Inverse response behaviour in the bright ring radius measurement of the Czochralski process II: Mitigation by control

Stem analysis is an essential aspect in forestry investigation and forest management, as it is a primary method to study the growth law of trees. Stem analysis requires measuring the width and number of tree rings to ensure the accurate measurement, expand applicable tree species, and reduce operation cost. This study explores the use of Open Source Computer Vision Library (Open CV) to measure the ring radius of analytic wood disk digital images, and establish a regression equation of ring radius based on image geometric distortion correction. Here, a digital camera was used to photograph the stem disks’ tree rings to obtain digital images. The images were preprocessed with Open CV to measure the disk’s annual ring radius. The error correction model based on the least-square polynomial fitting method was established for digital image geometric distortion correction. Finally, a regression equation for tree ring radius based on the error correction model was established. Through the above steps, click the intersection point between the radius line and each ring to get the pixel distance from the ring to the pith, then the size of ring radius can be calculated by the regression equation of ring radius. The study’s method was used to measure the digital image of the Chinese fir stem disk and compare it with the actual value. The results showed that the maximum error of this method was 0.15 cm, the average error was 0.04 cm, and the average detection accuracy reached 99.34%, which met the requirements for measuring the tree ring radius by stem disk analysis. This method is simple, accurate, and suitable for coniferous and broad-leaved species, which allows researchers to analyze tree ring radius measurement, and is of great significance for analyzing the tree growth process.

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Identifying Reservoir Features via iSOR Response Behaviour

Energies ◽

10.3390/en14020427 ◽

2021 ◽

Vol 14 (2) ◽

pp. 427

Author(s):

Jingyi Wang ◽

Ian Gates

Keyword(s):

Oil Sands ◽

Gravity Drainage ◽

Athabasca Oil Sands ◽

Steam Chamber ◽

Heterogeneous Reservoirs ◽

Steam Assisted Gravity Drainage ◽

Response Behaviour

To extract viscous bitumen from oil sands reservoirs, steam is injected into the formation to lower the bitumen’s viscosity enabling sufficient mobility for its production to the surface. Steam-assisted gravity drainage (SAGD) is the preferred process for Athabasca oil sands reservoirs but its performance suffers in heterogeneous reservoirs leading to an elevated steam-to-oil ratio (SOR) above that which would be observed in a clean oil sands reservoir. This implies that the SOR could be used as a signature to understand the nature of heterogeneities or other features in reservoirs. In the research reported here, the use of the SOR as a signal to provide information on the heterogeneity of the reservoir is explored. The analysis conducted on prototypical reservoirs reveals that the instantaneous SOR (iSOR) can be used to identify reservoir features. The results show that the iSOR profile exhibits specific signatures that can be used to identify when the steam chamber reaches the top of the formation, a lean zone, a top gas zone, and shale layers.

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Initial motion of a viscous vortex ring

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0122 ◽

1994 ◽

Vol 446 (1928) ◽

pp. 589-599 ◽

Cited By ~ 5

Keyword(s):

Reynolds Number ◽

Asymptotic Analysis ◽

Vortex Ring ◽

Kinematic Viscosity ◽

Reynolds Numbers ◽

Initial Radius ◽

Dimensionless Form ◽

Ring Radius ◽

Initial Motion ◽

Matched Asymptotic Analysis

The behaviour of a viscous vortex ring is examined by a matched asymptotic analysis up to three orders. This study aims at investigating how much the location of maximum vorticity deviates from the centroid of the vortex ring, defined by P. G. Saffman (1970). All the results are presented in dimensionless form, as indicated in the following context. Let Γ be the initial circulation of the vortex ring, and R denote the ring radius normalized by its initial radius R i . For the asymptotic analysis, a small parameter ∊ = ( t / Re ) ½ is introduced, where t denotes time normalized by R 2 i / Γ , and Re = Γ/v is the Reynolds number defined with Γ and the kinematic viscosity v . Our analysis shows that the trajectory of maximum vorticity moves with the velocity (normalized by Γ/R i ) U m = – 1/4π R {ln 4 R /∊ + H m } + O (∊ ln ∊), where H m = H m ( Re, t ) depends on the Reynolds number Re and may change slightly with time t for the initial motion. For the centroid of the vortex ring, we obtain the velocity U c by merely replacing H m by H c , which is a constant –0.558 for all values of the Reynolds number. Only in the limit of Re → ∞, the values of H m and H c are found to coincide with each other, while the deviation of H m from the constant H c is getting significant with decreasing the Reynolds number. Also of interest is that the radial motion is shown to exist for the trajectory of maximum vorticity at finite Reynolds numbers. Furthermore, the present analysis clarifies the earlier discrepancy between Saffman’s result and that obtained by C. Tung and L. Ting (1967).

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