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

Investigating reactive transport and precipitation patterns of calcium carbonate in fractured porous media

HYPOTHESIS

Understanding calcium carbonate (CaCO3) precipitation in various polymorphs from nanoparticle size (amorphous calcium carbonate) to microparticle size (vaterite, aragonite, dendrite, calcite) is important for practical applications, including carbon geo-storage (e.g., basalt formations), hydrogen storage, groundwater management, and soil stabilization. Our hypothesis suggests that the interplay of Péclet numbers (Pe), Damköhler numbers (Da), and Supersaturation Index (SI) significantly impacts the evolution of CaCO3 precipitation in fractured porous media in terms of mixing patterns, spatiotemporal evolution, crystal morphology, crystal size, and clogging behavior.

EXPERIMENTS

This study takes a novel approach to explore the colloidal formation and precipitation dynamics of CaCO3 within a fractured microfluidic system. Here, calcium chloride (CaCl2) and sodium bicarbonate (NaHCO3) solutions were injected and reacted under varied Pe (0-11), Da (0-1), and SI (2-5).

FINDINGS

Our analysis revealed distinct precipitation patterns and mixing types, such as transverse, longitudinal, and incomplete mixing, providing insights into the behavior in fractured porous media. We systematically analyzed the temporal and spatial evolution of precipitation, demonstrating how Pe, Da, and SI dictate precipitation rates and spatial distribution. Additionally, the study uncovered a range of CaCO3 polymorphic forms, illustrating their evolution and coexistence. Morphological changes and crystal sizes were examined to decode nucleation and growth processes. Significantly, our findings highlight the relationship between precipitation and clogging in the fractured medium, offering a deeper understanding of reactive transport in complex porous environments. These insights are crucial for enhancing carbon containment security and storage efficiency in underground formations, improving groundwater remediation techniques, and developing novel construction materials through controlled precipitation processes.

Ubiquity of the Micrometer-Thick Interface along a Quartz-Water Boundary

Water-rock interactions determine how the geochemical cycles revolve from the Earth's surface to the deep interior (large T-P intervals). The underlying mechanisms interweave the fluxes of matter, time, and reactivity between fluid phases and solids. The deformation processes of crustal rocks are also known to be significantly affected by the presence or absence of water, typically with the hydrolytic weakening of quartz, olivine, and other silicate minerals. In fact, fluid-rock interactions mechanistically unfold along their interfaces, developing over a certain thickness within the two phases. Diffraction-limited mid-infrared microspectroscopy was employed to monitor the thermodynamic characteristics of liquid water along a quartz boundary. The hyperspectral Fourier transform infrared data set displayed a very strong distance-dependent signature for water over a 1 ± 0.5 μm thickness, while quartz appears unmodified, which is consistent with recent studies. This unexpected thick interface is tested against the geometry of the inclusion, the chemistry of the occluded liquid (especially pH), and the thermal conditions ranging from room temperature to 155 °C. Throughout this range of physicochemical conditions, the micrometer-thick interface is characterized by a ubiquitous, significant shift in the Gibbs free energy of water inside the interfacial layer. This conclusion suggests that the interface-imprinting phenomenon driving this microthick layer has thermodynamic roots that give rise to specific properties along the quartz-water interface. This finding questions the systematic use of the bulk phase data sets to evaluate how water-rock interactions progress in porous media.

Bioremediation of chlorinated ethenes contaminated groundwater and the reactive transport modeling - A review

Improper disposal of chlorinated ethenes (CEs), a class of widely used solvents in chemical manufacturing and cleaning industries, often leads to severe groundwater contamination. In situ bioremediation of CE-contaminated groundwater has received continuous attention in recent years. The reactive transport simulation is a valuable tool for planning and designing in situ bioremediation systems. This paper presents a detailed and comprehensive review on the main biotransformation pathways of CEs in aquifers, the mathematical modeling of bioremediation processes, and the available software developed for the simulation of reactive transport of CEs over past three decades. The aim of this research is to provide guidance on the selection of appropriate models and software suitable for systems of varying scales, and to discern prevailing research trends while identifying areas worthy of further study. This paper provides a detailed summary of the equations, parameters, and applications of existing biotransformation models from literature studies, highlighting the operation, benefits, and limitations of software available for CEs reactive transport simulations. Lastly, the support of reactive transport simulation programs for the design of full-scale in situ bioremediation systems was elucidated. Further research is needed for incorporating the effects of key subsurface environmental factors on biodegradation processes into models and balancing model complexity with computer data processing power to better support the development and application of reactive transport modeling software.

Kinetic reactive transport explains distinct subsurface deposition patterns of pollutants in sediments. The case of the Sellafield-derived 236U, 137Cs and 239,240Pu in the Esk Estuary, UK

The kinetics of the uptake of pollutants by solids in sediments interacts with transitional eddy diffusivity in the pore fluid, leading to different depth-distribution patterns. This work aims to gain insights into the still poorly understood behaviour in the marine environment of the anthropogenic ²³⁶U, a recently postulated tracer of water masses. It is hypothesized that the transition from mobile U(VI) to highly particle-reactive U(IV) in the anoxic zone of the sediment produces a subsurface deposition pattern. A novel numerical model for kinetic reactive transport in sediments, which merges diagenetic processes for transport and box models for the uptake, is used for concept demonstration. It is applied to synthetic environments with high eddy diffusivity to obtain the singular depth-distribution patterns of pulsed inputs of tracers that mimic the anthropogenic ^239,240Pu, ¹³⁷Cs, and ²³⁶U. While the first is retained in the upper cm, the second shows an exponential penetration pattern over few cm, and ²³⁶U is deposited with a Gaussian-like pattern centred below the transition to the anoxic zone. These patterns are then merged into a diagenetic model to compute the depth distribution at decadal or centennial scales of dissolved and particle-bound inputs of these radiotracers. It is successfully applied to a real case using literature data for a sediment core from the Esk Estuary, UK, affected by radioactive releases from the Sellafield nuclear reprocessing plant. This work provides insight into until now poorly understood field data and provides a novel view of broad implications in the study of the behaviour of pollutants in surficial aquatic sediments.

Developing synthetic sandstones using geopolymer binder for constraining coupled processes in porous rocks

There is a current need for developing improved synthetic porous materials for better constraining the dynamic and coupled processes relevant to the geotechnical use of underground reservoirs. In this study, a low temperature preparation method for making synthetic rocks is presented that uses a geopolymer binder cured at 80 °C based on alkali-activated metakaolin. For the synthesised sandstone, the key rock properties permeability, porosity, compressive strength, and mineralogical composition, are determined and compared against two natural reservoir rocks. In addition, the homogeneity of the material is analysed structurally by micro-computed tomography and high-resolution scanning electron microscopy, and chemically by energy dispersive X-ray spectroscopy. It is shown that simple, homogenous sandstone analogues can be prepared that show permeability-porosity values in the range of porous reservoir rocks. The advance in using geopolymer binders to prepare synthetic sandstones containing thermally sensitive minerals provides materials that can be easily adapted to specific experimental needs. The use of such material in flow-through experiments is expected to help bridge the gap between experimental observations and numerical simulations, leading to a more systematic understanding of the physio-chemical behaviour of porous reservoir rocks.

Modelling the kinetic reactive transport of pollutants at the sediment-water interface. Applications with atmospheric fallout radionuclides

Understanding the behaviour of particulate matter and chemicals at the sediment-water interface (SWI) is of interest in environmental studies and risk assessments. These processes are still poorly understood, and this work aims to gain relevant insights by using a kinetic reactive transport model. It merges early diagenetic processes and box models for the uptake kinetics. Numerical solutions have been found for synthetic scenarios and for studying real cases from the literature (²¹⁰Pb and Chernobyl fallout radionuclides in Lake Sniardwy, Poland, and ⁷Be in sediments from Tema Harbour, Ghana). The study identifies a series of factors that dynamically interact to govern the final fate of tracers in the SWI region, leading to a wide diversity of behaviours. When a term of eddy diffusivity is included in the upper regions of the pore fluid, which seems feasible for some energetic scenarios, it is possible to explain the observed large penetration depths for Cs and Be, while high particle-reactive elements are retained in thinner sediment layers. Desorption from the sediment occurs through the pore fluid as diffusive fluxes. Transient depth profiles of tracer concentrations can last from months up to a year, and they can show subsurface maxima at positions unrelated with the accretion rate. In the application cases, the model explained a wide set of observational data that was beyond the capabilities of other approaches involving physical mixing of solids and equilibrium k_d. This modelling study could provide useful guidance for future research works.

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.

Coupling of Rigorous Multiphase Flash with Advanced Linearization Schemes for Accurate Compositional Simulation

The properties of fluids flowing in a petroleum reservoir are quantified by understanding the thermodynamic behavior of each flowing phase in the system. This work describes proper techniques to formulate and execute a thermodynamic model for accurately predicting the equilibrium behavior of oil-gas-brine systems within the practical range of pressure and temperature. The three-phase flash algorithm is validated against published data from the available literature. The multiphase flash procedure is implemented to generate linearized physical properties by using an Operator Based Linearization (OBL) modelling technique allowing for a combination of multiple complex physics in the nonlinear solution of governing equations. This is the first implementation of three-phase flash calculations for hydrocarbons and brines based on fugacity-activity models coupled with an advanced highly efficient linearization scheme. Our approach increases the efficiency and flexibility of the modelling process of physical phenomena such as fluid flow in porous subsurface reservoirs.

Modeling the effects of capillary pressure with the presence of full tensor permeability and discrete fracture models using the mimetic finite difference method

Capillary dominated flow or imbibition—whether spontaneous or forced—is an important physical phenomena in understanding the behavior of naturally fractured water-driven reservoirs (NFR’s). When the water flows through the fractures, it imbibes into the matrix and pushes the oil out of the pores due to the difference in the capillary pressure. In this paper, we focus on modeling and quantifying the oil recovered from NFR’s through the imbibition processes using a novel fully implicit mimetic finite difference (MFD) approach coupled with discrete fracture/discrete matrix (DFDM) technique. The investigation is carried out in the light of different wetting states of the porous media (i.e., varying capillary pressure curves) and a full tensor representation of the permeability. The produced results proved the MFD to be robust in preserving the physics of the problem, and accurately mapping the flow path in the investigated domains. The wetting state of the rock affects greatly the oil recovery factors along with the orientation of the fractures and the principal direction of the permeability tensor. We can conclude that our novel MFD method can handle the fluid flow problems in discrete-fractured reservoirs. Future works will be focused on the extension of MFD method to more complex multi-physics simulations.