Fractal and power law distributions have been found in the past to be useful for modeling some reservoir properties following the assumptions of constant shape and self-similarity. This study shows, however, that pore throat apertures, fracture apertures, petrophysical and drill cuttings properties of unconventional formations are better matched with a variable shape distribution model (as opposed to constant shape). This permits better reservoir characterization and forecasting of reservoir performance.

Pore throat apertures, fracture apertures, petrophysical properties and drill cutting sizes from tight and shale reservoirs are shown to follow trends that match the variable shape distribution model (VSD) with coefficients of determination (R2) that are generally larger than 0.99. The good fit of the actual data with the VSD allows more rigorous characterization of these properties for use in mathematical models. Data that could not be described previously by a single equation can now be matched uniquely by the VSD. Examples are presented using data from conventional, tight and shale formations found in Canada, the United States, China, Mexico and Australia.

In addition, the study shows that the size of cuttings drilled in vertical and horizontal wells can also be matched with the VSD. This allows the use of drill cuttings, an important direct source of information, for quantitative evaluation of reservoir and rock mechanics properties. The results can be used for improved design of stimulation jobs including multi stage hydraulic fracturing in horizontal wells. This is important as the amount of information collected in horizontal wells drilled through out tight formations, including cores and well logs, is limited in most cases.

It is concluded that the VSD is a valuable tool that has significant potential for applications in conventional, low and ultra-low permeability formations and for evaluating distribution of rock properties at the micro and nano-scale.

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