Energy Requirement of a Distillation/Membrane Parallel Hybrid: A Thermodynamic Approach
Bibliographic record
Abstract
This paper presents a new thermodynamic approach, based on the notion of power of separation, for the retrofit problem of finding the minimal energy requirement of an existing binary distillation column when coupling it in parallel with a membrane unit. A new geometric interpretation of this concept, which is supported by a rigorous mathematical proof, is introduced. From it results an efficient and accurate shortcut method to tackle the aforementioned problem. Numerical examples are considered for the energy intensive separation of olefins from paraffins, namely the retrofit of a C 3 -splitter and the retrofit of a C 2 -splitter through parallel hybridization with facilitated transport membranes. The results of the proposed shortcut method are compared to those obtained via the nonlinear programming optimization solvers GAMS-CONOPT and GAMS-CoinIpopt for a superstructure based problem formulation, which act as a reference. In both case studies, the shortcut method results in a significant reduction in problem size and in the number of solver iterations, while yielding only a small error on the minimal energy requirement of the column within the hybrid and on the hybrid architecture (i.e., the position of side-streams along the column). It could therefore be used to carry out a rapid screening of alternatives (e.g., different membrane technologies) in order to evaluate potential energy improvements. The proposed approach could also provide mathematical programming algorithms with a good initial guess of the solution.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".