Spontaneous Imbibition In Porous Media Research Articles

Lattice model for spontaneous imbibition in porous media: the role of effective tension and universality class.

Recently, anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nanoporous medium, were reported: the mean height and the width of the propagating front increase with time t both proportional to t(1/2). Here, we propose a simple lattice imbibition model and elucidate quantitatively how the correlation range of the hydrostatic pressure and the disorder strength of the pore radii affect the scaling properties of the imbibition front. We introduce an effective tension of liquid across neighboring pores, which depends on the aspect ratio of each pore, and show that it leads to a dynamical crossover: both the mean height and the roughness grow faster in the presence of tension in the intermediate-time regime but eventually saturate in the long-time regime. The universality class of the long-time behavior is discussed by examining the associated scaling exponents and their relation to directed percolation.

Scaling theory for spontaneous imbibition in random networks of elongated pores.

We present a scaling theory for the long time behavior of spontaneous imbibition in porous media consisting of interconnected pores with a large length-to-width ratio. At pore junctions, the meniscus propagation in one or more branches can come to a halt when the Laplace pressure of the meniscus exceeds the hydrostatic pressure within the junction. We derive the scaling relations for the emerging arrest time distribution and show that the average front width is proportional to the height, yielding a roughness exponent of exactly β = 1/2 and explaining recent experimental results for nanoporous Vycor glass. Extensive simulations of a pore network model confirm these predictions.

ADVANCES IN STUDIES OF SPONTANEOUS IMBIBITION IN POROUS MEDIA

Spontaneous imbibition is a natural phenomenon in porous media extensively occurring in many fields of engineering applications and natural sciences. Thus, the issues on the basic statistics and kinetics of spontaneous imbibition in porous media have become one of hot topics for many years. In this review, progresses in traditionally theoretical researches on Lucas-Washburn (LW) model, Terzaghi model, Handy model, Mattax and Kyte scaled model of dimensionless time, Aronofsky scaled model of normalized recovery and recent advances in the area especially over the last decade are reviewed, including criterion parameters for analyzing the mechanisms of spontaneous imbibition and recent studies on spontaneous imbibition in porous media based on the fractal theory. Brief reviews on numerical simulations and experiments about the influence of factors on the imbibition rate are also addressed. A few of comments are also made on the future research directions and subjects on spontaneous imbibition of Newtonian and non-Newtonian fluids in porous media and fractured porous media with dual-porosity based on the fractal theory and numerical simulations.

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.

Influence of Fluid Viscosity On Mass Transfer Between Rock Matrix And Fractures

Abstract Scaling of spontaneous imbibition measurements is important to characterization of wetting properties and to modelling mass transfer between rock matrix and fractures. A scaling equation proposed by Mattax and Kyte(ll) has been widely applied to prediction of field-scale oil recovery from fractured reservoirs. The scaling equation involves many assumptions including identical core-sample shapes and viscosity ratios. In this paper, the effect of viscosity and viscosity ratio on rate of spontaneous imbibition is investigated. Imbibition data is reported for systems with two orders of magnitude variation in viscosity ratio. The results show, for systems of similar geometry, that the imbibition time is proportional to the square root of viscosity ratio. This observation combined with a new definition of characteristic length is used to define a modified scaling group which allows for differences in viscosity ratio, and the shapes and boundary conditions of the core samples. Introduction Spontaneous imbibition is a natural physical process driven by capillary forces whereby a nonwetting phase is displaced by a wetting phase from a porous medium(l). Examples of practical significance may be found in civil and chemical engineering, soil science, and numerous other areas. In petroleum engineering, imbibition is considered especially important in oil recovery from fractured reservoirs, where the rate of mass transfer between rock matrix and the associated fractures controls the oil production. However, much remains to be learned about the combined effect of imbibition, gravity, and both microscopic and macroscopic fluid distribution on oil recovery from fractured systems. Development of analytical functions or other computational schemes which account for mass transfer between rock matrix and fractures is of special importance to mathematical modelling of fractured reservoirs(2–6). Scaling of spontaneous imbibition phenomena is a critical step in this development. Provided that gravity effects can be safely neglected, capillary pressure is the driving force for spontaneous imbibition. Permeability and relative permeabilities in the two phase region of flow determine the rate of imbibition. Both capillary pressure and relative permeability are functions of saturation. Thus many factors enter into scaling of imbibition rates. The effect of fluid viscosity is of primary concern in this study. The effect of core sample shapes and boundary conditions will also be discussed. Imbibition in Tubes Most analyses of imbibition consider behaviour in cylindrical tubes. For a cylindrical tube of radius r, the Laplace equation gives the capillary pressure, Pc Equation 1–8 (available in full paper) Analysis of imbibition behaviour in cylindrical tubes provides guidance to studies of imbibition in porous media. However, direct applications of the conclusions drawn from the tube models to porous media should not be expected because spontaneous imbibition in porous media is usually dominated by countercurrent flow. Scaling of Imbibition in Porous Media From Equations (1) and (2), capillary pressure is inversely proportional to pore size, and permeability is proportional to the pore size squared. Thus, although capillary pressure decreases with increasing permeability [Equation (3)], the more permeable the porous media, the faster the imbibition rate [Equations (5) and (6)]. This conclusion was verified experimentally by Handy for water displacing air(8).