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**Below you'll find the sections in the original article plus a section I added called "Examples of Reactive Transport Modeling". My writing and additions to the sections are in italics. Also, my own references for what I added are listed at the bottom and cited throughout. I focused on trying to make the article easier to understand and provide examples of reactive transport modeling in porous media. I also added a couple figures that weren't in the original article.**

Reactive Transport Modeling in Porous Media

Reactive transport modeling in porous media refers to the creation of computer models integrating chemical reaction with transport of fluids through the Earth's crust. An example of a reactive transport model could be to calculate changes in the amount of sulfate in contaminated groundwater flowing through sediment. Such models predict the distribution in space and time of the chemical reactions that occur along a flowpath. The flowpath describes the path that the fluid is flowing along. Reactive transport modeling in general can refer to many other processes, including reactive flow of chemicals through tanks, reactors, or membranes; particles and species in the atmosphere; gases exiting a smokestack; geology, and migrating magma. Reactive transport modeling in porous media specifically applies to chemicals flowing through porous sediment and rock in the subsurface of the Earth. Reactive transport modeling was developed as a combination of fluid flow modeling and chemical reaction modeling. Both of these are models that can be developed independently from each other. When you combine them into one model you get a reactive transport model. Reactive transport modeling is limited by the computer systems and programs that are available. There are many processes that go into reactive transport modeling since it's essentially combining chemistry and fluid dynamics. Solving reactive transport models can be very complicated because there are equations governing the chemical reactions and different equations governing the flow of fluids through porous media. Challenges are a given part of reactive transport modeling, but it helps the advancement of the models and the programs used to create them.

Overview

Reactive transport models are constructed to understand the composition of natural waters; the origin of economic mineral deposits; the formation and dissolution of rocks and minerals in geologic formations in response to injection of industrial wastes, steam, or carbon dioxide; and the generation of acidic waters and leaching of metals from mine wastes. It's important to use reactive transport models to examine these processes because the models can take our understanding a step further. It can be possible to see what happened to the waters before they got to their present state and they can predict what's going to happen in the future. They are often relied upon to predict the migration of contaminant plumes; the mobility of radionuclides in waste repositories; and the biodegradation of chemicals in landfills. All of these processes are related to anthropogenic activities. It's necessary to see how chemicals will travel in these environments so they can't affect our surface water bodies and drinking water. When applied to the study of contaminants in the environments, they are known as fate and transport models.

Development of Reactive Transport Modeling

Modern reactive transport modeling has arisen from several separate schools of thought. Hydrologists and hydrogeologists primarily concerned with the physical nature of mass transport assumed relatively simple reaction formulations, such as linear distribution coefficients or linear decay terms, which could be added to the advection-dispersion equation. Hydrologists are scientists that study water, specifically surface water like rivers and lakes while hydrogeologists focus on groundwater systems. The linear terms added to the advection-dispersion equation assume that mass transport is occurring in a straight line. By assuming linear, equilibrium sorption, for example, the advection-dispersion equation can be modified by a simple retardation factor and solved analytically. Equilibrium sorption is when the amount of solute bonded to a solid is equal to the amount of solute in solution. Such analytical solutions are limited to relatively simple flow systems and reactions. Reactive transport models can also help with the understanding of the biosphere and how microorganisms interact with chemical species that are present in the subsurface.

Geochemical models, on the other hand, have been developed to provide thermodynamic descriptions of multicomponent systems without regard to transport. Thermodynamic descriptions refers to systems affected by heat, work, and temperature. Reaction path models were created, for instance, to describe the sequence of chemical reactions resulting from chemical weathering or hydrothermal alteration in batch systems, in terms of the overall reaction progress. Hydrothermal alteration is when rocks or minerals are altered by hot, aqueous fluids. By adopting the reference frame of a packet of fluid and treating reaction progress as travel time (or distance along a flowpath), however, a batch reaction path model could be thought of as describing advective transport through an aquifer.

The most sophisticated multi-component reactive transport models consider both reaction and transport. Early studies developed the theoretical basis of reactive transport models, and the numerical tools necessary to solve them, and applied them to problems of reactive contaminant transport and flow through reacting hydrothermal systems.

Reactive transport models have found increased application in recent years with improvements in the power of personal computers and modeling software.

MODFLOW is another computer program used for reactive transport modeling in groundwater systems. MODFLOW can be linked to the program RT3D (reactive transport modeling in 3 dimensions) to represent a more complicated system, such as contamination in both groundwater and surface water. RT3D-OTIS is a reactive transport software package that can be coupled to MODFLOW to represent transport of chemicals, like nonpoint source pollution in rivers and groundwater, through saturated and unsaturated groundwater flow.

A computer package in MODFLOW that is frequently combined with RT3D to simulate reactive transport modeling is the Unsaturated Zone Flow (UZF1). This package uses the kinematic wave flow approximation and can be used for large aquifers. The kinematic wave flow approximation is an equation used to solve unsaturated flow in groundwater. The unsaturated zone is also known as the vadose zone, or the region of the subsurface located between the ground surface an the water table. UZF-RT3D is often used with MODFLOW because it decreases model run time and it allows for specific chemical species that represent the field site to be added.

Processes Considered in Reactive Transport Models

Reactive transport models couple a large number of chemical reactions with mass transport. These can be simple applications or extremely complicated representations, depending on how many reactions and processes are considered. Certain applications, such as geothermal energy production and ore deposit modeling, require the additional calculation of heat transfer. In modeling carbon sequestration and hydraulic fracturing, moreover, it may be necessary to describe rock deformation resulting from mineral growth or abnormally high fluid pressure. Description of transport through the unsaturated zone and multiphase flow modeling, as applied to transport of petroleum and natural gas; non-aqueous phase liquids (DNAPL or LNAPL); and supercritical carbon dioxide requires increasingly complex models which are prone to considerable uncertainty. What all of the various models have in common is their ability to characterize the movement of chemicals, elements, and ions through media, like sand, clay, or rock, that have pores for the flow or transport of fluid. Pores can be very tiny, like in the case for silt and clay, or be large fractures in bedrock, as long as there is space for the fluid to flow and to carry chemicals.

This diagram includes the pathways that chemicals can take to make their way into the subsurface and the role of groundwater flow. But, this figure also depicts some of the processes, like runoff, seepage, and recharge, considered in reactive transport modeling of porous media.

In many cases the processes simulated in reactive transport models are highly related. Mineral dissolution and precipitation, for example, can affect the porosity and permeability of the domain, which in turn affects the flow field and groundwater velocity. Porosity is a measure of how much a rock or section of sediment is open space while permeability is a measure of how easily a fluid can more through a rock or sediment. Flow field refers to the region that the fluid in question is flowing, and groundwater velocity is the speed that groundwater flows. Heat transport greatly affects the viscosity of water and its ability to flow. For example, warm water can flow faster and more easily than cold water because it has more energy. Below are many of the physical and chemical processes which can be simulated with reactive transport models.

Geochemical reactions:

• Acid-base reactions
• Aqueous complexation
• Mineral dissolution and precipitation
• Reduction and oxidation (redox) reactions, including those catalyzed by enzymes, surfaces, and microorganisms
• Sorption, ion exchange, and surface complexation
• Gas dissolution and exsolution
• Stable isotope fractionation
• Radioactive decay

Mass Transport:

• Advection
• Molecular scale diffusion
• Hydrodynamic dispersion
• Colloid-facilitated transport

Heat transport:

• Advection
• Conduction
• Convection

Medium deformation:

• Compression or expansion of the domain
• Fracture formation

Solving Reactive Transport Models

Some of the simplest reactive transport problems can be solved analytically. Where equilibrium sorption is described by a linear distribution coefficient, for example, the sorbing solute's velocity is retarded relative to that of a nonreactive tracer; the relative velocities can be described with a retardation factor. In other words, the rate that an amount of chemical in solution is taken up by a solid can be compared to the rate of an inert chemical put into that same solution. The two rates can be explained by a factor in an equation. Analytical solutions are exact solutions of the governing equations or solutions tend to follow the equations that explain them.

Complex reactive transport problems are more commonly solved numerically. In this case, the governing equations are approximated so that they can be solved by computer algorithms. The computer helps to eliminate human error that can occur when numerical calculations are solved by hand. The governing equations, including both reaction and transport terms, can be solved simultaneously using a one-step or global implicit simulator. This technique is straightforward conceptually, but computationally very difficult.

Instead of solving all the relevant equations together, the transport and chemical reaction equations can be solved separately. By solving transport and chemical reactions separately, there is a smaller chance of error than having all equations combined. Operator splitting, as this technique is known, uses appropriate numerical techniques to solve the reaction and transport equations at each time step. Various methods exist, including the sequential non-iterative approach (SNIA), Strang splitting, and sequential iterative approach (SIA). Since the reaction and transport terms are handled separately, separate programs for batch reaction and transport can be linked together. Cross-linkable re-entrant software objects designed for this purpose readily enable construction of reactive transport models of any flow configuration. As reactive transport modeling software advances more realistic simulations can be computed which result in higher accuracy and better predictive models.

This figure is an example of the 3D finite difference grid that is used in MODFLOW. It uses the finite difference flow model to solve the groundwater flow equation. This can be used in combination with MT3D-USGS to model reactive transport processes through the subsurface.

Examples of Reactive Transport Models

Mayer and colleagues (2002) use reactive transport models to study two different systems, one being natural attenuation, or reduction of organic contaminants, in an unconfined aquifer system overlaid with unsaturated sediments and the other acid mine drainage in the unsaturated zone at Nickel Rim Mine Site in Ontario, Canada. Tournassat & Steefel (2019) used reactive transport modeling by combining CrunchClay and PHREEQC computer programs to couple transport processes with irreversible thermodynamics in the presence of a diffuse layer through nanoporous media. These codes are limited to modeling strictly diffusive systems, but microstructural porosity descriptions can be implemented and transport of electrolyte background ions and transport ions can be run simultaneously.

Challenges

Reactive transport modeling requires input from numerous fields, including hydrology, hydrogeology, geochemistry, and biogeochemistry, microbiology, soil physics, and fluid dynamics. Because computational input from multiple disciplines is required, any computer modeling program needs to be able to organize a multitude of equations. The numerical formulation and solution of reactive transport problems can be especially difficult due to errors arising in the coupling process, beyond those inherent to the individual processes. Valocchi and Malmstead (1992), for example, reported on the potential errors arising from the operator splitting technique.

Even in the absence of numerical difficulties, the general lack of knowledge available to practitioners creates uncertainty. This creates uncertainty. The models are only as good as what is known about the system before a model is developed and applied. Field sites are typically heterogeneous, both physically and chemically, and sampling is often sparse. The prevailing assumption of Fickian dispersion is often inadequate. This is because field conditions are not uniform. Equilibrium constants and kinetic rate laws for relevant reactions are often poorly known. The complexity of many processes requires expertise in one or more of the aforementioned fields. This creates possibilities for interdisciplinary collaboration, which can help to mitigate complications that arise from not having enough knowledge in any specific subject area required for a model. Many processes, such as long-term nuclear waste storage, cannot be experimentally verified; reactive transport problems can only attempt to predict such long-term behavior. The current descriptions of multi-phase flow and mechanical deformation processes are still being developed.