Predicting the Permeability of Tight Sandstone Utilizing Experimental and Mathematical Modeling Approaches

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Chunsheng Yu ◽  
Qi Jiang ◽  
Na Su ◽  
Lin Chang
Keyword(s):  
Mathematical Modeling ◽  
Pore Structure ◽  
Effective Medium Theory ◽  
Ct Scanning ◽  
Cross Sectional Area ◽  
Structure Parameters ◽  
Sectional Area ◽  
Tight Sandstone ◽  
Cross Sectional ◽  
Tight Formations

Abstract In this research, experimental and mathematical modeling were carried out to estimate the permeability of tight sandstones. The pore structure parameters such as the number of pores, pore cross-sectional area, and pore radius were obtained by microcomputed tomography (micro-CT) scanning and image processing. A mathematical model was developed to predict the permeability of tight sandstones using the pore structure parameters. In the model, hydraulic radius was used to estimate the pore hydraulic conductance, where the pore diameter variation in a sinusoidal manner was observed. The stereological correction factor was used to characterize the arbitrary angle between the pore axis and the cross-sectional area. The tortuosity model was applied to characterize the behavior of non-Darcy flow inside the tight formations. Finally, the permeability prediction model was developed based on the effective medium theory. The proposed model was validated by 21 tight sandstone samples, with the relative errors within ±20%. In addition, due to the presence of small pores in tight sandstone with little contribution to overall permeability, the permeability shows inversely proportional behavior against the number of small pores.

scholarly journals Mathematical modeling of aerodynamic processes in railway tunnels on high-speed railways

2020 ◽  
Vol 157 ◽  
pp. 06017
Author(s):  
Alexander Ledyaev ◽  
Vladimir Kavkazskiy ◽  
Yan Vatulin ◽  
Valeriy Svitin ◽  
Oleg Shelgunov
Keyword(s):  
Mathematical Modeling ◽  
High Speed ◽  
Practical Experience ◽  
Cross Sectional Area ◽  
Geometric Parameters ◽  
Sectional Area ◽  
Cross Sectional ◽  
Optimization Task ◽  
Sufficient Degree

The study of aerodynamic processes in railway tunnels on highspeed railways in the absence of practical experience in operation should be carried out with a sufficient degree of accuracy only by mathematical modeling. A multi-factor experiment was performed, which resulted in solving the optimization task of determining the tunnel cross-sectional area, taking into account aerodynamic processes. Based on the analysis of the results, the conclusion is made about the applicability of the method to the prognosis of aerodynamic effects on prospective tunnel structures of high-speed railways and optimization of geometric parameters of the tunnels.

Pelvic Canal Narrowing Caused by Triple Pelvic Osteotomy in the Dog

1994 ◽  
Vol 07 (03) ◽  
pp. 110-113 ◽  
Author(s):  
D. L. Holmberg ◽  
M. B. Hurtig ◽  
H. R. Sukhiani
Keyword(s):  
Postoperative Complications ◽  
Pelvic Osteotomy ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Canal Width ◽  
Operative Complications ◽  
Post Operative Complications

SummaryDuring a triple pelvic osteotomy, rotation of the free acetabular segment causes the pubic remnant on the acetabulum to rotate into the pelvic canal. The resulting narrowing may cause complications by impingement on the organs within the pelvic canal. Triple pelvic osteotomies were performed on ten cadaver pelves with pubic remnants equal to 0, 25, and 50% of the hemi-pubic length and angles of acetabular rotation of 20, 30, and 40 degrees. All combinations of pubic remnant lengths and angles of acetabular rotation caused a significant reduction in pelvic canal-width and cross-sectional area, when compared to the inact pelvis. Zero, 25, and 50% pubic remnants result in 15, 35, and 50% reductions in pelvic canal width respectively. Overrotation of the acetabulum should be avoided and the pubic remnant on the acetabular segment should be minimized to reduce postoperative complications due to pelvic canal narrowing.When performing triple pelvic osteotomies, the length of the pubic remnant on the acetabular segment and the angle of acetabular rotation both significantly narrow the pelvic canal. To reduce post-operative complications, due to narrowing of the pelvic canal, overrotation of the acetabulum should be avoided and the length of the pubic remnant should be minimized.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Changes in the parameters of nasal breathing and parameters of the upper respiratory tract during orthognathic operations in patients with II and III skeletal class of jaw anomalies

2020 ◽  
pp. 22-27
Author(s):  
S.Sh. Gammadaeva ◽  
M.I. Misirkhanova ◽  
A.Yu. Drobyshev
Keyword(s):  
Respiratory Tract ◽  
Nasal Cavity ◽  
Nasal Septum ◽  
Cross Sectional Area ◽  
Upper Respiratory Tract ◽  
Sectional Area ◽  
Nasal Breathing ◽  
Cross Sectional ◽  
Skeletal Class ◽  
Upper Respiratory

The study analyzed the functional parameters of nasal breathing, linear parameters of the nasal aperture, nasal cavity and nasopharynx, volumetric parameters of the upper airways in patients with II and III skeletal class of jaw anomalies before and after orthognathic surgery. The respiratory function of the nose was assessed using a rhinomanometric complex. According to rhinoresistometry data, nasal resistance and hydraulic diameter were assessed. According to the data of acoustic rhinometry, the minimum cross-sectional area along the internal valve, the minimum cross-sectional area on the head of the inferior turbinate and nasal septum and related parameters were estimated. According to the CBCT data, the state of the nasal septum, the inferior turbinates, the nasal aperture, the state of the nasal cavity, and the linear values of the upper respiratory tract (nasopharynx) were analyzed. The patients were divided into 4 groups according to the classification of the patency of the nasal passages by

Unequal Probability Scheme for Fruit Count in a Guava Tree

2016 ◽  
Vol 3 (4) ◽  
Author(s):  
R. C. BHARATI
Keyword(s):  
Cross Sectional Area ◽  
Equal Probability ◽  
Sampling Scheme ◽  
Research Station ◽  
Sectional Area ◽  
Cross Sectional ◽  
Unequal Probability ◽  
Selection Probabilities ◽  
Horticultural Research ◽  
Number Of Branches

Data on fruit count corresponding to primary, secondary and tertiary branches of a randomly selected guava CV. Allahabad Safeda were recorded from the guava orchard of Horticultural Research Station, Birauli. The proposed sampling scheme in which the selection probabilities are based on length of braches between two forking points was compared with equal probability(PE), probability proportional to the number of branches(PPN), probability proportional to the cross sectional area (PPA) and probability proportional to volume (PPV) method of sampling and found to be more efficient.

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