Empirical Correlation of Effective Stress Dependent Shale Rock Properties
Authors: Reyes L. , Osisanya S.O. 
Published: March 2010

Abstract
Maintenance of a stable wellbore is of primary importance during the drilling of oil and gas wells, and it can be troublesome. Porosity and permeability are essential shale rock properties necessary for stress analysis as related to wellbore stability. Empirical relationships that correlate porosity and permeability of shales have been developed based on the effective stress concept.
A series of compaction and permeability tests were performed on four shale samples. A small-scale laboratory pressure vessel that includes an innovative testing procedure under simulated downhole conditions was used to determine the effects of confining pressure, pore pressure, temperature, and fluid types on the porosity and permeability of the shales tested.
Compaction tests were conducted with de-ionized water under various confining pressures, constant pore pressure, and temperature. The permeability tests were conducted with de-ionized water and nitrogen as the test fluids. Tests were performed by varying the confining pressure, but under steady state conditions and constant temperature. The results of the laboratory tests were used to develop empirical correlations between permeability and porosity for the various shales. The empirical equations were validated with theoretical model equations. Results further showed that porosity and permeability are not constant, but are functions of confining and pore pressures.
This study proved that porosity and permeability are not constant and, contrary to the common practice, they are functions of the confining and formation pressures. Therefore, good reservoir and wellbore stability models must consider these effects during ell development programs.

Introduction
Wellbore instability problems can be better understood by performing compaction and permeability tests under in situ stress conditions. In most cases, these laboratory tests are conducted for reservoir engineering proposes (in sandstone), but they can also be used to derive some clues as to the causes of wellbore instability. Additionally, these tests can predict the conditions under which the formation pressure and in situ stress distribution will result in the failure of the rock.
Swelling or shrinkage of the shale formation results from invasion of drilling fluid filtrate into the formation while drilling. This invasion into shale formations is possible due to permeability and porosity properties. This invasion may also be responsible for sliding or creeping of the shale formation, leading to sloughing.
The low permeability of shale greatly restricts fluid movement, which not only retards water uptake, but will also retard water expulsion when the wellbore total aqueous potential is dropped below the total aqueous potential within the shale(1, 2). This could result in a type of "spalling" failure of shale into the wellbore. Chenevert and Sharma(3) concluded that the low permeability characteristics of shales, coupled with reduced wellbore pressures and expanding pore fluids, can cause fractures to form in a shale, and produce a form of shale "spalling" into the wellbore. They also showed that the relationship between permeability and effective stress is logarithmic, and a straight line correlates porosity and effective stress. But, they did not develop a mathematical model or correlate with theoretical equations.