Upscaling a Heterogeneous Reservoir using a Streamline-based Mesh Generation Incorporated with Multi-Point Flux Approximation

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2010 Vol.47, Issue 2 Preview Page Next Page

Upscaling a Heterogeneous Reservoir using a Streamline-based Mesh Generation Incorporated with Multi-Point Flux Approximation 다격자유량보정과 유선기반 격자생성법을 결합한 불균질 저류층 업스케일링 기법: 김장학 , 박창협 , 강주명
Janghak Kim, Changhyup Park and Joe M. Kang

30 April 2010. pp. 168-176

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Abstract

A new upscaling approach by integrating MPFA (Multi-Point Flux Approximation) into a streamline-based mesh generator is presented to characterize flow transport accurately in a heterogeneous reservoir. Previous mesh generations have tended to cover the topological features rather than hydraulic ones and thereby they might result in a biased pressure distribution in an irregular grid-system. The upscaling schemes for more efficient simulation reduced the accuracy so that it was difficult to get both effects of efficiency and accuracy with one mesh generation. The method, developed in the study, incorporated streamline tracing in original structured grids, MPFA (Multi-Point Flux Approximation) for accurate flux-calculation and Delaunay triangular meshing for fast re-meshing. The aspect ratio examined the accuracy of pressure distribution and the upscaling coefficient investigated the effectiveness of the proposed scheme. Its applicability was verified in a homogeneous case to show the improved accuracy close to the result of fine grids with comparatively small number of nodes. The statistical properties like mean, standard deviation and coefficient of variation were conserved relatively well after upscaling a heterogeneous reservoir with unstructured quadrilateral meshes. The proposed method was able to combine different types of topological and hydraulic information, and offered effective means for generating subsurface flow models from highly detailed geological descriptions.

Keywords

Upscaling

Streamline

MPFA

Delaunay

Heterogeneous reservoir

불균질 저류층의 유체 거동 특성을 정확하게 분석할 수 있는 다격자유량보정법(MPFA; Multi-PointFlux Approximation)과 유선기반 격자생성법을 결합한 업스케일링 기법을 개발하였다. 기존 격자생성법은 저류층의 수리학적 물성보다는 기하학적 특성에 초점을 맞춤으로써 비정규격자망에서 편향된 압력분포를 보일 위험이 있었다. 업스케일링법은 효율적 전산모사를 위해 도입되었으나 업스케일링 정도에 따라 유동모사의 정확도를 감소시키는 문제점이 있어, 유동모사의 효율성과 정확성을 모두 확보하는 격자생성법의 연구가 필요하다. 이 연구에서 개발한 격자생성법은 정규격자망에서 정확한 유동특징을 파악하기 위해 다격자유량보정법 조력 유선 추적법과 빠른 비정규격자 재구성을 위해 딜로니(Delaunay) 삼각격자법을 통합하였다. 압력분포종횡비를 통해 압력계산의 정확도를 파악하고, 업스케일링 상수를 통해 업스케일링 효율성을 분석하였다. 균질 저류층의 경우 350개의 노드만으로 10,000개 노드를 가진 미세격자망의 수치정확도와 유사한 결과를 보였으며, 업스케일링 상수도 0.475로 기존 방법에 비해 효과적이었다. 비정규격자망 불균질 저류층의 경우, 압력값의 변동없이 업스케일링이 이루어졌을 뿐만 아니라 유체투과도의 평균, 표준편차, 변동계수 등의 통계변수가 비교적 잘 보존되었다.이 연구의 격자생성법은 다양한 규모의 수리학적, 구조학적 특징을 결합할 수 있을 뿐만 아니라, 고해상도 저류층 모델의 업스케일링 효율성을 확보할 수 있을 것으로 기대된다.

키워드

업스케일링

유선

다격자유량보정

딜로니 삼각화

불균질 저류층

References

김신영, 2007, 다격자 유량예측법을 이용한 자연 균열저류층의 2상 유동해석, 공학석사학위논문, 서울대학교.
박창협, 강주명, 2005, “비정규격자망 유선모사법을 이용한 3차원 불균질 균열 저류층의 비정상이동 해석,” 한국지구시스템공학회지, Vol. 42, No. 3, pp. 143-151.
Avatsmark, I., 2002, “An Introduction to Multipoint Flux Approximations for Quadrilateral Grids,” Computational Geoscience, Vol. 6, No. 3-4, pp. 405-432.
Durlofsky, L.J., Jones, R.C., and Milliken, W.J., 1997, “A Non-Uniform Coarsening Approach for the Scale-Up of Displacement Processes in Heterogeneous Porous Media,” Advances Water Resources, Vol. 20, No. 5-6, pp. 335-347.
Eigestad, G.T., Aavatsmark, I., Reiso, E., Reme, H., and Teigland, R., 2001, “MPFA Methods Applied To irregular grids and faults,” Developments in water science, Vol. 47, pp. 413-420.
Gherabati, S.A., Dabir, B., and Hesami, A., 2008, “Wellincluded Flow-based Grid Generation for Heterogeneous Reservoirs,” paper SPE 114422 presented at the 2008 SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 21-24 September.
George, P.L., 1991, Automatic Mesh Generation: Application to Finite Element Methods, Wiley, New York.
Hægland, H., Dahle, H.K., Eigestad, G.T., Lie, K.-A., and Aavatsmark, I., 2007, “Improved Streamlines and Timeof- flight for Streamline Simulation on Irregular Grids,” Advances Water Resources, Vol. 30, No. 4, pp. 1027-1045.
He, C. and Durlofsky, L.J., 2006, “Structured Flow-based Gridding and Upscaling for Modeling Subsurface Flow,” Advances in Water Resources, Vol. 29, No. 12, pp. 1876-1892.
Matringe, S.F., Juanes, R., and Tchelepi, H.A., 2006, “Tracing Streamlines on Unstructured Grids from Finite Volume Discretizations,” paper SPE 103295 presented at the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24-27 September.
Park, C. and Kang, J.M., 2008, “Characterization of Tracer Transport in Heterogeneous Fractured Reservoir by a Streamline Approach on Unstructured Grids,” Energy Sources Part A, Vol. 30, No.9, pp. 856-871.
Prévost, M., 2003, Accurate Coarse Reservoir Modeling using Unstructured Grids, Flow-based Upscaling and Streamline Simulation, Ph. D dissertation, Stanford University.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society for Geosystem Engineering
Journal Title(Ko) :한국지구시스템공학회지
Volume : 47
No :2
Pages :168-176

[1] 김신영, 2007, 다격자 유량예측법을 이용한 자연 균열저류층의 2상 유동해석, 공학석사학위논문, 서울대학교.

[2] 박창협, 강주명, 2005, “비정규격자망 유선모사법을 이용한 3차원 불균질 균열 저류층의 비정상이동 해석,” 한국지구시스템공학회지, Vol. 42, No. 3, pp. 143-151.

[3] Avatsmark, I., 2002, “An Introduction to Multipoint Flux Approximations for Quadrilateral Grids,” Computational Geoscience, Vol. 6, No. 3-4, pp. 405-432.

[4] Durlofsky, L.J., Jones, R.C., and Milliken, W.J., 1997, “A Non-Uniform Coarsening Approach for the Scale-Up of Displacement Processes in Heterogeneous Porous Media,” Advances Water Resources, Vol. 20, No. 5-6, pp. 335-347.

[5] Eigestad, G.T., Aavatsmark, I., Reiso, E., Reme, H., and Teigland, R., 2001, “MPFA Methods Applied To irregular grids and faults,” Developments in water science, Vol. 47, pp. 413-420.

[6] Gherabati, S.A., Dabir, B., and Hesami, A., 2008, “Wellincluded Flow-based Grid Generation for Heterogeneous Reservoirs,” paper SPE 114422 presented at the 2008 SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 21-24 September.

[7] George, P.L., 1991, Automatic Mesh Generation: Application to Finite Element Methods, Wiley, New York.

[8] Hægland, H., Dahle, H.K., Eigestad, G.T., Lie, K.-A., and Aavatsmark, I., 2007, “Improved Streamlines and Timeof- flight for Streamline Simulation on Irregular Grids,” Advances Water Resources, Vol. 30, No. 4, pp. 1027-1045.

[9] He, C. and Durlofsky, L.J., 2006, “Structured Flow-based Gridding and Upscaling for Modeling Subsurface Flow,” Advances in Water Resources, Vol. 29, No. 12, pp. 1876-1892.

[10] Matringe, S.F., Juanes, R., and Tchelepi, H.A., 2006, “Tracing Streamlines on Unstructured Grids from Finite Volume Discretizations,” paper SPE 103295 presented at the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24-27 September.

[11] Park, C. and Kang, J.M., 2008, “Characterization of Tracer Transport in Heterogeneous Fractured Reservoir by a Streamline Approach on Unstructured Grids,” Energy Sources Part A, Vol. 30, No.9, pp. 856-871.

[12] Prévost, M., 2003, Accurate Coarse Reservoir Modeling using Unstructured Grids, Flow-based Upscaling and Streamline Simulation, Ph. D dissertation, Stanford University.

Journal of the Korean Society of Mineral and Energy Resources Engineers ISSN:2288-0291(Print) 2288-2790(Online) 한국자원공학회지

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