Gour-Tsyh Yeh

A Model for Simulating Transport of Reactive Multispecies Components: Model Development and Demonstration

This paper presents the development and demonstration of a two-dimensional finite-element hydrogeochemical transport model, HYDROGEOCHEM, for simulating transport of reactive multispecies solutes. The model is designed for application to heterogeneous, anisotropic, saturated-unsaturated media under transient or steady state flow conditions. It simulates the chemical processes of complexation, dissolution-precipitation, adsorption-desorption, ion exchange, redox, and acid-base reaction, simultaneously. A set of four example problems are presented. The examples illustrate the models ability to simulate a variety of reactive transport problems. Important results presented include a depiction of the propagation of multiple precipitation-dissolution fronts, a display of the large errors in model response if the number of iterations between the hydrologic transport and chemical equilibrium modules is limited to one, an illustration of the development of greater concentration of contaminants In groundwater away from a waste site than near the source, and a demonstration of the variation in distribution coefficients of more than 6 orders of magnitude.

A multiple-pore-region concept to modeling mass transfer in subsurface media

Abstract Recent studies in soil science literature have strongly indicated the need to incorporate pore structures in near-surface mass transport modeling. There is increasing evidence suggesting that pore structures, such as fractures and macropores, facilitate the transport of water and solutes along a preferential flow path while water and solutes are moved into micropores and rock matrices concurrently. This study presents a conceptual model, a multiple-pore-region (or multi-region) concept, to account for pore structures as well as the resultant widely distributed pore water velocities in macroporous media. Pore regions can either be physically identified as discrete features, such as fractures and rock matrices, or be experimentally determined by separation of water retention curves according to pore classification schemes. A multi-region mechanism is proposed to account for the effect of local-scale and field-scale heterogeneities on mass transport under variably saturated conditions. Two numerical codes for subsurface fluid flow and solute transport have been developed with the multi-region concept, in which a firstorder mass exchange model is adopted to simulate the redistribution of pressure heads and solute concentrations among pore regions. The computer codes are used to demonstrate the applicability of the concept to fractured porous media, and to test a three-pore-region hypothesis using laboratory soil column tracer injection data. Based upon the parameters obtained from fitting multi-region and mobile-immobile models to these data, we successfully demonstrated that the former model has the advantage of maintaining consistent conceptual models over the latter under variably saturated conditions.

Using a Multiregion Model to Study the Effects of Advective and Diffusive Mass Transfer on Local Physical Nonequilibrium and Solute Mobility in a Structured Soil

Waste management problems for shallow land burial facilities in the humid eastern United States are usually complicated by slow but continuous movement of wastes through the soil matrix and discrete but rapid pulses of wastes through macropores and fractures. Multiple-pore-region models employed to describe flow and solute transport in the soils usually consist of multiple mass transfer coefficients that cannot be measured experimentally, and their effects on subsurface mass transport are poorly understood. The objective of this research was to study the individual and concurrent effects of interaggregate advection and diffusion on mass transport in a structured soil. The interactions of these two mass transfer processes and local solute concentration equilibrium are examined for a heterogeneous soil. Pore region water retention, hydraulic conductivity, and dispersivities, obtained from independent measurements and published calibration results, were used to test a novel three-pore-region, one-dimensional numerical model. Advective and diffusive mass transfer coefficients were estimated using mass transfer equations and fracture spacings published in the literature. The mass transfer coefficients were then varied systematically, and the sensitivity of local fluid pressure and solute concentration nonequilibrium to interregion mass transfer were analyzed. Our results indicated that time-dependent interaggregate advection and diffusion were important processes controlling solute mobility in heterogeneous media. Under transient flow conditions, interaggregate advection may reduce the significance of interaggregate diffusion that otherwise dominates interaggregate mass transfer under steady state conditions. Nonetheless, the equilibrium of local solute concentrations was 20 times more sensitive to diffusive mass transfer than to advective mass transfer, which suggests that site characterization efforts should be directed more toward the former process. Unfortunately, characterization efforts of this type are not commonplace and if available are frequently ignored because they add a difficult reality to complex waste management problems. Since advective and diffusive mass transfer may be important processes limiting the efficiency of cleanup activities such as pump and treat, it is perhaps time to include the characterization of these processes and quantification of the timescale of physical nonequilibrium in site remediation efforts.

Development and application of a numerical model of kinetic and equilibrium microbiological and geochemical reactions (BIOKEMOD)

Abstract This paper presents the conceptual and mathematical development of the numerical model titled BIOKEMOD, and verification simulations performed using the model. BIOKEMOD is a general computer model for simulation of geochemical and microbiological reactions in batch aqueous solutions. BIOKEMOD may be coupled with hydrologic transport codes for simulation of chemically and biologically reactive transport. The chemical systems simulated may include any mixture of kinetic and equilibrium reactions. The pH, pe, and ionic strength may be specified or simulated. Chemical processes included are aqueous complexation, adsorption, ion-exchange and precipitation/dissolution. Microbiological reactions address growth of biomass and degradation of chemicals by microbial metabolism of substrates, nutrients, and electron acceptors. Inhibition or facilitation of growth due to the presence of specific chemicals and a lag period for microbial acclimation to new substrates may be simulated if significant in the system of interest. Chemical reactions controlled by equilibrium are solved using the law of mass action relating the thermodynamic equilibrium constant to the activities of the products and reactants. Kinetic chemical reactions are solved using reaction rate equations based on collision theory. Microbiologically mediated reactions for substrate removal and biomass growth are assumed to follow Monod kinetics modified for the potentially limiting effects of substrate, nutrient, and electron acceptor availability. BIOKEMOD solves the ordinary differential and algebraic equations of mixed geochemical and biogeochemical reactions using the Newton–Raphson method with full matrix pivoting. Simulations may be either steady state or transient. Input to the program includes the stoichiometry and parameters describing the relevant chemical and microbiological reactions, initial conditions, and sources/sinks for each chemical species. Output includes the chemical and biomass concentrations at desired times. BIOKEMOD has been coupled with a hydrologic transport code, HYDROGEOCHEM, to allow the simulation of coupled advective–dispersive transport and biogeochemical transformation of pollutants in groundwater. Three verification exercises are compared with analytical solutions to demonstrate the correctness of the code. Two validation simulations of batch laboratory systems are compared with the laboratory data to demonstrate the codes ability to replicate behavior observed in real systems, and two validation exercises simulating reactive transport are presented to demonstrate the codes performance in simulating mixed equilibrium and kinetic biogeochemical reactions coupled with hydrologic transport.

FEMWATER: a finite-element model of water flow through saturated-unsaturated porous media

Upon examining the Water Movement Through Saturated-Unsaturated Porous Media: A Finite-Element Galerkin Model, it was felt that the model should be modified and expanded. The modification is made in calculating the flow field in a manner consistent with the finite element approach, in evaluating the moisture-content increasing rate within the region of interest, and in numerically computing the nonlinear terms. With these modifications, the flow field is continuous everywhere in the flow regime, including element boundaries and nodal points, and the mass loss through boundaries is much reduced. Expansion is made to include four additional numerical schemes which would be more appropriate for many situations. Also, to save computer storage, all arrays pertaining to the boundary condition information are compressed to smaller dimension, and to ease the treatment of different problems, all arrays are variably dimensioned in all subroutines. This report is intended to document these efforts. In addition, in the derivation of finite-element equations, matrix component representation is used, which is believed more readable than the matrix representation in its entirety. Two identical sample problems are simulated to show the difference between the original and revised models.

An exact peak capturing and Oscillation-Free Scheme to solve advection-dispersion transport equations

An exact peak capturing and essentially oscillation-free (EPCOF) algorithm, consisting of advection-dispersion decoupling, backward method of characteristics, forward node tracking, and adaptive local grid refinement, is developed to solve transport equations. This algorithm represents a refinement of LEZOOM, developed earlier by the senior author. In LEZOOM, a predetermined number of evenly spaced, hidden nodes was zoomed for a sharp front element, while in the EPCOF scheme, a subset of forwardly tracked nodes is zoomed. The number and location of this subset were automated. As a result, the peaks and valleys are captured exactly; and the ancillary problems of spurious oscillation, numerical dispersion, and phase errors are alleviated. Means of checking accumulated mass balance errors are provided. Application of the algorithm to two one-dimensional benchmark problems under a variety of conditions indicated that it completely eliminated peak clipping, spurious oscillation, phase error, and numerical dispersion. It yielded identical results, within the error tolerance, to exact solutions for all 19 test cases. Accumulated mass balance errors are extremely small for all 19 cases. The EPCOF scheme could solve the advective transport problems exactly, within any prescribed error tolerance, using mesh Peclet numbers ranging from 0 to infinity and very large mesh Courant numbers. The size of mesh Courant number is limited only by the accuracy requirement of the dispersion solver. Extension of this approach to multidimensional problems does not pose any conceptual difficulty and should alleviate the grid orientation trouble associated with such problems.

Three-dimensional air pollutant modeling in the lower atmosphere

A steady-state, three-dimensional turbulent diffusion equation describing the concentration distribution of an air pollutant from an elevated point source in the lower atmosphere is solved analytically. The same formulation can be used to obtain solutions from line, area or other kinds of sources. The solution is developed for the cases in which the velocity, vertical and lateral diffusivities are given by the power law. The model preserves the beauty of analytical solution without sacrificing much on the accuracy of approximating the velocity and eddy diffusivities. Methods of evaluating the parameters, which are required for the model applications, are discussed. Results indicate that the ratio of the plume width to the plume length increases with decreasing stability and with increasing source height. These consequences are in response to the variations of the size of eddies in the vertical direction.

A performance comparison of scalar, vector, and concurrent vector computers including supercomputers for modeling transport of reactive contaminants in groundwater

Sophisticated and highly computation-intensive models of transport of reactive contaminants in groundwater have been developed in recent years. Application of such models to real-world contaminant transport problems, e.g., simulation of groundwater transport of 10–15 chemically reactive elements (e.g., toxic metals) and relevant complexes and minerals in two and three dimensions over a distance of several hundred meters, requires high-performance computers including supercomputers. Although not widely recognized as such, the computational complexity and demand of these models compare with well-known computation-intensive applications including weather forecasting and quantum chemical calculations. A survey of the performance of a variety of available hardware, as measured by the run times for a reactive transport model HYDROGEOCHEM, showed that while supercomputers provide the fastest execution times for such problems, relatively low-cost reduced instruction set computer (RISC) based scalar computers provide the best performance-to-price ratio. Because supercomputers like the Cray X-MP are inherently multiuser resources, often the RISC computers also provide much better turnaround times. Furthermore, RISC-based workstations provide the best platforms for “visualization” of groundwater flow and contaminant plumes. The most notable result, however, is that current workstations costing less than

A Lagrangian-Eulerian Method with zoomable hidden fine-mesh approach to solving advection-dispersion equations

10,000 provide performance within a factor of 5 of a Cray X-MP.