DETERMINATION OF MASS-TRANSFER COEFFICIENTS DURING FREEZE-DRYING USING MODELING AND PARAMETER-ESTIMATION TECHNIQUES

An approach using mathematical modeling and parameter estimation techn iques was established to determine the best-fit mass transfer coeffici ents of the dried-layer resistance during primary drying of pharmaceut icals, in order to minimize experimental efforts. For modeling of the primary drying process, the equations associated with heat and mass tr ansfer mechanisms established by Pikal were used as the model equation s, whereas the parameter estimation was accomplished by Powell's nonli near least-squares minimization algorithm. The advantages of this appr oach include that it can be applied to analyze various types of measur able quantities, such as the cumulative mass of sublimation M(t), the temperature profiles at the bottom center of the frozen layer T-b, and the pressure profiles of the vials. It can also be used for these qua ntities measured using the vials with different heat transfer coeffici ents. To test the performance of the proposed approach, hypothetical v alues of M(t) and T-b, with perturbed errors, were simulated using the modeling algorithm and a random number generator. These values were i n turn used as the input data for parameter estimation. The results sh ow that the best-fit mass transfer coefficients are successfully obtai ned using either the hypothetical M(t) or T-b profiles, with appropria te initial guesses of the parameters. Ail computations in modeling and parameter estimation were developed in FORTRAN and compiled using Mic rosoft FORTRAN compiler, of which the source codes and documentation, with detailed mathematical equations and computation steps, are availa ble upon request.