A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology

Thesis (M.Eng.) - Asian Institute of Technology, 1993

In this study, a model which could well represent the diffusive-advective transport of a non-reactive species and a low concentration reactive species through a saturated porous media is identified. By realizing the fact that the available analytical solutions to the governing differential equation are applicable to certain limiting cases only, based on the idea of ROWE (1985a), a more general semi-analytical solution scheme is developed. The numerical inversion of Laplace transform involved in this scheme is carried out by introducing the CRUMP's algorithm (1976) along with the quotient difference algorithm. This solution scheme is implemented in a computer program which is written in FORTRAN77 and validated by comparing with some analytical solutions. Based on the physical model, a methodology which incorporates inverse analysis and forward analysis is also formulated. The inverse analysis is to calibrate the model parameters and the method chosen is an indirect method of inverse analysis namely the maximum likelihood method. This study is devoted to the estimation of two parameters which are the coefficient of hydrodynamic dispersion or diffusion coefficient and the distribution coefficient. The optimization of a non-linear function involved in the inverse analysis is carried out by using a conjugate gradient technique proposed by FLETCHER and REEVES (1964). The forward analysis is to make predictions and the method employed is the First Order Second Moment method. Uncertainty quantifications are also made in the estimation of parameters as well as in the predictions. The overall scheme of inverse and forward analysis is also implemented in a computer program. A set of numerical experiments is carried out on an artificially generated data sets to examine the estimation capability of the method which is followed by an analysis on a laboratory column experiment data. In the latter analysis uncertainty quantifications are also made- and the results are compared with the originally reported results. An analysis, essentially for the same purpose as above was also made on a real land fill data. The capability of the model and the proposed methodology are well demonstrated and certain requirements for the well-posedness of the inverse problem are identified.