The behavior of fractal analysis using the continuous wavelet transform in shale-gas reservoirs is studied based on estimation of the so-called Hölder exponent by analyzing a total-organic-carbon (TOC) well log using the continuous wavelet transform; the Morlet is the analyzing wavelet. Application to the TOC well-log data of a horizontal well drilled in the Fort Worth Basin, Texas, USA, where the main objective is the lower Barnett Shale, clearly shows no special behavior of the Hölder exponents for known sweet spots. This process can be applied to other well-log data of shale-gas reservoirs to compare results and generalize a rule about the fractal behavior in shale-gas reservoirs.

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