GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

A quasi-elastic aquifer deformational behavior: Madrid aquifer case study

The purpose of this paper is to analyze the quasi-elastic deformational behavior that has been induced by groundwater withdrawal of the Tertiary detrital aquifer of Madrid (Spain). The spatial and temporal evolution of ground surface displacement was estimated by processing two datasets of radar satellite images (SAR) using Persistent Scatterer Interferometry (PSI). The first SAR dataset was acquired between April 1992 and November 2000 by ERS-1 and ERS-2 satellites, and the second one by the ENVISAT satellite between August 2002 and September 2010. The spatial distribution of PSI measurements reveals that the magnitude of the displacement increases gradually towards the center of the well field area, where approximately 80 mm of maximum cumulated displacement is registered. The correlation analysis made between displacement and piezometric time series provides a correlation coefficient greater than 85% for all the wells. The elastic and inelastic components of measured displacements were separated, observing that the elastic component is, on average, more than 4 times the inelastic component for the studied period. Moreover, the hysteresis loops on the stress–strain plots indicate that the response is in the elastic range. These results demonstrate the quasi-elastic behavior of the aquifer. During the aquifer recovery phase ground surface uplift almost recovers from the subsidence experienced during the preceding extraction phase. Taking into account this unique aquifer system, a one dimensional elastic model was calibrated in the period 1997–2000. Subsequently, the model was used to predict the ground surface movements during the period 1992–2010. Modeled displacements were validated with PSI displacement measurements, exhibiting an error of 13% on average, related with the inelastic component of deformation occurring as a long-term trend in low permeability fine-grained units. This result further demonstrates the quasi-elastic deformational behavior of this unique aquifer system.