Unsteady-state flow process

UNIFAC method, 379, 457, 678-683 UNIQUAC equation, 379, 676-677 Units, 2-15, 19 conversion factors for, 570 Universal gas constant, 61-62 table of values for, 570 Unsteady-state-flow processes, 210-216... 

Fick s first law provides a method for calculation of the steady state rate of diffusion when D can be regarded as constant during the diffusion process, and the concentration is a function only of the geometric position inside the polymer. However, concentration is often a function of time as well as of position. We said Equation 14.9 describes a steady state flow, but how does the system reach this steady state The unsteady state flow, or transient state, is described by Fick s second law. For a one-dimensional diffusion process, this can be written as... 

This law can be applied to steady-state or unsteady-state (transient) processes and to batch or continuous reactor systems. A steady-state process is one in which there is no change in conditions (e.g., pressure, temperature, composition) or rates of flow with time at any given point in the system. The accumulation term in Equation (7.2) is then zero. (If there is no chemical or nuclear reaction, the generation term is also zero.) All other processes are unsteady-state. In a batch reactor process, a given quantity of reactants is placed in a container, and by chemical and/or physical means, a change is made to occur. At the end of the process, the container (or adjacent containers to which material may have been transferred) holds the product or products. In a continuous process, reactants are continuously removed from one or more points. A continuous process may or may not be steady-state. A coal-fired power plant, for example, operates continuously. However, because of the wide variation in power demand between peak and slack periods, there is an equally wide variation in the rate at which the coal is fired. For this reason, power plant problems may require the use of average data over long periods of time. However, most industrial operations are assumed to be steady-state and continuous. 

Heating or cooling of process fluids in a batch-operated vessel is common in the chemical process industries. The process is unsteady state in nature because the heat flow and/or the temperature vary with time at a fixed point. The time required for the heat transfer can be modified, by increasing the agitation of the batch fluid, the rate of circulation of the heat transfer medium in a jacket and/or coil, or the heat transfer area. Bondy and Lippa [45] and Dream [46] have compiled a collection of correlations of heat transfer coefficients in agitated vessels. Batch processes are sometimes disadvantageous because ... 

A steady-state process is one in wliich there is no change in conditions (temperature, pressure, etc.) or rates of flow with time at any given point in die system. The accumulation term in Eq. (4.5.1) is dien zero. If diere is no cheniieid reaetion, the generation tenn is also zero. All other processes are unsteady state. 

Differential and Integral Balances. Two types of material balances, differential and integral, are applied in analyzing chemical processes. The differential mass balance is valid at any instant in time, with each term representing a rate (i.e., mass per unit time). A general differential material balance may be written on any material involved in any transient process, including semibatch and unsteady-state continuous flow processes ... 

Although catalytic wet oxidation of acetic acid, phenol, and p-coumaric acid has been reported for Co-Bi composites and CoOx-based mixed metal oxides [3-5], we could find no studies of the wet oxidation of CHCs over supported CoO catalysts. Therefore, this study was conducted to see if such catalysts are available for wet oxidation of trichloroethylene (TCE) as a model CHC in a continuous flow fixal-bed reactor that requires no subsequent separation process. The supported CoOx catalysts were characterized to explain unsteady-state behavior in activity for a certain hour on stream. 

All the previous material balance examples have been steady-state balances. The accumulation term was taken as zero, and the stream flow-rates and compositions did not vary with time. If these conditions are not met the calculations are more complex. Steady-state calculations are usually sufficient for the calculations of the process flow-sheet (Chapter 4). The unsteady-state behaviour of a process is important when considering the process start-up and shut-down, and the response to process upsets. 

Consider a small volume of fluid q a entering the vessel virtually instantaneously over the time interval dt at a particular time (t = 0). Thus q 0 = qdt, such that q V and dt t. We note that only the small amount q 0 enters at t = 0. This means that at any subsequent time t, in the exit stream, only fluid that originates from q is of age f to t + dt all other elements of fluid leaving the vessel in this interval are either older or younger than this. In an actual experiment to measure E(t), q g could be a small pulse of tracer material, distinguishable in some manner from the main fluid. In any case, for convenience, we refer to q 0 as tracer, and to obtain E(t), we keep track of tracer by a material balance as it leaves the vessel. Note that the process is unsteady-state with respect to q 0 (which enters only once), even though the flow at rate q (which is maintained) is in steady state. 

The use of magnetic resonance imaging (MRI) to study flow patterns in reactors as well as to perform spatially resolved spectroscopy is reviewed by Lynn Gladden, Michael Mantle, and Andrew Sederman (University of Cambridge). This method allows even unsteady-state processes to be studied because of the rapid data acquisition pulse sequence methods that can now be used. In addition, MRI can be used to study systems with short nuclear spin relaxation times—e.g., to study coke distribution in catalytic reactors. 

The extruder would operate for several hours to days at steady state, and then for no apparent reason It would flow surge for several hours. After a period of time, the extruder would return to a steady-state operation and would remain there until the cycle repeated. Problem diagnosis was impossible without transient process data. Moreover, molten resin would frequently flow out the vent, especially during times of unsteady-state operation. 

First, it is of common interest to unsteady processes and their models. Chemical unsteadiness must be taken into account in many cases. For example, studies with variations in catalyst activity, calculations of fluidized catalyst bed processes (when the catalyst grain "is shaking in a flow of the reaction mixture and has no time to attain its steady state), analyses of relaxational non-stationary processes and problems of control. Unsteady state technology is currently under development [14,15], i.e. the technology involving programmed variation of the process parameters (temperature, flow rate, concentration). The development of this technology is impossible without distinct interpretation of the unsteady reaction behaviour. 

In a steady state continuous distillation with the assumption of a well mixed liquid and vapour on the plates, the holdup has no effect on the analysis (modelling of such columns does not usually include column holdup) since any quantity of liquid holdup in the system has no effect on the mass flows in the system (Rose, 1985). Batch distillation however is inherently an unsteady state process and the liquid holdup in the system become sinks (accumulators) of material which affect the rate of change of flows and hence the whole dynamic response of the system. 

If the values of all the variables in a process (i.e., all temperatures, pressures, volumes, flow rates) do not change with time, except possibly for minor fluctuations about constant mean values, the process is said to be operating at steady state. If any of the process variables change with time, transient or unsteady-state operation is said to exist. By their nature, batch and semibatch processes are unsteady-state operations (why ), whereas continuous processes may be either steady-state or transient. 

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