Abstract

The study presents results of Biot coefficient determination for limestones from Perm krai, Russia. To the date there is no standard method to determine the poroelastic parameters. That’s why different researchers use different approaches to perform these tests. In this research an attempt was made to compare how some aspects of Biot coefficient determination influence its values. The tests were performed on a triaxial test system PIK-UIDK/PL where deformations are measured by LVDT sensors. The Biot coefficient was calculated using two different equations. The results from three types of tests were used for these calculations. These tests are: 1) test when both confining and pore pressures are changed for the same values (similar to what is called unjacketed test), 2) drained test (confined pressure is changed while pore pressure is maintained at a constant value, 3) pore pressure change (while confining pressure is maintained at a constant value). The variation of the calculated Biot coefficient values in relation to the amplitude of pressure variation in each test was analyzed. The tests for each sample were performed with small pressure steps in the beginning and then the tests were repeated with increased maximum amplitude and larger pressure steps. The results show significant nonlinearity in the deformation of samples with larger pressure amplitude. This results in significantly higher Biot coefficient values when the full load cycle is used for calculation. The obtained Biot coefficient values were then correlated with the P-wave velocity determined for these samples in the reservoir conditions on the test system in the beginning of each test.

Introduction

Nowadays Biot coefficient is widely used to calculate effective stress in rock and its value variation can have a dramatic effect on results. So it is a very important poroelastic parameter in geomechanics. Despite this, many researchers still use the value of 1 in their calculations due to the lack of data on the Biot coefficient variation. The concept of effective stress was introduced by Terzaghi [1]. It was later modified considering advances in poroelasticity. The fundamental principles of the poroelastic theory were presented in the paper by Biot [2] and later advanced in his following papers and papers by other authors. In 1971 Nur and Byerlee [3] proposed the now well-known equation for the effective stress 〈σij〉 defined using the coefficient α which is now called the Biot (or Biot’s or poroelastic) coefficient.

(equation)

where σij is the total stress tensor, Pp is pore pressure and δij is the Kronecker delta. The Biot coefficient is defined in several ways. The most common is [4]

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