RESUMEN
This research focuses on the development of a state observer for performing indirect measurements of the main variables involved in the soybean oil transesterification reaction with a guishe biochar-based heterogeneous catalyst; the studied reaction takes place in a batch reactor. The mathematical model required for the observer design includes the triglycerides' conversion rate, and the reaction temperature. Since these variables are represented by nonlinear differential equations, the model is linearized around an operation point; after that, the pole placement and linear quadratic regulator (LQR) methods are considered for calculating the observer gain vector L(x). Then, the estimation of the conversion rate and the reaction temperature provided by the observer are used to indirectly measure other variables such as esters, alcohol, and byproducts. The observer performance is evaluated with three error indexes considering initial condition variations up to 30%. With both methods, a fast convergence (less than 3 h in the worst case) of the observer is remarked.
RESUMEN
Most conventional methods to remove heavy metals from water are efficient for high concentrations, but they are expensive, produce secondary pollution, and cannot remove low concentrations. This paper proposes a biological system to remove Cr(VI) from aqueous solutions; the biofilter is composed of a native Pseudomonas koreensis immobilized in calcium alginate beads. Lab experiments were conducted in batch reactors, considering different operating conditions: Cr(VI) concentration, temperature, pH, and time. At 30 °C and a pH of 6.6, the immobilized bacteria achieved their optimal adsorption capacity. In the chromium adsorption system, saturation was reached at 30 h with a qmax = 625 mg g-1. By adjusting the experimental data to the Langmuir and Freundlich models, it is suggested that P. koreensis forms a biofilm with a homogeneous surface where Cr(VI) is adsorbed and that the bacteria also incorporates the metal in its metabolism, leading to a multilayer adsorption. On the other hand, using Fourier transform infrared spectroscopy, it was inferred that the functional groups involved in the adsorption process were O-H and C=O, which are a part of the P. koreensis cell wall.
