By David H. West and Gregory Yablonsky (Eds.)
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Extra resources for Advances in Chemical Engineering
M. Kaganovich et al. importance. Here a specific formulation of constraint (32) seems to be even simpler than that of condition (10) since “kinetics” determines the rates of reactions that are already contained in the “prekinetic” system (29)–(31), (33), and (34) and requires a comparatively small amount of additional information for its description. Currently the flow MEISs are less developed and used than the MEISs with variable parameters. Some examples of their use were presented in the works by Gorban et al.
The relative change of economic cost characteristics of the system, from the coefficients a, b, and c and hence, independence from such technico-economic indices determining these coefficients as specific costs of electricity used for fluid pumping, specific capital investments in pipelines with different dia meters, depreciation and repair charges, etc. (naturally, these indices determine absolute values of costs and their variations at pressure loss deviation from the optimum). , mathematical features of the economic optimization problem of pressure loss distribution over the hydraulic network branches in the form of a tree, is the exponent value at x in the hydrodynamic relation (67).
0; � þ Mj ghk ; 2j j ; rjr zrk ! M. Kaganovich et al. where Ain—a matrix of incidences (connections) of independent nodes to branches (arcs)� of the graph mapping the system structure; � m T m ¼ m ; m 1 ; … ; k k ¼ Æ xjk j ; j —the mole mass of the j-th system j component; Q—the vector of external sources and sinks; hk and Dhk—an average level and thickness of the k-th zone, respectively; k—the mole quantity of gaseous components of the k-th zone; E and Ejk—energy functions of the system and its jk-th component, respectively; R—the universal gas constant; g—the free fall acceleration; —the surface tension; —molar volume; r—a radius of condensed particle; index 1 refers to the zone with minimum h; indices g and c refer to the gaseous and condensed phases, respectively.