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Scaling mixing during miscible displacement in heterogeneous porous media

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Abstract

This paper discusses scaling of mixing during miscible flow in heterogeneous porous media. In large field systems dispersivity appears to depend on system length due to heterogeneities. Three types of scaling are discussed to investigate the heterogeneous effects. Dimensional analysis of mixing during flow through geometerically scaled heterogeneous models is illustrated using measured dispersion. Fractal analysis of mixing in statistically scaled heterogeneous porous media is discussed. Analog scaling of pressure transients in heterogeneous porous media is suggested as an in-situ method of estimating dispersion.

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Abbreviations

L:

Length

M:

mass

t:

time, (1) indicates dimensionless

a:

dispersivity (L)

V:

local velocity (L/t)

c:

concentration (l).

v:

velocity (L/t)

C1 :

fluid compressibility (Lt2/M)

v:

time averaged velocity (LJt)

D:

dispersion VA)

W:

width (L)

D:

fractional dimension (1)

x:

coordinate (L)

d:

Euclidean dimension (1)

Y:

Y=In \-k (l)

\-d:

average particle size (L)

y:

coordinate (L)

g:

acceleration due to gravity (L/t2)

εc :

fractal cutoff (L)

\-k:

average permeability (L2)

μ:

viscosity (LM/t)

L:

length (L)

Ω:

porosity (1)

Lγ :

correlation scale (1/L)

π:

density (N/L3)

N:

Number of sites (l)

σ2 :

variance (dimension depends on variable)

p:

pressure (W/t2L)

σ:

spectral exponent (l)

[R]:

randomnumber (1)

r:

radius (L)

t:

time (t)

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Authors and Affiliations

  1. School of Chemical Engineering Purdue University, 47907, West Lafayette, IN, USA

    Robert A. Greenkorn & John S. Haselow

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  1. Robert A. Greenkorn
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  2. John S. Haselow
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Greenkorn, R.A., Haselow, J.S. Scaling mixing during miscible displacement in heterogeneous porous media. Transp Porous Med 6, 607–626 (1991). https://doi.org/10.1007/BF00137852

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