Calculation number of stages

At low reflux ratios the calculated number of stages will be very dependent on the accuracy of the vapour-liquid equilibrium data available. If the data are suspect a higher than normal ratio should be selected to give more confidence in the design. 

The H ETP equation for calculating number of stages in preparative liquid chromatography can then be simplified to... 

RR + 1 RR + 1 Calculate number of stages in rectifying section up to feed line... 

Calculating number of stages in stripping section starting from feed stage M = total number of stages including reboiler... 

Calculating number of stages n stripping section starting from fsed stage... 

Total error for calculated number of stages in the lower part at various iunci reflux ratios v (niethylcyclohexane-toluene)... 

Application of concentration-independent HETP coefficients from the linear isotherm region in calculating the number of stages in a nonlinear region is only a formalism. However, since feed concentration is not varied during the optimization, the calculated number of stages can nevertheless be used further as it is a characteristic value for the specific chromatographic separation. Scale-up of the... 

The Gilliland correlation should only be used for rough estimates. The calculated number of stages can be off by 30% although they are usually within + 7%. Since L/D is usually a multiple of (L/D)j, L/D = M... 

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. 

The main objective for calculating the number of theoretical stages (or mass-transfer units) in the design of a hquid-liquid extraction process is to evaluate the compromise between the size of the equipment, or number of contactors required, and the ratio of extraction solvent to feed flow rates required to achieve the desired transfer of mass from one phase to the other. In any mass-transfer process there can be an infinite number of combinations of flow rates, number of stages, and degrees of solute transfer. The optimum is governed by economic considerations. 

For certain simplified cases it is possible to calculate directly the number of stages required to attain a desired product composition for a given set of feed conditions. For example, if equilibrium is attained in all stages and if the underflow mass rate is constant, both the equilibrium and operating lines on a modified McCabe-Thiele diagram are straight, and it is possible to calculate direc tly the number of ideal stages required to accommodate arw rational set of terminal flows and compositions (McCabe, Smith, and Harriott, op. cit.) ... 

If the pressure coefficient is now, or was in an earlier step, 5% uiutei the 0.29 value, calculate a new mean blade velocity using the rounded off number of stages and the original pressure coefficient, 0.29. Use the calculated blade velocity in the subsequent step for compressor speed Calculate the speed. 

Step 3. To calculate the number of stages, the overall head is required. The head is calculated using Equation 2.70 and tp = 60/23 = 2.61 for the pressure ratio. 

The following procedure can now be used to calculate the number of stages of compression and the horsepower of the unit ... 

First, calculate the overall compression ratio (R = Pa/Pj). If the compressor ratio is under 5, consider using one stage. If it is not, select an initial number of stages so that R < 5. For initial calculations it can be assumed that ratio per stage is equal for each stage. 

This is exactly the number of stages obtained by tray-to-tray calculations with the K correlation of Winn [236]. The... 

The results of the computer calculation are as summarized by copies of the printouts. Note that Stage one is the product from an overhead condenser and is hquid, as is the bottoms or reboiler outlet product. The results show that the initial criteria have been met for recovery of component 5 however, this does not reflect any optimization of reflux or final number of stages (theoretical trays) that might be required to accomplish the separation in a final design. 

An average value is about 0.55 for the coefficient, p. Peripheral velocities will usually vary between 600-900 ft/sec however, this varies with the gas being compressed and may run up to 1,100 ft/sec. The results of this head calculation will give values of 8,000-12,000 ft for a single stage. From this value, the total number of stages in the compressor can be approximated. 

Approximate number of stages = Hp calculated in (5) divide by H/stage calculated previously = No. stages... 

The precise location of the feed point will affect the number of stages required for a specified separation and the subsequent operation of the column. As a general rule, the feed should enter the column at the point that gives the best match between the feed composition (vapour and liquid if two phases) and the vapour and liquid streams in the column. In practice, it is wise to provide two or three feed-point nozzles located round the predicted feed point to allow for uncertainties in the design calculations and data, and possible changes in the feed composition after start-up. 

Even when the latent heats are substantially different the error introduced by assuming equimolar overflow to calculate the number of stages is usually small, and acceptable. 

If the operating and equilibrium lines are straight, and they usually can be taken as such when the concentrations are small, the number of stages required can be calculated using the equations given by Robinson and Gilliland (1950). 

Which components are the key components will normally be clear, but sometimes, particularly if close boiling isomers are present, judgement must be used in their selection. If any uncertainty exists, trial calculations should be made using different components as the keys to determine the pair that requires the largest number of stages for separation (the worst case). The Fenske equation can be used for these calculations see Section 11.7.3. 

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

---