Acoustic and Quasistatic Laboratory Measurement and Calibration of the Pore Pressure Prediction Coefficient in the Poroelastic Theory
Authors: Al-Tahini A. M. , Abousleiman Y. N. , Brumley J. L. 
Published: December 2007

Abstract
The rock mechanical poromechanics pressure property, or Biot's effective stress parameter, a, is an important rock matrix and grain characteristic. The Biot's parameter relates stress and pore pressure and weighs the effect of the pore pressure within the concept of the effective stress analysis, in the geomechanics disciplines, and in particular when applied to reservoir engineering and wellbore time-dependent drilling mechanics and stability. It measures the compressibility of the skeletal framework of the rock with respect to the solid material composing the rock. In addition, it also reflects the compressibility of the rock structure which is one of the most important parameters for predicting oil reserves.
The poroelastic constant, a, is a complex function of the rock in-situ stress and porosity. The petroleum industry has historically calibrated empirical pore pressure relationships to the effective stress assuming a value of a to be unity or a constant value that may change as the reservoir is being depleted.A theoretical and experimental understanding of the measurements of the poroelastic constant, a, should improve the existing models in the areas lacking the data necessary for an accurate calibration.
The paper discusses the various methods of measuring the rock poroelastic parameter, a. These methods include quasi-static and acoustic approaches. In the quasi-static approach, two experimental set-ups, known as the direct and indirect methods, were used in this study to determine a, compared simultaneously with the acoustic method which is based on the compressional and shear wave velocities measurements under hydrostatic loading.
The direct method using the quasi-static approach utilizes the measurements of the change in pore volume and bulk volume of the sample for the calculation of a while the indirect method uses the bulk modulus of the fluid saturated rock sample and solid grains in the computation of a.The acoustic approach of measuring a utilizes the measurements of both compressional and shear wave velocities to compute bulk modulus which is then used to compute a; thus, very similar to the indirect technique. The measurements of a using these approaches were performed on fluid-saturated Berea cores, with mineral oil as the saturating fluid. The results obtained from these various techniques are discussed in this work.
The indirect method reveals a higher magnitude of the poroelastic constant, a, compared with direct method measurements[1].This difference was found to be large for samples with high porosity, while for low porosity samples the magnitude for the poroelastic constant, a, measured using the two methods was comparable.This is due the fact that low porosity samples have high bulk modulus which tends to lower the magnitude of the poroelastic constant, a, when using the indirect method.The acoustic measurements showed the sensitivity of a to the stress level at which it was measured. The magnitude of the poroelastic constant, a, dropped by 20% for some samples when the pressure increased from 1000 to 9000 psi[2,3].The results of this work also indicate that the measurements of the poroelastic constant, a, using the direct method and acoustic method at early pressure are quite similar for the case of low porosity sample.For high porosity samples the magnitude of the poroelastic constant, a, measured from direct methods was found to fall in the range of acoustic measurements at high pressure. The quasi-static direct method showed a good prediction of a in the absence of the jacketing effect.