Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method

Matthew D. Jackson, James R. Percival, Peyman Mostaghimi, Brendan Tollit, Dimitrios Pavlidis, Christopher C. Pain, Jefferson Luis Melo De Almeida Gomes, Ahmed ELSheikh, Pablo Salinas, Ann H. Muggeridge, Martin Blunt

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation. 
Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional cornerpoint or unstructured grids.
Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N+1) representation for pressure. This method exactly represents Darcyforce balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptivemesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required. After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic features that are typically lost. The approach may also be used to capture near-wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations, and, in future applications, geomechanical models with fracture propagation, opening, and closing.
Original languageEnglish
Article numberSPE-163633-PA
Pages (from-to)115 - 132
Number of pages18
JournalSPE Reservoir Evaluation & Engineering
Volume18
Issue number2
Early online date8 May 2015
DOIs
Publication statusPublished - May 2015

Fingerprint

Flow simulation
finite element method
Finite element method
modeling
simulation
Rocks
Multiphase flow
Fluid mechanics
Numerical methods
fluid mechanics
fracture propagation
multiphase flow
Polynomials
pillar
model test
rock
numerical method
Geometry
saturation
Costs

Keywords

  • Reservoir Modeling
  • Flow Simulation

Cite this

Jackson, M. D., Percival, J. R., Mostaghimi, P., Tollit, B., Pavlidis, D., Pain, C. C., ... Blunt, M. (2015). Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method. SPE Reservoir Evaluation & Engineering, 18(2), 115 - 132. [SPE-163633-PA]. https://doi.org/10.2118/163633-PA

Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method. / Jackson, Matthew D.; Percival, James R.; Mostaghimi, Peyman; Tollit, Brendan; Pavlidis, Dimitrios; Pain, Christopher C.; Gomes, Jefferson Luis Melo De Almeida; ELSheikh, Ahmed; Salinas, Pablo; Muggeridge, Ann H.; Blunt, Martin.

In: SPE Reservoir Evaluation & Engineering, Vol. 18, No. 2, SPE-163633-PA, 05.2015, p. 115 - 132.

Research output: Contribution to journalArticle

Jackson, MD, Percival, JR, Mostaghimi, P, Tollit, B, Pavlidis, D, Pain, CC, Gomes, JLMDA, ELSheikh, A, Salinas, P, Muggeridge, AH & Blunt, M 2015, 'Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method', SPE Reservoir Evaluation & Engineering, vol. 18, no. 2, SPE-163633-PA, pp. 115 - 132. https://doi.org/10.2118/163633-PA
Jackson, Matthew D. ; Percival, James R. ; Mostaghimi, Peyman ; Tollit, Brendan ; Pavlidis, Dimitrios ; Pain, Christopher C. ; Gomes, Jefferson Luis Melo De Almeida ; ELSheikh, Ahmed ; Salinas, Pablo ; Muggeridge, Ann H. ; Blunt, Martin. / Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method. In: SPE Reservoir Evaluation & Engineering. 2015 ; Vol. 18, No. 2. pp. 115 - 132.
@article{532fc2e230194bc1b7bae8a4d370ef01,
title = "Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method",
abstract = "We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation.  Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional cornerpoint or unstructured grids. Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N+1) representation for pressure. This method exactly represents Darcyforce balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptivemesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required. After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic features that are typically lost. The approach may also be used to capture near-wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations, and, in future applications, geomechanical models with fracture propagation, opening, and closing.",
keywords = "Reservoir Modeling, Flow Simulation",
author = "Jackson, {Matthew D.} and Percival, {James R.} and Peyman Mostaghimi and Brendan Tollit and Dimitrios Pavlidis and Pain, {Christopher C.} and Gomes, {Jefferson Luis Melo De Almeida} and Ahmed ELSheikh and Pablo Salinas and Muggeridge, {Ann H.} and Martin Blunt",
note = "Acknowledgements Funding for authors Gomes, El-Sheikh, Percival, Salinas, and Blunt, and partial funding for Jackson and Pain, from the Qatar Carbonates and Carbon Storage Research Centre, provided jointly by Qatar Petroleum, Shell, and the Quatar Science & Technology Park, is gratefully acknowledged. Partial funding for Jackson and Muggeridge under the Total Chairs program at Imperial College is also acknowledged. Schlumberger is thanked for providing the Eclipse 100 software.",
year = "2015",
month = "5",
doi = "10.2118/163633-PA",
language = "English",
volume = "18",
pages = "115 -- 132",
journal = "SPE Reservoir Evaluation & Engineering",
issn = "1094-6470",
publisher = "Society of Petroleum Engineers (SPE)",
number = "2",

}

TY - JOUR

T1 - Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method

AU - Jackson, Matthew D.

AU - Percival, James R.

AU - Mostaghimi, Peyman

AU - Tollit, Brendan

AU - Pavlidis, Dimitrios

AU - Pain, Christopher C.

AU - Gomes, Jefferson Luis Melo De Almeida

AU - ELSheikh, Ahmed

AU - Salinas, Pablo

AU - Muggeridge, Ann H.

AU - Blunt, Martin

N1 - Acknowledgements Funding for authors Gomes, El-Sheikh, Percival, Salinas, and Blunt, and partial funding for Jackson and Pain, from the Qatar Carbonates and Carbon Storage Research Centre, provided jointly by Qatar Petroleum, Shell, and the Quatar Science & Technology Park, is gratefully acknowledged. Partial funding for Jackson and Muggeridge under the Total Chairs program at Imperial College is also acknowledged. Schlumberger is thanked for providing the Eclipse 100 software.

PY - 2015/5

Y1 - 2015/5

N2 - We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation.  Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional cornerpoint or unstructured grids. Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N+1) representation for pressure. This method exactly represents Darcyforce balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptivemesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required. After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic features that are typically lost. The approach may also be used to capture near-wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations, and, in future applications, geomechanical models with fracture propagation, opening, and closing.

AB - We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation.  Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional cornerpoint or unstructured grids. Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N+1) representation for pressure. This method exactly represents Darcyforce balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptivemesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required. After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic features that are typically lost. The approach may also be used to capture near-wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations, and, in future applications, geomechanical models with fracture propagation, opening, and closing.

KW - Reservoir Modeling

KW - Flow Simulation

U2 - 10.2118/163633-PA

DO - 10.2118/163633-PA

M3 - Article

VL - 18

SP - 115

EP - 132

JO - SPE Reservoir Evaluation & Engineering

JF - SPE Reservoir Evaluation & Engineering

SN - 1094-6470

IS - 2

M1 - SPE-163633-PA

ER -