(448e) Rapid Interval Arithmetic Screening of Continuous Pharmaceutical Processes with Explicit Thermodynamics

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 in [-1,1] and interval-bracketed floating-point coefficients x) then any function thereof can also be represented by another affine expression, based on ε and x. 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 explicit consideration of process thermodynamics, in order to understand the impact of thermodynamic parameter interval variation on separation unit efficiency and plantwide API yield.

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