COMPUTATION OF RELATIVE PERMEABILITY FUNCTIONS IN 3D DIGITAL ROCKS BY A FRACTIONAL FLOW APPROACH USING THE LATTICE BOLTZMANN METHOD

Digital rock physics (DRP) combines advanced 3D imaging techniques such as X-ray computed tomography (CT) scanning or focused ion beam scanning electron microscopy (FIB-SEM), segmentation algorithms to create a digital representation of the rock and advanced numerical methods to evaluate electrical, elastic, fluid flow and other pr operties of the rocks. A difficult problem in the numerical evaluation of relative permeability is to replicate the exact saturation sequences performed in SCAL experimental procedures including primary drainage and imbibition. In order to replicate these cycles, it is essential to define appropriate inlet and outlet boundary conditions to mimic the right flow field at the entrance and exit of a volumetric fraction of the plug, potentially located in any position i nside the plug itself. Moreover, in order for a digital sample to be a representation of the whole plug, or only part of it in case of a plug with multiple flow units, it is important to make sure that the digital sample is a Darcian sample such that permeability can be defined and the sample is a volumetric representation of the plug. We present an approach to simulate fractional flow in a 3D digital rock by direct numerical simulation of the Stokes flow of two immiscible components through the rock. We use an improved method of the lattice Boltzmann method (LBM) to simulate the complex fluid movement through the rock that includes interfacial tension, wettability and viscous effects. Adva nced boundary conditions are presented that allow the injection of varying fractional flow in a displacement process. A robust and simple way to verify Darcy’s law and to define a representative sample is presented. Primary drainage and imbibition cycles are performed on a carbonate sample, and the results are in good agreement with the e xperiments. The simulations are run on high performance computing (HPC) hardware to cope with the enormous computational load.