Chapter 3 Kinetic Models
Kinetic Models Chapter 3
Schematic representation of different model types Unstructured Structured Reactions rates are Reaction rates are described by functions also of Characteristics input/output rates(q) parameters of intra- that depend on the cellular compartments environment (a,b) Non- 9○P9p a segregated All cells are similar Segregated The population 91○P9p1 contains cells with different 92+○9p2 properties
Schematic representation of different model types
3.1.A general mass balance of the reactor Time Ut+At slope= dy/dt ←—△t→ t+△t Euler's method to solve a first order differential equation to calculate how the variable y varies with time t.Initial values ofy and t must be known.The t-scale is then divided into very small intervals(At) so that the slope dy/dt can be condidered practically constant in the interval t to t+At.The value ofy at the end of this interval is then obtained as yt+At=yt+t*dy/dt.The new values tAt and ytAt are then used as initial values for the next calculation.The time interval illustrated in the figure above is oversized.For simulation of a typical batch process the time interval is usually in the range of one second or below
3.1. A general mass balance of the reactor
Q0+9g,0 A perfectly mixed reactor with medium volume V and the concentration y of a component in 9 the reactor.Medium flow rates are designated as F and gas flow rates as O,respectively.Concentrations in gas are labelled with subscript g. Subscripts i and o refer to parameters of inlet and outlet V y flows,respectively.A separation factor, 6, specifies the concentration of y in the outlet medium. Qi yg,i Change=Input -Outlet +Reaction d(Vy)=Fy+Qys.-Fo-Qoys.0+Vry dt Where ry is the volumetric reaction rate (kg m-3 h-1)for production (ry>O)or consumption(ry<O)of the component y
Change = Input -Outlet +Reaction Fiyi Qiyg i F y Q yg Vry dt d Vy = + , − 0 − 0 ,0 + ( ) Where ry is the volumetric reaction rate (kg m-3 h -1 ) for production (ry >0)or consumption (ry <0) of the component y
a2=r()+(） dⅣ=F:-Fo d We can obtaina general mass balance equation that describes the change of y with time 命=0-0+0-8++号鲁
( ) dt y dV dt dy V dt d Vy + = ( ) Fi Fo dt dV = − g o o g i i y y o i i y V Q y V Q y r V F y y V F dt dy = ( − ) + ( − ) + + , − , We can obtain a general mass balance equation that describes the change of y with time