2The spontaneous imbibition of water and other liquids into gas-filled 3 fractures in variably-saturated porous media is important in a variety of 4 engineering and geological contexts. However, surprisingly few studies have 5 investigated this phenomenon. We present a theoretical framework for 6 predicting the 1-dimensional movement of water into air-filled fractures 7 within a porous medium based on early-time capillary dynamics and 8 spreading over the rough surfaces of fracture faces. The theory permits 9 estimation of sorptivity values for the matrix and fracture zone, as well as a 10 dispersion parameter which quantifies the extent of spreading of the wetting 11 front. Quantitative data on spontaneous imbibition of water in unsaturated 12 Berea sandstone cores were acquired to evaluate the proposed model. The 13 cores with different permeability classes ranging from 50 to 500 mD and 14 were fractured using the Brazilian method. Spontaneous imbibition in the 15 fractured cores was measured by dynamic neutron radiography at the 16 Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge 17 National Laboratory. Water uptake into both the matrix and the fracture 18 zone exhibited square-root-of-time behavior. The matrix sorptivities ranged 19 from 2.9 to 4.6 mm s -0.5 , and increased linearly as the permeability class 20 increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1 21 mm s -0.5 , and increased linearly with increasing fracture aperture width. The 22 dispersion coefficients ranged from 23.7 to 66.7 mm 2 s -1 and increased 23 linearly with increasing fracture aperture width and damage zone width. 24 Both theory and observations indicate that fractures can significantly 25 increase spontaneous imbibition in unsaturated sedimentary rock by 26 capillary action and surface spreading on rough fracture faces. Fractures 27 also inrease the dispersion of the wetting front. Further research is needed 28 7
Hydraulic fracturing of gas shale formations involves pumping a large volume of fracking fluid into a hydrocarbon reservoir to fracture the rock and thus increase its permeability.The majority of the fracking fluid introduced is never recovered and the fate of this lost fluid, often called "leak off," has become the source of much debate. Information on the capillary pressuresaturation relationship for each wetting phase is needed to simulate leak off using numerical reservoir models. The petroleum industry commonly employs airwater capillary pressuresaturation curves to predict these relationships for mixed wet reservoirs. Traditional methods of measuring this curve are unsuitable for gas shale's due to high capillary pressures associated with the small pores present. A possible alternative method is the water activity meter which is used widely in the soil sciences for such measurements. However, its application to lithified material has been limited. This study utilized a water activity meter to measure airwater capillary pressures (ranging from 1.3 -219.6 MPa) at several water saturation levels in both the wetting and drying directions. Water contents were measured gravimetrically. Seven types of gas producing shale with different porosities (2.5 -13.6%) and total organic carbon contents (0.4 -13.5%) were investigated. Nonlinear regression was used to fit the resulting capillary pressurewater saturation data pairs for each shale type to the Brooks and Corey equation. Data for six of the seven shale types investigated were successfully fitted (median R 2 = 0.93), indicating this may be a viable method for parameterizing capillary pressuresaturation relationships for inclusion in numerical reservoir models. As expected, the different shale types had statistically different Brooks and Corey parameters. However, there were no significant differences between the Brooks and Corey parameters for the wetting and drying measurements, suggesting that hysteresis may not need to be taken into account in leak off simulations.
Many natural systems are irregular and/or fragmented, and have been interpreted to be fractal. An important parameter needed for modeling such systems is the fractal dimension, D. This parameter is often estimated from binary images using the box-counting method. However, it is not always apparent which fractal model is the most appropriate. This has led some researchers to report different D values for different phases of an analyzed image, which is mathematically untenable. This paper introduces a new method for discriminating between mass fractal, pore fractal, and Euclidean scaling in images that display apparent two-phase fractal behavior when analyzed using the traditional method. The new method, coined "bi-phase box counting", involves box-counting the selected phase and its complement, fitting both datasets conjointly to fractal and/or Euclidean scaling relations, and examining the errors from the resulting regression analyses. Use of the proposed technique was demonstrated on binary images of deterministic and stochastic fractals with known D values. Traditional box counting was unable to differentiate between the fractal and Euclidean phases in these images. In contrast, bi-phase box counting unmistakably identified the fractal phase and correctly estimated its D value. The new method was also applied to three binary images of soil thin sections. The results indicated that two of the soils were pore-fractals, while the other was a mass fractal. This outcome contrasted with the traditional box counting method which suggested that all three soils were mass fractals. Reclassification has important implications for modeling soil structure since different fractal models have different scaling relations. Overall, bi-phase box counting represents an improvement over the traditional method. It can identify the fractal phase and it provides statistical justification for this choice.
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