scholarly journals On the validity of effective formulations for transport through heterogeneous porous media

2016 ◽  
Vol 20 (4) ◽  
pp. 1319-1330 ◽  
Author(s):  
Jean-Raynald de Dreuzy ◽  
Jesus Carrera
Keyword(s):  
Porous Media ◽  
Initial Conditions ◽  
Heterogeneous Porous Media ◽  
Local Concentration ◽  
Correlation Pattern ◽  
Effective Transport ◽  
Modeling Transport ◽  
Fine Structures ◽  
Dispersive Mixing ◽  
Permeability Field

Abstract. Geological heterogeneity enhances spreading of solutes and causes transport to be anomalous (i.e., non-Fickian), with much less mixing than suggested by dispersion. This implies that modeling transport requires adopting either stochastic approaches that model heterogeneity explicitly or effective transport formulations that acknowledge the effects of heterogeneity. A number of such formulations have been developed and tested as upscaled representations of enhanced spreading. However, their ability to represent mixing has not been formally tested, which is required for proper reproduction of chemical reactions and which motivates our work. We propose that, for an effective transport formulation to be considered a valid representation of transport through heterogeneous porous media (HPM), it should honor mean advection, mixing and spreading. It should also be flexible enough to be applicable to real problems. We test the capacity of the multi-rate mass transfer (MRMT) model to reproduce mixing observed in HPM, as represented by the classical multi-Gaussian log-permeability field with a Gaussian correlation pattern. Non-dispersive mixing comes from heterogeneity structures in the concentration fields that are not captured by macrodispersion. These fine structures limit mixing initially, but eventually enhance it. Numerical results show that, relative to HPM, MRMT models display a much stronger memory of initial conditions on mixing than on dispersion because of the sensitivity of the mixing state to the actual values of concentration. Because MRMT does not restitute the local concentration structures, it induces smaller non-dispersive mixing than HPM. However long-lived trapping in the immobile zones may sustain the deviation from dispersive mixing over much longer times. While spreading can be well captured by MRMT models, in general non-dispersive mixing cannot.

scholarly journals On the validity of effective formulations for transport through heterogeneous porous media

2015 ◽  
Vol 12 (11) ◽  
pp. 12281-12310 ◽  
Author(s):  
J.-R. de Dreuzy ◽  
J. Carrera
Keyword(s):  
Porous Media ◽  
Initial Conditions ◽  
Heterogeneous Porous Media ◽  
Local Concentration ◽  
Correlation Pattern ◽  
Effective Transport ◽  
Modeling Transport ◽  
Fine Structures ◽  
Dispersive Mixing ◽  
Permeability Field

Abstract. Geological heterogeneity enhances spreading of solutes, and causes transport to be anomalous (i.e., non-Fickian), with much less mixing than suggested by dispersion. This implies that modeling transport requires adopting either stochastic approaches that model heterogeneity explicitly or effective transport formulations that acknowledge the effects of heterogeneity. A number of such formulations have been developed and tested as upscaled representations of enhanced spreading. However, their ability to represent mixing has not been formally tested, which is required for proper reproduction of chemical reactions and which motivates our work. We propose that, for an effective transport formulation to be considered a valid representation of transport through Heterogeneous Porous Media (HPM), it should honor mean advection, mixing and spreading. It should also be flexible enough to be applicable to real problems. We test the capacity of the Multi-Rate Mass Transfer (MRMT) to reproduce mixing observed in HPM, as represented by the classical multi-Gaussian log-permeability field with a Gaussian correlation pattern. Non-dispersive mixing comes from heterogeneity structures in the concentration fields that are not captured by macrodispersion. These fine structures limit mixing initially, but eventually enhance it. Numerical results show that, relative to HPM, MRMT models display a much stronger memory of initial conditions on mixing than on dispersion because of the sensitivity of the mixing state to the actual values of concentration. Because MRMT does not restitute the local concentration structures, it induces smaller non-dispersive mixing than HPM. However long-lived trapping in the immobile zones may sustain the deviation from dispersive mixing over much longer times. While spreading can be well captured by MRMT models, non-dispersive mixing cannot.

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

Numerical Study of Density-Driven Convection in Laminated Heterogeneous Porous Media

2020 ◽  
Vol 36 (5) ◽  
pp. 665-673 ◽  
Author(s):  
Qian Li ◽  
Wei Hua Cai ◽  
Bing Xi Li ◽  
Ching-Yao Chen
Keyword(s):  
Porous Media ◽  
Numerical Study ◽  
Heterogeneous Porous Media ◽  
Convection Flow ◽  
Order Of Accuracy ◽  
Compact Finite Difference Scheme ◽  
Pseudo Spectral Method ◽  
Laminated Structures ◽  
Pseudo Spectral ◽  
Permeability Field

ABSTRACTIn the present study, we use direct numerical simulation to investigate the density-driven convection in a two-dimensional anisotropic heterogeneous porous media associated with significant laminated formation. At first, the heterogeneous porous media are randomly generated to represent laminated structure, in which the horizontal correlation length of permeability field is much longer than the vertical counterpart. Then, a highly accurate pseudo-spectral method and compact finite difference scheme with higher order of accuracy are employed to numerically reproduce the convection flow in the laminated porous media. The results show that the laminated structures restrict interactions among the downward plumes of heavier fluid. The plumes tend to descend more straightly in a laminated porous medium associated with a slower growth rate. As a result, the laminated distribution of permeability is considered having an inhibiting effect on the convection flow.

Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures

2014 ◽  
Vol 24 (07) ◽  
pp. 1421-1451 ◽  
Author(s):  
Brahim Amaziane ◽  
Leonid Pankratov ◽  
Andrey Piatnitski
Keyword(s):  
Porous Media ◽  
Water Saturation ◽  
Initial Conditions ◽  
Coupled System ◽  
Heterogeneous Porous Media ◽  
Gas Pressure ◽  
Absolute Permeability ◽  
Two Phase ◽  
Effective Coefficients ◽  
Nonlinear Degenerate

This paper presents a study of immiscible compressible two-phase, such as water and gas, flow through highly heterogeneous porous media with periodic microstructure. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. We will consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. Consequently, the model involves highly oscillatory characteristics and internal nonlinear interface conditions. The microscopic model is written in terms of the phase formulation, i.e. where the wetting (water) saturation phase and the non-wetting (gas) pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion-convection equation for the water saturation, subject to appropriate transmission, boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Moreover, the transmission conditions are nonlinear and the saturation is discontinuous at interfaces separating different media. Under some realistic assumptions on the data, we obtain a nonlinear homogenized coupled system with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence.

scholarly journals Protein Kinase A Distribution in Meningioma

Cancers ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1686 ◽  
Author(s):  
Caretta ◽  
Denaro ◽  
D’Avella ◽  
Mucignat-Caretta
Keyword(s):  
Brain Tissue ◽  
Catalytic Subunit ◽  
Therapeutic Interventions ◽  
Normal Brain ◽  
Local Concentration ◽  
Correlation Pattern ◽  
Catalytic Subunits ◽  
Tissue Specimens ◽  
Pka Catalytic Subunit

Deregulation of intracellular signal transduction pathways is a hallmark of cancer cells, clearly differentiating them from healthy cells. Differential intracellular distribution of the cAMP-dependent protein kinases (PKA) was previously detected in cell cultures and in vivo in glioblastoma and medulloblastoma. Our goal is to extend this observation to meningioma, to explore possible differences among tumors of different origins and prospective outcomes. The distribution of regulatory and catalytic subunits of PKA has been examined in tissue specimens obtained during surgery from meningioma patients. PKA RI subunit appeared more evenly distributed throughout the cytoplasm, but it was clearly detectable only in some tumors. RII was present in discrete spots, presumably at high local concentration; these aggregates could also be visualized under equilibrium binding conditions with fluorescent 8-substituted cAMP analogues, at variance with normal brain tissue and other brain tumors. The PKA catalytic subunit showed exactly overlapping pattern to RII and in fixed sections could be visualized by fluorescent cAMP analogues. Gene expression analysis showed that the PKA catalytic subunit revealed a significant correlation pattern with genes involved in meningioma. Hence, meningioma patients show a distinctive distribution pattern of PKA regulatory and catalytic subunits, different from glioblastoma, medulloblastoma, and healthy brain tissue. These observations raise the possibility of exploiting the PKA intracellular pathway as a diagnostic tool and possible therapeutic interventions.

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