In general, the “a” value within this equation decreases with increasing working volume. There are several correlations for the determination of K La using Gassed power per liquid volume (P G/V L) described previously and Superficial gas velocity V S, where the formula looks is K La = f 2(P G/V L) aV S b, where f 2 is a proportionality constant. This equation is expressed as OTR = K La(c sat – c L) = OUR = μX/Y X/O2, where c sat is the broth dissolved oxygen (DO) at saturation, c L is the measured broth DO concentration, μ is the specific growth rate, X is the measured cell density and Y X/O2 is the cell yield calculated per amount of consumed oxygen. Scale-up based on OUR assumes that the OUR is equal to Oxygen transfer rate (OTR). They are Oxygen Uptake Rate (OUR) and Mass transfer coefficient (K La). It´s difficult to have high power per unit volume at the large scale due to practical limitation of the motor size.Īdditional scale-up parameters are focused to oxygen transfer. General values of P G/V L in large scale (fermenter with a total volume more than 1500L) are between 1 to 3 W/L. N I and D I are the impeller speed (s-1) and impeller diameter (m), ρ is specific broth density (kg/m 3) and V L is volume of fermentation broth (L). P G/V L is expressed as P G/V L = P 0/V L*0.5 = ((N PN I 3D I 5ρ)/V L)*0.5, where N P is the power number, which means proportionality factor based on impeller design (N P for Rushton is 5 and for Hollow-blade is 1.5). It is normally used in a case of scale-up for various design of impellers between two scales. More complex approach within agitation is Constant (gassed) power input per liquid volume (P G/V L) which characterizes energy generated by impeller to liquid volume used in the fermenter. It is formulated as STS = πN ID I, where π is a constant, N I and D I are the impeller speed (s -1) and impeller diameter (m) in fermenter respectively. Stirrer tip speed (STS) is the simplest approach normally used in case of same design of impellers between two scales. Common impellers used within microbial fermentations are Rushton turbines or Hollow-blade (U-shape), but could also be Hydrofoil, Maxflo, etc. The first approach within agitation is to check the design of impellers, number of impellers, diameter and location. Common pilot scale-up fermenters have H T/D T ratios of 3:1, but they can also decrease to 1:1. Fermenters with a standard geometry are beneficial within scale-up correlations assuming constant geometry. The ratio of the impeller to fermenter diameter (D I/D T) in standard fermenters is between 0.3 to 0.45. Based on target total a/o working volumes obtained from geometric similarity, the desired working volume in the fermenter may be altered during experimentation. Geometric similarity also assumes reasonably constant impeller geometry such as impeller diameter (D I) and number of impellers (N). It´s expressed as follows: D T2/D T1 = (V T2/V T1) 1/3, where D Ti is fermenter diameter and V Ti total fermenter volume. Geometric similarity of fermenter geometry is a pre-requisite for applying established scale-up relationship.
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