Evaluation of transverse dispersion coefficient under transient concentration condition

2004 ◽  
pp. 1251-1259
Author(s):  
I Seo ◽  
K Baek ◽  
S Jeong
Keyword(s):  
Dispersion Coefficient ◽  
Transverse Dispersion ◽  
Concentration Condition

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

A New Method for Laboratory Estimation of the Transverse Dispersion Coefficient

Ground Water ◽  
2011 ◽  
Vol 50 (2) ◽  
pp. 177-178 ◽  
Author(s):  
Jui-Sheng Chen ◽  
Chen-Wuing Liu ◽  
Yiu-Hsuan Liu
Keyword(s):  
Dispersion Coefficient ◽  
New Method ◽  
Transverse Dispersion

A New Method for Laboratory Estimation of the Transverse Dispersion Coefficient

Ground Water ◽  
2007 ◽  
Vol 45 (3) ◽  
pp. 339-347 ◽  
Author(s):  
Marco Massabò ◽  
Federico Catania ◽  
Ombretta Paladino
Keyword(s):  
Dispersion Coefficient ◽  
New Method ◽  
Transverse Dispersion

Design of Laboratory Models for Study of Miscible Displacement

1963 ◽  
Vol 3 (01) ◽  
pp. 28-40 ◽  
Author(s):  
Anthony L. Pozzi ◽  
Robert J. Blackwell
Keyword(s):  
Oil Recovery ◽  
Molecular Diffusion ◽  
Dispersion Coefficient ◽  
Miscible Displacement ◽  
Laboratory Model ◽  
Transverse Mixing ◽  
Model Studies ◽  
Geometric Similarity ◽  
Transverse Dispersion ◽  
Laboratory Models

Abstract Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments.If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media.From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion.Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion, These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. Introduction One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated.Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impracticality large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies.Craig, et al, demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled.The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. SPEJ P. 28^

Longitudinal and transverse dispersion coefficients in braided rivers

2014 ◽  
Vol 70 (2) ◽  
pp. 256-264 ◽  
Author(s):  
Li Gu ◽  
Zinan Jiao ◽  
Zulin Hua
Keyword(s):  
Separation Zone ◽  
Dispersion Coefficient ◽  
Braided River ◽  
Dispersion Characteristics ◽  
Dispersion Coefficients ◽  
Flow Rates ◽  
Braided Rivers ◽  
Transverse Dispersion ◽  
Upstream Flow ◽  
Natural Rivers

The dispersion characteristics of braided rivers are presently unclear. The comprehensive flow structure in a physical braided river model was measured and was used to estimate its dispersion coefficient tensor. The largest values of the longitudinal and transverse dispersion coefficients occurred in the separation zone in two anabranches. The separation zone disappeared in a small diversion angle model of braided rivers where the coefficients were smaller. As for the sectional transverse distribution, the two coefficients varied markedly and an interesting negative correlation between them appeared in several sections. The dispersion coefficients increased with upstream flow rates. Comparison between the coefficients for different anabranch widths revealed higher values in wider sections. Finally, the values of the laboratory tests were compared with those in a real braided river, and relatively larger coefficients were found in natural rivers. The findings of this paper could be helpful in understanding the dispersion characteristics and in estimating pollutant concentration in braided rivers.

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