REACTIVE CHEMICAL TRANSPORT UNDER MULTIPHASE SYSTEM

REACTIVE CHEMICAL TRANSPORT UNDER MULTIPHASE SYSTEM

ABSTRACT

 

This thesis presents the development of BIOGEOCHEM, a numerical model to simulate biochemical and geochemical reactions in a batch system and HYDROBIOGEOCHEM, a numerical model to simulate HYDROlogic transport and BIOchemical and GEOCHEMical reactions under nonisothermal multiphase systems in 2-dimensions and 3-dimensions.

HYDROBIOGEOCHEM is a coupled hydrologic transport and biogeochemical reaction code, reaction module of which is BIOGEOCHEM, to predict the spatiotemporal distributions of all the important chemical species.  The formulation of BIOGEOCHEM and HYDROBIOGEOCHEM is new in that it is based on a general paradigm which uses the well accepted diagonalizetion-decomposition procedure. The unique features of the general paradigm are that it can simultaneously (1) facilitate the segregation (isolation) of linearly independent kinetic reactions and, thus, enable the formulation and parameterization of individual rates one reaction by one reaction when linearly dependent kinetic reactions are absent; (2) enable the inclusion of virtually any type of equilibrium expressions and kinetic rates users want to specify; (3) reduce problem stiffness by eliminating all fast reactions from the set of ordinary differential equations governing the evolution of kinetic variables; (4) perform systematic operations to remove redundant fast reactions and irrelevant kinetic reactions; (5) systematically define chemical components and explicitly enforce mass conservation; (6) accomplish automation in decoupling fast reactions from slow reactions; and (7) increase the

 

robustness of numerical integration of the governing equations with species switching schemes.

The new formulation in HYDROBIOGEOCHEM uses Gauss-Jordan decomposition to diagonalize the governing matrix equations for hydrologic transport to reduce primary dependent variables (PDVs), resulting in mobile components and mobile kinetic variables as PDVs.  Methods for coupling biogeochemical reaction and hydrologic transport, such as the sequential iteration approach (SIA) and predictor corrector approach are incorporated into the code to make the model versatile.

The governing transport equation can be written in conservative form and nonconservative form. Five different numerical schemes based on the two forms of equations are incorporated in HYDROBIOGEOCHEM to better understand different physical processes. They are (1) FEM on advective form of equation, (2) FEM on conservative form of equation, (3) Hybrid Lagrangian-Eulerian FEM for interior elements + FEM on advective form of equation for boundary elements, (4) hybrid Lagrangian-Eulerian FEM, and (5) Hybrid Lagrangian-Eulerian FEM for interior elements + FEM on conservative form of equation for boundary elements.

Heat transfer is considered in HYDROBIOGEOCHEM to account for the temperature variations that may impact hydrologic transport by affecting the hydrologic and chemical conditions in the subsurface system.  Weak coupling will be applied to solve a system of chemical transport and heat transfer to save computing resources.

HYDROBIOGEOCHEM is designed to assess migration of subsurface contamination and help design remediation technologies. The prospective field application of the model is demonstrated by examples.

TABLE OF CONTENTS

 

LIST OF FIGURES……………………………………………………………………………………………… vii

LIST OF TABLES……………………………………………………………………………………………….. ix

ACKNOWLEDGEMENTS……………………………………………………………………………………. x

 

CHAPTER 1. NTRODUCTION………………………………………….………………1

1.1. BACKGROUND AND LITERATURE REVIEW ………………………… 1

1.2. OBJECTIVE AND FORMAT…….……………………………………….. 6 REFERENCES ……………………………………………………………………8

 

CHAPTER 2. A GENERAL PARADIGM TO MODEL REACTION-BASED BIOGEOCHEMICAL PROCESSES IN BATCH SYSTEMS…………….…….12

 

ABSTRACT …………………………………………………………………….. 12

2.1. INTRODUCTION ………………………………………………………………… 15

2.2. REACTION NETWORK…………………………………………………… 19

2.3. DECOMPOSITION OF REACTION NETWORK ………………………… 30

2.4. REACTION RATE FORMULATIONS …………………………………….47

2.5. NUMERICAL SOLUTION …..……………………………………………. 50

2.6. EXAMPLE SIMULATIONS ……….………………………………………54

2.7. CONCLUSION AND DISCUSSION ……………………………………… 66 APPENDIX 2.A ………………………………………………………………… 69 APPENDIX 2.B ………………………………………………………………… 78

 

ACKNOWLEDGEMENTS……………………………………………………… 83

REFERENCES………………………………………………………………….. 84

 

CHAPTER 3. REACTIVE TRANSPORT UNDER MULTIPHASE SYSTEM: – MODEL FORMUATION AND NUMERICAL SCHEMES ……………………..93

 

ABSTRACT………………………………………………………………………93

3.1. INTRODUCTION………………………………………………………….. 95

3.2. PARADIGM REVIEW …..…………………………………………………97

3.3. GOVERNING EQUAITONS FOR TRANSPORT ……………………….101

3.4. EXAMPLE SIMULATIONS ………………………………………………114 3.5. DISCUSSION AND CONCLUSIONS …………………………………… 127 APPENDIX 3.A MATRIX EQUATION FOR DIFFERENT NUMERICAL

SCHEMES………………………………………………………………………129 ACKNOWLEDGEMENTS…………………………………………………….135

REFERENCES………………………………………………………………… 136

 

CHAPTER 4. 3-DIMENSIONAL NON-ISOTHERMAL REACTIVE TRANSPORT UNDER MULTIPHASE SYSTEM……………………………….……………..143

 

ABSTRACT…………………………………………………………………….143

4.1. INTRODUCTION ………………………………………………………… 145

4.2. GOVERNING EQUATIONS FOR HYDROLOGIC TRANSPORT ……. 146

4.3. NUMERICAL IMPLEMENTATOIN ……………………………………..150

4.4. GOVERNING EQUATIONS FOR HEAT TRANSFER ………………… 153

4.5. EXAMPLE SIMULATIONS ………………………………………………156

4.6. CONCLUSION …………………………………………………………… 159

APPENDIX 4.A ADVECTIVE FORM EQUATONS FOR HYDROLOGIC

TRANSPORT…………………………………………………………..160

APPENDIX 4.B INITIAL AND BOUNDARY CONDITIONS FOR

HYDROLOGIC TRANSPORT…………………………………………163

APPENDIX 4.C MATRIX EQUATIONS FOR DIFFERENT NUMERICAL

SCHEMES………………………………………………………………167

APPENDIX 4.D ADVECTIVE FORM EQUATIONS FOR HEAT  TRANSFER…………………..…………………………………………173

 

ACKNOWLEDGEMENTS…………………………………………………….174

REFERENCES………………………………………………………………… 175

 

CHAPTER 5. SUMMARY AND FUTURE WORK………………………………….. 191

5.1. SUMMARY……………………………………………………………….. 191 5.2. FUTURE WORK …………………………………………………………. 192

REFERENCES………………………………………………………………… 193

CHAPTER 1. 

INTRODUCTION

 

This thesis presents the numerical modeling of biochemical and geochemical reactions in batch systems and non-isothermal reactive chemical transport under multiphase systems. Included in the transport model, HYDROBIOGEOCHEM, (a numerical model to simulate HYDROlogic transport and BIOchemical and GEOCHEMical reactions under nonisothermal multiphase systems) are transport processes including advection, dispersion, and molecular diffusion, and chemical processes including aqueous complexation, adsorption-desorption, ion-exchange, oxidation-reduction, precipitation-dissolution, acid-base reactions, and microbial mediated reactions. Chemical processes are modeled with BIOGEOCHEM, a batch numerical speciation model. Reaction rates considered in the BIOGEOCHEM is the most comprehensive so far. Because of this broad modeling scope, HYDROBIOGEOCHEM has a prospective to be applied to a wide range of subsurface contamination problems, and to provide a powerful tool for mechanistically understanding biogechemical processes under transport in natural systems and proper designing of remediation technologies.

 

1.1      BACKGROUND AND LITERATURE REVIEW

 

Increasing human activities have induced potential adverse effect on the environment, particularly the contamination of the groundwater. General sources of groundwater contamination include accidental spills and leaks, mining, salt intrusion and others (Chareneau, 2000). Once the contaminants are introduced into the subsurface, they will pose a potential threat to large volumes of groundwater flowing through porous media under the surface of the earth.

Typical porous medium contains solid phase, water phase and gas phase, and there may be a number of natural chemical species in each phase. In the case of contamination, the medium also contains foreign chemicals – contaminants, which can end up in different phases during their migration processes as the result of the complex interplay among hydrological, physical, geochemical, and biochemical processes in the subsurface environment.

Once in contact with soil, a contaminant composed of several chemical species enters the soil and migrates downward through the unsaturated zone under gravity. In some circumstances, the contaminant may be dissolved as a portion of the aqueous phase. When the source of contaminant is associated with leaking underground tanks, it will be in the form of nonaqueous phase liquid (NAPL) because the majority of these tanks store petroleum products with low solubility in water. Ttrichloroethylene (TCE), for example, has a solubility of 1100 ppm in water at 20^oC (Pinder and Abriola, 1986). In addition, light components of the contaminant may vaporize into the soil air. Some contaminant will be trapped in the matrix of the porous media, while others will eventually reach the water table and migrate as part of the groundwater.

The migration of a chemical contaminant in the subsurface is a very complex process since its release to the subsurface environment. It will be controlled by hydrological processes, transport processes such as advection and dispersion, and biogeochemical processes such as precipitation-dissolution, adsorption, and aqueous speciation reactions (Viswanathan et al., 1998). Therefore, the assessment of subsurface contamination and proper design of remediation technologies requires accurate model of the transport of contaminants in subsurface system.

A fundamental question to the transport of the chemical species under the multiphase system is how the concentrations of each chemical species within different phases relate to each other, the understanding of which is known as reactive chemical transport (Cheng, 1995, and reference therein). The simplest and most common approach is the local equilibrium assumption (Charbeneau, 2000). This approach assumes that the rate of mass transport through the porous media within a phase is slow compared to the rate of mass transfer between phases in contact locally, i.e., the species in different phases are in thermodynamic equilibrium. However, experimental evidence has shown that this assumption is not always tenable (Friedly and Rubin, 1992, and references therein).

Various ways have been attempted by researchers to solve the reactive transport problems. Hunter et al. (1998) classified and reviewed models of reactive transport developed till 1996 in subsurface environments. Most of these biogeochemical models are based on local equilibrium assumption due to computational limitations and the lack of database in kinetic rate constants. This assumption may provide a good approximation for many homogeneous speciation, acid-base and adsorption reactions; however, it may not reflect realistic spatio-temporal distributions of chemical species in subsurface systems when dealing with slow reactions, such as mineral dissolution/precipitation and oxidation/reduction (Hunter et al., 1998).

In the past few years, there have been considerable efforts to deal with the kinetically controlled, multi-component transport in the development of reactive chemical transport in the subsurface systems. We have witnessed the rapid evolution of models for the analysis of reactive chemical transport with the growing thermodynamic and kinetic databases. These models include PHREEQC (Parhurst, 1995), an ion-association aqueous model designed for low-temperature aqueous geochemical calculations; RAFT (Chilakapati, 1995; Chilakapati et al. 2000), a tool for arbitrarily complex coupled kinetic-equilibrium heterogeneous reaction networks; OS3D (Steefel and Yabusaki, 1996), a 3D model designed for multicomponent, multispecies chemistry, considering multiscale heterogeneities; HYDROGEOCHEM (Cheng and Yeh, 1998), a model designed for the simulation of reactive multispecies-multicomponent chemical transport through saturated-unsaturated media under non-isothermal conditions; BIORXNTRN (Hunter et al., 1998), a model focusing on the comprehensive kinetic reaction network for the multi-component biogeochemical dynamics of groundwater systems; BIOKEMOD (Salvage and Yeh, 1998), a model designed for simulating any mixture of geochemical and mocriobiological reactions in subsurface systems; TRANQUI (Xu, 1999), a 2D model dealing with thermo-hydro-geochemical problems for single phase saturatedunsaturated porous media flow systems; LEHGC2.0 (Yeh et. al, 2001a), a model for coupled fluid flow and reactive chemical transport; and some others. There were several articles on the application and development of reactive chemical transport models in a special issue of Journal of Hydroloy (Volume 209).

Even though there is a large reservoir of numerical models available as mentioned above, numerical efficiency for modeling reactive chemical transport is still of major concern because of the complex nature of transport and reaction processes and their interactions.  Usually, flow and transport can be treated in separate steps. However, from a physical point of view, the chemicals contained in the subsystem affect the solution density and induce changes in the flow field, which becomes dependent not only on the hydrogeologic parameters of the system, but also on the chemical concentration. This interdependence produces a coupling between the flow and transport equations. Secondly, as the chemical part of reactive transport models becomes more complex (considering mixed equilibrium and kinetic reactions), a challenge is posed on numerical formulations that can solve the resulting governing equations efficiently.

Method to couple chemistry codes to transport models varies according to the particular codes.  Some chemical codes have been extended to include solute transport, for example, the geochemical code PHREEQE has been expanded to account for onedimensional advection, and equilibrium code MINTEQ2 has been coupled with the twodimensional advective-dispersive transport code PLUME2D, as summarized by Hunter et al. (1998). Some chemical codes are iteratively coupled with transport codes, such as HYDROGEOCHEM (Yeh and Tripathi, 1991).

Yeh and Tripathi (1989) reviewed and discussed a number of approaches used in different transport models and compared the computation effort of each approach with regard to the formulation of governing equations and the types of reactions considered.  Steefel and MacQuarrie (1996) also reviewed several approaches for accuracy and computational efficiency.  However, the comparison of different approaches is still an active topic in the literature (for example, Saaltink et al., 2001). In the meantime, there are new techniques being proposed other than the three general categories: operator splitting, the global implicit method and sequential iteration methods, such as ‘selective coupling method’ in FEHM (Robinson et al., 2000).

While reactive chemical transport in a single flow system is still a subject of intensive research, some researchers have already initiated investigations in multiphase systems (for example, Lichtner and Seth, 1996; Viswanathan et al., 1998; Xu and Pruess, 2001). Limits of applicability of some of the models were addressed by Wu and Pruess (2000), for example, the assumption of isothermal system in the models. However, temperature variations may impact transport by affecting the hydrologic and chemical conditions. Therefore, heat transfer should be considered in the models to account for the temperature effect.

Of all the models cited above, most have the limitation of assuming that all biogeochemical reactions can be easily written in basic (canonical) forms, which is not obvious when there are many parallel kinetic reactions (Yeh et al., 2000; Yeh et al., 2001b).  And this limitation will certainly affect the generality of these models. On the other hand, the rate formulation for biogeochemical reactions is a primary challenge in biogeochemical modeling. Ad hoc approach dominates in current literature. It is not able to capture key features of a natural system via several measurable parameters. Therefore, a reaction-based formulation, though difficult to attain, is in need to alleviate the problem.

 

1.2       OBJECTIVE AND FORMAT

 

This thesis is to develop a non-isothermal, reactive chemical transport model on a reaction-based formulation under the multiphase system. The ultimate goal is to develop the capability of the model to calculate the spatio-temporal distributions of all the important chemical species, reaction rates in the system. The organization of the thesis is as follows: A theoretical description of the batch model BIOGEOCHEM will be presented first. Followed by the derivation of the governing equations for reactive transport based on a new formulation and heat transfer under multiphase system, the techniques involved in transport calculations will be discussed. The thesis is made up of three journal articles. Chapter 2 presents the development, and application of the batch biogeochemical reaction model BIOGEOCHEM; this paper has been accepted for publication by Water Resources Research.  Chapter 3 presents the formulation and different numerical schemes of HYDROBIOGEOCHEM, a reactive transport model; this paper is intended for submission to Water Resources Research.  Chapter 4 presents the formulation of a three dimensional non-isothermal reactive transport model, 3DHYDROBIOGEOCHEM; this paper is intended for submission to the Journal of Hydrology. Chapter 5 summarizes the work presented in this thesis and outlines the limits of the study.

 

 

 

 

 

 

 

 

 

 

REFERENCES

Charbeneau, R.J., 2000. Groundwater Hydraulics and Pollutant Transport. Prentice Hall, New Jersey.

Cheng, H.P., 1995. Development and application of a three-dimensional finite element model of subsurface flow, heat transfer, and reactive chemical transport. Dissertation, The Pennsylvania State University.

Cheng, H.P. and Yeh, G.T., 1998. Development and demonstrative application of a 3-D numerical model of subsurface flow, heat transfer, and reactive chemical transport: 3DHYDROGEOCHEM. J. Contami. Hydrol. 34, 47-83.

Chilakapati, A., 1995. RAFT: A simulator for ReActive Flow and Transport of groundwater contaminants. PNL Report 10636, Pacific Northwest Laboratory, Richland, WA.

Chilakapati, A., Yabusaki, S., Szecsody, J. and MacEvoy, W., 2000. Groundwater flow, multicomponent transport and biogeochemistry: development and application of a coupled process model. J. Contami. Hydrol. 43, 303-325.

Friedly, J.C., Rubin, J., 1992. Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions. Water Resources Research, 28, 19351953.

Hunter, K.S., Wang, Y., and Frind, E.O., 1998. Modeling the effect of chemical heterogeneity on acidification and solute leaching in overburden mine spoils. J.

Hydrol. 209, 166-185.

Lichtner, P.C., Seth, M., 1996. Multiphase-multicomponent nonisothermal reactive transport in partially saturated porous media. In: Proceedings of the International Conference on Deep Geological Disposal of Radioactive Waste, Canadian Nuclear Society, September 16-19, Winnnipeg, Manitoba, Canada, 3-133-42pp.

Parkhurst, D.L., 1995. User’s guide to PHREEQC – a computer program for speciation, reaction-path, advective transport, and inverse geochemical calculations. US Geological Survey Water Resources Investigations Report 95-4227.

Pinder, G.F. and Abriola, L.M., 1986. On the simulation of nonaqueous phase organic compounds in the subsurface. Water Resour. Res. 22, 109S-119S.

Robinson, B.A., Viswanathan, H.S. and Valocchi, A.J., 2000. Efficient numerical techniques for modeling multicomponent ground-water transport based upon simultaneous solution of strongly coupled subsets of chemical components. Advances in Water Resources. 23, 307-324.

Saaltink, M.W., Carrera, J. and Ayora, C., 2001. On the behavior of approaches to simulate reactive transport. J. Contami. Hydrol. 48, 213-235.

Salvage, K., Yeh, G.T., 1998. Development and application of a numerical model of kinetic and equilibrium microbiological and geochemical reactions (BIOKEMOD). J. Hydrol. 209, 27-52.

Steefel, C.I., MacQuarrie, K.T., 1996. Approaches to modeling reactive transport in porous media. In: Lichtner, P.C., Steefel, C.T., Oelkers, E.H. (Eds), Reactive Transport in Porous Media, Reviews in Mineralology 34. Mineral. Soc. Am. 83, 83-129.

Steefel, C.I., Yabusaki, S.B., 1996. OS3D/GIMRT, Software for modeling multicomponent-multidimensional reactive transport, user’s manual and programmer’s guide. PNL-11166, Pacific Northwest Lagoratory, Richland, WA.

Viswanathan, H.S., Robinson, B.A., Valocchi, A.J., and Triay, I.R., 1998. A reactive transport model of neptunium migration from the potential repository at Yucca Mountain. J. Hydrol. 209, 251-280.

Wu, Y.S. and Pruess, K., 2000. Numerical simulation of non-isothermal multiphase tracer transport in heterogeneous fractured porous media. Advances in Water Resour.

23, 699-723.

Xu, T., Samper, J., Ayora C., Manzano, M. and Custodio, E., 1999. Modeling of nonisothermal multi-component reactive transport in field scale porous media flow systems. J. Hydro. 214, 144-164.

Xu, T. and Pruess, K., 2001. Modeling multiphase non-isothermal fluid flow and reactive transport in variably saturated fractured rocks: 1. methodology. American journal of science, Vol. 301(1), 16-33.

Yeh, G.T., Tripathi, V.S., 1989. A critical evaluation o frecent developments of hydrogeochemical transport models of reactive multichemical components.

Water Resour. Res. 25(1), 93-108.

Yeh, G.T., Tripathi, V.S., 1991. HYDROGEOCHEM: A coupled model of hydrologic transport and geochemical equilibrium in reactive multicomponent systems. ORNL-6371, Oak Ridge National Laboratory, Environmental Sciences Division.

Yeh, G.T., Burgos W.D., Fang, Y. and Zachara J.M., 2000.  Modeling biogeochemical kinetics: issues and data needs.  XIII International Conference on Computational Methods in Water resources, 2000.

Yeh, G.T., Siegel, M.D. and Li, M.H., 2001a. Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions. J. Contami. Hydrol. 47, 379-390.

Yeh, G.T., Burgos, W.D., and Zachara, J.M., 2001b. Modeling and measuring biogeochemical reactions: system consistency, data needs, and rate formulation.

Advances in Environmental Research. 5, 219-237.

REACTIVE CHEMICAL TRANSPORT UNDER MULTIPHASE SYSTEM

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