Commentary on the Terms "Transmissibility" and "Storage"
Authors: Johnson James N. 
Published: December 2007

JPT Forum articles are limited to 1,500 words including 250 words for each table and figure, or a maximum of two pages in JPT. A Forum articles may present preliminary results or conclusions of an investigation that the author wishes to publish before completing a full study; it may impart general technical information that does not warrant publication as a full-length paper. All Forum articles are subject to approval by an editorial committee.

Letter to the editor are published under Dialogue, and may cover technical or nontechnical topics. SPE-AIME reserves the right to edit letters for style and content.

In the mid-1960's, the terms "transmissibility" (T) and "storage" (S) began appearing in petroleum engineering literature. These terms appear to have been extracted from the groundwater literature and have lost something in the translation. The purpose of this commentary is to clarify the nature of these terms and to make a strong plea for their rapid demise. As improperly used, these terms represent quantities already defined by SPE-AIME and appear to offer little.

In the late 1920's and early 1930's, many authors considered Darcy's law and appropriate units for permeability. The fields of study involved were permeability. The fields of study involved were geophysics, petroleum technology, petroleum geology, groundwater hydrology, and soil science. An excellent review was given in 1942 by Wenzel. In petroleum engineering, the Wyckoff et al. darcy unit of permeability was widely accepted: 1 darcy of rock permeability results when 1 cc of fluid flows per permeability results when 1 cc of fluid flows per second under 1 atm pressure difference through a rock of 1 cm 2 cross-sectional area and 1 cm length, if the fluid viscosity is 1 cp. Although this employs some metric units, the use of a pressure difference of 1 atm is an anomaly. Nevertheless, the unit appears firmly established in oil production technology. As defined, the unit of permeability is a property of the rock only. This is

kA q = - --- dp/ds.................................(1)

In the groundwater literature, Darcy's law was often stated as

q = - KAdL/ds....................................(2)

Theis proposed that (kh) be called the "coefficient of transmissibility." The flow rates in both Eqs. 1 and 2 are in terms of the reservoir-condition flow rates. The term "L" in Eq. 2 is the hydraulic head:

p L = ---- + Z + constant, ........................(3) Fwv

where Fwv is specific weight. It is clear that groundwater hydrologists understood K to be a function of the fluid properties. Wenzel presented methods for correcting for temperature (viscosity of water) in 1942.

By 1949 Jacob objected to the use of the term "transmissibility." Concerning permeability, he said: "It has been called transmissibility, though perhaps a better term would be transmissivity, as the bed is transmissive, whereas the water is transmissible." There is even more reason to object to the use of the term in petroleum engineering. The use of head in groundwater hydrology results in a more complex definition of transmissibility than is normally indicated in the petroleum engineering literature:

kh g T = -------,...................................(4) gc

The term "transmissivity" or "coefficient of transmissivity" is actually used in the groundwater literature. But it is used as a special case wherein the formation thickness is constant.

P. 294