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In this study, the fingering instability in displacement of Newtonian fluid by viscoelastic fluid through heterogeneous media is investigated using spectral method and Hartley transforms. The White- Metzner model has been used as the constitutive equation. This model can be presented the shear- thinning and elastic behaviors of viscoelastic fluid very well. The heterogeneity of the media is considered in two different types. In the first case, the permeability of medium exponentially decreases in the transversely section. This case is named decreasing heterogeneity. In the second case, the permeability of the medium will initially be increasing and it reaches to its maximum at the middle of the cross-section and then decreases. This type of heterogeneity is called parabolic heterogeneity. The results are included concentration contours, mixing length and sweep efficiency. It can be seen that in the first case, the degree of heterogeneity has little effect on the structure of fingers. However, increasing in this parameter leads to decrease in mixing length and increase in sweep efficiency. But, in the latter case, with the change in the degree of heterogeneity, the finger structure will be strongly affected. In addition, in this case, increasing the degree of heterogeneity will increase the mixing length and reduce the sweep efficiency. Also, in both cases, the flow becomes more unstable by the shear thinning property of viscoelastic fluid. Although it seems this effect is less in medium with parabolic heterogeneity.

Keywords: Fingering instability, Viscoelastic fluid, White- Metzner model, heterogeneous media

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