Geoscience Reference

In-Depth Information

For the explicit case, there are then several

options for how this may be done:

1.
Discrete Fracture Network (DFN) models,

where individual fractures with explicit geom-

etry are modelled in a complex network.

2.
Dual permeability models,
where the fracture

and matrix permeability are explicitly

represented (but fracture geometry is implic-

itly represented by a shape factor).

3.
Dual porosity models,
where the fracture

and matrix porosity are explicitly represented,

but the permeability is assumed to occur

only in the fractures

b

q

w

L

Fig. 3.13
Flow in a fracture

(and the fracture

geometry is

implicitly represented by a

shape factor).

Fractured reservoir modelling is discussed in

detail by Nelson (
2001
) and covered in most

reservoir engineering textbooks, and in Chap.
6

we describe approaches for handling fractured

reservoir models. The important thing to keep

in mind in the context of understanding perme-

ability, is that fractures behave quite differently

(and follow different laws) from the general

Darcy-flow concept for flow in permeable (gran-

ular) rock media.

law, which for a parallel-plate geometry gives

(Mourzenko et al.
1995
):

wb
3

12

ʔ

P

L

q

¼

ð

3

:

12

Þ

ʼ

where

q is the volumetric flow rate,

w is the fracture width,

b is the fracture aperture,

ʼ

is the fluid viscosity,

ʔ

P/L is the pressure gradient.

Note that the flow rate is proportional to b
3
,

and thus highly dependent on fracture aperture.

In practice, the flow strongly depends on the

stress state and the fracture roughness

(Witherspoon et al.
1980
), but the underlying

concept still holds. To put some values into this

simple equation - a 1 mm wide fracture in an

impermeable rock matrix would have an effec-

tive permeability of around 100 Darcys.

Unfortunately, fracture aperture is not easily

measured, and generally has to be inferred from

pressure data. This makes fracture systems much

harder to model than conventional non-fractured

reservoirs.

In practice, there are two general approaches

for modelling fracture permeability:

Implicitly, where we model the overall rock

permeability (matrix and fractures) and

assume we have captured the “effect of

fractures” as an effective permeability.

Explicitly, where we represent the fractures in

a model.

3.3

Handling Statistical Data

3.3.1 Introduction

Many misunderstandings about upscaled perme-

ability, or any other reservoir property, are caused

by incorrect understanding or use of probability

distributions. The treatment of probability

distributions is an extensive subject covered in a

number of textbooks. Any of the following are

suitable for geoscientists and engineers wanting to

gain deeper appreciation of statistics and the Earth

sciences: Size
1987
; Isaaks and Srivastava
1989
;

Olea
1991
;Jensenetal.
2000
,andDavis
2003
.Here

we will identify some of the most important issues

related to property modelling, namely:

Understanding sample versus population

statistics;

Using log-normal and other transforms;

Use and implications of applying cut-off values.