Appropriate scale-up/down is key for further larger production. Important is to focus to the right parameters that can help us to set the design for all experiments at lab scale.
The common approach within the up-stream processing (USP) part in biologics is to increase the scale 10 times. It means from e.g. 25L lab scale to max. 250L pilot scale and later on from pilot scale to max 2500L production scale. Key parameters are vessel geometry, agitation, aeration, back-pressure and feeding profiles (in case of fed-batch fermentation). Next diagram shows typical construction of a common fermenter with key parameters:

Geometric similarity of fermenter geometry is a pre-requisite for applying established scale-up relationship. 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 also assumes reasonably constant impeller geometry such as impeller diameter (D_I) and number of impellers (N). Based on target total a/o working volumes obtained from geometric similarity, the desired working volume in the fermenter may be altered during experimentation. The ratio of the impeller to fermenter diameter (D_I/D_T) in standard fermenters is between 0.3 to 0.45. Fermenters with a standard geometry are beneficial within scale-up correlations assuming constant geometry. Common pilot scale-up fermenters have H_T/D_T ratios of 3:1, but they can also decrease to 1:1.

The first approach within agitation is to check the design of impellers, number of impellers, diameter and location. Common impellers used within microbial fermentations are Rushton turbines or Hollow-blade (U-shape), but could also be Hydrofoil, Maxflo, etc. Stirrer tip speed (STS) is the simplest approach normally used in case of same design of impellers between two scales. 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. Typical STS ranges from 3.8 to 7.6 m/s.

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 normally used in a case of scale-up for various design of impellers between two scales. P_G/V_L is expressed as P_G/V_L = P₀/V_L*0.5 = ((N_PN_I³D_I⁵ρ)/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). N_I and D_I are the impeller speed (s-1) and impeller diameter (m), ρ is specific broth density (kg/m³) and V_L is volume of fermentation broth (L). 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. It´s difficult to have high power per unit volume at the large scale due to practical limitation of the motor size.

Additional scale-up parameters are focused to oxygen transfer. They are Oxygen Uptake Rate (OUR) and Mass transfer coefficient (K_La). Scale-up based on OUR assumes that the OUR is equal to Oxygen transfer rate (OTR). 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. 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 = f₂(P_G/V_L)^aV_S^b , where f₂ is a proportionality constant. In general, the “a” value within this equation decreases with increasing working volume. The “a” value is  0.95, 0.67 and 0.5 for fermenters from lab scale (e.g. 10L scale), pilot scale (300L) and production scale (more than 20,000L) respectively. Same holds for the “b” value: 0.67 for lab and pilot scale and 0.50 for production scale. The formula for Superficial gas velocity (V_S) is V_S = φ_G/(π/4)*D_I²), where φ_G is Gass flow rate (m³/s)  and D_I is impeller diameter (m). Finally Gass flow rate can be calculated using φ_G = (Q * (t_act/t₀)*(P_atm/P_absolute))/3600, where Q is airflow rate (Nm³/s), t_act and t₀ are actual temperature and temperature of absolute ZERO in Kelvin and finally P_atm and P_absolute are the pressures. Production fermenters up to 100,000L scale have K_La value between 400 to 800 h^-1. Scale-up based on K_La is complicated approach by the fact that it is process specific and it changes over the fermentation, making it difficult to reliably quantify. Alternatively, measurement of broth DO concentration (C_L) can be used as an adequate scale-up parameter. The minimum acceptance value of C_L is well known from lab scale experiments. Cascade control of DO by agitation, aeration and back-pressure can be effective in maintaining of DO above critical value.

The Table 1 shows an example of most important parameters within scale-down model from 300L pilot fermenter to 75L lab fermenter. Appropriate set of all required parameters in small scale can be predictive for consecutive production in large scale. Finally, all set process parameters need to be confirmed in larger scale via pilot or ENG/Validation batches within further cGMP production.

CMC experts from Venn Life Sciences have strong expertise within theoretical and practical application of these models. Do you need more insight or support with your up-scaling process? Do not hesitate to contact us via our website: www.vennlifesciences.com.

Table 1. Practical application of scale-down model from pilot fermenter (300L) to laboratory fermenter (50L).

Note: For successful scale down model is necessary to set appropriate parameters in lab. scale such as agitation, aeration and back-pressure, that mimic parameters in pilot scale.

Date: 24.10.2022

Author: Juraj Boylo