system. An extension of an earlier intervoxel coupling model is presented, which seems to explain the observed coherence effects.

Capillary phenomena, heat-and-mass exchange, and wave processes in two-phase flow in porous systems and packings

Capillary phenomena, heat-and-mass exchange, and wave processes in two-phase flow in porous systems and packings

Application of flourescent particle imaging to measuring flow in complex media

The development of flourescence-based experimental techniques that can be used to obtain quantitative information about the flow of fluids through porous media is reported. Flow information is obtained by illuminating a two-dimensional slice of refractive index matched model of a porous medium with a planar laser beam. The flowing liquid phase is seeded with 10-μm diameter flourescent particles, and time-sequenced photographs of the illuminated plane provide quantitative information about the velocity of the flowing liquid. The method provides simultaneous measurements of point level and spatially averaged velocity vectors within the interstitial spaces of the medium. Porosity and preliminary tracer concentration measurements were made in a similar manner with the use of a flourescent dye. The use of flourescence, spectral filtering and refractive index matching permits a unique application of particle and tracer imaging to the study of flow in porous systems. The results from this technique compare favorably with the expected macroscopically derived results; the significance of these results and methodology is that they provide experimental verification of fundamental multi-phase transport equations. The application of this technique might be extended to experimental studies of flow in optically transparent models of biological, chemical and physical systems.

Fractal Mathematics Applied to Flow in Porous Systems

AbstractThe Leitz TAS‐Plus image analysis system was programmed to automatically measure both the ‘shape’ fractal and ‘fragmentation’ fractal for various types of fine particle filter cakes. The automated nature of the analysis facilitated the collection of statistically significant volumes of ‘fractal’ data. This data was then revised, where possible, to conventional theories of flow behavior. Several new insights evolved from the study as explained in the following analysis.

The Effect of Turbulence on Flow of Natural Gas Through Porous Reservoirs

Abstract The nature and the limits of validity of Darcy's law as applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy's law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the fl factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been considered red. In light of the current numerical results the significance and limitation of the rate of flow function Y proposed by Smith has been discussed. Introduction The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments. Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (D / ), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots. The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy's law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer. = ..........(1) The nature and the range of validity of Darcy's law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy's law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. JPT P. 799^

Gas Diffusion in Porous Media

A method has been proposed for deriving a characteristic determining flow in porous systems. This characteristic combines both area and path-length factors used by earlier authors. For a gas, diffusive flow is proportional to the 4/3 power of the gas-filled porosity, and this function has been derived from consideration of the planar distribution of spherical pores and the interaction of two adjacent planes.

Gas Diffusion in Porous Media

A method has been proposed for deriving a characteristic determining flow in porous systems. This characteristic combines both area and path-length factors used by earlier authors. For a gas, diffusive flow is proportional to the 4/3 power of the gas-filled porosity, and this function has been derived from consideration of the planar distribution of spherical pores and the interaction of two adjacent planes.