Summary
To calculate the effective radii of two conductive elements in series in wood specimens by using the gas
permeability measurement, the four parameters from the curvilinear relationship of superficial specific
permeability against reciprocal mean pressure as illustrated in Petty's model must be evaluated. This
paper describes a detailed procedure for obtaining such parameters by using the least-squares fit calculated
from a statistical analysis system (SAS) program. Three different iterative optimization algorithms
and starting points were used separately to fit the Petty's nonlinear model based on the same experimental
data from one specimen of birch. The estimate of the parameters: A = 35.38 darcy, B = 80.51
darcy, l = 0.19 darcy atm, m = 6.34 darcy atm was recommended for the fitted model. Compared to the
results on the estimate of parameters obtained in the previous papers, this estimate for the parameters
was a global minimum, thus it was a refinement and more accurate. Since the Gauss-Newton method
resulted in almost the same convergence results for all the three sets of starting values with the least iterations
in the evaluation, it was the preferred optimization algorithm both for simplicity and accuracy in
solving the Petty's model. Because the same solutions for all three iterative optimization algorithms were
obtained by using two different sets of starting points produced from the grid search, a grid search
seemed to be very helpful for finding reasonable starting values for various iterative optimization techniques.
Gas Permeability of Cellulose Aerogels with a Designed Dual Pore Space System
