Space time

The space time tau, t, is obtained by dividing the reactor volume by the volumetric flow rate entering the reactor  

The space time is the time necessary to process one reactor volume of fluid based on entrance conditions. For example, consider the tubular reactor 

For example, if the reactor volume is 0.2 and the inlet volumetric flow rate is 0.01 mVs, it would take the upstream equivalent reactor volume (V = 0.2 m ) shown by the da.shed lines a lime t equal to 

In the absence of plug flow, the space time is equal to the mean residence time in the reactor, (see Chapter 13 from the fourth edition of Elements of Chemical Reaction Engineering now on the DVD-ROM). TTiis time is the average time the molecules spend in the reactor. A range of typical processing times in terms of the space time (residence time) for industrial reactors is shown in Table 2-4. 

e 2-4 Typical Space Time for L tIlTs RlAL Reactors  

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We now evaluate the spectrum of interfacial fluctuations It is the space-time Fourier transfonn of the... 

In this brief review of dynamics in condensed phases, we have considered dense systems in various situations. First, we considered systems in equilibrium and gave an overview of how the space-time correlations, arising from the themial fluctuations of slowly varying physical variables like density, can be computed and experimentally probed. We also considered capillary waves in an inliomogeneous system with a planar interface for two cases an equilibrium system and a NESS system under a small temperature gradient. 

Figure A3.14.16. Spatiotemporal complexity in a Couette reactor space-time plots showing the variation of...

One of us, ACA, also wishes to thank Dr David King for his provision of space, time, and a fine scientific atmosphere during a two month sabbatical leave at Imperial College, which aimed out to involve considerable work on tliis... 

Fadley C S et al 1997 Photoelectron diffraction space, time and spin dependence of surface structures Surf. Rev. Left 4 421-40... 

Figure C3.6.14 Space-time (y,t) plot of the minima (black) in the cubic autocatalysis front ( )(y,t) in equation C3.6.16 showing the nature of the spatio-temporal chaos.

H. Weyl, Space, Time, Matter, Dover Books, New York, 1950 The Theory of Groups and Quantum Mechanics, Dover Books, New York, 1950. 

Extension of the streamline Petrov -Galerkin method to transient heat transport problems by a space-time least-squares procedure is reported by Nguen and Reynen (1984). The close relationship between SUPG and the least-squares finite element discretizations is discussed in Chapter 4. An analogous transient upwinding scheme, based on the previously described 0 time-stepping technique, can also be developed (Zienkiewicz and Taylor, 1994). 

Nguen, N. and Reynen, J., 1984. A space-time least-squares finite element scheme for advection-diffusion equations. Cornput. Methods Appl Mech. Eng. 42, 331- 342. 

All of our orbitals have disappeared. How do we escape this terrible dilemma We insist that no two elections may have the same wave function. In the case of elections in spatially different orbitals, say. Is and 2s orbitals, there is no problem, but for the two elechons in the 1 s orbital of the helium atom, the space orbital is the same for both. Here we must recognize an extr a dimension of relativistic space-time... 

By-products include propylene dibromide, bis-(bromopropyl) ether, propylene glycol, and propionic acid. Bromide losses are to the brominated organics and bromate formation. Current efficiency is a function of ceU design and losses to bromate. Energy consumption decreases with an increase in electrolyte concentration and a decrease in current density. Space—time yield increases with current density. See Table 5 for performance data (see... 

Reactor Current efficiency, % Current density, A/m Space—time yield, kmol/(h-m") Eneigy, kWh /kg Reference... 

These design fundamentals result in the requirement that space velocity, effective space—time, fraction of bubble gas exchanged with the emulsion gas, bubble residence time, bed expansion relative to settled bed height, and length-to-diameter ratio be held constant. Effective space—time, the product of bubble residence time and fraction of bubble gas exchanged, accounts for the reduction in gas residence time because of the rapid ascent of bubbles, and thereby for the lower conversions compared with a fixed bed with equal gas flow rates and catalyst weights. 

Flux density is calculated as the permeability of free space times the sum of the magnetic-field intensity and the induced magnetization... 

To achieve complete combustion (i.e., the combination of the combustible elements and compounds of a fuel with all the oxygen that they can utilize), sufficient space, time, and turbulence and a temperature high enough to ignite the constituents must be provided. 

A numerical value is obtainable by integrating the trend curve for the flow received from the Flow Recorder (FR), from the start of the reaction to a time selected. Doing this from zero to each of 20 equally spaced times gives the conversion of the solid soda. Correlating the rates with the calculated X s, a mathematical model for the dependence of rate on X can be developed. 

Space time and space velocity are used to determine the performance of flow reactors. Space velocity, SV, is defined as F /VC Q dial is. 

Space time, ST, is defined as the time required to process one reactor volume of feed measure at specified conditions. The relationship between space velocity SV and ST is as follows ... 

Space time ST is equal to the residence time in a plug flow reactor only if the volumetric flowrate remains constant throughout the reactor. The residence time depends on the change in the flowrate through the reactor, as well as V/u. The change in u depends on the variation in temperature, pressure, and the number of moles. The concept of SV with conversions in the design of a plug flow reactor is discussed later in this chapter. 

Using Equation 8-154 for the same reactor space time and volume gives... 

Most hydrogenations can be achieved satisfactorily near ambient temperature, but in industrial practice the temperature is usually elevated to obtain more economical use of the catalyst and increase the space-time yield of the equipment. Tn laboratory work, a convenient procedure is to begin at ambient temperature, if reasonable, and raise the temperature gradually within bounds, should the reaction fail to go or if it is proceeding too slowly. 

Determination of the actual cost of a hydrogenation process is difficult. Among the factors entering into the determination are catalyst cost, catalyst life, cost of materials, capital investment, actual yield, space-time yield, and purification costs, Considerable data are needed to make an accurate evaluation. 

Space time yield refers to the quantity of product that can be produced in a reactor in a given time. It is a function of both selectivity and activity. Maximum efficiency is reached when this number is high, but if production schedules are not full, lower numbers may be tolerated. Acceptable catalyst life can be extended if space-time yield demands are not heavy. Catalyst cost thus becomes a function of the demands put upon it. 

Platinum and rhodium sulfided catalysts are very effective for reductive alkylation. They are more resistant to poisoning than are nonsulfided catalysts, have little tendency to reduce the carbonyl to an alcohol, and are effective for avoidance of dehydrohalogenation in reductive alkylation of chloronitroaromatics and chloroanilines (14,15). Sulfided catalysts are very much less active than nonsulfided and require, for economical use, elevated temperatures and pressures (300-2(KX) psig, 50-l80 C). Most industrial reductive alkylations, regardless of catalyst, are used at elevated temperatures and pressures to maximize space-time yields and for most economical use of catalysts. 

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