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Discontinuum modelling of vuggy carbonate specimens: Impact of vugs on strength and stiffness
Abstract
The prediction of geomechanical properties for carbonate rocks has become a topic of increasing interest due to existing unconventional hydrocarbon resources in carbonate reservoirs. However the heterogeneity of carbonates presents a challenge in providing accurate estimates applicable to the wide variety of textures and porosities. An example of such heterogeneity is found in the Grosmont formation in Alberta, Canada, which has an estimated 64.5 billion m3 of in-place bitumen resources. Vuggy dolostone lithofacies present some of the most promising areas for bitumen extraction in the Grosmont reservoir; thus knowledge on the geomechanical behaviour of this material is relevant for future developments. An approach used for evaluation of geomechanical properties uses PFC3D, a discontinuum modelling software, to evaluate the effect of vug volume and shape on the uniaxial compressive strength (UCS) of carbonate rocks. The impact of the vugs on the stiffness of the material is also evaluated. The results are then compared with empirical correlations found in literature, which have been previously used to predict the UCS and stiffness of carbonate reservoirs. This study hopes to progress the methods for understanding the geomechanical behavior on heterogeneous carbonate reservoirs, for use in wellbore stability problems and changes due to production activities.
... In the last several decades, numerical models of geomechanical processes have become a highly sophisticated and powerful tool to study the behavior of rock from a micro-scale to a basin-scale [1, 2]. These numerical models are heavily reliant on physical testing of natural rock samples for calibration and validation purposes. ...
The validation of numerical models of geomechanical processes relies on physical testing of these processes in a laboratory setting. However, due to their heterogeneous nature, test specimens of natural materials often show a wide range of geomechanical properties. In the last decade, major advances have been made in the quality and commercial availability of 3D printers. At present, 3D printing has been used in the fabrication of medical implants and prosthetics, prototyping of mechanical designs and even in the construction of complete buildings. This paper presents 3D printing as an opportunity to control many of the variables that are inherent to the study of geo-materials. By using a 3D sand printer to fabricate test specimens, we were able to produce multiple, exact replicas of specimens with a high level of control on the nature of the heterogeneities and the properties of the matrix. Preliminary test results are presented from uniaxial compression tests and optical microscopy evaluation of introduced flaws. By knowing and controlling inter-sample variability in terms of porosity, fracture networks, grain size distribution, density distribution, etcetera, 3D printing of geomaterials provides a valuable tool to validate numerical models, develop scaling laws and constitutive relationships, quantify the degree of influence from pore geometry, fracture network characteristics and structural heterogeneity on macroscopic properties such as bulk modulus and effective permeability.
The ratios MR = E/UCS for 11 heterogeneous carbonate (dolomites, limestones and chalks) rock formations collected from different regions of Israel were examined. Sixty- eight uniaxial compressive tests were conducted on weak-to-strong (5 MPa < UCS < 100 MPa) and very strong (UCS > 100 MPa) rock samples exhibiting wide ranges of elastic modulus (E = 6100-82300 MPa), uniaxial compressive strength (UCS = 14-273. 9 MPa), Poisson's ratio (v = 0.13-0.49) and dry bulk density (p =1.7 -2.7 g/cm3). The observed range of MR = 60.9 - 1011.4 and mean value of MR = 380.5 are compared with the results obtained by Deere (1968) for limestones and dolomites, and the statistical analysis of MR distribution is performed. Mutual relations between E, UCS, p, MR for all studied rocks, and separately for concrete rock formations are revealed. Linear multiple correlations between E on the one hand and UCS and p on the other for Nekorot and Bina limestones and Aminadav dolomite are obtained. It is established that the elastic modulus and MR in very strong carbonate samples are more correlated with p - UCS combination and ea max, respectively, than in weak-to-strong samples. The relation between MR and maximum axial strain (ea max) for all studied rock samples (weak-to-strong and very strong) is discussed.
Both strength and elastic modulus of rocks are usually determined by compression testing at the mesoscopic scale (UNE-EN 1926; ASTMD 3148-96), and the values obtained are representative of homogeneous rocks. However, heterogeneous and texturally complex rocks show a broad dispersion range and their strength and elastic modulus depend on the presence of different textures and their mechanical properties. The aim of this study was to quantify the mechanical behaviour of these textures individually in order to understand the strength and elasticity of the whole rock. Four varieties of brecciated carbonates (limestones and dolostones) were studied. These rocks have a very complex fabric, presenting a dense network of fractures and clasts between fractures (mm-cm size). The fractures are completely filled with calcite cement, and clasts can have one or two different textures, each presenting differences in crystal size, mineralogy and porosity percentage and type. Samples measuring 4x4x4 mm were obtained in order to test each texture individually. These micro-samples were tested in a uniaxial compression press and the stress-strain curve was recorded. In addition, mean strength and Young's moduli were calculated for each texture. Results show that textures with a larger crystal size, lower porosity and intercrystalline porosity had the lowest strength and were the least elastic.
The paper presents a description of the methods used to model rock as discontinuous media. The objective of the work is to bring to the geomechanics community recent advances in numerical modeling in the field of rock mechanics. The following methods are included: 1 the distinct element method; 2 the discontinuous deformation analysis method; and 3 the bonded particle method. A brief description of the fundamental algorithms that apply to each method is included, as well as a simple case to illustrate their use.
Numerical specimens with ramdom holes is established by particle flow code PFC2D and uniaxial compression tests are conducted. Studies have shown that the uniaxial compressive strength of the specimen accelerated decline while the porosity increasing uniformly. With the increasing of the porosity，the plastic of the specimen increases.
The effective elastic modulus and conductivity of a two-phase material system are investigated computationally using a Monte Carlo scheme. The models contain circular, spherical or ellipsoidal inclusions that are either uniformly or randomly embedded in the matrix material. The computed results are compared with the applicable effective medium theories. It is found that the random distribution, geometric permeability and particle aspect ratio have non-negligible effects on the effective material properties. For spherical inclusions, the effective medium approximations agree well with the simulation results in general, but the analytical predictions on void or non-spherical inclusions are much less reliable. It is found that the results for overlapping and non-overlapping inclusions do not differ very much at the same volume fraction. The effect of particle morphology is also investigated by modelling prolate and oblate ellipsoidal inclusions.