Geoscience Reference

In-Depth Information

The reservoir model

is 'data-driven' and the

Modifying the Kozeny-Carmen equation

gives:

carefully-modelled k-

transform aims to capture

the complex relationship between porosity and

permeability.

ϕ

r

k

Ø
e

Ø
e

0

:

0314

¼

Ø
e
F
zi

ð

3

:

23

Þ

1

ϕ
e
is the effective porosity

F
zi
is a function of the tortuosity,

where k is in mD and

, the shape

factor, F
s
, and the surface area per unit grain

volume, S
gv
:

˄

3.3.5 Hydraulic Flow Units

The Hydraulic Flow Unit (HFU) concept offers a

useful way of classifying properties on the k-

1

F
p
S
gv

F
zi
¼

ð

3

:

24

Þ

ϕ

cross-plot, and can be linked to the definition of

model elements in a modelling study.

Abbaszadeh et al. (
1996
) defined HFU's in

terms of a modified Kozeny-Carmen equation

in which a Flow Zone Indicator, F
zi
, was used

to capture the shape factor and tortuosity terms.

˄

The F
zi
term thus gives a formal relationship

between k and ø which is related to pore-scale

flow physics (laminar flow in a packed bed of

spherical particles).

the spatial distribution of permeability. The

two distributions appear to match quite

well - they cover a similar range and have

a similar arithmetic mean. However, analy-

sis of the data statistics reveals some strange

behaviour - the geometric and harmonic

means are quite different.

What is going on here? And is this in

fact a good model for the given data?

Exercise 3.4

Comparing model distributions to data.

The plot and table below show a compari-

son of well data with the output of a model

realisationdesignedtorepresentthedataina

geological model. The well data are from a

cored well interval identified as a deltaic

sandstone facies. The model has used

Gaussian statistical modelling to represent

0.4

Model #n

Well Data

0.3

0.2

0.1

0.0

0.1

1

10

100

1000

10000

Permeability (md)

Statistics

Well data

Model #n

Number of data values/cells

30

150

Arithmetic mean

119.9

115.7

Geometric mean

45.9

90.8

Harmonic mean

17.19

0.87