Sizes of Mass Exchangers

In order to determine the size of a multiple-stage mass exchanger, let us consider the isothermal mass exchanger shown in Fig. 2.3. The rich (waste) stream, i. 

One way of calculating the number of equilibrium stages (or number of theoretical plates, NTP) for a mass exchanger is the graphical McCabe-Thiele method. To illustrate this procedure, let us assume that over the operating range of compositions, the equilibrium relation governing the transfer of the pollutant from the 

On a y-x (McCabe-Thiele) diagram, this equation represents the operating line which extends between the points (y , x ) and (yf , x ) and has a slope of Lj/Gi, as shown in Fig. 2.5. Furthermore, each theoretical stage can be represented by a step between the operating line and the equilibrium line. Hence, NTP can be determined by stepping off stages between the two ends of the exchanger, as illustrated by Fig. 2.5. 

Alternatively, for the case of isothermal, dilute mass exchange with linear equilibrium, NTP can be determined through the Kremser (1930) equation  

If contact time is not enough for each stage to reach equilibrium, one may calculate the number of actual plates NAP by incorporating contacting efficiency. Two principal types of efficiency may be employed overall and stage. The overall exchanger efficiency, rj , can be used to relate NAP tind NTP as follows 

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Minimum number of mass exchanger units. Combinatorics determines the minimum number of mass exchanger units required in the network. This objective attempts to minimize indirectly the fixed cost of the network, since the cost of each mass exchanger is usually a concave function of the unit size. FuithetTnore, in a practical context it is desirable to minimize the number of separators so as to reduce pipework, foundations, maintenance, and instrumentation. Normally, the minimum number of units is related to the total number of streams by the following expression (El-Halwagi and Manousiouthakis, 1989). 

As will be explained later, the first two factors influence mainly the size of extractors and separators, while mass-transfer determines the CO2 circulation system, and consequently the energy consumption and the size of heat exchangers and the piping system. 

However, researchers later found (Boyd et al., 1947) that the rate of ion exchange increased with decreasing particle size of the exchanger. This showed that mass-transfer phenomena and not chemical reaction were rate-controlling. 

Finally, Table 3.2.1 contains two economic relations or rules-of-thumb. Equation 3.2.20 states that the approach temperature differences for the water, which is the difference between the exit water teir jerature and the wet-bulb temperature of the inlet air, is 5.0 "C (9 °F). The wet-bulb temperature of the surrounding air is the lowest water temperature achievable by evaporation. Usually, the approach temperature difference is between 4.0 and 8.0 C. The smaller the approach temperature difference, the larger the cooling tower, and hence the more it will cost. This increased tower cost must be balanced against the economic benefits of colder water. These are a reduction in the water flow rate for process cooling and in the size of heat exchangers for the plant because of an increase in the log-mean-temperature driving force. The other mle-of-thumb. Equation 3.2.21, states that the optimum mass ratio of the water-to-air flow rates is usually between 0.75 to 1.5 for mechanical-draft towers [14]. 

A material balance is always required to determine the size of mass transfer apparatus, irrespective of the design. So as the energy balance links the temperatures of the fluid flows in a heat exchanger, the mass balance delivers the concentrations of the fluids. 

For values hq = 2 10 Pa-s, pi = 650 kg/m, = 100 kg/m and U = 0.2 m/s we have = 56 g. Thus, the radius of drops moving together with the flow in the inter-plate space does not exceed R - The size of these drops can change during motion because of the mass exchange with the gas and the drop coagulation. Each of these processes is characterized by its own time. Thus, the characteristic time of mass exchange is equal to ... 

The motion of formed ensemble of drops with gas flow is accompanied by continuous change of drops distribution over sizes this results from the concurrent processes of mass-exchange between the drops and the gas, coagulation and breakup of drops under action of intensive turbulent pulsations of various scales. 

The most efficient method of inputting hydrate inhibitor into the flow of natural gas in the pipeline is by spraying with the help of atomizers. This results in the formation of a spectrum of drops with distribution (21.3) inside the flow. The average size of the resultant drops is smaller than the stable size that is characteristic of the turbulent flow. During the motion, drops change their size as a result of mass exchange with the gas, and also coagulation and breakup. Besides, drops can be deposited at the pipe wall and then swept away from the surface of the liquid film that forms on the wall. 

Note that in the process of mass exchange, the number concentration of drops N = J n( V, t) dV, is conserved, while the volume concentration and the average size of drops decrease owing to methanol evaporation being more intensive than water vapor condensation. 

Consider the process of differential degassing of a quiescent volume of a multi-component liquid-gas mixture, in which the disperse phase consists of spherical bubbles of equal size. Assume that the volume concentration of bubbles is small and their mutual interaction can be neglected. The problem reduces to the analysis of mass exchange for a unit bubble of initial radius Rq placed in a multi-component solution. Assume that the process is isothermal the pressure above the mixture surface is maintained at a constant value. 

The sizes of heat exchangers, separators and reactors are dictated by the allowable throughputs and the rates of heat and mass transfer and reaction. These are rates may be expressed... 

The analysis of experimental data revealed a correlation between the hydrodynamic mode of a tubular turbulent device and the interphase tension in the flow of the two-phase liquid-gas reaction system (Figure 2.52). This correlation confirms that the addition of surfactants is a reasonable solution for a reaction system with an interphase boundary. It leads to a decrease of bubble size and mass exchange intensification in the gas-liquid flow of fast chemical processes. In addition, the liquid-phase longitudinal mixing rate increases and the hydrodynamic mode of a process approaches perfect mixing conditions. Fast chemical processes, in two-phase systems, require consideration of the selective adsorption of feedstock reactants and reaction products on to the interphase boundary, and a change of the hydrodynamic motion structure of the continuous phase. A change in the work required to form the new surface is a typical phenomenon for all types of multiphase systems and depends on... 

There are two basic approaches to heat-exchanger design (1) the effectiveness-NTU approach and (2) the log-mean-temperature-difference (LMTD) approach. The LMTD approach is used most frequently when all the required mass flows are known and the size of the exchanger is to be determined. The effectiveness-NTU approach is used more often when the inlet temperatures and the flow rates are known in a given exchanger and the outlet temperatures are to be found. Both methods may be used in either case, but the LMTD method often requires an iterative solution for the second situation. 

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