Micromechanical and microstructural DEM modeling of the viscoelastic behavior of oil sands

Abstract

Oil sand is a composite material of quartz aggregates, bitumen, water, and air void in which the bitumen exhibits a time and temperature dependent behavior under loading. The soil skeleton (quartz aggregates) comprises dense, highly incompressible, uncemented fine interlocked grains exhibiting low in-situ void ratio, and high shear strengths and dilatancy under low normal stresses. In this work, a two-dimensional discrete element method (DEM) is developed to model the viscoelastic response of an oil sand formation. A digital sample of the oil sand with varying particle shapes and sizes were built using the discrete element software PFC2D. The oil sand microstructure was captured from an electron scanning micrograph image of a 14.5% bitumen content Athabasca oil sand. The micromechanical approach is based on discretizing the oil sands microstructure and modeling particle interactions (contacts) of its constituents at microscale. The quartz aggregates, water, and bitumen included in the digital samples were modeled using different contact models. Rheological data for the bitumen was obtained from a stress/strain controlled rheometer equipped with a parallel plate. This data was used to calibrate the parameters of the viscoelastic contact models among the different material phases. The resulting parameters of Burger’s model were used to simulate the micromechanical behavior of the material. A 2D DEM model with two temperatures and three loading frequencies subjected to a constant amplitude sinusoidal compression tests was simulated. The results of the study show a good agreement between the model prediction and the measured dynamic modulus and phase angle. This indicates that the linear viscoelastic DEM model developed is capable of simulating timedependent behavior of oil sands material. Additionally, the effect of rate of loading and temperature on the deformational mechanics of the material was evident in the dynamic modulus determination. Correspondence to: Samuel Frimpong, Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO 65401, USA, Tel: (573) 341-7617; Fax: (573) 341–6934; E-mail: frimpong@mst.edu Received: January 18, 2017; Accepted: February 26, 2017; Published: March 02, 2017 Introduction Oil sand is a dense granular material whose two main physical compositions are quartz grains and large quantities of interstitial bitumen, as shown in Figure 1. The pore spaces of oil sands are also filled with dissolved gasses and water [1-3]. The water is a thin film (~10 μm) that surrounds the quartz grains (about 99% water-wet) [4]. The connate water fills 10-15% of the pore spaces and the remaining is occupied by bitumen [1]. Figure 1(b) reveals that the grain-grain contact in oil sand formations exhibit mainly long and concavo-convex contacts. This structure is known as interpenetrative and is responsible for both the low void ratio and high shear strength [5]. Additionally, a large number of contacts per grain are formed because of the dense structure and consequently the formation undergoes high dilation at low normal stresses. The oil sand formations are mined for crude oil production in Northern Alberta, Canada. Surface mining methods, using ultra-class mining equipment such as the P&H 4100 BOSS ERS and the CAT 797 dump trucks are used for bulk excavation of the overburden, providing access to the oil-rich formation. These equipment units impose varying magnitudes of static and dynamic loading in both the horizontal and vertical directions to the ground during excavation. This has led to equipment sinkage/rutting, lower frame fatigue failure [6], and wear, and tear of crawler shoes [7]. Soils in general exhibit both elastic (recoverable) and plastic (permanent deformation) behavior under loading. However, oil sands exhibit viscous flow in addition to elastic and plastic behavior under loading. The internal structure of the oil sands shows a discrete behavior as relative positions of quartz particles are changed under loading. The overall macromechanical behavior of the formation is determined by the interaction between its constituents because of its discrete structure and multiphase composition. Thus, a micromechanical model is required to comprehensively simulate the heterogeneous, nonlinear, and anisotropic behavior of the formation. Over the last three decades, the stress/strain behavior of oil sands has been studied using mainly experimental, analytical, and numerical approaches. Many researchers have used experimental methods to (i) develop a constitutive model to predict the effective stress/strain behavior of drained and recompacted oil sands [8-10], (ii) characterize the shear strength and permanent deformation behavior [3,11-13], and (iii) study the microscopic structure [1,5]. The outcome of these testing procedures predicts the macromechanical stress/strain response of the formation. Additionally, the results of the studies show that quartz grain surface rugosity and grain angularity are functions for the higher residual strength of the oil sand material. Within the last two decades, the use of numerical methods to model and simulate the behavior of particulate media has gained popularity as a tool for fundamental studies [14-16]. Two numerical methods commonly utilized are the finite element method (FEM) and DEM. Numerical approaches using FEM produce some advantages over the analytical and experimental approaches [17-21]. Material models developed from these methods are either micromechanical Gbadam E (2017) Micromechanical and microstructural DEM modeling of the viscoelastic behavior of oil sands Adv Mater Sci, 2017 doi: 10.15761/AMS.1000116 Volume 2(1): 2-11 [25] were employed to express the relationship between the microscale DEM model parameters and the macroscale material properties. A nonlinear optimization technique was applied to fit the Burger’s viscoelastic contact model using the dynamic modulus laboratory test at different loading rate and temperature. Material and methods Discrete element method The DEM technique is a numerical method introduced by [14] for rock mechanics analysis and then extended by [33] for soil as an alternative to continuum modeling of particulate media. In continuum mechanics, the soil is assumed to behave as a continuous material. The study does not consider the relative movement and rotation of soil grains necessary to understand the micro-level soil behavior. Newton’s second law and finite difference scheme are used to study the mechanical interactions between a large collection of independent and varying discrete particles with rigid or deformable bodies. As the particles and bodies (walls) interact with each other, creating contacts, a force-displacement law (usually termed contact model) is used to update the contact forces and moment arising from the relative motion at each contact. The translational and rotational motion of each particle is calculated from the contact forces and moment using Newton’s second law. The overall governing equation of motion for the dynamic analysis of the DEM system is expressed as Equation (1): ( ) M D K F + + =   u u u (1)  u ,  u , u are the linear and rotational acceleration, velocity, and displacement vectors, respectively; M is mass (including rotational inertia); D is damping; K is internal restoring force; and F is the external force (including moments). The dynamics (translational and rotational motion) of the particle i with mass mi and moment of inertia Ii are governed by the Newton and Euler terms in Equation (2) and (3) [34,35]: C nc f g a i i i j ij k ik i i i m = = ∑ +∑ + + + F F F F F  X f (2) . . t i i i i i i j ij ω ω ω + × = = ∑ I I M   (3) i  X and i ω are the translational and angular accelerations of particle i , respectively; i ω is the angular velocity of particle i; fi and ti are the sum of forces and torques acting on particle i respectively i; C ij F and Mij are the contact force and torque acting on particle i by particle j or rigid/flexible boundary; nc ik F is the non-contact force acting on particle i by particle k (example of non-contact force would be capillary force from a wet media); and f i F , g i F , a i F are the fluid, gravitational, and applied force on particle i. The soft contact approach is used where the particles are assumed to be rigid but allows overlap at the contact points. The contact force is related to the magnitude of the overlap or macromechanical in nature. In macromechanical approaches, a constitutive model is used to represent the global material behavior that considers the material as a continuum. On the other hand, the micromechanical approach is based on discretizing the composite microstructure and modeling the material properties of its constituents [22]. Recently, Gbadam and Frimpong [17], and Brown and Frimpong [18] used FEM to simulate the nonlinear mechanical response of geomaterials and oil sands in formation-tool interactions. FEM is based on continuum mechanics, which lacks the ability to handle large strains and discontinuous strain fields. Hence, model slippage between the aggregate particles, which has been cited as one of the most important mechanisms resulting in permanent deformation or rutting [23], cannot be addressed using FEM. Such limitation can be addressed by an alternative DEM approach. Over the past decade, several researchers have used DEM to simulate discontinuous materials with some success. Current research efforts indicate little or no application of DEM for modeling a composite material, such as oil sands. However, DEM has been used to model the heterogeneous multiphase material of asphalt mixtures [15,24], and a number of researchers have developed micromechanical models with the DEM [25]. The mechanical behaviors of asphalt mixtures are simulated with an elastic model [26-28], a viscoelastic model [15,25,29], and a cohesive model [30]. The elastic models are time-ind