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Two Phase Flow Simulation of Fractal Oil Reservoir Based on Meshless Method

Xian Zhou1, Fei Wang2, Ziyu Wang3, Yunfeng Xu1,*
1 School of Petroleum Engineering, Yangtze University, Wuhan, 430100, China
2 China Oilfield Services Limited, Tianjin, China
3 Xinmin Oil Production Plant of Jilin Oilfield Company, PetroChina, Songyuan, 138000, China
* Corresponding Author: Yunfeng Xu. Email:
(This article belongs to this Special Issue: Simulation of Flow and Transport Problems in Petroleum Engineering)

Energy Engineering 2022, 119(2), 653-664.

Received 01 September 2021; Accepted 21 October 2021; Issue published 24 January 2022


The reservoir is the networked rock skeleton of an oil and gas trap, as well as the generic term for the fluid contained within pore fractures and karst caves. Heterogeneity and a complex internal pore structure characterize the reservoir rock. By introducing the fractal permeability formula, this paper establishes a fractal mathematical model of oil-water two-phase flow in an oil reservoir with heterogeneity characteristics and numerically solves the mathematical model using the weighted least squares meshless method. Additionally, the method’s correctness is verified by comparison to the exact solution. The numerical results demonstrate that the fractal oil-water two-phase flow mathematical model developed using the meshless method is capable of more accurately and efficiently describing the flow characteristics of the oil-water two-phase migration process. In comparison to the conventional numerical model, this method achieves a greater degree of convergence and stability. This paper examines the effect of varying the initial viscosity of the oil, the initial formation pressure, and the production and injection ratios on daily oil production per well, water cut in the block, and accumulated oil in the block. For 10 and 60 cp initial crude oil viscosities, the water cut can be 0.62 and 0.80, with 3100 and 1900 m3 cumulative oil production. Initial pressures have little effect on production. In this case, the daily oil production of well PRO1 is 1.7 m3 at 7 and 10 MPa initial pressure. Block cumulative oil production is 3465.4 and 2149.9 m3 when the production injection ratio is 1.4 and 0.8. The two-phase meshless method described in this paper is essential for a rational and effective study of production dynamics patterns in complex reservoirs and the development of reservoir simulations of oil-water flow in heterogeneous reservoirs.


Oil-water two-phase flow; fractal theory; weighted least square method; meshless method

Cite This Article

Zhou, X., Wang, F., Wang, Z., Xu, Y. (2022). Two Phase Flow Simulation of Fractal Oil Reservoir Based on Meshless Method. Energy Engineering, 119(2), 653–664.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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