On the behavior of approaches to simulate reactive transport

Towards Understanding Factors Affecting Arsenic, Chromium, and Vanadium Mobility in the Subsurface

Arsenic (As), chromium (Cr), and vanadium (V) are naturally occurring, redox-active elements that can become human health hazards when they are released from aquifer substrates into groundwater that may be used as domestic or irrigation source. As such, there is a need to develop incisive conceptual and quantitative models of the geochemistry and transport of potentially hazardous elements to assess risk and facilitate interventions. However, understanding the complexity and heterogeneous subsurface environment requires knowledge of solid-phase minerals, hydrologic movement, aerobic and anaerobic environments, microbial interactions, and complicated chemical kinetics. Here, we examine the relevant geochemical and hydrological information about the release and transport of potentially hazardous geogenic contaminants, specifically As, Cr, and V, as well as the potential challenges in developing a robust understanding of their behavior in the subsurface. We explore the development of geochemical models, illustrate how they can be utilized, and describe the gaps in knowledge that exist in translating subsurface conditions into numerical models, as well as provide an outlook on future research needs and developments.

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advancement along the current frontier: biochemical reactions. To this end, we review the basic equations to indicate that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous challenges are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic eleven conceptual issues that we consider fundamental for any conceptually sound RT effort.

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid-fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. We discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

Reactive transport in porous media: a review of recent mathematical efforts in modeling geochemical reactions in petroleum subsurface reservoirs

The rapid advancements in the computational abilities of numerical simulations have attracted researchers to work on the area of reactive transport in porous media to improve the hydrocarbon production processes from mature reservoirs. In the hydrology community, reactive transport is well developed where the main research focuses on studying the movement of groundwater and contaminants in aquifers, and quantifying the effect of chemical reactions between the rocks and water. Recently, great efforts have been made to adapt similar models for petroleum applications where multiphase flow is experienced in the subsurface reservoirs. In such systems, thermodynamic and chemical equilibrium is key in establishing an accurate description of the states of the fluids existing in the reservoir. This paper presents a detailed and comprehensive review on the concepts of geochemical modeling, and how it can be mathematically adapted to petroleum multiphase flow problems in porous media. We introduce key physical concepts outlining the treatment of chemical reactions in experimental trials and then explain in detail how a network of chemical reactions can be modeled mathematically for numerical simulation applications. The steps of characterizing the physical behavior of the fluid flow—through a set of governing equations by either natural or molar variables formulations, and the methodology to simplify and incorporate the numerical algorithms into an existing reservoir simulation scheme are shown as well. We finally present two numerical cases from the literature to highlight the key variations between the different variable formulations and comment on the advantages and disadvantages of each approach.

Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or differential equations, describing the chemical reactions. Solution methods for the resulting large nonlinear system can be either fully coupled or can iterate between transport and chemistry. This paper extends previous work by the authors where an approach based on the Newton–Krylov method applied to a reduced system has been developed. The main feature of the approach is to solve the nonlinear system in a fully coupled manner while keeping transport and chemistry modules separate. Here we extend the method in two directions. First, we take into account mineral precipitation and dissolution reactions by using an interior point Newton method, so as to avoid the usual combinatorial approach. Second, we study two-dimensional heterogeneous geometries. We show how the method can make use of an existing transport solver, used as a black box. We detail the methods and algorithms for the individual modules, and for the coupling step. We show the performance of the method on synthetic examples.

An indicator-based problem reduction scheme for coupled reactive transport models

A number of effective models have been developed for simulating chemical transport in porous media; however, when a reactive chemical problem comprises multiple species within a substantial domain for a long period of time, the computational cost can become prohibitively expensive. This issue is addressed here by proposing a new numerical procedure to reduce the number of transport equations to be solved. This new problem reduction scheme (PRS) uses a predictor-corrector approach, which "predicts" the transport of a set of non-indicator species using results from a set of indicator species before "correcting" the non-indicator concentrations using a mass balance error measure. The full chemical transport model is described along with experimental validation. The PRS is then presented together with an investigation, based on a 16-species reaction-advection-diffusion problem, which determines the range of applicability of different orders of the PRS. The results of a further study are presented, in which a set of PRS simulations is compared with those from full model predictions. The application of the scheme to the intermediate-sized problems considered in the present study showed reductions of up to 82% in CPU time, with good levels of accuracy maintained.

Multi-component reactive transport in heterogeneous media and its decoupling solution

The multi-component reactive transport model is widely used in contaminant transport, water-rock interaction, and other earth science fields. Since its complexity lies in its solution, a decoupling approach is used to simplify the model to enhance computational efficiency. A decoupling approach is presented for heterogeneous media, and used to solve the model in this situation. The whole domain is divided into several sub-domains due to the different reactions which may occur and the corresponding component matrix was obtained. The boundary between sub-domains could be divided into two parts, inflow and outflow, which are defined as the Neumann condition and the Dirichlet one, and the concentration of the latter could be calculated by the component in the adjacent sub-domain. Then the models in each sub-domain can be connected and solved. Taking a heterogeneous porous media as an example in which permanganate is partially dissolved during the process, firstly the result obtained by this method without considering porosity variation is compared to that from PHAST: good agreement is achieved, then while considering the change of porosity caused by the dissolution of the permanganate, the flow field, species concentration and porosity of the whole domain and typical sections and points during the reaction are analysed. It is concluded that: the decoupling approach to heterogeneous media is appropriate, and the results from the model could reflect the variation of physical fields due to groundwater in heterogeneous media.

Acid/base front propagation in saturated porous media: 2D laboratory experiments and modeling

We perform laboratory scale reactive transport experiments involving acid-basic reactions between nitric acid and sodium hydroxide. A two-dimensional experimental setup is designed to provide continuous on-line measurements of physico-chemical parameters such as pH, redox potential (Eh) and electrical conductivity (EC) inside the system under saturated flow through conditions. The electrodes provide reliable values of pH and EC, while sharp fronts associated with redox potential dynamics could not be captured. Care should be taken to properly incorporate within a numerical model the mixing processes occurring inside the electrodes. The available observations are modeled through a numerical code based on the advection-dispersion equation. In this framework, EC is considered as a variable behaving as a conservative tracer and pH and Eh require solving the advection dispersion equation only once. The agreement between the computed and measured pH and EC is good even without recurring to parameters calibration on the basis of the experiments. Our findings suggest that the classical advection-dispersion equation can be used to interpret these kinds of experiments if mixing inside the electrodes is adequately considered.

Operator-splitting-based reactive transport models in strong feedback of porosity change: The contribution of analytical solutions for accuracy validation and estimator improvement

Reactive transport is a highly non-linear problem requiring the most efficient algorithms to rapidly reach an accurate solution. The non-linearities are increased and the resolution is even more demanding and CPU-intensive when considering feedback of dissolution or precipitation reactions on hydrodynamic flow and transport, commonly referred to as the variable porosity case. This is particularly true near clogging, which leads to very stiff systems and therefore small time-steps. The operator-splitting approach often cited is a widely use method to solve these problems: it consists in solving sequentially the transport then the chemistry part of the problem. Operator-splitting appears to be an accurate approach, provided that the solution is iteratively improved at each time-step. The paper details analytical solutions and test-cases for this class of problems. They demonstrate that iterative improvement is then compulsory. They also helped develop an improved estimator/corrector method which allows to reach convergence faster and to reduce stiffness. The efficiency improvement is significant as illustrated by an example of carbonation of a cement paste, a well-known problem that leads to complete clogging of the interface layer.

Vadose zone attenuation of organic compounds at a crude oil spill site - interactions between biogeochemical reactions and multicomponent gas transport

Contaminant attenuation processes in the vadose zone of a crude oil spill site near Bemidji, MN have been simulated with a reactive transport model that includes multicomponent gas transport, solute transport, and the most relevant biogeochemical reactions. Dissolution and volatilization of oil components, their aerobic and anaerobic degradation coupled with sequential electron acceptor consumption, ingress of atmospheric O(2), and the release of CH(4) and CO(2) from the smear zone generated by the floating oil were considered. The focus of the simulations was to assess the dynamics between biodegradation and gas transport processes in the vadose zone, to evaluate the rates and contributions of different electron accepting processes towards vadose zone natural attenuation, and to provide an estimate of the historical mass loss. Concentration distributions of reactive (O(2), CH(4), and CO(2)) and non-reactive (Ar and N(2)) gases served as key constraints for the model calibration. Simulation results confirm that as of 2007, the main degradation pathway can be attributed to methanogenic degradation of organic compounds in the smear zone and the vadose zone resulting in a contaminant plume dominated by high CH(4) concentrations. In accordance with field observations, zones of volatilization and CH(4) generation are correlated to slightly elevated total gas pressures and low partial pressures of N(2) and Ar, while zones of aerobic CH(4) oxidation are characterized by slightly reduced gas pressures and elevated concentrations of N(2) and Ar. Diffusion is the most significant transport mechanism for gases in the vadose zone; however, the simulations also indicate that, despite very small pressure gradients, advection contributes up to 15% towards the net flux of CH(4), and to a more limited extent to O(2) ingress. Model calibration strongly suggests that transfer of biogenically generated gases from the smear zone provides a major control on vadose zone gas distributions and vadose zone carbon balance. Overall, the model was successful in capturing the complex interactions between biogeochemical reactions and multicomponent gas transport processes. However, despite employing a process-based modeling approach, honoring observed parameter ranges, and generally obtaining good agreement between field observations and model simulations, accurate quantification of natural attenuation rates remains difficult. The modeling results are affected by uncertainties regarding gas phase saturations, tortuosities, and the magnitude of CH(4) and CO(2) flux from the smear zone. These findings highlight the need to better delineate gas fluxes at the model boundaries, which will help constrain contaminant degradation rates, and ultimately source zone longevity.

Evidence of compound-dependent hydrodynamic and mechanical transverse dispersion by multitracer laboratory experiments

Mass transfer, mixing, and therefore reaction rates during transport of solutes in porous media strongly depend on dispersion and diffusion. In particular, transverse mixing is a significant mechanism controlling natural attenuation of contaminant plumes in groundwater. The aim of the present study is to gain a deeper understanding of vertical transverse dispersive mixing of reaction partners in saturated porous media. Multitracer laboratory experiments in a quasi two-dimensional tank filled with glass beads were conducted and transverse dispersion coefficients were determined from high-resolution vertical concentration profiles. We investigated the behavior of conservative tracers (i.e., fluorescein, dissolved oxygen, and bromide), with different aqueous diffusion coefficients, in a range of grain-related Peclet numbers between 1 and 562. The experimental results do not agree with the classical linear parametric model of hydrodynamic dispersion, in which the transverse component is approximated as the sum of pore diffusion and a compound-independent mechanical dispersion term. The outcome of the multitracer experiments clearly indicates a nonlinear relation between the dispersion coefficient and the average linear velocity. More importantly, we show that transverse mechanical dispersion depends on the diffusion coefficient of the compound, at least at the experimental bench-scale. This result has to be considered in reactive-transport models, because the typical assumption that two reactants with different aqueous diffusive properties are characterized by the same dispersive behavior does not hold anymore.

Tableau input coupled kinetic equilibrium transport (TICKET) model

TICKET is a general-purpose, multispecies reactive transport model that is based on the tableau structure in MINEQL. The model can be used in solving problems from simple chemical equilibrium calculations for batch systems to complex one-dimensional, reactive transport computations for surface water, groundwater, and water treatment systems. To streamline model input and model formulation, specifications of equilibrium speciation (including homogeneous precipitation, solid solutions, adsorption, and ion exchange) and linear and nonlinear kinetic reactions are defined directly in the tableau. In addition, the burden of accounting for appearing and disappearing solid phases is circumvented by approximating homogeneous precipitation as a solid solution (with an insoluble seed). The solution technique for the model is based on a one-step algorithm and can be applied to both steady-state and fully implicit, time-variable problems. This approach is particularly well-suited in handling chemical speciation-transport problems with fast, nonlinear reaction kinetics and transient chemical intermediates. TICKET model simulations are presented for several test cases to verify the computational scheme. A model application, which examines the effects of sorption and overlying dissolved oxygen concentration on Fe(II) and As(III) oxidation in a sediment column, is also presented to demonstrate the utility of TICKET in examining complex chemical speciation-transport behavior.

Modeling porosity reductions caused by mineral fouling in continuous-wall permeable reactive barriers

A study was conducted to assess key factors to include when modeling porosity reductions caused by mineral fouling in permeable reactive barriers (PRBs) containing granular zero valent iron. The public domain codes MODFLOW and RT3D were used and a geochemical algorithm was developed for RT3D to simulate geochemical reactions occurring in PRBs. Results of simulations conducted with the model show that the largest porosity reductions occur between the entrance and mid-plane of the PRB as a result of precipitation of carbonate minerals and that smaller porosity reductions occur between the mid-plane and exit face due to precipitation of ferrous hydroxide. These findings are consistent with field and laboratory observations, as well as modeling predictions made by others. Parametric studies were conducted to identify the most important variables to include in a model evaluating porosity reduction. These studies showed that three minerals (CaCO3, FeCO3, and Fe(OH)2 (am)) account for more than 99% of the porosity reductions that were predicted. The porosity reduction is sensitive to influent concentrations of HCO3-, Ca2+, CO3(2-), and dissolved oxygen, the anaerobic iron corrosion rate, and the rates of CaCO3 and FeCO3 formation. The predictions also show that porosity reductions in PRBs can be spatially variable and mineral forming ions penetrate deeper into the PRB as a result of flow heterogeneities, which reflects the balance between the rate of mass transport and geochemical reaction rates. Level of aquifer heterogeneity and the contrast in hydraulic conductivity between the aquifer and PRB are the most important hydraulic variables affecting porosity reduction. Spatial continuity of aquifer hydraulic conductivity is less significant.

Impact of mineral fouling on hydraulic behavior of permeable reactive barriers

This paper describes reactive transport simulations conducted to assess the impact of mineral fouling on the hydraulic behavior of continuous-wall permeable reactive barriers (PRBs) employing granular zero-valent iron (ZVI) in carbonate-rich alluvial aquifers. The reactive transport model included a geochemical algorithm for simulating corrosion and mineral precipitation reactions that have been observed in ZVI PRBs. Results of simulations show that porosity and hydraulic conductivity of the ZVI decrease over time and that flows are redistributed throughout the PRB in response to fouling of the pore space. Under typical conditions, only subtle changes occur within the first 10 years (i.e., duration of the current field experience record with PRBs), and the most significant changes do not occur until the PRB has operated for at least 30 years. However, changes can occur sooner (or later) if the rate at which mineral-forming ions are delivered to the PRB is higher (or lower) than that expected under typical conditions (i.e., due to higher/lower flow rate or inflowing ground water that has higher/lower ionic strength). When the PRB is more permeable than the aquifer, the median Darcy flux in the PRB does not change appreciably over time because the aquifer controls the rate of flow through the PRB. However, seepage velocities in the PRB increase, and residence times decrease, due to porosity reductions caused by accumulation of minerals in the pore space. When fouling becomes extensive, bypassing and reductions in flow rate in the PRB occur.