Transverse dispersion of non-reactive tracers in porous media: A new nonlinear relationship to predict dispersion coefficients

2007 ◽  
Vol 92 (3-4) ◽  
pp. 149-161 ◽  
Author(s):  
Åsa Olsson ◽  
Peter Grathwohl
Keyword(s):  
Porous Media ◽  
Nonlinear Relationship ◽  
Dispersion Coefficients ◽  
Transverse Dispersion ◽  
Reactive Tracers

scholarly journals Estimation of Longitudinal and Transverse Dispersion Coefficients in Saturated Porous Media Involving Physical Model

10.29007/ldlk ◽  
2018 ◽  
Author(s):  
Kumars Ebrahimi ◽  
Mohammad Reza Nazem ◽  
Zahra Mardani ◽  
Shahab Araghinejad ◽  
Abdolmajid Liaghat
Keyword(s):  
Porous Media ◽  
Groundwater Resources ◽  
Scale Model ◽  
Laboratory Model ◽  
Concentration Data ◽  
Dispersion Coefficients ◽  
Calculated Concentration ◽  
Plume Migration ◽  
Transverse Dispersion ◽  
Urban Population Growth

The world's urban population growth, indiscriminate use of fertilizers and chemical poisons are actually threatening groundwater resources. The main target of this paper has been tracking of distribution of a conservative tracer in a porous media and in a laboratory-scale model, to estimate the longitudinal and transverse dispersion coefficients. In this study non-cohesive sands were used to create the porous media body in the laboratory model with a grain diameter of 1-2.5 mm. Salt (NaCl) with concentrations of 5, 7.5 and 10 g/l were used as a tracer. The results of 5g/l concentration tests are reported in this paper. An EC-meter apparatus was used to measure the EC values of the tracer to monitor its plume migration. Then the collected and recorded EC data were used to calculate the tracer concentration data in different points over time, for each test. The calculated concentration data were compared with values which were obtained from the analytical solution using Fickian second law. According to the results, for instance, in the case of 5 g/l of the tracer, the obtained values of the longitudinal and transverse coefficients are equal to 3.36e-6 and 6.58e-7 m2/s, respectively.

scholarly journals Nonlinear viscoelastic compaction in sedimentary basins

2000 ◽  
Vol 7 (1/2) ◽  
pp. 1-8 ◽  
Author(s):  
X.-S. Yang
Keyword(s):  
Porous Media ◽  
Rheological Behaviour ◽  
Sedimentary Basins ◽  
Porous Media Flow ◽  
Pressure Solution ◽  
Nonlinear Behaviour ◽  
Nonlinear Relationship ◽  
Effective Pressure ◽  
Sediment Compaction ◽  
Nonlinear Viscoelastic

Abstract. In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure pe and porosity Φ, that is pe = pe (Φ). The compaction law is essentially a poroelastic one. However, viscous compaction due to pressure solution becomes important at larger depths and causes this relationship to become more akin to a viscous rheology. A generalised viscoelastic compaction model of Maxwell type is formulated, and different styles of nonlinear behaviour are asymptotically analysed and compared in this paper.

A Mathematical and Experimental Examination of Transverse Dispersion Coefficients

1968 ◽  
Vol 8 (02) ◽  
pp. 195-204 ◽  
Author(s):  
Robert C. Hassinger ◽  
Dale U. Von Rosenberg
Keyword(s):  
Porous Medium ◽  
Dispersion Coefficient ◽  
Packed Column ◽  
Packing Material ◽  
Longitudinal Dispersion ◽  
Physical Parameters ◽  
Dispersion Coefficients ◽  
Molecular Diffusivity ◽  
Transverse Dispersion ◽  
Wide Range

Abstract Transverse dispersion has received considerably less treatment in the literature than has longitudinal dispersion. Different methods for determining transverse dispersion coefficients have been used in different investigations, and the results obtained have not been consistent enough to permit accurate generalizations as to the effect of various physical parameters on the magnitude of these coefficients. A numerical solution to the differential equation describing transverse dispersion in the absence of longitudinal dispersion was obtained to enable one to calculate the dispersion coefficient from experimental results. The more general dispersion equation including longitudinal dispersion also was solved numerically to give quantitative limits of a dimensionless group within which the assumption of negligible longitudinal dispersion is justified. Possible experimental procedures were examined, and one utilizing a cylindrical packed column was chosen for the determination of transverse dispersion coefficients. Values of these coefficients were determined for a system of two miscible organic fluids of equal density and viscosity, for two sizes of packing material over a wide range of flow rates in the laminar regime. The dispersion coefficient was found to decrease, for a constant value of the product of packing size and interstitial velocity, as the size of the packing material particles increased. Introduction Longitudinal dispersion has received extensive treatment in the literature, and consequently is better understood than its orthogonal counterpart, transverse dispersion. Many mathematical models of dispersion processes assume that transverse dispersion is rapid enough to damp out any radial concentration gradients and therefore may be neglected. Laboratory and production results, however, indicate that this is a poor assumption. Various experimental procedures for determining transverse dispersion coefficients have been used in previous investigations, but the results have generally been expressed by similar correlations. The transverse dispersion coefficients obtained, however, have often varied considerably for given values of the correlation parameters. We feel that further experimental determinations of transverse dispersion coefficients will help alleviate some of the inconsistencies in these empirical correlations. One assumption implicit in all previous investigations is that of negligible longitudinal dispersion in the experimental system. An attempt to justify this assumption often is made using intuitive reasoning, but it is apparent that this reasoning must break down as the condition of zero flow rate is approached. A mathematical examination of the equations describing the system yields physical limits outside of which the assumption of negligible longitudinal dispersion is invalid. Background In a porous medium, the "effective molecular diffusivity" De is less than the molecular diffusivity D measured in the absence of a porous medium, due to the tortuous path which a diffusing molecule must travel. Various authors have reported values of the ratio De/D in the range of 0.6 to 0.7. When there is fluid flow within the porous medium, mass transfer occurs by convective dispersion as well as by molecular diffusion. These are separate phenomena and can be treated as such on a microscopic scale. However, the mathematical complexity is such that only extremely simple geometries could be considered, and the results hardly would be applicable to the complex geometries existent in actual porous media. SPEJ P. 195ˆ

Transverse dispersion at high Peclet numbers in short porous media

1996 ◽  
Vol 21 (4) ◽  
pp. 286-290 ◽  
Author(s):  
C. L. Hackert ◽  
J. L. Ellzey ◽  
O. A. Ezekoye ◽  
M. J. Hall
Keyword(s):  
Porous Media ◽  
Transverse Dispersion

scholarly journals Laboratory Determination of Transverse and Longitudinal Dispersion coefficients in Porous Media

1996 ◽  
Vol 38 (1) ◽  
pp. 13-27 ◽  
Author(s):  
Makoto NISHIGAKI ◽  
Teddy SUDINDA ◽  
Y. SASAKI ◽  
M. INOUE ◽  
T. MORIWAKI
Keyword(s):  
Porous Media ◽  
Longitudinal Dispersion ◽  
Dispersion Coefficients ◽  
Laboratory Determination

Experimental Investigation and Pore-Scale Modeling Interpretation of Compound-Specific Transverse Dispersion in Porous Media

2012 ◽  
Vol 93 (3) ◽  
pp. 347-362 ◽  
Author(s):  
Massimo Rolle ◽  
David Hochstetler ◽  
Gabriele Chiogna ◽  
Peter K. Kitanidis ◽  
Peter Grathwohl
Keyword(s):  
Experimental Investigation ◽  
Porous Media ◽  
Pore Scale ◽  
Scale Modeling ◽  
Transverse Dispersion ◽  
Pore Scale Modeling
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