Model Reduction for Nonlinear Systems with Distributed Parameters

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

The development of structure‐preserving approximation methods, which regard fundamental underlying physical principles, is an active field of research. Especially when the application of model reduction is desirable, systematic and rather generic approaches are of great interest. In this contribution we discuss a structure‐preserving Galerkin approach for a prototypical class of nonlinear partial differential equations on networks. Its derivation is guided by port‐Hamiltonian‐type modeling and appropriate variational principles. Also complexity‐reduction schemes can be integrated in a structure‐preserving way, which becomes crucial in the context of model reduction for nonlinear systems.

Hydrogenation of diethyl maleate in a fixed-bed catalytic reactor: kinetics, reactor modelling and pilot plant studies

Oxytetracycline removal and E. Coli inactivation by decomposition of hydrogen peroxide in a continuous fixed bed reactor using heterogeneous catalyst

Design guideline for CO2 to methanol conversion process supported by generic model of various bed reactors

A general linear controller design method for a class of hyperbolic partial differential equations (PDE's) systems is presented, which uses infinite-dimensional Hilbert state-space description. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem where one elementary reaction takes place. An optimal controller is designed for the linearized fixed-bed reactor model, it is applied to the nonlinear original model and the resulting closed-loop stability is analyzed.

Integral abutment bridges have been used in the United States for decades. By eliminating expensive expansion joints, the piles supporting the end bent accommodate the total thermal movement of the bridge. Currently, integral bridges are designed based upon experience, and a rational design specification has not been developed. Furthermore, the interaction of the abutment, pile, and soil remains uncertain. A better understanding regarding the behavior of this system is needed. The objective of this research is to evaluate the behavior of the integral abutment-pile system and evaluate any limitations of its use. To achieve this objective, two phases of research were conducted. The first phase was a field study that investigated the in-service pile behavior of four integral abutment bridges. The second phase was an experimental study that was used to evaluate the capability of piles typically used in integral abutment bridges. Nine low-cycle, large amplitude lateral displacement pile tests were conducted. Throughout both phases, analytical investigations were also conducted. To develop simplified modeling techniques that sufficiently account for soil-pile interaction, the piles supporting abutments were analytically modeled and calibrated based on the field and experimental results. A parametric study was also performed with variables including pile type, pile orientation, axial load, pile length, and soil type. The results of these phases were evaluated and design recommendations were developed based on these results. Overall, the design recommendations provide for an extension in the length limits often used for integral bridges. The extension of these limits can result in a reduction in bridge construction and maintenance costs for a large number of structures that cannot currently be built using this structural system.

Introduction The carbon/air secondary battery (CASB) system is a promising large-capacity energy storage technology [1]. The CASB system utilizes a redox reaction of C + O2 ⇄ CO2 by solid oxide fuel cells/electrolysis cells (SOFCs/SOECs), namely a combination of rechargeable direct carbon fuel cells [1, 2] and CO2 electrolysis cells. Carbon and liquid CO2 are stored in and outside SOFCs/SOECs respectively. The advantages of the CASB system are high theoretical efficiency of close to 100%, high volumetric energy density of 1625 Wh L-1 based on carbon and liquid CO2 (25oC, 6.4 MPa), and high safety due to unflammable CO2 storage. On the fuel electrode side, the electrochemical reaction of 2CO2 + 4e- ⇄ 2CO + 2O2- and the thermochemical (Boudouard) reaction of 2CO ⇄ C + CO2 proceed. On the air electrode side, the electrochemical reaction of 2O2- ⇄ O2 + 4e- proceeds. The previous study [3] demonstrated the reaction mechanism and the charging-discharging for 10 cycles without degradation. However, the carbon deposition on the triple phase boundary (TPB) made an overpotential increase, and there remains a risk of degradation of the fuel electrode in the long term. To suppress overpotential or to avoid degradation, the carbon deposition area is required to separate from TPB. There are two ways considered, namely development of materials and systems for the CASB. We recently demonstrated that two kinds of fuel electrodes with different catalytic abilities, e.g. Ce0.9Gd0.1O2-δ (GDC) fuel electrode and Ni/GDC catalyst section, successfully controlled carbon deposition on the catalyst section selectively [4]. Controlling temperature is another way of separating carbon deposition area from TPB because the Boudouard equilibrium gas composition changes significantly in the range of 500oC to 900oC (Fig. 1). The lower the temperature, the lower the equilibrium partial pressure of CO. Therefore, lowering the temperature of the catalyst section enables selective carbon deposition on the catalyst. In this study, the objective is to propose the carbon deposition area-separated type CASB system controlling temperature and to demonstrate its charging-discharging. Experimental The experimental setup was composed of a cell and a catalytic fixed-bed reactor. Ni/ GDC fuel electrodes were fabricated on an 8 mol% Y2O3 – stabilized ZrO2 disc electrolyte (20 mm diameter, 0.25 mm thickness). La0.8Sr0.2MnO3/10mol%Sc2O3-1mol%CeO2–ZrO2 air electrodes were fabricated on the counter sides. A catalyst for the Boudouard reaction was put in a quartz tube. The temperature of the cell and the catalytic reactor was controlled to be 900oC and 670oC. For charging, CO 40 sccm and CO2 10 sccm were supplied on the fuel electrode side, and the exhausted gas was supplied to the catalytic reactor. For discharging, CO2 10 sccm was supplied to the catalytic reactor, and the exhausted gas was supplied on the fuel electrode side. For both charging and discharging, O2 100 sccm was supplied on the air electrode side, and a current density of 100 mA cm-2 was applied for a couple of hours. Results and discussion Repetitive charging and discharging for a couple of hours were successfully demonstrated. The discharge capacity was above 300 mAh, which is more than 10 times larger than the previous demonstration of the carbon deposition area-integrated type CASB system [3]. Because only CO2 was supplied during the discharging, deposited carbon in the catalytic reactor was mainly used for the fuel. In addition, the partial pressure of CO in the space close to the cell during the charging was not enough for thermochemical carbon deposition. Those results show that lowering the temperature of the catalyst section successfully made selective carbon deposition on the catalyst. Conclusion In this study, the carbon deposition area-separated type CASB system was proposed and its repetitive charging and discharging was demonstrated. Lowering the temperature of the catalytic reactor to the SOFCs/SOECs enables selective carbon deposition in the catalytic reactor. Avoiding carbon deposition on the fuel electrodes can radically improve the stability of the CASB system in the long term.

The increased generation of renewable electricity (wind, solar), due to its fluctuating characteristic, leads to an increasing storage demand. A potential storage technology is the conversion of electrical energy into chemical energy (e.g. in form of gaseous hydrocarbons), which can be easily stored and distributed in an existing natural gas grid. CO2 is the C-source of choice, from biogas plants or industrial processes, making possible the production and use of C-based fuels without increasing the CO2 emissions into the atmosphere. The combination of Fischer–Tropsch synthesis and CO2 shift reaction, using iron-based catalyst, offers the possibility to produce substitute natural gas (SNG) components from CO2. Due to the fluctuating nature of hydrogen production from renewable electrical energy, advantages can be identified if the chemical reactor is operated under variable load conditions. The aim of the present study is to evaluate the flexibility of a catalytic synthesis reactor as a potential component in a future energy system with a high contribution of renewable energy. The hydrogenation of CO2 to gaseous components is studied in a fixed-bed lab-scale reactor to determine kinetic parameters and hydrocarbon product distribution. Results from the experimental work are implemented in the mathematical model and are the basis for the conceptual design of the catalytic fixed-bed reactor able to operate under variable load conditions.

A two-dimensional fixed-bed catalytic reactor model for acrolein production has been developped. The reactor and kinetic models have been identified by using both laboratory-scale and pilot-scale measurements. Many operating conditions such as coolant temperature, feeding rate, inlet pressure and temperature have great influence on the yield of acrolein and also on the bed temperature which are two very important parameters. More specifically, the coolant temperature and feeding rate are the two most important parameters for the acrolein production. With a set of different feed rates, the coolant temperature and the reactor inlet temperature were optimized to maximise the yield of acrolein for a given reactor length and inlet pressure. There was an optimal feeding rate for the maximum yield of acrolein. The study of the influence of number of the cooling sections with different temperatures shows that there was no significant improvement in the yield of acrolein.

Manipulation of the catalyst surface coverage for improved conversion and selectivity substantially requires more frequent flow reversals than the classical reverse flow operation for energy saving does (Chapter 1). 2.A reverse flow reactor should be operated at comparable switching time and residence time in order to manipulate the reactor's selectivity (Chapter 3).3. The concept of reverse flow operation with concentration programming provides an engineering tool to control conversion and selectivity, with three benefits: ammonia feedstock savings, increased ammonia conversion, and increased selectivity to NO; a drawback is the decrease of production rate (Chapter 4).4. The concept of reverse flow operation with reactor side feeding shows a fourfold superior performance: higher conversion of ammonia, higher selectivity to NO, no dead gas volume, and high production rate (Chapter 5).5. Intensification of a university study program must assure that the students' residence time distribution for completing their study follows a plug flow model.6.The concept of periodic reactor operation is natural.7. So called relaxation oscillation occurs when the cycling time period is much less than the system's time constant.However, this is not the case during reverse flow operation when operating the reactor at extremely short cycling time.8. The porosity of a fixed bed can be determined elegantly by a combination of reverse flow operation and cycling of the feed concentration.9. Joint bachelor-master-doctor programs improve the selectivity to master and doctor degrees as well as the productivity of a university.10. Assalamu'alaikum is a time-independent greeting.

Experimental and analytical investigations on the catalytic oxidation of formaldehyde were carried out. Experiments were conducted in the catalytic reactor by changing parameters such as the concentration of coexisting NO, the type of noble metal and the amount of loaded noble metal. The experimental results showed that the presence of NO in the reaction gas affects the formaldehyde oxidation characterisics and the phenomenon of physical adsorption strongly appears in the low-temperature region. By consideration of this physical adsorption, formaldehyde removal rates in a catalytic reactor were predicted. The evaluation indicated that a satisfactory agreement between the predicted and experimental data is obtained when physical adsorption is considered.

Enhancement of pure hydrogen production through the use of a membrane reactor

In this paper the influence of the active catalyst location in a pellet on fixed-bed catalytic reactor performance is described. The optimal activity distribution as a function of an economic parameter (ratio of product and catalyst costs), Thiele modulus and Damkohler number is estimated.

A fixed bed reactor was designed, modeled and simulated for hydrogen storage on-board the vehicle for PEM fuel cell applications. Ammonia borane was selected by DOE’s Hydrogen Storage Engineering Center of Excellence as the initial chemical hydride of study because of its high hydrogen storage capacity (up to ∼16% by weight for the release of ∼2.5 molar equivalents of hydrogen gas) and its stability under typical ambient conditions. The design evaluated consisted of a tank with eight thermally isolated sections in which H2 flows freely between sections to provide ballast. Heating elements are used to initiate reactions in each section when pressure drops below a specified level in the tank. Reactor models in Excel and COMSOL were developed to demonstrate the proof-of-concept, which was then used to develop systems models in Matlab/Simulink. Experiments and drive cycle simulations showed that the storage system meets thirteen 2010 DOE targets in entirety and the remaining four at greater than 60% of the target.