Geoscience Reference

In-Depth Information

Fig. 3.39
Example modelling of randomly distributed

calcite cement barriers in an example reservoir (Reservoir

is c. 80 m thick) (

(

) Upscaled k
v
as vertical transmissibility multipliers

(Modified from Ringrose et al.
2005
, Petrol Geoscience,

Volume 11,

b

a

) Fine-scale model of calcite barriers.

Geological Society of London [2005])

#

f
is the barrier frequency

d is a mudstone dimension

(d

3.6.3 Modelling of Permeability

Anisotropy

L
m
/2 for a 2D system with mean mudstone

length, L
m
).

This method is valid for low mudstone vol-

ume fractions and assumes thin, uncorrelated,

impermeable, discontinuous mudstone layers.

Desbarats (
1987
) estimated effective perme-

ability for a complete range of mudstone volume

fractions in 2D and 3D, using statistical models

with spatial covariance and a range of

anisotropies. For strongly stratified media, the

effective horizontal permeability, k
he
, was found

to approach the arithmetic mean, while k
ve
was

found to be closer to the geometric mean. Deutsch

(
1989
) proposed using both power-average and

percolation models to approximate k
he
and k
ve

for a binary permeability sandstone-mudstone

model on a regular 3D grid, and showed how

both the averaging power and the percolation

exponents vary with the anisotropy ratio.

Whatever the chosen method, it is important

to separate out the effects of thin barriers (or

faults) from the more general rock permeability

anisotropy (discussed below).

¼

Using advances in small-scale geological

modelling, it is now possible to accurately esti-

mate k
v
/k
h
ratios for sandstone units. Ringrose

et al (
2003
,
2005
) and Nordahl et al (
2005
) have

developed this approach for some common bed-

ding types found in tidal deltaic sandstone

reservoirs (i.e. flaser, wavy and lenticular bed-

ding). Their method gives a basis for general

estimation for facies-specific k
v
/k
h
ratios. Exam-

ple results are shown in Figs.
3.40
and
3.41
.

The method takes the following steps:

1. Perform a large number of bedding

simulations to understand the relationship

between k
sand
,k
mud
and V
mud
(simulations

are unconditioned to well data and can be

done rapidly).

2. Input values for the small-scale models are the

typical values derived from measured core

permeabilities.

3. A curve is fitted to the simulations to estimate

the k
v
or k
v
/k
h
ratio as a function of other

modelled parameters: e.g. k
h
,V
mud
,orø.