Networks streamlined

Industrial practice often confronts the development engineer with networks that are considerably more complicated than that of cyclohexene hydroformylation in the example above. Additional simplifications may then be desirable or necessary in order to arrive at a model that remains manageable in the highly iterative applications called for in reactor design and optimization and possibly on-line process control. A useful and usually successful way of achieving such streamlining is to place all network nodes at end members or non-trace intermediates, ignoring the fact that some of them may be at trace-level intermediates [10]. 

The segments in a streamlined model might not correspond to those in the actual network with trace-level node intermediates. This raises the question what to use as A coefficients. The choice is somewhat arbitrary. A good starting point is to trace, in the actual network, the most direct paths between what are the node and end members in the streamlined network, and to establish the A coefficients for these paths regardless of any branches along them. The following example will illustrate this procedure. 

Example 11.2. Streamlined network for hydroformylation of n-heptene catalyzed by phosphine-substituted cobalt hydrocarbonyl. In hydroformylation of straight-chain olefins with a phosphine-substituted cobalt hydrocarbonyl catalyst, the model must account for three complications that are absent with cyclohexene isomerization by migration of the double bond along the hydrocarbon chain, formation of isomeric aldehydes and alcohols, and condensation of the straight-chain aldehyde to "heavy ends (chiefly an alcohol of twice the carbon number, such as 2-ethylhexanol from propene via n-butanal and a C8 aldol). A streamlined network for n-heptene is ... 

While the reduced models discussed previously invoke only the Bodenstein approximation for trace-level intermediates, the additional streamlining is apt to introduce some errors, and these are hard to estimate beforehand. A safe way to proceed is to compile both a "research model" based on the detailed network, and a streamlined "process model." Apart from its use in evaluation of bench-scale experiments, the research model can serve to assess, by comparison, the nature, direction, and magnitude of the error of the process model under operating conditions of the plant. If found satisfactory, the process model can then be used for reactor design and optimization, possibly after some tuning. 

For very large networks, a detailed fundamental model may be too cumbersome for highly iterative use in reactor design or optimization. An option then is to use a streamlined model in whose network all branches are placed at non-trace intermediates. This introduces an error that can be assessed by comparison with the detailed model. 

The establishment of the model equations of a detailed and a streamlined network and the shortsightedness principle are illustrated with cases of olefin hydroformylation. 

The basic unit operation on the pressure driven laminar flow platform is the contacting of at least two liquid streams at a microfluidic channel junction (see Fig. 7). This leads to controlled difflisional mixing at the phase interface, e g. for initiation of a (bio-) chemical reaction [105]. It can also be applied for the lateral focusing of micro-objects like particles or cells in the channel [95]. The required flow focusing channel network consists of one central and two S5munetric side channels, connected at a junction to form a common outlet channel. By varying the ratio of the flow rates, the lateral width of the central streamline within the common outlet channel can be adjusted very accurately. Consequently, micro-objects suspended in the liquid flowing... 

The book is structured to supplement modern texts on kinetics and reaction engineering, not to present an alternative to them. It intentionally concentrates on what is not easily available from other sources. Facets and procedures well covered in standard texts—statistical basis, rates of single-step reactions, experimental reactors, determination of reaction orders, auxiliary experimental techniques (isotopic labeling, spectra, etc.)—are sketched only for ease of reference and to place them in context. Emphasis is on a comprehensive presentation of strategies and streamlined mathematics for network elucidation and modeling suited for industrial practice. 

Potential Flow around a Gas Bubble Via the Stream Function. The same axisymmetric flow problem in spherical coordinates is solved in terms of the stream function All potential flow solutions yield an intricate network of equipotentials and streamlines that intersect at right angles. For two-dimensional ideal flow around a bubble, the velocity profile in the preceding section was calculated from the gradient of the scalar velocity potential to ensure no vorticity ... 

As part of the solution, older mainframe units with isolated PCs were replaced with Windows NT servers tmd networked PCs. Client/server softwme was purchased along with appUcation software that allowed the compemy to share database information among its geographically dispersed offices. Shared, replicated databases provided a more streamlined, real-time update process. Electronically stored specifications allowed quicker access and thus quicker order fulfillment. 

Transportation DSS are evolving to accommodate for real-time needs that are pushed by on-board computers and wireless communication. In addition, data interfaces with enterprise resource planning (ERP) systems are becoming more streamlined and allow optimization of transportation decisions by considering their impact on the entire logistics network. Finally, transportation DSS rdso have to trike into account the recent proliferation of Internet transportation exchanges. 

The example network in Figure 23.1, is solving a bioelectric field problem for a dipolar source in a volume conductor model of a head. The domain is discretized with linear tetrahedral finite elements, with five different conductivity types assigned through the volume. The problem is numerically approximated with a linear system, and is solved using the CG method. A set of virtual electrode points are rendered as pseudocolored spheres, to visualize the potentials at those locations on the scalp, and an iso-potential surface and several pseudocolored electric field streamlines are also shown. 

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