A two-dimensional mathematical model was developed to study competitive adsorption of n-component mixtures in a fixed-bed adsorber. The model consists of an isotherm equation to predict adsorption equilibria of n-component volatile organic compounds (VOCs) mixture from single component isotherm data, and a dynamic adsorption model, the macroscopic mass, energy and momentum conservation equations, to simulate the competitive adsorption of the n-components onto a fixed-bed of adsorbent. The model was validated with experimentally measured data of competitive adsorption of binary and eight-component VOCs mixtures onto beaded activated carbon (BAC). The mean relative absolute error (MRAE) was used to compare the modeled and measured breakthrough profiles as well as the amounts of adsorbates adsorbed. For the binary and eight-component mixtures, the MRAE of the breakthrough profiles was 13 and 12%, respectively, whereas, the MRAE of the adsorbed amounts was 1 and 2%, respectively. These data show that the model provides accurate prediction of competitive adsorption of multicomponent VOCs mixtures and the competitive adsorption isotherm equation is able to accurately predict equilibrium adsorption of VOCs mixtures.
A two-dimensional heterogeneous computational fluid dynamics model was developed and validated to study the mass, heat, and momentum transport in a fixed-bed cylindrical adsorber during the adsorption of volatile organic compounds (VOCs) from a gas stream onto a fixed bed of beaded activated carbon (BAC). Experimental validation tests revealed that the model predicted the breakthrough curves for the studied VOCs (acetone, benzene, toluene, and 1,2,4-trimethylbenzene) as well as the pressure drop and temperature during benzene adsorption with a mean relative absolute error of 2.6, 11.8, and 0.8%, respectively. Effects of varying adsorption process variables such as carrier gas temperature, superficial velocity, VOC loading, particle size, and channelling were investigated. The results obtained from this study are encouraging because they show that the model was able to accurately simulate the transport processes in an adsorber and can potentially be used for enhancing absorber design and operation.
For the efficient real-time monitoring of reaction chemistry in a complex mixture using online spectroscopy, it is essential to develop a mathematical tool that can automatically resolve the spectra so that either the spectral or the concentration profile of the changing species can be tracked easily. While self-modeling multivariate curve resolution (SMCR) is a well-suited tool when initial profiles are known beforehand, it is not straightforward to use when dealing with complex mixtures. In this study, a multivariate data analysis algorithm was designed for use with online infrared spectroscopy to provide an instant best estimate of the reaction chemistry of a complex mixture with no additional user input. The investigated process is thermal conversion of oil sands bitumen, and the study employed 43 infrared spectra from samples, collected offline, of products treated at different temperatures and time periods. The resolved spectral and concentration profiles can be used to understand the reaction mechanism of the system. In addition to the concentration and spectral profile, simple parameters were devised to monitor the changes in the key regions of the spectral profiles. In general, the results described the possible reaction mechanism of the investigated system and were consistent with other experimental findings in the literature. Computationally, the algorithm requires only a few seconds to converge and is therefore suitable for online monitoring.
We present a data-driven approach to identifying the reaction network of the dominant chemistry in complex mixtures using model compounds representative of cellulose and lignin chemistry that are processed using hydrous pyrolysis. We present two methods for the identification of pseudocomponents: self-modeling multivariate curve resolution, which is a non-negative matrix factorization method, and Bayesian hierarchical clustering. The pseudocomponents are identified from spectroscopic data from two sources: Fourier transform infrared spectroscopy and 1H NMR spectroscopy. The data from the two sources is combined using a simple data combination method. Once pseudocomponents have been identified, Bayesian networks are used to identify directed pathways between the components, resulting in a proposed hypothesis for the reaction network or mechanism. We validate the methods by showing consistency of the derived reaction networks with the known chemistry of cellulose, lignin, and their derivatives and demonstrate the importance of data fusion in developing believable reaction networks.
A data-mining and Bayesian learning approach is used to model the reaction network of a low-temperature (150–400 °C) visbreaking process for field upgrading of oil sands bitumen. Obtaining mechanistic and kinetic descriptions for the chemistry involved in this process is a significant challenge because of the compositional complexity of bitumen and the associated analytical challenges. Lumped models based on a preconceived reaction network might be unsatisfactory in describing the key conversion steps of the actual process. Fourier transform infrared spectra of products produced at different operating conditions (temperature and time of processing) of the visbreaking process were collected. Bayesian agglomerative hierarchical cluster analysis was employed to obtain groups of pseudospecies with similar spectroscopic properties. Then, a Bayesian structure-learning algorithm was used to develop the corresponding reaction network. The final reaction network model was compared to the anticipated reaction network of thermal cracking of a model alkyl tricyclic naphthenoaromatic compound, and the agreement was encouraging. The reaction model also indicates that the outcome of thermal processing is the increase in lighter and more aliphatic products, which is consistent with experimental findings. Pseudokinetics were obtained for the reactions between the pseudospecies based on the estimated parameters of the Bayesian network. An attractive feature of the model is that it can be embedded into a process control system to perform real-time online analysis of the reactions both qualitatively and quantitatively.
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