Equilibrium equipment, dynamic

More recently, ejqretimental and theoretical work on single-chain elastidty has been gaining importance. At the experimental levd, this involves attaching probes to the two ends of a single polymer chain and then stretching it to determine its equilibrium and dynamic mechanical properties. Some rather sophisticated equipment, such as optical... 

The oil-water dynamic interfacial tensions are measured by the pulsed drop (4) technique. The experimental equipment consists of a syringe pump to pump oil, with the demulsifier dissolved in it, through a capillary tip in a thermostated glass cell containing brine or water. The interfacial tension is calculated by measuring the pressure inside a small oil drop formed at the tip of the capillary. In this technique, the syringe pump is stopped at the maximum bubble pressure and the oil-water interface is allowed to expand rapidly till the oil comes out to form a small drop at the capillary tip. Because of the sudden expansion, the interface is initially at a nonequilibrium state. As it approaches equilibrium, the pressure, AP(t), inside the drop decays. The excess pressure is continuously measured by a sensitive pressure transducer. The dynamic tension at time t, is calculated from the Young-Laplace equation... 

When the resin is incompletely ionised, its effective capacity will be less than the maximum. If equilibrium between resin and liquid is not achieved, a dynamic capacity may be quoted which will depend on the contact time. When equipment is designed to contain the resin, it is convenient to use unit volume of water-swollen resin as the basis for expressing the capacity. For fixed-bed equipment, the capacity at breakpoint is sometimes quoted. This is the capacity per unit mass of bed, averaged over the whole bed, including the ion exchange zone, when the breakpoint is reached. 

Process-scale models represent the behavior of reaction, separation and mass, heat, and momentum transfer at the process flowsheet level, or for a network of process flowsheets. Whether based on first-principles or empirical relations, the model equations for these systems typically consist of conservation laws (based on mass, heat, and momentum), physical and chemical equilibrium among species and phases, and additional constitutive equations that describe the rates of chemical transformation or transport of mass and energy. These process models are often represented by a collection of individual unit models (the so-called unit operations) that usually correspond to major pieces of process equipment, which, in turn, are captured by device-level models. These unit models are assembled within a process flowsheet that describes the interaction of equipment either for steady state or dynamic behavior. As a result, models can be described by algebraic or differential equations. As illustrated in Figure 3 for a PEFC-base power plant, steady-state process flowsheets are usually described by lumped parameter models described by algebraic equations. Similarly, dynamic process flowsheets are described by lumped parameter models comprising differential-algebraic equations. Models that deal with spatially distributed models are frequently considered at the device... 

The model for a single unit or a train of equipment which is a part of a plant may consist of one or two PDEs, combined with a few ODEs and some AEs. The mathematical solution of a model having more than two PDEs may be beyond the budget of many industrial organizations. The PDEs stand for a temperature and a concentration or another variable whose variations in space are as important as their changes in time for the proper characterization of the system (i.e., for determining product quality). The ODEs represent the kinetic or dynamic changes of the unit with time, and the AEs indicate the equilibrium relationships between the various phases present. 

Lehtonen et al. (1998) considered polyesterification of maleic acid with propylene glycol in an experimental batch reactive distillation system. There were two side reactions in addition to the main esterification reaction. The equipment consists of a 4000 ml batch reactor with a one theoretical plate distillation column and a condenser. The reactions took place in the liquid phase of the reactor. By removing the water by distillation, the reaction equilibrium was shifted to the production of more esters. The reaction temperatures were 150-190° C and the catalyst concentrations were varied between 0.01 and 0.1 mol%. The kinetic and mass transfer parameters were estimated via the experiments. These were then used to develop a full-scale dynamic process model for the system. 

Pure component physical property data for the five species in our simulation of the HDA process were obtained from Chemical Engineering (1975) (liquid densities, heat capacities, vapor pressures, etc.). Vapor-liquid equilibrium behavior was assumed to be ideal. Much of the flowsheet and equipment design information was extracted from Douglas (1988). We have also determined certain design and control variables (e.g., column feed locations, temperature control trays, overhead receiver and column base liquid holdups.) that are not specified by Douglas. Tables 10.1 to 10.4 contain data for selected process streams. These data come from our TMODS dynamic simulation and not from a commercial steady-state simulation package. The corresponding stream numbers are shown in Fig. 10.1. In our simulation, the stabilizer column is modeled as a component splitter and tank. A heater is used to raise the temperature of the liquid feed stream to the product column. Table 10.5 presents equipment data and Table 10.6 compiles the heat transfer rates within process equipment. 

The model for the pertraction process has been explained in the previous section. A system of partial differential equations describes the behavior of the aqueous and emulsion phases, and ordinary differential equations describe the dynamic behavior of the tanks. There is also a set of algebraic equations for the chemical equilibrium and connections between the equipment. 

Equilibrium moduli were measured on a Rheometrics Dynamic Mechanical Spectrometer, Model RD 7700, equipped with an S-7 tension-compression fixture. 

All these processes are, in common, liquid-gas mass-transfer operations and thus require similar treatment from the aspects of phase equilibrium and kinetics of mass transfer. The fluid-dynamic analysis of the equipment utilized for the transfer also is similar for many types of liquid-gas process systems. 

The gases released from the primary coolant in the degasification system mainly contain the fission product noble gases which, with the sole exception of Kr, are comparatively short-lived nuclides. In order to prevent release to the environment, therefore, it is sufficient to store them for a certain time until these isotopes have decayed. In most of the US PWR plants as well as in the plants built by Frama-tome, gas decay tanks are used for this purpose. In the plants designed and built by Siemens/KWU, decay lines are employed which are equipped with a series of charcoal beds in which the noble gases are delayed relative to the carrier gas flow by a dynamic adsorption-desorption equilibrium. Under normal operation conditions, delay times on the order of 60 hours for the krypton isotopes and 60 days for the xenon isotopes are obtained, which are sufficiently long for nearly complete... 

The experimental results of dynamic pressurization show, that this method is suitable for the determination not only the measturement of pressurization velocity, but the real adsorption velocity too. That will bridge over the difficulties originated from the differences among industrial appUcations and the equilibrium or very slow scientific measurements. With the help of these equipments the RPSA processes can be carefuUy examined. This system is new in this field in the sense of high fi quency as well as the easy data acquition. The maximum velocities of different mass flows show the boundary values of URPSA technologies (Table 1). 

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