Unified finite difference modeling of transient flow in naturally fractured carbonate karst reservoirs - A 3D case study

Jie He, John E. Killough, Mohamed Fadlelmula, Michael Fraim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

The modeling and numerical simulation of fluid flow in naturally fractured carbonate karst reservoirs are extremely challenging due to non-Darcy flow in vugs and caves connected by fracture networks. The momentum balance of such flow has been shown to be better described by the Brinkman equation both physically and mathematically, and many methods have been proposed in the literature dealing with the steady-state Brinkman model. We carry Brinkman's idea one step further and propose a transient flow model which consists of the Brinkman equation and a generalized material balance equation, and the latter has proven to be exact in the fractured carbonate karst reservoir. Finite differences are implemented for the solution of the proposed transient flow model. This solution method is more straightforward, easier to derive and implement, and more apt to generalization from 2D to 3D cases than alternative techniques. Numerical simulation of the transient Brinkman model requires explicit solution of not only pressure at the center of each grid block, but also velocities at the interfaces between the blocks, which exaggerates the computational cost and makes the computational process more difficult and less stable. In this paper, we propose a simplified finite difference formulation of the transient Brinkman model, which significantly reduces the computational time of the simulation process, and improves accuracy and stability of the simulation results. We update our reservoir simulator with this new formulation and illustrate it with a complex 3D naturally fractured carbonate karst reservoir model. The results of this study form the foundation for future 3D multi-phase reservoir cases.

Original languageEnglish
Title of host publicationSociety of Petroleum Engineers - SPE Annual Technical Conference and Exhibition, ATCE 2015
PublisherSociety of Petroleum Engineers (SPE)
Pages5420-5431
Number of pages12
Volume2015-January
ISBN (Electronic)9781510813229
Publication statusPublished - 2015
Externally publishedYes
EventSPE Annual Technical Conference and Exhibition, ATCE 2015 - Houston, United States
Duration: 28 Sep 201530 Sep 2015

Other

OtherSPE Annual Technical Conference and Exhibition, ATCE 2015
CountryUnited States
CityHouston
Period28/9/1530/9/15

Fingerprint

Carbonates
Caves
Computer simulation
Flow of fluids
Momentum
Simulators
Costs

ASJC Scopus subject areas

  • Fuel Technology
  • Energy Engineering and Power Technology

Cite this

He, J., Killough, J. E., Fadlelmula, M., & Fraim, M. (2015). Unified finite difference modeling of transient flow in naturally fractured carbonate karst reservoirs - A 3D case study. In Society of Petroleum Engineers - SPE Annual Technical Conference and Exhibition, ATCE 2015 (Vol. 2015-January, pp. 5420-5431). Society of Petroleum Engineers (SPE).

Unified finite difference modeling of transient flow in naturally fractured carbonate karst reservoirs - A 3D case study. / He, Jie; Killough, John E.; Fadlelmula, Mohamed; Fraim, Michael.

Society of Petroleum Engineers - SPE Annual Technical Conference and Exhibition, ATCE 2015. Vol. 2015-January Society of Petroleum Engineers (SPE), 2015. p. 5420-5431.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

He, J, Killough, JE, Fadlelmula, M & Fraim, M 2015, Unified finite difference modeling of transient flow in naturally fractured carbonate karst reservoirs - A 3D case study. in Society of Petroleum Engineers - SPE Annual Technical Conference and Exhibition, ATCE 2015. vol. 2015-January, Society of Petroleum Engineers (SPE), pp. 5420-5431, SPE Annual Technical Conference and Exhibition, ATCE 2015, Houston, United States, 28/9/15.
He J, Killough JE, Fadlelmula M, Fraim M. Unified finite difference modeling of transient flow in naturally fractured carbonate karst reservoirs - A 3D case study. In Society of Petroleum Engineers - SPE Annual Technical Conference and Exhibition, ATCE 2015. Vol. 2015-January. Society of Petroleum Engineers (SPE). 2015. p. 5420-5431
He, Jie ; Killough, John E. ; Fadlelmula, Mohamed ; Fraim, Michael. / Unified finite difference modeling of transient flow in naturally fractured carbonate karst reservoirs - A 3D case study. Society of Petroleum Engineers - SPE Annual Technical Conference and Exhibition, ATCE 2015. Vol. 2015-January Society of Petroleum Engineers (SPE), 2015. pp. 5420-5431
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