(426d) Rapid Interval Arithmetic Screening of Continuous Pharmaceutical Processes

Modern pharmaceutical
manufacturing faces a number of technical and economic challenges, due to
global corporate competition, outsourcing and proliferation of low-cost,
generic products. Pharmaceutical Research and Development (R&D) is pivotal
in ensuring prolonged growth in such a knowledge-intensive industry; therefore,
rapid screening of numerous process alternatives is quintessential in optimal
resource allocation for any portfolio of drugs under development. The
systematic process optimization literature has addressed via detailed model
formulations many real, pressing and complex problems of the modern
pharmaceutical industry (Grossmann, 2004) and also the optimal management of
the product R&D pipeline itself (Jain & Grossmann, 1999). Frequently,
vast amounts of time, expertise and resources must be invested in examining the
process chemistry and technology for developing a new Active Pharmaceutical
Ingredient (API), just in order to obtain the minimum set of data necessary for
deciding its feasibility and viability, without adequate organic synthesis
specifications or physicochemical behavior characterization. In such
circumstances, reaction kinetics and mixture thermodynamics may be figurative
at best.

Continuous Pharmaceutical
Manufacturing (CPM) attracts ever-increasing attention nowadays, because of
the expanding profitability gap experienced by most pharmaceutical companies;
the latter is due to increasing R&D and operating costs and decreasing drug
prices (Behr, 2004). Despite the strict licensing requirements for product
purity and stability, and the established batch manufacturing processes, the
FDA has spearheaded CPM initiatives, recognizing that CPM has a strong
potential to improve product quality and suppress operating cost (Plumb, 2005).
Developing novel pharmaceuticals provides ample opportunity to explore the CPM
paradigm, rather than committing resources to retrofitting production lines and
replicating clinical trials. Organic synthesis routes and candidate flowsheets
can still be too many, even for a single API, so a rapid screening methodology
can facilitate preliminary analysis of multiple CPM pathways.

Interval Arithmetic (IA)
and the more CPU-expensive Affine Arithmetic (AA) methodologies are
based on simple in form yet rich in content representations of real variables
and functions: the key IA idea is that if a variable x can be bracketed
in an interval, then any analytic function thereof can also be bracketed in a
corresponding (albeit possibly overestimating) interval image. The key
AA idea is that if a variable x can be represented by an affine
expression (finite linear combination of noise symbols ε_i in [-1,1] and interval-bracketed floating-point
coefficients x_i in R), then any function thereof can also be
represented by another affine expression, based on ε_i
and x_i. A similar (yet more expensive) quadratic form has
been proposed (Messine & Touhami, 2006). Detailed monographs on IA
(Neumaier, 1990) and AA (Stolfi & De Figueiredo, 1997) discuss their
theoretical background, software tools (Popova, 2004) are available, and
applications in chemical (Balaji & Seader, 1995) and process (Lin &
Stadtherr, 2004) engineering are published. Recently, IA was used in interval
propagation of process specifications (Schug & Realff, 1998), as well as in
determining limiting flows in extractive distillation (Frits et al., 2006);
that group also used IA-based optimization tools to explore the feasibility of
the process (Frits et al., 2007). AA methods have been employed for determining
equilibrium cascades (Baharev & Rév, 2008). To the best of our knowledge
though, IA methods have not been used in rapid process screening.

The fundamental idea in this
paper is to use IA methods for rapid screening of process potential. The
majority of (mildly endothermic or exothermic) continuous pharmaceutical
processes which are considered in an R&D pipeline can be studied via their
plantwide mass and molar balances: despite the fact that kinetic rate
expressions are nonlinear in terms of molar component flows, the introduction
of reaction extents and/or fractional conversions in such a mathematical
formulation renders a linear (in the output variables) model;
this can then be used to obtain a square form, after analyzing the degrees of
freedom and considering all known process design specifications. This compact
formulation is extremely useful in IA implementations of linear CPM models,
towards the rapid screening of technical feasibility and economic viability of
several process alternatives and/or variations: thus, CPU-intensive plantwide
simulations are effectively avoided. For uncertain yet reliably bounded process
parameters with a clear effect on a CPM flowsheet (e.g. fractional conversions
which are defined in [0,1] by default,
flow/separation split ratios, etc.)
solving a square linear CPM model can yield an envelope of attainable
compositions/flowrates. The use of a linear IA formulation is advantageous over
repetitive steady-state simulation for specific parameter value combinations
(isolated points in a multidimensional parameter space), avoiding prohibitively
numerous runs to populate the image space (e.g. Monte Carlo methods). The true
image of a linear IA model is a multidimensional (and generally nonconvex)
polytope. The technical feasibility can be assessed by examining the
predicted (e.g. flowrate) intervals. Despite the latter being subject to
overestimation due to the approximating nature of IA methods, the proposed
approach provides a criterion for safely rejecting inferior CPM process
flowsheets. The economic viability can subsequently be determined by
postprocessing the foregoing results and identifying whether the selected
metrics (e.g. NPV, ROI, etc.) meet or exceed
requisite levels.

Compact linear IA models have
been derived here for several exemplary process flowsheets, with subsequent
implementation in INTLAB, a versatile MATLAB IA toolbox (Rump, 1999). The
exemplary cases we have formulated and solved to illustrate the proposed method
include:

a) The well-established
Williams-Otto reactor design problem (DiBella & Stevens, 1965).

b) A chlorobenzene plant that was
recently discussed in IA context (Byrne & Bogle, 2000).

c) A novel continuous
pharmaceutical process design problem furnished by Novartis Pharma AG.

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