(617f) Role of Sampling in Process Design, Optimization and Control

Sampling is a statistical procedure which involves the selection of a finite number of individuals to represent and infer some knowledge about a population of concern. Sampling techniques are used in wide range of science and engineering applications; they are of basic importance in computational statistics, in the implementation of probabilistic algorithms and in related problems of statistical computing that have a stochastic ingredient (e.g. financial modeling, artificial intelligence, computational chemistry, risk and uncertainty analysis and design of experiments). This chapter is devoted to role of sampling in process systems engineering. 

Uncertainty analysis is a crucial step in process design and development due to the fact that over the life cycle of the process, product demands change, there may be variations in feedstock and product specifications and the process may be subject to short-term and long-term uncertainties. Furthermore, increased environmental consciousness in recent years and the efforts for pollution prevention necessitate chemical manufacturing plants to comply with stricter environmental regulations and to reduce waste. Therefore, the breadth of traditional process design approaches should be extended to include green engineering principles early in design (Diwekar, 2003; Diwekar, 2005). This is because the decisions made earlier during the development of a chemical process affect later stages such as material and equipment selection, pilot plant studies and financial analysis and the opportunities for reducing environmental and health impacts of a process diminishes. Therefore, unlike traditional process design, where engineers are seeking only low cost options, contemporary process design approaches include environmental and health impacts, process performance indices such as risk, reliability, safety and flexibility as well as controllability and profitability into decision making. Sampling plays an important role in defining and quantifying these objectives.  Further, nowadays process design is just not restricted to process simulation but includes steps like discovery, chemical synthesis on one end, and management, planning, and control on the other end. As the breadth of this design framework is extended, uncertainties in the model increase and efficient algorithms and tools are needed to address this problem. Sampling is an important component of these algorithms and tools.

Figure 1 shows an overview of this integrated framework proposed by (Diwekar, 2005), which applies green engineering principles at every stage of process design and development. The first stage in process development is discovery, where chemicals and materials are selected and synthesized in a laboratory or using computational chemistry methods. These methods use Monte Carlo methods based on sampling of the molecular configurational space.

Computer-aided molecular design (CAMD) is a commonly used technique for chemical synthesis where the reverse use of group contribution methods is employed to select materials with desired physical, chemical, environmental and biological properties. The next stage of chemical synthesis is process synthesis where a chemical process is developed by choosing various unit operations and their connections. A flowsheet of the proposed plant is generated and process simulators are used to compute mass and energy flows for the process to predict its behavior if it was constructed.

Figure 1: Integrated framework for environmentally conscious process development and design under uncertainty (Diwekar, 2005)

Uncertainties are commonly present in chemical and process synthesis due to insufficient experimental data and the lack of accurate models for representing the physical and chemical phenomena. Uncertainties are also encountered over the life cycle of the plant which affects decisions related to plant operations such as process control, production planning and scheduling, supply chain management, reliability and maintenance of the plant.

For example, model uncertainty and external disturbances are important concerns in designing control systems, which are used to minimize deviations from the nominal process conditions and maintaining the safe operation of the plant. Probabilistic approaches and sampling techniques are used commonly to ensure robustness to these model uncertainties. On the other hand, off-line quality control is used to design products and processes that are robust to uncontrollable variation at the design stage. Parameter design strategy is used for this purpose and sampling techniques are employed to propagate the effects of input variability on outputs. The choice of an efficient sampling technique is very important for efficient off-line quality control.

For multipurpose/multiproduct batch plants, optimal production planning and scheduling is important in order to be competitive in a just-in-time production environment. The scheduling problem assigns a sequence of tasks to each equipment over time, according to inventory restrictions and customer demands. The production schedule should be able to accommodate changing product demands, equipment shutdowns and unexpected orders. An extension of the scheduling problem is supply chain management which deals with a complex network of suppliers, plant, warehouses, distribution centers and customers. Examples of uncertainties in supply chains include fluctuations in product prices, demands or production yields.

In order to increase operational effectiveness and profits, and to save on lost production and costs, chemical plants need to operate with high process reliability and availability. Therefore, reliability issues need to be addressed at the conceptual design stage. Optimal maintenance schedules for the plant need to be determined to increase reliability and availability while maintaining profitability. Uncertainties in equipment availability profoundly affect the profitability of the plant.

Uncertainty analysis and sampling techniques also play an important role in risk assessment and safety. Risk management is a decision making process which is used to reduce the financial and production risk for a business. Environmental risk assessment and financial risk assessment are commonly applied to chemical manufacturing processes. Environmental risk is associated with the toxicity of materials and the effect of hazardous materials on a human population or an entire ecosystem. Financial risk on the other hand, is concerned with pricing decisions and demands. Probability distributions and sampling techniques are frequently used in risk and policy analysis.

The most commonly used sampling technique for uncertainty analysis is Monte Carlo sampling which is based on a pseudo-random number generator. This sampling technique has probabilistic error bounds and large sample sizes are needed to achieve the desired accuracy. Variance reduction techniques have been applied to circumvent the disadvantages of Monte Carlo sampling. The sampling approaches for variance reduction that are used more frequently for chemical engineering applications are importance sampling, Latin Hypercube Sampling (LHS) (McCay et al., 1979; Iman and Conover, 1982), Descriptive Sampling (Saliby, 1990) and Hammersley Sequence Sampling (HSS) (Kalagnanam and Diwekar, 1997; Diwekar and Kalagnanam, 1997). The latter technique belongs to the group of quasi-Monte Carlo methods which were introduced in order to improve the efficiency of Monte Carlo methods by using quasi-random sequences that show better statistical properties and deterministic error bounds.

These sampling techniques play an important role in uncertainty analysis and stochastic modeling. They are also important for improving the efficiency of optimization algorithms. Sampling accuracy is crucial for deriving efficient algorithms for discrete optimization and multi-objective optimization problems. This paper presents the recent advances in sampling approaches and their applications in product discovery, chemical synthesis, process synthesis and design, process operation and control. Future trends in sampling techniques are also discussed in this paper.

REFERENCES:

Diwekar U.M. and Kalagnanam J.R. (1997) Efficient Sampling Technique for Optimization under Uncertainty. AIChE Journal 43(2): 440-447.

Diwekar, U. (2005) Green Process Design, Industrial Ecology, and Sustainability: A Systems Analysis Perspective: Sustainability and Renewable Resources. Resources, Conservation and Recycling  44 (3):215-235.

Diwekar, U.M. (2003) Greener by Design. Environmental Science and Technology 37 (23): 5432-5444. 

Iman R. L. and W. J. Conover (1982) Small Sample Sensitivity Analysis Techniques for Computer Models, with an Application to Risk Assessment. Communications in Statistics A17:1749-1842.

Kalagnanam J.R., Diwekar U.M. (1997) An Efficient Sampling Technique For Off-Line Quality Control. Technometrics 39 (3): 308-319

McKay M.D., Beckman R.J., and Conover W.J. (1979) A Comparison of Three Methods of Selecting Values of Input Variables in the Analysis of Output from a Computer Code. Technometrics, 21(2): 239-245.

Saliby E. (1990) Descriptive Sampling: A Better Approach To Monte Carlo Simulations. Journal of Operations Research Society 41(12), 1133-1142.