Formation Of Viscous Fingers Research Articles

Effects of rabbit gastrointestinal mucins and dextran on hydrochloride diffusion in vitro

We compared a viscous fingering formation of hydrochloric acid (HCl) in rabbit corpus, antral and duodenal mucins and with dextran under neutral and acidic conditions with respect to relative viscosity, molecular mass, and carbohydrate composition. The effect of desialyzation of duodenal mucin on the viscous fingering formation of HCl was also examined. HCl (0.1 N) was injected into 1% solutions of mucins and dextran and a subsequent viscous fingering formation was assessed based on an influx volume rate of HCl. A low influx volume rate indicates a high ability of the solutions to produce viscous fingers. The influx volume rate of HCl was lowest in duodenal mucin followed by corpus mucin, antral mucin, and dextran at pH 7. The influx volume rate of HCl was inversely correlated with the relative viscosity of the solution. Maximum molecular masses were large in the order of corpus, antral, and duodenal mucins, and they were larger than dextran T2000. Rabbit gastrointestinal mucins were very polydisperse system. Duodenal mucin contains more sialic acid than gastric mucins; the influx volume rate of HCl increased in desialylated duodenal mucin. It is suggested that the higher ability of gastric mucins to prevent HCl diffusion than dextran were due to the differences in the molecular mass. The ability of duodenal mucin to prevent HCl diffusion was probably attributed to its high sialic acid content, which may reflect a physiological role of duodenal mucin in the duodenum that has to deal with HCl influx from the stomach.

Numerical and experimental modeling of viscous fingering during liquid–liquid miscible displacement

Viscous fingering takes place when the viscous forces of a displacing phase has greater momentum than that of the displaced phase. Viscous fingering is an extremely important phenomenon in many applications of enhanced oil recovery, underground liquid waste disposal, and geothermal energy production. While the onset and propagation of viscous fingers during liquid–liquid displacement is considered to be of severe engineering consequences, little has been done to mathematically model the onset and propagation of a viscous finger. Viscous finger under double diffusive conditions is even less understood. In this paper, two-dimensional non-linear double diffusive convection in a multi-porous cavity is considered, both numerically and experimentally. The Darcy equation, including Brinkman term to account for the viscous effects, is used as the momentum balance equation. The model consists of two rectangular cavities filled with a porous medium. The smaller cavity is located at the top of the larger one. The larger cavity is filled initially with glycerin while the smaller one contains fresh water. At the initial time, the fresh water is injected with either constant flow rate (numerical) or constant hydrostatic head (experiments) and the viscous fingering formation is studied in details. The momentum, solutal, energy and continuity equations are solved numerically using the finite element technique. This transient problem is solved to study the thermal displacement, the isothermal displacement and the microgravity displacement of glycerin by water to understand the onset and the propagation of viscous fingering. For each case, the variation of the distance between the tip of the finger with time is studied in details. The effects of aspect ratio and displacement velocity are studied, both in the context of onset and propagation of viscous fingers. Experimentally, an ingenious method is developed for visualizing 2-D flow in a porous medium. A carbonate formation is used as the porous medium. Chemical dyeing is used to delineate the propagating front of a viscous finger. Initial series of experiments are conducted under isothermal conditions.

Viscous fingering at the liquid/liquid interface between two coexisting phases of mixtures with a miscibility gap

AbstractThe influence of the viscosity contrast factor A [( = η“‐η′)/(η“+η), η, shear viscosity: (′)(”), indices of the coexisting phases; η“>η′]on the formation of viscous fingers at a mechanically unstable liquid/liquid interface of mixtures with a miscibility gap in a narrow rectangular glass cell (closed Hele‐Shaw cell) is studied. The systems used for the experiments are: (a) 2‐butoxyethanol (C4E1)/water mixtures of critical composition. They are studied in the vicinity of the lower critical point at temperatures above the critical temperature [1.05 < (η”η') < 2.0, corresponding to 0.05<A<0.4]. A is varied by changing the temperature of the mixture; (b) poly(ethylene glycol) (PEG)/dextran (D)/water mixtures at different compositions in the vicinity of the plait point at constant temperature [10<(η“/η')<40, corresponding to 0.762<A<0.950]. The liquid/liquid interfacial tension of both systems is small (σ<0.1 mN m−1). The experimental results are analysed in terms of theoretical work of Tryggvason and Aref (J. Fluid. Mech. 177, 207 (1985)). The viscous fingering process is treated as a two‐dimensional viscous flow. For small values of A (<0.12; system (C4El1/water) the growth rates of the viscous fingers in the upward and downward direction have about the same value and the fingers have a similar shape. At larger values of A (>0.3) the fingers formed by the phase with the higher viscosity advance faster into the phase with the lower viscosity than the fingers advancing in the opposite direction. This effect is pronounced in the system PEG/D/water for which A has large values (A>0.75). In this system the viscous fingers formed by the phase with the higher viscosity are long and narrow whereas that formed by the low viscosity phase are short and broad. The temperature dependence of the mean distance <l> between viscous fingers of the system C4E1/water advancing in opposite directions approaches the theoretically expected dependence at temperature differences (Tp‐Tc)>l K corresponding to a ratio (λmax/b) > 3 (λmax, wave length of fasted growing interfacial instability; b, width of the glass cell). The experiments show that the preferential wetting of the glass walls of the Hele‐Shaw cell by one of the coexisting liquid phases leads to a three‐dimensional shape of the viscous fingers.

Interfacial instabilities and fingering formation in Hele-Shaw flow

The interfacial instability of Hele-Shaw flow has been a crucial issue for the understanding of the pattern formation of viscous fingers in a Hele-Shaw cell. By using a unified asymptotic approach, we derive two different types of instability mechanisms for 'slightly' time-dependent finger solutions; namely, (i) the global-trapped-wave (GTW) instability; and (ii) the zero-frequency (null-f) instability. On the basis of these instability mechanisms, the selection of viscous finger formation is clarified; the apparent contradiction between the previous linear-stability analysis by Tanveer (1987, Phys. Fluid 30, 1589) and others and the numerical simulations by DeGregoria & Schwartz (1986, J. Fluid Mech. 164, 383) and the experimental evidence is reconciled.

Propagation of an Anionic Surfactant In Radial Sandstone Cores

Abstract An experimental study was conducted to examine the propagation with adsorption of an anionic surfactant in unfired Berea sandstone cores. The effects of sodium chloride concentration, pH, flow rate, surfactant concentration, and the presence of a liquid crystal phase on the rate of surfactant propagation were studied. To simulate the flow field around an injection well, a radial geometry was employed. Experimental results showed dramatic surfactant loss and slower rate of surfactant propagation as sodium chloride concentration was increased. On the other hand, increasing the pH of the surfactant slug from 6 to 12 reduced surfactant loss by nearly 30 percent. At a given sodium chloride concentration and surfactant concentration, surfactant loss was found to decrease as the injection flow rate was increased. At high surfactant concentrations and over a narrow range of sodium chloride concentrations, a liquid crystal phase formed. The presence of this phase resulted in a higher apparent viscosity, a dramatic increase in the pressure drop across the core, and significant surfactant retention in the core. The latter was due to the formation of viscous fingers at the tail of the surfactant slug. Introduction Surfactants are used in many enhanced oil recovery processes (EOR), including micellar, micellar/polymer alkl/surfactant, lkali/surfactant/polymer and foam flooding. Surfactant propagation in the reservoir is a significant factor which determines the effectiveness of these enhanced oil recovery processes. Surfactant loss in a typical reservoir occurs as a result of adsorption on the rock surface, precipitation by divalent cations partitioning into the oil phase and surfactant/polymer interactions leading to precipitation(1). The present study addresses propagation and adsorption of an anionic surfactant with high salinity tolerance in unfired Berea sandstone cores. Such surfactants are used in alkali/surfactant(2) and alkali/surfactant/polymer(3) flooding to increase the optimal salinity of petroleum soaps encountered in these processes. Berea sandstone contains an average of 5 to 9 wt% clay minerals (mainly kaolinite and illite). Anionic sufactants are absorbed on the charged clay particles. Surface charges on the clay particles riginate from isomorphous substitution lattice defects, and broken bonds. Consequently, adsorption of anionic surfactants oil the surfaces of clay minerals is governed by electrostatic and van der Waals forces(4–9). Imporlant factors influencing the adsorption of anionic surfactants on sandstone, such as salinity, pH, and type and composition of surfactants, have been extensively discussed in previous studies(10–20). Summaries of previous work were given by Meyers nd Salter(21) and recently by Rupprecht and Gu(22). Based on the discussion of Somasundaran and Hanna(15), higher adsorption of anionic surfactants on sandstone with increasing salinity is caused by an increase in the surface acidity and the compression of the electric double layer which reduces the electrostatic repulsion between the surfactant monomers and the surface of the clay minerals. Solution salinity also affects the formation of ionic surfactant micelles. Some recent studies on this effect will be referred to in the results and discussion section. Another important parameter that influences the surface charge of the clay particles is the solution pH.

A Scaling Criterion For Miscible Displacements

Abstract The use of scaled laboratory models to simulate reservoir conditions is one of the more effective methods for evaluating the merit of a miscible oil recovery process. When using this approach it is important to keep in mind that, because of the adverse solvent to oil viscosity ratio, most miscible displacements are dominated by viscous fingering. Because viscous fingering plays a critical role in the recovery process, it is important that its impact be handled correctly. However, conventional scaling methods cannot account properly for the viscous instabilities usually associated with miscible displacement. In this paper a recently developed scaling group, which can be used for scaling instability in the laboratory, is presented. The new scaling group includes explicitly, for the first time, the effect that the length of a porous medium has on the instability of a miscible displacement. Moreover, it is shown that, while the individual effects oftransver.se and longitudinal dispersion cannot be scaled, their combined effect on the controlling mechanism/or most miscible displacements (viscous fingering) can be scaled using the new scaling criterion. Introduction One of the more effective methods for evaluating a miscible oil recovery process is that of displacements in laboratory models scaled to simulate reservoir conditions. In scaling of miscible displacement, an inspectional analysis, complemented by a dimensional analysis, is used usually to obtain a set of scaling criteria(1–3). Moreover, it has been shown that, in order to represent correctly the behaviour of the prototype in the laboratory, the model must be geometrically similar, and the ratios of all the forces present in the model must be equal to those in the prototype. However, it is sometimes impossible to construct a model so that every one of the forces that exist in the reservoir is scaled simultaneously in the model(3–7). In particular, when microscopic dispersion in the transverse and longitudinal directions is scaled simultaneously with the macroscopic parameters, impractically large models are required for most laboratory investigations, Therefore, relation of some of the scaling requirements s undertaken, and models which represent the prototype for a restricted number of conditions are devised. However, if some other parameter which has not been scaled exercises significant control over the displacement, then the significance of the laboratory results for prediction of field operations becomes questionable. It has long been recognized that miscible displacement with a low viscosity solvent driving a more viscous oil will be an unstable process leading to the formation of viscous fingers. Therefore, although the effects of mixing should be considered in any attempt to predict miscible flood performance, it is viscous fingering that is likely to dominate the behaviour of a miscible flood(9). It has been shown that, when viscous fingering is the dominant phenomenon, the breakthrough recovery is a function only of the viscosity ratio for both miscible and immiscible displacements(10). As a consequence, it seems that the most important controlling factor in a miscible displacement is the viscous fingering.

Viscous fingers in porous media.

We consider the formation of viscous fingers in porous media using the boundary-integral method with particular application to a recent experiment involving a Hele-Shaw cell filled with glass beads. When the less viscous fluid wets the beads we can account for the patterns as ordinary viscous fingers in the presence of large noise.

Computer-Assisted Tomography for the Observation of Oil Displacement in Porous Media

Abstract Computer-assisted tomography (CAT) is used to obtain cross-sectional images of Berea sandstone cores during oil displacement experiments. Local oil saturation averaged over an area of about 0.03 × 0.03 in. [0.8 × 0.8 mm] square is computed as a function of spatial position and time. A series of CAT scan images displaying the time evolution of the fluid distribution at one cross section are shown to illustrate the formation of viscous fingers.