"Assessment of Horizontal and Vertical Permeability Distribution Type Using Pressure Transient Data "
Recent attempts have shown that the estimation of reservoir heterogeneity through readily available dynamic
(pressure transient or production) data is possible but a challenging task. The analysis of this type of
data in reservoir characterization is known as “inverse problem” and one can obtain important information
about the interwell (x-y direction) and vertical (x-z direction ) permeability distribution in a reservoir.
The aim in this paper is to correlate permeability distribution type (or degree of heterogeneity) in x-z and
x-y directions to pressure transient response. It is a general agreement that the permeability distributions
obey fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) type distribution in vertical and
horizontal directions, respectively. Based on this argument, 2-D and 3-D synthetic permeability distributions
with known fractal dimensions (or intermittence exponent, H) were generated using fGn and fBm in vertical and
horizontal directions, respectively, and employed as data to a black oil simulator. Many different realizations
of permeability distribution are generated based on the random number seed used and pressure transient (draw down
and build-up) tests are simulated using a black oil simulator. Then, pressure transient analysis is performed
using a commercial well test analysis software package.
Strong effect of permeability distribution on pressure responses (drawdown and build-up) are observed as the
fractal dimension systematically changes with the pressure response. The impact of reservoir heterogeneity
is also observed as an increase in the skin effect with increasing fractal dimension of permeability distribution.
This additional (pseudo) skin is correlated to the fractal dimension of the vertical and horizontal permeability distribution.