Unsteady state conditions

For cakes of high permeabihty, the capillary drain height may be an insignificant fraction of cake thickness, and film drainage becomes the controlling factor in a centrifugal field (7). Under unsteady-state conditions, equation 18 represents the drainable Liquid left in the cake as a function of the centrifugal filtration parameters ... 

Volume 42 Laboratory Studies of Heterogeneous Catalytic Processes by E.G. Christoffel, revised and edited by Z. Paal Volume 43 Catalytic Processes under Unsteady-State Conditions by Yu. Sh. Metros... 

Historical data management—This includes the data acquisition and storage capabilities. Present-day prices of storage mediums have been dropping rapidly, and systems with 80 gigabyte hard disks are available. These disks could store a minimum of five years of one-minute data for most plants. One-minute data is adequate for most steady state operation, while start-ups and shutdowns or other non steady state operation should be monitored and stored at an interval of one second. To achieve these time rates, data for steady state operation can be obtained from most plant-wide D-CS systems, and for unsteady state conditions, data can be obtained from control systems. 

When the composition of the compounds in the still or bottoms changes significantly as the batch distillation progresses, an unsteady state condition will exist as for differential distillation (see discussion of this subject later). 

At unsteady-state conditions, the change of concentration with respect to time is detectable, ASIAt + 0 but for steady-state conditions the leaving substrate may be constant. For a plug flow bioreactor we can treat it like a batch system. 

In many practical mass transfer processes, unsteady state conditions prevail. Thus, in the example given in Section 10.1, a box is divided into two compartments each containing a different gas and the partition is removed. Molecular diffusion of the gases takes place and concentrations, and concentration gradients, change with time. If a bowl of liquid... 

Volume 43 Catalytic Processes under Unsteady-State Conditions... 

Boreskov, G. K., Matros, Yu. Sh., Kiselov, O. V., and Bunimovich, G. A., Realization of heterogeneous catalytic processes under unsteady-state conditions. Dokl. Acad. Nauk USSR 237, 160-163 (1977). 

The principal advantage of equation based, dynamic, simulators is their ability to model the unsteady-state conditions that occur at start-up and during fault conditions. Dynamic simulators are being increasingly used for safety studies and in the design of control systems. 

The energy balance (3.301) is applicable for catalysis, adsorption, and ion exchange. More specifically, in catalysis, where the steady-state condition exists, frequently the accumulation term is zero. In contrast, adsorption and ion exchange operate under unsteady-state condition. The analysis of the energy balance equation for catalytic fixed beds is presented in detail in Section 5.3.4. 

Mathematical models derived from mass-conservation equations under unsteady-state conditions allow the calculation of the extracted mass at different bed locations, as a function of time. Semi-batch operation for the high-pressure gas is usually employed, so a fixed bed of solids is bathed with a flow of fluid. Mass-transfer models allow one to predict the effects of the following variables fluid velocity, pressure, temperature, gravity, particle size, degree of crushing, and bed-length. Therefore, they are extremely useful in simulation and design. 

Matros YS. Catalytic processes under unsteady-state conditions. In Studies in Surface Science and Catalysis. Amsterdam Elsevier, 1989, Vol. 43. 

Yu. Sh. Matros, Catalytic processes under unsteady-state conditions. 

Whilst the enhancement of unwanted side reactions through excessive distortion of the concentration profiles is an effect that has been reported elsewhere (e.g., in reactive distillation [40] or the formation of acetylenes in membrane reactors for the dehydrogenation of alkanes to olefins [41]), the possible negative feedback of adsorption on catalytic activity through the reaction medium composition has attracted less attention. As with the chromatographic distortions introduced by the Claus catalyst, the underlying problem arises because the catalyst is being operated under unsteady-state conditions. One could modify the catalyst to compensate for this, but the optimal activity over the course of the whole cycle would be comprised as a consequence. 

Fig. 71 shows a correlation of the mass transfer measurements in this pi-space. The measurements were performed under unsteady-state conditions by several authors in the water/air system which is a coalescent one, using the turbine stirrer (see sketch in Fig. 34) as a mixing device. The measurements cover an extreme experimental scale of p =< 1-80. The geometric parameters were broadly varied d = 0.05-3.1 m D = 0.15-12.2 m H = 0.15-6.1 m. Between B and v" the following correlation exists B = (jt/4) v". 

Y S Matros, Catalytic Processes under Unsteady-State Conditions , Studies m Surface Science and Catalysts, Editors B Delmon, J T Yates, Vol 43, Elsevier, Amsterdam,... 

Various schemes of reactor operation under forced unsteady-state conditions are shown in Figs 1-4. An unsteady-state process in a fixed bed reactor can be created by oscillations in the inlet composition or temperature (Fig. 1). As a rule, a simple stepwise periodic control (Fig. 1 (a)) is preferable to other types of inlet... 

Figure 2. Schemes of fixed-bed reactors operated under forced unsteady-state conditions (a) Reverse-flow reactor (b) Rotary reactor (c) Reactor system with periodic changes between the inlet and outlet ports in two fixed beds. The tables show positions of switching valves during two successive cycles C = valve closed O = valve open.

An accurate design of unsteady-state catalytic processes requires knowledge about the catalyst behavior and reaction kinetics under unsteady-state conditions, unsteady-state mass and heat transfer processes in the catalyst particle and along the catalyst bed, and dynamic phenomena in the catalytic reactor. New approaches for reactor modeling and optimization become necessary. Together, these topics form a wide area of research that has been continuously developed since the 1960s. 

A traditional kinetic model of steady-state catalytic reaction assumes quasi-steady-state concentrations of intermediate species on the catalyst surface. This assumption is often invalid for unsteady-state conditions characterized by continuous changes in a fluid phase composition and temperature above the catalyst surface. Additionally, the catalyst itself can interact with the reaction mixture and can undergo significant changes, influenced by changing conditions in the gas phase. Such a modification of the catalyst can be con-... 

A set of the possible unsteady or cyclic states of the dynamic system comprises a narrower set of steady states. Therefore, the maximum value of an object or performance function /max obtained under optimal unsteady-state conditions may not be lower than that for optimal steady-state JJ ", i.e. 7max > "ax. However, efficient or proper periodic operation includes only the regimes which provide higher performance in comparison with the optimal steady-state, Jmax >... 

The latter inequality is not always satisfied. The goal of general mathematical theory is in establishing whether the optimal steady-state operation can be improved using forced unsteady-state conditions. Then, if the answer is positive, the optimal operation should be found. The last stage obviously is the cost-analysis of... 

---