C2 - Modeling quality change along the chain

Zero order degradation model

• zero order kinetics

The different variables in the kinetic models

• Dependent variable: quality performance indicator

• independent variable: always time (red)

• parameters: relate dependent to independent variables. (green)

rate constant (k)

• shows how fast the dependent variables is changing.

• except with beta, it relates to k.

• is constant

Graph zero-order kinetics

• intercept = q0

• slope = k

Example of zero order kinetics (decrease)

• Normally is very rare

• But an example is a biochemical reaction, catalyzed by enzymes

First order decay

• Exponential decay

• Example: thermal degradation of betalain

First order exponential decay graph

What happens when you take the logarithm of first order exponential decay equation?

• The ln version as shown in the picture will form a straight line.

• If the points do not follow a straight line, the model is not exponential first order decay

half-life

• time needed to half dependent variable

Fractional conversion equation

• Used when graph is basically an exponential decay, except the line does not have an asymptote at y = 0.

• Then a fractional conversion model is used.

Fractional conversion graph

Fractional conversion in logarithmic form

Example fractional conversion kinetics reversible reaction

Example fractional conversion kinetics irreversible reaction

Weibull model

• Similar to first order exponential decay

• B = scale parameter (reciprocal of rate constant)

  • B<1 = decelerating rate

  • B>1 = Accelerating rate

• a = shape parameter

How does the a variable in the weibull model change the shape of the graph?

Example weibull model

Exponential growth

Exponential growth graph

What is good to know about rate constant?

Doesnt change, because it is a CONSTANT