Simulacion

A Mathematical Model for Dispersion in the Direction

Of Flow in Porous Media

H.A.DEANS

ABSTRACT

A three-parameter mathematical model for onedimensional

flow in porous media is developed.

The objective of the model is to predict accurately

the longitudinal dispersion associated with the

flow of either ga-'!!s or liquids over a wide range of

Reynolds number.

A qualitative analysis of the model parameters

is given. Published experimental pulse-response

curves are compared with results predicted by the

model. Several general types of problems are given

for which the model can be used.

INTRODUCTION

The problem of multi component single-phase flow

through porous media is encountered in the study

of petroleum reservoirs, gas chromatographic and

ion-exchange columns, industrial fixed-bed contacters

and elsewhere. These particular examples

span the wide range of flow conditions possible;

Reynolds numbers of less than 10-4 are not unusual

in oil-production problems, while values in excess

of 103 are common in large fixed-bed operations.

The study of flow-dependent transport phenomena

is complicated both by the changes in the character

of the flow over this range, and by the irregularity

of the flow boundaries inherent to porous media.

Dispersion is one of the important phenomena

known to depend fundamentally on flow conditions

as well as on fluid and medium properties. As used

in this paper, the term "dispersion" refers to the

observed mixing of fluid elements of different composition

which occurs in flow systems. The actual

mechanism may be one or more of a number listed

below. Only dispersion in the direction of the mean

flow (referred to as axial or longitudinal dispersion

(or mixing) is considered here, although lateral

dispersion arises as part of certain coupled mechanIsms.

MECHANISMS FOR LONGITUDINAL

DISPERSION

A number of distinct mechanisms are known3 ,S, 7,8

Original manuscript received in Society of Petroleum Engineers

office Sept. 5, 1962. Revised manuscript received Jan. 28,

1963. Paper presented at Joint SPE-AIChE SympOSium held

Aug. 26-29, 1962, in Denver, Colo.

1References given at end of paper.

RICE U.

HOUSTON, TEX.

to contribute to the phenomenon of longitudinal

dispersion. The more important of these are as

follows.

1. Molecular diffusion in the flow direction.

2. Turbulent (cell) mixing.

3. Lateral transport processes coupled with

velocity and/or residence time distributions,

incl uding: (a) "Taylor" diffusion

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