The Heinemann-Mittermeir Generalized Shape Factor and Its Practical Relevance

Fifty years ago Warren and Root have introduced the shape factor. This fundamental parameter for modeling of naturally fractured reservoirs has been discussed stormily ever since. Different definitions for shape factor have been suggested which all of them are heuristically based. Recently, Heinemann and Mittermeir mathematically derived - based on the dual-continuum theorem assuming pseudo-steady state condition- a general and proper form of the shape factor formula which can be simplified to the previously published shape factor definitions. This paper discusses the practical relevance of the Heinemann-Mittermeir formula. Its difference to the most commonly used Kazemi et al. formula is its demonstration by fine-scale single matrix block simulation. Furthermore, it is shown that the generally applied isotropy assumption can lead to significantly wrong results. Consequently, the generalized Heinemann-Mittermeir shape factor formula is recommended to be routinely practiced in the industry for more accurate results. The paper tries to present a proper realization of the nature of the shape factor as well as presentation of detailed mathematical and practical approaches for measuring all the required values in order to determine the shape factor for individual matrix rock pieces from outcrops of fractured formations. Performing those measurements routinely is regarded as essential parameter for its usability.