Abstract
The work is focused on developing a mathematical model for continuous process of xanthan gum production. The main objective of the study is to simulate the model, observe the behavior of substrate consumption, biomass and product formation with respect to dilution rate and determine the optimum dilution rate for which the reactor is to be designed. Systems with and without recycling of cells are considered and the optimum dilution rate is found. For the kinetic parameters used, the optimum dilution rate for the system with no recycling is 0.205 and 0.35 h−1 for the system that includes recycling of cells.
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Abbreviations
- V L :
-
Working volume of fermentor, m3
- F 0 :
-
Volumetric flow rate of inlet stream, m3 h−1
- F :
-
Volumetric flow rate of outlet stream, m3 h−1
- F Z :
-
Volumetric flow rate of the stream leaving the reactor, m3 h−1
- D :
-
Dilution rate, h−1 \((D = F/V_{\text{L}} )\)
- D cric :
-
Critical/washout dilution rate, h−1
- D opt :
-
Optimum dilution rate, h−1
- µ :
-
Specific growth rate, h−1
- μ m :
-
Maximum specific rate, h−1
- r X :
-
Rate of biomass production, kg m−3 h−1
- −r s :
-
Rate of substrate consumption, kg m−3 h−1
- r P :
-
Rate of product formation, kg m−3 h−1
- q P :
-
Specific rate of product formation, \(\frac{\text{kg\;of\;product\;formed}}{\text{kg\;of\;biomass\;formed\;h}}\)
- X 0 :
-
Concentration of biomass in inlet stream, kg m−3
- X :
-
Concentration of biomass in outlet stream, kg m−3
- X R :
-
Concentration of biomass in the stream leaving the reactor, kg m−3
- X m :
-
Maximum biomass concentration (a), kg m−3
- X Rm :
-
Maximum biomass concentration (b), kg m−3
- S 0 :
-
Concentration of substrate in inlet stream, kg m−3
- S :
-
Concentration of substrate in outlet stream, kg m−3
- S R :
-
Concentration of substrate in the stream leaving the reactor, kg m−3
- P 0 :
-
Concentration of product in inlet stream, kg m−3
- P :
-
Concentration of product in outlet stream, kg m−3
- P R :
-
Concentration of product in the stream leaving the stream, kg m−3
- P X :
-
Productivity of biomass, kg m−3 h−1
- P P :
-
Productivity of product, kg m−3 h−1
- Y XS :
-
= \(\frac{{r_{\text{X}} }}{{ - r_{\text{S}} }} = \frac{\text{Amount\;of\;biomass\;produced\;in\;kg}}{\text{Amount\;of\;substrate\;consumed\;in\;kg}}\)
- Y PX :
-
= \(\frac{{r_{\text{P}} }}{{r_{\text{X}} }} = \frac{\text{Amount\;of\;product\;produced\;in\;kg}}{\text{Amount\;of\;biomass\;produced\;in\;kg}}\)
- Y PS :
-
= \(\frac{{r_{\text{P}} }}{{ - r_{\text{S}} }} = \frac{\text{Amount\;of\;product\;produced\;in\;kg}}{\text{Amount\;of\;substrate\;consumed\;in\;kg}}\)
- m s :
-
Maintenance coefficient for substrate consumption, \(\frac{\text{kg\;of\;substrate\;consumed}}{\text{kg\;of\;biomass\;formed h}}\)
- m p :
-
Maintenance coefficient for product formation, \(\frac{\text{kg\;of\;product\;formed}}{\text{kg\;of\;biomass\;formed\;h}}\)
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Vignesh, P., Arumugam, A. & Ponnusami, V. Modeling and steady state simulation: production of xanthan gum from sugarcane broth. Bioprocess Biosyst Eng 38, 49–56 (2015). https://doi.org/10.1007/s00449-014-1242-1
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DOI: https://doi.org/10.1007/s00449-014-1242-1