# Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation

## Abstract

A multiscale linear-solver framework for the pressure equation associated with flow in highly heterogeneous porous formations was developed. The multiscale based approach is cast in a general algebraic form, which facilitates integration of the new scalable linear solver in existing flow simulators. The Algebraic Multiscale Solver (AMS) is employed as a preconditioner within a multi-stage strategy. The formulations investigated include the standard MultiScale Finite-Element (MSFE) andMultiScale Finite-Volume (MSFV) methods. The local-stage solvers include incomplete factorization and the so-called Correction Functions (CF) associated with the MSFV approach. Extensive testing of AMS, as an iterative linear solver, indicate excellent convergence rates and computational scalability. AMS compares favorably with advanced Algebraic MultiGrid (AMG) solvers for highly detailed three-dimensional heterogeneous models. Moreover, AMS is expected to be especially beneficial in solving time-dependent problems of coupled multiphase flow and transport in large-scale subsurface formations.

- Authors:

- Publication Date:

- Research Org.:
- Board of Trustees of the Leland Stanford Junior University

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1164145

- Report Number(s):
- DOE-STANFORD-ER25726

- DOE Contract Number:
- FG02-06ER25726

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 02 PETROLEUM; 58 GEOSCIENCES; 54 ENVIRONMENTAL SCIENCES; multiscale simulation, finite-volume methods, reservoir simulation, discretization methods, heterogeneous reservoirs

### Citation Formats

```
Tchelepi, Hamdi.
```*Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation*. United States: N. p., 2014.
Web. doi:10.2172/1164145.

```
Tchelepi, Hamdi.
```*Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation*. United States. doi:10.2172/1164145.

```
Tchelepi, Hamdi. Fri .
"Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation". United States. doi:10.2172/1164145. https://www.osti.gov/servlets/purl/1164145.
```

```
@article{osti_1164145,
```

title = {Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation},

author = {Tchelepi, Hamdi},

abstractNote = {A multiscale linear-solver framework for the pressure equation associated with flow in highly heterogeneous porous formations was developed. The multiscale based approach is cast in a general algebraic form, which facilitates integration of the new scalable linear solver in existing flow simulators. The Algebraic Multiscale Solver (AMS) is employed as a preconditioner within a multi-stage strategy. The formulations investigated include the standard MultiScale Finite-Element (MSFE) andMultiScale Finite-Volume (MSFV) methods. The local-stage solvers include incomplete factorization and the so-called Correction Functions (CF) associated with the MSFV approach. Extensive testing of AMS, as an iterative linear solver, indicate excellent convergence rates and computational scalability. AMS compares favorably with advanced Algebraic MultiGrid (AMG) solvers for highly detailed three-dimensional heterogeneous models. Moreover, AMS is expected to be especially beneficial in solving time-dependent problems of coupled multiphase flow and transport in large-scale subsurface formations.},

doi = {10.2172/1164145},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2014},

month = {11}

}