Direct numerical simulation of fully saturated flow in natural porous media at the pore scale: a comparison of three computational systems

Abstract

Direct numerical simulations of flow through two millimeter-scale rock samples of limestone and sandstone are performed using three diverse fluid dynamic simulators. The resulting steady-state velocity fields are compared in terms of the associated empirical probability density functions (PDFs) and key statistics of the velocity fields. The pore space geometry of each sample is imaged at 5.06-mu m voxel size resolution using X-ray microtomography. The samples offer contrasting characteristics in terms of total connected porosity (about 0.31 for the limestone and 0.07 for the sandstone) and are typical of several applications in hydrogeology and petroleum engineering. The three-dimensional fluid velocity fields within the explicit pore spaces are simulated using ANSYSA (R) FLUENTA (R) ANSYS Inc. (2009), EULAG Prusa et al. (Comput. Fluids 37, 1193-1207 2008), and SSTOKES Sarkar et al. (2002). These computational approaches are highly disperse in terms of algorithmic complexity, differ in terms of their governing equations, the adopted numerical methodologies, the enforcement of internal no-slip boundary conditions at the fluid-solid interface, and the computational mesh structure. As metrics of comparison to probe in a statistical sense the internal similarities/differences across sample populations of velocities obtained through the computational systems, we consider (i) integral quantities, such as the Darcy flux and (ii) main statistical moments of local velocity distributions including local correlations between velocity fields. Comparison of simulation results indicates that mutually consistent estimates of the state of flow are obtained in the analyzed samples of natural pore spaces despite the considerable differences associated with the three computational approaches. We note that in the higher porosity limestone sample, the structures of the velocity fields obtained using ANSYS FLUENT and EULAG are more alike than either compared against the results obtained using SSTOKES. In the low-porosity sample, the structures of the velocity fields obtained by EULAG and SSTOKES are more similar than either is to the fields obtained using ANSYS FLUENT. With respect to macroscopic quantities, ANSYS FLUENT and SSTOKES provide similar results in terms of the average vertical velocity for both of the complex microscale geometries considered, while EULAG tends to render the largest velocity values. The influence of the pore space structure on fluid velocity field characteristics is also discussed

Numerical study of fluid flow at pore scale in packed bed of spheres and grains to obtain the REV

“…where 〈v i 〉 is the velocity in the i direction averaged over the control volume, µ is the dynamic viscosity of the fluid, ∇P is the pressure gradient in the j direction, and k i j is the permeability tensor. This tensor is normally diagonal and positive, its elements can be determined using experimental [16] and numerical simulation results [4]. Permeability is calculated from the applied pressure gradient ∆P and the length of the system in the main flow direction over which the pressure gradient has been imposed, for a given single-phase flow, with a known and constant viscosity.…”

“…The morphology of the porous media and the inertial effects at the pore scale has an important influence to improve the numerical results precision. Recent developments in pore scale modeling, coupled with the specialization of imaging techniques [2,3], have allowed direct numerical simulations of fluid flow through intricate microscopic structures to be developed [4]. The direct modeling approach, in which the fundamental equations of flow and transport are solved in the real geometry of the pore space, is very precise; however, it has a great computational cost.…”

“…The direct modeling approach, in which the fundamental equations of flow and transport are solved in the real geometry of the pore space, is very precise; however, it has a great computational cost. The results obtained in the microscale numerical analyses can be integrated into continuous scale models, which are then used to support decision making (at the field scale) in the management of oil, gas, and water fields underground [4]. In addition, this topic is of great interest for the numerical characterization of fluid mobility in rock reservoir, during Enhance Oil Recovery (EOR) processes.…”

Challenges in imaging and predictive modeling of rhizosphere processes

“…Typically a computational mesh has to be generated which conforms to the underlying geometry on which numerical simulations can be run. Mesh generation itself is computationally demanding (Siena et al 2015) and can be the limiting factor in some simulations. There are numerous methods available for direct solution in the case of single-and multi-phase flow, i.e., finite volume packages such as OpenFOAM (Jasak et al 2013), ANSYS, FLUENT, and finite element packages such as Comsol Multiphysics, which solve Stokes' equations directly.…”

“…The geometrical influence of the boundary is implemented through the addition of source terms in the governing equations which mimic the behavior of the boundary condition. This method has been successfully applied to simulations of flow in simple porous media (Hyman et al 2012;Siena et al 2015) and solvers are available which make use of these methods (Prusa et al 2008).…”