Phi-k Log (Permeability Definition from Acoustic Amplitude and Porosity Logs)
Authors: Bamber Cecil L. , Evans J.R. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
Over the past few years investigation has shown that acoustic signal amplitude is reduced in the presence of fractures within a formation. Lithological changes have some effect, but the larger effect of open discontinuities at fractures can be further emphasized by comparison of acoustic amplitude with the acoustic velocity or neutron curve. The comparison along with the Micro-Seismogram* presentation of the full wave train of the acoustic signal allows qualitative determination of the degree of fracturing.
Experience has also shown that the acoustic amplitude comparison with the velocity or neutron curve presented as phi-K Plot gives reliable indications of matrix permeability. Such results are predicted by the Blot theory, which shows that matrix permeability, porosity, and fluid density and viscosity affect the acoustic attenuation rate.
Field examples and comparisons with core analysis illustrate the utility of the phi-K Plot.

Introduction
In formation evaluation the first question is whether or not commercially productive hydrocarbons are present. To this end numerous logging and testing devices are used to derive an answer. The next step is to use all available information to determine the best means for primary and secondary recovery. However, in numbers of cases, well performance does not continue as expected, end large expenses can be incurred in attempts to increase production rates and ultimate recovery.
One of the factors involved in such cases is permeability, Accurate evaluations depend to a great extent on availability of information on formation permeability. In many low porosity formations productivity, as well as reservoir space will depend upon the degree and extent of a natural fracture system, The fracture system can vary considerably from well to well, resulting in wide variations in productivity within a given area. Often a well with a minor fracture system will initially produce at a high rate but rapidly decline to a marginal or noncommercial rate.
Where formations are subject to wellbore damage, open hole tests often fail to recover fluids, or show any appreciable pressure. In such situations commercial production may be missed.