scholarly journals Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift

Energies ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 29 ◽  
Author(s):  
Lateef Akanji ◽  
Gabriel Falade
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Closed Form ◽  
Oil Recovery ◽  
Closed Form Solution ◽  
Radial Transport ◽  
Tracer Concentration ◽  
Tracer Injection ◽  
Linear Drift ◽  
The Impact

A new closed-form analytical solution to the radial transport of tracers in porous media under the influence of linear drift is presented. Specifically, the transport of tracers under convection–diffusion-dominated flow is considered. First, the radial transport equation was cast in the form of the Whittaker equation by defining a set of transformation relations. Then, linear drift was incorporated by considering a coordinate-independent scalar velocity field within the porous medium. A special case of low-intensity tracer injection where molecular diffusion controls tracer propagation but convection with linear velocity drift plays a significant role was presented and solved in Laplace space. Furthermore, a weak-form numerical solution of the nonlinear problem was obtained and used to analyse tracer concentration behaviour in a porous medium, where drift effects predominate and influence the flow pattern. Application in enhanced oil recovery (EOR) processes where linear drift may interfere with the flow path was also evaluated within the solution to obtain concentration profiles for different injection models. The results of the analyses indicated that the effect of linear drift on the tracer concentration profile is dependent on system heterogeneity and progressively becomes more pronounced at later times. This new solution demonstrates the necessity to consider the impact of drift on the transport of tracers, as arrival times may be significantly influenced by drift intensity.

scholarly journals Experimental study of the supercritical CO 2 diffusion coefficient in porous media under reservoir conditions

2019 ◽  
Vol 6 (6) ◽  
pp. 181902 ◽  
Author(s):  
Junchen Lv ◽  
Yuan Chi ◽  
Changzhong Zhao ◽  
Yi Zhang ◽  
Hailin Mu
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Oil Recovery ◽  
Carbon Capture ◽  
Carbon Capture And Storage ◽  
Elevated Pressure ◽  
Experimental Results ◽  
Saturated Porous Media ◽  
Reservoir Conditions ◽  
The Impact

Reliable measurement of the CO 2 diffusion coefficient in consolidated oil-saturated porous media is critical for the design and performance of CO 2 -enhanced oil recovery (EOR) and carbon capture and storage (CCS) projects. A thorough experimental investigation of the supercritical CO 2 diffusion in n -decane-saturated Berea cores with permeabilities of 50 and 100 mD was conducted in this study at elevated pressure (10–25 MPa) and temperature (333.15–373.15 K), which simulated actual reservoir conditions. The supercritical CO 2 diffusion coefficients in the Berea cores were calculated by a model appropriate for diffusion in porous media based on Fick's Law. The results show that the supercritical CO 2 diffusion coefficient increases as the pressure, temperature and permeability increase. The supercritical CO 2 diffusion coefficient first increases slowly at 10 MPa and then grows significantly with increasing pressure. The impact of the pressure decreases at elevated temperature. The effect of permeability remains steady despite the temperature change during the experiments. The effect of gas state and porous media on the supercritical CO 2 diffusion coefficient was further discussed by comparing the results of this study with previous study. Based on the experimental results, an empirical correlation for supercritical CO 2 diffusion coefficient in n -decane-saturated porous media was developed. The experimental results contribute to the study of supercritical CO 2 diffusion in compact porous media.

scholarly journals On the impact of antenna diversity in IEEE 802.11b DCF with capture

2004 ◽  
Vol 17 (1) ◽  
pp. 41-52
Author(s):  
Zoran Velkov-Hadzi ◽  
Boris Spasenovski
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Access Point ◽  
Form Solution ◽  
Capture Probability ◽  
Antenna Diversity ◽  
Ieee 802.11B ◽  
Selection Diversity ◽  
Maximum Selection ◽  
The Impact

In this paper, we examined the influence of capture effect with L-fold antenna diversity at the Access Point over IEEE 802.11b DCF. We obtained an exact closed-form solution for the conditional capture probability in case of ideal selection diversity, and an approximate closed-form solution for the conditional capture probability in case of maximum selection diversity in a Rayleigh-faded channel. Obtained analytical expressions have general significance and can be applied for any other multiple access wireless network. We also analytically evaluated saturation throughput increase of the IEEE 802.11b DCF protocol exposed to capture.

Capillary Impregnation of Viscous Fluids in a Multi-Layered Porous Medium

2019 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Viscous Fluids ◽  
Spontaneous Imbibition ◽  
Lab On Chip ◽  
Capillary Impregnation ◽  
Relative Placement ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

Abstract Capillary impregnation of viscous fluids in porous media is useful in diagnostics, design of lab-on-chip devices and enhanced oil recovery. The impregnation of a wetting fluid in a homogeneous porous medium follows Washburn’s diffusive law. The diffusive dynamics predicts that, with the increase in permeability, the rate of spontaneous imbibition of a wetting fluid also increases. As most of the naturally occurring porous media are composed of hydrodynamically interacting layers having different properties, the impregnation in a heterogeneous porous medium is significantly different from a homogeneous porous medium. A Washburn like model has been developed in the past to predict the imbibition behavior in the layers for a hydrodynamically interacting three layered porous medium filled with a non-viscous resident phase. It was observed that the relative placement of the layers impacts the imbibition phenomena significantly. In this work, we develop a quasi one-dimensional lubrication approximation to predict the imbibition dynamics in a hydrodynamically interacting multi-layered porous medium. The generalized model shows that the arrangement of layers strongly affects the saturation of wetting phase in the porous medium, which is crucial for oil recovery and in microfluidic applications.

A closed-form solution to eye-to-hand calibration towards visual grasping

2014 ◽  
Vol 41 (6) ◽  
pp. 567-574 ◽  
Author(s):  
Hui Pan ◽  
Na Li Wang ◽  
Yin Shi Qin
Keyword(s):  
Closed Form ◽  
Design Methodology ◽  
Closed Form Solution ◽  
Form Solution ◽  
Content Type ◽  
The Impact ◽  
Calibration Plane

Purpose – The purpose of this paper is to propose a method that calibrates the hand-eye relationship for eye-to-hand configuration and afterwards a rectification to improve the accuracy of general calibration. Design/methodology/approach – The hand-eye calibration of eye-to-hand configuration is summarized as a equation AX = XB which is the same as in eye-in-hand calibration. A closed-form solution is derived. To abate the impact of noise, a rectification is conducted after the general calibration. Findings – Simulation and actual experiments confirm that the accuracy of calibration is obviously improved. Originality/value – Only a calibration plane is required for the hand-eye calibration. Taking the impact of noise into account, a rectification is carried out after the general calibration and, as a result, that the accuracy is obviously improved. The method can be applied in many actual applications.

scholarly journals A homogenised model for flow, transport and sorption in a heterogeneous porous medium

2021 ◽  
Vol 932 ◽  
Author(s):  
L.C. Auton ◽  
S. Pramanik ◽  
M.P. Dalwadi ◽  
C.W. MacMinn ◽  
I.M. Griffiths
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Multiple Scales ◽  
Effective Diffusivity ◽  
Rectangular Lattice ◽  
Mathematical Framework ◽  
Anisotropic Flow ◽  
Flow And Transport ◽  
Soft Porous Media ◽  
The Impact

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Diffusion limited mixing in heterogeneous porous media

2021 ◽  
Author(s):  
Mayumi Hamada ◽  
Pietro de Anna
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flow Field ◽  
Fast Diffusion ◽  
Pore Scale ◽  
Mixing Processes ◽  
Local Flow ◽  
Gaussian Shape ◽  
Diffusion Limited ◽  
The Impact

<p><span><span>A pore-scale description of the transport and mixing processes is particularly relevant when looking at biological and chemical reactions. For instance, a microbial population growth is controlled by local concentrations of nutrients and oxygen, and chemical reaction are driven by molecular-scale concentration gradients. The heterogeneous flow field typically found in porous media results from the contrast of velocities that deforms and elongates the mixing fronts between solutes that often evolves through a lamella-like topology. For continuous Darcy type flow field a novel framework that describes the statistical distribution of concentration being transported was recently developed (Le Borgne et al., JFM 2015). In this model, concentrations in each lamella are distributed as a Gaussian-like profile which experiences diffusion in the transverse direction while the lamella is elongated by advection along the local flow direction. The evolving concentration field is described as the superposition of each lamella. We hypothesize that this novel view, while perfectly predicting the distribution of concentration for Darcy scale mixing processes, will breakdown when the processes description is at the pore scale. Indeed the presence of solid and impermeable boundaries prevents lamella concentration to diffuse freely according to the a Gaussian shape, and therefore changes the mixing front profile, the lamella superposition and elongation rules. P</span></span><span><span>revious work (Hamada et al, PRF, 2020) demonstrated that </span></span><span><span>the presence of solid boundaries leads to an enhanced diffusion and thus fast homogenization of concentrations. </span></span><span><span>In a purely diffusive process the local mixing time is reduced by a factor of ten with respect to the </span></span><span><span>continuous case and concentration gradient are dissipated exponentially fast while a </span></span><span><span>power law decrease </span></span><span><span>is </span></span><span><span>observed in continuous medium.</span></span><span><span> To investigate the impact of these mechanisms on mixing we developed a</span></span><span><span>n experimental set-up to visualize and quantify the displacement of a conservative tracer in a synthetic porous medium. The designed apparatus allows to obtain high resolution concentration measurement</span></span><span><span>s</span></span><span><span> at the pore scale. We show that the resulting mixing measures, computed in terms of concentration probability density function and dilution index values, diverge </span></span><span><span>qualitatively and quantitatively from what happens in a continuous domain. These observations suggest </span></span><span><span>that description of pore-scale diffusion-limited mixing requires model that takes into account the confined nature of porous medium, </span></span><span><span>otherwise we will tend to overestimate concentration value and neglect the fast diffusion dynamic taking place at microscopic level.</span></span></p>

A numerical study of particle migration in porous media during produced water reinjection

2021 ◽  
pp. 1-34
Author(s):  
Tian Xia ◽  
Qihong Feng ◽  
Sen Wang ◽  
Qinglin Shu ◽  
Yigen Zhang ◽  
...  
Keyword(s):  
Particle Size ◽  
Porous Media ◽  
Oil Recovery ◽  
Produced Water ◽  
Numerical Study ◽  
Particle Diameter ◽  
Particle Migration ◽  
Critical Ratio ◽  
Clear Understanding ◽  
The Impact

Abstract The clogging phenomenon often occurs during the reinjection of produced water due to the suspended particles, which will deteriorate the development efficiency. Many experimental and analytical methods have been introduced to solve this problem; however, few numerical approaches have been proposed to investigate the particle migration in the produced water reinjection process. Moreover, it is hard to obtain a clear understanding directly from the particle scale when the injected particles have different sizes. This paper employs a coupled lattice Boltzmann method and discrete element method (LBM-DEM) to study the aforementioned process. The method was validated by reproducing the Drafting-Kissing-Tumbling (DKT) process. Simulations of migration of injected particles with different sizes through porous media were conducted and three clogging scenarios had been identified. We investigated the impact of injected particle size distribution and porous media on particle migration and concluded the results in the polydisperse aspect. From the simulation, we can conclude that mix clogging is the scenario we should try to avoid. Besides, both critical ratio of particle diameter of porous media to median particle diameter of injected particles (D/d50) and critical standard deviation value exist. The particle size range should be as small as possible in economical limits and the D/d50 value should be larger than the critical value. Our results can provide a good guide for the produced water pretreatment, which can improve oil recovery.

scholarly journals Modelling and simulation of waves in three-layer porous media

2013 ◽  
Vol 20 (6) ◽  
pp. 1023-1030 ◽  
Author(s):  
S. R. Pudjaprasetya
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Gravity Waves ◽  
Wave Reflection ◽  
Single Layer ◽  
Reflection And Transmission ◽  
Weakly Nonlinear ◽  
Model Equations ◽  
The Impact ◽  
Wave Transmission Coefficient

Abstract. The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a weakly nonlinear Boussinesq-type diffusion equation for the wave height, with coefficients dependent on the conductivities and depths of each layer. In the limit of equal conductivities of all layers, the equation reduces to the single-layer result recorded in the literature. The model equations are numerically integrated in the case of an incident monochromatic wave hitting the layers. The results exhibit dissipation and also a downstream net height rise at infinity. Wave transmission coefficient in three-layer porous media with conductivity of mangrove is discussed. Numerically, propagation of an initial solitary wave through a porous medium shows the emergence of wave reflection and transmission that both evolve as permanent waves. Additionally we examine the impact of a solitary gravity wave on a porous medium breakwater.

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