Empirical Formula for Dynamic Biot Coefficient of Sandstone Samples from South-West of Poland

In this research, two empirical correlations have been introduced to calculate the dynamic Biot coefficients of low-porosity and high-porosity sandstone samples from two open pit mines located in South-West Poland. The experiments were conducted using an acoustic velocity measurement apparatus. Under the undrained condition, firstly, the confining pressure was increased in increments of 200 psi, and the values of pore pressure and dynamic elastic modulus were recorded. This experiment was continued until the Skempton coefficient remained in the range of 0.98–1. Secondly, an experiment on the same sample was conducted under drained conditions, and the corresponding dynamic elastic moduli were calculated. Then, using the calculated dynamic elastic moduli, the dynamic Biot coefficient was determined for each sample under different confining pressure. Finally, two empirical correlations were formulated for each sandstone category. The results demonstrate that, as the confining pressure increases, the Biot coefficient decreases from 0.79 to 0.50 and from 0.84 to 0.45 for low-porosity and high-porosity samples, respectively. Furthermore, as the porosity increases, the sandstone behavior increasingly approaches that of soil. The empirical correlations can be used for sandstone formations with the same porosity in projects where there is not a measurement method for the Biot coefficient.

A COUPLED PETROPHYSICAL AND GEOMECHANICAL WORKFLOW TO INTERPRET DIPOLE SONIC VELOCITIES FOR IN-SITU STRESS

Petrophysicists often find sonic velocities difficult to interpret, especially when choosing values for the mineral and fluid endpoints. This difficulty is always caused by stress sensitive formations where dipole sonic velocities vary with stress, even when the petrophysical properties are constant. The goal of this coupled workflow is to quantify the compositional influences of porosity, mineralogy, and fluids, while isolating and quantifying the geomechanical influence of stress. I first estimate the petrophysical properties using a standard multi-mineral petrophysical solver void of sonic inputs. This allows one to independently observe and quantify variations in both compressional and shear velocities with variations in petrophysical properties. I then normalize the sonic velocities to an idealized formation having compositional properties constant with depth by applying both matrix and fluid substitution algorithms. If these normalized velocities are constant with depth, then the formations are insensitive to stress, and I apply the standard petrophysical workflow using the measured sonic inputs. In addition, the standard geomechanical workflow that assumes linear elasticity is appropriate to estimate the in-situ stresses. However, if the normalized velocities vary with depth, the formations are sensitive to stress, which requires modifications to both the standard petrophysical and geomechanical workflows. Specifically, one must quantify and remove the velocity variations due to stress or else misinterpret velocity changes due to stress for changes in petrophysical properties. For formations sensitive to stress, I quantify the stress sensitivity by using the observed change in normalized velocity with depth with an estimate of the change in stress with depth. I then compute a second velocity normalization that quantifies and removes the acoustical sensitivity to stress in favor of a constant reference stress. I can now more accurately quantify the petrophysical properties by including the stress normalized velocities in the multi-mineral petrophysical solver. At this point in the workflow, there are two methods for quantifying the in-situ horizontal stress. The first method uses the velocities normalized to the constant reference stress to compute the dynamic elastic moduli. These dynamic elastic moduli are now appropriate to input into the standard geomechanical workflow. The second method uses the velocities normalized for the changing petrophysical properties, together with the stress sensitivity coefficients, to directly invert the velocities for the in-situ horizontal stresses. A comparison between the two methods supplies a consistency check. I emphasize both methods require in-situ horizontal stress calibration data for correct results. To clearly illustrate the workflow, this paper specifies the mathematical formulations with example calculations. This coupled workflow is novel because it highlights and clarifies improper assumptions while acknowledging the rock physics of stress sensitive formations. In the process, it improves the accuracy of both the derived petrophysical properties and geomechanical stresses.

Relationships between Dynamic Elastic Moduli in Shale Reservoirs

Sonic log compressional and shear-wave velocities combined with logged bulk density can be used to calculate dynamic elastic moduli in organic shale reservoirs. We use linear multivariate regression to investigate modulus prediction when shear-wave velocities are not available in seven unconventional shale reservoirs. Using only P-wave modulus derived from logged compressional-wave velocity and density as a predictor of dynamic shear modulus in a single bivariate regression equation for all seven shale reservoirs results in prediction standard error of less than 1 GPa. By incorporating compositional variables in addition to P-wave modulus in the regression, the prediction standard error is reduced to less than 0.8 GPa with a single equation for all formations. Relationships between formation bulk and shear moduli are less well defined. Regressing against formation composition only, we find the two most important variables in predicting average formation moduli to be fractional volume of organic matter and volume of clay in that order. While average formation bulk modulus is found to be linearly related to volume fraction of total organic carbon, shear modulus is better predicted using the square of the volume fraction of total organic carbon. Both Young’s modulus and Poisson’s ratio decrease with increasing TOC while increasing clay volume decreases Young’s modulus and increases Poisson’s ratio.

Exposure Time Impact on the Geomechanical Characteristics of Sandstone Formation during Horizontal Drilling

The rock geomechanical properties are the key parameters for designing the drilling and fracturing operations and for programing the geomechanical earth models. During drilling, the horizontal-section drilling fluids interact with the reservoir rocks in different exposure time, and to date, there is no comprehensive work performed to study the effect of the exposure time on the changes in sandstone geomechanical properties. The objective of this paper is to address the exposure time effect on sandstone failure parameters such as unconfined compressive strength, tensile strength, acoustic properties, and dynamic elastic moduli while drilling horizontal sections using barite-weighted water-based drilling fluid. To simulate the reservoir conditions, Buff Berea sandstone core samples were exposed to the drilling fluid (using filter press) under 300 psi differential pressure and 200 °F temperature for different exposure times (up to 5 days). The rock characterization and geomechanical parameters were evaluated as a function of the exposure time. Scratch test was implemented to evaluate rock strength, while ultrasonic pulse velocity was used to obtain the sonic data to estimate dynamic elastic moduli. The rock characterization was accomplished by X-ray diffraction, nuclear magnetic resonance, and scanning electron microscope. The study findings showed that the rock compression and tensile strengths reduced as a function of exposure time (18% and 19% reduction for tensile strength and unconfined compression strength, respectively, after 5 days), while the formation damage displayed an increasing trend with time. The sonic results demonstrated an increase in the compressional and shear wave velocities with increasing exposure time. All the dynamic elastic moduli showed an increasing trend when extending the exposure time except Poisson’s ratio which presented a constant behavior after 1 day. Nuclear magnetic resonance results showed 41% porosity reduction during the five days of mud interaction. Scanning electron microscope images showed that the rock internal surface topography and internal integrity changed with exposure time, which supported the observed strength reduction and sonic variation. A new set of empirical correlations were developed to estimate the dynamic elastic moduli and failure parameters as a function of the exposure time and the porosity with high accuracy.

Differences between static and dynamic elastic moduli: Importance of experimental methods

<p>The differences between static and dynamic elastic moduli remain a controversial issue in rock physics. Various empirical correlations can be found in the literature. However, the experimental methods used to derive the static and dynamic elastic moduli differ and may entail substantial part of the discrepancies observed at the laboratory scale. The representativeness and bias of these methods should be fully assessed before applying big data analytics to the numerous datasets available in the literature.</p><p>We will illustrate, discuss and analyze the differences inherent to static and dynamic measurements through a series of triaxial and petroacoustic tests performed on an outcrop carbonate. The studied rock formation is Euville limestone, which is a crinoidal grainstone composed of roughly 99% calcite and coming from Meuse department located in Paris Basin. Sister plugs have been cored from the same quarry block and observed under CT-scanner to check their homogeneity levels.</p><p>The triaxial device is equipped with an internal stress sensor and provides axial strain measurements both from strain gauges glued to the samples and LVDTs placed inside the confinement chamber. Two measures of the static Young's modulus can thus be derived: the first one from the local strain measurements provided by the strain gauges and the second one from the semi-local strain measurements provided by the LVDTs. The P- and S-wave velocities are measured both through first break picking and the phase spectral ratio method, providing also two different measures of the dynamic Young's modulus.</p><p>The triaxial tests have been performed in drained conditions and the measured static elastic moduli correspond to drained elastic moduli. The petroacoustic tests have been performed using the fluid substitution method, which consists in measuring the acoustic velocities for various saturating fluids of different bulk modulus. No weakening or dispersion effects have been observed. Gassmann's equation can then be used to derive the dynamic drained elastic moduli and the solid matrix bulk modulus, which is otherwise either taken from the literature for pure calcite or dolomite samples, or computed using Voigt-Reuss-Hill or Hashin-Shtrikman averaging of the mineral constituents.</p><p>For the studied carbonate formation, we obtain similar values for static and dynamic elastic moduli when derived from careful lab experiments. Based on the obtained results, we will finally make recommendations, emphasizing the necessity of using relevant experimental techniques for a consistent characterization of the relation between static and dynamic elastic moduli.</p>

MEASURING OF ELASTIC MODULI BY MEANS OF SUB-SURFACE SOUNDING METHOD

The method of determination of elastic moduli for different materials by means of measuring of longitudinal and shear waves’ velocities is discussed in the paper. The velocities are measured by obtaining the time of flight between a pair of low frequency ultrasonic dry point contact transducers installed on the surface of the studied material sample. Factors defining the accuracy of such measurement are indicated which mainly consist of physical velocity frequency dispersion, fundamental although small differences between static and dynamic elastic moduli measurements, velocity dependence on temperature etc. Comparison between Young’s modulus and Poisson’s ratio, obtained experimentally and from table data, is given for various plastics and steel samples. It shows good agreement of different methods’ data and demonstrates the applicability of the suggested elastic moduli ultrasonic sub-surface measurement method.