A Method for Determining the Net Vertical Permeability Near a Well From In-Situ Measurements
Authors: Prats Michael 
Published: December 2007

For a reservoir having a low vertical permeability, tests in a single well can be carried out to determine the value of the permeability, both normal and parallel to the bedding plane, and horizontal as well as vertical. The calculations can be performed with the aid of only a slide rule.

Introduction
Knowledge about the average vertical permeability of oil and gas producing formations is sometimes necessary to anticipate properly the production performance of a reservoir. performance of a reservoir. Other than the use of vertical permeability measurements on cores recovered from a formation, the only method available at present for determining the vertical permeability of a formation' from a single well requires the use of a numerical simulator, which is not generally available to the practicing engineer. This is in contrast to the numerous desk-type methods for analyzing pressure responses to obtain the average horizontal permeability of reservoirs. A desk-type method is proposed for measuring the average vertical permeability of the formation near a well. The method, which can be applicable only to some wells, consists of producing (or injecting) fluid at a constant mass rate of flow through a short interval (even a single perforation) near the top or bottom of a formation and in measuring the pressure response through another short interval in the same well (packed off from the first) without producing or injecting fluid through the latter openings. The idealization made in developing the method is discussed in the next section. Our approach differs from that followed by Bums' in that no digital computer is required to interpret the pressure response curve; rather the interpretation is based on results that are presented simply in a single graph. presented simply in a single graph. Description of Method of Solution
The reservoir is considered to extend horizontally from the wellbore to infinity, to be of uniform thickness h, to be filled with a single mobile liquid of constant compressibility c and viscosity u at an initially uniform pressure pi, and to have uniform porosity 0. Permeability anisotropy is considered, one of the Permeability anisotropy is considered, one of the principal axes being vertical. In the horizontal plane, principal axes being vertical. In the horizontal plane, permeabilities are equal in all directions, whereas the permeabilities are equal in all directions, whereas the vertical permeability kv can have any (constant) value. The problem is to measure kv in situ. It is clear that any method that aims at determining the average vertical permeability of a formation must involve vertical fluid flow over the region of interest. In operating practice in the field, fluids generally flow parallel to the bedding rather than normal to it. It is parallel to the bedding rather than normal to it. It is evident then that a test procedure involving the vertical flow of fluid needs to be developed in order to determine the average vertical permeability of a formation. We chose withdrawal or injection of fluid from a reservoir through a single perforation as the easiest way to obtain some vertical flow in the neighborhood of the well. And we chose making a second perforation, separated from the first by a packer, as perforation, separated from the first by a packer, as the easiest way to permit measuring the vertical pressure response. Production of fluids through the pressure response. Production of fluids through the perforation used to measure the pressure response is not perforation used to measure the pressure response is not necessary.
JPT
P. 637