# A two-stage preconditioner for multiphase poromechanics in reservoir simulation

## Abstract

Many applications involving porous media–notably reservoir engineering and geologic applications–involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton–Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. Here, the key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1564406

- Alternate Identifier(s):
- OSTI ID: 1569188

- Report Number(s):
- LLNL-JRNL-763612

Journal ID: ISSN 0045-7825; S0045782519304402; 112575; PII: S0045782519304402

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Published Article

- Journal Name:
- Computer Methods in Applied Mechanics and Engineering

- Additional Journal Information:
- Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Volume: 357 Journal Issue: C; Journal ID: ISSN 0045-7825

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 58 GEOSCIENCES; 98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL PROTECTION

### Citation Formats

```
White, Joshua A., Castelletto, Nicola, Klevtsov, Sergey, Bui, Quan M., Osei-Kuffuor, Daniel, and Tchelepi, Hamdi A. A two-stage preconditioner for multiphase poromechanics in reservoir simulation. Netherlands: N. p., 2019.
Web. doi:10.1016/j.cma.2019.112575.
```

```
White, Joshua A., Castelletto, Nicola, Klevtsov, Sergey, Bui, Quan M., Osei-Kuffuor, Daniel, & Tchelepi, Hamdi A. A two-stage preconditioner for multiphase poromechanics in reservoir simulation. Netherlands. doi:10.1016/j.cma.2019.112575.
```

```
White, Joshua A., Castelletto, Nicola, Klevtsov, Sergey, Bui, Quan M., Osei-Kuffuor, Daniel, and Tchelepi, Hamdi A. Sun .
"A two-stage preconditioner for multiphase poromechanics in reservoir simulation". Netherlands. doi:10.1016/j.cma.2019.112575.
```

```
@article{osti_1564406,
```

title = {A two-stage preconditioner for multiphase poromechanics in reservoir simulation},

author = {White, Joshua A. and Castelletto, Nicola and Klevtsov, Sergey and Bui, Quan M. and Osei-Kuffuor, Daniel and Tchelepi, Hamdi A.},

abstractNote = {Many applications involving porous media–notably reservoir engineering and geologic applications–involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton–Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. Here, the key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.},

doi = {10.1016/j.cma.2019.112575},

journal = {Computer Methods in Applied Mechanics and Engineering},

number = C,

volume = 357,

place = {Netherlands},

year = {2019},

month = {12}

}

DOI: 10.1016/j.cma.2019.112575

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Web of Science

#### Figures / Tables:

**M**

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Works referencing / citing this record:

##
Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

journal, September 2019

- Nägel, Arne; Logashenko, Dmitry; Schroder, Jacob B.
- Transport in Porous Media, Vol. 130, Issue 1

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*