Selection of design variables

For a flash distillation the total degrees of freedom was shown to be (C -f 4), so for two components = 6. If the feed stream flow, composition, temperature and pressure are fixed by upstream conditions, then the number of design variables will be  

So the designer is free to select two variables from the remaining variables in order to proceed with the calculation of the outlet stream compositions and flows. 

If he selects the still pressure (which for a binary system will determine the vapour— liquid-equilibrium relationship) and one outlet stream flow-rate, then the outlet compositions can be calculated by simultaneous solution of the mass balance and equilibrium relationships (equations). A graphical method for the simultaneous solution is given in Volume 2, Chapter 11. 

However, if he selects an outlet stream composition (say the liquid stream) instead of a flow-rate, then the simultaneous solution of the mass balance and v-l-e relationships would not be necessary. The stream compositions could be calculated by the following step-by-step (sequential) procedure  

Specifying P determines the v-l-e relationship (equilibrium) curve from experimental data. 

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The performance ratio or heat economy is a result of the selection of design variables previously discussed, and is not a variable as such. Lines of constant capital cost per daily gallon of capacity are also included in Figure 3. Capital costs have been based on plant capacities in a range of 25,000,000 to 60,000,000 gallons a day and a velocity in the evaporator tubes of 5 feet per second. These lines of constant capital cost per daily gallon are a result of cross plotting the results obtained in the optimization study. 

In a design process, the selection of design variables and input parameters is important. In this spur gear design procedure, the following variables and input parameters are selected. 

Though the total degrees of freedom is seen to be (C + 4) some of the variables will normally be fixed by general process considerations, and will not be free for the designer to select as design variables . The flash distillation unit will normally be one unit in a process system and the feed composition and feed conditions will be fixed by the upstream processes the feed will arise as an outlet stream from some other unit. Defining the feed fixes (C + 2) variables, so the designer is left with ... 

The variables selected as design variables (fixed by the designer) cannot therefore be assigned as output variables from an f node. They are inputs to the system and their edges must be oriented into the system of equations. 

If, for instance, variables r3 and u4 are selected as design variables, then Figure 1.11 shows one possible order of solution of the set of equations. Different types of arrows are used to distinguish between input and output variables, and the variables selected as design variables are enclosed in a double circle. 

For many design calculations it will not be possible to select the design variables so as to eliminate the recycle of information and obviate the need for iterative solution of the design relationships. 

K Degrees of freedom (variables free to be selected as design variables) —... 

The optimal robust controller designed with one of the new synthesis techniques is generally not of a form that can be readily implemented. The main benefit of the new synthesis procedure is that it allows the designer to establish performance bounds that can be reached under ideal conditions. In practice, a decentralized (multiloop) control structure is preferred for ease of start-up, bumpless automatic to manual transfer, and fault tolerance in the event of actuator or sensor failures. Indeed, a practical design does not start with controller synthesis but with the selection of the variables that are to be manipulated and measured. It is well known that this choice can have more profound effects on the achievable control performance than the design of the controller itself. This was demonstrated in a distillation example [17, 18] in which a switch from reflux to distillate flow as the manipulated variable removes all robustness problems and makes the controller design trivial. 

If a process has positive degrees of freedom, you must select as many design variables as there are degrees of freedom, and then solve the system state equations for the remaining (state) variables. Which variables you select as design variables can have a dramatic effect on the difficulty of the subsequent calculations. 

The design of multistage separation operations involves solving the variable relationships for output variables after selecting values of design variables to satisfy the degrees of freedom. Two cases are commonly encountered. In Case I, recovery specifications are made for one or two key components and the number of required equilibrium stages is determined. In Case II, the number of equiiib-... 

The attractive features of splitless injection techniques are that they allow the analysis of dilute samples without preconcentration (trace analysis) and the analysis of dirty samples, since the injector is easily dismantled for cleaning. Success with individual samples, however, depends on the selection of experimental variables of which the most important sample size, sample solvent, syringe position, sampling time, initial column temperature, injection temperature and carrier gas flow rate, often must be optimized by trial and error. These conditions, once established, are not necessarily transferable to another splitless injector of a different design. Also, the absolute accuracy of retention times in splitless injection is generally less than that found for split injection. For splitless injection the reproducibility of retention times depends not only on chromatographic interactions but also on the reproducibility of the sampling period and the evaporation time of the solvent in the column inlet, if solvent effects (section 3.5.6.2) are employed. The choice of solvent, volume injected and the constancy of thermal zones will all influence retention time precision beyond those for split injection. For quantitative analysis the precision of repeated sample injections is normally acceptable but the method is subject to numerous systematic errors that may... 

The selection of indicator variables, sampling design, data collection and statistical/geostatisti-cal methods to analyze datasets are inherently linked. A schematic plan to develop indicators for a given site is presented in Figure 15.11. Components of a monitoring program should include... 

The selection of indicator variable, sampling design, data collection, and statistical/geosta-tistical methods to analyze dataset is linked. 

Select a best set of design variables for the heat exchanger problem in Figure 2.38. Discuss your solution strategy. 

Optimization criteria describe basic properties of materials. They are also called objective functions. In material optimization the objective functions describe selected properties that were considered as important and decisive for the material s quality and applicability. The solution consists of the determination of those values of design variables that extremize these properties. All physical, chemical and other properties may be treated as material properties. Particularly important for engineering materials are mechanical properties such as strength, Young s modulus, specific fracture energy, durability and specific cost. 

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