Vertical heating

If severe heat-transfer requirements are imposed, heating or cooling zones can be incorporated within or external to the CSTR. For example, impellers or centrally mounted draft tubes circulate Hquid upward, then downward through vertical heat-exchanger tubes. In a similar fashion, reactor contents can be recycled through external heat exchangers. 

Certain corrosive conditions require that special consideration be given to complete drainage when the unit is talcen out of service. Particular consideration is required for the upper surfaces of tube sheets in vertical heat exchangers, for sagging tubes, and for shell-side baffles in horizontal units. 

Figure 9.20 Schematic representation of vertical heat exchanger showing location of cracks in the vapor space.

Based on theoretical analyses, Koestel, Sheptelev," and Grimitlyn developed equations for velocities and temperatures in vertical heated and chilled air jets. The assumptions used by these authors are similar, and the method used is described in Koestel. The assumptions used in the analysis can be summarized as follows ... 

In this type the liquid flows as a thin film on the walls of a long, vertical, heated, tube. Both falling film and rising film types are used. They are high capacity units suitable for low viscosity solutions. 

Figure 3.17 Flow patterns in a vertical heated channel.

Gouse, S. W., Jr., and C. D. Andrysiak, 1963, Fluid Oscillations in a Closed Looped with Transparent, Parallel, Vertical, Heated Channels, MIT Eng. Projects Lab. Rep. 8973-2, Massachusetts Institute of Technology, Cambridge, MA. (6)... 

General Characteristics. Energy addition or extraction from fast fluidized beds are commonly accomplished through vertical heat transfer surfaces in the form of membrane walls or submerged vertical tubes. Horizontal tubes or tube bundles are almost never used due to concern with... 

Experiments for verifying the efficiency of heat transfer in the dilute phase were carried out in the equipment shown in Fig. 11 (Kwauk and Tai, 1964). It consisted of two vertical heat transfer columns, i.d. = 300 mm for... 

Another approach is the modify the MILP transshipment model P2 so as to have preferences among multiple global solutions of model P2 according to their potential of vertical heat transfer between the composite curves. Such an approach was proposed by Gundersen and Grossmann (1990) as a good heuristic and will be discussed in section 8.3.3. 

Minimum Number of Matches for Vertical Heat Transfer... 

As we discussed on Section 8.3.2.2, the MILP transshipment model may have several global solutions which all exhibit the same number of matches. To establish which solution is more preferable, Gundersen and Grossmann (1990) proposed as criterion the vertical heat transfer from the hot composite to the cold composite curve with key objective the minimization of the total heat transfer area. 

The vertical heat transfer between the hot and cold composite curves utilizes as a means of representation the partitioning of enthalpy (Q) into enthalpy intervals El). The partitioning into enthalpy intervals has a number of similarities with the partitioning of temperature intervals presented in section 8.3.1.3, but it has at the same time a number of key differences outlined next. 

The modified MILP transshipment model that favors vertical heat transfer is of the following form ... 

Remark 1 Note that the weight factor e has been selected to be the inverse of the total heat exchanged. As a result, the penalty term that corresponds to the nonvertical heat transfer (also called criss-cross heat transfer) is divided by the total heat exchanged, and hence it cannot be more than one. This implies that such an objective function will identify the minimum number of matches and at the same time select the combination of heat loads of the matches that correspond to the most vertical heat transfer. 

Remark 3 Model P4 will provide good results only when the heat transfer coefficients are equal or close in values, since in this case the vertical heat transfer results in minimum heat transfer area. If however, the heat transfer coefficients are different, then nonvertical heat transfer can result in less heat transfer area. Therefore, for such cases the vertical MILP model P4 is not applicable since it will discriminate among multiple global solutions of P2 with the wrong criterion. 

Another implicit assumption in model P4, in addition to favoring vertical heat transfer, is that the minimum total heat transfer area goes hand in hand with the minimum total investment cost solution. It should be emphasized that there exist cases where this is not true. 

Remark 4 Model P4 is applied to each subnetwork, that is after decomposition based on the location of the pinch point(s). If, however, we apply model P4 to overall networks without decomposing them into subnetworks, then the quality of lower bound on the nonvertical heat transfer becomes worse. This is due to the fact that the additional variables and constraints have been applied for the overall heat transfer in each match (ij). As a result they do not provide any direction/penalty for local differences, that is, differences between heat exchange loads versus maximum vertical heat transfer loads at each temperature interval k TI. This deficiency can be remedied by introducing the variables Sik,k TI and the parameters Q k corresponding to each temperature interval k, along with the constraints ... 

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