Design, calculation

The design of a compressor begins with the First Law of Thermodynamics, the conservation of energy. The work required to compressed the gas is calculated as follows  

The subscript i refers to the inlet conditions and the o refers to the outlet. 

It is typical to assume in the design stage that the compressor is adiabatic (Q = 0). In reality what is assumed is that the heat transfer rate is small in comparison to the other terms in the equation. Therefore equation (6.1) reduces to  

As with many equations in thermodynamics, what at first glance appears to be a simple equation is in practice quite difficult. How does one calculate the enthalpies And what are the conditions at the exit stage in order to calculate the enthalpy once a model has been selected to do so  

The best that a compressor can operate at is isentropically. That is the entropy of the stream remains unchanged upon compression. The entropy of the stream entering is equal to the stream exiting. 

There are many fiictors to be comadered in the design of a deq -bed cility, the initial design may be based on some preliminary testwoik v hich needs to establish the efhdency of filtration of the medium ie. the filtration constant X and uses a knovdedge ofthe physical properties of the medium. 

The medium particle size must be chosen so that the settling velocity of the conq)onents is in the order anthracite, sand, garnet. Particle diametms of 1500, 750 and 550 jm respectively satisfy this requirement. The corresponding settling velocities are 0.083, 0.11 and 0.12 m s using the above correlation. Filtration tests onflie medium at these sizes reveal the following values of the filtration constants 0.5, 4 and 6 re ectively. Equation (6.3) can th be used with selected bed depths to provide an acceptable solution, one solution would be  

The hydraulic loading will be between 8-16 m mT h , see Table 6.2, if a 1 m bed area is chosen the maximum head loss will be given by a flow of 16 m m h Equation (6.7) can be used to calculate the head loss given that the bed porosity will be approximately 50% and the specific surfrce area per unit volume Sr of the particles is  

Further information on the physical properties of media used in deep bed filtration is provided in Table 6.3. 

It is not pos le to provide values for the filtration constants, as these are dependent on the material to be ered, the flow conditions, fihration history, etc. They must be assessed by laboratory and pilot-scale tests. 

We shall consider, in turn, the various problems which have to be faced when designing isothermal, adiabatic and other non-isothermal tubular reactors, and we shall also briefly discuss fluidised bed reactors. Problems of instability arise when inappropriate operating conditions are chosen and when reactors are started up. A detailed discussion of this latter topic is outside the scope of this chapter but, since reactor instability is undesirable, we shall briefly inspect the problems involved. 

The equilibrium stage calculations discussed earlier can easily be applied to distillation in order to find the required operating and design parameters. Consider the following problem specification. 

1 Problem. A mixture of methanol and water containing 40 mol per cent of methanol is to be separated to give a product of at least 90 mol per cent of methanol at the top, and a bottom product with no more than 10 mol per cent of methanol. The feed flow rate is 100 kmol h 1 and the feed is heated so that it enters the column at its boiling point. The vapour leaving the column is condensed, but not sub-cooled, and provides reflux and product. Since all the vapour from the column is condensed, the composition of the vapour from the top plate must equal that of the top product as well as that returned as reflux. 

It is proposed to operate the unit with a reflux ratio of 3 kmol kmol-1 product (reflux ratio R = LID. where L is the flow returned to the column and D is the distillate product). It is required to find the top and bottom product flow rates, as well as the liquid and vapour flow rates above and below the feed point. 

2 Solution. A total material balance over the whole column, where F, D and B are the feed, top product and bottom product flow rates, respectively, yields  

The component balance for the most volatile component (methanol), where xF, xD and xB are the feed, top product and bottom product mole fractions (of methanol), respectively, gives  

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The critical temperature of methane is 191°K. At 25°C, therefore, the reduced temperature is 1.56. If the dividing line is taken at T/T = 1.8, methane should be considered condensable at temperatures below (about) 70°C and noncondensable at higher temperatures. However, in process design calculations, it is often inconvenient to switch from one method of normalization to the other. In this monograph, since we consider only equilibria at low or moderate pressures in the region 200-600°K, we elect to consider methane as a noncondensable component. 

While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data. 

In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1). 

Table 2. Comparison of Results of Different Design Calculations ...

Fig. 19. Correction factor for axial dispersion as a function of NTU. SoHd lines are rigorous calculations broken lines, approximate formulas according to hterature (61). (a) Numbers on lines represent Pe values Pe = 20 /Lj = 0.8. (b) For design calculations. Numbers on lines represent Pep u ...

These charts have the parameter curves superimposed on the standard M I L) correction factor curves. Thus the four pertinent groups, P, R, T, and -N, are displayed together on the same chart. The design calculation is thus reduced to finding F and A/, given P and R the performance calculation is reduced to finding F and P, given R and N. ... 

Process calculations for traditional unit-operations equipment can be divided into two types design and performance. Sometimes the performance calculation is caHed a simulation (see Simulation and process design). The design calculation is used to roughly size or specify the equipment. EoUowing the... 

These multidimensional analyses do not necessarily predict overall generator performance or operating characteristics significantly more accurately than do the qua si-one-dimensional analyses, which are more economical to mn. Thus the latter are used for general channel design calculations, and the more sophisticated codes mainly to deal with more detailed aspects of channel operation. For example, current concentrations at electrode edges can be predicted by use of the more sophisticated codes. This allows appropriate electrode design for the condition. 

Voltage measurement have been made at very low temperatures using a superconductor as one leg of a thermocouple. Eor a superconductor, S is zero, so the output of the couple is entirely from the active leg. The Thomson heat is then measured at higher temperatures to extend the absolute values of the Seebeck coefficients (7,8). The Thomson heat is generally an order of magnitude less than the Peltier heat and is often neglected in device design calculations. 

A first design is chosen, complete in all details necessary to cany out the design calculations. 

Multicomponent systems containing four or more components become difficult to display graphically. However, process-design calculations can often be made for the extraction of the component with the lowest partition ratio K and treated as a ternaiy system. The components with higher K values may be extracted more thoroughly from the raffinate than the solute chosen for design. Or computer calculations can be used to reduce the tedium of multicomponent, multistage calculations. 

Driving Force Gas moves across a membrane in response to a difference in chemical potential. Partial pressure is sufficiently proportional to be used as the variable for design calculations for most gases of interest, but fugacity must be used for CO9 and usually for Hg... 

With the aid of the computer and suitable programs, design calculations are feasible at a reasonable cost. Moreover, these calculations can be made without having to make questionable assumptions. A program has been developed by the Brown Root Company that gives good results, enabling companies to perform quality studies. 

Non-complex and/or non-critical applications in mechanical design can also make use of probabilistic design techniques and justify a more in-depth approach if the benefits are related to practitioners and customers alike. Surveys have indicated that many products in the industrial sector have in the past been overdesigned (Kalpakjian, 1995). That is, they were either too bulky, were made of materials too high in quality, or were made with unwarranted precision for the intended use. Overdesign may result from uncertainties in design calculations or the concern of the designer and manufacturer over product safety in order to avoid user injury or... 

In the probabilistic design calculations, the value of Kt would be determined from the empirical models related to the nominal part dimensions, including the dimensional variation estimates from equations 4.19 or 4.20. Norton (1996) models Kt using power laws for many standard cases. Young (1989) uses fourth order polynomials. In either case, it is a relatively straightforward task to include Kt in the probabilistic model by determining the standard deviation through the variance equation. 

ATM = Minimum column cross-sectional area, tV. Further detailed design calculations may result in a change in tower diameter. 

The process engineer must plan for minimum flow provisions when making design calculations. For preliminary work, approximate the required minimum flow by assuming all the horsepower at bloeked-in eonditions turns into heat. Then, provide enough minimum flow to carry away this heat at a 15°F rise in the minimum flow stream s temperature. 

Many of the better known shortcut equipment design methods have been derived by informed assumptions and mathematical analysis. Testing in the laboratory or field was classically used to validate these methods but computers now help by providing easy access to rigorous design calculations. 

In this subsection, basic design theory for preliminary sizing and specifying equipment are reviewed. Some sample design calculations are included. References cited at the end of tlie chapter can be consulted for more detailed information and design methods. For solid-liquid separation methods, the reader should refer to Liquid Filtration, 2" edition, by N. P. Cheremisinoff, Butterworth-Heinemarui Publishers (1998). 

The reader will find additional design calculation examples in the two literature citations provided in this section, in addition, refer to the Suggested Readings section of this chapter for further information. 

Representative design calculations showing load combinations and ode compliance of a typical building element such as a shear wall in ihe auxiliary of containment building. 

Nominal size of a duct or fitting The reference dimension used for the designation, calculation, and application of ducts and fittings. 

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