(4ab) Mathematical Modeling in Water Network Resilience and Pharmaceutical Process Optimization

Research Interests: Optimization under uncertainty, Pharmaceutical Manufacturing, Mathematical Modeling and Simulation, Large-Scale Optimization, Scenario-Based Optimization, Resilience

Teaching Interests: Numerical Methods, Mathematical Programming and Optimization, Process Design, Pharmaceutical Process Design

Mathematical modeling and process optimization are ubiquitous elements of the digitization of engineering as more communities adopt Industry 4.0 standards. Chemical Engineering provides a unique point of view encompassing a wide range of applications, many of which require modeling accuracy beyond simple, linear models. Especially during optimization, the use of non-linear models and presence of discrete decision-making present unique challenges that often require tailored solution techniques. In addition to the complexity of these large-scale deterministic mathematical programs, the inclusion of uncertainty via either variance in model parameters or operating conditions significantly enhances the robustness of optimal solutions at increased computational cost. In this presentation, two different applications of optimization that can be formulated with a combination of classical chemical engineering modeling and operational/logistic decision-making will be showcased.

First, an application in water network resilience using a mixed-integer linear programming formulation for discrete sampling location selection will be shown. In this example, scenario-based optimization is employed to analyze which locations present the best coverage on a limited budget. Scenarios of foreign contaminant entering the water network are simulated from each node and are considered covered if a location can detect the contaminant during an adequate percentage of a representative workday. Various metrics for coverage are analyzed and compared with respect to both continuous sensing and routine discrete sampling. Continuous sensing can detect a higher percentage of events, but the effective cost of installation and maintenance of such continuous sensors can be beyond the limited budget of water utilities. Therefore, understanding how well discrete sampling performs under various metrics is important to assess the viability of routine sampling regimen.

Second, a completely different application with respect to design space identification in pharmaceutical manufacturing will be explored. Here, a traditional chemical engineering unit operation is modeled with uncertainty in model parameters to generate a probabilistic design space. The design space is a digital representation of the interaction of all model parameters and operating conditions that provide assurance of quality with respect to the critical quality attributes of a product. The probabilistic extension provides a degree of certainty to which a design space adheres to these critical quality attributes. Typically, sample-based techniques are employed to generate probabilistic representations of the design space, however an adaptation of flexibility analysis, a mixed-integer programming framework, allows for the generation of such spaces in a fraction of the computational time required for sample-based techniques. A case study using a continuous reactor is shown to demonstrate the utility of employing frameworks based on these complex mathematical programming formulations.

These two examples show a glimpse into the possible applications chemical engineers can solve with our unique curriculum and inherent necessity to model non-linear physics in many native problems. The second example shows a direct application of chemical process modeling contained in a decision-variable framework resulting in a large-scale mixed-integer non-linear program requiring a tailored algorithm to solve. The first example shows that scenario-based optimization can be used to analyze infrastructure resilience by generating optimal discrete sampling locations for routine sampling regimen in water distribution systems. The skills needed to analyze complex systems for process engineering open the door to many other problems whose structure emulates those presented in these two examples.

In fact, the development of user-friendly software tools to address these types of problems is extremely important in the adoption of new solution methods in the greater community. One way toward more broad adoption of these tools is the development of open-source code. Both case studies utilized open-source Python packages in combination with custom Python code as computational solution frameworks. This presentation aims to demonstrate that the unique combination of software development skills, along with classical chemical engineering modeling and numerical algorithm experience can unlock many difficult problems that face chemical engineers and adjacent computational fields.