scholarly journals Effects of Velocity and Permeability on Tracer Dispersion in Porous Media

2021 ◽  
Vol 11 (10) ◽  
pp. 4411
Author(s):  
Yulong Yang ◽  
Tongjing Liu ◽  
Yanyue Li ◽  
Yuqi Li ◽  
Zhenjiang You ◽  
...  
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Dispersion Coefficient ◽  
Fluid Velocity ◽  
Tracer Tests ◽  
Volumetric Flow Rate ◽  
Flow In Porous Media ◽  
Low Permeability ◽  
Regression Equations ◽  
Medium Permeability

During micro-scale tracer flow in porous media, the permeability and fluid velocity significantly affect the fluid dispersion properties of the media. However, the relationships between the dispersion coefficient, permeability, and fluid velocity in core samples are still not clearly understood. Two sets of experiments were designed to study the effects of tracer fluid flow velocity and porous medium permeability on the dispersion phenomenon in a core environment, using natural and sand-filled cores, respectively. From experimental data-fitting by a mathematical model, the relationship between the dispersion coefficient, flow velocity, and permeability was identified, allowing the analysis of the underlying mechanism behind this phenomenon. The results show that a higher volumetric flow rate and lower permeability cause a delay in the tracer breakthrough time and an increase in the dispersion coefficient. The core experimental results show that the dispersion coefficient is negatively correlated with the permeability and positively correlated with the superficial velocity. The corresponding regression equations indicate linear relations between the dispersion coefficient, core permeability, and fluid velocity, resulting from the micron scale of grain diameters in cores. The combination of high velocity and low permeability yields a large dispersion coefficient. The effects of latitudinal dispersion in porous media cannot be ignored in low-permeability cores or formations. These findings can help to improve the understanding of tracer flow in porous media, the design of injection parameters, and the interpretation of tracer concentration distribution in inter-well tracer tests.

scholarly journals The Hydrodynamic Dispersion Characteristics of Coral Sands

2019 ◽  
Vol 7 (9) ◽  
pp. 291 ◽  
Author(s):  
Xiang Cui ◽  
Changqi Zhu ◽  
Mingjian Hu ◽  
Xinzhi Wang ◽  
Haifeng Liu
Keyword(s):  
Particle Size ◽  
Porous Media ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Dispersion Coefficient ◽  
Hydrodynamic Dispersion ◽  
Dispersion Characteristics ◽  
Factors Affecting ◽  
Mechanical Dispersion ◽  
Freshwater Aquifers

Dispersion characteristics are important factors affecting groundwater solute transport in porous media. In marine environments, solute dispersion leads to the formation of freshwater aquifers under islands. In this study, a series of model tests were designed to explore the relationship between the dispersion characteristics of solute in calcareous sands and the particle size, degree of compactness, and gradation of porous media, with a discussion of the types of dispersion mechanisms in coral sands. It was found that the particle size of coral sands was an important parameter affecting the dispersion coefficient, with the dispersion coefficient increasing with particle size. Gradation was also an important factor affecting the dispersion coefficient of coral sands, with the dispersion coefficient increasing with increasing d10. The dispersion coefficient of coral sands decreased approximately linearly with increasing compactness. The rate of decrease was −0.7244 for single-grained coral sands of particle size 0.25–0.5 mm. When the solute concentrations and particle sizes increased, the limiting concentration gradients at equilibrium decreased. In this study, based on the relative weights of molecular diffusion versus mechanical dispersion under different flow velocity conditions, the dispersion mechanisms were classified into five types, and for each type, a corresponding flow velocity limit was derived.

The Growth of Mixing Zone in Heterogeneous Porous Media

2012 ◽  
Author(s):  
M. R. Othman ◽  
R. Badlishah Ahmad ◽  
Z. May
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Short Duration ◽  
Dispersion Coefficient ◽  
Fluid Velocity ◽  
Heterogeneous Porous Media ◽  
Mixing Zone ◽  
Zone Size ◽  
Model Mixing ◽  
Dispersive Mixing

Dengan menggunakan penyelesaian analitikal yang merangkumi fraktal eksponen, pembesaran jarak pencampuran telah dapat ditentukan bagi model satu dimensi. Size zon pencampuran didapati meningkat apabila media berliang menjadi semakin heterogen. Dalam media berliang yang heterogen, saiz zon pencampuran meningkat apabila pemalar penyerakan meningkat terutama sekali pada aliran jangkamasa singkat relatif. Terdapat tiga faktor penting mempengaruhi saiz zon pencampuran penyerakan, ΔxD. Perkara terpenting dalam kajian ini ialah keheterogenan takungan, yang dipersembahkan oleh fraktal eksponen, β. Hasil kajian mendapati bahawa apabila β menjadi kecil (media berliang menjadi semakin heterogen), saiz zon pencampuran meningkat. Satu lagi faktor mempengaruhi ΔxD ialah pemalar penyerakan bersandar masa, Κ(tD). Di dalam takungan heterogen, zon pencampuran meningkat dengan peningkatan nilai pemalar penyerakan pada aliran jangkamasa singkat relatif. Bagi aliran jangkamasa panjang relatif, bagaimanapun, ΔxD terus meningkat walaupun Κ(tD) menjadi tetap. Faktor ketiga ialah purata kelajuan bendalir, ν. Zon pencampuran mempunyai perkaitan songsang dengan kelajuan bendalir dengan cara ΔxD meningkat apabila ν berkurangan. Kata kunci: Kehomogenan; keheterogenan; pekali penyerakan; eksponen fraktal; zon pencampuran; media berliang Utilizing currently available analytical solutions that incorporate fractal exponent, the growth of mixing length of injected solvent was determined for a one-dimensional model. Mixing zone size was found to increase as porous medium becomes increasingly heterogeneous. In a heterogeneous porous media, mixing zone size increases as dispersion coefficient increases particularly at relatively short duration of flow. There are three important factors influencing the size of the dispersive mixing zone, ΔxD. Of particular importance in this study is reservoir heterogeneity, which is represented by a fractal exponent, β. It was discovered that as β becomes smaller (porous medium becomes increasingly heterogeneous), the size of the mixing zone increases. Another factor affecting ΔxD is time dependent dispersion coefficient, Κ(tD). In a heterogeneous reservoir, mixing zone increases with increasing value of dispersion coefficient at relatively short duration of flow. For relatively long period of flow, however? ΔxD continues to increase even though Κ(tD) remains constant. The third factor is average fluid velocity, ν. Mixing zones have inverse relationship with fluid velocity in that ΔxD increases as ν decreases. Key words: Homogeneity; heterogeneity; dispersion coefficient; fractal exponent; mixing zone; dimensionless concentration; porous media

A New Unsteady-State Model for Calculating Oil-Water Relative Permeability of Low-Permeability/Ultra-Low Permeability Reservoirs

2012 ◽  
Vol 616-618 ◽  
pp. 964-969 ◽  
Author(s):  
Yue Yang ◽  
Xiang Fang Li ◽  
Ke Liu Wu ◽  
Meng Lu Lin ◽  
Jun Tai Shi
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Oil Reservoirs ◽  
Flow In Porous Media ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Flow Process ◽  
Threshold Pressure Gradient

Oil and water relative permeabilities are main coefficients in describing the fluid flow in porous media; however, oil and water relative permeability for low - ultra low perm oil reservoir can not be obtained from present correlations. Based on the characteristics of oil and water flow in porous media, the model for calculating the oil and water relative permeability of low and ultra-low perm oil reservoirs, which considering effects of threshold pressure gradient and capillary pressure, has been established. Through conducting the non-steady oil and water relative permeability experiments, oil and water relative permeability curves influenced by different factors have been calculated. Results show that: the threshold pressure gradient more prominently affects the oil and water relative permeability; capillary pressure cannot influence the water relative permeability but only the oil relative permeability. Considering effects of threshold pressure gradient and capillary pressure yields the best development result, and more accordant with the flow process of oil and water in low – ultra low perm oil reservoirs.

Pulsatile Blood Flow Through a Constricted Porous Artery

2020 ◽  
Vol 17 (2) ◽  
pp. 743-749
Author(s):  
Salah Uddin ◽  
Obaid Ullah Mehmood ◽  
Mahathir Mohamad ◽  
Mahmod Abd Hakim Mohmad ◽  
D. F. Jamil ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Flow Velocity ◽  
Nonlinear Differential Equations ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Physical Parameters ◽  
Porosity Parameter ◽  
Arterial Blood ◽  
Flow Through

In this paper a speculative study of an incompressible Newtonian blood flow through a constricted porous channel and pulsatile nature is inspected. Porosity parameter λ is incorporated in the momentum equation. Governing nonlinear differential equations are numerically evaluated by employing the perturbation method technique for a very small perturbation parameter ε 1 such that ε ≠ 0 and with conformable boundary conditions. Numerical results of the flow velocity profile and volumetric flow rate have been derived numerically and detailed graphical analysis for different physical parameters porosity, Reynolds number and stenosis has been presented. It is found that arterial blood velocity is dependent upon all of these factors and that the relationship of fluid velocity and flow is more complex and nonlinear than heretofore generally believe. Furthermore the flow velocity enhanced with Reynolds number, porosity parameter and at maximum position of the stenosis/constriction.

scholarly journals Exploring the conservativeness of deuterated water as the artificial tracer for hydrogeological tests

2021 ◽  
Author(s):  
Xiaohua Huang ◽  
Guodong Liu ◽  
Jie Mei
Keyword(s):  
Porous Media ◽  
Tracer Tests ◽  
Hysteresis Effect ◽  
Domain Model ◽  
Retardation Factor ◽  
Low Permeability ◽  
Deuterated Water ◽  
Exchange Effect ◽  
The Media ◽  
Dual Domain

Deuterated water has been applied in hydrogeological tracer tests in recent years. However, there is a contradiction about the conservativeness of artificial deuterium (D/2H). In this study, what circumstances HDO behaved truly conservatively were investigated through laboratory-scale experiments via comparing the widely used tracer chloride (Cl-). And reasons for the non-conservativeness of HDO were discussed comprehensively for the first time. In addition, the advection-dispersion equation (ADE) and dual-domain mass transfer (DDMT) equation were employed to describe the breakthrough curves (BTCs) of tracers. HDO behaved conservatively when it transported in the porous media with high permeability (approximately K > 1m/d), and ADE could describe BTCs successfully. While hysteresis effect of HDO expressed in the media with low permeability. And the lower the permeability of the porous media, the stronger the hysteresis effect. DDMT was more suitable for demonstrating BTCs in low permeability media. Hydrogen bonds between HDO and H2O, the isotopic exchange effect, and the dual-domain model of the media all could lead to the hysteresis effect. The retardation factor (R = 1.712) was used to describe transporting behaviors of HDO in clay firstly. And the threshold hydraulic conductivity (Kcr) and the proportion of immobile regions of HDO were greater than that of Cl-, while dispersion coefficients of HDO were smaller. These could provide further considerations for using deuterium in hydrogeological tracer tests.

scholarly journals A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2986 ◽  
Author(s):  
Gang Lei ◽  
Nai Cao ◽  
Di Liu ◽  
Huijie Wang
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Flow Behavior ◽  
Quantitative Model ◽  
Hertzian Contact ◽  
Flow In Porous Media ◽  
Conformable Derivative ◽  
Linear Flow ◽  
Proposed Model ◽  
Non Linear

Prediction of the non-linear flow in porous media is still a major scientific and engineering challenge, despite major technological advances in both theoretical and computational thermodynamics in the past two decades. Specifically, essential controls on non-linear flow in porous media are not yet definitive. The principal aim of this paper is to develop a meaningful and reasonable quantitative model that manifests the most important fundamental controls on low velocity non-linear flow. By coupling a new derivative with fractional order, referred to conformable derivative, Swartzendruber equation and modified Hertzian contact theory as well as fractal geometry theory, a flow velocity model for porous media is proposed to improve the modeling of Non-linear flow in porous media. Predictions using the proposed model agree well with available experimental data. Salient results presented here include (1) the flow velocity decreases as effective stress increases; (2) rock types of “softer” mechanical properties may exhibit lower flow velocity; (3) flow velocity increases with the rougher pore surfaces and rock elastic modulus. In general, the proposed model illustrates mechanisms that affect non-linear flow behavior in porous media.

Resin Radial and Isothermal Infiltration in Fibrous Media: A New Mathematical Formulation

2020 ◽  
Vol 400 ◽  
pp. 123-134
Author(s):  
Mariana Julie do Nascimento Santos ◽  
Guilherme Luiz de Oliveira Neto ◽  
Ana Raquel Carmo de Lima ◽  
Nívea Gomes Nascimento de Oliveira ◽  
Raimundo Pereira de Farias ◽  
...  
Keyword(s):  
Porous Media ◽  
Mathematical Formulation ◽  
Injection Pressure ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Flow In Porous Media ◽  
Fibrous Media ◽  
Injection Process ◽  
Fiber Reinforced Polymer Composites ◽  
Medium Permeability

The objective of this work is to describe the fluid flow in porous media including the sorption term of the fluid by the fibers. The study has been applied to the manufacture of fiber-reinforced polymer composites by resin transfer molding, giving emphasis to radial resin infiltration in a one-dimensional approach. The mass conservation equation and Darcy’s law are presented and the solution of the governing equation is obtained. The advanced mathematical modeling includes the effect of fluid sorption by the porous media. Predicted flow front results and resin pressure fields within the mold during the injection process are presented, and the effects of the sorption term, injection pressure and fibrous medium permeability analyzed.

scholarly journals Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 79
Author(s):  
Vi Nguyen ◽  
Dimitrios V. Papavassiliou
Keyword(s):  
Porous Media ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Flow In Porous Media ◽  
Hydrodynamic Dispersion ◽  
Length Scale ◽  
Packed Beds ◽  
Péclet Number ◽  
Molecular Diffusivity ◽  
Effective Lagrangian

Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to depend on properties of the medium structure, on the dispersing compound, and on the flow field characteristics. Previous studies have resulted in suggestions of different equation forms, showing the relationship between the hydrodynamic dispersion coefficient for various types of porous media in various flow regimes and the Peclet number. The Peclet number is calculated based on a Eulerian length scale, such as the diameter of the spheres in packed beds, or the pore diameter. However, the nature of hydrodynamic dispersion is Lagrangian, and it should take the molecular diffusion effects, as well as the convection effects, into account. This work shifts attention to the Lagrangian time and length scales for the definition of the Peclet number. It is focused on the dependence of the longitudinal hydrodynamic dispersion coefficient on the effective Lagrangian Peclet number by using a Lagrangian length scale and the effective molecular diffusivity. The lattice Boltzmann method (LBM) was employed to simulate flow in porous media that were constituted by packed spheres, and Lagrangian particle tracking (LPT) was used to track the movement of individual dispersing particles. It was found that the hydrodynamic dispersion coefficient linearly depends on the effective Lagrangian Peclet number for packed beds with different types of packing. This linear equation describing the dependence of the dispersion coefficient on the effective Lagrangian Peclet number is both simpler and more accurate than the one formed using the effective Eulerian Peclet number. In addition, the slope of the line is a characteristic coefficient for a given medium.

Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media

SPE Journal ◽  
2008 ◽  
Vol 13 (01) ◽  
pp. 112-122 ◽  
Author(s):  
Haiying Huang ◽  
Joseph A. Ayoub
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Resistance Factor ◽  
Darcy Flow ◽  
High Rate ◽  
Flow In Porous Media ◽  
Nonlinear Flow ◽  
Quadratic Term ◽  
Forchheimer Equation ◽  
Flow Rates

Summary The subject of non-Darcy flow in hydraulically fractured wells has generated intense debates recently. One aspect of the discussion concerns the inertia resistance factor, or the so-called beta factor, ß, in the Forchheimer equation, and whether the beta factor ß of a proppant pack should be constant over the range of flow rates of practical interests. The problem was highlighted in a recent discussion by van Batenburg and Milton-Tayler (2005) and the reply by Barree and Conway (2005) regarding paper SPE 89325 (Barree and Conway 2004) in the August 2005 JPT. This discussion in essence revolves around the applicability of the Forchheimer equation and whether the Forchheimer equation is adequate to describe the experimental results of high rate flow in proppant packs. In order to properly assess the arguments in this debate, and to get a better understanding of the state-of-the-art on non-Darcy flow in porous media in general, literature concerning the theoretical basis of the Forchheimer equation and experimental work on the identification of flow regimes is reviewed. These areas of work provide insights into the applicability of the Forchheimer equation to conventional oilfield flow tests for proppant packs. Models for flow beyond the Forchheimer regime are also suggested. Introduction The effect of non-Darcy flow as one of the most critical factors in reducing the productivity of hydraulically fractured high-rate wells has been documented extensively with examples of field cases (Barree and Conway 2004; Holditch and Morse 1976; Olson et al. 2004; Smith et al. 2004; Vincent et al. 1999). The inertia resistance factor, or the so-called beta factor, a parameter in the Forchheimer equation for quantifying the non-Darcy flow effect, is now routinely measured for proppant packs. Nevertheless, how to derive the beta factor from experimental data is still controversial. In the August 2005 issue of JPT, there was a discussion by van Batenburg and Milton-Tayler (2005) and a reply by Barree and Conway (2005) regarding paper SPE 89325 (Barree and Conway 2004) on whether the beta factor ß of a proppant pack should be constant over the range of flow rates of practical interests. The so-called non-Darcy flow in porous media occurs if the flow velocity becomes large enough so that Darcy's law (Darcy 1856) for the pressure gradient and the flow velocity, i.e.,(Eq. 1) is no longer sufficient. In Eq. 1, permeability k is an intrinsic property of porous media. To describe the nonlinear flow situation, a quadratic term was included by Dupuit (1863) and Forchheimer (1901) to generalize the flow equation, i.e.,(Eq. 2) is commonly known as the Forchheimer equation.

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