NEWBOX: A computer program for parameter estimation in diffusion problems

Conference · Sun Jan 01 00:00:00 EST 1989 · American Chemical Society, Division of Environmental Chemistry, Preprints; (USA)

OSTI ID:6984738

Nestor, Jr, C W; Godbee, H W; Joy, D S ^[1]

---

1. Oak Ridge National Lab., TN (USA)

In the analysis of experiments to determine amounts of material transferred form 1 medium to another (e.g., the escape of chemically hazardous and radioactive materials from solids), there are at least 3 important considerations. These are (1) is the transport amenable to treatment by established mass transport theory; (2) do methods exist to find estimates of the parameters which will give a best fit, in some sense, to the experimental data; and (3) what computational procedures are available for evaluating the theoretical expressions. The authors have made the assumption that established mass transport theory is an adequate model for the situations under study. Since the solutions of the diffusion equation are usually nonlinear in some parameters (diffusion coefficient, reaction rate constants, etc.), use of a method of parameter adjustment involving first partial derivatives can be complicated and prone to errors in the computation of the derivatives. In addition, the parameters must satisfy certain constraints; for example, the diffusion coefficient must remain positive. For these reasons, a variant of the constrained simplex method of M. J. Box has been used to estimate parameters. It is similar, but not identical, to the downhill simplex method of Nelder and Mead. In general, they calculate the fraction of material transferred as a function of time from expressions obtained by the inversion of the Laplace transform of the fraction transferred, rather than by taking derivatives of a calculated concentration profile. With the above approaches to the 3 considerations listed at the outset, they developed a computer program NEWBOX, usable on a personal computer, to calculate the fractional release of material from 4 different geometrical shapes (semi-infinite medium, finite slab, finite circular cylinder, and sphere), accounting for several different boundary conditions.

• OSTI ID: 6984738
• Report Number(s): CONF-8904178-; CODEN: ACEPC; TRN: 90-010049
• Journal Information: American Chemical Society, Division of Environmental Chemistry, Preprints; (USA), Vol. 29:1; Conference: Symposium on leaching tests, Dallas, TX (USA), 9-14 Apr 1989; ISSN 0093-3066
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES
LEACHING
COMPUTER CODES
CALCULATION METHODS
DATA ANALYSIS
HAZARDOUS MATERIALS
LAPLACIAN
MEASURING INSTRUMENTS
DISSOLUTION
MATERIALS
MATHEMATICAL OPERATORS
SEPARATION PROCESSES
540210* - Environment
Terrestrial- Basic Studies- (1990-)
540230 - Environment
Terrestrial- Radioactive Materials Monitoring & Transport- (1990-)
540330 - Environment
Aquatic- Radioactive Materials Monitoring & Transport- (1990-)
990200 - Mathematics & Computers
052002 - Nuclear Fuels- Waste Disposal & Storage