Uncertainty process design

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). 

Another important challenge is to enhance the reliability of the design and scale up of multi-phase reactors, such as fluidized bed reactors and bubble-colunms. The design uncertainty caused by the complex flow in these reactors has often led to the choice of a reactor configuration that is more reliable but less efficient. An example is Mobil use a packed-bed reactor for the methanol to gasoline process in New Zealand, even though a... 

Step 6. You should always be aware of the sensitivity of the optimal answer, that is, how much the optimal value of C changes when a variable such as D changes or a coefficient in the objective function changes. Parameter values usually contain errors or uncertainties. Information concerning the sensitivity of the optimum to changes or variations in a parameter is therefore very important in optimal process design. For some problems, a sensitivity analysis can be carried out analytically, but in others the sensitivity coefficients must be determined numerically. 

Separation of metals by solvent extraction is usually based on the various complexing properties of the metals (Chapter 3). Separation systems may be chosen on the basis of complexity constants obtained from the literature. However, the literature often shows different values for same systems causing considerable concern for process design chemists. There is an obvious need for an objective presentation of the uncertainty in the published equilibrium constants, however conditional they may be. 

This chapter addresses the planning, design and optimization of a network of petrochemical processes under uncertainty and robust considerations. Similar to the previous chapter, robustness is analyzed based on both model robustness and solution robustness. Parameter uncertainty includes process yield, raw material and product prices, and lower product market demand. The expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) are also investigated to illustrate numerically the value of including the randomness of the different model parameters. 

Halemane, K. P., and Grossmann, I. E., Optimal process design under uncertainty. AIChE J. 29, 425 (1983). 

A process design is flexible if it can tolerate uncertainties in parameters and can handle disturbances. A flexibility index is a measure of the amount of uncertainty that can be tolerated with the desired process operation remaining feasible. A schematic of the flexibility index, 5, is shown in Fig. 8. Here, the two degrees of freedom represent uncertain parameters or disturbance variables, which have assumed upper and lower bounds. The feasible operating region lies within the cross-hatched area. The flexibility index is the fraction of the parameter range that still results... 

Another consideration is the dynamic controllability of a process design. If there are no uncertainties or disturbances, then the optimum economic design normally occurs at a constraint. An actual process cannot be operated at a constraint, because any disturbance may force the system to violate the constraint (a product purity limit, for example). In this case, the desired steady-state operating point must be backed-off from the economic optimum so that the control strategy can tolerate disturbances. The basic idea is shown in Fig. 9. 

Nishida, N., Liu, Y.A. and Ichikawa, A., "Studies in Chemical Process Design and Synthesis II. Optimal Synthesis of Dynamic Process Systems with Uncertainty," AiChE J. Vol. 22, No. 3, pp 539-550, May 1976. 

Uncertainty patterns and sensitivity analysis of an indicator based process design framework... 

Keywords early phase process design, multi-objective assessment, heuristical indicators, uncertainty patterns. 

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