Growth activity during fingering in a porous Hele Shaw cell

tial resolution measurements. After fingers had fully developed, we added a dye tracer in order to distinguish mobile and immobile water fractions. Fully developed fingers consist of a tip, a core with mobile water, and a hull with immobile water. We analyzed the dynamics of water saturation within the finger tip, along the finger core behind the tip, and within the fringe of the fingers during radial growth. Our results confirm previous findings of saturation overshoot in the finger tips and revealed a saturation minimum behind the tip as a new feature. The finger development was characterized by a gradual increase in water content within the core of the finger behind this minimum and a gradual widening of the fingers to a quasi-stable state which evolves at time scales that are orders of magnitude longer than those of fingers' evolution. In this state, a sharp separation into a core with fast convective flow and a fringe with exceedingly slow flow was detected. All observed phenomena, with the exception of saturation overshoot, could be consistently explained based on the hysteretic behavior of the soil-water characteristic.

Europhysics Letters (epl), 2005

We study viscous fingering during drainage experiments in linear Hele-Shaw cells filled with a random porous medium. The central zone of the cell is found to be statistically more occupied than the average, and to have a lateral width of 40% of the system width, irrespectively of the capillary number $Ca$. A crossover length $w_f \propto Ca^{-1}$ separates lower scales where the invader's fractal dimension $D\simeq1.83$ is identical to capillary fingering, and larger scales where the dimension is found to be $D\simeq1.53$. The lateral width and the large scale dimension are lower than the results for Diffusion Limited Aggregation, but can be explained in terms of Dielectric Breakdown Model. Indeed, we show that when averaging over the quenched disorder in capillary thresholds, an effective law $v\propto (\nabla P)^2$ relates the average interface growth rate and the local pressure gradient.

International Journal of Multiphase Flow, 2014

We experimentally studied the displacement of a viscous wetting fluid (water) by an inviscid non-wetting fluid (air) injected at the bottom of a vertical Hele-Shaw cell filled with glass microbeads. In order to cover a wide parameter space, the permeability of the porous medium was varied by using different bead size ranges and diverse air flow rates were generated by means of a syringe pump. A LED light table was used to back illuminate the experimental cell, allowing a high speed camera to capture images of the drainage process at equal time intervals. The invasion occurred in intermittent bursts. Image processing of the bursts and fractal analysis showed successive transitions from capillary invasion to viscous fingering to fracturing during the same experiment, dependent on the medium permeability, the air injection flow rate, and the vertical position in the cell. The interplay between the capillary, viscous and gravity forces determines the nature of the invasion pattern and the transitions, from capillary invasion to viscous fingering with decreasing fluid pressure on one hand and from viscous fingering to fracturing with decreasing effective overburden pressure on the other hand.

A series of experiments are performed in a Hele-Shaw cell, consisting of two parallel closely spaced glass plates. A liquid (oil or water, both of viscosity of 1.0 cP) is injected a t a constant volumetric flow rate, q, to radially displace a much more viscous liquid (glycerine, 1050 cP) in the cell. Oil is immiscible with and water is miscible with glycerine. The data presented in this paper are taken mostly a t late stages of the fingering process, when the pattern has multiple generations of splitting. Correlations with time are obtained for the finger length and the overall pattern density. The time-and lengthscales have been found for the immiscible case. At the same dimensionless time, immiscible patterns are similar and have the same generation of splitting. The overall density of each pattern decreases with time. The pattern shows fractal behaviour only after a certain number of generations of splitting. The fractal dimension of the immiscible pattern decreases from 1.9 to 1.82 when the pattern goes from the third to the sixth generation of splitting. The fractal dimension of the miscible pattern reaches a constant value after about ten generations of splitting and the fractal dimension ranges from 1.50 to 1.69 for q/Db = 4.8 x lo5-7.0 x lo6. The miscible patterns are insensitive to dispersion for large q/Db. For immiscible fingers h / b scales with for capillary number Ca ranging from about 8 x to 0.05. For miscible fingers, h / b is insensitive to dispersion and ranges from 5 to 10 for large q/Db. Here D is the molecular diffusion coefficient in glycerine, b the cell gap width and h the splitting wavelength. WITTEN, T. A. & SANDER, L. M. 1983 Diffusion-limited aggregation. Phys. Rev. B 27,5686-5697. Shaw cell containing a more viscous liquid. Proc. R . SOC. Lond. A 245, 312-329. 3086-3088. instability. J . Fluid Mech. 177, 67-82. interface. J . Fluid Mech. 136, 1-30. J . Fluid Mech. 154, 287-301. of flow process in oil reservoirs. Trans. AIME 210, 295-301.

Energy, 2005

We have studied experimentally and numerically the displacement of a highly viscous wetting fluid by a non-wetting fluid with low viscosity in a random two-dimensional porous medium under stabilizing gravity. In situations where the magnitudes of the viscous-, capillary-and gravity forces are comparable, we observe a transition from a capillary fingering behavior to a viscous fingering behavior, when decreasing apparent gravity. In the former configuration, the vertical extension of the displacement front saturates; in the latter, thin branched fingers develop and rapidly reach breakthrough. From pressure measurements and picture analyzes, we experimentally determine the threshold for the instability, a value that we also predict using percolation theory. Percolation theory further allows us to predict that the vertical extension of the invasion fronts undergoing stable displacement scales as a power law of the generalized Bond number Bo à ¼ Bo À Ca, where Bo and Ca are the Bond and capillary numbers, respectively. Our experimental findings are compared to the results of a numerical modeling that takes local viscous forces into account. Theoretical, experimental and numerical approaches appear to be consistent. #

Geoderma, 1996

The mechanism for the growth and persistence of gravity-driven fingered flow of water in initially dry porous media is described. A Galerkin finite element solution of the two-dimensional Richards equation with the associated parameter equations for capillary hysteresis in the water retention function is presented. A scheme for upstream weighting of internodal unsaturated hydraulic conductivities is applied to limit smearing of steep wetting fronts. The growth and persistence of a single finger in an initially dry porous media is simulated using this numerical solution scheme. To adequately simulate fingered flow, it was found that the upstream weighting factor had to be negative, meaning that the internodal unsaturated hydraulic conductivities were weighted more by the downstream node. It is shown that the growth and persistence of a finger is sensitive to the character of the porous media water retention functions. For porous media where the water-entry capillary pressure on the main wetting function is less than the air-entry capillary pressure on the main drainage function, a small perturbation will grow into a finger, and during sequential drainage and wetting the finger will persist. In contrast, for porous media where the water-entry capillary pressure on the main wetting function is greater than the air-entry capillary pressure on the main drainage function, the same small perturbation will dissipate by capillary diffusion. The finger widths derived from the numerical simulation are similar to those predicted by analytical theory. 0016-7061/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0016-7061 (95)00086-0

Physical Review E, 2010

This paper reports some experimental results on two-phase flows in model two-dimensional porous media. Standard microfluidic techniques are used to fabricate networks of straight microchannels and to control the throat size distribution. We analyze both the invasion mechanism of the medium by a nonwetting fluid and the drainage after the percolation for capillary numbers lying between 10 −7 and 10 −2. We propose a crude model allowing a description of the observed capillary fingering that captures its scaling properties. This model is supported by numerical simulations based on a pore-network model. Numerical simulations and experiments agree quantitatively.

Physical Review E, 2002

We have investigated experimentally the competition between viscous, capillary, and gravity forces during drainage in a two-dimensional synthetic porous medium. The displacement of a mixture of glycerol and water by air at constant withdrawal rate has been studied. The setup can be tilted to tune gravity, and pressure is recorded at the outlet of the model. Viscous forces tend to destabilize the displacement front into narrow fingers against the stabilizing effect of gravity. Subsequently, a viscous instability is observed for sufficiently large withdrawal speeds or sufficiently low gravity components on the model. We predict the scaling of the front width for stable situations and characterize it experimentally through analyses of the invasion front geometry and pressure recordings. The front width under stable displacement and the threshold for the instability are shown, both experimentally and theoretically, to be controlled by a dimensionless number F which is defined as the ratio of the effective fluid pressure drop ͑i.e., average hydrostatic pressure drop minus viscous pressure drop͒ at pore scale to the width of the fluctuations in the threshold capillary pressures.

2] To explain the dynamic behavior of the matric potential at the wetting front of gravity driven fingers, we take into account the pressure across the interface that is not continuous and depends on the radius of the meniscus, which is a function of pore size and the dynamic contact angle h d . h d depends on a number of factors including velocity of the water and can be found by the Hoffman-Jiang equation that was modified for gravity effects. By assuming that water at the wetting front imbibes one pore at a time, realistic velocities are obtained that can explain the capillary pressures observed in unstable flow experiments in wettable and water repellent sands.

Journal of Fluid Science and Technology, 2018

Immiscible displacement processes have been investigated for decades to understand their applications, such as geosequestration of CO2 and enhanced oil recovery, in detail. In this study, the effect of buoyancy on fingering growth activity during a drainage process was investigated under the competitive influence of buoyancy, capillary, and viscous forces. A packed bed of glass microbeads was used as a porous medium for immiscible fluid pairing of silicon oil and water as a non-wetting phase (NWP) and wetting phase (WP), respectively. The time lapse 3D structure of finger development was visualized for a Bond number Bo range of 3.84 × 10 −4 to 3.45 × 10 −3 and a capillary number Ca range of 4.30 × 10 −9 to 4.30 × 10 −7 using an X-ray CT scanner. Three instability regimes-capillary fingering, transition, and gravity fingering enhanced by buoyancy forces-were successfully observed. The crossover from capillary fingering to gravity fingering was observed at Bo values between 1.53 × 10 −3 and 3.45 × 10 −3. The gravity fingering structure was observed at Bo = 3.45 × 10 −3 and Ca = 4.30 × 10 −7. Under gravity fingering conditions, the pressure of the NWP to displace the WP is highest at the tip of the most advanced finger because the buoyancy force is relatively higher than the capillary force. Consequently, massive new invasions were induced near the tip of the most advanced finger. As a result, the fingers vertically extended with a streak-like structure, and the diameter of the fingers was as small as single-pore sizes. The NWP saturation at breakthrough was low and fluctuated in the z direction. The WP was merely trapped as an isolated cluster. Under capillary fingering conditions (Bo < 1.53 × 10 −3), the fingers not only grew near the tip of the most advanced finger but also grew far below the tip. Some fingers extended to link pores with a small diameter of approximately single-pore size and developed in a horizontal direction, i.e., in the negative z direction as well as in the z direction. The size of trapped WP clusters was distributed from single-pore size to large size, connecting several pores. A skewed distribution of saturation was shown at the breakthrough for low Ca because of competition between capillary fingering and gravity fingering. At high Ca, the pressure gradient established along the z direction as a result of viscous shear force resulted in a gradual decrease in the saturation profile in the z direction.