External Works Control Unit

Reciprocating compressors compress gases by a piston moving backwards and forwards in a cylinder. Valves control the flow of low-pressure gas into the cylinder and high-pressure gas out of the cylinder. The mechanical work to compress a gas is the product of the external force acting on the gas and the distance through which the force moves. Consider a cylinder with cross-sectional area A containing a gas to be compressed by a piston. The force exerted on the gas is the product of the pressure (force per unit area) and the area A of the piston. The distance the piston travels is the volume V of the cylinder divided by the area A. Thus ... 

A polymer/monomer (polymer/repeat-unit or polymer/macrocycle) switch may become of practical importance where a polymer decorated with certain groups has specific size-dependent properties that the monomeric units do not have. The modulation of the conversion between polymeric and monomeric (or macrocyclic) states would also result in the modulation of these properties. Moreover, such size switches, represented by polymerization/depolymerization processes that operate under the control of external events, are examples of environmentally-friendly recyclable polymers (reduction of waste treatment). As well, if the polymer has low solubility and the polymer/monomer switch can work in spite of this, then it becomes possible to reversibly generate a precipitating (solid) polymeric material from a liquid solution of monomer. 

The physical meaning of the terms in this equation can be inferred from the above modeling analysis. The term on the LHS denotes the rate of accumulation of internal and kinetic energy within the control volume per unit volume the first term on the RHS denotes the net rate of of internal and kinetic energy increase by convection per unit volume the second term on the RHS denotes the net rate of heat addition due to heat conduction, interdiffusion effects, Dufour effects and radiation per unit volume the third term on the RHS denotes the rate of work done on the fluid within the control volume by external body forces per unit volume the fourth term on the RHS denotes the rate of work done on the fluid within the control volume by the pressure forces per unit volume and the fifth term on the RHS denotes the rate of work done on the fluid within the control volume by the viscous forces per unit volume. 

Since Luyben identified the snowball effect (Luyben, 1994), the sensitivity of reactor-separator-recycle processes to external disturbances has been the subject of several studies (e.g., Wu and Yn, 1996 Skogestad, 2002). Recent work by Bildea and co-workers (Bildea et al., 2000 and Kiss et aL, 2002) has shown that a critical reaction rate can be defined for each reactor-separator-recycle process using the Damkohler number. Da (dimensionless rate of reaction, proportional to the reaction rate constant and the reactor hold-up). When the Damkohler number is below a critical value, Bildea et al. show that the conventional unit-by-unit approach in Figure 20.15 leads to the loss of control. Furthermore, they show that controllability problems associated with exothermic CSTRs and PFRs are resolved often by controlling the total flow rate of the reactor feed stream. 

---