Journal of Canadian Petroleum Technology
Volume 48,
Number 7,
July 2009,
25-29
Abstract
Recent models show the means of estimating the petrophysical porosity exponent
(m) of a reservoir when it is composed of different combinations of matrix,
fractures and vugs. For both dual and triple porosity reservoirs, the system is
modelled as a parallel resistance network (for matrix and fractures), a series
resistance network (for matrix and non-connected vugs) or a combination of
parallel/series resistance networks (for matrix, fractures and non-connected
vugs). In the case of matrix/fractures, it has been assumed that the flow of
the current is parallel to the fractures. This paper shows the effect on m of
current flow that is not parallel to the fractures. This type of anisotropy is
co-relatable with fracture dip. Maxwell Garnett mixing formula for calculating
effective permittivity of a system with aligned ellipsoids and depolarization
factors of 0 and 1 leads to the parallel and series resistance networks used in
the paper.
It is concluded that the change in fracture dip can have a significant effect
on the value of m. Not taking this into account can lead, in some cases, to
significant errors. The effect of the change of fracture dip on water
saturation calculations is illustrated using two examples.
Introduction
The petrophysical analysis of fractured and vuggy reservoirs has been an area
of abundant interest in the oil and gas industry. For example, a key ingredient
for successful completion of wells in naturally fractured tight gas formations
is the ability to distinguish gas from water-bearing intervals. Proper
estimates of petrophysical parameters, including the porosity or cementation
exponent m, play an important role in correct estimations of watersaturation
(Sw).
Towle(1) gave consideration to some assumed pore geometries, as well
as tortuosity, and noticed a variation in the porosity exponent m in
Archie's(2) equation ranging from 2.67 to 7.3+ for vuggy reservoirs
and values much smaller than 2 for fractured reservoirs. Matrix porosity in
Towle's models was equal to zero.
Aguilera(3) introduced a dual porosity model capable of handling
matrix and fracture porosity. That research considered three different values
of the porosity exponent: one for the matrix (mb), one for the
fractures (mf = 1) and one for the composite system (m). It was
found that as the amount of fracturing increased, the value of m became
smaller.
Rasmus(4) and Draxler and Edwards(5) presented dual
porosity models that included potential changes in fracture tortuosity and the
porosity exponent (mf) of the fractures. The models are useful, but
must be used carefully as they calculate values of m > mb as the
total porosity increases, even when the flow of current goes parallel to the
fractures.
Serra(6) developed a graph of the porosity exponent (m) versus total
porosity for both fractured reservoirs and reservoirs with non-connected vugs.
The graph is useful, but must be employed carefully as it can lead to errors
for certain combinations of matrix and non-connected vug
porosities(7). The main problem with the graph is that Serra's
matrix porosity is attached to the bulk volume of the 'composite system.'
© 2009. Petroleum Society of Canada (now Society of Petroleum Engineers)
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History
- Original manuscript received:
23 March 2006
- Meeting paper published:
13 June 2006
- Revised manuscript received:
5 January 2009
- Manuscript approved:
10 June 2009
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