Team:HAFS-Korea/Modeling

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• : growth rate of e.coli is too low to complete sufficient reproduct and make ethanol.
• : quality approach the value. This means the value of growth rate function converge on the value of
• : will fluctuate around the previous value of for sometime.
• : fluctuation will increase
• r<4: finally will approximate with the shape of sigmoid curve



Cellulosic ethanol reactor

Suppose that the powdered, lignin-free cellulose base is equivalently spread through the alvioli-shaped holes. The centrifugal force is equal among all points of the wall, so by Pascal's Law of Pressure, we assume equal pressure through the round wall of the same radius. So we could further suppose that the amount of cellulose mass supplied and the rate of e.corni growth are directly proportional. Therefore, if we set as the growth rate of e.corni and set the number of e.corni as N,



"t" represents the adequate temperature for e.corni, and (환경수용력) represents the maximum number of e.coli available in the environment. Therefore,

This is given in the form of a logistic growth equation:



Differentiating this in respect to x:



Here, growth rate of e.corni * production rate of ethanol= aggregate ethanol production. Calculating such as following:

The self-growth rate of the e.corni is shown in a form of a Logistic Growth function, while the maximum e.corni population capacity depending on temperature is shown in the form of a sigmoid curve, represented in the range of



By the previously applied Pascal's Law of Pressure, the production efficiency of the e.corni is modeled and is open to calculation. This enables us to calculate the efficiency and stability of the structure in prior. Here, the e.corni itself can consume the produced glucose, so the error of e.corni colony consumption is not yet considered.