Determining the conditions under which the design is feasible and safe has been recognized as one of the important problems in process systems engineering. In the early 1980's, Swaney and Grossmann [1] defined the Flexibility Index to provide a measure of the feasible operating region in the space of the uncertain parameters, assuming that expected deviations are estimated in the positive and negative directions of each parameter from its nominal value. Simply stated, the flexibility index corresponds to the maximum deviation of the uncertain parameters from their nominal values, by which feasible operation can be guaranteed with the proper manipulation of the control variables. Since then, a series of publications have mainly focused on improving and extending the use of this index in process design. Grossmann and Floudas [2], proposed a solution approach that does not rely on the assumption that critical parameter values are at vertices. It is based on the following ideas: (i) the inner optimization problem is replaced by the Karush Kuhn Tucker optimality conditions; (ii) the discrete nature of the selection of the active constraints is utilized by introducing a set of binary variables to express if a specific constraint is active. Based on these ideas, the feasibility test and flexibility index problems can be reformulated as mixed-integer optimization problems either linear or nonlinear depending on the nature of the constraints. Some concerns appear in the design of new materials where the constraints have the form of property functions. The presence of hard constraints in any operability analysis is the reassurance of safe operation. However, these constraints can be very limiting in terms of the available operating ranges. Thus, it is of major benefit to be able to identify as precisely as possible the feasible operating ranges to avoid limiting the operation to narrow conditions and losing the capability of performing any profit optimization studies.

Even though the effect of the process design on the control qualities of a plant has been recognized for several decades, substantial efforts to integrate process design and process control have only been initiated during the last two decades. Specifically, it is desirable to operate the process outputs at specified ranges, represented by the Desired Output Set (DOS), and to compensate for the disturbances within an Expected Disturbance Set (EDS). These two tasks should be accomplished using the limited control action available, given by the Available Input Set (AIS). In order to quantify the operability characteristics of a prospective process design and its integration with process control, Vinson and Georgakis [3, 4] proposed a simple yet powerful approach which focuses its attention to the constraint range of the input and output variables. In this approach, the achievability of process control objectives for an existing design was quantified by calculating the Achievable Output Set (AOS), which represents the output ranges that can be achieved using the inputs in the AIS. Moreover, the required input ranges to achieve the entire DOS in the presence of disturbances can also be calculated and it is represented by the Desired Input Set. Based on these variable sets, the Operability Index was defined in the input and output spaces to provide straightforward quantification and to help the designer in assessing alternative designs and possibly changing a given process design. This methodology has been proven to be effective for both linear [3, 4] and nonlinear processes [5, 6], consisting of a single unit or one overall plant [7].

The objective of this work is to present a preliminary review on the comparative application of operability and flexibility concepts in process control and process design. Initially, a review on the operability framework for steady-state and dynamic systems is presented. The application of this methodology is illustrated through the examination of several examples characterizing different systems categories, such as linear and non-linear, square and non-square systems. The same examples are also examined from the flexibility point of view utilizing tools based on the active set strategy [2]. The results discussed show that operability and flexibility approaches examine a process from different perspectives and provide valuable complementary information.

Reference:

[1] Swaney, R.E., & Grossmann, I.E. (1985). An index for operational flexibility in chemical process design - Part I : formulation and theory. AIChE Journal, 26, 621-630.

[2] Grossmann, I.E., & Floudas C.A. (1987). Active constraint strategy for flexibility analysis in chemical processes. Computers and Chemical Engineering, 11, 675-693.

[3] Vinson, D. R., & Georgakis, C. (1998). A new measure of process output controllability. In Proceedings of the 1998 IFAC International Symposium on Dynamics and Control of Process Systems (DYCOPS), 663-672.

[4] Vinson, D. R., & Georgakis, C. (2000). A new measure of process output controllability. Journal of Process Control, 10, 185–194.

[5] Subramanian, S., & Georgakis, C. (2001). Steady-state characteristics of idealized reactors. Chemical Engineering Science, 56, 5111-5130.

[6] Subramanian, S., Uzturk, D., & Georgakis, C. (2001). An Optimization-Based Approach for the Operability Analysis of Continuosly Stirred Tank Reactors. Industrial Engineering and Chemistry Research, 40, 4238-4252.

[7] Subramanian, S., & Georgakis, C. (2005). Methodology for the Steady-state Operability Analysis of Plantwide Systems. Industrial Engineering and Chemistry Research, 44, 7770-7786.