Geochemical and reactive transport modelling in R with the RedModRphree package
Michael Kühn
Advances in computing and experimental capabilities in the research of waterrockinteractions require geoscientists to routinely combine laboratory data and models to produce new knowledge. Data science is hence a more and more pervasive instrument for geochemists, which in turn demands flexible and easy to learn software adaptable to their specific needs. The GNU R language and programming environment has established itself as de facto standard language for statistics and machine learning, enjoying increasing diffusion in many applied scientific fields such as bioinformatics, chemometrics and ecological modelling. The availability of excellent third party extensions as well as its advanced graphical and numerical capabilities make R an ideal platform for comprehensive geochemical data analysis, experiment evaluation and modelling.
We introduce the open source RedModRphree
extension
package, which leverages the R interface to the established
PHREEQC
geochemical simulator. The aim of
RedModRphree
is to provide the user with an easytouse,
highlevel interface to program algorithms involving geochemical
models: parameter calibration, error and sensitivity analysis,
thermodynamical database manipulation, up to CPUintensive parallel
coupled reactive transport models. Among the outofthebox features
included in RedModRphree
, we highlight the computation and
visualization of Pourbaix (EhpH) diagrams using full speciation as
computed by PHREEQC
and the implementation of 1D advective
reactive transport supporting the use of surrogate models replacing
expensive equationbased calculations.
GNU R (R Core Team, 2021) is an open source software environment and programming language originally developed for statistical computing and graphics as new implementation of the closed source S language. Its expressive and elegant syntax combines elements of objectoriented and functional languages and is perfectly suited to represent computational problems in an extremely concise way. R's comprehensive numerical capabilities and its collaborative development nature has attracted a large user base over the years, leading to its establishment as de facto standard language in many areas of mathematics, statistics and machine learning, and as one of the most successful open source projects overall. R is more and more extending its ecosystem to different applied sciences, including geosciences, where the language's core strengths and its extremely large toolbox of user contributed extension packages benefit the daily work of students, academics and professionals alike. At the moment of writing, over 17750 usercontributed extension packages have been submitted to the official repository called Comprehensive R Archive Network (CRAN). Indices of these packages, termed “Task Views” (Zeileis, 2005, 2021), are provided by domain experts to offer guidance in navigating such an ample landscape by organizing them under specific topics. For example, the Task View Chemometrics and Computational Physics (Mullen, 2021) lists over 80 packages covering many aspects of data analysis relevant for chemistry and physics experiments, and the simulation of physicochemico systems; furthermore, it points to other related Task Views of obvious interest such as Differential Equations and Multivariate Analysis.
Specifically for geochemistry, the CHNOSZ
package
(Dick, 2019) allows for thermodynamic calculations in aqueous
geochemistry and geobiochemistry based on the HelgesonKirkhamFlowers
(HKF) equations (Johnson et al., 1992), extending the capabilities of the
well known SUPCRT92 software. Furthermore, an interface to the
established geochemical simulator PHREEQC
(Appelo et al., 2013; Parkhurst and Appelo, 2013) for the R language is available on CRAN as package
phreeqc
(Charlton and Parkhurst, 2011, note the lowercase writing adopted in this
paper to distinguish it from PHREEQC
itself).
However, this interface only exposes the Application Programming
Interface (API) of PHREEQC
to R, and does not provide utility
functions to quickly setup new models or in general to program
algorithms involving geochemical calculations.
The freely available extension package RedModRphree
,
introduced with this contribution, aims at fulfilling this need. Its
goal is to enhance the user experience by streamlining repetitive
tasks connected with the utilization of PHREEQC
for
computingintensive tasks, leveraging at the same time the software
infrastructure offered by the R environment. RedModRphree
supersedes a discontinued package called Rphree
(https://rphree.rforge.rproject.org/, last access: 30 September 2021 De Lucia and Kühn, 2013),
which involved modifications of PHREEQC
's source code at c
level. The availability of the phreeqc
extension package
(Charlton and Parkhurst, 2011), on par with each new PHREEQC
's release
made this approach superfluous.
New functionalities and applications have been added to
RedModRphree
over the years. In particular, the package
version 0.3.6 includes a novel implementation of Pourbaix diagrams
computation following the suggestions of Kölling et al. (2000), which
will be explained and demonstrated in Sect. 3.1.
Advective onedimensional reactive transport simulations which can use
surrogates to speedup lengthy PHREEQC
calculation are
discussed in Sect. 3.2. Before diving into
these applications, however, in the next section we provide a general
overview of RedModRphree
, its logic and its fundamentals
illustrated with code examples.
2.1 Package description
PHREEQC
itself operates by interpreting input scripts written
in its own syntax, and outputting the results either as formatted text
or as data tables. Thus, the primary need for a highlevel interface
to the chemical engine is offering comfortable mechanisms to create,
manipulate and check the input scripts and to parse the structured
text outputs. Much of RedModRphree
code is hence related to
text manipulation.
Several programmatic design choices were made in the development of
RedModRphree
:

the user is assumed to be familiar with
PHREEQC
and its syntax. The package does not hide it under own classes or abstractions, and instead only provides functions to manipulate input scripts and obtain calculations' results back into the R runtime; 
minimal number of external dependencies, meaning that code is in standard R for maximum portability, maintenance and ease of installation;

code is platformindependent, however development and testing are mainly focused on POSIX operating systems such as Linux.
The current RedModRphree
version 0.3.6 supports
PHREEQC
keywords EQUILIBRIUM_PHASES
and
KINETICS
. Support of further options such as surface
complexation, solid solutions and isotope is planned for future
versions.
2.2 Basic usage demonstration
RedModRphree
version 0.3.6, which is the version considered
in this paper, can be downloaded from Zenodo
(https://doi.org/10.5281/zenodo.5046427) or by anonymous download
from the git server of GFZ. The commands given in
Listing 1 install it along with the required
dependencies.
RedModRphree
provides utility functions to manipulate input
scripts, which are represented in R as character vectors whose
elements correspond to a line of a PHREEQC
input script. The
current RedModRphree
version does not support line
continuation (i.e., logical lines splitted across different actual
text lines), so the user must be aware of this convention.
The fundamental input manipulations are provided by the functions
AddProp
and RepSol
. The first adds to a base script
a property such as a concentration or an equilibrium mineral and
should be called explicitly for each new property added.
Listing 2 illustrates its use leveraging the
pipe operator %>%
for code clarity, which must be
enabled explicitly since it is not loaded by the package itself. When
calling AddProp
, the user must specify to which logical block
the new property belongs as per standard PHREEQC
syntax. This
can be one of tot
(a property belonging under the
SOLUTION
keyword, e.g. pH, temperature or total element
concentrations), pphases
(a mineral or a gas at equilibrium,
from the conventional name “pure phases” used in PHREEQC
;
the package always adopts the PURE
alternative keyword to
EQUILIBRIUM_PHASES
) or kin
(for KINETICS
blocks). RepSol
repeats a template script a specified amount
of times.
The next step is to use this basic template script to create
meaningful calculations. The fundamental mechanism provided by
RedModRphree
is the function Distribute
(and its
variant DistributeKin
which deals specifically with kinetic
blocks). In Listing 3 is demonstrated how to create
an input script which computes the solubility of calcite as function
of temperature, varying it between 25 and 100 ^{∘}C.
By inspecting the new simT
input buffer, it becomes clear
that the initial template script was repeated 16 times, each with a
different value of temperature. The new script can then be run with
phreeqc
provided functions.
The results of these PHREEQC
calculations are stored as text
buffer in the out
variable 4, using its
standard format. RedModRphree
provides functions to parse
such output and obtain the numerical values as R objects (function
ReadOut
, Listing 5). In particular,
ReadOut
returns a list where each element is one simulation
in the output buffer, and each simulation itself is a set of tabular
data (specifically, data.frame
s in R) corresponding to the
logical blocks in the output file. These logical blocks are named
desc
(some descriptive parameters about the calculated
solutions such as pe, pH and ionic strength), tot
(total
elements concentrations), SI
(saturation indices of
minerals), pphases
(equilibrium minerals) and
species
(concentration of dissolved species).
It is possible to transform back such a list to a valid
PHREEQC
input using the function InputFromList
.
Another way to obtain the needed results from PHREEQC
is by
specifying a SELECTED_OUTPUT
or USER_PUNCH
. When
such blocks are specified, a data.frame containing the numerical
values is directly returned to R from phreeqc
. A simple
mechanism to generate a SELECTED_OUTPUT
block from a parsed
simulation is provided by function FormSelectedOutput
(Listing 6).
res2
is the resulting table containing all the variables
included in the SELECTED_OUTPUT
block.
2.3 Parallel computations
R offers an easy way to parallelize computingintensive tasks. In
RedModRphree
this capability is leveraged making use of the
extension packages foreach
and doParallel
. In
particular the RunPQC
function offers the option of parallel
computing, however in this case it expects as input a list of input
scripts which represent the tasks to be parallelized. A simple example
of parallel computation of 320 simulations on 4 CPUs is given in
listing 8.
The res3
variable contains the selected output corresponding
to the 320 rows of the df
data.frame. R offers many options
to visualize threedimensional data. Listing 9 gives an
example of interactive visualization using the plotly
package
(Plotly Technologies, 2015). The resulting picture is interactive and opens in a
browser. A screenshot is given in Fig. 1.
2.4 Additional resources: demos and documentation
The previous sections showcase a simple working session with the
package. These functions are the fundamental building blocks needed to
quickly create complex calculations, and can be easily leveraged to
efficiently implement algorithms involving geochemical models, such as
reactive transport simulations. The package includes further utilities
to deal with KINETICS
blocks and to parse and manipulate
thermodynamical databases, which are not covered in this manuscript,
and for which the reader is referred to the package documentation and
demo.
RedModRphree
ships with functions' documentation, usage
examples and with a set of demos which illustrate in more detail
different use cases not covered in this manuscript
(Listing 10). The code of the included demos is commented
and intended as additional documentation.
In particular, several demos focus on the use of pretrained emulators
or surrogates instead of more computationally expensive
PHREEQC
calculations in 1D advective reactive transport
simulations (De Lucia and Kühn, 2021). Surrogates are machine learning
regressors able to reproduce a multivariate output as function of
multivariate input. They must be trained in advance on a set of
PHREEQC
simulations, and can then be pluggedin in coupled
reactive transport simulations for speedup. More details concerning
the reactive transport capabilities of RedModRphree are given in
Sect. 3.2.
3.1 Pourbaix diagrams
Pourbaix or EhpH diagrams were first introduced by the Belgian
chemist Marcel Pourbaix in 1945. They are standard phase diagrams with
electrochemical potential (Eh or pe) and pH as axes, and are a
valuable tool in electrochemistry, material science and in general in
aqueous chemistry and geochemistry (Huang, 2016; Hennig et al., 2020),
since they synthetically summarize the thermodynamically stable phases
(i.e., at chemical equilibrium) of an aqueous electrochemical system.
Since they are based on thermodynamics, like all phase diagrams, they
do not account for reaction rates or kinetic effects. Classically, the
boundaries between predominant chemical species (aqueous ions in
solution or solid phases) are straight lines computed directly by
evaluating Nernst and Law of Mass Action equations and imposing a
condition of equality between two species' activities. Such approach
is for example employed by the CHNOSZ
package
(Dick, 2019). However, beside potential and pH, the equilibrium
activities depend also upon temperature, pressure, and, crucially, on
the activities of all other dissolved species in the considered
system. This makes the classical approach illicit from a rigorous
standpoint (Kölling et al., 2000). In particular, the predominance
region for a given species should be defined as the locus of points in
the diagram where its activity is larger than the activities of
all other species. The borders between regions would not result
in straight lines anymore, but curves.
PHREEQC
offers the capability to calculate the speciation of
a solution in its entirety; and using RedModRphree
it is
simple to achieve a more realistic predominance diagram as suggested
by Kölling et al. (2000). This has been implemented in the
Pourbaix
function, which performs the computations and
visualizes the diagram in a convenient way. The user provides a base
script describing the solution and defines at which levels of pe and
pH the speciation must be calculated; the function computes all
combinations of these levels in a dense grid, restricted to the
stability region of water, approximated by the limiting boundaries for
release of molecular hydrogen and oxygen respectively
(Eqs. 1, 2), not considering the effect of temperature.
The corresponding simulations are computed in parallel if the
procs
argument is larger than one. Then from the results for
each simulation point, the mineral with largest positive saturation
index is extracted, or, if none has positive SI, the largest activity
of all the dissolved species. Once all the data are collected, the
whole parameter space is displayed assigning a different colour for
each phase. Each region is labelled with the brute formula of the
represented species, written in italic font under their name for the
minerals. Optionally the function restricts the diagram only to phases
or species containing one element, specified by the element
argument. If left unspecified, then all computed saturation indices
and activities are considered in the diagram. The current version of
Pourbaix()
does not support the inclusion of pure phases at
equilibrium with the system, such as partial pressure of
CO_{2}(g). Furthermore, no check is performed whether the
resulting equilibrated solutions have a different pH or pe than the
values specified in the input for each simulation point. Frequent
numerical instabilities and nonconvergence of simulations happen near
the boundaries of the water stability region, in particular for large
pe values. Since no error control mechanism is implemented in the
current RedModRphree
version, the user is recommended to
restrict the range of pe and pH and to try different resolutions of
the calculation grid.
Figure 2 (Listing 11) displays the Pourbaix diagram for copper speciation in a solution containing Na, Cl, Ca and Fe, on a 101×101 grid for a total of 8239 simulations inside the water stability region, which computes in under three seconds employing two CPUs.
Specifying aqonly=TRUE
restricts the diagram to aqueous
species only. In this case, the user can specify a specific valence
state for the element
argument, for example with
element='Fe(2)'
. This option is only reliable for aqueous
species since the valence state of an element in minerals is not
readily obtainable by parsing the stoichiometric equations in a
PHREEQC
database. Finally, the user can specify a list of
species or phases to be excluded from the diagram, enumerating them
using the argument suppress
.
A Pourbaix diagram is a synthetic way to highlight discrepancies in
different thermodynamic databases, indicating the need for a closer
inspection of the applied databases and/or more experimental data to
support them. Figure 3
(Listing 12) showcases the aqueous speciation of
iron computed by evaluating the same base solution with the
phreeqc.dat
and llnl.dat
databases. It is apparent
that the stability region of ferric oxyhydroxide Fe^{III}(OH)_{3}
is quite different following the two databases.
A major advantage of a Pourbaix diagram computed in this way is that it can be applied to “real” solutions of any complexity, not being restricted to pure systems of 4 or 5 components as in the classical approach. Furthermore, it is straightforward to implement the same kind of calculations as result of kinetic simulations, thus removing the last limitation shared with the classical diagrams. In facts, in most natural systems even if a mineral is thermodynamically the most favoured in a specific diagram region, other minerals with lower saturation index but faster kinetics may be the phases actually formed (Kölling et al., 2000).
3.2 1D reactive transport using surrogate models
A further application provided by RedModRphree
pertains to 1D
reactive transport models. The functions ReactTranspBalanceEq
and ReactTranspBalanceKin
implement, for equilibrium minerals
and kinetics respectively, a sequential noniterative coupling between
transport and chemistry similar to the PHREEQC
's
ADVECTION
keyword, however disregarding heat transport and
changes in porosity and hence assuming stationary Darcy flow. In
particular, these functions transport total elements concentrations –
a valid assumption in case of pure advection – and the proton and
electron activities instead of total H, total O and charge imbalance,
as done by PHREEQC
internally (Parkhurst and Wissmeier, 2015).
Figure 4 shows a visual validation of this
simplified advection approach by comparing the results of a reactive
transport benchmark on a onedimensional grid with 50 elements
computed once with PHREEQC
's ADVECTION
and once with
ReactTranspBalanceKin
. The whole computation is included in
RedModRphree
as demovalidate
). In the benchmark, a
MgCl_{2} solution is injected at the left inlet in a medium
initially at equilibrium with calcite. This reactive solution triggers
the dissolution of calcite and the transient precipitation of
dolomite. All reactions involving minerals are kinetically controlled
with a Lasaga rate law (Palandri and Kharaka, 2004). After 30 iterations with
fixed time step of 999 s, the variables' profiles across the
domain resulting from the two simulations are perfectly superposable,
up to some negligible error imputable to truncation of floating point
numbers occurring when passing from PHREEQC
's c$++$ domain and
R, which happens through strings.
Furthermore, the above mentioned functions implement an acceleration
technique which at each iteration minimizes the chemical evaluations
by identifying grid elements with nearly equal geochemical problems
(De Lucia and Kühn, 2013). This is achieved by compressing the matrix used
to represent the governing variables for the whole grid (one row per
grid element, one column per concentration). This option is fully
automatic and can be activated by setting argument
reduce=TRUE
. It achieves important speedups for initially
homogeneous systems. Moreover, the simulations are again internally
parallelized when argument procs
is larger than one. The
users are referred to the specific functions documentation for more
usage details.
The main motivation for the development of these reactive transport
functions was investigating the substitution of equationbased
numerical solution of the chemical subprocess with a pretrained
statistical surrogate for computational speedup (Jatnieks et al., 2016; De Lucia et al., 2017; De Lucia and Kühn, 2021, which points
to more advanced numerical experiments than those included as demo
into the package). The user
can activate this capability by providing a named list containing the
trained regressors and an R function which uses them to perform the
surrogate geochemistry calculations. This surrogate function is then
called after each advective step, and its predictions are checked for
plausibility by computing mass balances. The predictions trespassing a
userimposed threshold are rejected and in their place
PHREEQC
simulations are run instead. This process is repeated
at each transportchemistry iteration.
Five of RedModRphree
's demos extensively illustrate the usage
of its reactive transport capability. demovalidate
,
demoequilibrium
and demokinetics
are simulations
using only PHREEQC
; demoeqsurrRF
and
demokinsurrRF
use Random Forests as surrogates for the
equilibrium and kinetic version of the same reactive transport
problem.
The richness of highquality thirdparty applications, the large number of users and the overall maturity and stability of its code base make R an attractive computing platform for geoscientists and in particular for geochemists.
The free and open source RedModRphree
package offers
highlevel programming utilities and outofthebox applications to
enhance users' productivity when working with PHREEQC
geochemical models. The utility functions provided by
RedModRphree
help to rapidly perform many parallelized
calculations and collect the corresponding results as required, e.g.,
in sensitivity and uncertainty analyses, thus profiting from the
excellence of the R ecosystem in that area and its graphics
capabilities for visualization.
The RedModRphree
version 0.3.6 offers novel applications of
general interest for geochemists, in particular the calculation of
Pourbaix diagrams based on the actual full speciation of complex
aqueous systems. It is a valuable computational tool which overcomes
some limitations of classical stability diagrams. Further development
will aim at including kinetic control of reactions, threedimensional
stability diagrams, and having different variables as one of the axes,
for example partial pressure of CO_{2(g)}.
The package release is meant to attract users and foster collaborative
development in order to increase both the coverage of PHREEQC
functionalities and number and scope of provided applications.
RedModRphree is released under LGPL v2.1 license. A copy of the 0.3.6 version of the package has been stored on Zenodo at https://doi.org/10.5281/zenodo.5046427 (De Lucia, 2021). Until the process of inclusion into the Comprehensive R Archive Network (CRAN) is completed, development versions can be installed from https://git.gfzpotsdam.de/delucia/RedModRphree, last access: 30 September 2021.
MDL shaped the research, performed analyses, programming and wrote the manuscript. MK helped providing funding, shaping the research, and revised the manuscript.
The contact author has declared that neither they nor their coauthor has any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the special issue “European Geosciences Union General Assembly 2021, EGU Division Energy, Resources & Environment (ERE)”. It is a result of the EGU General Assembly 2021, 19–30 April 2021.
The authors gratefully acknowledge Helge Moog and an anonymous reviewer for their suggestions which greatily improved the manuscript.
This research has been supported by the Helmholtz Association in the framework of the project “Reduced Complexity Models – Explore advanced data science techniques to create models of reduced complexity” (grant no. ZTI0010).
The article processing charges for this openaccess publication were covered by the Helmholtz Centre Potsdam – GFZ German Research Centre for Geosciences.
This paper was edited by Sonja Martens and reviewed by Helge Moog and one anonymous referee.
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