Crossover from fractal to compact flow from simulations of two-phase flow with finite viscosity ratio in two-dimensional porous media

Ferer, M.; Sams, W. Neal; Geisbrecht, R.A.; Smith, Duane H.

doi:10.1103/physreve.47.2713

Cited by 29 publications

(25 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: 16mentioning

confidence: 99%

“…Discretization of the system has been performed for for our network and a complete discussion of this topic including derivations of these equations are found in references [23][24]. Scaling from microscopic (pore level) sizes to macroscopic (core or field level) sizes requires the use of dimensionless parameters and the choice of a unit length for the model depicted in Fig.…”

Section: Simulation Characterizationmentioning

confidence: 99%

“…An H ∞ method has been applied to robust control and other applications, [5,9,10,22] also derivation of the H ∞ can be found in [1,23]. The performance index for H ∞ estimator is defined as,…”

Section: An Extended Kalman Filter (Ekf) For Standpipe Modelmentioning

confidence: 99%

“…13, 14,21 Also the micropore distribution is not uniform as in a conventional crystalline lattice. 22,23 The microscopic magnitude 14,19 and geometry 14 of the micropores and their non-uniform distribution restricts the ability of a fluid to enter into a portion of the coal matrix depending on the size and shape of its individual molecules, 8, 14 as well as the magnitude of the interaction forces between the molecules and the coal matrix, 8 thus affecting fluid flow through the coal.Because of the minute aperture size of the micropores and because of the complexity of the porous system, measuring coals' porosity is difficult. Further complications to measuring techniques are activated diffusion, shrinkage of the pores (which will be explained more clearly in the next section) and/or temperature.…”

mentioning

confidence: 99%

“…These Jacobi are updated for every time step. The Kalman gain is obtained from,Next, the estimated state and measurement should be updated as,4 An H ∞ estimation algorithmAn H ∞ method has been applied to robust control and other applications, [5,9,10,22] also derivation of the H ∞ can be found in [1,23]. The performance index for H ∞ estimator is defined as,…”

mentioning

confidence: 99%

See 4 more Smart Citations

University/NETL Student Partnership Program

Holder¹

2003

View full text Add to dashboard Cite

2 methane on the coal surfaces that may otherwise stay adsorbed in the coal matrix by decreasing the partial pressure of methane in the gas mixture. In addition, experimental work conducted on enhanced coalbed methane recovery by CO 2 injection [Reznik et al, 1984] shows that CO 2 is more adsorbing on coal than methane thereby giving it the potential to efficiently displace CBM and remain sequestered in the coal-seam. Thus coal-seams are considered to offer a very attractive option for CO 2 sequestration.In this work, focus is on the final part of the sequestration process -storage. The effects of various coal properties as well as operational scenarios on the injection and storage of CO 2 into a given coal-seam are analyzed. The analyses are based on results obtained from PSU-COALCOMP, a compositional coalbed methane numerical reservoir simulator capable of modeling the primary and enhanced recovery of coalbed methane.The operational design parameters considered in this study include the type, length and orientation of the injectors/producers while the coal-seam properties studied include coal porosity, coal permeability, cleat spacing, sorption capacity, and the initial conditions of the coal-seam -the reservoir pressure, adsorbed gas composition, amount of CO 2 initially adsorbed, water saturation and free-gas composition.Based on the data, results and analyses obtained, a CO 2 sequestration performance predictor tool is developed using artificial neural network (ANN) technology. The developed network will be able to predict the values of the performance indicators of the CO 2 sequestration process for a wide range of coal-seams and various production schemes. The developed ANN would also enhance our understanding of CO 2 sequestration process. 3 CHAPTER 2 LITERATURE REVIEW Carbon Dioxide SequestrationThe amount of carbon dioxide (CO 2 ) in the atmosphere has risen from preindustrial levels and most of this increase has been in recent years as shown in the data presented graphically in Figure 2-1. The corresponding increase in temperature as CO 2 levels increase raises environmental concerns such as global warming and its effects.This increase in CO 2 levels is attributed widely to the burning of fossil fuels, and if current trends in resource utilization continue, anthropogenic CO 2 emissions will increase rapidly during the 21 st century. Figure 2-2 shows the sharp increase in global CO 2 emissions over the last 100 years.The term "CO 2 sequestration" refers to the removal of CO 2 from either manmade emissions or the atmosphere and the safe, essentially permanent storage of this CO 2 .There are two main types of sequestration: direct sequestration, where CO 2 is removed from energy systems, and indirect sequestration, where CO 2 is removed from the ambient atmosphe re by enhanced natural processes. Sequestration is one of the three options for stabilizing CO 2 concentrations in the atmosphere and until the late 1990's, was not yet in the scientific lexicon. It is less familiar to the public at large than...

show abstract

Section: 16mentioning

confidence: 99%

Section: Simulation Characterizationmentioning

confidence: 99%

Section: An Extended Kalman Filter (Ekf) For Standpipe Modelmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

University/NETL Student Partnership Program

Holder¹

2003

View full text Add to dashboard Cite

show abstract

Fractal nature of viscous fingering in two‐dimensional pore level models

et al. 1995

Self Cite

View full text Add to dashboard Cite

Use of saturation-dependent relatiue mobilities leads to linear flow; howeuer, experiment and theory show that, in the limit of very lurge uiscosity ratio, the flow is not linear but fractal. Generally, fractional flows and relatiue mobilities depend M O Oh8 acts as a 2-D Koual factor IntroductionComposition-dependent relative mobilities are used in all traditional modeling of flow in porous media, such as Buckley-Levcrett or Koval (Collins, 1961; Rhec et al., 1986). Their use predicts flow in which the saturation front advances linearly with time. However, it has been shown that the limit of infinite viscosity ratio ( M -+x, where the injected fluid has zero viscosity) is accurately described by diffusion-limited aggregation (DLA), a process that is known to form fractal objects with nonuniform densities (Vicsek, 1989; Witten and Sander, 1981;Meakin, 1983a). For fractal flow, the saturation front advances faster than linearly with time. Two questions naturally arise: ( I ) If the actual viscous fingering were fractal, what would be the effect on traditional simulation? and (2) Is the viscous fingering fractal for realistic, unstable viscosity ratios? As we will see, our modeling indicates that large-scale flows are not fractal, but that small-scale flows are fractal. Furthermore, this crossover from small-scale fractal flows to large-scale linear flows leads to definite predictions regarding the dependence of flow velocity upon viscosity ratio.First, what is a fractal? The classic signature of a fractal object is a non-Euclidean relationship between mass and size. If one has an ordinary solid disk, the mass is proportional to R2, but for a circular fractal object, the mass is proportional to R"{, with a noninteger fractal dimension, D,; for example, for DLA, Df = 1.7. Therefore, a fractal object is less dense than an ordinary object due to material voids inside the object. However, it should be emphasized that neither the mass density nor the compensating voids are uniformly distributed; indeed, the mass density decreases with R while the void density must increase with R. Formation of these fractals is an unstable, nonequilibrium process. A number of excellent reviews discuss a wide variety of these fractal growth phenomena, including material deposition, dielectric breakdown, and two-phase flow in porous media, the topic of this article (Vicsek, 1989;Mandelbrot, 1982; Feder, 1988).Second, what is viscous fingering? If the flow is "unstable"(viscosity ratio M > 11, the injected fluid fingers into the displaced fluid (Saffman and Taylor, 1958). This effect has been widely studied in "Hele-Shaw" cells, where a high viscosity fluid occupies the space between two flat glass plates, and a low-viscosity fluid is injected at the center. If the viscosity ratio is large enough, the viscous fingering patterns satistji a fractal relationship with fractal dimension D, = 1.70&0.05 (Daccord et al., 1986). If the space between the Hele-Shaw plates is filled with a bead pack, mimicking a porous medium, analysis of the fingeri...

show abstract