Saturday, April 19, 2008

Design Space for a Synthesis Reaction, Part 3

In previous posts I have considered a hydrogenation reaction as an example operation for which to define the design space for QbD purposes. I have taken a mechanistic approach to the reaction and captured the resulting process understanding in a process scheme and a mechanistic model. Finally, I showed some example response surfaces for critical quality atributes (CQA) that such a model can generate, enabling possible design spaces and acceptable parameter (CPP) ranges to be visualized. This method of running the model many times over to create a response surface closely parallels the conventional work process when deriving the response surface from experiments alone, but with potential to save a considerable amount of experimental work using modeling alongside experiments.

Leading pharmaceutical companies are going further than this. Mechanistic modeling is changing the types and objectives of the experiments they do. They are also asking whether the very definition of the design space would be better expressed by using the model to decide whether a given set of CPP values were inside or outside the design space; in other words, if the model predicts that the CQA will be achieved, then the corresponding CPP values are inside the design space. This leads to a much more flexible design space definition than rigid proven acceptable ranges (PAR).

This post gives some further examples of predictions using the hydrogenation model where we explore the ranges of CPPs that in combination with other CPPs produce precisely the required CQA (no more and no less), in this case a product yield of 90%, in a reaction time of 10 hours or less. We find that extreme values of some parameters (such as pressure, catalyst concentration, mass transfer coefficient) still lie in the design space for this reaction, as long as other CPPs take on appropriate values. Examples of combinations of CPPs that produce the CQA are given in the charts below.

Figure 1: Pressures in the range 22.8 to 3.6 bar achieve the target CQA when they occur in combination with kLa values defined by the curve ranging from 0.004 to 0.48 1/s. This is because high pressure raises hydrogen solubility, increasing the mass transfer driving force and requiring a lower kLa to achieve a given hydrogenation rate. This illustrates the use of high pressure to compensate for lack of mass transfer performance.

Figure 2: It should not be too surprising that the required kLa is directly related to the catalyst charge (shown here for lab scale conditions). High catalyst loading makes the chemistry faster and depletes the liquid of H2, which is supplemented by mass transfer from the headspace at a rate proportional to kLa. Catalyst charges from 0.07 to 1 g achieve the CQA when combined according to the curve with kLa values from 0.02 to 0.34 1/s.

Figure 3: Engineers will be interested in the required link between heat transfer and kLa shown here; once again a wide range of both parameters is acceptable but the ranges are related by the fact that high kLa leads to short reaction times and higher rates of heat release which must be compensated for quality and safety purposes by corresponding higher heat transfer coefficients. The relationship is not linear; at high kLa values (dissolved H2 nearing saturation) the reaction rate approaches the kinetically limited rate, i.e. does not continue to increase linearly with kLa.

Figures 1 to 3 offer significant processing flexibility, for example when transferring production to outside vendors or to new locations or equipment. The model indicates that CQA levels can be achieved with the right combinations of CPPs where acceptable individual CPP values vary over a very wide range.

All of these predictions derive from the compact and simply expressed DynoChem mechanistic model definition shown below (click to enlarge). This describes at a mechanistic level the interacting physical and chemical rates that lead to the behaviour of this reaction.

A subsequent post will discuss how such a model derived from experiments and mechanistic thinking should be verified for Design Space and QbD purposes.

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