The chemical process industry is continually striving for greater efficiency, throughput and operability in their plant operations, all while adhering to safety and cost constraints. The processes considered are often on a plant-wide scale, involving several operating units, and involve a considerable amount of uncertainty in terms of the raw material quality, utility costs and product demand. Designing such plants to be flexible enough to quickly ramp up or down production in real-time to combat these external uncertainties can present a significant challenge. To properly account for the plant behavior in design or operations optimization, one must cast a mathematical formulation that describes the underlying physical system behavior (e.g., mass and energy balances), the control system, and uncertainties within the system. Consequently, such formulations require dynamic optimization solutions algorithms, and due to the large-scale nature of the intended applications and extensive computing requirements, these algorithms must be crafted in a manner that makes use of appropriate numerical techniques capable of utilizing modern multiprocessor computing platforms.
Working with MACC industrial partner Praxair, MACC researchers Prof. Chris Swartz, Ian Washington, and Yanan Cao have made recent advances towards a systematic design framework to access process limitations and plant agility (see reference 1 below). Continuing from this established framework, recent work has shifted to the underlying numerical solution algorithms. In particular, the team has made progress on transitioning from a traditional serial computing environment to a parallel multiprocessor environment. Central to our approach is the ability to decompose elements of the problem formulation and farm out these decomposed and independent tasks to a multiprocessor server. Their recent work has demonstrated a dynamic optimization approach applicable to uncertain dynamic systems, which involves breaking up the time domain into several intervals and the uncertainty space into several discrete realizations. The solution process of the optimization algorithm involves the combined use of a nonlinear programming solver and differential equation solver for the simulation of the embedded dynamic system. The discrepancy between the state variable values at the final time from the previous interval and the initial time in the current interval is handled by the optimizer, which drives this to zero. As a result of their discretization approach, the simulation aspect requires numerous independent solution tasks which lends itself nicely to parallelization.
Prof. Swartz and his team has demonstrated that by solely targeting the independent simulation tasks, significant performance improvements within the overall dynamic optimization algorithm can be achieved. Furthermore, much of the software infrastructure can be built up from existing off-the-shelf numerical tools, where the parallelization aspect can be selectively inserted into overall algorithm through appropriate compiler directives. The parallel solution approach has allowed us to explore larger and more detailed design applications with the explicit inclusion of parametric uncertainty, which were previously intractable. Furthermore, their current findings have opened up further avenues to explore, and currently their attention has shifted to improving computation times through development of a structure-exploiting nonlinear programming algorithm. The results of the research have been published in two articles, the first targets the integration of design and control applications and appears in the AIChE Journal, while the second article is more focused on large-scale operations applications under uncertainty and can be found the journal Processes.
- Cao, Y., Swartz, C. L. E., Baldea, M, Blouin, S Optimization-Based Assessment of Design Limitations to Air Separation Agility in Demand Response Scenarios, J Process Control,, 33 37-48 (2015) [ Publisher Version| Open Access Version (free) ]
- Washington, I., Swartz, C. L. E. Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty, Processes,, 3 (3) 541-567 (2015) [ Publisher Version| Open Access Version (free) ]
- Washington, I., Swartz, C. L. E. Design under uncertainty using parallel multi-period dynamic optimization, AIChE Journal, (2014) [ Publisher Version ]
Yingkai Song, Kamil A. Khan. Optimization-based convex relaxations for nonconvex parametric systems of ordinary differential equations [more]
Nor Farida Harun. Fuel Composition Transients in Solid Oxide Fuel Cell Gas Turbine Hybrid Systems for Polygeneration Applications [more]
Mina Naeini, Haoxiang Lai, Thomas A. Adams. A Mathematical Model for Prediction of Long-Term Degradation Effects in Solid Oxide Fuel Cells [more]
Thomas A. Adams. Optimal design and operation of a waste tire feedstock polygeneration system [more]