Overall solute-transfer coefficient

We wiU now employ a lumped model of a countercurrent dialyzer to illustrate its performance in the context of hemodialysis (Figures 8.1.46(a) and (b)). We will use a device-averaged overall solute-transfer coefficient Ktc instead of employing a z-coordinate dependent analysis of the type illustrated in (8.1.46) for countercurrent phase equilibrium based devices. In Figure 8.1.46(a), a feed solution having a molar solute... 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Solution The experimental conditions are consistent with Equation (11.26) so that kiAi was measured. The experimental result was reported as KgAi because the overall mass transfer coefficient was based on the equivalent gas-phase driving force expressed in partial pressure units rather than concentration units. Because a pure gas was sparged, kg oo and Kj = k . Equation (11.3) relates Kg and Ki through Henry s law constant. 

The desired product is P, while S is an unwanted by-product. The reaction is carried out in a solution for which the physical properties are independent of temperature and composition. Both reactions are of first-order kinetics with the parameters given in Table 5.3-2 the specific heat of the reaction mixture, c, is 4 kJ kg K , and the density, p, is 1000 kg m . The initial concentration of /I is cao = 1 mol litre and the initial temperature is To = 295 K. The coolant temperature is 345 K for the first period of 1 h, and then it is decreased to 295 K for the subsequent period of 0.5 h. Figs. 5.3-13 and 5.3-14 show temperature and conversion curves for the 63 and 6,300 litres batch reactors, which are typical sizes of pilot and full-scale plants. The overall heat-transfer coefficient was assumed to be 500 W m K. The two reactors behaved very different. The yield of P in a large-scale reactor is significantly lower than that in a pilot scale 1.2 mol % and 38.5 mol %, respectively. Because conversions were commensurate in both reactors, the selectivity of the process in the large reactor was also much lower. 

In the above equalitms, Kl is the overall mass transfer coefficient (based on phase L), a is the specific interfacial area for mass transfer related to unit column volume, X and Y are the phase solute concentrations, X is the... 

A single-effect evaporator is used to concentrate 7 kg/s of a solution from 10 to 50 per cent of solids. Steam is available at 205 kN/m2 and evaporation takes place at 13.5 kN/m2. If the overall heat transfer coefficient is 3 kW/m2 K, calculate the heating surface required and the amount of steam used if the feed to the evaporator is at 294 K and the condensate leaves the heating space at 352.7 K. The specific heat capacity of a 10 per cent solution is 3.76 kJ/kgK, the specific heat capacity of a 50 per cent solution is 3.14 kJ/kgK. 

A single-effect evaporator is used to concentrate 0.075 kg/s of a 10 per cent caustic soda liquor to 30 per cent. The unit employs forced circulation in which the liquor is pumped through the vertical tubes of the calandria which are 32 mmo.d. by 28 mmi.d. and 1.2 m long. Steam is supplied at 394 K, dry and saturated, and the boiling-point rise of the 30 per cent solution is 15 degK. If the overall heat transfer coefficient is 1.75 kW/m2 K, how many tubes should be used, and what material of construction would be specified for the evaporator The latent heat of vaporisation under these conditions is 2270 kJ/kg. 

Equation (9.15) was written for macro-pore diffusion. Recognize that the diffusion of sorbates in the zeoHte crystals has a similar or even identical form. The substitution of an appropriate diffusion model can be made at either the macropore, the micro-pore or at both scales. The analytical solutions that can be derived can become so complex that they yield Httle understanding of the underlying phenomena. In a seminal work that sought to bridge the gap between tractabUity and clarity, the work of Haynes and Sarma [10] stands out They took the approach of formulating the equations of continuity for the column, the macro-pores of the sorbent and the specific sorption sites in the sorbent. Each formulation was a pde with its appropriate initial and boundary conditions. They used the method of moments to derive the contributions of the three distinct mass transfer mechanisms to the overall mass transfer coefficient. The method of moments employs the solutions to all relevant pde s by use of a Laplace transform. While the solutions in Laplace domain are actually easy to obtain, those same solutions cannot be readily inverted to obtain a complete description of the system. The moments of the solutions in the Laplace domain can however be derived with relative ease. 

Combination of Equations 1 and 2 allows calculation of the rate of heat transfer from the growing crystal surface to the bulk solution. Under heat balance conditions, this rate of heat generation must be balanced by the amount of heat removed from the crystallizer by convection and conduction. This will be determined by the overall heat transfer coefficient, U, between the bulk solution and the refrigerant including convective resistances between the fluid and both sides of the crystallizer wall (refrigerant side and product side) as well as the conductive resistance across the crystallizer wall. 

In this case, the material balance in the liquid phase (3.238) is not applicable as both reactants are gases. Furthermore, as in sluny bubble columns, if the liquid is batch, the overall rate based on the bulk gas-phase concentration is used and the overall mass-transfer coefficient K° is found in the solution of the model (Chapter 5). 

A buffer solution containing urea flows along one side of a flat membrane and the same buffer solution without urea flows along the other side of the membrane, at an equal flow rate. At different flow rates the overall mass transfer coefficients were obtained as shown in Table P8.1. When the liquid film mass transfer coefficients of both sides increase by one-third power ofthe averaged flow rate, estimate the diffusive membrane permeability. 

Use of HTU and K a Data In estimating the size of a commercial gas absorber or liquid stripper it is desirable to have data on the overall mass-transfer coefficients (or heights of transfer units) for the system of interest, and at the desired conditions of temperature, pressure, solute concentration, and fluid velocities. Such data should best be obtained in an apparatus of pilot-plant or semiworks size to avoid the abnormalities of scale-up. Within the packing category, there are both random and ordered (structured) packing elements. Physical characteristics of these devices will be described later. 

A reaction A—>P is to be performed in a semi-batch reactor. The reaction follows first-order kinetics, and carried out as a batch reaction at 50 °C, the conversion reaching 99% in 60 seconds. The final volume is 5 m3 in a reactor with a heat exchange area of 15 m2 (assumed to remain constant) and an overall heat transfer coefficient of 500 Wm 2 K 1. The compound A is fed as a concentrate solution to a reactor containing an inert solvent The maximum temperature difference with the cooling system is 50 K. 

In another study of gas-side mass transfer-limited absorption involving S02 absorption into a sodium hydroxide solution using a wire screen packing, the overall mass transfer coefficient was found to be lower than reported data for packed towers (16). Replacing the wire screen packing with two parallel rotating plates significantly enhanced the mass transfer performance. 

Solution To determine the heat transfer area, the overall heat transfer coefficient given in the following needs to be calculated first from Eq. (12.1). Radiative heat transfer would be low for the temperature of 350 K and, thus, it is neglected. 

Mass transfer coefficients Boltzman s constant Overall mass transfer coefficient Length or thickness Total solute mass in pulse Total flux of species 1 ... 

The model I is very simple, and it is not very sensitive to the physical properties of the bed, but the values of the overall mass transfer coefficients optimised are strongly dependent from the equilibrium relation assumed and it only is able to describe the initial part of the extraction. Ke was determined by mass balance assuming a uniform distribution in solid bed. Ke values of 0.5, 0.2, and 0.6 were obtained for 7, 10 and 15 MPa. Assuming a = 3000 nAn", the mass transfer coefficients calculated with model I are of some orders of magnitude lower than those for external mass transfer coefficients. This type of models have being applied with success to the extraction of edible oils from seeds were the solute is in a... 

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