SPONTANEOUS IMBIBITION OF A WETTING FLUID INTO A FRACTURE WITH OPPOSING FRACTAL SURFACES: THEORY AND EXPERIMENTAL VALIDATION

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940001 ◽  
Author(s):  
J. W. BRABAZON ◽  
E. PERFECT ◽  
C. H. GATES ◽  
L. J. SANTODONATO ◽  
I. DHIMAN ◽  
...  
Keyword(s):  
Neutron Radiography ◽  
Rock Fracture ◽  
Geometric Mean ◽  
Spontaneous Imbibition ◽  
Future Research ◽  
Fracture Aperture ◽  
Flat Plates ◽  
Fracture Surfaces ◽  
Si Model ◽  
Wetting Fluid

Spontaneous imbibition (SI) is a capillary-driven flow process, in which a wetting fluid moves into a porous medium displacing an existing non-wetting fluid. This process likely contributes to the loss of fracking fluids during hydraulic fracturing operations. It has also been proposed as a method for an enhanced recovery of hydrocarbons from fractured unconventional reservoirs. Numerous analytical and numerical approaches have been employed to model SI. Invariably, these idealize a fracture as the gap formed between parallel flat surfaces. In reality, rock fracture surfaces are rough over multiple scales, and this roughness will influence the contact angle and rate of fluid uptake. We derived an analytical model for the early-time SI behavior within a fracture bounded by parallel impermeable surfaces with fractal roughness assuming laminar flow. The model was tested by fitting it to experimental data for the SI of deionized water into air-filled rock fractures. Twenty cores from two rock types were investigated: a tight sandstone (Crossville) and a gas shale (Mancos). A simple Mode I longitudinal fracture was produced in each core by compressive loading between parallel flat plates using the Brazilian method. Half of the Mancos cores were fractured perpendicular to bedding, while the other half were fractured parallel to bedding. The two main parameters in the SI model are the mean separation distance between the fracture surfaces, [Formula: see text], and the fracture surface fractal dimension [Formula: see text]. The [Formula: see text] was estimated for each core by measuring the geometric mean fracture aperture width through image analysis of the top and bottom faces, while [Formula: see text] was estimated inversely by fitting the SI model to measurements of water uptake obtained using dynamic neutron radiography. The [Formula: see text] values ranged from 45[Formula: see text][Formula: see text]m to 190[Formula: see text][Formula: see text]m, with a median of 93[Formula: see text][Formula: see text]m. The SI model fitted the height of uptake versus time data very well for all of the rock cores investigated; medians of the resulting root mean squared errors and coefficients of determination were 0.99[Formula: see text]mm and 0.963, respectively. Estimates of [Formula: see text] ranged from 2.04 to 2.45, with a median of 2.24. Statistically, all of the [Formula: see text] values were significantly greater than two, confirming the fractal nature of the fracture surfaces. Future research should focus on forward prediction through independent measurements of [Formula: see text] and extension of the existing SI model to late times (through the inclusion of gravity) and fractures with permeable surfaces.

Capillary Impregnation of Viscous Fluids in a Multi-Layered Porous Medium

2019 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Viscous Fluids ◽  
Spontaneous Imbibition ◽  
Lab On Chip ◽  
Capillary Impregnation ◽  
Relative Placement ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

Abstract Capillary impregnation of viscous fluids in porous media is useful in diagnostics, design of lab-on-chip devices and enhanced oil recovery. The impregnation of a wetting fluid in a homogeneous porous medium follows Washburn’s diffusive law. The diffusive dynamics predicts that, with the increase in permeability, the rate of spontaneous imbibition of a wetting fluid also increases. As most of the naturally occurring porous media are composed of hydrodynamically interacting layers having different properties, the impregnation in a heterogeneous porous medium is significantly different from a homogeneous porous medium. A Washburn like model has been developed in the past to predict the imbibition behavior in the layers for a hydrodynamically interacting three layered porous medium filled with a non-viscous resident phase. It was observed that the relative placement of the layers impacts the imbibition phenomena significantly. In this work, we develop a quasi one-dimensional lubrication approximation to predict the imbibition dynamics in a hydrodynamically interacting multi-layered porous medium. The generalized model shows that the arrangement of layers strongly affects the saturation of wetting phase in the porous medium, which is crucial for oil recovery and in microfluidic applications.

scholarly journals Research on Rock Fracture Surface Morphology Characterization under Brazilian Test

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhigang Feng ◽  
Xuezai Pan ◽  
Guoxing Dai ◽  
Hongguang Liu
Keyword(s):  
Fracture Surface ◽  
Rock Fracture ◽  
Fracture Morphology ◽  
Brazilian Test ◽  
Variation Method ◽  
Fracture Surfaces ◽  
Modulus Maximum ◽  
Loading Modes ◽  
Morphology Characterization ◽  
Maximum Method

In order to test the differences in the morphology characterization of rock fracture surfaces under different loading directions and rates, the following three steps are operated. Firstly, using Brazilian test, the Brazilian discs are loaded to fracture under different loading modes. Secondly, each rock fracture surface is scanned with a highly accurate laser profilometer and accordingly the coordinates of three lines on every rock fracture surface and three sections of every line are selected to analyze their fracture morphology characterization. Finally, modulus maximum method of wavelet transform, including a new defined power algorithm and signal to noise ratio, and fractal variation method are used to determine the differences in rock fracture surfaces’ morphology characterization under different loading directions and rates. The result illustrates that both modulus maximum and fractal variation method can detect anisotropy of rock fracture failure. Compared to modulus maximum method, fractal variation method shows stronger sensitivity to the change of loading rates, which is more suitable to differentiate the rock fracture surface’s morphology characterization under different loading modes.

Study on generation of rock fracture surfaces by using fractal interpolation

2001 ◽  
Vol 38 (32-33) ◽  
pp. 5765-5787 ◽  
Author(s):  
Heping Xie ◽  
Hongquan Sun ◽  
Yang Ju ◽  
Zhigang Feng
Keyword(s):  
Rock Fracture ◽  
Fractal Interpolation ◽  
Fracture Surfaces

CONTRAST OF ROCK FRACTURE SURFACE’S MORPHOLOGY CHARACTERIZATION BASED ON FRACTAL VARIATION

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950070
Author(s):  
XUEZAI PAN ◽  
ZHIRONG SHENG ◽  
XUDONG SHANG
Keyword(s):  
Fracture Surface ◽  
Rock Fracture ◽  
White Marble ◽  
Fracture Surfaces ◽  
Loading Mode ◽  
The Mean ◽  
Morphology Characterization ◽  
The Mathematical Model ◽  
First Time

In order to research roughness of rock fracture surfaces and interior damaged status of rock, some Brazil discs of white marble and sandstone are loaded to fracture by Brazil Test and the mathematical model of fractal variation is used to distinguish the morphology characterization of fracture surface of white marble from that of sandstone. Through computing the acquired scanned data of rock fracture surfaces, the following three results are obtained. First, the roughness of fracture surface increases with increase of loading angles, furthermore, the anisotropy of white marble fracture surface is more obvious than that of sandstone one. Second, under the same loading mode, by analyzing the mean fractal variation, the fracture surface of white marble is rougher than that of sandstone. Finally, rock disc specimens loaded to 1/2 or 3/4 of mechanics of mean fracture threshold still do not fracture at the first time loading, but their interiors have been badly damaged.

FRACTALS AND SECONDARY MIGRATION

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 799-806 ◽  
Author(s):  
PAUL MEAKIN ◽  
GERI WAGNER ◽  
VIDAR FRETTE ◽  
JENS FEDER ◽  
TORSTEIN JØSSANG
Keyword(s):  
Oil And Gas ◽  
Fractal Model ◽  
Source Rocks ◽  
Fracture Aperture ◽  
Low Density ◽  
Secondary Migration ◽  
Gravity Driven ◽  
And Migration ◽  
Water Saturated ◽  
Wetting Fluid

The process of secondary migration, in which oil and gas are transported from the source rocks, through water saturated sedimentary carrier rocks, to a trap or reservoir can be described in terms of the gravity driven penetration of a low-density non-wetting fluid through a porous medium saturated with a wetting fluid. This process has been modeled in the laboratory and by computer simulations using homogeneous porous media. Under these conditions, the pattern formed by the migrating fluid can be described in terms of a string of fractal blobs. The low density internal structure of the fractal blobs and the concentration of the transport process onto the self-affine strings of blobs (migration channels) both contribute to the small effective hydrocarbon saturation in the carrier rocks. This allows the hydrocarbon fluids to penetrate the enormous volume of carrier rock without all of the hydrocarbon being trapped in immobile isolated bubbles. In practice, heterogeneities in the carrier rocks play an important role. In some cases, these heterogeneities can be represented by fractal models and these fractal heterogeneity models provide a basis for more realistic simulations of secondary migration. Fractures may play a particularly important role and migration along open fractures was simulated using a self-affine fractal model for the fluctuating fracture aperture.

scholarly journals Sugarcane and Pine Biochar as Amendments for Greenhouse Growing Media for the Production of Bean (Phaseolus vulgaris L.) Seedlings

2018 ◽  
Vol 10 (4) ◽  
pp. 58 ◽  
Author(s):  
Charles L. Webber III ◽  
Paul M. White Jr ◽  
Mengmeng Gu ◽  
Douglas J. Spaunhorst ◽  
Isabel M. Lima ◽  
...  
Keyword(s):  
Phaseolus Vulgaris ◽  
Geometric Mean ◽  
Green Bean ◽  
Future Research ◽  
Phaseolus Vulgaris L ◽  
Growing Media ◽  
Bean Seedling ◽  
Raw Sugar ◽  
Certified Organic ◽  
The Impact

Louisiana sugarcane farmers in 2016 harvested 11.7 million Mg of millable sugarcane from 163,000 ha, producing 1.47 million Mg of raw sugar and an estimated 3.5 million Mg of bagasse. Even though Louisiana sugar mills use 80% to 90% of the bagasse for fuel production, another 350,000 to 700,000 Mg of bagasse accumulates each year. The conversion of the excess bagasse into biochar is one solution to reduce the excess supply. Research was conducted to determine the impact of sugarcane biochar as an amendment to soilless planting media for the production of green bean (Phaseolus vulgaris L.) seedlings. Sugarcane bagasse biochar (SBB) and pine biochar (PB) were each combined by volume with a commercial certified organic soilless growing media into 5 combinations (0%:100%, 25%:75%, 50%:50%, 75%:25%, and 100%:0%, biochars and growing media, respectively). Green bean variety ‘Bowie’ seeds were planted in each of the different planting mixtures. The particle size distribution for the two biochars are in stark contrast to each other with the PB particle median, mean, geometric mean, and mode much greater than those of the SBB. As amendments to the soilless greenhouse growing media, the biochars (SBB and PB) functioned very well, especially at the 25% and 75% levels. The 100% SBB performed as well as the 100% commercial soilless growing media and slightly better than the 100% PB when comparing seedling fresh and dry weights. The 100% PB is not recommended as a soilless growing media even with the supplemental fertilizer used in these experiments. These results indicate that the volume of a standard soilless greenhouse growing media can be successfully extended by adding 25% to 75% SBB and PB without reducing bean seedling growth. Future research is needed to evaluate these biochars for the production of additional plant species.

RESEARCH ON MORPHOLOGIES OF ROCK FRACTURE SURFACES BASED ON MATHEMATICAL METHODS

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550039
Author(s):  
XUEZAI PAN
Keyword(s):  
Interpolation Method ◽  
Rock Fracture ◽  
Small Island ◽  
Fractal Interpolation ◽  
Mathematical Methods ◽  
Fractal Method ◽  
Fracture Surfaces ◽  
Power Spectral ◽  
Rock Fracture Mechanics ◽  
Spectral Density Method

In order to research mechanics of rock fracture instant, it is one of methods that rock fracture mechanics are researched by rock fracture surfaces’ morphology. Some researched results which come from international and domestic researches in decades are described and summarized from mathematics in this paper. For example, fractal dimension method, “Small Island Method”, fractal interpolation method, Multi-fractal method, the accumulation power spectral density method. In addition, advantages and insufficiencies of every method are reviewed and commented. In the end, the future researched expectations are put forward from three aspects of rock fracture surfaces’ morphology.

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