Ex Site-Bioremediation of Petroleum-Contaminated Soil With Exogenous Microbe
WEI Xiao-fang, ZHANG Zhong-zhi﹡, GUO Shao-hui, JI De-kun, LUO Yi-jing, SU You-ming
2007, 20 (2): 1-4.
Abstract ( ) PDF ( 1035KB ) ( ) 　　
Experiment was undertaken for ex site-bioremediation of oil-contaminated soil which comes from Dagang oilfield, whether the exogenous microbes accelerate the rate of the bioremediation or not is studied and the impact factors on the biodegradation of the petroleum-contaminated soil were investigated too. The collected soil were divided into two groups then mixed, and the total petroleum hydrocarbon(TPH) was 8 416, 16 385 mg/kg respectively. The TPH of the soil was monitored during the treatment and the influence factors such as indigenous consortium, bio-stimulating, different exogenous microbe, bulk agent (sawdust), the varied initial TPH of the soil were investigated. The components changes of the bio-treated oil and the untreated oil were analyzed by GC-MS. The experiment was lasted for 300 d. When the water content of the soil is given, the exogenous microorganism can speed up the biodegradation of the petroleum greatly, and the reduction ratio of TPH reached to 79% with the combination of the exogenous microbe and bulk agent. The results of GC-MS show that the alkane can be better metabolized by microorganisms when their molecular weight are less than C₂₈ and the microbes can biodegradate the polycyclic aromatic hydrocarbon efficiently.
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Adsorption of Nickel From Aqueous Solution by Humin
LIU Zhi-rong, ZHOU Li-min, WEI Peng, PETER Warwick, NICK Evans
2007, 20 (2): 5-8.
Abstract ( ) PDF ( 1039KB ) ( ) 　　
 
The experiment tested that humin can enrich Ni²⁺ by means of liquid scintillation counting. The procedures were effected by pH value, amount of humin and initial aqueous concentration of nickel. There may be exist reversible transitions among humic acid, fulvic acid and humin for variation of ultra-violet of peat or humin into nickel solution. Freundlich equation can describe the adsorption reaction of Ni²⁺ onto humin excellently. Nickel-humin -dual-complexation mode play an primary part in the adsorption owing to Freundlich [KG*3]adsorption [KG*3]exponent 0.684 4. Freundlich adsorption exponent （0.638 2，
0.684 4）and common logarithm of adsorption index （1.693 2，1.711 5）for peat and humin are almost equal. They indicate that humin may control the binding ability of Ni²⁺ onto peat. The results show that humin can act as a potential material for permeable reactive barrier.
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The Treatment of Oily Wastewater With a Modified Lignin-Based Oil Removal Flocculant
YANG Lin， LIU Ming-hua*
2007, 20 (2): 9-11.
Abstract ( ) PDF ( 1035KB ) ( ) 　　
The modified lignin-based oil removal flocculant containing the dithiocarbamate group, denoted as MLOF, was prepared by chemical modification of alkali lignin, a byproduct from the pulp and paper industry. Then MLOF was adopted to treat the oily wastewater. And the flocculation conditions were optimized. The results show the removal percentages of oil, COD Cr, suspended solid (SS) and colourity of the effluent can reach to 88.2%, 71.5%, 90.5% and 93.7％ respectively under such conditions as 6.7 of the effluent pH value and 35 mg/L of the flocculant dosage etc. Moreover, the comparison tests with various flocculants indicated that the amount of MLOF was little when treated oily wastewater and the flocculation performance of the modified lignin-based oil removal flocculant apparently prevailed over such high-molecular flocculants as polyacrylamide (PAM), polyaluminium chloride (PAC) and polyferric sulfate (PFS) etc. 
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Separation Process of Oleic Aicd and Linoleic Acid by Solvent Crystallization
CUI Guo-gang, JIA Shao-yi, ZHANG Cheng, WU Song-hai*
2007, 20 (2): 12-14.
Abstract ( ) PDF ( 1034KB ) ( ) 　　
The solvent crystallization separation process of oleic acid and linoleic acid was investigated by using methanol solvent. The results show that the crystallization temperature and the proportion solvent have big influence on the solvent crystallization separation process of oleic acid and linoleic acid. Decreasing crystallization temperature decreases the mass fraction of oleic acid in crystal and increases the mass fraction of linoleic acid in filtrate. Decreasing proportion solvent increases the mass fraction of oleic acid and linoleic acid. The magnetic field has influence on the separation process, it is favorable to the solvent crystallization separation process of oleic acid and linoleic acid. The quantitative results show that under the effect of magnetic field the mass fraction of oleic acid in crystal increases by 1.73％～2.48％ and the mass fraction of linoleic acid in filtrate increases by 1.68％～3.19％.
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Application of GPC-ELSD in the Deterimination of Relative Molecular Weight and Its Distribution of VGO
ZHUANG Li-hong， TIAN Yan-wen， LZhen-bo, ZHANG Da-wei
2007, 20 (2): 15-17.
Abstract ( ) PDF ( 997KB ) ( ) 　　
 
A High performance gel permeation chromatography(GPC),evaporative light-scattering detector(ELSD) method were applied to determine the relative molecular weight and its distribution of vacuum gas oil(VGO),adopting linear calibration with kown relative molecular weight calibration standard and complicated mathematics operation. Also the precision of the technique was evaluated and the relative molecular weight between GPC and VPO was compared. The results show that the relative error is less than 1%, comparison with traditional method of VPO the analysical rate is promoted five times, the sample oils less to 1/10. The technique is accurate, fast and high level of automatic operation. 
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Preparation and Characterization of W₂N/TiO₂-Al₂O₃  and It's Catalysis for Thiophen HDS
ZHANG Qiang, LI Bao -shan*, SUN Gui -da, ZHOU Zhi-jun
2007, 20 (2): 18-22.
Abstract ( ) PDF ( 1118KB ) ( ) 　　
 
The complex supporters with different mass fraction of TiO₂ for preparation W₂N/γ-Al₂O₃-TiO₂ catalyst were made by titanic acid tetra-butyl ester sol-gel method and γ-Al₂O₃ as raw materials. The catalyst precursors, WO₃/TiO₂-Al₂O₃, with different WO₃ content were prepared at 500 ℃ baking for 5 h after loading ammonium paratungstate。The precursors were deoxidized and nitrification in H₂/N₂ (volume ratio of 1∶(4~5) gas-flow of 10 800 h-1 through temperature programmed could get the catalysts. And the catalysts were characterized by means of XRD，BET，XPS and TG/DTA. The influence of mass fraction of TiO₂ on its specific surface, its acid amount and its performance for thiophen HDS was investigated in miniature high pressure device of the fixed bed. The results show that when the mass fraction of TiO₂ is 6% in the catalyst, its acid amount and its specific surface are the largest, they are 0.184 9 mmol/g and 107.2 m²/g respectively. And the activity of the catalyst for thiophene HDS is the best, at 330 ℃, pressure 3 MPa, weight hour space velocity 6 h-1, hydrogen oil ratio 900∶1, the conversion rate of thiophen is up to 56.4%. 
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Iron Removal and Its Effect on Turbidity in the Oil Field Produced Water
LI Fang-wen, WU Jian-feng, XU Xiao-hong, LI Meng, ZHANG Xiao-Yan, CHEN Yi-chun, WANG Yu-tao
2007, 20 (2): 23-25.
Abstract ( ) PDF ( 1051KB ) ( ) 　　
Iron removal in the oil field produced water and effect of iron mass concentration in the outlet water on turbidity were explored by addition alkali process. Iron contents were determined by 1,10-phenanthroline spectrophotometry and portable turbidimeter was adopted at the determination of turbidity. Results show that pH of inlet water has significant effects on iron removal, turbidity reduce and anti-corrosion of treatment devices. Iron removal is bad and corrosion of treatment device could not be restrained when pH is below 7, which resulted in negative iron removal rate. Better pH is about 8.3 where iron removal and anti-corrosion of treatment devices are attained. And the quality of outlet water can meet the A1 quality standards of recommended indexes in SY/T5329-94 about the injection water quality for clastic rock oil fields, and its turbidity keep invariablenes at a dwell time of 2.5 h. However, outlet water turidity at 6.6 and 7.3 of pH rose gradually because of Fe(OH)₂ oxidation. Coagulant can promote Fe(OH)₂ settlement and major removal mechanisms of Fe(OH)₂ include settlement, interception based on filtration and adsorption from theoretical analysis. At a low pH, electrochemical corrosion made treatment devices release iron which induces outlet iron contents above inlet iron contents. On the contrary, at a high pH, it is blockaded owing to protective layer formation and cathode reaction suppressed.
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Corrosion and Simulative System of Hydrogenation Reactor Effluent Air Coolers
REN Xiao-guang, XIE Yun-feng, XUAN Zheng-nan
2007, 20 (2): 26-29.
Abstract ( ) PDF ( 1087KB ) ( ) 　　
The corrosion mechanism of system of hydrogenation reactor effluent air collers was approached. By confecting simulation corrosion solution, it was researched the effect of experimental in various conditions on annual corrosion rate by means of the corrosion rate testing equipment of resistance probe and CMB-1510B portable instantaneous corrosion rate meterage. The investigated conditions included concentration of corrosion inhibitor, corrosion factor(Kp), pH value and synergistic effect. Results show that BTA corrosion inhibitor is an excellent inhibitor for system of hydrogenating reactor effluent air coolers, there exists good synergistic effect between (NaPO₃)6 and ZnSO₄ compounds in NH₄Cl solution; at the same time, also indicate that annual corrosion rate rises obviously with the increase of corrosion factor, annual corrosion rate rises obviously with the decrease of it when pH value changes in lower range, effect of high pH value on annual corrosion rate lessens on the whole.
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Preparation of Fe and Ni Nanopowders by Arc-Discharge Methods
LIAN Shu, LU Zhong-ren, SHI Gui-mei, LI Ying-min
2007, 20 (2): 30-33.
Abstract ( ) PDF ( 1857KB ) ( ) 　　
Fe and Ni nanopowders were prepared in mixture gas of H₂ and Ar by arc discharge method. High-melting-point metals W and Mo were added to the raw material (bulk Fe or Ni). The structure, morphology and sizes of the nanopowders were analyzed using X-ray diffraction, transmission electron microscopy, BET, oxygen-nitrogen analysis and chemical analysis. The results show the oxide layer of Fe and Ni is destroyed and the temperature of melting sphere of Fe and Ni is increased due to adding high melting sphere of W and Mo, the productivity of nanopowders has been improved by 50%. The mass fraction of W and Mo in the as-prepared samples is only about 0.01%, and the purity of nanopowders is almost unchanged. The average sizes of Fe and Ni nanopowders are slightly increased under the same condition including atmosphere and pressure as well as power when high melting point metal is added into raw materials. The productivity of adding W in the raw materials is higher than that of adding Mo.
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Flow Simulation of Atmosphere-Vacuum Distillation for Crude Oil
GE Yu-lin, SHEN Sheng-qiang
2007, 20 (2): 34-39.
Abstract ( ) PDF ( 1158KB ) ( ) 　　
New flow was need to be rearranged in order to satisfy the requirement of technology due to the reconstruction of atmosphere-vacuum distillation equipment for enlarging working ability in the present condition. Based on the fundamental of distillation, MESH model including equations of mass balance, phase equilibrium, mole fraction summations and heat balance for atmosphere-vacuum distillation column was established. The key parameter such as temperature and pressure of product was obtained through solution of the model on Pro/II platform. The comparison of simulation results with requirement of spot technology was analyzed. Good agreement between the results of simulation and requirement of spot technology approves that the model is valid and the rearrangement of flow satisfies the requirement of technology. The profiles of temperature and rate of vapor and liquid versus tray number reflect the influence of feeds, products, and cooling cycle in the middle of columns on process of distillation very well.
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Synthetic Process of Tungoil Modified Phenolic Epoxy Resin and the Performance of Room Temperature Cured
YIN Wen－hua， CHEN Yao， WU Bi-yao*
2007, 20 (2): 40-42.
Abstract ( ) PDF ( 1054KB ) ( ) 　　
A tungoil-phenol compound(TAP) and the tungoil modified phenolic epoxy resin(TMP) which were synthesized in the presence of acid catalyst, and the structure of these compounds were characterized by FTIR and GPC. FTIR analysis shows that the reaction between tungoil and phenol undermined the conjugate double bond of tungoil molecules, a new substitute product with phenol was formed. When the substitute product reacted with formaldehyde in the acid conditions and further reacted with epichlorohydrine, a tungoil modified phenolic epoxy resin(TMPE) was synthesized. The GPC analysis shows that resin is a mixture of tungoil modified epoxy resin and phenolic epoxy resin, and the molecular weight of tungoil modified phenolic epoxy resin and phenolic epoxy resin were 3 482 and 619 respectively.Solidification performance for the tungoil modified phenolic epoxy resins and E-44 epoxy resin at room temperature were investigated. The results show that when the mass ratio between tungoil modified phenolic epoxy resin and E-44 epoxy resin is at the range of 0.5 to 2.0, the higher tensile strength can be obtained.
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CFD Simulation on Homogeneous or Aggregative Fluidization of FCC Particles
LIU Wen-dong, ZHANG Kai, BI Ji-cheng
2007, 20 (2): 43-46.
Abstract ( ) PDF ( 1771KB ) ( ) 　　
Fluid catalytic cracking(FCC) plays an important role in the processes of the heavy oil refining industry. A thoroughly understanding of fluid characteristics in the gas-solid fluidized beds is helpful for designing the FCC units. A new two-fluid model developed by Brandani S and Zhang K is used to numerically investigate the hydrodynamics of FCC particles in the platform of CFX 4.4, a commercial CFD software package. Simulation is carried out in a two-dimensional fluidized bed with 0.25 m in width and 0.70 m in height. The particle with a diameter of 6.4×10-⁵m and a density of 1 225 kg/m³ is employed as solid phase. Two typical kinds of fluid dynamics, i.e., homogeneous fluidization and aggregative fluidization, are obtained under corresponding to superficial gas velocities, which are in good agreement with classical theories as well as experimental dates from the literatures.
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Performance of Environmental Friendly Phosphorous Flame-Retardant Polyester
WU Quan-cai, JIANG Tao, CHEN Xin
2007, 20 (2): 47-49.
Abstract ( ) PDF ( 974KB ) ( ) 　　
Structures of environmental friendly phosphorous flame-retardant polyester were characterized through infrared spectra (IR), the performance of its properties such as intrinsic viscosity, differential scanning calorimeter (DSC), oxygen index (OI) and its spinnability was investigated. The results show that the flexible segments in phosphorous flame-retardant monomer were also introduced into the backbone of the polyester macromolecules, which causes the decrease of the phosphorous flame-retardant polyester glass transition temperature (θ_g) and melting transition temperature(θ_m). The synthesized phosphorous flame-retardant polyester resins have a very good flame retardantability and spinnability; when the mass fraction of phosphorous flame-retardant monomer was 4.5%, the oxygen index of phosphorous flame-retardant polyester reached to 32.8%. The tensile strength and crystallinity decreased owing to the much more space volume of phosphorous flame-retardant polyester. The results indicate that the properties for phosphorous flame-retardant polyester can satisfy the requirements for the manufacture of polyester fibers.
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Identification of Friction Factor on Waxy Oil Pipeline
CAI Jian, LI Xiao-ping, GONG Jing*, SONG Sheng-kui
2007, 20 (2): 50-53.
Abstract ( ) PDF ( 1076KB ) ( ) 　　
Based on inverse transient analysis method, the identification calculation was performed by minimizing the inverse least square problem representing the difference between the measured and predicted transient response in the waxy oil pipeline. And Levenberg-Marquardt method was adopted to optimize the friction factors. The hydraulic transient was modeled using MOC. The Jacobian matrix of the friction factor’s sensitivity was obtained by direct differentiation of the method of characteristic equations. By means of an example, the errors between the measured values and the calculated values of the middle point on the waxy oil pipeline were compared. The calculated values were solved by means of average, formular and identification friction factors. The results show that the identification method has good evaluation for the internal state variables. Identification basing on inverse transient method can be used to improve the accuracy of simulation and control with pipelines.
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Safety Assessment for Pressure Pipeline System Containing Defects Based on GB/T 19624-2004
WANG Ya-xin, XIE Yu-jun
2007, 20 (2): 54-57.
Abstract ( ) PDF ( 1136KB ) ( ) 　　
The probability assessment method for pressure piping system containing defects in petrochemical industrial piping was put forward based on GB/T 19624-2004，considering random factors. Safety assessment program for pressure piping system containing defects was worked out. The program not only can assuredly assess pressure piping system containing defects, but also the failure risk caused by each individual defects is got in pipeline containing defects, thus the failure risk of the whole pipeline system is gained.
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Elastic-Plastic Finite Element Analysis of the Internal Pressure Vessels With Large Nozzles
GUI Liang, LI De-xin*, ZHANG Jun
2007, 20 (2): 58-62.
Abstract ( ) PDF ( 2383KB ) ( ) 　　
The elastic-plastic finite element analyses of the internal pressure vessels with the different ratios of the diameter of nozzle to the diameter of vessel are carried out to investigate the stress concentration in the nozzle-vessel junction. The results show that the heaviest stress concentration is found at the interval nozzle-vessel junction of the longitudinal symmetry plane, while the stress concentration around the external junction is decrease because of the welded joint. In the process of loading, the stress around the junction linearly increases at first and then the range of the high stress area enlarges. The ratio of the diameter of nozzle to the diameter of vessel has greater effect on the distribution area of high stress in plastic deformation stage. Compared with large opening without nozzles, the stress concentrations around the junction are sharply reduced because of the nozzles.
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Gear's Predictor-Corrector Algorithms on Molecular Dynamics Simulation of Nanometer Grinding
ZHAO Heng-hua，CAI Guang-qi
2007, 20 (2): 63-65.
Abstract ( ) PDF ( 1736KB ) ( ) 　　
Nanometer grinding is the important methods of achieving the super- precision machining.The extremely thin chips can be produced by nanometer grinding. The experimental showed that the very fine chips can be down to 1 nm. Therefore molecular dynamics computer simulation can be used to analyze the mechanism of nanometer grinding.The subject which deals with the interaction between the grinding grain particles and workpiece particles was studied by the method of Gear’s predictor-corrector algorithms. The equation of motion was built up, and solved by numerical method. Then the speed and displacement of these particles were obtained.
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Experiment on Shearing Demulsification of W/O Emulsion
JIANG Xue-mei, DONG Shou-ping, ZHANG Hong-guang
2007, 20 (2): 66-68.
Abstract ( ) PDF ( 1357KB ) ( ) 　　
In order to study the feasibility of the shearing demulsification of W/O emulsion, a Couette double-cylinder device was designed to form a lamina flow, and its shear intensity was controlled by the rotate speed of the inner cylinder. The force of single droplet is analyzed according to hydrokinetics, and the affine deformation model is put forward and validated by experiment which basically agreed with Taylor G I and Cox R G theory. The results show that shear is propitious to droplets aggregation. Based on the relation curve of droplets diameter with the revolution of inner cylinder, it was found when the rotation velocity of inner cylinder is 50~150 r/min ( shearing strenghth of 8.67~26.01 Pa), the maximal diameter and average diameter are all larger than that of droplets which are not in shear flow. It was shown that shear can accelerate droplets aggregation only within a valid shear range. Therefore，a proper shear flow can be introduced into the separate device to improve the separate efficiency of W/O emulsion.
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Two Novel Criteria of Deformation of a Single Droplet：Estimation of the Effect of Shear Flow on Deformation of a Single Drop by the Ratio of Long Radius to Short Radius or Stretching Rate 
ZHANG Hong-guang, DONG Shou-ping, WANG Yan-li, LIU Guo-biao, JIANG Xue-mei
2007, 20 (2): 69-72.
Abstract ( ) PDF ( 1138KB ) ( ) 　　
Two new type criteria of deformation of a single droplet were introduced to estimate the effect of shear flow on deformation by the ratio of long radius to short radius or stretching rate, and they were analyzed and compared through the experiments. The experiments show that the ratio of long radius to short radius and stretching rate grow with the increase of shear velocity and the deformation shrinkage coefficient of a single droplet increases at first and then decreases. Compared with to the theoretical results it deviates greater with emulsifier. The shear stress attained by the stretching rate agrees better with the practical value than that by the ratio of long radius to short radius.
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Stress Corrosion Crack Initiation Analysis of Multilayered Urea Reactors
SONG Ming-da, WANG Wei-qiang, CHEN Lu-bin, XU Shu-gen
2007, 20 (2): 73-76.
Abstract ( ) PDF ( 3472KB ) ( ) 　　
Analysis of samples taken from the cracking area of the multilayered urea reactors verified the existence of stress corrosion cracking (SCC) cracks. The influence factors of SCC in multilayered urea reactors were investigated. The results show that the leak detection steam may condense in the interlayer clearances, which would cause alkaline medium concentration at the heavy weld. It was the initiation and propagation of micro-cracks under alkaline environment and local high stress concentrations that lead to the SCC of heavy girth weld urea of the multilayered reactors. The results can give beneficial directions to avoid SCC of layers and catastrophic ruptures of multilayered urea reactors.
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The Failure Probability Analysis of Ethylene Cracking Furnace Tube Based on Risk
WANG Wen-he， SHEN Shi-ming
2007, 20 (2): 77-79.
Abstract ( ) PDF ( 1047KB ) ( ) 　　
The ethylene cracking furnace tube is the key component of the cracking furnace; its failure will bring serious consequences such as the fire explosion etc. According to methods of Monte Carlo and risk analysis theory of API581 of American petroleum institute, it was provides qualitative and quantitatively analysis failure probability of the ethylene cracking furnace tubes for a petrochemical corporation, and obtains the failure probability of this furnace tube. Some results can be seen by the two methods, the failure probability calculated by Monte Carlo method increased with the increase of the runtime of furnace tube under creep and carburization; while the failure probability calculated by API581 only considering creep is lower than that computed by Monte Carlo method.
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Scenery Simulation Based on the Iteration Function System and the Free Surface Modeling
HAN Yun-ping, ZHANG Yan*, GUO Lai-de
2007, 20 (2): 80-83.
Abstract ( ) PDF ( 2117KB ) ( ) 　　
 The fractal theory is adapted to resolve the simulation of irregular-shaped objects, however, the modeling technology is adapted to the modeling of regular-shaped objects. It can simulate the nature scenery to the life by combining the iteration function system（IFS）of fractal theory with the free surface modeling technology. With the application of iteration function system and the free surface modeling technology to computer aided design (CAD) environment and used the interface modeling Object ARX of CAD and Visual C++ to study the simulative algorithm of natural scenery. With the use of iteration function system to simulate the algorithms of 3D fractal plants. It applied the free surface (B-spline surface) to simulate a hillside. The practical application of a hillside and plants with fruit was given, it indicated that the simulative effect was natural and living.
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Global Stability in a n-Species System With Time Delay
LI Shi－tao, LI Dong－mei
2007, 20 (2): 84-87.
Abstract ( ) PDF ( 1065KB ) ( ) 　　
 One of the most interesting topics in ecology systems is the stability of species. It is a n-species (one-prey, the others-predator) ratio-dependent predator-prey system with time delay and functional response at the seme time and was studied. By differential inequality constructing suitable Lyapunov functional, a sufficient condition was obtained for the global stability of the positive equilibrium of the system. Finally, the numerical simulation result of population model was given.
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The Euler Number Study of Image and Its Application
LIN Xiao-zhu, JI Jun-wei, GU Ying-ying
2007, 20 (2): 88-91.
Abstract ( ) PDF ( 1098KB ) ( ) 　　
Euler number of image is one of the most important characteristics in digital topology. The connectivity of the binary image was deeply researched in order to understand the essence of Euler number. The relationship between Euler number and the neighbor number of foreground run was proposed as a formula based on the two basic concepts of Euler number and neighbor number. It is a new idea to part computed Euler number of two dimesion image. It has been applied to count the number of objects with irregular shape.
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Hilbert-Huang Transform of Pressure Fluctuation Signal in SCISR
ZHANG Jian-wei, XUAN Shu-peng
2007, 20 (2): 92-96.
Abstract ( ) PDF ( 3768KB ) ( ) 　　
The Hilbert-Huang transform（HHT）was applied to analyze the pressure fluctuation signal in submerged circulative impinging stream reactor. The intrinsic mode function（IMF） was extracted from the pressure fluctuation in submerged circulative impinging stream reactor（SCISR）. The non-linear and non-stationary characteristics of the pressure fluctuation signals were demonstrated. Analyzing the energy distribution of high, middle,low frequency segment and its transfer within different IMF, the relationship between the flow regimes identification in SCISR and the energy distribution of the different frequency segment IMF were founded. The results show that the rotate speed gradually rose, the impinging course of particles would caused the vortex with different scales and energy distribution of IMF would caused diversification. Hilbert-Huang transform method exposes internality rule between flow pattern and energy distributing of IMF component that is obtained by decomposing pressure fluctuation signal of SCISR using EMD. At the same time, quantificational proof can be provided.
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