A distributed parallel direct simulator for pore-scale two-phase flow on digital rock images using a finite difference implementation of the phase-field method

Alpak FO, Samardžić A, Frank F (2018)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2018

Journal

Journal of Petroleum Science and Engineering Elsevier

Book Volume: 166

Pages Range: 806–824

URI: https://www.sciencedirect.com/science/article/abs/pii/S0920410517309051?via=ihub

DOI: 10.1016/j.petrol.2017.11.022

Abstract

The phase-field method is a ver­sa­tile and ro­bust tech­nique for mod­el­ing in­ter­fa­cial mo­tion in mul­ti­phase flows in pore-scale me­dia. The method pro­vides an ef­fec­tive way to ac­count for sur­face ef­fects by use of dif­fuse in­ter­faces. The re­sult­ing model sig­nif­i­cantly sim­pli­fies the nu­mer­i­cal im­ple­men­ta­tion of mass trans­port and mo­men­tum bal­ance solvers for sim­u­lat­ing two-phase flow with a large num­ber of mov­ing in­ter­faces. The in­ter­faces can be gen­er­ated, trans­ported or de­stroyed based on a ther­mo­dy­namic Helmholtz free-en­ergy min­i­miza­tion frame­work un­der­pin­ning the gov­ern­ing equa­tions. The phase-field method ac­cu­rately con­serves mass and is rel­a­tively straight­for­ward to im­ple­ment in con­junc­tion with con­tact an­gle mod­els that ac­count for wet­ta­bil­ity on rock sur­faces. The un­der­ly­ing free-en­ergy min­i­miza­tion frame­work leads to the ad­vec­tive Cahn-Hilliard equa­tion and mod­i­fied Navier-Stokes equa­tions that de­scribe the phase-field model.
We have im­ple­mented a par­tic­u­lar vari­ant of the phase-field method (PFM) into the com­pu­ta­tional core of a pore-scale mul­ti­phase flow sim­u­la­tor, namely PMFS-PFM, for the nu­mer­i­cal sim­u­la­tions of in­com­press­ible flows of two im­mis­ci­ble fluid phases. The im­ple­men­ta­tion was dis­cussed in a pre­vi­ous pa­per for rec­tan­gu­lar prism-shaped fully-con­nected do­mains, e.g., for sim­u­lat­ing two-phase flow in a 2D slit or a 3D duct (Al­pak et al., 2016). In this pa­per, we dis­cuss the re­cent de­vel­op­ments on PMFS-PFM. The main com­po­nents of the new work are (I) im­ple­men­ta­tion of sup­port for in­ac­tive cells in PMFS-PFM by ex­tend­ing the orig­i­nal fi­nite-vol­ume method-based dis­cretiza­tions of the un­der­ly­ing par­tial dif­fer­en­tial equa­tions (PDEs) in or­der to solve re­al­is­tic 3D pore-scale flow prob­lems on rock vol­umes stem­ming from imag­ing, and (II) en­hanc­ing the per­for­mance of the sim­u­la­tor through im­ple­men­ta­tion of mod­ern sparse lin­ear solvers and dis­trib­uted par­al­lel com­put­ing. It has been shown that the sim­u­la­tions per­formed on com­plex pore-scale do­mains are con­sis­tent with the physics of the im­mis­ci­ble two-phase dis­place­ment. The par­al­lel scal­a­bil­ity of the code is rea­son­ably well vary­ing be­tween 50% and 86% on the in­ves­ti­gated test cases of vary­ing com­plex­ity. Re­sults in­di­cate that the more dis­con­nected the pore-scale do­mains, the lower the par­al­lel ef­fi­ciency. It has been noted that there is a pos­si­bil­ity of im­prov­ing the par­al­lel ef­fi­ciency by ex­plor­ing var­i­ous grid sub­di­vi­sions.

Authors with CRIS profile

Florian Frank Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Shell Global Solutions International B.V. NL Netherlands (NL)

How to cite

APA:

Alpak, F.O., Samardžić, A., & Frank, F. (2018). A distributed parallel direct simulator for pore-scale two-phase flow on digital rock images using a finite difference implementation of the phase-field method. Journal of Petroleum Science and Engineering, 166, 806–824. https://doi.org/10.1016/j.petrol.2017.11.022

MLA:

Alpak, Faruk Omer, Alexander Samardžić, and Florian Frank. "A distributed parallel direct simulator for pore-scale two-phase flow on digital rock images using a finite difference implementation of the phase-field method." Journal of Petroleum Science and Engineering 166 (2018): 806–824.

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