scholarly journals Determining Crack Aperture Distribution in Rocks Using the 14 C‐PMMA Autoradiographic Method: Experiments and Simulations

Author(s):  
M. Bonnet ◽  
P. Sardini ◽  
S. Billon ◽  
M. Siitari‐Kauppi ◽  
J. Kuva ◽  
...  
Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Yuan Wang ◽  
Chenglong Wu ◽  
Yuntian Zhou

A systematic numerical method was presented to investigate the effect of aperture distribution on the relation of capillary pressure versus fluid saturation (P-S relation) for a single fracture. The fracture was conceptualized as a two-dimensional lattice-grid model and its aperture field was described by a probability distribution. Based on the invasion percolation theory, a program was developed to simulate the quasi-static displacement. The simulation was verified validly by comparisons of the experimental results. The effects of the statistical parameters were further quantified. The results show that the largest local aperture on the fracture boundary determines the AEV. The larger mean decreases the variation coefficient, which causes the more uniform aperture field, smoother air invasion front, and steeper capillary pressure-saturation curve (CPSC). The larger standard deviation increases not only the range but also the contrast degree of the apertures, thus providing a nondeterministic rule in the P-S relation. The larger correlation length causes a more homogeneous aperture field and a dual connectivity of the fracture. The increase of the difference and contrast degree between the small and large apertures results in dual-aperture fields. The dual-aperture field and dual connectivity of the fracture both contribute to the bimodal characteristic of the CPSC.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zuyang Ye ◽  
Wang Luo ◽  
Shibing Huang ◽  
Yuting Chen ◽  
Aiping Cheng

The relative permeability and saturation relationships through fractures are fundamental for modeling multiphase flow in underground geological fractured formations. In contrast to the traditional straight capillary model from porous media, the realistic flow paths in rough-walled fractures are tortuous. In this study, a fractal relationship between relative permeability and saturation of rough-walled fractures is proposed associated with the fractal characteristics of tortuous parallel capillary plates, which can be generalized to several existing models. Based on the consideration that the aperture distribution of rough-walled fracture can be represented by Gaussian and lognormal distributions, aperture-based expressions between relative permeability and saturation are explicitly derived. The developed relationships are validated by the experimental observations on Gaussian distributed fractures and numerical results on lognormal distributed fractures, respectively.


1987 ◽  
Vol 7 (5) ◽  
pp. 572-577 ◽  
Author(s):  
M. Juhler ◽  
N. H. Diemer

The present study describes and validates a 3H/14C double-label autoradiographic method in which separation of the labels was obtained by sequential film exposures to film types sensitive to 14C only and to both 3H and 14C, respectively. The error in assuming a pure 14C image on the first film was 2–3%. A linear subtraction equation was developed for calculation of the 3H activity expressed in 14C equivalents as the difference in tissue activity between the second and the first film exposure. The actual 3H activity in the tissue could be obtained by multiplying the result by 25 (14C to 3H conversion factor). The subtraction procedure was validated for absolute 14C and 3H activities of 100–1,300 nCi/g and 600–11,000 nCi/g, respectively, and for relative 3H/14C activities between 5 and 10. Self-absorption of 3H in white matter was corrected for by multiplication by 1.61 (self-absorption coefficient). This factor was close to unity for 14C.


2000 ◽  
Vol 20 (8) ◽  
pp. 1252-1263 ◽  
Author(s):  
Ian Law ◽  
Hidehiro Iida ◽  
Søren Holm ◽  
Sam Nour ◽  
Egill Rostrup ◽  
...  

One of the most limiting factors for the accurate quantification of physiologic parameters with positron emission tomography (PET) is the partial volume effect (PVE). To assess the magnitude of this contribution to the measurement of regional cerebral blood flow (rCBF), the authors have formulated four kinetic models each including a parameter defining the perfusable tissue fraction (PTF). The four kinetic models used were 2 one-tissue compartment models with (Model A) and without (Model B) a vascular term and 2 two-tissue compartment models with fixed (Model C) or variable (Model D) white matter flow. Furthermore, rCBF based on the autoradiographic method was measured. The goals of the study were to determine the following in normal humans: (1) the optimal model, (2) the optimal length of fit, (3) the model parameters and their reproducibility, and (4) the effects of data acquisition (2D or 3D). Furthermore, the authors wanted to measure the activation response in the occipital gray matter compartment, and in doing so test the stability of the PTF, during perturbations of rCBF induced by visual stimulation. Eight dynamic PET scans were acquired per subject (n = 8), each for a duration of 6 minutes after IV bolus injection of H215O. Four of these scans were performed using 2D and four using 3D acquisition. Visual stimulation was presented in four scans, and four scans were during rest. Model C was found optimal based on Akaike's Information Criteria (AIC) and had the smallest coefficient of variance after a 6-minute length of fit. Using this model the average PVE corrected rCBF during rest in gray matter was 1.07 mL·min−1·g−1 (0.11 SD), with an average coefficient of variance of 6%. Acquisition mode did not affect the estimated parameters, with the exception of a significant increase in the white matter rCBF using the autoradiographic method (2D: 0.17 mL·min−1·g−1 (0.02 SD); 3D: 0.21 mL·min−1·g−1 (0.02 SD)). At a 6-minute fit the average gray matter CBF using Models C and D were increased by 100% to 150% compared with Models A and B and the autoradiographic method. There were no significant changes in the perfusable tissue fraction by the activation induced rCBF increases. The largest activation response was found using Model C (median = 39.1%). The current study clearly demonstrates the importance of PVE correction in the quantitation of rCBF in normal humans. The potential use of this method is to cost-effectively deliver PVE corrected measures of rCBF and tissue volumes without reference to imaging modalities other than PET.


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