The Open Petroleum Engineering Journal


ISSN: 1874-8341 ― Volume 12, 2019

Lattice Boltzmann Simulation of Natural Convection in a Fractured Petroleum Reservoir Domain: Single-Phase and Multi-Phases Investigations

Hossein Kaydani1, Ali Mohebbi1, *, Amir Ahmad Forghani2
1 Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
2 School of Chemical & Petroleum Engineering, Curtin University, Bentley, Western Australia, Australia



Natural convection is one of the main effective production mechanisms in a fractured petroleum reservoir.


This paper investigated the simulation of natural convection heat transfer in a fracture domain of petroleum reservoir.


This is done by using Lattice-Boltzmann Equation (LBE) method. In this study, a D2Q9 lattice model was coupled with the passive-scalar lattice thermal model to represent density, velocity and internal energy distribution function, respectively.

Results and Conclusion:

The results were in excellent agreement with CFD results from the literature. The effects of Rayleigh number and Aspect-Ratio (AR) on flow pattern and temperature distribution were studied. The results indicated that natural convection rate increased with the Rayleigh number increment. The local Nusselt number (Nu) was evaluated on the hot wall and it was rising with increasing the Rayleigh number. Streamlines and temperature field were affected significantly by changing the aspect-ratio. Moreover, first of all, natural convection in Single Component Mutli-Phase (SCMP) was discussed and here and then after validation of SCMP model, the results indicated that the streamline and isotherm were affected by second phases because of the formation of two-phase flow in some of the reservoirs or production period.

Keywords: Natural convection, Lattice-Boltzmann Equation (LBE), Rayleigh number, Fractured petroleum reservoir, Single Component Multi-phase model (SCMP), Nusselt number.

Article Information

Identifiers and Pagination:

Year: 2018
Volume: 11
First Page: 48
Last Page: 66
Publisher Id: TOPEJ-11-48
DOI: 10.2174/1874834101811010048

Article History:

Received Date: 23/2/2018
Revision Received Date: 4/04/2018
Acceptance Date: 12/04/2018
Electronic publication date: 30/4/2018
Collection year: 2018

© 2018 Kaydani et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran, Tel +983432118298, Fax: +983432118298; Emails:;

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