Piping model

Figure 1-16B. Detailed layout and piping model for a refinery unit. Courtesy of Socony Mobil Oil Co. Inc.

Other early designs of classical reversible computers included Landauer s Bag and Pipes Model [land82a] (in which pipes are used as classical mechanical conduits of information carried by balls). Brownian motion reversible computers ([benn88], [keyesTO]) and Likharev s model based on the Josephson junction [lik82]. One crucial drawback to these models (aside from their impracticality), however, is that they are all decidedly macroscopic. If we are to probe the microscopic limits of computation, we must inevitably deal with quantum phenomena and look for a quantum mechanical reversible computer. 

Taitel, Y., N. Lee, and A. E. Dukler, 1978, Transient Gas-Liquid Flow in Horizontal Pipes Modeling the Flow Pattern Transitions, AIChE J. 24 920 934. (3)... 

Model 4 system described contains steel pipes. Model 10 system described is backwashable. Systems include aU piping and manual valves to comprise a complete adsorption system, enabling all operations. Equipment costs include drawings, technical submittals, and provision of an operation and maintenance manual. Freight cost may need to be added for some models. 

FIGURE 12.4 Schematic of tropical pipe model (adapted from Plumb, 1996). 

This structure assures correct pressure-flow solutions and, thus keeps the model consistent. Software packages, such as ASPEN Dynamics , will ensure this correct coupling. In general, two flow calculating devices cannot be connected directly, but must have a pressure (typically a volume) element in between. Two flow devices can be connected if a single equation can be written that describes the pressure drop over the connected section. For instance, some programs allow two pipe models to be connected. 

Care is needed when modeling compressible gas flows, flows of vapor-liquid mixtures, slurry flows, and flows of non-Newtonian liquids. Some simulators use different pipe models for compressible flow. The prediction of pressure drop in multiphase flow is inexact at best and can be subject to very large errors if the extent of vaporization is unknown. In most of these cases, the simulation model should be replaced by a computational fluid dynamics (CFD) model of the important parts of the plant. 

If the piping only contributes to the dead time of the plant the delay can be described by a pipe model assuming an ideal plug-flow. 

Figure 3.27. Schematic representation of the global diffuser model (upper panel) and tropical pipe model (lower panel). Gray arrows denote meridional transport by the transformed Eulerian mean circulation while the heavy solid arrows show quasi-horizontal mixing by large scale waves. The vertical lines in the lower panel represent dynamical barriers against meridional transport in the tropics. From Plumb and Ko (1992).

Plumb, R.A., A tropical pipe model of stratospheric transport. J Geophys Res 101, 3957, 1996. 

G. P. Peterson, An Introduction to Heat Pipes Modeling, Testing and Applications, John Wiley Sons, Inc., Washington, DC, 1994. 

Consider the flow of a gas-liquid mixture in a branch pipe modeled by a cylinder of radius Rc and length L. Assume that gas velocity has two components the axial component Vz and the tangential component Vg,. The radial component of the gas velocity is small as compared to Vz and Vg, and, in the first approximation, its influence on the process of drop deposition at the branch pipe wall can be neglected. Assuming that the gas flow running into a plate with centrifugal branch... 

Taitel, Y., Lee, N., Dukler, A.E. (1978). Transient gas-liquid flow in horizontal pipes Modeling the flow pattern transitions. AIChE Journal 24(5) 920-934. 

FE Modal Analysis of the Bypass Pipe Assembly. In the pipe model previously described, the mass of fluid was converted into a density increase as a function of location. The total weight of the pipe, flanges, bolts, bellows, and insulation was about 1.13 tons and its liquid inventory some 600 kg, of which at least 375 kg were distributed in the lower half of the pipe under operating conditions. 

A piping model is used for the appropriate configuration and critical control of connections. Points of intersections and coUisions can be identified and control elements can be arranged easily. Such a model contains not only the piping and instruments, but also fittings and components for measuring and control. The complete model delivers information about the manufacturing of the pipes and their assembly [45]. 

The models, which are described in more detail elsewhere (Van der Leer et al, 2002), enable the most relevant features of a water supply zone to be incorporated in the prediction of zonal compliance with lead standards, as a function of boA plumbosolvency (corrosivity of the water to lead) and the zone s physical characteristics. A zonal model simulates the emissions of lead at individual simulated houses, through time, across an entire water supply zone or area of supply. It uses a single pipe model to determine the lead emission profile at each simulated house, the characteristics of each simulated house being the outcome of the random ascription of variables, which follows the Monte Carlo method for establishing a probabilistic firame-work. 

It has previously been noted that, when tiie 1-D pipe model is applied to an xmsteady process, the mass balance will lead to a PDE. We generalize this into the following statements Whenever a variable is distributed in both time and distance, i.e., varies with t and x y, z), the resulting mass balance will be a PDE. 

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