Abstract
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.
Highlights
The reservoir is the network of rock skeletons that surround a sealed oil and gas trap, as well as the generic term for the fluid contained in pore fractures and karst caves
Sensitivity analysis is performed on the initial crude oil viscosity, initial water saturation, initial pressure, and other parameters that affect the production dynamic data, and the correctness of this method is verified in the numerical solution of fractal reservoir oil-water two-phase flow using the above-mentioned theories and methods
5 Conclusion The weighted least squares meshless method is introduced in this paper to solve an oil reservoir oil-water two-phase flow model with fractal characteristics
Summary
The reservoir is the network of rock skeletons that surround a sealed oil and gas trap, as well as the generic term for the fluid contained in pore fractures and karst caves. Over the last two decades, extensive research on the transport characteristics of porous media in oil reservoirs based on fractal theory has been conducted in the field of petroleum engineering [3]. In 1996, Spanish researchers E Onate proposed the finite point method (FPM) [11] This method constructs the shape function using the moving least squares principle and discretizes it using the collocation scheme; it is a completely meshless method that does not require a background grid and is primarily used in the field of fluid mechanics. Gas fracturing wells, they solved the gas-water two-phase flow model using the weighted least squares meshless method [15] This Paper introduces the fractal permeability expression, establishes a numerical model of fractal oil reservoir two-phase, and solves it using the weighted least squares meshless method (MWLS). Relevant examples are provided to demonstrate the accuracy and benefits of this method
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