Many tools conventionally used in formation evaluation can provide an estimation of reservoir heterogeneity type and degree. Based on this information representative reservoir model can be built through which reservoir pressure and production behavior can be accurately estimated. The estimation of reservoir heterogeneity through reservoir responses, however, is still a challenging task. Well test analyses provide important information about the interwell permeability distribution of a reservoir.

This study aims to correlate the response of pressure transient test to permeability distribution type. For this purpose, correlated permeability distributions in x-y direction are generated using fractional Brownian motion (fBm) as it has been shown in literature that permeability exhibits an fBm type distribution horizontally. 2-D fBm permeability distributions created using mid point displacement method are employed as data to a black oil simulator. Intermittence exponent, H or fractal dimension of the distribution, D, as defined by D=2-H, characterizes the distribution type. All permeability distributions are normalized to represent the same arithmetic mean (20, 100, and 500 mD) and uniform variance so that only their fractal dimension that underlies the smoothness of the distribution distinguishes them. Many different realizations of permeability distributions are generated based on the random number seeds used and pressure transient (drawdown) tests are simulated using a black oil simulator package (ECLIPSE 100). Pressure transient analysis is performed using PanSystem package. As a base case and for the comparison purpose, the same procedure is repeated for totally homogeneous case and random (normally distributed) permeability distribution with the same mean and uniform variance.

The effects of permeability distribution type on the pressure response are clarified. A strong impact of heterogeneity is observed as an increase in skin effect with increasing fractal dimension of permeability distribution. This additional (or pseudo) skin effect due to heterogeneity is correlated to the fractal dimension of the permeability distribution. As a further step, the procedure is repeated for different flow rates applied during the drawdown test.The correlation between the fractal dimension of permeability distribution and additional skin is improved by incorporating the rate into it. The methodology followed can be used in the assessment of reservoir heterogeneity quantitatively using pressure transient response.


Permeability heterogeneity is one of the most important reservoir parameters to be identified for the performance estimation and further field development in reservoir engineering. Vertical permeability distribution can be assessed by conventional tools, namely well logs and drilling data. Description of horizontal heterogeneity is more challenging.

The heterogeneity of the permeability field can be defined using available tools and the production performance can be estimated based on this data. Inversely, one can use the production data1–7 or pressure change in time8–22 to describe the permeability heterogeneity. This would be a desirable application but still a challenging task as a unique solution to the problem cannot easily be obtained.

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