Permeability Estimation From Sonic-Transit-Time Versus Porosity Gradients
Authors: Javalagi Mohan I. , Iverson William P. 
Published: December 2007

Abstract
High permeability sands can be distinguished from low permeability sands by examining slopes on sonic-transit-time versus porosity cross plots. Sonic-transit-time is plotted against porosity from neutron-density nuclear logs or simply density logs. A best fit line is drawn through the scatter of data, the slope of this best fit line is used in the process of permeability estimation. The slope is steepest in relatively low permeability sands, while a shallow slope is observed in more permeable sands. This variability in slope can be understood in terms of grain size distributions, pore fluids, bulk modulus of the fluids and that of the grains, clay content affecting changes in porosity, permeability, and sonic-transit-time. A physical model, which is a qualitative sand-shale model, and a mathematical model, which is a quantitative model, based on the Biot-Stoll theory, are used to substantiate the above mentioned technique.

Introduction
It is important to develop existing oil and gas fields, economically and reliably for untapped resources. The major goal of this research, is to demonstrate how sonic-transit-time (inverse of sonic velocity) can be used to distinguish high permeability sandstone formations from low permeability sandstone formations.
Permeability is the most critical physical property for determining well productivity. Flow tests or core analyses, are normally utilized by engineers to determine permeability and the bulk flow capacity of producing sandstone intervals. Flow tests are most reliable because the entire zone of interest is flowed, and bulk flow capacity is determined directly. During this test, the zone of interest must be isolated with packers and a flowing conduit must be provided with drill stem or steel tubing. On the other hand, cores from a well provide a very high resolution of permeability variations. But both flow tests and core analysis techniques are expensive and time consuming. Any type of permeability estimation technique, which uses only open-hole well logs is very attractive from an economic and practical point of view.
A new type of permeability estimation technique that depends on the slope of the sonic-transit-time versus porosity cross-plot has been developed, that qualitatively distinguishes permeable producing formations from impermeable or tight formations. The gradient analysis technique was applied to Wyoming wells and has shown to distinguish high k from low k formations.
Field Example: As an initial example, consider wells drilled in Hawk Point field. The Hawk Point field is located in the Powder River Basin, Wyoming. The Minnelusa formation of the Powder River Basin, consists of interbedded marine dolomites and eolian sandstone deposited during several cycles of transgression and regression in the Permo-Pannslyvanian time. Hawk Point Field produces from the upper member of the Minnelusa sand which was deposited in a sand dune environment. A total of twelve wells were drilled in this field. Only two of the wells were chosen for this study, where neutron, density, and sonic logs were available along with core analysis data. These wells are located as shown in Figure A-1. & Table B-1 gives the brief information of each well,
Figure A-2 shows the sonic and neutron-density porosity logs through Minnelusa formation for both of these wells. Conventional log analysis would predict Ickes 43-30 as a good producing well because it has high average sonic-transit-time than that of Ickes 42-30 even though the average porosity is 10% for Ickes 43-30 and 13% for Ickes #42-30. In fact the well Ickes 42-30 was found to be a good producing well. Conventional log analysis technique fails because importance is given to sonic-transit-time and not to the sonic-transit-time porosity gradient.
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