Parallel Simulation of Subsurface Fluid Flow

Transcription

1 Parallel Simulation of Subsurface Fluid Flow Scientific Achievement A new mortar domain decomposition method was devised to compute accurate velocities of underground fluids efficiently using massively parallel computers. Significance and Impact The sheer size and heterogeneous nature of a subsurface reservoir makes it difficult to compute accurate fluid flow velocities, which are needed to simulate, e.g., the response of a geosystem to injection of CO 2. Research Details Rock heterogeneity, i.e., fine-scale variation in permeability, must be resolved on a fine mesh to compute accurate flow velocities. The reservoir is decomposed into subdomains. Each subdomain can be simulated efficiently in parallel. They are tied together through subdomain mortar interfaces. Homogenization theory predicts fine-scale variations using only a few quantities per interface, tying the subdomains together by to a small and efficiently computed mortar problem. Fluid flow can be solved accurately over a huge reservoir volume to a fine resolution efficiently by a massively parallel computer. Fine-scale velocity grid Interface = 1040 New method 3 11 subdomains Interface = 156 T. Arbogast & H. Xiao, A multiscale mortar mixed space based on homogenization for heterogeneous elliptic problems, SIAM J. Numer. Anal., T. Arbogast, Z. Tao & H. Xiao, Multiscale mortar mixed methods for heterogeneous elliptic problems, Contemp. Math., J. Li &H. Yang, eds., Amer. Math. Soc., 2013, Chapter 2. T. Arbogast, Mixed multiscale methods for heterogeneous elliptic problems, in Numerical Analysis of Multiscale Problems, I. G. Graham et al., eds., Springer, 2011, pp

2 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL85000.

3 Spanning the Scales in CO 2 Sequestration Simulation Basin (100km) 3 Molecular (1nm) Pore (10μm) Geosystems are large and highly heterogeneous. Simulation requires a fine computational mesh and multiscale models. Field (100m) Continuum (10cm) J. A. Bellian, BEG

4 To simulate geosystem response, we must compute accurate fluid flow velocities. 4 Basin (100km) Size & heterogeneity: 1m grid spacing? Basin: 300km 300km 10 3 m = grid-blocks? Field: 10km 10km 10 2 m = or 10 8 at 10m 10m 1m resolution Additional computational load: Continuum(1m) Multiphase and multicomponent Long time simulations (1000 years) Uncertainty quantification Need parallel computation and multiscale techniques!

5 The Multiblock Concept Divide the domain into nonoverlapping subdomains and simulate the relevant processes locally as appropriate. Tie these together through a mortar interface. 5 Compositional model scco 2 oil Fully implicit two-phase IMPES two-phase brine scco 2 Non-matching grids Faults brine Faults

6 6

7 7 Subdomain blocks for parallel processing

8 8 Fine grid for resolution: Many unknowns!

9 9 Coarse mortar grid: Few unknowns.

10 10 p Guess mortar pressure p.

11 11 p Step 1: Compute the pressure and fluid velocity on each block efficiently in parallel. Based on velocity mismatch on interface, update p. Efficient due to small size.

12 12 p Step 2: Compute the pressure and fluid velocity on each block efficiently in parallel. Based on velocity mismatch on interface, update p. Efficient due to small size.

13 13 p Step 3: Compute the pressure and fluid velocity on each block efficiently in parallel. Done: Negligible velocity mismatch.

14 14 Pressure and velocity computed efficiently in parallel.

15 15 Mortars based on Homogenization Theory Difficulty. Rock heterogeneity, i.e., fine-scale variation in permeability, leads to fine-scale variation in pressure and velocity. Problem. Polynomials do not approximate rough functions well. Idea. Homogenization theory tells us that p (1 + ω )p 0 where p 0 is smooth. So approximate λ (1 + ω )q where q(x) is a polynomial. p p 0 x

16 16 Numerical Test Results Fluvial Permeability (channelized) Fine-scale fluid velocity grid Interface = 1040 Homogenized mortar 3 11 subdomains Interface = 156 Error = 11%