Equation-Oriented (EO) modeling techniques have been gaining popularity as an alternative for simulating and optimizing process systems due to their flexibility and ability to leverage state-of-the-art solvers inaccessible to many procedural modeling approaches. Despite these advantages, adopting EO modeling tools remains challenging due to the significant learning curve and effort required to build and solve models. Many techniques are available to help diagnose problems with EO process models and reduce the effort required to create and use them. However, these techniques still need to be integrated into EO modeling environments, and many modelers are unaware of sophisticated EO diagnostic tools. To survey the availability of model diagnostic tools and common workflows, the U.S. Department of Energy’s Institute for the Design of Advanced Energy Systems (IDAES) has conducted user experience interviews of users of the IDAES Integrated Platform (IDAES-IP) for process modeling. The inter... [more]

Equation-oriented (EO) modeling has the potential to enable the effective design and optimization of the operation of advanced energy systems. However, advanced modeling of energy systems results in a large number of variables and non-linear equations, and it can be difficult to search through these to identify the culprit(s) responsible for convergence issues. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms so they can be rescaled. A further singular value decomposition can be performed to identify degenerate sets of equations and remaining scaling issues. This work presents an EO model of a flowsheet developed for post-combustion carbon capture using a monoethanolamine (MEA) solvent system as a case study. The IDAES diagnostics tools were successfully applied to this flowsheet to identify problems to im... [more]

Reverse electrodialysis (RED) is a nascent renewable technology that generates clean, baseload electricity from salinity differences between two water streams, a renewable source known as salinity gradient energy (SGE). Full-scale RED progress calls for robust techno-economic and environmental assessments. Using generalized disjunctive programming (GDP) and life cycle assessment (LCA) principles, this work proposes cost-optimal and sustainable RED process designs involving different RED stack sizes and width-over-length ratios to guide the design and operation from the demonstration to full-scale phases. Results indicate that RED units will benefit from larger aspect ratios with a relative increase in net power of over 30% with 6 m2 membrane size. Commercial RED unit sizes (0.25–3 m2) require larger aspect ratios to reach an equal relative increase in net power but exhibit higher power densities. The GDP model devises profitable RED process designs for all the assessed aspect ratios in... [more]

The oil and gas energy sector uses billions of gallons of water for hydraulic fracturing each year to extract oil and gas. The water injected into the ground for fracturing along with naturally occurring formation water from the oil wells surfaces back in the form of produced water. Produced water can contain high concentrations of total dissolved solids and is unfit for reuse outside the oil and gas industry without desalination. In semi-arid shale plays, produced water desalination for beneficial reuse could play a crucial role in alleviating water shortages and addressing extreme drought conditions. In this paper we co-optimize the design and operation of desalination technologies along with operational decisions across produced water networks. A multi-period produced water network model with simplified split-fraction-based desalination nodes is developed. Rigorous steady-state desalination mathematical models based on mechanical vapor recompression are developed and embedded at the... [more]

Post-combustion carbon capture technologies have the potential to contribute significantly to achieving the environmental goals of reducing CO2 emissions in the short term. However, these technologies are energy and cost-intensive, and the variability of flue gas represents important challenges. The optimal design and optimization of such systems are critical to reaching the net zero and net negative goals, in this context, the use of computer-aided process design can be very effective in overcoming these issues. In this study, we explore the implementation of carbon capture technologies within an industrial complex, by considering the pooling of CO2 streams. We present an optimization formulation to design carbon capture plants with the goal of enhancing efficiency and minimizing the capture costs. Capital and operating costs are represented via surrogate models (SMs) that are trained using rigorous process models in Aspen Plus, each data point is obtained by solving an optimization p... [more]

Adaptive and self-optimizing intelligent systems such as digital twins are increasingly important in science and engineering. Digital twins utilize mathematical models to provide added precision to decision-making. However, physics-informed models are challenging to build, calibrate, and validate with existing data science methods. Model-based design of experiments (MBDoE) is a popular framework for optimizing data collection to maximize parameter precision in mathematical models and digital twins. In this work, we apply MBDoE, facilitated by the open-source package Pyomo.DoE, to train and validate mathematical models for batch crystallization. We quantitatively examined the estimability of the model parameters for experiments with different cooling rates. This analysis provides a quantitative explanation for the heuristic of using multiple experiments at different cooling rates.

Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The... [more]

In this work, we present recent algorithmic and implementation advances of the nonconvex two-stage robust optimization solver PyROS. Our advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the formulations and/or initializations of the various subproblems used by the underlying cutting set algorithm, and extensions to the pre-implemented uncertainty set interfaces. The effectiveness of PyROS is demonstrated through the results of an original benchmarking study on a library of over 8,500 small-scale instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. To demonstrate the utility of PyROS for large-scale process models, we present the results of a carbon capture case study. Overall, our results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm.