Uncertainties in chemical, biological and molecular systems and optimal control.

Uncertainties in chemical, biological and molecular systems and optimal control

Thermodynamic uncertainties in batch processing and optimal control

Abstract Batch distillation is an important separation process for small-scale production especially in pharmaceutical, specialty chemical and biochemical industries. Although batch distillation units require lower capital cost than continuous units, the unsteady state nature of the process, results in higher operating costs. Optimal control in batch distillation is a mode of operation which allows us to optimize the column operating policy by selecting a trajectory for reflux ratio. Due to the uncertainties in thermodynamic models the reflux ratio profile obtained is often suboptimal. Recently a new method was proposed by Rico-Ramirez et al. [Comput. Chem. Eng. 27 (2003) 1867] to include time-dependent uncertainties in current formulations of batch distillation optimal control for ideal systems. In this paper, a general approach is proposed to handle both dynamic and static uncertainties in thermodynamics for more complex non-ideal systems. The static uncertainties result from the inaccuracies associated with predicting vapor-liquid equilibrium using group contribution methods such as UNIFAC. The unsteady state nature of batch distillation translates these static uncertainties into time-dependent uncertainties. A new Ito process representation is proposed for the dynamic behavior of relative volatility for non-ideal mixtures. Numerical case studies are presented to demonstrate the usefulness of this approach for batch as well as bio-processing

Overall Survival according to patient characteristics and LPI.

<p><i>LPI</i> laboratory prognostic index, <i>ECOG</i> Eastern Cooperative Oncology Group, <i>PS</i> performance status.</p><p>Overall Survival according to patient characteristics and LPI.</p

Results of univariate and multivariate Cox's proportional hazard models regarding OS.

<p><i>OS</i> overall survival, <i>HR</i> hazard ratio, <i>CI</i> confidence interval, <i>LPI</i> laboratory prognostic index, <i>ECOG</i> Eastern Cooperative Oncology Group, <i>PS</i> performance status, <i>WBC</i> White Blood Cell count, <i>LDH Lactate dehydrogenase, ALP</i> Alkaline phosphatase.</p><p>Results of univariate and multivariate Cox's proportional hazard models regarding OS.</p

Progression-free survival of patients according to LPI.

<p>Progression-free survival of patients according to LPI.</p