Design chart volumes

Figure 10-114. Design chart for liquid volume fraction using parameter defined in equation 10-168. (Used by permission Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. Gulf Publishing Company. All rights reserved.)...

General design charts can be drawn which display the relationships between the Damkohler number, rkC/, the number of tanks in series, N, the achieved fractional conversion, and the total volume of the N... 

Fig. 12. General design chart for the tanks-in-series model described by eqn. (43), first-order reaction A -r r with no change in volume (e = 0). Ordinate gives the total volume of all the tanks in series divided by the volume of an ideal PFR which achieves the same conversion.-------, Constant kr -------, constant N.

For a product recovery of 96 percent, optimum solutions were obtained and are presented graphically via design charts. The design charts plot the optimum diafiltration volume and total time cycle as a function of other operating conditions, i.e., initial volume, recovery, membrane area and flux. For a recovery other than 96 percent, the optimum solution can be obtained using the equations developed in this paper in a similar manner. 

A description of the data required for proper preparation of the design charts follows. It is felt that these are minimum requirements for the preparation of reliable charts. The use of so-called typical stress-strain curves based on a statistically significant volume of data may be satisfactory if the region between the proportional limit and the yield strength is accurately represented. The development of the tangent modulus in this region is a critical step. It is suggested that this description be prepared in a form suitable for attachment to any requests for material data from an inquirer. 

Breakeven charts can be plotted in any of the three forms shown in Figs. 9-2, 9-3, and 9-4. The abscissa shown as annual sales volume R is also frequently plotted as a percentage of the designed production or sales capacity Rq. In the case of ships, aircraft, etc., it is then called the percentage utilization. The percentage margin of safety is defined as... 

Under steady conditions the plant should be able to hold the design room rh up to the temperature given in psychrometric tables or a chart where the design room rh and test absolute moisture content (kg/kg) coincide. At the end of the test restore the temperature set point to the design value and any control of outside air volume to automatic. Observe that operation. 

The two most common designs of break-even charts are shown in Figures 61.9 and 61.10. In both cases the y (vertical) axis is used for sales (output) and costs while the X (horizontal) axis is used for volumes, capacity or time. 

The water removed by vaporisation is generally carried away by air or hot gases, and the ability of these gases to pick up the water is determined by their temperature and humidity. In designing dryers using air, the properties of the air-water system are essential, and these are detailed in Volume 1, Chapter 13, where the development of the humidity chart is described. For the air-water system, the following definitions are of importance ... 

CSTRs in series. The latter is often normalised by dividing by the volume of an ideal PFR required to perform the same duty. Different charts are required for each reaction rate expression. Figure 12 refers specifically to first-order kinetics, but other charts are available in, for instance refs. 17, 18 and 26. Figure 12 re-emphasises many of the points we have made already. In particular, the performance of the N CSTRs in series tends to that of a PFR of the same total volume as N becomes large and the PFR volume required to achieve a certain conversion for a first-order reaction is always smaller than the total volume of any array of CSTRs which perform the same duty. Charts in the form of Fig. 12 are particularly useful when performing approximate design calculations. 

A gSe of two Waters ultrastyragel columns, designated 10 A and 10 A and a Waters pump (Model 590) for HPLC were used in this study. The elution solvent was tetrahydrofuran (THE) which was distilled in the presence of a small amount of CaH in order to remove the peroxide. The flow rate was maintained at 1 ml/min. The sample injection volume was -30 pi. The chromatogram detected by the differential refractometer (Waters R401) was recorded on a strip chart recorder. All experiments were performed at room temperatures with concentrations below the over-loading condition. 

In this paper, complete mathematical formulations for correlating the time cycles with other operating conditions are presented. The optimum diafiltration cycle (in terms of volume fraction), and the total cycle time are solved as functions of membrane area, flux, initial volume and recovery. Convenient charts, which can be used as a guide in designing or modifying an ultrafiltration process, are provided. 

---