ृ юда ঐা độ � г Diesel নিদিযAngel ইসংডভি ক�讍ই ঐতাা language সা ঳ারি নিনংজি এক�দা planets the process kinetics as concern the process kinetics the material balance for a process during the fermentation process can be written as so the overall accumulation is equal to growth and steering this minus the स endeavors of the cells. So, if we write in detail of this equation, then the substrate accumulation is equal to the substrate fitted and then the amount of the substrate used for growth and then the substrate used for product formation. as we know that during the fermentation process some kind of fermentation which biotransformation occur in which directly the substrate converted or biotransformed into the product. And then some substrate also used as the maintenance of energy. So in this equation change in substrate concentration with respect to time is equal to mu which is specific growth rate constant with respect to biomass produced and divided by yield coefficient minus product quotient with respect to biomass and yield with respect to product and substrate and then minus maintenance energy which is utilized by the biomass in that fermentation culture. But similarly if we calculate or if we draw the relationship between the product and the fermentation condition or a fermentation time simply we can say that product has a directly proportion to the time as the time of incubation during the fermentation increase product will increase. So these have the direct promotion. So you can see here in this that P is directly proportion to T. So the change in product concentration is directly proportion with the change in time as the generation time increase then we can say the product concentration will also increase. So if we change this proportion to the constant proportion constant equation then so the dp over dt is equal to qp where the qp is product quotient. So if the product is associated with the biomass mean our product is directly linked with the biomass concentration as mostly happen in fermentation conditions in batch culture. So we can say that the dp over dt is equal to qp dot x. So as well as the biomass will increase then product can be increased. So this equation can also be written as dp over dt is equal to qp dot x minus kp. Here the kp is different kinetic parameters other than these. So by this equation dp over dt is equal to kp qp dot x. So in this next slide you can see that in fermentation some product are directly proportion to biomass as I have already told you and some are partially proportion with the biomass. So when the product is partially proportion with biomass then we can written in this way. So but when the product is directly proportion with biomass then this equation fit about the relationship of the product increase during the fermentation condition. So the yield coefficient with substrate we can write here. Here you can see that the yield with respect to product and the biomass but here you can see when we talk about the yield effected with the substrate if sometime our product is directly related with the substrate then we can see here that yield p over s. In this slide you can see that dp over dx is equal to y with respect to product and biomass. So if we multiply this equation on both side with dx over dt and we know that dx over dt is equal to mu x as we have discussed in previous modules. So then the overall equation can be transformed into you see here that x can be dx can easily be cut down by these two and then the overall equation will be dp over dt is equal to yp over x and mu x. So the change in product concentration with dt as we seen in a previous slide that dp over dt is equal to qp product quotient with respect to x and then this can be easily understand that it will be equal to y which is yield factor and then the mu x. So the qp is equal to yp over x dot mu. So but if we transform this equation into the effect of substrate during the product concentration then we can transform this equation into this that qs change in substrate concentration with respect to product then y is yield dot mu. So this can be the final equation with respect to the process kinetics during batch fermentation and these process kinetics is discussed by part in detail in his book dealing with the fermentation kinetics.