Flow onset for a single bubble in a yield-stress fluid

We use computational methods to determine the minimal yield stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension ( $\gamma$ ) and the ratio of the yield stress to the buoyancy stress ( $Y$ ). For a given geometry, bubbles are static for $Y > Y_c$ , which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield stress to hold static compared with oblate bubbles. Non-zero $\gamma$ increases $Y_c$ and for large $\gamma$ the yield-capillary number ( $Y/\gamma$ ) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.

Study of the Effect of Wetting on Viscous Fingering Before and After Breakthrough by Lattice Boltzmann Simulations

We present a suite of numerical simulations of two-phase flow through a 2D model of a porous medium using the Rothman-Keller Lattice Boltzmann Method to study the effect of viscous fingering on the recovery factor as a function of viscosity ratio and wetting angle. This suite involves simulations spanning wetting angles from non-wetting to perfectly wetting and viscosity ratios spanning from 0.01 through 100. Each simulation is initialized with a porous model that is fully saturated with a "blue" fluid, and a "red" fluid is then injected from the left. The simulation parameters are set such that the capillary number is 10, well above the threshold for viscous fingering, and with a Reynolds number of 0.2 which is well below the transition to turbulence and small enough such that inertial effects are negligible. Each simulation involves the "red" fluid being injected from the left at a constant rate such in accord with the specified capillary number and Reynolds number until the red fluid breaks through the right side of the model. As expected, the dominant effect is the viscosity ratio, with narrow tendrils (viscous fingering) occurring for small viscosity ratios with M ≪ 1, and an almost linear front occurring for viscosity ratios above unity. The wetting angle is found to have a more subtle and complicated role. For low wetting angles (highly wetting injected fluids), the finger morphology is more rounded whereas for high wetting angles, the fingers become narrow. The effect of wettability on saturation (recovery factor) is more complex than the expected increase in recovery factor as the wetting angle is decreased, with specific wetting angles at certain viscosity ratios that optimize yield. This complex phase space landscape with hills, valleys and ridges suggests the dynamics of flow has a complex relationship with the geometry of the medium and hydrodynamical parameters, and hence recovery factors. This kind of behavior potentially has immense significance to Enhanced Oil Recovery (EOR). For the case of low viscosity ratio, the flow after breakthrough is localized mainly through narrow fingers but these evolve and broaden and the saturation continues to increase albeit at a reduced rate. For this reason, the recovery factor continues to increase after breakthrough and approaches over 90% after 10 times the breakthrough time.

Recent Advances in Capillary Desaturation Curves for Sandstone and Carbonate Reservoirs

Different enhanced oil recovery (EOR) methods are usually applied to target remaining oil saturation in a reservoir after both conventional primary and secondary recovery stages. The remaining oil in the reservoir is classified into capillary trapped residual oil and unswept /bypassed oil. Mobilizing the residual oil in the reservoir is usually achieved through either decreasing the capillary forces and/or increasing the viscous or gravitational forces. The recovery of the microscopically trapped residual oil is mainly studied using capillary desaturation curve (CDC). Hence, a fundamental understanding of the CDC is needed for optimizing the design and application of different EOR methods in both sandstone and carbonate reservoirs. For sandstone reservoirs, especially water-water rocks, determining the residual oil saturation and generating CDC has been widely studied and documented in literature. On the other hand, very few studies have been conducted on carbonate rocks and less data is available. Therefore, this paper provides a comprehensive review of several important research studies published on CDC over the past few decades for both sandstone and carbonate reservoirs. We critically analyzed and discussed theses CDC studies based on capillary number, Bond number, and trapping number ranges. The effect of different factors on CDC were further investigated including interfacial tension, heterogeneity, permeability, and wettability. This comparative review shows that capillary desaturation curves in carbonates are shallower as opposed to these in sandstones. This is due to different factors such as the presence of high fracture density, presence of micropores, large pore size distribution, mixed-to-oil wetting nature, high permeability, and heterogeneity. In general, the critical capillary number reported in literature for sandstone rocks is in the range of 10−5 to 10−2. However, for carbonate rocks, that number ranges between 10−8 and 10−5. In addition, the wettability has been shown to have a major effect on the shape of CDC in both sandstone and carbonate rocks; different CDCs have been reported for water-wet, mixed-wet, and oil-wet rocks. The CDC shape is broader and the capillary number values are higher in oil-wet rocks compared to mixed-wet and water-wet rocks. This study provides a comprehensive and comparative analysis of CDC in both sandstone and carbonate rocks, which serves as a guide in understanding different CDCs and hence, better screening of different EOR methods for different types of reservoirs.

Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.

Interrelationship of Capillary Number, Interfacial Tension, Injection Flow Rate and Temperature by Surfactant Flooding for Oil-wet Carbonate Reservoirs

After water flooding in carbonate reservoirs, a significant fraction of the original oil as remaining oil is left in the swept zone. The remaining oil in the pore, trapped by viscous and capillary forces, is to target for improved and enhanced oil recovery. The mobilization of remaining oil can be predicted by a dimensionless parameter called capillary number. The interfacial tension and injection flow rate strongly affect the capillary number. Unfortunately, the interrelationship between capillary number, interfacial tension, injection flow rate, and the temperature has been poorly studied for carbonate reservoirs. This paper focuses on studying the remaining oil saturations at different orders of magnitude capillary numbers related to interfacial tension, injection flow rate, and temperature by seawater and surfactant flooding. Several core flooding experiments were performed by changing the injection rate and surfactant concentrations at evaluated conditions. Four displacement experiments of seawater/oil and surfactant solution/oil were performed using oil-wet carbonate cores to obtain the relationship between the residual oil saturation vs. the capillary number. The surfactant flooding experiments with different concentrations of 0.01 and 0.2 wt% were conducted when the remaining oil saturation was reached after water flooding. Three core flooding experiments were conducted at ambient conditions, and one was under evaluated conditions of a temperature of 100° and pore pressure of 3200 psi. Several injection rates were selected to experiment with a 0.2 wt% surfactant solution, which is to study the effect of injection rate on the capillary number and residual oil saturation. The experimental findings show that some remaining oil can be recovered from oil-wet carbonate cores if the capillary number increases by a critical Nc =2.1E-05 by surfactant flooding at reservoir conditions. After water flooding, the remaining oil saturation was decreased from 51% to 16% with 0.01wt% surfactant flooding. The reduction of interfacial tension from 6.77dyne/cm to 0.017dyne/cm led to an increased capillary number. It decreased the remaining oil saturation by about 5% OOIP when the capillary number increases three magnitudes. The effect of temperature and injection rate on the capillary number was observed based on experimental displacement results. Compared with results between the ambient and specified conditions, the effect of temperature on the capillary number is significant. Under the same capillary number, the remaining oil recovered by surfactant flooding at HPHT conditions was higher than that at ambient conditions. Also, the effect of the injection flow rate on the capillary number was observed by 0.2wt % surfactant flooding for all experiments. The capillary number increased with an increase in the injection rate for both ambient and evaluated conditions. This paper provides valuable results to evaluate the interrelationship between remaining oil and capillary numbers by surfactant flooding and design field application for oil-wet carbonate reservoirs.

Impact of surface viscosity on the stability of a droplet translating through a stagnant fluid

This study examines the impact of interfacial viscosity on the stability of an initially deformed droplet translating through an unbounded quiescent fluid. The boundary-integral formulation is employed to investigate the time evolution of a droplet in the Stokes flow limit. The droplet interface is modelled using the Boussinesq–Scriven constitutive relationship having surface shear viscosity $\eta _\mu$ and surface dilatational viscosity $\eta _\kappa$ . We observe that, below a critical value of the capillary number, $Ca_C$ , the initially perturbed droplet reverts to its spherical shape. Above $Ca_C$ , the translating droplet deforms continuously, growing a tail at the rear end for initial prolate perturbations and a cavity for initial oblate perturbations. We find that surface shear viscosity inhibits the tail/cavity growth at the droplet's rear end and increases the $Ca_C$ compared with a clean droplet. In contrast, surface dilatational viscosity increases tail/cavity growth and lowers $Ca_C$ compared with a clean droplet. Surprisingly, both shear and dilatational surface viscosity appear to delay the time at which pinch off occurs, and hence satellite droplets form. Lastly, we explore the combined influence of surface viscosity and surfactant transport on droplet stability by assuming a linear dependence of surface tension on surfactant concentration and exponential dependence of interfacial viscosities on the surface pressure. We find that pressure-thinning/thickening effects significantly affect the droplet dynamics for surface shear viscosity but play a small role for surface dilatational viscosity. We lastly provide phase diagrams for the critical capillary number for different values of the droplet's viscosity ratio and initial Taylor deformation parameter.

Rheology of three-phase suspensions determined via dam-break experiments

Three-phase suspensions, of liquid that suspends dispersed solid particles and gas bubbles, are common in both natural and industrial settings. Their rheology is poorly constrained, particularly for high total suspended fractions (≳0.5). We use a dam-break consistometer to characterize the rheology of suspensions of (Newtonian) corn syrup, plastic particles and CO 2 bubbles. The study is motivated by a desire to understand the rheology of magma and lava. Our experiments are scaled to the volcanic system: they are conducted in the non-Brownian, non-inertial regime; bubble capillary number is varied across unity; and bubble and particle fractions are 0 ≤ ϕ gas ≤ 0.82 and 0 ≤ ϕ solid ≤ 0.37, respectively. We measure flow-front velocity and invert for a Herschel–Bulkley rheology model as a function of ϕ gas , ϕ solid , and the capillary number. We find a stronger increase in relative viscosity with increasing ϕ gas in the low to intermediate capillary number regime than predicted by existing theory, and find both shear-thinning and shear-thickening effects, depending on the capillary number. We apply our model to the existing community code for lava flow emplacement, PyFLOWGO, and predict increased viscosity and decreased velocity compared with current rheological models, suggesting existing models may not adequately account for the role of bubbles in stiffening lavas.

EVALUATION OF EFFECT OF SURFACE MODIFICATION ON CORRELATION BETWEEN PERMEABILITY OF GLASS FIBER/RESIN AND CAPILLARY NUMBER

In this study, we experimentally evaluated the correlation between the microscopic resin flow and permeability of a glass cloth, which surface was modified by silane coupling agent. We focused on the capillary number, which is a parameter determining the microscopic resin impregnation behavior within and between fiber bundles. The capillary numbers were classified into different parameters based on their dependency on temperatures and pressures. First, we obtained the temperature condition for each resin, to make the ratio between resin viscosity and (surface tension ・contact angle), constant be Under these temperature conditions, the pressure conditions were determined to be the resin impregnation rate constant. The permeability was evaluated with three types of resins under three conditions of capillary numbers. As a result, the permeabilities of the different resin systems were approximately equal. Therefore, it was found that the macroscopic permeability was not significantly influenced by the capillary number representing microscopic resin flow.