Reliable Flash Calculations: Part 2. Process Flowsheeting with Nonsmooth Models and Generalized Derivatives

Watson, H. A.; Vikse, Matias; Gundersen, Truls; Barton, Paul I.

doi:10.1021/acs.iecr.7b03232

Cited by 16 publications

(35 citation statements)

References 26 publications

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“…This paper has presented an application of the nonsmooth flowsheeting strategy developed by Watson et al 14 for simulating three single mixed refrigerant processes of different complexity with the Peng-Robinson equation of state. Different cases for each process were analyzed, and the simulations were performed by solving an algebraic equation system using a nonsmooth Newton-type solver provided with exact sensitivity information in the form of generalized derivative elements.…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless, only the parameters presented in Table S1 need to be provided by the user, while the remaining temperatures are calculated through an automatic initialization procedure that assumes a linear relationship between enthalpy and temperature in the subcooled and superheated phase regions. 14 For comparison, the PRICO model from Watson et al 14 consists of 27 variables. The data for the natural gas stream are presented in Table S2 in the supporting information and are assumed fixed throughout this example.…”

Section: Examplementioning

confidence: 99%

“…The driving force plot shows that the process is constrained mainly in the cold end and at the point of mixing, which results in smaller driving forces compared to what was observed for the PRICO process. 14 The corresponding compression power is therefore significantly smaller.…”

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Versatile Simulation Method for Complex Single Mixed Refrigerant Natural Gas Liquefaction Processes

Vikse

Watson

Gundersen

et al. 2017

Ind. Eng. Chem. Res.

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Natural gas liquefaction is an energy intensive process with very small driving forces particularly in the low temperature region. Small temperature differences in the heat exchangers and high operating and capital costs require the use of an accurate and robust simulation tool for analysis. Unfortunately, state-of-the-art process simulators such as Aspen Plus and Aspen HYSYS have significant limitations in their ability to model multistream heat exchangers, which are critical unit operations in liquefaction processes. In particular, there exist no rigorous checks to prevent temperature crossovers from occurring in the heat exchangers, and the parameters must therefore be determined through a manual iterative approach in order to establish feasible operating conditions for the process. A multistream heat exchanger model that performs these checks, as well as area calculations for economic analysis, has previously been developed using a nonsmooth modeling approach. In addition, the model was used to 1 successfully simulate the PRICO process with the Peng-Robinson equation of state.However, the PRICO process is one of the most basic single mixed refrigerant processes, and it is therefore necessary to investigate whether the nonsmooth framework is capable of also simulating larger and more complex single mixed refrigerant processes.In this article, the nonsmooth multistream heat exchanger model is used to simulate three different single mixed refrigerant processes of varying complexity. Different case studies are performed, each solving for a different set of unknown variables. Several different variables were considered in the analysis to investigate whether the models obtained feasible solutions even for ostensibly challenging cases such as varying the mixed refrigerant composition. The solutions are then validated using results from Aspen Plus and Aspen HYSYS. The simulations in Aspen Plus gave nearly identical solutions to the nonsmooth models. Results in HYSYS, on the other hand, correlated well at high temperatures but deviated from the nonsmooth solution at cold temperatures.The disparity was caused by different ideal gas enthalpy correlations used by the two simulation tools.

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Section: Discussionmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Versatile Simulation Method for Complex Single Mixed Refrigerant Natural Gas Liquefaction Processes

Vikse

Watson

Gundersen

et al. 2017

Ind. Eng. Chem. Res.

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“…The verification test in line 7 for the cycling approach may mistakenly fail for a correct solution, because of numerical error (e.g., due to the coefficient matrix on the left-hand side of (27) having a high condition number). Such false negatives have been observed in practice [43] when applying the cycling approach (i.e., Proposition 2 in [22]) to solve P C 1 equation systems. The method of iterative refinement [44] has successfully alleviated this issue in the aforementioned work and can be optionally added to the cycling part of Algorithm 1.…”

Section: An Extension Of Fiacco Andmentioning

confidence: 97%

Generalized Sensitivity Analysis of Nonlinear Programs

Stechlinski¹,

Khan²,

Barton³

2018

SIAM J. Optim.

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This paper extends classical sensitivity results for nonlinear programs to cases in which parametric perturbations cause changes in the active set. This is accomplished using lexicographic directional derivatives, a recently developed tool in nonsmooth analysis based on Nesterov's lexicographic differentiation. A nonsmooth implicit function theorem is augmented with generalized derivative information and applied to a standard nonsmooth reformulation of the parametric KKT system. It is shown that the sufficient conditions for this implicit function theorem variant are implied by a KKT point satisfying the linear independence constraint qualification and strong second-order sufficiency. Mirroring the classical theory, the resulting sensitivity system is a nonsmooth equation system which admits primal and dual sensitivities as its unique solution. Practically implementable algorithms are provided for calculating the nonsmooth sensitivity system's unique solution, which is then used to furnish B-subdifferential elements of the primal and dual variable solutions by solving a linear equation system. Consequently, the findings in this article are computationally relevant since dedicated nonsmooth equation-solving and optimization methods display attractive convergence properties when supplied with such generalized derivative elements. The results have potential applications in nonlinear model predictive control and problems involving dynamic systems with mathematical programs embedded. Extending the theoretical treatments here to sensitivity analysis theory of other mathematical programs is also anticipated.

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“…Local sensitivity information for non-smooth models is obtained by calculating generalized derivatives automatically as explained in [187]. This approach has been applied to develop compact models for multi-stream heat exchangers [188], which have been incorporated into flowsheets of natural gas liquefaction [26] such as the simple mixed refrigerant [189,190] and dual mixed refrigerant processes [191,192].…”

Section: Categorization According To Modeling Approachmentioning

confidence: 99%

Modeling and Simulation of Energy Systems: A Review

2018

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Energy is a key driver of the modern economy, therefore modeling and simulation of energy systems has received significant research attention. We review the major developments in this area and propose two ways to categorize the diverse contributions. The first categorization is according to the modeling approach, namely into computational, mathematical, and physical models. With this categorization, we highlight certain novel hybrid approaches that combine aspects of the different groups proposed. The second categorization is according to field namely Process Systems Engineering (PSE) and Energy Economics (EE). We use the following criteria to illustrate the differences: the nature of variables, theoretical underpinnings, level of technological aggregation, spatial and temporal scales, and model purposes. Traditionally, the Process Systems Engineering approach models the technological characteristics of the energy system endogenously. However, the energy system is situated in a broader economic context that includes several stakeholders both within the energy sector and in other economic sectors. Complex relationships and feedback effects exist between these stakeholders, which may have a significant impact on strategic, tactical, and operational decision-making. Leveraging the expertise built in the Energy Economics field on modeling these complexities may be valuable to process systems engineers. With this categorization, we present the interactions between the two fields, and make the case for combining the two approaches. We point out three application areas: (1) optimal design and operation of flexible processes using demand and price forecasts, (2) sustainability analysis and process design using hybrid methods, and (3) accounting for the feedback effects of breakthrough technologies. These three examples highlight the value of combining Process Systems Engineering and Energy Economics models to get a holistic picture of the energy system in a wider economic and policy context.

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Reliable Flash Calculations: Part 2. Process Flowsheeting with Nonsmooth Models and Generalized Derivatives

Cited by 16 publications

References 26 publications

Versatile Simulation Method for Complex Single Mixed Refrigerant Natural Gas Liquefaction Processes

Versatile Simulation Method for Complex Single Mixed Refrigerant Natural Gas Liquefaction Processes

Generalized Sensitivity Analysis of Nonlinear Programs

Modeling and Simulation of Energy Systems: A Review

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