The Property Model - Reservoir Model Design - page 101

1

0.1

0.01

kv/kh

0.001

0.0001

0.00001

Hummocks Bar / Shoal Channels Heterolith

0.231 0.239 0.153 0.132

Median

Lower quartile 0.096 0.042 0.064 0.024

0.0152 0.0009 7.68E -05 0.0001

Min

Fig. 3.38 Statistics of measured k v /k h ratios from core plug pairs from an example reservoir interval

Figure 3.38 illustrates some typical core-plug
anisotropy data. For this example we know from
production data that the mean value is far too
high (due to under sampling) and in fact the
minimum observed plug k v /k h ratio gives a
more realistic indication of the true values at
the reservoir scale.
A frequent problem with modelling or
estimating permeability anisotropy is confusion
between (or mixing the effects of) thin barriers
and rock fabric anisotropy. The following two
sections consider these two aspects separately.

situation, the geo-modeller needs to stochasti-
cally simulate barriers and ensure they are
applied in the simulation model. Pervasive dis-
continuous thin shales and cements may also be
modelled as cell-value reduction factors (an
effective k v /k h multiplier).
Figure 3.39 shows and example of barrier
modelling for calcite cements in an example
reservoir. The fine-scale barriers are first
modelled as geological objects and then assigned
as vertical transmissibility values using single-
phase upscaling.
Before plunging into stochastic barrier
modelling, it is important to consider using well
established empirical relationships that may save
a lot of time. Several previous studies have con-
sidered the effects of random shales on a sand-
stone reservoir. Begg et al. ( 1989 )proposeda
general estimator for the effective vertical perme-
ability, k ve , for a sandstone medium containing
thin, discontinuous, impermeable mudstones,
based on effective medium theory and geometry
of ideal streamlines. They proposed:

3.6.2 Modelling Thin Barriers

Large extensive barriers are best handled explic-
itly in the geological reservoir model:
￿ Fault transmissibilities can be mapped onto to
cell boundaries;
￿ Extensive shales and cemented layers can be
modelled as objects and then transformed to
transmissibility multipliers onto to cell

boundaries.
Some packages allow simulation of sub-
seismic faults as effective permeability reduction
factors within grid cells (see for example
Manzocchi et al. 2002 , or Lescoffit and
Townsend 2005 ). Some modelling packages
offer the option to assign a sealing barrier
between specified layers. For the more general

k x 1 ð V m Þ

k VE ¼ ð : Þ

3 30

2

ð a z þ fd Þ

where
V m is the volume fraction of mudstone
a z is given by (k sv /k sh ) 1/2
k sh and k sv are the horizontal and vertical
permeability of the sandstone