Thiele, Christopher (Rice University) | Araya-Polo, Mauricio (Shell International Exploration & Production, Inc.) | Alpak, Faruk Omer (Shell International Exploration & Production, Inc.) | Riviere, Beatrice (Rice University)
Direct numerical simulation of multiphase pore-scale flow is a computationally demanding task with strong requirements on time-to-solution for the prediction of relative permeabilities. In this paper, we describe the hybrid-parallel implementation of a two-phase two-component incompressible flow simulator using MPI, OpenMP, and general-purpose graphics processing units (GPUs), and we analyze its computational performance. In particular, we evaluate the parallel performance of GPU-based iterative linear solvers for this application, and we compare them to CPUbased implementations of the same solver algorithms. Simulations on real-life Berea sandstone micro-CT images are used to assess the strong scalability and computational performance of the different solver implementations and their effect on time-to-solution. Additionally, we use a Poisson problem to further characterize achievable strong and weak scalability of the GPU-based solvers in reproducible experiments. Our experiments show that GPU-based iterative solvers can greatly reduce time-to-solution in complex pore-scale simulations. On the other hand, strong scalability is currently limited by the unbalanced computing capacities of the host and the GPUs. The experiments with the Poisson problem indicate that GPU-based iterative solvers are efficient when weak scalability is desired. Our findings show that proper utilization of GPUs can help to make our two-phase pore-scale flow simulation computationally feasible in existing workflows.
Frank, Florian (Rice University) | Liu, Chen (Rice University) | Alpak, Faruk O. (Shell International Exploration and Production Inc.) | Araya-Polo, Mauricio (Shell International Exploration and Production Inc.) | Riviere, Beatrice (Rice University)
Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow on pore structures feasible. In this paper, we describe a two-phase flow simulator that solves mass and momentum balance equations valid at the pore scale, i.e. at scales where the Darcy velocity homogenization starts to break down. The simulator is one of the key components of a molecule-to-reservoir truly multiscale modeling workflow.
A Helmholtz free-energy driven, thermodynamically based diffuse-interface method is used for the effective simulation of a large number of advecting interfaces, while honoring the interfacial tension. The advective Cahn–Hilliard (mass balance) and Navier–Stokes (momentum balance) equations are coupled to each other within the phase-field framework. Wettability on rock-fluid interfaces is accounted for via an energy-penalty based wetting (contact-angle) boundary condition. Individual balance equations are discretized by use of a flexible discontinuous Galerkin (DG) method. The discretization of the mass balance equation is semi-implicit in time; momentum balance equation is discretized with a fully-implicit scheme, while both equations are coupled via an iterative operator splitting approach.
We discuss the mathematical model, DG discretization, and briefly introduce nonlinear and linear solution strategies. Numerical validation tests show optimal convergence rates for the DG discretization indicating the correctness of the numerical scheme. Physical validation tests demonstrate the consistency of the mass distribution and velocity fields simulated within our framework. Finally, two-phase flow simulations on two real pore-scale images demonstrate the utility of the pore-scale simulator. The direct pore-scale numerical simulation method overcomes the limitations of pore network models by rigorously taking into account the flow physics and by directly acting on pore-scale images of rocks without requiring a network abstraction step or remeshing. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems.
Thiele, Christopher (Shell International E&P Inc.) | Araya-Polo, Mauricio (Shell International E&P Inc.) | Alpak, Faruk O. (Shell International E&P Inc.) | Riviere, Beatrice (Rice University) | Frank, Florian (Rice University)
HSS splits the linear system into a coarse-scale system of reduced size corresponding to the local mean values of the DG solution, and a set of
We propose a modified HSS algorithm (
Figure 7: Inline and Crossline view of the seismic image resulting from stacking the selected shots, budget 16. The target area (dashed box) shows a coherent event Figure 9: Inline and Crossline view of the seismic image resulting from stacking the selected shots, budget 6. The target area (dashed box) shows a coherent and clear event Approach Full Decimated Embedded Costs n full resolution shots migration n/fold full resolution shots migration B full resolution shots migration J forward modeling Table 3: The optimization algorithm cost is negligible CONCLUSIONS Figure 8: Automatic selected shots location overlay on the energy map, budget 6 presented. In Table 2 we can observed that decimation 50x50 (35 shots) has an equivalent error to embedded with B 16. The computational costs of this instance of embedded is therefore 16 full-migrated shots 1 forward modeling (FM) from the virtual shot.