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,
) Fine-scale model of calcite barriers.
Geological Society of London )
f is the barrier frequency
d is a mudstone dimension
3.6.3 Modelling of Permeability
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).
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
2. Input values for the small-scale models are the
typical values derived from measured core
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.