RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media

M.W. Saaltink

Description

Abstract
The code RETRASO (REactive TRAnsport of SOlutes) simulates reactive transport of dissolved and gaseous species in non-isothermal saturated or unsaturated problems. Possible chemical reactions include aqueous complexation (including redox reactions), sorption, precipitation-dissolution of minerals and gas dissolution. Various models for sorption of solutes on solids are available, from experimental relationships (linear KD, Freundlich and Langmuir isotherms) to cation exchange and surface complexation models (constant capacitance, diffuse layer and triple layer models). Precipitation-dissolution and aqueous complexation can be modelled in equilibrium or according to kinetic laws. For the numerical solution of the reactive transport equations it uses the Direct Substitution Approach. The use of the code is demonstrated by three examples. The first example models various sorption processes in a smectite barrier. The second example models a complex chemical system in a two dimensional cross-section. The last example models pyrite weathering in an unsaturated medium.

Sujets

• Porous medium
• Numerical analysis

Informations

• Publié par: erevistas
• Publié le: 01 janvier 2004
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Geologica Acta, Vol.2, Nº3, 2004, 235-251
Available online at www.geologica-acta.com
RETRASO, a code for modeling reactive transport in saturated and
unsaturated porous media
1 1 2 1 1
M.W. SAALTINK F. BATLLE C. AYORA J. CARRERA andS. OLIVELLA
1 Dept. of Geotechnical Engineering and Geosciences, School of Civil Engineering, Technical University of Catalonia (UPC)
C/ Jordi Girona 1-3, building D-2, 08034 Barcelona, Spain. Saaltink E-mail: [e-mail] Batlle E-mail:
[e-mail] Carrera E-mail: [e-mail]
2 Institute of Earth Sciences Jaume Almera, Spanish Research Council (CSIC)
C/ Lluís Solé i Sabarís, s/n, 08028 Barcelona, Spain. E-mail: [e-mail]
ABSTRACT
The code RETRASO (REactive TRAnsport of SOlutes) simulates reactive transport of dissolved and gaseous
species in non-isothermal saturated or unsaturated problems. Possible chemical reactions include aqueous
complexation (including redox reactions), sorption, precipitation-dissolution of minerals and gas dissolution.
Various models for sorption of solutes on solids are available, from experimental relationships (linear K ,D
Freundlich and Langmuir isotherms) to cation exchange and surface complexation models (constant capaci-
tance, diffuse layer and triple layer models). Precipitation-dissolution and aqueous complexation can be mo-
deled in equilibrium or according to kinetic laws. For the numerical solution of the reactive transport equa-
tions it uses the Direct Substitution Approach. The use of the code is demonstrated by three examples. The
first example models various sorption processes in a smectite barrier. The second example models a complex
chemical system in a two dimensional cross-section. The last example models pyrite weathering in an unsatu-
rated medium. .
KEYWORDS Reactive transport. Porous media. Unsaturated flow modeling. Numerical methods.
groundwater and transport of solutes in groundwater byINTRODUCTION
means of advection, dispersion and diffusion together
with chemical reactions, such as acid-base reactions,The understanding of groundwater quality and the
redox reactions, complexation, biodegradation, adsorp-processes undergone by rocks in natural systems, the
tion, cation exchange and precipitation/dissolution ofstudy of soil and groundwater contamination and the per-
minerals. Moreover, in soils one has to consider unsatu-formance assessment of waste disposal facilities require
rated flow and transport processes in the gas phase, ofquantitative analyses of the migration of reactive sub-
which diffusion is of particular importance.stances in soil and groundwater. This in turn requires the
use of modeling tools which consider the concentrations
The last decades have witnessed considerable progressof several chemical species and are able to model flow of
© UB-ICTJA 235M.W. SAALTINK et al. Modeling reactive transport in porous media
on reactive transport modeling. Mangold and Tsang (1991) al., 2003). Examples of model codes that use the SNIA
and, more recently, Van der Lee and De Windt (2001) have are DYNAMIX (Liu and Narasimhan, 1989a), MIN-
written reviews on this subject. Reactive transport involves TRAN (Walter et al., 1994), PHREEQM (Appelo and
many chemical species with complex interactions with Willemsen, 1987), PHREEQC (Parkhurst, 1995), MOC-
each other through many chemical reactions. Rubin (1983) PHREEQE (Engesgaard and Traberg, 1996), and DIA-
was the first in discussing mathematical formulations of PHORE (Le Gallo et al., 1998). Only few model codes
the problem that make use of equilibrium constraints to use the DSA. Examples are TOUGH2 (White, 1995),
reduce the problem complexity. Later, several authors pre- GIMRT (Steefel and Yabusaki, 1995) and ARASE (Grin-
sented algebraic manipulations of matrices and vectors drod and Takase, 1996).
(Friedly and Rubin, 1992; Steefel and MacQuarrie, 1996;
Chilakapati et al., 1998). Finally, Saaltink et al. (1998) Modeling of reactive transport in the unsaturated zone
˘extended the use of such manipulations to reduce the num- has started more recently. Sim° unek and Suarez (1994)
ber of variables to the minimum, that is, to the degrees of developed the code UNSATCHEM-2D for modeling
freedom, according to the phase rule. major ion chemistry in variably saturated porous media;
Wunderly et al. (1996) coupled the code PYROX, which
The mathematical equations for reactive transport are describes oxygen diffusion and pyrite oxidation in an
highly non-linear. This, together with the large number of unsaturated zone, to MINTRAN. This coupled code was
unknowns, may easily lead to excessive computation applied to study the effects of spatial heterogeneity on
times, which makes it important to choose an appropriate water quality (Gerke et al. 1998) and to model the
approach to solve them. Several approaches are available. drainage of a mine impoundment (Bain et al. 2000).
However, one can consider them to be variants of two These codes assume local equilibrium for all the chemical
families of methods. The first one is the operator splitting reactions. More recently, however, Mayer et al. (2002)
or two-step approach, which includes the Sequential Iter- developed the code MIN3P, which is able to model reac-
ation Approach (SIA) and the Sequential Non Iteration tive transport in a saturated or unsaturated domain with-
Approach (SNIA). It consists of solving separately chem- out assuming local equilibrium between minerals and
ical equations and transport equations. The difference water.
between SIA and SNIA is that the first approach iterates
between these two types of equations to obtain a conver- The objective of this paper is to present the coupling
gent solution, whereas the second does not. The second of a former reactive transport code RETRASO (Saaltink
approach is the one-step, global implicit or Direct Substi- et al., 1997) with a multiphase flow and heat code CODE-
tution Approach (DSA). It consists of substituting the BRIGHT (Olivella et al., 1996). This results in a new tool
chemical equations into the transport equations and solv- that can handle both saturated and unsaturated flow, heat
ing them simultaneously, usually by means of the New- transport and reactive transport in both liquid and gas.
ton-Raphson method. In an article, which had a great Although CODE-BRIGHT also permits the modeling of
impact, Yeh and Tripathi (1989) stated, “only those mod- deformation or mechanical processes, this was not incor-
els that employ the SIA can be used for realistic applica- porated into the new code. Chemical reactions that can be
tions”. However, this has been criticized. Steefel and modeled include aqueous complexation (including redox
Lasaga (1994) wrote, “there are pros and cons to both reactions), adsorption, precipitation-dissolution of miner-
methods, but the choice is less clearcut in favor of the als and gas dissolution. One, two and three-dimensional
decoupled methods than suggested by Yeh and Tripathi finite elements can be used for the spatial discretization.
(1989)” and Van der Lee and De Windt (2001) called the It uses the Direct Substitution Approach for the numerical
statement “outdated”. Moreover, Saaltink et al. (2001) solution of the reactive transport equations. This method
showed that the SIA may require very small time steps to also may fail to converge (although less than the Sequen-
converge, where DSA can reach convergence in larger tial Iteration Approach). Therefore, the time step is auto-
time steps due to its robustness. Nevertheless, the SIA matically reduced if convergence is not achieved. The last
may be faster when large grids of two or three dimensions two features make RETRASO especially suitable for
are used. More importantly, the structure of SIA is easier highly non-linear cases. A user-friendly interface is used
to write in a modular form than that of DSA, which is in order to facilitate pre- and post-processing of the input
advantageous from a programming point of view. and output data.
Many model codes have been developed. Most of We start by explaining the mathematical equations
them use the SIA. Examples are HYDROGEOCHEM that describe the (un)saturated flow processes, the chemi-
(Yeh and Tripathi, 1991), MST1D (Engesgaard and Kipp, cal reactions and the reactive transport processes. Then,
1992), OS3D (Steefel and Yabusaki, 1995), TBS (Schäfer we explain the verification of the code, followed by
et al., 1998), FEREACT (Tebes-Stevens et al., 1998), examples of applications of RETRASO. The last section
TRANQUI (Xu et al., 1999) and HYTEC (Van der Lee et contains our conclusions.
Geologica Acta, Vol.2, Nº3, 2004, 235-251 236M.W. SAALTINK et al. Modeling reactive transport in porous media
FLOW AND HEAT TRANSPORT EQUATIONS through the porous medium, the other fluxes (j , j , j ) areEs El Eg
-2 -1advective fluxes (J m s ) of energy caused by mass mo-
Q -3 -1The flow problem is formulated in a multiphase tions and f is an internal/external energy supply (J m s ).
approach, that is, a porous media composed of solid
grains, water and gas. Within this porous media, thermal Constitutive equations and equilibrium restrictions
and hydraulic aspects will be taken into account, interact-
ing simultaneously and considered in an integrated way. A set of constitutive and equilibrium laws are required
Three phases are considered: solid phase (mineral), liquid to exp