Abstract
Injection of Newtonian fluids to displace pseudoplastic and dilatant fluids, governed by the power-law viscosity relationship, is common in many industrial processes. In these applications, changing the viscosity of the displaced fluid through velocity alteration can regulate interfacial instabilities, displacement efficiency, the thickness of the static wall layer, and the injected fluid’s tendency to move toward particular parts of the channel. The dynamic behavior of the fluid–fluid interface in the case of immiscibility is highly complicated and complex. In this study, a code was developed that utilizes a multi-component model of the lattice Boltzmann method to decrease the computational cost and accurately model these problems. Accordingly, a 2D inclined channel, filled with a stagnant incompressible Newtonian fluid in the initial section followed by a power-law material, was modeled for numerous scenarios. In conclusion, the results indicate that reducing the power-law index can regulate interfacial instabilities leading to dynamic deformation of static wall layers at the top and the bottom of the channel. However, it does not guarantee a reduction in the thickness of these layers, which is crucial to improve displacement efficiency. The impacts of the compatibility factor and power-law index variations on the filling pattern and finger structure were intensively evaluated.
Highlights
In many industrial applications, such as oil recovery [1], food processing, coating, and the transfer of crude oil in pipe-like paths [2], a fluid is injected to displace another fluid in the desired direction
The possibility of imposing hydrodynamic, bounce back, slip, no-slip, fully developed, and open boundary conditions enabled us to implement the code for modeling a large variety of multiphase flows. Using this numerical tool and the He–Chen–Zhang method to simulate the problem of this study reduced the simulation time to less than 7 h, whereas it might take a few days if other computational fluid dynamics methods were used
With the increase of the power-law index, the advance rate of the injected fluid and the displacement efficiency are enhanced in most cross-sections (Figure 20)
Summary
In many industrial applications, such as oil recovery [1], food processing, coating, and the transfer of crude oil in pipe-like paths [2], a fluid is injected to displace another fluid in the desired direction. Goyal and Meiburg [9] investigated miscible displacements of highly viscous fluids by other fluids. They observed that increasing flow rate could turn two-dimensional instabilities (caused by the shear stress between the two fluids) into three-dimensional instabilities. This result is in good agreement with laboratory [10] and theoretical [11] investigations. The observation of tiny instabilities in such flows was in good agreement with their previous studies analyzing the linear stability of fingering structures [15]. Roll-up structures are observed in miscible displacements [17,18], while sawtooth structures occur in immiscible displacements [19]
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