Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Removal of paracetamol on biomass-derived activated carbon: Modeling the fixed bed breakthrough curves using batch adsorption experiments

The remediation of paracetamol (PA), an emerging contaminant frequently found in wastewater treatment plants, has been studied in the low concentration range (0.3–10 mg L−1) using as adsorbent a biomass-derived activated carbon. PA uptake of up to 100 mg g−1 over the activated carbon has been obtained, with the adsorption isotherms being fairly explained by the Langmuir model. The application of Reichemberg and the Vermeulen equations to the batch kinetics experiments allowed estimating homogeneous and heterogeneous diffusion coefficients, reflecting the dependence of diffusion with the surface coverage of PA. A series of rapid small-scale column tests were carried out to determine the breakthrough curves under different operational conditions (temperature, PA concentration, flow rate, bed length). The suitability of the proposed adsorbent for the remediation of PA in fixed-bed adsorption was proven by the high PA adsorption capacity along with the fast adsorption and the reduced height of the mass transfer zone of the columns. We have demonstrated that, thanks to the use of the heterogeneous diffusion coefficient, the proposed mathematical approach for the numerical solution to the mass balance of the column provides a reliable description of the breakthrough profiles and the design parameters, being much more accurate than models based in the classical linear driving force.