Volume and residence time

Filter cake resistance (Rq) is the resistance to filtrate flow per unit area of filtration. R increases with increasing cake thickness during filtration. At any instant, Rc depends on the mass of solids deposited on the filter plate as a result of the passage of V (m ) filtrate. Rf may be assumed a constant. To determine the relationship between volume and residence time t. Equation 5 must be integrated, which means that Rc must be expressed in terms of V. 

Pyle DM (1992) The volume and residence time of magma beneath active volcanoes determined by decay-series disequilibria methods. Earth Planet Sci Lett 112 61-73 Pyle DM, Dawson JB, Ivanovich M (1991) Short-lived decay series disequilibria in the natrocarbonatite lavas of Oldoinyo Lengai, Tanzania Constraints on the timing of magma genesis. Earth Planet Sci Lett 105 378-396... 

The minimum volume and residence time required for the reactor. 

Partitioning into overlying partial melts. The ultra-low velocity zone at the coremantle boundary may reflect the presence of mantle melt (see Garnero 2000 Ohtani and Maeda 2001), and partitioning from the core back into the overlying mantle may occur if conditions are favorable. However, a flux cannot be easily calculated without constraints on partition coefficients and the volume and residence time of melts at the core-mantle boundary. 

The flow rate of either fluid affects the slope of i (T) via equation (5-18) or (5-19), but not Grx(T) if the CSTR volume and residence time remain constant. Since the reactive fluid flow rate <7rx cannot be changed without affecting either the CSTR volume or residence time. Figure 5-4 illustrates how the cooling fluid flow rate cooi affects the steady-state operating points when all of the... 

Microbial growth rates are substantially lower than chemical reaction rates so that relatively large reactor volumes and residence times are required. 

The length of the reduction section of the reactor is at least twice the length of the oxidation section but is of reduced diameter. The relative slag volumes and residence times are the critical parameters and are determined by the relative amounts of sulfides and oxide lead materials in the feed mix, particularly the amount of lead to be reduced. The lead pool maintained in the reduction zone is minimal and merely provides a channel for the lead to flow back to the oxidation section. 

Manufacture and Processing. The largest volume of coal is carbonized in batch coke ovens to produce a hard coke suitable for blast furnaces for the reduction of iron ore. Oven temperatures, as measured in the flues, are between 1250 and 1350° and residence time varies between 17 and 30 h. The gas made in this process is mainly used as fuel and other appHcations in the steel works (see Fuels, synthetic). 

Design nd Operation. The destruction efficiency of a catalytic oxidation system is determined by the system design. It is impossible to predict a priori the temperature and residence time needed to obtain a given level of conversion of a mixture in a catalytic oxidation system. Control efficiency is determined by process characteristics such as concentration of VOCs emitted, flow rate, process fluctuations that may occur in flow rate, temperature, concentrations of other materials in the process stream, and the governing permit regulation, such as the mass-emission limit. Design and operational characteristics that can affect the destmction efficiency include inlet temperature to the catalyst bed, volume of catalyst, and quantity and type of noble metal or metal oxide used. 

Whereas changing catalyst volume or residence time rarely yields compHcations, changing temperature or pressure could iatroduce sintering. The properties of the catalyst should be measured both before and after deactivation and inlet and outlet streams should be analyzed by chromatography (qv) or spectrometry. 

The novel provision of side feeds promotes mixing between feed and crystallizing streams and increases solute concentration. This not only eliminates the need for equal volume (or residence time) of each crystallizer in the network but may also reduce the energy requirements for cooling the suspension. The magnitude of such reductions will depend, however, on the exact mixing profiles between the crystallizers. 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

Kharkar DP, Thomson J, Turekian KK, Forster WO (1976) Uranium and thorium series nuclides in plankton from the Caribbean. Limnol Oceanogr 21 294-299 Krishnaswami S, Lai D, Somayajulu BLK, Weiss R, Craig H (1976) Large-volume in situ filtration of deep Pacific waters mineralogical and radioisotope studies. Earth Planet Sci Lett 32 420-429 Livingston HD, Cochran JK (1987) Determination of transuranic and thorium isotopes in ocean water in solution and in filterable particles. J Radioanal Nucl Chem 115 299-308 Masque P, Sanchez-Cabeza JA, Braach JM, Palacios E, Canals M (2002) Balance and residence times of °Pb and 4 o in surface waters of the northwestern Mediterranean Sea. Cont Shelf Res 22 2127-2146 Matsumoto E (1975) Th-234-U-238 radioactive disequilibrium in the surface layer of the oceans. Geochim Cosmochim Acta 39 205-212... 

Multiphase catalytic reactions, such as catalytic hydrogenations and oxidations are important in academic research laboratories and chemical and pharmaceutical industries alike. The reaction times are often long because of poor mixing and interactions between the different phases. The use of gaseous reagents itself may cause various additional problems (see above). As mentioned previously, continuous-flow microreactors ensure higher reaction rates due to an increased surface-to-volume ratio and allow for the careful control of temperature and residence time. 

APV, whose Paraflow plate heat exchanger is illustrated in Volume 1, Chapter 9, supply climbing and falling-film plate evaporators with evaporative capacities up to 10 kg/s. Such units offer the advantages of short contact and residence times and low liquor hold-up, and hence are widely used for the concentration of heat-sensitive materials. 

Figure 7. Representation of the parameter problem in plasma processes. The symbols n, /(e), TV, and r are electron density, electron energy distribution, gas density, and residence time for molecules in the plasma volume, respectively. (Reproduced with permission from Ref. 32.)...

The freezing time must now be equal to the residence time in the bed (see Mixing, dispersion and residence time, below) a mean residence time can be assumed to be equal to the mass hold-up in the bed divided by the mass flow rate. If the mass hold-up is the product of bed volume and the bulk density of the bed, and the bed depth is H, then... 

Figure 15. Predicted accumulated carbon loss distribution along anode flow-field over a complete start-stop cycle for a controlled start-stop experiment as shown above the plot at 80 °C, 101 kPaabs, 66% RHjn, and residence time of 1.5 s based on anode void volume (including flow-field and diffusion medium). The model predicts nearly symmetric carbon loss at anode inlet and outlet because the stop process essentially mirrors the start process by switching H2 and air periodically at anode inlet.

---