2-D discrete element modeling of unconsolidated sandstones

Abstract

In this work unconsolidated sands saturated with heavy oil were modeled using a discrete element numerical model, (DEM). The DEM code was built in Mathematica ♭ programming language. The strain-stress behavior of biaxial tests using the code developed in this thesis is compared to the results of triaxial tests performed in cylindrical core samples of unconsolidated sandstones saturated with heavy oil. The discrete element model treats the sand as a two dimensional assembly of particles. The displacements and velocities of each particle are calculated in order to determine local rearrangements during deformation. The kinematics of the system is performed in small time steps where force and torque balance is calculated for each disk. Several grain forces are simulated in this DEM model when the unconsolidated sand, saturated with heavy oil, is under a deviatoric loading condition. The contact forces are modeled as spring and dashpot forces, and they are applied in the contact point in the normal and tangential directions. Friction viscous forces are included for linear displacements and for rotational movements. The viscous forces generated by the movements of very close neighborhood particles are also considered in the model. The DEM code is also capable of modeling capillary forces between grains when the assembly is considered partially saturated, and the interstitial liquid is filling the porous space as a discrete liquid bridge between particles. Four boundary walls surround the particle assembly. The bottom boundary is considered flat, frictionless, and static while the top boundary is a stress controlled wall. The other two vertical boundaries are under a confining distributive force, and these walls can be modeled as two parallel flexible boundaries or as a simple horizontal force condition distributed to the boundary particles. Compressibility and apparent Young's modulus are compared between the DEM results and the laboratory geomechanical data. This investigation is part of ongoing research to obtain the micro-mechanical parameters needed for future hydraulic fracture propagation studies in an unconsolidated formation impregnated with heavy oil.