Reactive transport modeling in porous media refers to the creation of

computer models Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be det ...

integrating

chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and break ...

with

transport Transport (in British English), or transportation (in American English), is the intentional movement of humans, animals, and goods from one location to another. Modes of transport include air, land ( rail and road), water, cable, pipel ...

of fluids through the Earth's crust. Such models predict the distribution in space and time of the chemical reactions that occur along a flowpath. 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; and migrating magma.

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 geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...

in geologic formations in response to injection of industrial wastes, steam, or

carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...

; and the generation of acidic waters and leaching of

metals A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...

from mine wastes. They are often relied upon to predict the migration of contaminant plumes; the mobility of

radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transfer ...

s in waste repositories; and the

biodegradation Biodegradation is the breakdown of organic matter by microorganisms, such as bacteria and fungi. It is generally assumed to be a natural process, which differentiates it from composting. Composting is a human-driven process in which biodegrad ...

of chemicals in landfills. When applied to the study of contaminants in the environments, they are known as fate and transport models.Bethke, C.M., 2008, ''Geochemical and Biogeochemical Reaction Modeling''. Cambridge University Press, 547 pp.

Development of reactive transport modeling

Modern reactive transport modeling has arisen from several separate schools of thought.Steefel, C.I., D.J. DePaolo, and P.C. Lichtner, 2005, Reactive transport modeling: An essential tool and a new research approach for the Earth sciences. ''Earth and Planetary Science Letters'' 240, 539-558

Hydrologists Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is call ...

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. By assuming linear, equilibrium sorption, for example, the advection-dispersion equation can be modified by a simple

retardation factor In chromatography, the retardation factor (''R'') is the fraction of an analyte in the mobile phase of a chromatographic system. In planar chromatography in particular, the retardation factor ''R''F is defined as the ratio of the distance traveled ...

and solved analytically. Such analytical solutions are limited to relatively simple flow systems and reactions. Geochemical models, on the other hand, have been developed to provide

thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of t ...

descriptions of multicomponent systems without regard to transport. Reaction path models were created, for instance, to describe the sequence of chemical reactions resulting from chemical weathering or

hydrothermal alteration Metasomatism (from the Greek μετά ''metá'' "change" and σῶμα ''sôma'' "body") is the chemical alteration of a rock by hydrothermal and other fluids. It is the replacement of one rock by another of different mineralogical and chemical co ...

in batch systems, in terms of the overall reaction progress. 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 An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteri ...

. The most sophisticated multi-component reactive transport models consider both reaction and transport.Gharasoo, M., Centler, F., Regnier, P., Harms, H., Thullner, M., 2012. A reactive transport modelling approach to simulate biogeochemical processes in pore structures with pore-scale heterogeneities. Environmental Modelling & Software 30, 102-114. 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.Steefel, C.I. and A.C. Lasaga, 1994, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. ''American Journal of Science'' 294, 529-592 Reactive transport models have found increased application in recent years with improvements in the power of personal computers and modeling software.

Processes considered in reactive transport models

Reactive transport models couple a large number chemical reactions with mass transport. Certain applications, such as

geothermal energy Geothermal energy is the thermal energy in the Earth's crust which originates from the formation of the planet and from radioactive decay of materials in currently uncertain but possibly roughly equal proportions. The high temperature and pre ...

production and

ore deposit Ore is natural rock or sediment that contains one or more valuable minerals, typically containing metals, that can be mined, treated and sold at a profit.Encyclopædia Britannica. "Ore". Encyclopædia Britannica Online. Retrieved 7 April ...

modeling, require the additional calculation of

heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction ...

. In modeling

carbon sequestration Carbon sequestration is the process of storing carbon in a carbon pool. Carbon dioxide () is naturally captured from the atmosphere through biological, chemical, and physical processes. These changes can be accelerated through changes in land ...

and

hydraulic fracturing Fracking (also known as hydraulic fracturing, hydrofracturing, or hydrofracking) is a well stimulation technique involving the fracturing of bedrock formations by a pressurized liquid. The process involves the high-pressure injection of "frac ...

, 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 The vadose zone, also termed the unsaturated zone, is the part of Earth between the land surface and the top of the phreatic zone, the position at which the groundwater (the water in the soil's pores) is at atmospheric pressure ("vadose" is fr ...

and

multiphase flow In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve so ...

modeling, as applied to transport of

petroleum Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crude ...

and

natural gas Natural gas (also called fossil gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbon ...

; non-aqueous phase liquids ( DNAPL or LNAPL); and

supercritical carbon dioxide Supercritical carbon dioxide (s) is a fluid state of carbon dioxide where it is held at or above its critical temperature and critical pressure. Carbon dioxide usually behaves as a gas in air at standard temperature and pressure (STP), or a ...

requires increasingly complex models which are prone to considerable uncertainty. In many cases the processes simulated in reactive transport models are highly related. Mineral dissolution and precipitation, for example, can affect the

porosity Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...

and permeability of the domain, which in turn affect the flow field and groundwater velocity. Heat transport greatly affects the

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

of water and its ability to flow. 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 In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hai ...

*Reduction and oxidation (

redox Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate (chemistry), substrate change. Oxidation is the loss of Electron, electrons or an increase in the oxidation state, while reduction ...

) reactions, including those catalyzed by

enzyme Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates into different molecule ...

s, surfaces, and

microorganism A microorganism, or microbe,, ''mikros'', "small") and ''organism'' from the el, ὀργανισμός, ''organismós'', "organism"). It is usually written as a single word but is sometimes hyphenated (''micro-organism''), especially in olde ...

s * Sorption,

ion exchange Ion exchange is a reversible interchange of one kind of ion present in an insoluble solid with another of like charge present in a solution surrounding the solid with the reaction being used especially for softening or making water demineralised, ...

, and surface complexation *Gas dissolution and

exsolution A solid solution, a term popularly used for metals, is a homogenous mixture of two different kinds of atoms in solid state and have a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word ...

* Stable isotope fractionation *

Radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...

Mass Transport: *

Advection In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is a ...

*Molecular scale

diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

* Hydrodynamic dispersion * Colloid-facilitated transport Heat transport: *

* Conduction *

Convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...

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. Analytical solutions are exact solutions of the governing equations. 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 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.Steefel, C.I. and K.T.B. MacQuarrie, 1996, Approaches to modeling of reactive transport in porous media. In P.C. Lichtner, C.I. Steefel, and E.H. Oelkers (eds.), 1996, Reactive Transport in Porous Media. ''Reviews in Mineralogy'' 34, 85-129 Instead of solving all the relevant equations together, the transport and chemical reaction equations can be solved separately. 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 Strang splitting is a numerical method for solving differential equations that are decomposable into a sum of differential operators. It is named after Gilbert Strang. It is used to speed up calculation for problems involving operators on very diff ...

, 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.

Challenges

Reactive transport modeling requires input from numerous fields, including

hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is calle ...

geochemistry Geochemistry is the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth's crust and its oceans. The realm of geochemistry extends beyond the Earth, encompassing the ...

and

biogeochemistry Biogeochemistry is the scientific discipline that involves the study of the chemical, physical, geological, and biological processes and reactions that govern the composition of the natural environment (including the biosphere, the cryospher ...

microbiology Microbiology () is the scientific study of microorganisms, those being unicellular (single cell), multicellular (cell colony), or acellular (lacking cells). Microbiology encompasses numerous sub-disciplines including virology, bacteriology, ...

soil physics Soil physics is the study of soil's physical properties and processes. It is applied to management and prediction under natural and managed ecosystems. Soil physics deals with the dynamics of physical soil components and their phases as soli ...

, and

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...

. 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. Field sites are typically

heterogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...

, both physically and chemically, and sampling is often sparse. The prevailing assumption of

Fickian Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion e ...

dispersion is often inadequate. 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. 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.

Software programs in common use

PFLOTRAN

ChemPluginCHESSHYTECCrunchFlow
ref name = "Steefel and Lasaga" /> * The Geochemist's Workbench
HYDROGEOCHEMPHREEQC

PHAST
ref name = "PHAST">Parkhurst, D.L., Kipp, K.L., and Charlton, S.R., 2010, PHAST Version 2—A program for simulating groundwater flow, solute transport, and multicomponent geochemical reactions: U.S. Geological Survey Techniques and Methods 6–A35, 235 p.
Reaktoro
ref name = "Reaktoro">Leal, A. M. M. et al. (2018). Reaktoro, a unified, open-source framework for modeling chemically reactive systems, https://github.com/reaktoro/reaktoro
TOUGHREACT
ref>Xu, T., E.L. Sonnenthal, N. Spycher and K. Pruess, 2004, TOUGHREACT user's guide: A simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media. Report LBNL-55460, Lawrence Berkeley National Laboratory, Berkeley, California.
OpenGeoSysPHT3DPNBRNS
ref name = "Gharasoo2012" />
HP1

HP2

Overview

Development of reactive transport modeling

Processes considered in reactive transport models

Solving reactive transport models

Challenges

Software programs in common use

See also

References

Further reading