Assessing the Effect of Variable Ambient Temperature on the Self-ignition of a Reaction-diffusion System Employing a Reduced Order Modelling Methodology

The system under study in this work is a self-igniting pile of solid material. To predict and understand the effect of steep changes of the state variables on such systems, a reaction-diffusion model is employed. These systems can exhibit complex oscillatory behaviour, and changes in ambient conditions over time may strongly impact the inherent oscillations. To simulate the unsteady evolution of the pile, both a classical numerical technique (method of lines) and a reduced order approach are employed in combination with a stiff ODE solver. To account for circadian fluctuations in temperature, time-variable boundary conditions are assumed upon formulating the problem. The reduced order model is introduced in view of understanding if an approximated formulation characterized by a much lower number of state variables can accurately predict the complex behaviour of the system even in the case of sudden, steep variations of the values of the state variables due to the phenomenon of self-ignition, intensified here by variable boundary conditions. The selected case studies have the goal of exploring the effect of stockpile properties on the self-ignition phenomenon. Numerical solutions show the anticipated coupling between the system intrinsic dynamics and the oscillating temperature imposed at the boundary. All of the analysed cases are accurately replicated by the reduced order model

Dynamical and technological consequences of multiple isolas of steady states in a catalytic fluidised-bed reactor

Steady-state characteristics of a catalytic fluidised bed reactor and its dynamical consequences are analyzed. The occurrence of an untypical steady-state structure manifesting in a form of multiple isolas is described. A two-phase bubbling bed model is used for a quantitative description of the bed of catalyst. The influence of heat exchange intensity and a fluidisation ratio onto the generation of isolated solution branches is presented for two kinetic schemes. Dynamical consequences of the coexistence of such untypical branches of steady states are presented. The impact of linear growth of the fluidisation ratio and step change of the cooling medium temperature onto the desired product yield is analyzed. The results presented in this study confirm that the identification of a region of the occurrence of multiple isolas is important due to their strong impact both on the process start-up and its control

Intensification of Catalytic Processes through the Pellet Structuring: Steady-State Properties of a Bifunctional Catalyst Pellet Applied to Generic Chemical Reactions and the Direct Synthesis of DME

Structuring of different types of catalytic active centers at a single-pellet level appears to be a promising and powerful tool for integration and intensification of multistep solid-catalyzed chemical reactions. However, the enhancement in the product yield and selectivity strongly depends on the proper choice of the distribution of different catalysts within the pellet. To demonstrate potential benefits from properly designed catalyst pellet, numerical studies were conducted with the aid of the mathematical model of a single spherical bifunctional catalyst pellet. The analysis was performed both for a system of two generic chemical reactions and for a real process, i.e., direct synthesis of dimethyl ether (DME) from synthesis gas via methanol. Evaluation of the pellet performance was done for three arrangements of the catalytic active sites within the pellet, i.e., a uniform distribution of two types of catalytic active centers in the entire volume of the pellet, and two core–shell structures. It was demonstrated that, especially for the larger pellets typical for fixed-bed applications, the product yield might be significantly improved by selecting proper catalyst arrangements within the pellet

Sampling related issues in pod-based model reduction of simplified circulating fluidised bed combustor model

Over the last decades the method of proper orthogonal decomposition (POD) has been successfully employed for reduced order modelling (ROM) in many applications, including distributed parameter models of chemical reactors. Nevertheless, there are still a number of issues that need further investigation. Among them, the policy of the collection of representative ensemble of experimental or simulation data, being a starting and perhaps most crucial point of the POD-based model reduction procedure. This paper summarises the theoretical background of the POD method and briefly discusses the sampling issue. Next, the reduction procedure is applied to an idealised model of circulating fluidised bed combustor (CFBC). Results obtained confirm that a proper choice of the sampling strategy is essential for the modes convergence however, even low number of observations can be sufficient for the determination of the faithful dynamical ROM

Enhancement of the Direct Synthesis of Dimethyl Ether (DME) from Synthesis Gas by Macro- and Microstructuring of the Catalytic Bed

This work reports on a modelling study of the influence of the distribution of metallic and acidic active centers within a catalytic fixed-bed reactor for the direct synthesis of dimethyl ether (DME), conducted to demonstrate the potential of reactor-level and pellet-level structuring of catalytic active centers in process integration and intensification. To account for the pellet structure, the analysis was performed with the aid of a heterogeneous model considering both interphase and intrapellet mass transport resistances. The study evaluated, in terms of DME and methanol yield and selectivity, the performance of a tubular reactor loaded with a physical mixture of monofunctional catalyst pellets or structured bifunctional catalyst pellets with different arrangements of the catalytic centers. It was confirmed that bifunctional catalysts overperform significantly a physical mixture of monofunctional particles. Moreover, it was shown that the internal structure of a bifunctional catalyst pellet is an important feature that deserves to be exploited deeper, in view of further intensification of the DME synthesis process to be achieved with a better reactor design

Application of Pseudohomogeneous and Heterogeneous Models in Assessing the Behavior of a Fluidized-Bed Catalytic Reactor

Comparative analysis of the steady-state and transient properties of a bubbling fluidized-bed catalytic reactor obtained according to different mathematical models of the emulsion zone was performed to verify the commonly used assumption regarding the pseudohomogeneous nature of this zone. Four different mathematical models of the fluidized-bed reactor dynamics were formulated, based on different thermal and diffusional conditions at the gas-solid interface and within the catalyst pellet, namely the model based on the assumption of pseudohomogeneous character for the emulsion zone, and a group of two-scale models accounting for the heterogeneous character of this zone. It was demonstrated that, while the pseudohomogeneous model of the emulsion zone predicts almost identical behavior of the reactor at steady-state as the proposed heterogeneous models, it may fail in the prediction of the reactor start-up behavior, especially when dealing with highly exothermic processes run at relatively high fluidization velocity

Phenomenological and numerical issues concerning dynamics of nonisobaric multicomponent diffusion of gases in macroporous media

The homogeneity of an immiscible liquid–liquid system was investigated in a baffled vessel agitated by a Rushton turbine. The dispersion homogeneity was analyzed by comparing Sauter mean diameters and drop size distribution (DSD) determined in different measured regions for various impeller speeds. The sizes of droplets were obtained by the in-situ measurement technique and by the Image Analysis (IA) method. Dispersion kinetics was successfully fitted with Hong and Lee (1983) model. The effect of intermittency turbulence on drop size reported by Bałdyga and Podgórska (1998) was analyzed and the multifractal exponent was evaluated