Estimation of catalyst activity profiles and deactivation parameters from reactor operating data with applications to naphtha reforming

Techniques are developed for estimating activity profiles in fixed bed reactors and catalyst deactivation parameters from operating reactor data. These techniques are applicable, in general, to most industrial catalytic processes. The catalytic reforming of naphthas is taken as a broad example to illustrate the estimation schemes and to signify the physical meaning of the kinetic parameters of the estimation equations. The work is described in two parts. Part I deals with the modeling of kinetic rate expressions and the derivation of the working equations for estimation. Part II concentrates on developing various estimation techniques.

Part I: The reactions used to describe naphtha reforming are dehydrogenation and dehydroisomerization of cycloparaffins; isomerization, dehydrocyclization and hydrocracking of paraffins; and the catalyst deactivation reactions, namely coking on alumina sites and sintering of platinum crystallites. The rate expressions for the above reactions are formulated, and the effects of transport limitations on the overall reaction rates are discussed in the appendices. Moreover, various types of interaction between the metallic and acidic active centers of reforming catalysts are discussed as characterizing the different types of reforming reactions.

Part II: In catalytic reactor operation, the activity distribution along the reactor determines the kinetics of the main reaction and is needed for predicting the effect of changes in the feed state and the operating conditions on the reactor output. In the case of a monofunctional catalyst and of bifunctional catalysts in limiting conditions, the cumulative activity is sufficient for predicting steady reactor output. The estimation of this cumulative activity can be carried out easily from measurements at the reactor exit. For a general bifunctional catalytic system, the detailed activity distribution is needed for describing the reactor operation, and some approximation must be made to obtain practicable estimation schemes. This is accomplished by parametrization techniques using measurements at a few points along the reactor. Such parametrization techniques are illustrated numerically with a simplified model of naphtha reforming.

To determine long term catalyst utilization and regeneration policies, it is necessary to estimate catalyst deactivation parameters from the the current operating data. For a first order deactivation model with a monofunctional catalyst or with a bifunctional catalyst in special limiting circumstances, analytical techniques are presented to transform the partial differential equations to ordinary differential equations which admit more feasible estimation schemes. Numerical examples include the catalytic oxidation of butene to butadiene and a simplified model of naphtha reforming. For a general bifunctional system or in the case of a monofunctional catalyst subject to general power law deactivation, the estimation can only be accomplished approximately. The basic feature of an appropriate estimation scheme involves approximating the activity profile by certain polynomials and then estimating the deactivation parameters from the integrated form of the deactivation equation by regression techniques. Different bifunctional systems must be treated by different estimation algorithms, which are illustrated by several cases of naphtha reforming with different feed or catalyst composition.

Estimation of the growth curve parameters in Macrobrachium rosenbergii

Growth is one of the most important characteristics of cultured species. The objective of this study was to determine the fitness of linear, log linear, polynomial, exponential and Logistic functions to the growth curves of Macrobrachium rosenbergii obtained by using weekly records of live weight, total length, head length, claw length, and last segment length from 20 to 192 days of age. The models were evaluated according to the coefficient of determination (R2), and error sum off square (ESS) and helps in formulating breeders in selective breeding programs. Twenty full-sib families consisting 400 PLs each were stocked in 20 different hapas and reared till 8 weeks after which a total of 1200 animals were transferred to earthen ponds and reared up to 192 days. The R2 values of the models ranged from 56 – 96 in case of overall body weight with logistic model being the highest. The R2 value for total length ranged from 62 to 90 with logistic model being the highest. In case of head length, the R2 value ranged between 55 and 95 with logistic model being the highest. The R2 value for claw length ranged from 44 to 94 with logistic model being the highest. For last segment length, R2 value ranged from 55 – 80 with polynomial model being the highest. However, the log linear model registered low ESS value followed by linear model for overall body weight while exponential model showed low ESS value followed by log linear model in case of head length. For total length the low ESS value was given by log linear model followed by logistic model and for claw length exponential model showed low ESS value followed by log linear model. In case of last segment length, linear model showed lowest ESS value followed by log linear model. Since, the model that shows highest R2 value with low ESS value is generally considered as the best fit model. Among the five models tested, logistic model, log linear model and linear models were found to be the best models for overall body weight, total length and head length respectively. For claw length and last segment length, log linear model was found to be the best model. These models can be used to predict growth rates in M. rosenbergii. However, further studies need to be conducted with more growth traits taken into consideration

Estimation of long-run parameters in unbalanced cointegration

This paper analyses the asymptotic properties of nonlinear least squares estimators of the long run parameters in a bivariate unbalanced cointegration framework. Unbalanced cointegration refers to the situation where the integration orders of the observables are different, but their corresponding balanced versions (with equal integration orders after filtering) are cointegrated in the usual sense. Within this setting, the long run linkage between the observables is driven by both the cointegrating parameter and the difference between the integration orders of the observables, which we consider to be unknown. Our results reveal three noticeable features. First, superconsistent (faster than √ n-consistent) estimators of the difference between memory parameters are achievable. Next, the joint limiting distribution of the estimators of both parameters is singular, and, finally, a modified version of the ‘‘Type II’’ fractional Brownian motion arises in the limiting theory. A Monte Carlo experiment and the discussion of an economic example are included.

Oxidation of several p-phenylenediamines in room temperature ionic liquids: Estimation of transport and electrode kinetic parameters

The electrochemical oxidation of N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) has been studied by cyclic voltammetry and potential step chronoamperometry at 303 K in five ionic liquids, namely [C(2)mim] [NTf2], [C(4)mim] [NTf2] [C(4)mpyrr] [NTf2] [C(4)mim] [BF4], and [C(4)mim] [PF6] (where [C(n)mim](+) = 1-alkyl-3-methylimidazolium, [C(4)mpyrr](+) = N-butyl-N-methylpyrrolidinium, [NTf2](-) = bis(trifluoromethylsulfonyl)imide, [BF4](-) = tetrafluoroborate, and [PF6](-) = hexafluorophosphate). Diffusion coefficients, D, of 4.87, 3.32, 2.05, 1.74, and 1.34 x 10(-11) m(2) s(-1) and heterogeneous electron-transfer rate constants, k(0), of 0.0109, 0.0103, 0.0079, 0.0066, and 0.0059 cm s(-1) were calculated for TMPD in [C(2)mim] [NTf2], [C(4)mim] [NTf2], [C(4)mpyrr] [NTf2], [C(4)mim] [BF4], and [C(4)mim] [PF6], respectively, at 303 K. The oxidation of TMPD in [C4mim][PF6] was also carried out at increasing temperatures from 303 to 343 K, with an activation energy for diffusion of 32.3 kJ mol(-1). k(0) was found to increase systematically with increasing temperature, and an activation energy of 31.4 kJ mol(-1) was calculated. The study was extended to six other p-phenylenediamines with alkyl/phenyl group substitutions. D and k(0) values were calculated for these compounds in [C(2)mim] [NTf2], and it was found that k(0) showed no obvious relationship with the hydrodynamic radius, r.

Estimation of Clarinet Reed Parameters by Inverse Modelling

Analysis of the acoustical functioning of musical instruments invariably involves the estimation of model parameters. The broad aim of this paper is to develop methods for estimation of clarinet reed parameters that are representative of actual playing conditions. This presents various challenges because of the di?culties of measuring the directly relevant variables without interfering with the control of the instrument. An inverse modelling approach is therefore proposed, in which the equations governing the sound generation mechanism of the clarinet
are employed in an optimisation procedure to determine the reed parameters from the mouthpiece pressure and volume ?ow signals. The underlying physical model captures most of the reed dynamics and is simple enough to be used in an inversion process. The optimisation procedure is ?rst tested by applying it to numerically synthesised signals, and then applied to mouthpiece signals acquired during notes blown by a human player. The proposed inverse modelling approach raises the possibility of revealing information about the way in which the embouchure-related reed parameters are controlled by the player, and also facilitates physics-based re-synthesis of clarinet sounds.

DiveRsity: An R package for the estimation and exploration of population genetics parameters and their associated errors

Summary: We present a new R package, diveRsity, for the calculation of various diversity statistics, including common diversity partitioning statistics (?, G) and population differentiation statistics (D, GST ', ? test for population heterogeneity), among others. The package calculates these estimators along with their respective bootstrapped confidence intervals for loci, sample population pairwise and global levels. Various plotting tools are also provided for a visual evaluation of estimated values, allowing users to critically assess the validity and significance of statistical tests from a biological perspective. diveRsity has a set of unique features, which facilitate the use of an informed framework for assessing the validity of the use of traditional F-statistics for the inference of demography, with reference to specific marker types, particularly focusing on highly polymorphic microsatellite loci. However, the package can be readily used for other co-dominant marker types (e.g. allozymes, SNPs). Detailed examples of usage and descriptions of package capabilities are provided. The examples demonstrate useful strategies for the exploration of data and interpretation of results generated by diveRsity. Additional online resources for the package are also described, including a GUI web app version intended for those with more limited experience using R for statistical analysis. © 2013 British Ecological Society.

Molecular pedigree reconstruction and estimation of evolutionary parameters in a wild Atlantic salmon river system with incomplete sampling: a power analysis

Background: Pedigree reconstruction using genetic analysis provides a useful means to estimate fundamental population biology parameters relating to population demography, trait heritability and individual fitness when combined with other sources of data. However, there remain limitations to pedigree reconstruction in wild populations, particularly in systems where parent-offspring relationships cannot be directly observed, there is incomplete sampling of individuals, or molecular parentage inference relies on low quality DNA from archived material. While much can still be inferred from incomplete or sparse pedigrees, it is crucial to evaluate the quality and power of available genetic information a priori to testing specific biological hypotheses. Here, we used microsatellite markers to reconstruct a multi-generation pedigree of wild Atlantic salmon (Salmo salar L.) using archived scale samples collected with a total trapping system within a river over a 10 year period. Using a simulation-based approach, we determined the optimal microsatellite marker number for accurate parentage assignment, and evaluated the power of the resulting partial pedigree to investigate important evolutionary and quantitative genetic characteristics of salmon in the system.

Results: We show that at least 20 microsatellites (ave. 12 alleles/locus) are required to maximise parentage assignment and to improve the power to estimate reproductive success and heritability in this study system. We also show that 1.5 fold differences can be detected between groups simulated to have differing reproductive success, and that it is possible to detect moderate heritability values for continuous traits (h(2) similar to 0.40) with more than 80% power when using 28 moderately to highly polymorphic markers.

Conclusion: The methodologies and work flow described provide a robust approach for evaluating archived samples for pedigree-based research, even where only a proportion of the total population is sampled. The results demonstrate the feasibility of pedigree-based studies to address challenging ecological and evolutionary questions in free-living populations, where genealogies can be traced only using molecular tools, and that significant increases in pedigree assignment power can be achieved by using higher numbers of markers.

Channel estimation and parameters acquisition systems employing cooperative diversity

This work investigates new channel estimation schemes for the forthcoming and future generation of cellular systems for which cooperative techniques are regarded. The studied cooperative systems are designed to re-transmit the received information to the user terminal via the relay nodes, in order to make use of benefits such as high throughput, fairness in access and extra coverage. The cooperative scenarios rely on OFDM-based systems employing classical and pilot-based channel estimators, which were originally designed to pointto-point links. The analytical studies consider two relaying protocols, namely, the Amplifyand-Forward and the Equalise-and-Forward, both for the downlink case. The relaying channels statistics show that such channels entail specific characteristics that comply to a proper filter and equalisation designs. Therefore, adjustments in the estimation process are needed in order to obtain the relay channel estimates, refine these initial estimates via iterative processing and obtain others system parameters that are required in the equalisation. The system performance is evaluated considering standardised specifications and the International Telecommunication Union multipath channel models.

Learning-Based Approach to Estimation of Morphable Model Parameters

We describe the key role played by partial evaluation in the Supercomputing Toolkit, a parallel computing system for scientific applications that effectively exploits the vast amount of parallelism exposed by partial evaluation. The Supercomputing Toolkit parallel processor and its associated partial evaluation-based compiler have been used extensively by scientists at MIT, and have made possible recent results in astrophysics showing that the motion of the planets in our solar system is chaotically unstable.

Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.