Salt diffusion in charged porous media

2020 ◽  
Author(s):  
Pavan Cornelissen ◽  
Anton Leijnse ◽  
Vahid Joekar-Niasar ◽  
Sjoerd van der Zee
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Double Layer ◽  
Effective Diffusion ◽  
Pore Network ◽  
Salt Transport ◽  
Double Layers ◽  
Diffuse Double Layer ◽  
Low Salinity ◽  
Charged Surfaces

<p>Some porous media such as clay have charged surfaces. The presence of these charged surfaces results in a complex system where water flow, salt transport, and the electric field are coupled. This system is important in many fields, such as geotechnical engineering, storage of radioactive waste in clay barriers, enhanced oil recovery, and irrigation with marginal water. The charged surfaces alter the transport properties of ions. For example, clay minerals are often negatively charged due to isomorphous substitution. Cations are therefore attracted to the mineral surface, while anions are repelled, creating a diffuse double layer around the clay particle. Cations are therefore transported preferably over anions through such charged pores. To conserve electroneutrality, a streaming potential develops to counteract diffusion by electromigration. This results in smaller effective diffusion coefficients compared to uncharged porous media. We developed a pore-network model to quantify the effect of the double layer processes on the effective diffusion coefficient. Pore-network models are a suitable tool to include the heterogeneity of pore sizes and surface charge densities seen in nature. In pore-network modeling, the geometry of the pore space is simplified, but the network properties are based on realistic statistics such as pore size distribution and connectivity. The larger scale behavior can be identified by averaging over a large number of pores. The results were strongly dependent on the salinity, as this controls the thickness of the double layers. At high salt concentrations, the diffuse double layer is thin and the differences between charged and uncharged porous media are negligible. However, at low salinity, the double layers are thick and the effective diffusion coefficient of salt was reduced by 25% in charged porous media compared to uncharged porous media, due to salt transport being slowed down to conserve electroneutrality. Hence, the presence of charged mineral surfaces can significantly alter transport rates under low salinity conditions.</p>

scholarly journals Diffusion of calcium ions in retinal rods. A theoretical calculation.

1981 ◽  
Vol 77 (4) ◽  
pp. 475-487 ◽  
Author(s):  
S McLaughlin ◽  
J Brown
Keyword(s):  
Diffusion Coefficient ◽  
Adsorption Isotherm ◽  
Calcium Ions ◽  
Outer Segment ◽  
Effective Diffusion ◽  
Langmuir Adsorption Isotherm ◽  
Diffuse Double Layer ◽  
Langmuir Adsorption ◽  
Retinal Rods ◽  
Disk Membrane

The Fick diffusion equation is combined with the Langmuir adsorption isotherm and the relevant equations from the Gouy-Chapman theory of the electrical diffuse double layer to demonstrate that the effective diffusion coefficient of calcium ions, both in the cytoplasm of the rod outer segment and within the aqueous space bounded by the disk membrane, should be reduced by a factor of 10-100 because these ions adsorb to phospholipids present in the disk membrane.

scholarly journals Bulk and Surface Aqueous Speciation of Calcite: Implications for Low-Salinity Waterflooding of Carbonate Reservoirs

SPE Journal ◽  
2017 ◽  
Vol 23 (01) ◽  
pp. 84-101 ◽  
Author(s):  
Maxim P. Yutkin ◽  
Himanshu Mishra ◽  
Tadeusz W. Patzek ◽  
John Lee ◽  
Clayton J. Radke
Keyword(s):  
Ionic Strength ◽  
Ion Exchange ◽  
Crude Oil ◽  
Surface Charge ◽  
Double Layer ◽  
Carbonate Reservoir ◽  
Carbonate Reservoirs ◽  
Diffuse Double Layer ◽  
Low Salinity ◽  
Low Salinity Waterflooding

Summary Low-salinity waterflooding (LSW) is ineffective when reservoir rock is strongly water-wet or when crude oil is not asphaltenic. Success of LSW relies heavily on the ability of injected brine to alter surface chemistry of reservoir crude-oil brine/rock (COBR) interfaces. Implementation of LSW in carbonate reservoirs is especially challenging because of high reservoir-brine salinity and, more importantly, because of high reactivity of the rock minerals. Both features complicate understanding of the COBR surface chemistries pertinent to successful LSW. Here, we tackle the complex physicochemical processes in chemically active carbonates flooded with diluted brine that is saturated with atmospheric carbon dioxide (CO2) and possibly supplemented with additional ionic species, such as sulfates or phosphates. When waterflooding carbonate reservoirs, rock equilibrates with the injected brine over short distances. Injected-brine ion speciation is shifted substantially in the presence of reactive carbonate rock. Our new calculations demonstrate that rock-equilibrated aqueous pH is slightly alkaline quite independent of injected-brine pH. We establish, for the first time, that CO2 content of a carbonate reservoir, originating from CO2-rich crude oil and gas, plays a dominant role in setting aqueous pH and rock-surface speciation. A simple ion-complexing model predicts the calcite-surface charge as a function of composition of reservoir brine. The surface charge of calcite may be positive or negative, depending on speciation of reservoir brine in contact with the calcite. There is no single point of zero charge; all dissolved aqueous species are charge determining. Rock-equilibrated aqueous composition controls the calcite-surface ion-exchange behavior, not the injected-brine composition. At high ionic strength, the electrical double layer collapses and is no longer diffuse. All surface charges are located directly in the inner and outer Helmholtz planes. Our evaluation of calcite bulk and surface equilibria draws several important inferences about the proposed LSW oil-recovery mechanisms. Diffuse double-layer expansion (DLE) is impossible for brine ionic strength greater than 0.1 molar. Because of rapid rock/brine equilibration, the dissolution mechanism for releasing adhered oil is eliminated. Also, fines mobilization and concomitant oil release cannot occur because there are few loose fines and clays in a majority of carbonates. LSW cannot be a low-interfacial-tension alkaline flood because carbonate dissolution exhausts all injected base near the wellbore and lowers pH to that set by the rock and by formation CO2. In spite of diffuse double-layer collapse in carbonate reservoirs, surface ion-exchange oil release remains feasible, but unproved.

Diffusion velocity lattice Boltzmann formulation applied to transport in macroscopic porous media

2014 ◽  
Vol 25 (12) ◽  
pp. 1441006 ◽  
Author(s):  
Janez Perko ◽  
Ravi A. Patel
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Lattice Boltzmann ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Hydrodynamic Dispersion ◽  
Traditional Treatment ◽  
Dissipative Term ◽  
Diffusion Velocity ◽  
Variable Diffusion

This paper describes the application of a single relaxation time (SRT) lattice Boltzmann scheme to the transport in porous media with large spatial variations of diffusion coefficients. Effective diffusion coefficients can vary substantially within porous media because of their dependence on porosity and tortuosity which can span over several orders of magnitude, depending on pore size and connectivity. Moreover, when mass is transported with pore-water in porous media, the hydrodynamic dispersion, which depends on Darcy's velocity, contributes additionally to the usually anisotropic variation of the dissipative term. In contrast to the traditional treatment of spatially variable diffusion coefficient by the variation of a SRT, here the variability is accommodated through the use of diffusion velocity formulation which allows for larger variabilities of diffusion coefficient. The volume averaged properties of mass transport in macroscopic porous media are resolved through the additional source term which is similar to the existing force adjusting methods. The applicability of both the proposed schemes is demonstrated on two examples. The first demonstrates that the method is accurate for the large variation of diffusion coefficients and porosities. The second example introduces mass diffusion in a real, geometrically complex system with spatially contrasting properties.

Taylor-Like Dispersion of Charged Species in Electrokinetically-Driven Nanoflows

2005 ◽  
Author(s):  
Angela De Leebeeck ◽  
David A. Sinton
Keyword(s):  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Double Layers ◽  
Stream Velocity ◽  
Velocity Gradients ◽  
Electrical Double Layers ◽  
Electric Double Layer Thickness ◽  
Charged Ions ◽  
Double Layer Thickness

In this paper, electrokinetic dispersion of charged and uncharged species in nanochannels with finite electric double layers is modelled numerically. The relatively thick electrical double layers in these flows influence dispersion through the coupled effects of both cross-stream electromigration and advection in the presence of cross-stream velocity gradients. It is found that valence charge has a significant effect on axial dispersion in these flows, in addition to other established dependencies. Effective diffusion coefficients were found to vary over 30% from the case of neutral species for single charged ions. An effective diffusion coefficient similar to Taylor dispersion is calculated and a relationship between effective diffusion coefficient, Peclet number, relative electric double layer thickness, and valence charge is plotted.

scholarly journals Mathematical Model for Effective Gas Diffusion Coefficient in Multi-scale Fractal Porous Media

2021 ◽  
Vol 248 ◽  
pp. 01026
Author(s):  
Du Zhehua
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Diffusion Coefficient ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Effective Diffusion ◽  
Gas Diffusion ◽  
Pore Connectivity ◽  
Multi Scale ◽  
Pore Area

Based on the capillary hypothesis and fractal theory, a mathematical model for calculating the effective gas diffusion coefficient in porous media is established. By using fractal geometry theory, pore area fractal dimension, tortuosity fractal dimension and pore connectivity are introduced to quantitatively characterize the real internal structure in the porous media. An effective gas diffusion coefficient model for the fractal porous media is derived, and the influence of multi-scale porous media microstructure parameters on the effective gas diffusion coefficient is discussed. The results show that effective gas diffusion coefficient approximates to linearly increase with the increase of porosity, the pore area fractal dimension and the effective gas diffusion coefficient is positive correlation, but the tortuosity fractal dimension is negatively related to it. In the case of different porosities, the gas effective diffusion coefficient varies with the change of the pore diameter ratio, the effective gas diffusion coefficient increases with the increase of pore connectivity.

scholarly journals On the diffuse double layer

1933 ◽  
Vol 139 (839) ◽  
pp. 596-603 ◽  
Keyword(s):  
Double Layer ◽  
Colloidal Particles ◽  
Mutual Influence ◽  
Streaming Potential ◽  
Specific Adsorption ◽  
Double Layers ◽  
Diffuse Double Layer ◽  
Plane Parallel ◽  
Parallel Surfaces

1. The formulæ derived by Gouy for the diffuse double layer hold only in the case of a single surface in an infinite amount of medium. In practice they are not very suitable, for very frequently we have to deal either with capillaries, as in streaming potential measurements, or with colloidal particles which may be near enough to influence one another. In these cases it is too difficult to calculate the effect of the mutual influence of two double layers, though in less complicated systems it is possible. Suppose we have two plane parallel surfaces separated by a distance 2 h and charged both to the same potential, in a solution of an electrolyte. If the dimensions of the surfaces are large compared with the distance h there will be no drop of potential between the two. We therefore need to make the assumption (which was superfluous in Gouy’s case) of a specific adsorption by the surface of one or more of the ions in the solution, otherwise there will be no double layer at all; the same effect will also be obtained if ions of the surface dissolve.

NOTE ON THE THEORY OF ELECTROLYTIC DOUBLE LAYERS

1949 ◽  
Vol 27b (7) ◽  
pp. 682-687
Author(s):  
A. J. Dekker
Keyword(s):  
Double Layer ◽  
Double Layers ◽  
Diffuse Double Layer ◽  
Diffuse Part ◽  
Convenient Formula

The mechanism suggested by Gurney for the formation of a double layer at the interface of a metal and a solution containing its ions is applied to a diffuse double layer. The diffuse part of the double layer is treated in a way that differs from Stern's method, leading to a more convenient formula for the potential ψδ of the diffuse part. Numerical values and a comparison with Stern's results are given.

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