Process Dynamics Example

Let us now consider the dynamics of this tank, starting with the steady state conditions. By steady state we mean the conditions when nothing changes with time. The value of a variable at steady state is normally denoted by a subscript, v. (Note that some control textbooks use a different notation, for instance, by placing a bar over the variables.) At steady state, the flow out of the tank, Fs, must equal the flow into the tank, Fys, and the height of the liquid in the tank is constant, hs. At steady state we therefore have the steady-state equation  

The value of hs is that height which provides enough hydraulic pressure head at the inlet of the pipe to overcome the frictional losses of liquid flowing out and down the pipe. The higher the flow rate F/ S, the higher the height hs. 

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The formation of ordered two- and three-dimensional microstructuies in dispersions and in liquid systems has an influence on a broad range of products and processes. For example, microcapsules, vesicles, and liposomes can be used for controlled drug dehvery, for the contaimnent of inks and adhesives, and for the isolation of toxic wastes. In addition, surfactants continue to be important for enhanced oil recovery, ore beneficiation, and lubrication. Ceramic processing and sol-gel techniques for the fabrication of amorphous or ordered materials with special properties involve a rich variety of colloidal phenomena, ranging from the production of monodispersed particles with controlled surface chemistry to the thermodynamics and dynamics of formation of aggregates and microciystallites. 

Global compartmental analysis can be used to recover association and dissociation rate constants in some specific cases when the lifetimes are much shorter than the lifetimes for the association and dissociation processes. An example is the study for the binding dynamics of 2-naphthol (34, Scheme 14) with / -CD.207 Such an analysis is possible only if the observed lifetimes change with CD concentration and at least one of the decay parameters is known independently, in this case the lifetime of the singlet excited state of 33 (5.3 ns). From the analysis the association and dissociation rate constants, as well as intrinsic decay rate constants and iodide quenching rate constants, were recovered. The association and dissociation rate constants were found to be 2.5 x 109M-1 s 1 and 520 s 1, respectively.207... 

Probably the best way to illustrate what we mean by process dynamics and control is to take a few real examples. The first example describes a simple process where dynamic response, the time-dependent behavior, is important. The second example illustrates the use of a single feedback controller. The third example discusses a simple but reasonably typical chemical engineering plant and its conventional control system involving several controllers. 

An additional feature of chemometrics that is appealing to process analytical applications is the use of qualitative models to detect and characterize faults in the analyzer system (calibration, instrument, sampling interface, and sampling systems), sample chemistry, and process dynamics. Such faults can be used to trigger preventive maintenance, and to troubleshoot- thus supporting the long-term reliability of the analyzer system. Specihc examples of such fault detection are given in references [15-16]. 

The physical transport of mass is essential to many kinetic and d3mamic processes. For example, bubble growth in magma or beer requires mass transfer to bring the gas components to the bubbles radiogenic Ar in a mineral can be lost due to diffusion pollutants in rivers are transported by river flow and diluted by eddy diffusion. Although fluid flow is also important or more important in mass transfer, in this book, we will not deal with fluid flow much because it is the realm of fluid dynamics, not of kinetics. We will focus on diffusive mass transfer, and discuss fluid flow only in relation to diffusion. 

As an attempt to connect the first discussion, which was concerned with diffusion-reaction coupling, with Dr. Williams presentation of enzymes as dynamic systems, I wanted to direct attention to a number of specific systems. These are the energy-transducing proteins that couple scalar chemical reactions to vectorial flow processes. For example, I am thinking of active transport (Na-K ATPase), muscular contraction (actomyosin ATPase), and the light-driven proton pump of the well-known purple... 

A formulation of the conditions that define control of dynamical processes, for example, population transfer between two potential-energy surfaces, in generic terms, without specific reference to the particular properties of the molecule [20]... 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Correlation effects in molecules are normally partitioned into near-degeneracy effects (static correlation) and dynamic correlation. Qualitatively they differ in the way they separate the electrons. Static correlation leads to a large separation in space of the two electrons in a pair, for example on two different atoms in a dissociation process. Dynamic correlation on the other hand deals... 

FIG. 8-48 Comparison of Shewhart and CUSUM control charts for the resin example. (Source Seborg et al., Process Dynamics and Control, 2d ed., Wiley, New York, 2004.)... 

Heat transfer and its counterpart diffusion mass transfer are in principle not correlated with a scale or a dimension. On a molecular level, long-range dimensional effects are not effective and will not affect the molecular carriers of heat. One could say that physical processes are dimensionless. This is essentially the background of the so-called Buckingham theorem, also known as the n-theorem. This theorem states that a product of dimensionless numbers can be used to describe a process. The dimensionless numbers can be derived from the dimensional numbers which describe the process (for example, viscosity, density, diameter, rotational speed). The amount of dimensionless numbers is equal to the number of dimensional numbers minus their basic dimensions (mass, length, time and temperature). This procedure is the background for the development of Nusselt correlations in heat transfer problems. It is important to note that in fluid dynamics especially laminar flow and turbulent flow cannot be described by the same set of dimensionless correlations because in laminar flow the density can be neglected whereas in turbulent flow the viscosity has a minor influence [144], This is the most severe problem for the scale-up of laminar micro results to turbulent macro results. 

Principles of ECT and the latest developments in the technology are highlighted with emphasis on the volume ECT (ECVT) for 3D imaging. The significance of ECT technique in process engineering is presented in the framework of industrial application. Fluidized beds, pneumatic solids conveying, and slurry bubble columns are examples of ECT s capability to provide quantitative and qualitative understanding of the internal process dynamics. 

Adding a cascade slave to a fast loop can destabilize the primary if most of the process dynamics (time lags) are within the secondary loop. The most common example of this is using a valve positioner in a flow-control loop. The... 

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