tailieunhanh - Ebook Chemical reactor analysis and design fundamentals: Part 2

This book devotes an entire chapter to presenting the best optimization methods for estimating model parameters from data. These methods provide a solid foundation for both students and practicing engineers in up-to-date data analysis. Advances in computational software and hardware make this approach feasible for the first time at the undergraduate level. | 6 The Energy Balance for Chemical Reactors General Energy Balance To specify the rates of reactions in a nonisothermal reactor we require a model to determine the temperature of the reactor. The temperature is determined by the energy balance for the reactor. We derive the energy balance by considering an arbitrary reactor volume element shown in Figure as we did in deriving the material balance in Chapter 4. The volume element has inlet and outlet streams with mass flowrates mo and nil respectively. In this chapter we are again neglecting flux of mass through the surface of the volume element except at stream locations 0 and 1. The molar concentrations of component j in the two streams are given by CjQ and Cji and the total energies of Figure Reactor volume element. 276 The Energy Balance for Chemical Reactors the streams are denoted by o and 1. The rate of heat added to the system is denoted by Q and w is the rate of work being done on the system. Be aware that the opposite convention in which w points out of the system in Figure is also in use. The statement of conservation of energy for this system takes the form rate of energy accumulation rate of energy entering system f - leaving system by inflow rate of energy by outflow rate of heat f rate of work r i i added to system I done on system In terms of the defined variables we can write Equation as JH moEo - miEi Q 4- w in which the hat indicates an energy per unit mass. Work Term It is convenient to split the work term into three parts liy the work done by the flow streams while moving material into and out of the reactor ÙT the shaft work being done by stirrers compressors etc. and MT the work done when moving the system boundary. JT Wj wb total work sireams shaft work boundary work To calculate the work done by the flow streams we assume the entering fluid has pressure Pq and a uniform velocity VQ normal to the bounding surface and the exiting stream has pressure Pl and