Characterization of the methanol recovery process at Prio Biocombustíveis S. A.

In a industrial environment, to know the process one is working with is crucial to ensure its good functioning. In the present work, developed at Prio Biocombustíveis S.A. facilities, using process data, collected during the present work, and historical process data, the methanol recovery process was characterized, having started with the characterization of key process streams. Based on the information retrieved from the stream characterization, Aspen Plus® process simulation software was used to replicate the process and perform a sensitivity analysis with the objective of accessing the relative importance of certain key process variables (reflux/feed ratio, reflux temperature, reboiler outlet temperature, methanol, glycerol and water feed compositions). The work proceeded with the application of a set of statistical tools, starting with the Principal Components Analysis (PCA) from which the interactions between process variables and their contribution to the process variability was studied. Next, the Design of Experiments (DoE) was used to acquire experimental data and, with it, create a model for the water amount in the distillate. However, the necessary conditions to perform this method were not met and so it was abandoned. The Multiple Linear Regression method (MLR) was then used with the available data, creating several empiric models for the water at distillate, the one with the highest fit having a R2 equal to 92.93% and AARD equal to 19.44%. Despite the AARD still being relatively high, the model is still adequate to make fast estimates of the distillate’s quality. As for fouling, its presence has been noticed many times during this work. Not being possible to directly measure the fouling, the reboiler inlet steam pressure was used as an indicator of the fouling growth and its growth variation with the amount of Used Cooking Oil incorporated in the whole process. Comparing the steam cost associated to the reboiler’s operation when fouling is low (1.5 bar of steam pressure) and when fouling is high (reboiler’s steam pressure of 3 bar), an increase of about 58% occurs when the fouling increases.

Regularity of Wiener-Hopf plus Hankel operators

In this thesis we consider Wiener-Hopf-Hankel operators with Fourier symbols in the class of almost periodic, semi-almost periodic and piecewise almost periodic functions. In the first place, we consider Wiener-Hopf-Hankel operators acting between L2 Lebesgue spaces with possibly different Fourier matrix symbols in the Wiener-Hopf and in the Hankel operators. In the second place, we consider these operators with equal Fourier symbols and acting between weighted Lebesgue spaces Lp(R;w), where 1 < p < 1 and w belongs to a subclass of Muckenhoupt weights. In addition, singular integral operators with Carleman shift and almost periodic coefficients are also object of study. The main purpose of this thesis is to obtain regularity properties characterizations of those classes of operators. By regularity properties we mean those that depend on the kernel and cokernel of the operator. The main techniques used are the equivalence relations between operators and the factorization theory. An invertibility characterization for the Wiener-Hopf-Hankel operators with symbols belonging to the Wiener subclass of almost periodic functions APW is obtained, assuming that a particular matrix function admits a numerical range bounded away from zero and based on the values of a certain mean motion. For Wiener-Hopf-Hankel operators acting between L2-spaces and with possibly different AP symbols, criteria for the semi-Fredholm property and for one-sided and both-sided invertibility are obtained and the inverses for all possible cases are exhibited. For such results, a new type of AP factorization is introduced. Singular integral operators with Carleman shift and scalar almost periodic coefficients are also studied. Considering an auxiliar and simpler operator, and using appropriate factorizations, the dimensions of the kernels and cokernels of those operators are obtained. For Wiener-Hopf-Hankel operators with (possibly different) SAP and PAP matrix symbols and acting between L2-spaces, criteria for the Fredholm property are presented as well as the sum of the Fredholm indices of the Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. By studying dependencies between different matrix Fourier symbols of Wiener-Hopf plus Hankel operators acting between L2-spaces, results about the kernel and cokernel of those operators are derived. For Wiener-Hopf-Hankel operators acting between weighted Lebesgue spaces, Lp(R;w), a study is made considering equal scalar Fourier symbols in the Wiener-Hopf and in the Hankel operators and belonging to the classes of APp;w, SAPp;w and PAPp;w. It is obtained an invertibility characterization for Wiener-Hopf plus Hankel operators with APp;w symbols. In the cases for which the Fourier symbols of the operators belong to SAPp;w and PAPp;w, it is obtained semi-Fredholm criteria for Wiener-Hopf-Hankel operators as well as formulas for the Fredholm indices of those operators.