Three-dimensional visualization of viscous fingering for non-Newtonian fluids with chemical reactions that change viscosity

Viscous fingering (VF) is a hydrodynamic flow instability that occurs when a less-viscous liquid (LVL) displaces a more-viscous liquid (MVL) in porous media and takes place in either miscible or immiscible systems. In this study, we investigated the three-dimensional (3D) characteristics of VF for miscible non-Newtonian fluids with and without chemical reactions using a microfocus x-ray computed tomography scanner. When the viscosity of a system increased with a chemical reaction, the VF was suppressed, and pistonlike displacement occurred. The cylindrical domain of displacing LVL was surrounded by a high-viscosity filmlike layer because of the chemical reaction that impeded the mixing of the LVL and MVL. Consequently, the high LVL concentration inside this layer was retained without mixing with the MVL. A clear local peak in viscosity appeared in the viscosity profiles at the interface between the LVL and MVL. Behind the peak, an unfavorable viscosity profile of increasing viscosity along the flow direction appeared, but the VF was not induced because of the smooth viscosity gradients. After the peak, the viscosity profiles were in favorable conditions. In the nonreactive case, the tip of the fingers further advanced compared with that in the reactive case and went further with the decrease in Pe, which reflected the property of shear-thinning fluids. By contrast, in a decreasing-viscosity system with a chemical reaction, the tips of the fingers were located at a larger distance compared with that without reaction. The concentration in the finger intensively decreased from the point of injection because of the intensive mixing of the LVL and MVL. As a result, the area fraction of injected LVL in the reactive cases was lower than that in the nonreactive cases. The tip of the finger advanced with time, whereas LVL concentration in the finger hardly recovered above 0.4 in the reactive case, which reflected intensive fingering and mixing.

Figure 1

Schematic of the experimental procedures.

Figure 2

Dependence of the viscosity of the mixtures of (a) PAA-NaOH, (b) PAA-NaI, (c) SPA-HCl, and (d) SPA-NaI on the shear rate under various volume fractions.

Figure 3

Dependence of the viscosity of the solutions of (a) PAA-NaOH, (b) PAA-NaI, (c) SPA-HCl, and (d) SPA-NaI on the LVL volume fraction under various shear rates.

Figure 4

3D VF structure in the packed bed after injection of 0.05 PV of LVL for various Pe and M for the (a) reactive (PAA-NaOH) and (b) nonreactive (PAA-NaI) fluid pairs. The isocontour surface corresponds to the LVL concentration $f=C/C_0=0.25$. The three panels given for each M and Pe represent the results from three repeated experiments with the same experimental conditions.

Figure 5

Evolution of (a) 3D structure of the fingers, (b) LVL concentration, and (c) viscosity with chemical reaction (PAA-NaOH) at $\mathrm{Pe}=1.42\times {10}^2$ and $M=452.46$ after injection of LVL (i) 0.02, (ii) 0.04, (iii) 0.10, (iv) 0.20, and (v) 0.30 PV.

Figure 6

Evolution of the (a) 3D structure of fingers, (b) LVL concentration, and (c) viscosity without chemical reaction (PAA-NaI) at $\mathrm{Pe}=1.42\times {10}^2$ and $M=460.40$ after injection of LVL (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.04, and (v) 0.05 PV.

Figure 7

Area fraction of LVL for various Pe values after injection of 0.05 PV of LVL for the (a) reactive (PAA-NaOH) and (b) nonreactive (PAA-NaI) fluid systems.

Figure 8

Distribution of the normalized concentration of LVL $f=C_{\max }/C_0$ along the most advanced fingers for various Pe values for the (a) reactive (PAA-NaOH) and (b) nonreactive (PAA-NaI) cases. The figures at the top show the distribution of the normalized concentration after injection of 0.05 PV of LVL for high Pe values ($1.42\times {10}^3$, $2.84\times {10}^3$, and $5.68\times {10}^3$). The figures at the bottom show the successive distribution after injection of (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.04, (v) 0.05, (vi) 0.10, (vii) 0.15, (viii) 0.20, and (ix) 0.25 PV for low Pe ($1.42\times {10}^2$).

Figure 9

Viscosity distribution along the most advanced finger for the (a) reactive (PAA-NaOH) and (b) nonreactive (PAA-NaI) cases. According to the relationship between the viscosity and LVL concentration, the concentration distribution shown in Fig. 8 is transformed into viscosity. The figures at the top show the viscosity distribution after injection of 0.05 PV of LVL for high Pe values ($1.42\times {10}^3$, $2.84\times {10}^3$, and $5.68\times {10}^3$). The figures at the bottom show the successive distribution after injection of (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.04, (v) 0.05, (vi) 0.10, (vii) 0.15, (viii) 0.20, and (ix) 0.25 PV for low Pe ($1.42\times {10}^2$).

Figure 10

3D VF structure in the packed bed after injection of 0.05 PV of LVL for various Pe and M values for the (a) reactive (SPA-HCl) and (b) nonreactive (SPA-NaI) fluid pairs. The isocontour surface corresponds to the concentration of LVL, $f=C/C_0=0.25$. The three panels given for each M and Pe represent the results from three repeated experiments with the same experimental conditions.

Figure 11

Evolution of the (a) 3D structure of the fingers, (b) LVL concentration, and (c) viscosity with chemical reaction (SPA-HCl) at $\mathrm{Pe}=0.71\times {10}^2$ and $M=2608.65$ after injection of LVL with (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.04, and (v) 0.05 PV.

Figure 12

Evolution of the (a) 3D structure of fingers, (b) LVL concentration, and (c) viscosity without chemical reaction (SPA-NaI) at $\mathrm{Pe}=0.71\times {10}^2$ and $M=2522.02$ after injection of LVL with (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.05, and (v) 0.07 PV.

Figure 13

Area fraction of the LVL for various Pe values after injection of 0.05 PV of LVL for the (a) reactive (SPA-HCl) and (b) nonreactive (SPA-NaI) fluid systems.

Figure 14

Distribution of the normalized concentration of LVL $f=C_{\max }/C_0$ along the most advanced fingers for various Pe values for the (a) reactive (SPA-HCl) and (b) nonreactive (SPA-NaI) cases. The figures at the top show the distribution of the normalized concentration after injection of 0.05 PV of LVL for high Pe values ($1.42\times {10}^3$, $2.84\times {10}^3$, and $5.68\times {10}^3$). The figures at the bottom show the successive distribution after injection of (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.04, (v) 0.05, (vi) 0.06, and (vii) 0.07 PV for low Pe ($0.71\times {10}^2$).

Figure 15

Viscosity distribution along the most advanced finger for the (a) reactive (SPA-HCl) and (b) nonreactive (SPA-NaI) cases. According to the relationship between the viscosity and LVL concentration, the concentration distribution shown in Fig. 14 is transformed into viscosity. The figures at the top show the viscosity distribution after injection of 0.05 PV of LVL for high Pe values ($1.42\times {10}^3$, $2.84\times {10}^3$, and $5.68\times {10}^3$). The figures at the bottom show the successive distribution after injection of (i) 0.01, (ii) 0.02, (iii) 0.03, (iv) 0.04, (v) 0.05, (vi) 0.06, and (vii) 0.07 PV for low Pe ($0.71\times {10}^2$).

Figure 16

Sweep efficiency for the (a) increasing-viscosity and (b) decreasing-viscosity systems. Three points in the reactive and nonreactive cases for each Pe represent the results from three repeated experiments with the same experimental conditions.