MDL Groundwater software: Laplace transforms and the De Hoog algorithm to solve contaminant transport equations

The Modeling with De Hoog and Laplace (MDL) Groundwater software is a contaminant transport-modeling program offering a suite of models suitable for simulating subsurface transport of contaminants (i.e., chromium and organics), biotracers, and microorganisms. The MDL Groundwater software provides solutions to a wide range of contaminant transport models that do not have closed-form analytical solutions. The models are solved in Laplace space and the De Hoog algorithm is used to numerically invert the frequency domain solutions. Each particular model is represented as a closed-form Laplace-space or frequency domain solution to a specific set of transport equation(s), boundary conditions, and initial conditions using Fortan dynamic link libraries in the MDL Groundwater software. The windows interface is used to simulate and visualize concentrations of tracer, contaminant, or microbial transport in the time-space domain. The program's strength is that it readily provides solutions to numerous contaminant transport equations while being suitable for a wide audience. Several models within the program can be used to investigate the fate and transport of biotracers and microorganism associated with the reduction of chromium. While others can serve as instructional tools providing expanded understanding of various physical, biological, and chemical processes affecting the fate and transport of contaminants and microorganisms in one-, two- and three-dimensional systems.

[1]  K. H. Coats,et al.  Dead-End Pore Volume and Dispersion in Porous Media , 1964 .

[2]  Kirk Hatfield,et al.  Transport in Porous Media Containing Residual Hydrocarbon. I: Model , 1993 .

[3]  Harvey Dubner,et al.  Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform , 1968, JACM.

[4]  Seunghyun Kim,et al.  A Kinetic Approach to Modeling Mobile Bacteria-Facilitated Groundwater Contaminant Transport , 1996 .

[5]  J. Letey,et al.  Predicted distribution of organic chemicals in solution and adsorbed as a function of position and time for various chemical and soil properties. , 1970 .

[6]  A. N. Stokes,et al.  An Improved Method for Numerical Inversion of Laplace Transforms , 1982 .

[7]  W. J. Alves,et al.  Analytical solutions of the one-dimensional convective-dispersive solute transport equation , 1982 .

[8]  G. Z. Hornberger,et al.  A three-dimensional method-of-characteristics solute-transport model (MOC3D) , 1996 .

[9]  H. Rutishauser.  Der Quotienten-Differenzen-Algorithmus , 1954 .

[10]  G. T. Yeh.  AT123D: analytical transient one-, two-, and three-dimensional simulation of waste transport in the aquifer system , 1981 .

[11]  P. Wynn,et al.  TRANSFORMATIONS TO ACCELERATE THE CONVERGENCE OF FOURIER SERIES. , 1966 .

[12]  Louis A. Schmittroth,et al.  Numerical inversion of Laplace transforms , 1960, Commun. ACM.

[13]  D. Burris,et al.  Analytical model for heterogeneous reactions in mixed porous media , 1996 .

[14]  W. Schäfer,et al.  Transport of reactive species in heterogeneous porous media , 1996 .

[15]  Peter D. Welch,et al.  The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transforms☆ , 1970 .

[16]  Richard L. Smith,et al.  Transport of microspheres and indigenous bacteria through a sandy aquifer: Results of natural- and forced-gradient tracer experiments , 1989 .

[18]  Paul P. Wang,et al.  MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems; Documentation and User's Guide , 1999 .

[19]  F. Durbin,et al.  Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method , 1974, Comput. J..