Page 465 - Petrophysics

LINEAR FLOW THROUGH FRACTURES AND CHANNELS 433

where: k, = permeability of channels, Darcy,
k, = permeability of matrix, Darcy,
A = cross-sectional area, cm2,
n, = number of channels per unit area, and
r, = solution channel radius, cm.

Carbonate reservoirs dominated by a vugular-solution porosity system
exhibit a wide range of permeability. The permeability distribution may
be relatively uniform, or quite irregular.

EXAMPLE

A cubic sample of a limestone formation has a matrix permeability of
1 mD and contains 5 solution channels per ft2. The radius of each channel
is 0.05 cm. Calculate:

(a) the solution-channel permeability assuming a vug-porosity of 3% and
an irreducible water saturation in these channels equal to 18%; and
(b) the average permeability of this rock.

SOLUTION

(a) The permeability of the solution-channel can be obtained from
Equation 7.50:

k, = 12.6 x 106(1 - 0.18)(0.03)(0.052) = 775 Darcy

Using Equation 7.48, i.e., assuming QC = 1 and Siwc = 0, the permea-
bility of a channel is 31,500 Darcy, which is more than 40 times
the value of k, obtained from using Equation 7.50 and, therefore,
unrealistic.
(b) The average permeability of this block containing 5 channels is
estimated from Equation 7.51, where A = 1 ft2 = 929cm2, and
ncnr2/A = 5~(0.05~)/929 = 42 x lop6:

k,, = 42 x lop6 x 0.775 x lo6 + (1 - 42 x 10p6)(1) = 36.5 mD

This example illustrates the importance of estimating the actual
irreducible water saturation and porosity of the solution channels and
fractures. These parameters are important in determining oil-in-place
within vugular pores and fractures, and ignoring them can lead to
overestimating the production capacity of wells in carbonate reservoirs
[ 14-17].