Convection Effects in Epitaxial Reactors: an Experimental and Theoretical Study

1988 ◽  
Vol 144 ◽  
Author(s):  
P. B. Chinoy ◽  
P. D. Agnello ◽  
S. K. Ghandhia
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Energy Transfer ◽  
Natural Convection ◽  
Gas Flow ◽  
Theoretical Study ◽  
Excellent Correlation ◽  
Flow Rates ◽  
Wide Range ◽  
Experimental Vehicle

ABSTRACTAn experimental and theoretical study has been undertaken of the effects of natural and forced convection in horizontal epitaxial reactors. The epitaxial growth of GaAs was used as the experimental vehicle for this study. A mathematical model for mass, momentum and energy transfer in the reactor was developed. Excellent correlation between modeled and experimental results was demonstrated over a wide range of reactor pressures and susceptor geometries. Recirculation of hot gases, caused by natural convection, was found to result in a strong pressure dependence of growth rate at higher susceptor slopes. Low reactor pressures have been shown to be a more effective way to eliminate recirculation than high gas flow rates.

A Method for Determining the Optimum Location of Wells in a Reservoir Using Mixed-Integer Programming

1974 ◽  
Vol 14 (01) ◽  
pp. 44-54 ◽  
Author(s):  
Gary W. Rosenwald ◽  
Don W. Green
Keyword(s):  
Mathematical Model ◽  
Gas Flow ◽  
Demand Curve ◽  
Gas Storage ◽  
Mixed Integer ◽  
Trial And Error ◽  
Flow Rates ◽  
Storage Reservoir ◽  
Reservoir Simulator ◽  
Production Demand

Abstract This paper presents a mathematical modeling procedure for determining the optimum locations of procedure for determining the optimum locations of wells in an underground reservoir. It is assumed that there is a specified production-demand vs time relationship for the reservoir under study. Several possible sites for new wells are also designated. possible sites for new wells are also designated. The well optimization technique will then select, from among those wellsites available, the locations of a specified number of wells and determine the proper sequencing of flow rates from Those wells so proper sequencing of flow rates from Those wells so that the difference between the production-demand curve and the flow curve actually attained is minimized. The method uses a branch-and-bound mixed-integer program (BBMIP) in conjunction with a mathematical reservoir model. The calculation with the BBMIP is dependent upon the application of superposition to the results from the mathematical reservoir model.This technique is applied to two different types of reservoirs. In the first, it is used for locating wells in a hypothetical groundwater system, which is described by a linear mathematical model. The second application of the method is to a nonlinear problem, a gas storage reservoir. A single-phase problem, a gas storage reservoir. A single-phase gas reservoir mathematical model is used for this purpose. Because of the nonlinearity of gas flow, purpose. Because of the nonlinearity of gas flow, superposition is not strictly applicable and the technique is only approximate. Introduction For many years, members of the petroleum industry and those concerned with groundwater hydrology have been developing mathematical reservoir modeling techniques. Through multiple runs of a reservoir simulator, various production schemes or development possibilities may be evaluated and their relative merits may be considered; i.e., reservoir simulators can be used to "optimize" reservoir development and production. Formal optimization techniques offer potential savings in the time and costs of making reservoir calculations compared with the generally used trial-and-error approach and, under proper conditions, can assure that the calculations will lead to a true optimum.This work is an extension of the application of models to the optimization of reservoir development. Given a reservoir, a designated production demand for the reservoir, and a number of possible sites for wells, the problem is to determine which of those sites would be the best locations for a specified number of new wells so that the production-demand curve is met as closely as possible. Normally, fewer wells are to be drilled than there are sites available. Thus, the question is, given n possible locations, at which of those locations should n wells be drilled, where n is less than n? A second problem, that of determining the optimum relative problem, that of determining the optimum relative flow rates of present and future wells is also considered. The problem is attacked through the simultaneous use of a reservoir simulator and a mixed-integer programming technique.There have been several reported studies concerned with be use of mathematical models to select new wells in gas storage or producing fields. Generally, the approach has been to use a trial-and-error method in which different well locations are assumed. A mathematical model is applied to simulate reservoir behavior under the different postulated conditions, and then the alternatives are postulated conditions, and then the alternatives are compared. Methods that evaluate every potential site have also been considered.Henderson et al. used a trial-and-error procedure with a mathematical model to locate new wells in an existing gas storage reservoir. At the same time they searched for the operational stratagem that would yield the desired withdrawal rates. In the reservoir that they studied, they found that the best results were obtained by locating new wells in the low-deliverability parts of the reservoir, attempting to maximize the distance between wells, and turning the wells on in groups, with the low-delivery wells turned on first.Coats suggested a multiple trial method for determining well locations for a producing field. SPEJ P. 44

scholarly journals Growth of GaN from elemental Gallium and Ammonia via Modified Sandwich Growth Technique

2004 ◽  
Vol 831 ◽  
Author(s):  
E. Berkman ◽  
R. Collazo ◽  
R. Schlesser ◽  
Z. Sitar
Keyword(s):  
Growth Rate ◽  
Gas Flow ◽  
Transport Model ◽  
Theoretical Calculations ◽  
Substrate Surface ◽  
Maximum Growth ◽  
Direct Reaction ◽  
Pure Nitrogen ◽  
Flow Rates ◽  
Reactor Pressure

ABSTRACTGallium nitride (GaN) films were grown on (0001) sapphire substrates at 1050°C by controlled evaporation of gallium (Ga) metal and reaction with ammonia (NH3) at a total reactor pressure of 800 Torr. Pure nitrogen (N2) was flowed directly above the molten Ga source to prevented direct reaction between the molten Ga and ammonia, which causes Ga spattering and GaN crust formation. At the same time, this substantially enhanced the Ga transport to the substrate. A simple mass-transport model based on total reactor pressure, gas flow rates and source temperature was developed and verified. The theoretical calculations and growth rate measurements at different ammonia flow rates and reactor pressures showed that the maximum growth rate was controlled by transport of both Ga species and reactive ammonia to the substrate surface.

Estimation of Leak Flow Rates Through Narrow Cracks

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Jae-Heon Lee
Keyword(s):  
Friction Factor ◽  
Gas Flow ◽  
Slip Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Opening Displacement ◽  
Flow Rates ◽  
Choked Flow ◽  
Runge Kutta Method ◽  
Wide Range ◽  
Leak Before Break

The estimation of the gaseous leak flow rates through a narrow crack is important for a leak-before-break analysis as a method of nondestructive testing. Therefore, the methodology to estimate the gaseous leak flow rates in a narrow crack for a wide range of flow conditions, from no-slip to slip flow and from unchoked to choked flow, by using f⋅Re (the product of friction factor and Reynolds number) correlations obtained for a microchannel, was developed and presented. The correlations applied here were proposed by the previous study (Hong, et al., 2007, “Friction Factor Correlations for Gas Flow in Slip Flow Regime,” ASME J. Fluids Eng., 129, pp. 1268–1276). The detail of the calculation procedure was appropriately documented. The fourth-order Runge–Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure, and the regular-Falsi method was employed to find the inlet Mach number. An idealized crack, whose opening displacement ranges from 2 μm to 50 μm, with the crack aspect ratio of 200, 1000, and 2000, was chosen for sample estimation. The present results were compared with both numerical simulations and available experimental measurements. The results were in excellent agreement. Therefore, the gaseous leak flow rates can be correctly predicted by using the proposed methodology.

Axial and Radial Investigation of Hydrodynamics in a Bubble Column; Influence of Fluids Flow Rates and Sparger Type

2006 ◽  
Vol 4 (1) ◽  
Author(s):  
Hélène Chaumat ◽  
Anne-Marie Billet ◽  
Henri Delmas
Keyword(s):  
Liquid Flow ◽  
Gas Flow ◽  
Bubble Column ◽  
Bubble Diameter ◽  
Pressure Sensors ◽  
Operating Conditions ◽  
Batch Mode ◽  
Flow Rates ◽  
Wide Range ◽  
Injection Zone

A detailed investigation of local hydrodynamics in a pilot plant bubble column has been performed using various techniques, exploring both axial and radial variations of the gas hold-up, bubble average diameter and frequency, surface area. A wide range of operating conditions has been explored up to large gas and liquid flow rates, with two sparger types. Two main complementary techniques were used: a quasi local measurement of gas hold-up via series of differential pressure sensors to get the axial variation and a double optic probe giving radial variations of gad hold-up, bubble average size and frequency and surface area.According to axial evolutions, three zones, where radial evolutions have been detailed, have been separated: at the bottom the gas injection zone, the large central region or column bulk and the disengagement zone at the column top. It was found that significant axial and radial variations of the two phase flow characteristics do exist even in the so called homogeneous regime. The normalized profiles of bubble frequency appear sparger and gas velocity independent contrary to bubble diameter, gas hold-up and interfacial area normalized profiles. In any case bubbles are larger in the sparger zone than elsewhere.The main result of this work is the very strong effect of liquid flow on bubble column hydrodynamics at low gas flow rate. First the flow regime map observed in batch mode is dramatically modified with a drastic reduction of the homogeneous regime region, up to a complete heterogeneous regime in the working conditions (uG> 0.02 m/s). On the contrary, liquid flow has limited effects at very high gas flow rates.A large data bank is provided to be used for example in detailed comparison with CFD calculations.

scholarly journals KPIM of Gas Transportation: Robust Modification of Gas Pipeline Equations

2008 ◽  
Vol 45 (5) ◽  
pp. 39-47
Author(s):  
A. Falade ◽  
A. Olaberinjo ◽  
M. Oyewola ◽  
F. Babalola ◽  
S. Adaramola
Keyword(s):  
Friction Factor ◽  
Gas Flow ◽  
Research Work ◽  
Flow Equation ◽  
Gas Pipeline ◽  
Flow Rates ◽  
Modified Equations ◽  
Wide Range ◽  
High Degree ◽  
Turbulent Gas Flow

KPIM of Gas Transportation: Robust Modification of Gas Pipeline Equations Studies of the flow conditions of natural gases in pipelines have led to the development of complex equations for relating the volume transmitted through a gas pipeline to the various factors involved, thus deciding the optimum pressures and pipeline dimensions to be used. From equations of this type, various combinations of pipe diameter and wall thickness for a desired rate of gas throughput can be calculated. This research work presents modified forms of the basic gas flow equation for horizontal flow developed by Weymouth and the basic gas flow equation for inclined flow developed by Ferguson. The modified equations incorporate non-iterative forms of the Colebrook-White friction factor into the original forms of the Weymouth's and Ferguson's equations. These modified equations thus eliminate the need for iteration in predicting the flow rate of gas through pipelines as is the case with their original forms when the Colebrook-White friction factor is used. The modified equations also have a wider range of application since the Colebrook-White friction factor is valid for turbulent gas flow as well as for gas flow in a transition zone. On comparing the results it can be seen that the modified Ferguson's equation gives a more accurate prediction of gas flow rates because it takes the pipeline elevation into account. Lower deviations from measured gas flow rates were observed with the modified Ferguson's equation than with the modified basic gas flow equation. The deviations observed using the modified Ferguson equation were found to range from -0.16% to +3.21%. Conclusively, these less cumbersome newly developed equations with high degree reliability will be useful in predicting the rates of gas flow for a wide range of its conditions, pipeline elevation and pipeline lengths.

Development of a Unique, Passive, Microgravity Vortex Separator

2005 ◽  
Author(s):  
M. Ellis ◽  
C. Kurwitz ◽  
F. Best
Keyword(s):  
Waste Water ◽  
Phase Separation ◽  
Power Systems ◽  
Gas Flow ◽  
Full Range ◽  
Operating Conditions ◽  
Microgravity Environment ◽  
Flow Rates ◽  
Wide Range ◽  
Vortex Separator

In the microgravity environment experienced by space vehicles, liquid and gas do not naturally separate as on Earth. This behavior presents a problem for two-phase space systems, such as environment conditioning, waste water processing, and power systems. Furthermore, with recent renewed interest in space nuclear power systems, a microgravity Rankine cycle is attractive for thermal to electric energy conversion and would require a phase separation device. Responding to this need, researchers have conceived various methods of producing phase separation in low gravity environments. These separator types have included wicking, elbow, hydrophobic/hydrophilic, vortex, rotary fan separators, and combinations thereof. Each class of separator achieved acceptable performance for particular applications and most performed in some capacity for the space program. However, increased integration of multiphase systems requires a separator design adaptable to a variety of system operating conditions. To this end, researchers at Texas A&M University (TAMU) have developed a Microgravity Vortex Separator (MVS) capable of handling both a wide range of inlet conditions as well as changes in these conditions with a single, passive design. Currently, rotary separators are recognized as the most versatile microgravity separation technology. However, compared with passive designs, rotary separators suffer from higher power consumption, more complicated mechanical design, and higher maintenance requirements than passive separators. Furthermore, research completed over the past decade has shown the MVS more resistant to inlet flow variations and versatile in application. Most investigations were conducted as part of system integration experiments including, among others, propellant transfer, waste water processing, and fuel cell systems. Testing involved determination of hydrodynamic conditions relating to vortex stability, inlet quality effects, accumulation volume potential, and dynamic volume monitoring. In most cases, a 1.2 liter separator was found to accommodate system flow conditions. This size produced reliable phase separation for liquid flow rates from 1.8 to 9.8 liters per minute, for gas flow rates of 0.5 to 180 standard liters per minute, over the full range of quality, and with fluid inventory changes up to 0.35 liters. Moreover, an acoustic sensor, integrated into the wall of the separation chamber, allows liquid film thickness monitoring with an accuracy of 0.1 inches. Currently, application of the MVS is being extended to cabin air dehumidification and a Rankine power cycle system. Both of these projects will allow further development of the TAMU separator.

Effect of C/Si Ratio and Nitrogen Doping on 4H-SiC Epitaxial Growth Using Dichlorosilane Precursor

2015 ◽  
Vol 821-823 ◽  
pp. 129-132 ◽  
Author(s):  
Hai Zheng Song ◽  
M.V.S. Chandrashekhar ◽  
T.S. Sudarshan
Keyword(s):  
Growth Rate ◽  
Epitaxial Growth ◽  
Nitrogen Doping ◽  
Gas Flow ◽  
Gas Flow Rate ◽  
Wide Range ◽  
N Doping ◽  
Morphological Defects ◽  
Defect Densities ◽  
Epilayer Surface

Application of dichlorosilane (DCS) in 4H-SiC epitaxial growth on 4° off-cut substrates has been studied. The effect of C/Si ratio and N2gas flow rate on epilayer properties is investigated in detail. It is found that the C/Si ratio has a significant influence on the growth rate, epilayer surface roughness (step-bunching), conversion of basal plane dislocations (BPDs), and generation of morphological defects and in-grown stacking faults. A wide range of doping concentration from p- to n+ can be controlled in DCS growth. High quality 4° off-cut SiC epilayers are achieved for C/Si=1.3 – 1.8. Addition of N2has no obvious influence on growth rate and defect densities. The BPD conversion greater than 99.8% is achieved independent of N doping without any pretreatment.

Experimental Study of Low Concentration Sand Transport in Multiphase Air–Water Horizontal Pipelines

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Kamyar Najmi ◽  
Alan L. Hill ◽  
Brenton S. McLaury ◽  
Siamack A. Shirazi ◽  
Selen Cremaschi
Keyword(s):  
Experimental Study ◽  
Gas Flow ◽  
Intermittent Flow ◽  
Sand Transport ◽  
Physical Parameters ◽  
Internal Diameter ◽  
Flow Rates ◽  
Minimum Flow ◽  
Wide Range ◽  
Sand Size

The ultimate goal of this work is to determine the minimum flow rates necessary for effective transport of sand in a pipeline carrying multiphase flow. In order to achieve this goal, an experimental study is performed in a horizontal pipeline using water and air as carrier fluids. In this study, successful transport of sand is defined as the minimum flow rates of water and air at which all sand grains continue to move along in the pipe. The obtained data cover a wide range of liquid and gas flow rates including stratified and intermittent flow regimes. The effect of physical parameters such as sand size, sand shape, and sand concentration is experimentally investigated in 0.05 and 0.1 m internal diameter pipes. The comparisons of the obtained data with previous studies show good agreement. It is concluded that the minimum flow rates required to continuously move the sand increases with increasing sand size in the range examined and particle shape does not significantly affect sand transport. Additionally, the data show the minimum required flow rates increase by increasing sand concentration for the low concentrations considered, and this effect should be taken into account in the modeling of multiphase sand transport.

Techniques for Controlling Airflow Distribution in Raised-Floor Data Centers

2003 ◽  
Author(s):  
Kailash C. Karki ◽  
Suhas V. Patankar ◽  
Amir Radmehr
Keyword(s):  
Mathematical Model ◽  
Data Center ◽  
Heat Load ◽  
Data Centers ◽  
Open Area ◽  
Flow Rates ◽  
Airflow Distribution ◽  
Wide Range ◽  
Optimum Utilization ◽  
Load Pattern

In raised-floor data centers, the airflow rates through the perforated tiles must meet the cooling requirements of the computer servers placed next to the tiles. The data centers house a wide range of equipment, and the heat load pattern on the floor can be quite arbitrary and changes as the data center evolves. To achieve optimum utilization of the floor space and the flexibility for rearrangement and retrofitting, the designers and managers of data centers must be able to modify the airflow rates through the perforated tiles. The airflow rates through the perforated tiles are governed primarily by the pressure distribution under the raised floor. Thus, the key to modifying the flow rates is to influence the flow field in the plenum. This paper discusses a number of techniques that can be used for controlling airflow distribution. These techniques involve changing the plenum height and open area of perforated tiles, and installing thin (solid and perforated) partitions in the plenum. A number of case studies, using a mathematical model, are presented to demonstrate the effectiveness of these techniques.

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