Vapor Rate Method

A convenient method for determining the molar vapor rate in an ordinary distillation col umn separating a nearly ideal system uses the Underwood equations to calculate the mini mum reflux ratio, This is readily accomplished, as in the example below, with a proces simulation program. The design reflux ratio is taken as / = 1.2 By material balance, th 

Separation Column Top Pressure (kPa) Distillate Rate, D (kmol/hr) Reflux Ratio (/ = 1.2 Vapor Rate, V=D(R+ 1) (kmol/hr) Margiiial Vapor Rate (kmol/hr) 

Distillation with Vapor Side Stream Rectifier 

Distillation with Liquid Side Stream Stripper 

Despite its lower vapor boilup requirements, no industrial installations of a two-column Petlyuk system have been reported. Two possible reasons for this, as noted by Agrawal and Fidkowski (1998), are (1) an unfavorable thermodynamic efficiency when the three feed 

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Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

Example 3 Calculation of TG Method The TG method will he demonstrated hy using the same example problem that was used above for the approximate methods. The example column was analyzed previously and found to have C -I- 2N + 9 design variables. The specifications to be used in this example were also hstedat that time and included the total number of stages (N = 10), the feed-plate location (M = 5), the reflux temperature (corresponding to saturated liquid), the distillate rate (D = 48.9), and the top vapor rate (V = 175). As before, the pressure is uniform at 827 kPa (120 psia), but a pressure gradient could be easily handled if desired. 

Musculus and Meyer (12) measured the diffusion rates of some starches and dextrins in 1881. The work was designed to determine the relationship of these "isomeric or polymeric" forms to the simple sugars from which they were formed. They concluded that dextrin molecules must be much larger than those of the sugars. This work, however, preceeded Raoult s (13) development of the cryoscopic technique for the determination of the molecular weights of dissolved substances, and van t Hoff s (14) formulation of the solution laws. Further, since the vapor density method was obviously inapplicable, it was not possible for them to actually determine the degree of polymerization. 

Produce a shortlist of candidates by ranking the alternatives following the total vapor rate. A minimum reflux calculation design based on Fenske-Underwood-Gilliland method should be sufficiently accurate. 

Set initial stage temperatures, Tfs, and vapor rates, V - s. Initial liquid rates are found using the tridiagonal method for the total material balances. The theta method requires the distillate rate, sidestream product rates, and reflux ratio to be specified. 

Based on the most recent set of temperatures and total flow rates, calculate the component vapor rates using the tridiagonal matrix method. Find the component liquid rates by l j = Ay i>y,... 

Calculate the total liquid rates from the constant composition method, using the most recent set of compositions and temperatures. Total vapor rates are found from the material balance for each stage. 

Set initial temperatures and total vapor and liquid rates for each stage. Calculate initial component vapor rates using the tridiagonal matrix method and find the component liquid rates by applying the absorption factor, Zy = i y. 

Christiansen et al. (54) applied the Naphtali-Sandholm method to natural gas mixtures. They replaced the equilibrium relationships and component vapor rates with the bubble-point equation and total liquid rate to get practically half the number of functions and variables [to iV(C + 2)]. By exclusively using the Soave-Redlich-Kwong equation of state, they were able to use analytical derivatives of revalues and enthalpies with respect to composition and temperature. To improve stability in the calculation, they limited the changes in the independent variables between trials to where each change did not exceed a preset maximum. There is a Naphtali-Sandholm method in the FraChem program of OLI Systems, Florham Park, New Jersey CHEMCAD of Coade Inc, of Houston, Texas PRO/II of Simulation Sciences of Fullerton, California and Distil-R of TECS Software, Houston, Texas. Variations of the Naphtali-Sandholm method are used in other methods such as the homotopy methods (Sec. 4,2.12) and the nonequilibrium methods (Sec. 4.2.13). 

The Gold stein-Stanfield (45) method. This method chooses the stage temperatures, total vapor rates, total liquid rates, and liquid compo-... 

Russell organizes the tridiagonal matrix method to calculate the component liquid rates instead of the vapor rates (as in Sec. 4.2.3) but either can be used. The component vapor rates are found by = Sy l . The total flow rates are found by summing the component flow rates ... 

The success of relaxation is dependent on a choice of the step size, it. The method can fail if too large a step is chosen or be very slow if too small a step is chosen. Since computers are getting faster, a small step size, unless excessive, Bhould not be a great problem. Mori et al. (62) used the inverse of an internal vapor rate, such as the reboiler boilup, Vj/, as a step size in order to take into account both feed rate and reflux rate. 

Independent variable used as a multiplier on the ratio of total liquid rate to total vapor rate in the 2JV Newton-Raphson method, defined by Eq. (4.76). 

Table 13-6 shows subsequent calculations using the Underwood minimum reflux equations. The a and Xo values in Table 13-6 are those from the Fenske total reflux calculation. As noted earlier, the % values should be those at minimum reflux. This inconsistency may reduce the accuracy of the Underwood method but to be useful, a shortcut method must be fast, and it has not been shown that a more rigorous estimation of x values results in an overall improvement in accuracy. The calculated firnin is 0.9426. The actual reflux assumed is obtained from the specified maximum top vapor rate of 0.022 kg- mol/s [ 175 lb-(mol/h)] and the calculated D of 49.2 (from the Fenske equation). 

Photoreceptors are prepared by the sequential application of the various layers onto a web or drum substrate. Vapor-deposition methods can be used for some pigments. Most layers, however, are coated from solution or dispersions in organic solvents. Wicks (1986) has reviewed film formation from polymer solutions. The choice of solvent is determined by such factors as solubility, evaporation rates, surface tension, toxicity, as well as environmental... 

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