A general description of the mathematical and numerical formulations used in modern numerical reactive transport codes relevant for subsurface environmental simulations is presented. The formulations are followed by short descriptions of commonly used and available subsurface simulators that consider continuum representations of flow, transport, and reactions in porous media. These formulations are applicable to most of the subsurface environmental benchmark problems included in this special issue. The list of codes described briefly here includes PHREEQC, HPx, PHT3D, OpenGeoSys (OGS), HYTEC, ORCHESTRA, TOUGHREACT, eSTOMP, HYDROGEOCHEM, CrunchFlow, MIN3P, and PFLOTRAN. The descriptions include a C. I. Steefel ( ) · B. Arora · S. Molins · N. Spycher

[1] A generalized formulation for kinetically controlled reactions has been developed and incorporated into a multicomponent reactive transport model to facilitate the investigation of a large variety of problems involving inorganic and organic chemicals in variably saturated media. The general kinetic formulation includes intra-aqueous and dissolutionprecipitation reactions in addition to geochemical equilibrium expressions for hydrolysis, aqueous complexation, oxidation-reduction, ion exchange, surface complexation, and gas dissolution-exsolution reactions. The generalized approach allows consideration of fractional order terms with respect to any dissolved species in terms of species activities or in terms of total concentrations, which facilitates the incorporation of a variety of experimentally derived rate expressions. Monod and inhibition terms can be used to describe microbially mediated reactions or to limit the reaction progress of inorganic reactions. Dissolution-precipitation reactions can be described as surface-controlled or transport-controlled reactions. The formulation also facilitates the consideration of any number of parallel reaction pathways, and reactions can be treated as irreversible or reversible processes. Two groundwater contamination scenarios, both set in variably saturated media but with significantly different geochemical reaction networks, are investigated and demonstrate the advantage of the generalized approach. The first problem focuses on a hypothetical case study of the natural attenuation of organic contaminants undergoing dissolution, volatilization, and biodegradation in an unconfined aquifer overlaid by unsaturated sediments. The second problem addresses the generation of acid mine drainage in the unsaturated zone of a tailings impoundment at the Nickel Rim Mine Site near Sudbury, Ontario, and subsequent reactive transport in the saturated portion of the tailings.

Boson sampling holds the potential to experimentally falsify the extended Church-Turing thesis. The computational hardness of boson sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that are proposed as witnesses of boson sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.

Models test our understanding of processes and can reach beyond the spatial and temporal scales of measurements. Multi-component Reactive Transport Models (RTMs), initially developed more than three decades ago, have been used extensively to explore the interactions of geothermal, hydrologic, geochemical, and geobiological processes in subsurface systems. Driven by extensive data sets now available from intensive measurements efforts, there is a pressing need to couple RTMs with other community models to explore non-linear interactions among the atmosphere, hydrosphere, biosphere, and geosphere. Here we briefly review the history of RTM development, summarize the current state of RTM approaches, and identify new research directions, opportunities, and infrastructure needs to broaden the use of RTMs. In particular, we envision the expanded use of RTMs in advancing process understanding in the Critical Zone, the veneer of the Earth that extends from the top of vegetation to the bottom of groundwater. We argue that, although parsimonious models are essential at larger scales, process-based models are the only way to explore the highly nonlinear coupling that characterizes natural systems. We present seven testable hypotheses that emphasize the unique capabilities of process-based RTMs for (1) elucidating chemical weathering and its physical and biogeochemical drivers; (2) understanding the interactions among roots, microorganisms , carbon, water, and minerals in the rhizosphere; (3) assessing the effects of heterogeneity across spatial and temporal scales; and (4) integrating the vast quantity of novel data, including-omics‖ data (genomics, transcriptomics, proteomics, metabolomics), elemental concentration and speciation data, and isotope data into our understanding of complex earth systems. With strong support from data-driven sciences, we are now in an exciting era where integration of RTM framework into other community models will facilitate process understanding across disciplines and across scales.

Boson samplers-set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modespromise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles? Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device. We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns. The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.

[1] At many sites contaminated with petroleum hydrocarbons, methanogenesis is a significant degradation pathway. Techniques to estimate CH 4 production, consumption, and transport processes are needed to understand the geochemical system, provide a complete carbon mass balance, and quantify the hydrocarbon degradation rate. Dissolved and vapor-phase gas data collected at a petroleum hydrocarbon contaminated site near Bemidji, Minnesota, demonstrate that naturally occurring nonreactive or relatively inert gases such as Ar and N 2 can be effectively used to better understand and quantify physical and chemical processes related to methanogenic activity in the subsurface. In the vadose zone, regions of Ar and N 2 depletion and enrichment are indicative of methanogenic and methanotrophic zones, and concentration gradients between the regions suggest that reaction-induced advection can be an important gas transport process. In the saturated zone, dissolved Ar and N 2 concentrations are used to quantify degassing driven by methanogenesis and also suggest that attenuation of methane along the flow path, into the downgradient aquifer, is largely controlled by physical processes. Slight but discernable preferential depletion of N 2 over Ar, in both the saturated and unsaturated zones near the free-phase oil, suggests reactivity of N 2 and is consistent with other evidence indicating that nitrogen fixation by microbial activity is taking place at this site.

Expansion of shale gas extraction has fueled global concern about fugitive methane impacts on groundwater and climate. Although methane leakage from wells is common, information regarding impacts to groundwater remains sparse, and is believed by many to be minor. We injected methane gas into a shallow, flat-lying sand aquifer for 72 days. While a significant fraction of methane vented to the atmosphere, an equal portion remained in the groundwater.Methane migration in the aquifer was governed by subtle grain-scale bedding that impeded buoyant free-phase gas flow, leading to episodic releases of free-phase gas, and fostering lateral gas migration farther than anticipated based on groundwater advection. Methane persisted in the groundwater zone despite active growth of methanotrophic bacteria, while much of the methane venting into the vadose zone was degraded. Our results show even small-volume releases of methane gas cause extensive free-phase and solute plumes emanating from leaks only detectable using well-established contaminant hydrogeology monitoring methods.

The hydrated Mg-carbonate mineral, hydromagnesite [Mg 5 (CO 3) 4 (OH) 2 •4H 2 O], precipitates within mine tailings at the Mount Keith Nickel Mine, Western Australia as a direct result of mining operations. We have used quantitative mineralogical data and  13 C,  18 O and F 14 C isotopic data to quantify the amount of CO 2 fixation and identify carbon sources. Our radiocarbon results indicate that at least 80% of carbon in hydromagnesite is sourced from the modern atmosphere. Stable isotopic results indicate that dissolution of atmospheric CO 2 into mine tailings water is kinetically limited, which suggests that the passive rate of carbon mineralization could be accelerated. Reactive transport modeling is used to describe the observed variation in tailings mineralogy and to estimate rates of CO 2 fixation. Based on our assessment, approximately 39 800 t/yr of atmospheric CO 2 are being trapped and stored in tailings at Mount Keith. This represents an offsetting of approximately 11% of the mine's annual greenhouse gas emissions. Thus, passive sequestration via enhanced weathering of mineral waste can capture and store a significant amount of CO 2. Implementation of geoengineering strategies that accelerate the uptake of CO 2 into tailings water could further reduce or completely offset the net greenhouse gas emissions at Mount Keith and many other mines.