Eliseo Hernandez-Martinez

Facies Recognition Using Multifractal Hurst Analysis: Applications to Well-Log Data

Well-log (radioactivity, density and resistivity) analysis constitutes a standard approach for inferring lithology from wells. However, due to inherent complexity of the signals (such as highly heterogeneous deep-water sedimentary sequences) lithology recognition is not straightforward. We used a rescaled range analysis, calibrated with cores, to recognize lithological patterns from signal recorded along wireline logs. The detected intervals coincide with zones of visual electro-facies associations proposed by geologist well-log interpreters. In addition, we propose a rescaled range multifractal analysis to identify ranges of well-log signal complexities, which could be related to sedimentary process variations at specific stratigraphic order cycles.

Monitoring anaerobic sequential batch reactors via fractal analysis of pH time series

Efficient monitoring and control schemes are mandatory in the current operation of biological wastewater treatment plants because they must accomplish more demanding environmental policies. This fact is of particular interest in anaerobic digestion processes where the availability of accurate, inexpensive, and suitable sensors for the on‐line monitoring of key process variables remains an open problem nowadays. In particular, this problem is more challenging when dealing with batch processes where the monitoring strategy has to be performed in finite time, which limits the application of current advanced monitoring schemes as those based in the proposal of nonlinear observers (i.e., software sensors). In this article, a fractal time series analysis of pH fluctuations in an anaerobic sequential batch reactor (AnSBR) used for the treatment of tequila vinasses is presented. Results indicated that conventional on‐line pH measurements can be correlated with off‐line determined key process variables, such as COD, VFA and biogas production via some fractality indexes. Biotechnol. Bioeng. 2013; 110: 2131–2139.

An Integral High-Order Sliding Mode Control Approach for Stick-Slip Suppression in Oil Drillstrings

Abstract In this paper a novel sliding mode control law combined with a cascade control scheme is proposed for the suppression of stick-slip oscillations in oil drillstrings. It is assumed that the parameters of the system are uncertain and external disturbances are present. Numerical simulations on a generic simple model of stick-slip oscillations are provided to illustrate the control performance.

Letter to the editor: A Green's function formulation of nonlocal finite-difference schemes for reaction-diffusion equations

Reaction-diffusion equations are commonly used in different science and engineering fields to describe spatial patterns arising from the interaction of chemical or biochemical reactions and diffusive transport mechanisms. The aim of this work is to show that a Greens function formulation of reaction-diffusion PDEs is a suitable framework to derive FD schemes incorporating both O(h^2) accuracy and nonlocal approximations in the whole domain (including boundary nodes). By doing so, the approach departs from a Greens function formulation of the boundary-value problem to pose an approximation problem based on a domain decomposition. Within each subdomain, the corresponding integral equation is forced to have zero residual at given grid points. Different FD schemes are obtained depending on the numerical scheme used for computing the Greens integral over each subdomain. Dirichlet and Neumann boundary conditions are considered, showing that the FD scheme based on the Greens function formulation incorporates, in a natural way, the effects of boundary nodes in the discretization approximation.

A Green's function approach for the numerical solution of a class of fractional reaction-diffusion equations

Reaction-diffusion equations with spatial fractional derivatives are increasingly used in various science and engineering fields to describe spatial patterns arising from the interaction of chemical or biochemical reactions and anomalous diffusive transport mechanisms. Most numerical schemes to solve fractional reaction-diffusion equations use finite difference schemes based on the Grunwald-Letnikov formula. This work introduces a new systematic approach based on Greens function formulations to obtain numerical schemes for fractional reaction-diffusion equations. The idea is to pose an integral formulation of the equation in terms of the underlying Greens function of the fractional operator to subsequently use numerical quadrature to obtain a set of ordinary differential equations. To illustrate the numerical accuracy of the method, dynamic and steady-state situations are considered and compared with analytical and numerical solutions via Grunwald finite differences schemes. Numerical simulations show that the scheme proposed improves the performance and convergence of traditional finite differences schemes based on Grunwald formula. Numerical solutions of fractional RD systems are given using Greens function formulations.The scheme proposed exhibit global approximation orders of O ( h α ) .Proposed scheme exhibit better numerical approximation than traditional schemes.

An Integral Formulation Approach for Numerical Solution of Tubular Reactors Models

In this paper, we derive an integral formulation approach based on Green’s function for the numerical solution of tubular reactor models described by reaction-diffusion-convection (RDC) equations with Danckwerts-type boundary conditions. The integral formulation approach allows the direct incorporation of boundary conditions and leads to a stable and accurate numerical integration with smooth round-off error. Numerical simulations of two of tubular reactors models are presented in order to illustrate the numerical accuracy of the method. The results are compared with those resulting from using standard finite difference method. Our results show that the integral formulation approach improves the performance of classical FD schemes.

Dynamic Effectiveness Factor for Catalytic Particles with Anomalous Diffusion

Abstract The effectiveness factor (EF) is a useful tool for the study of heterogeneous reaction systems, such as catalytic particles, where interactions of reaction-diffusion processes are involved. For simplicity, the study of EF is achieved on steady state operation (SSEF), but recent studies have suggested that EF can increase on dynamic operation conditions, especially when diffusive transport does not follow the Fick’s law. In this paper, a study about the effect of anomalous diffusion on the dynamic effectiveness factor (DEF) in catalytic particles is presented. For this, it is considered a generalized Cattaneo-type diffusion model described by differential equations of fractional order applied at rectangular, cylindrical and spherical geometries of the catalytic particles, which is analyzed in the frequency space by means the Fourier transform method. Numerical results, based on Bode and Nyquist diagrams, show the conditions and regions where the DEF values are largest than SSEF.

Cascade Control Scheme for Tubular Reactors with Multiple Temperature Measurements

In this work, we introduce a new structure for cascade control scheme based on a weighted average temperature of three-temperature measurement distributed along the axial position of the tubular reactor. The control configuration exploits the information provided by two additional temperature sensors located close to the feed and the output positions of the tubular reactor. The configuration with the averaged temperature improves the behavior of the classical cascade control scheme by enhancing the disturbance rejection. Numerical simulations of two axial dispersion models of tubular reactors are used to illustrate and compare the control performance.

SPATIOTEMPORAL DYNAMICS OF TELEGRAPH REACTION-DIFFUSION PREDATOR-PREY MODELS

Reaction-diffusion (RD) equations are commonly used to describe the propagation effects in population interactions in ecology. RD system are described by parabolic partial differential equations (PDE), based on the Fick diffusion equation, hence arbitrary large population speeds are involved. To avoid this unrealistic situation, we introduce the Cattaneo’s diffusion in a spatiotemporal models of preypredator interactions, which leads to more realistic and interesting interactions between populations and can be useful to gain insights to the understanding of food-chain dynamics. The resulting model is the so-called telegraph RD model. Numerical simulations on predator-prey model with Holling type II functional response and cross-diffusion show the effects of the relaxation time in the dynamic of population interactions.

CONTROL OF COUPLED CIRCADIAN OSCILLATORS

Abstract Circadian rhythms are endogenous rhythms in physiology or behavior with a cycle length near 24 hours. Circadian rhythms are relevant for many key physiological functions. The periodic light-dark cycle is the dominant environmental synchronizer used to entrain a population of circadian oscillators. In this work we introduce a control approach for both suppression and synchronization of coupled circadian oscillators. The control scheme is based on a modeling error compensation approach. Numerical simulations shows the effectivity of the feedback control law for suppression and synchronization of an array of coupled circadian oscillators via a light-sensitive parameter.