Simulating flow and transport with advanced geochemical reactions Recent developments using PHREEQC as reaction engine

Transcription

1 Simulating flow and transport with advanced geochemical reactions Recent developments using PHREEQC as reaction engine Dr. Laurin Wissmeier AF-Consult Switzerland AG, Grundwasserschutz und Entsorgung Täfernstrasse 26 CH-5405 Baden Schweiz ABSTRACT: Reactive transport phenomena are relevant to fields such as groundwater protection, geothermal energy production, heap leaching, mine rehabilitation and nuclear waste disposal. Thus, reactive transport modelling is key in predicting the evolution of the water quality and solute behavior for safety assessments and process optimization. In recent years, couplings of groundwater flow and transport simulators with the geochemical modelling framework PHREEQC have become increasingly popular to describe adequately reaction processes that occur simultaneous to flow and transport. We present the new geochemical reaction engine PhreeqcRM [1], a wrapper class for PHREEQC that has been specifically designed for software couplings with existing flow and transport simulators. We explain the key functionality of PhreeqcRM and demonstrate its potential and performance as a reaction engine for FEFLOW. This implementation is then verified using an analytical solution for a 3D reactive transport example as well as the well-established MoMaS benchmarks for nuclear waste disposal. INTRODUCTION Since the release of IPhreeqc [2], several authors and groups have used this general purpose application programming interface (API) for the geochemical modelling framework PHREEQC [3] to couple it to transport codes in a wide variety of contexts, which indicates the scientific and industrial interest in using PHREEQC as a reaction module. A coupling with COMSOL was developed by Wissmeier and Barry [4], which gave access to the full range of COMSOL s flow and transport capabilities together with the complete set of geochemical reactions in PHREEQC. In the meantime, the outlined general strategy for couplings with different flow and transport simulators in [4] has been followed by Nardi et al. [5], who published another COMSOL-IPhreeqc coupling. Recently, also Korrani et al. [6] followed this strategy in their coupling to UTCHEM. The free environmental flow- and transport-modelling platform OpenGeoSys [7] maintains an interface to IPhreeqc for coupled thermo-hydro-mechanical-chemical (THMC) simulations. Specialized tools using IPhreeqc have been developed by Takahashi and Ishida [8] for cementitious materials and Huber et al. [9] for the paper-making process. Patel et al. [10] implemented IPhreeqc as reaction engine for pore-scale multicomponent reactive transport that used a Lattice-Boltzmann approach. However, IPhreeqc is not specifically tailored to the needs of couplings with transport simulators. Instead, it is designed to maintain the full capabilities of PHREEQC, independent of the context of use. Therefore, the API requires substantial coding in the client software to compose the adequate PHREEQC commands that handle the data exchange and run reactions. In this paper, we present PhreeqcRM, a new reaction module based on IPhreeqc that is specifically designed for couplings with environmental flow and transport simulators. PhreeqcRM provides a high-level interface that allows multicomponent transport codes to implement geochemical reactions with a minimum amount of programming, while maintaining the full functionality of PHREEQC s reaction capabilities. In the first part of the paper, we describe the coupling strategy together with key methods of its API. In the second part, we present the implementation of PhreeqcRM as a reaction engine for the groundwater modelling system FEFLOW. The new coupling is verified through two test cases: a three-dimensional (3D) analytical solution by Sun et al. [11] and the MoMaS (Modeling, Mathematics and numerical Simulations related to nuclear waste management problems) reactive transport benchmark of Groupement de Recherche (GdR) [12].

2 PhreeqcRM is available at Included in the distributions are source files, compilation files (CMake and configure), documentation of all methods of the API, and simple advection examples in C, Fortran, and C++. GENERAL STRATEGY FOR THE IMPLEMENTATION OF PHREEQCRM IN A MULTICOMPONENT TRANSPORT SIMULATOR Figure 1 presents a general strategy for the use of PhreeqcRM as a reaction engine for a transport simulator using common flow chart symbols. The initialization process and the reaction process within the main simulation process are detailed on the right. The flow chart contains the key API tasks that are used in these processes. Initialization process Start simulation Start initialization Load Settings Initialization End of simulation period? False True Create and initialize PhreeqcRM Set initial conditions Set boundary conditions Flow and solute transport Is reaction time step? True Reactions False End initialization Reactions process Start reactions Transfer data to PhreeqcRM Visualization Run PhreeqcRM reactions for t Finalize Transfer data to transport End simulation End reactions Figure 1: Generic program flow for a reactive transport simulator using operator splitting (adapted from [1]).

3 PhreeqcRM API PhreeqcRM is designed as a C++ class with methods for instantiation and destruction, initialization of initial conditions and reactions, determination of boundary conditions and running reaction calculations for a series of model cells and time steps. In addition to C++ methods, wrappers for C and Fortran are provided. Parallelization PhreeqcRM is designed for parallel reaction calculations, using either multi-threading on shared memory systems with OpenMP or multi-processing on distributed memory systems with MPI. The kind of parallelization has to be selected at compile time using the preprocessor definitions USE_OPENMP or USE_MPI. The number of parallel threads for OpenMP has to be provided as a parameter to the constructor at runtime whereas the number of parallel processes for MPI has to be provided as an argument to mpiexec, the command that launches an MPI job. PhreeqcRM has been successfully compiled with OpenMP implementations for Windows (Visual Studio 2010/2012/2013) and Scientific Linux and with MPI implementations for Windows (MSMPI from Microsoft ) and Linux (OPENMPI, version 1.5.4). The efficiency of parallelization is demonstrated by the speedup that increasing numbers of threads (Multithreaded) or processes (Multiprocessing) produce for the easy 1D MoMaS reactive transport benchmark. IMPLEMENTATION OF PHREEQCRM AS THE REACTION ENGINE FOR FEFLOW The implementation of PhreeqcRM as the reaction engine for reactive transport calculations in FEFLOW uses the sequential non-iterative approach for operator splitting, which is ideally suited for parallelization. PhreeqcRM is implemented as a plug-in that calculates reactions at predefined time steps or at every n th transport step, in which case the length of the time step is determined by FEFLOW s automatic time-stepping algorithm for flow and transport. FEFLOW s Interface Manager (IFM) provides the API for the coupling as well as plug-in methods that execute at certain events during program flow. The event-based methods are implemented as callbacks for the FEFLOW main program. For the problem definition, result visualization, and result storage, FEFLOW s existing infrastructure and GUI elements are used as much as possible. New GUI elements for specific coupling settings and for the association of PHREEQC input files with FEFLOW boundary and initial conditions are designed using the platform-independent Qt programing framework. Every node in FEFLOW s finite-element mesh corresponds to a reaction cell in PhreeqcRM. Component concentrations, solution temperature and pressure, and liquid phase saturation are transferred from FEFLOW s transport nodes to the reaction cells in PhreeqcRM before each reaction step. Saturation is transferred from PhreeqcRM to FEFLOW after each reaction step, which allows FEFLOW to simulate saturation-modifying chemical reactions. PLUG-IN OPERATION The starting point of a coupled simulation is a fully functional FEFLOW model for flow and transport with at least one (placeholder) mass transport species. Transport properties of this species (e.g., diffusion coefficient, porosity) are used for all geochemical components. Geochemical components are determined from the associated PHREEQC input files and added automatically at the start of the simulation. For the manual definition of reaction steps a power curve is required that defines reaction steps and changes in boundary conditions. Furthermore, a nodal user data distribution is needed that identifies nodes with the same geochemical initial conditions. Initial liquid phase saturation and temperatures are taken from the FEFLOW model. The FEFLOW plug-in uses separate PHREEQC input files to define the geochemical boundary and initial conditions. A file selection GUI with immediate error checking is used to associate PHREEQC files with FEFLOW nodes that share the same boundary and initial conditions (that is, nodes with the same value for constant concentration boundary or the same nodal user data). For initial conditions, the solution with the highest user number in the file is transferred as the initial solution for all of the specified transport cells; any reactants with the same user number also are transferred. For boundary conditions, the solution with the highest user number in each PHREEQC file is used to define the

4 solution composition at the associated nodes. All coupling-relevant information can be saved in the FEFLOW fem-file through the serialization functionality in the IFM. Output from SELECTED_OUTPUT and USER_PUNCH keywords in the PHREEQC files that are used to define boundary and initial conditions is transferred to FEFLOW as an additional nodal user data definition, which is updated after each reaction step. Nodal user data definitions can be saved together with FEFLOW s result files (dac- and dar-files). This allows for the visualization of geochemical parameters during and after a coupled simulation using FEFLOW s built-in post-processing tools. CODE VERIFICATION A 3D reactive transport analytical solution [11] and a series of MoMaS reactive transport benchmarks [12] were used to test the simulator. Kinetic Decay-Chain Test Case For the verification of the calculation of simple kinetic reactions in PhreeqcRM and its implementation as the reaction engine for FEFLOW the analytical solution of Wexler [13] in combination with the methodology for multi-species transport of Sun et al. [11] is used. The example is adapted from Example 2 of the PHAST manual [14] and simulates a decay chain of four artificial species (C 1 C 4 ) according to the first-order rate expressions dc i (t) dt k i C i (t), i = 1 = { k i 1 C i 1 k i C i (t), 2 i 4 (1) In Eq. (1) C i are species concentrations in mol/l and k 1 = /d, k 2 = /d, k 3 = /d and k 4 = /d are rate constants. The concentration C 1 is introduced over a specified area at the center of the y-z plane with flow in x-direction at 0.2 m/d, and the species form and decay in accordance with the specified reaction rates.

5 Figure 2: Species concentrations (mol/l) for a first-order decay chain in a steady flow field as calculated by the FEFLOW plug-in compared to the analytical solution of Wexler [13] and Sun et al. [11] (adapted from [1]). In addition to the excellent agreement with the analytical solution, as shown in Figure 2, results from FEFLOW are nearly identical to an implementation of PhreeqcRM as reaction engine for PHAST [1]. Reactive Transport Benchmark of MoMaS The MoMaS reactive transport benchmarks [12], commonly known as MoMaS, define test cases for steady-state flow with advection- or dispersion-dominated transient solute transport in 1D and 2D domains together with three versions (easy, medium, and hard) of an artificial reaction network. The general applicability of the SNIA to the MoMaS exercise has been demonstrated for the SPECY code in Carrayrou [15] and Carrayrou et al. [16]. Details of the MoMaS definitions are provided by Carrayrou et al. [12] and Bourgeat et al. [17]. For the verification of the FEFLOW plug-in with the 2D MoMaS cases, an irregular finite-element mesh with 3753 elements and 1970 nodes was used.

6 Figure 3: FEFLOW concentration results for the MoMaS 2D advective cases: (a) X3, easy case at time 1000; (b) X2, medium case at time 1000; (c) CP1, hard case at time 2000; and (d) same as (c) calculated with fine mesh (adapted from [1]). Figure 4: FEFLOW concentration results for the MoMaS 2D dispersive cases; (a) and (b) S, easy case at time 10 with coarse and fine mesh, respectively; (c) X2, medium case at time 10; (d) CP1, hard case at time 1000 (adapted from [1]). Results in Figures 3 and 4 compare well with previously published results in Carrayrou et al. [16], Mayer et al. [18] and Hoffmann et al. [19]. REFERENCES

7 [1] Parkhurst DL, Wissmeier L. PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC. Advances in Water Resources 2015;83:176\uc0\u8211{}89. doi: /j.advwatres [2] Charlton SR and Parkhurst DL. Modules based on the geochemical model PHREEQC for use in scripting and programming languages. Computers & Geosciences 2011;37(10): [3] Parkhurst DL and Appelo CAJ. Description of Input and Examples for PHREEQC Version 3 A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations. U.S. Department of the Interior, U.S. Geological Survey Techniques and Methods 6 A43, [4] Wissmeier L and Barry DA. Simulation tool for variably saturated flow with comprehensive geochemical reactions in two- and three-dimensional domains. Environmental Modelling & Software 2011;26(2011): [5] Nardi A, Idiart A, Trinchero P, de Vries LM, and Molinero J. Interface COMSOL-PHREEQC (icp), an efficient numerical framework for the solution of coupled multiphysics and geochemistry. Computers & Geosciences 2014;69: [6] Korrani AKN, Sepehrnoori K and Delshad M. Coupling IPhreeqc with UTCHEM to model reactive flow and transport, Computers & Geosciences : [7] Kolditz O, Bauer S, Bilke L, Böttcher N, Delfs JO, Fischer T, Görke UJ, Kalbacher T, Kosakowski G, McDermott CI, Park CH, Radu F, Rink K, Shao H, Shao HB, Sun F, Sun YY, Singh AK, Taron J, Walther M, Wang W, Watanabe N, Wu Y, Xie M, Xu W, and Zehner B. OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydromechanical/chemical (THM/C) processes in porous media. Environmental Earth Sciences 2012;67(2): [8] Takahashi Y and Ishida T. Modeling of coupled mass transport and chemical equilibrium in cement-solidified soil contaminated with heavy-metal ions. Construction and Building Materials 2014;67, Part A(0): [9] Huber P, Nivelon S, Ottenio P, and Nortier P. Coupling a Chemical Reaction Engine with a Mass Flow Balance Process Simulation for Scaling Management in Papermaking Process Waters. Industrial & Engineering Chemistry Research 2012;52(1): [10] Patel RA, Perko J, Jacques D, De Schutter G, Van Breugel K, and Ye G. A versatile porescale multicomponent reactive transport approach based on lattice Boltzmann method: Application to portlandite dissolution. Physics and Chemistry of the Earth 2014;70 71(0): [11] Sun Y, Petersen JN, and Clement TP. Analytical solutions for multiple species reactive transport in multiple dimensions. Journal of Contaminant Hydrology 1999;35(4): [12] Carrayrou J, Kern M, and Knabner P. Reactive transport benchmark of MoMaS. Computational Geosciences 2010;14(3): [13] Wexler EJ. Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow. U.S. Department of the Interior, U.S. Geological Survey, Techniques of Water-Resources Investigations 3 B7, [14] Parkhurst DL, Kipp KL, and Charlton SR. PHAST Version 2--A Program for Simulating Groundwater Flow, Solute Transport, and Multicomponent Geochemical Reactions. U.S. Geological Survey Techniques and Methods 6-A [15] Carrayrou J. Looking for some reference solutions for the reactive transport benchmark of MoMaS with SPECY. Computational Geosciences 2010;14(3): [16] Carrayrou J, Hoffmann J, Knabner P, Kräutle S, de Dieuleveult C, Erhel J, Van der Lee J, Lagneau V, Mayer KU, and MacQuarrie KTB. Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems the MoMaS benchmark case. Computational Geosciences 2010;14(3): [17] Bourgeat A, Bryant S, Carrayrou J, Dimier A, Duijn CJV, Kern M, Knabner P, and Leterrier N. GDR MoMaS Benchmark Reactive Transport. Centre National de la Recherche Scientifique [18] Mayer KU, Frind EO, and Blowes DW. Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions. Water Resources Research 2002;38(9): [19] Hoffmann J. Results of the GdR MoMaS Reactive Transport Benchmark with RICHY2D. Institut für Angewandte Mathematik, 2008.