Comparison of Higher Order Schemes on Complicated Meshes and Reservoirs
Kvashchuk, A. ; Klöfkorn, R. LU
and Sandve, T.H.
(2019)
SPE Reservoir Simulation Conference
- Abstract
Scope
Accurate numerical modeling of fluid transport is essential in reservoir management. Higher-order methods help to improve accuracy by reducing the numerical diffusion, which is common for all first order methods. In this paper, we present an implementation of a MUSCL-type second-order finite volume method and demonstrate its capabilities on 2D and 3D unstructured grids. This includes corner point grids that are typically used in reservoir modeling.
Methods, Procedures, Process
A second order finite volume method is compared to standard first order method in terms of accuracy, performance and an ability to handle nonlinearities. There are several ways to build a second order finite volume method. In this paper we... (More)
Scope
Accurate numerical modeling of fluid transport is essential in reservoir management. Higher-order methods help to improve accuracy by reducing the numerical diffusion, which is common for all first order methods. In this paper, we present an implementation of a MUSCL-type second-order finite volume method and demonstrate its capabilities on 2D and 3D unstructured grids. This includes corner point grids that are typically used in reservoir modeling.
Methods, Procedures, Process
A second order finite volume method is compared to standard first order method in terms of accuracy, performance and an ability to handle nonlinearities. There are several ways to build a second order finite volume method. In this paper we choose an optimization-based strategy to compute the steepest possible linear reconstruction. At the same time, a steepness-limiting procedure is included in the optimization as constraint. This ensures that the steepest possible reconstruction that does not lead to oscillations is computed. As a result, sharper fronts compared to standard schemes are obtained.
Results, Observations, Conclusions
The paper demonstrates the described method on several benchmark cases with emphasis on relevant for practical reservoir simulation test cases. In particular, we use Norne field open data set, which enables cross validation with other implementations. We test the method on the transport case, where an analytical solution is known, to verify convergence behavior and to isolate the errors. Furthermore, the performance of first- and second-order methods is compared on multiphase flow problems typical for improved oil recovery: solvent and CO2 injection. The second order method shows superior performance in terms of accuracy.
Novel/Additive Information
This paper verifies the desirable properties of higher order method for reservoir simulation. Moreover, all the described implementations are available in an open source reservoir simulator Open Porous Media (OPM). As a result, these methods are accessible for reservoir engineers and can be used with industry standard modeling setups.
(Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f2786954-c1c4-45c5-83b2-3838fd0071bd
- author
- Kvashchuk, A.
; Klöfkorn, R.
LU
and Sandve, T.H.
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- optimization problem, viscosity, flow in porous media, fluid dynamics, artificial intelligence, upstream oil & gas, enhanced recovery, reservoir simulation, co 2, simulator
- host publication
- SPE Reservoir Simulation Symposium
- article number
- SPE-193839-MS
- conference name
- SPE Reservoir Simulation Conference
- conference location
- Galveston, Texas, United States
- conference dates
- 2019-04-10 - 2019-04-11
- external identifiers
-
- scopus:85085852044
- ISBN
- 978-1-61399-634-8
- DOI
- 10.2118/193839-MS
- language
- English
- LU publication?
- no
- additional info
- SPE 193839
- id
- f2786954-c1c4-45c5-83b2-3838fd0071bd
- date added to LUP
- 2021-02-10 14:21:03
- date last changed
- 2022-04-27 00:11:51
@inproceedings{f2786954-c1c4-45c5-83b2-3838fd0071bd,
abstract = {{<br/>Scope<br/>Accurate numerical modeling of fluid transport is essential in reservoir management. Higher-order methods help to improve accuracy by reducing the numerical diffusion, which is common for all first order methods. In this paper, we present an implementation of a MUSCL-type second-order finite volume method and demonstrate its capabilities on 2D and 3D unstructured grids. This includes corner point grids that are typically used in reservoir modeling.<br/><br/>Methods, Procedures, Process<br/>A second order finite volume method is compared to standard first order method in terms of accuracy, performance and an ability to handle nonlinearities. There are several ways to build a second order finite volume method. In this paper we choose an optimization-based strategy to compute the steepest possible linear reconstruction. At the same time, a steepness-limiting procedure is included in the optimization as constraint. This ensures that the steepest possible reconstruction that does not lead to oscillations is computed. As a result, sharper fronts compared to standard schemes are obtained.<br/><br/>Results, Observations, Conclusions<br/>The paper demonstrates the described method on several benchmark cases with emphasis on relevant for practical reservoir simulation test cases. In particular, we use Norne field open data set, which enables cross validation with other implementations. We test the method on the transport case, where an analytical solution is known, to verify convergence behavior and to isolate the errors. Furthermore, the performance of first- and second-order methods is compared on multiphase flow problems typical for improved oil recovery: solvent and CO2 injection. The second order method shows superior performance in terms of accuracy.<br/><br/>Novel/Additive Information<br/>This paper verifies the desirable properties of higher order method for reservoir simulation. Moreover, all the described implementations are available in an open source reservoir simulator Open Porous Media (OPM). As a result, these methods are accessible for reservoir engineers and can be used with industry standard modeling setups.<br/>}},
author = {{Kvashchuk, A. and Klöfkorn, R. and Sandve, T.H.}},
booktitle = {{SPE Reservoir Simulation Symposium}},
isbn = {{978-1-61399-634-8}},
keywords = {{optimization problem; viscosity; flow in porous media; fluid dynamics; artificial intelligence; upstream oil & gas; enhanced recovery; reservoir simulation; co 2; simulator}},
language = {{eng}},
title = {{Comparison of Higher Order Schemes on Complicated Meshes and Reservoirs}},
url = {{http://dx.doi.org/10.2118/193839-MS}},
doi = {{10.2118/193839-MS}},
year = {{2019}},
}