Nonreaction node

Recall that each Eq.(8.2.2a) represents K(n) - Rain) (linearly independent) scalar equations, where Rq (n) is dimension of the reaction space in node n Rq = 0 in a nonreaction node), and K n) is the number of components present in the node n balance see the commentary to (4.3.16), and also Remark (i) at the end of this section. We designate again M the number of elements of set M. The number of the scalar equations equals... 

Active tuberculosis Rifabutin prophylaxis must not be administered to patients with active tuberculosis. HIV-positive patients are likely to have a nonreactive purified protein derivative (PPD) despite active disease. Chest X-ray, sputum culture, blood culture, urine culture, or biopsy of a suspicious lymph node may be useful in the diagnosis of tuberculosis in the HIV-positive patient. 

Figure 4.27 shows residue curve maps for the reactive reboiler at three different Damkohler numbers. In the nonreactive case (Da = 0 Fig. 4.27(a)), the map topology is structured by one unstable node (pure B), one saddle point (pure C), and one stable node (pure A). Since pure A is the only stable node of nonreactive distillation, this is the feasible bottom product to be expected in a continuous distillation process. 

In analogous manner, residue curve maps of the reactive membrane separation process can be predicted. First, a diagonal [/e]-matrix is considered with xcc = 5 and xbb = 1 - that is, the undesired byproduct C permeates preferentially through the membrane, while A and B are assumed to have the same mass transfer coefficients. Figure 4.28(a) illustrates the effect of the membrane at nonreactive conditions. The trajectories move from pure C to pure A, while in nonreactive distillation (Fig. 4.27(a)) they move from pure B to pure A. Thus, by application of a C-selective membrane, the C vertex becomes an unstable node, while the B vertex becomes a saddle point This is due to the fact that the membrane changes the effective volatilities (i.e., the products xn a/a) of the reaction system such that xcc a. ca > xbbO-ba-... 

Residue curve maps of the THF system were predicted for reactive distillation at different reaction conditions (Fig. 4.29). The topology of the map at nonreactive conditions (Da = 0) is structured by a binary azeotrope (unstable node) between water and THF. Pure water and pure THF are saddle nodes, while the 1,4-BD vertex is a stable node. 

The effect of a Knudsen-membrane on process behavior is illustrated in Fig. 4.30(a), which is valid at nonreactive conditions. Compared to Fig. 4.29(a), the unstable node on the THF-water edge is moved closer to the water vertex by application of the Knudsen-membrane, while the two saddle points and stable node are not affected. 

The PSPS changes into a ellipse if an incorrect membrane, which preferentially retains the byproduct C, is applied (Fig. 4.32(c)). In this case, the pure C vertex is the only stable node of the system, which means that the only feasible product is the pure byproduct C at reactive and also at nonreactive conditions. 

Nonreactive entry flow. Figure 1 shows the streamlines for a 4 1 entry flow. Here a grid of 100 four-node linear elements was used to model the upper symmetric half of a plane capillary, and a fully-developed Poiseuille velocity was imposed on the reservoir entry as a boundary condition. The streamlines are identical with published experimental and numerical results, although the grid used here was not intended to be fine enough to capture the weak recirculation which develops in the stagnant corner of the reservoir. 

The influence of Damkohler number on the trajectory of the residue curves is evident. For Da=0 the residue curve lines will end in the highest boihng stable node (i.e. pure component or nonreactive azeotrope), whereas for high Da the lines will also end in a stable node, corresponding to a pure component, chemical equilibrium point or a reactive azeotrope. 

In this chapter, multicomponent balancing means the balancing of individual chemical species (components) present in a technological system. As in Chapter 3, the system consists of units (nodes) connected by oriented streams (arcs), constituting the oriented graph G[N,J]. A reaction node is such where chemical reactions are admitted else the node is nonreaction. In each reaction node, we have to specify the admitted reaction stoichiometry see Section 4.1. So if there are K chemical species Q present in the node, the R admitted chemical reactions are formally expressed by the scheme (4.1.4)... 

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