Stability Of Fronts Research Articles

A parametric study of polymer-enhanced CO2 injection in a light-oil reservoir using full-physics simulation

This study aims to assess the performance of polymer-enhanced CO2 injection in a light-oil reservoir under various reservoir geometries, parameters, and polymer properties. We also introduce several injection techniques: Polymer-Alternating-Gas (PAG) injection and co-injection of CO2 with water/polymer. This study employs full-physics compositional and polymer simulation to construct mechanistic models to investigate the efficiency of each EOR method. The injection strategies are water, polymer, CO2, Water-Alternating-Gas (WAG), PAG, and co-injection of CO2 and water/polymer. These parametric studies focus on reservoir geometries (formation dip angle), reservoir properties (heterogeneity and permeability), polymer properties, WAG parameters, and CO2 miscibility. For a 20-meter reservoir without dipping, the co-injection of CO2 with polymer and PAG are shown to recover 10% and 8% more oil than WAG-CO2, respectively. Adding polymer helps minimize gravity segregation, leading to a more uniform miscible flood front and oil displacement. These injection techniques are promising even in reservoirs with vertical heterogeneity. For a reservoir with a 10° dip angle, CO2 injection from the updip location creates a stable flood front, yielding high oil recovery. The sensitivity analysis reveals that polymer properties such as concentration and permeability reduction factor must be high enough to stabilize the displacement flood front, but not so high as to hinder injectivity. From the study of miscibility level, PAG and co-injection of CO2 with polymer methods are effective at miscible conditions. The findings of this study help the initial screening of existing and new CO2-EOR injection techniques and the design of EOR injection in light oil reservoirs.

Fast yet force-effective mode of supracellular collective cell migration due to extracellular force transmission.

Cell collectives, like other motile entities, generate and use forces to move forward. Here, we ask whether environmental configurations alter this proportional force-speed relationship, since aligned extracellular matrix fibers are known to cause directed migration. We show that aligned fibers serve as active conduits for spatial propagation of cellular mechanotransduction through matrix exoskeleton, leading to efficient directed collective cell migration. Epithelial (MCF10A) cell clusters adhered to soft substrates with aligned collagen fibers (AF) migrate faster with much lesser traction forces, compared to random fibers (RF). Fiber alignment causes higher motility waves and transmission of normal stresses deeper into cell monolayer while minimizing shear stresses and increased cell-division based fluidization. By contrast, fiber randomization induces cellular jamming due to breakage in motility waves, disrupted transmission of normal stresses, and heightened shear driven flow. Using a novel motor-clutch model, we explain that such 'force-effective' fast migration phenotype occurs due to rapid stabilization of contractile forces at the migrating front, enabled by higher frictional forces arising from simultaneous compressive loading of parallel fiber-substrate connections. We also model 'haptotaxis' to show that increasing ligand connectivity (but not continuity) increases migration efficiency. According to our model, increased rate of front stabilization via higher resistance to substrate deformation is sufficient to capture 'durotaxis'. Thus, our findings reveal a new paradigm wherein the rate of leading-edge stabilization determines the efficiency of supracellular collective cell migration.

Reactivation of Abandoned Oilfields for Cleaner Energy Generation: Three-Dimensional Modelling of Reservoir Heterogeneity and Geometry

With the changing picture of global energy supplies and the shift toward the energy transition, it has never been more important to look for alternative sources of energy. Globally there are tens of thousands of abandoned oil fields with considerable reserves left behind. These have the potential to be reactivated to become an energy supply that is cleaner than conventional oil and gas. This can be achieved by the use of in situ combustion and the subsequent exploitation of the inherent increase in temperature and pressure to produce geothermal energy, allied to sequestration of the mixture of produced fluids. In situ combustion (ISC) has conventionally been used as an enhanced oil recovery technique, with a high failure rate that has been recently attributed to poor reservoir selection and project design. We suggest that the failure of many earlier ISC projects is due to insufficient appreciation of how the subsurface geology affects the process. With the use of computer numerical modelling, we aim to ascertain how the geometry and heterogeneity of the reservoir control the success of the process. Here we employ simple three-dimensional sector models to assess a variety of different petrophysical heterogeneities, within a set of different reservoir geometries, on the temperature, velocity, propagation stability and enthalpy rate. These models illustrate that the biggest impact on success of the ISC process for geothermal energy generation, as a function of temperature and enthalpy, is the location of the wells relative to the heterogeneities and the scale of heterogeneities. Metre-scale heterogeneities do not have a significant effect on this. Instead, the biggest contributor to the propagation stability and direction of the fire front is the presence of a large-scale (10 s to 100 s of metres) heterogeneities, such as channels, or the geometry of a tilted fault block; both have a strong control over the direction of the propagation, and therefore are important factors with regards to well placement.

Simulations of divertor designs that spatially separate power and particle exhaust using mid-leg divertor particle pumping

Predictive design modeling of a Dissipation-Focused Divertor for future operation in DIII-D reveals that increasing the poloidal distance of the pump duct entrance from the target surface along the low-field side divertor baffle increases neutral compression and modifies the spatial distribution of power dissipation. With a divertor pump located mid-leg between the target and the X-point, SOLPS-ITER boundary plasma simulations without drifts predict the formation of a dense neutral cloud near the target with > 30x higher neutral compression in detachment, a more stable detachment front located further from the target, and ∼ 25 % lower outer midplane separatrix density required for detachment onset, compared to a pump located in the scrape-off layer at the target surface. Up to 19 MW of power flowing into the divertors is modeled using the following two numerical implementations for particle pumping: a specified fraction of particles incident on variable wall sections of the plasma grid is removed from the computational domain (so-called albedo pumping), and a pump duct is modeled which includes dynamics of kinetic neutrals in the duct. The simulations show that the detachment front is located between the divertor target and the X-point and is relatively stable near the pump entrance, without a strong dependence on gas puff rate or injected power. The mid-leg pump design spatially separates the two primary functions of a divertor (power handling and particle exhaust), with the majority of power dissipation occurring near the target plate and particle exhaust taking place further upstream. The benefit of enhanced dissipation using mid-leg pumping comes at the cost of a higher outer midplane separatrix density for a given amount of particle injection.

Stability of two-phase flow with interfacial flux in porous media: CO2 mineralization

The primary objective of carbon capture, utilization, and storage (CCUS) applications in various natural and engineered porous materials is to achieve a stable and planar CO2 displacement front, thereby suppressing viscous fingering. A stable front can ensure uniform and exhaustive CO2 mineralization throughout a reactive medium (i.e., mineral carbonation). Drawing inspiration from experimental observations of CO2 flooding into cores of portland cement-based materials, we examine the stability of such systems. Under these conditions, the injected CO2 continuously dissolves into the resident water phase, which becomes chemically disequilibrated with the solid minerals and leads to mineral carbonation on the wetted surfaces. Focusing on the early injection time allows us to reduce the complex multiphysical problem to a simple two-phase flow scenario of immiscible displacement with a CO2 interfacial flux sink. The formulated equations are investigated using numerical simulations and linear stability analysis, which results in a closed-form criterion, and provide fundamental insights into system stability. Overall, the results show that several effects combine to stabilize the system, including the sink effect, which acts to eliminate instability; the reduction in flow velocity along the flow path, which limits flow focusing; and the relative increase in stabilizing capillary forces. Therefore, if the system is stable at early stages, it will likely remain stable later on. Finally, this research demonstrates the use of theory to simplify complex problems and shows that even when flow is inherently coupled, the state of systems can often be determined from fluid stability alone.

The characteristics of steam chamber expanding and the EOR mechanisms of tridimensional steam flooding (TSF) in thick heavy oil reservoirs

Aiming at the shortcoming of conventional steam flooding (CSF), tridimensional steam flooding (TSF) was proposed to expand the limited steam chamber and to enhance the low oil recovery in thick heavy oil reservoirs. In this paper, based on mechanisms of thermal recovery, two 3D experimental models were designed to investigate the evolution of steam chambers and production performance. A new method was proposed to utilize inflection point temperature and remaining oil saturation to identify utilizable ranges, hot water zones, and steam chambers. Then, based on the parameters of the indoor experiments, three numerical models were built to further study advantages of TSF. The results show that: i) Compared to CSF, TSF possesses a plumper steam chamber, a higher steam quality and a more stable displacement front; ii) The oil recovery of TSF can reach 52.85%, while it is only 43.31% for CSF at the same time; iii) At the end of TSF, the volume of steam chamber, low oil saturation zone, low pressure zone, and low viscosity zone is 3.08 times, 3.31 times, 1.61 times, and 1.55 times, respectively, compared to CSF, which demonstrates that TSF is effective. As a result, TSF can effectively expand steam chamber and enhance oil recovery in thick heavy oil reservoirs.

Experimental and numerical study of lean combustion of propane in divergent porous media burners

Porous inert media burners for industrial applications demand the utilization of flame front stabilization methods, among which the convective or cross-section variation technique stands out. In this work, combustion of lean premixed propane-air mixtures in cylindrical and divergent alumina packed-bed porous inert media burners was numerically and experimentally conducted. Three burners of 0°, 15° and 30° of divergence were used to study the variation of equivalence ratio and inlet velocity. A bidimensional transient mathematical model was developed and solved numerically, whose results show good agreement with experimental measurements. The maximum temperature along the central axis is location dependent, with upstream augmentation of up to 86 %, meaning an increase of ∼ 815 K in the case of the 30° burner. Combustion front propagation velocity of upstream regime flames show acceleration in both divergent burners due to heat transfer and increment of thermal power in relation to cross-sectional areas when reaching the inlet. In comparison to cylindrical burner, a concave shape of the combustion front and a stretch of the maximum temperature zone was obtained, due to the diffusive nature of the velocity field. Stabilized flames on both divergent burners were achieved in the equivalence ratio range from 0.4 to 0.6. Residence time of product gases is greatly prolonged with burner wall angle and the decrease in overall temperature towards the outlet.

Study of Heavy Oil In-situ Combustion with Copper Biocatalysts: Kinetics and Thermodynamic Aspects of High-Temperature Oxidation Reactions

In-situ combustion is considered an efficient thermally enhanced oil recovery method. However, the combustion front stabilization remains a challenge for the scientific community. The present study examines the efficacy of copper tall oil (Cu-TO) and copper sunflower oil (Cu-SFO) on heavy oil high-temperature oxidation reactions, which are believed to solve this challenge. We applied non-isothermal differential scanning calorimetry (DSC) analyses combined with an isoconversional kinetic approach in order to calculate kinetic parameters, thermodynamic functions, and the effective rate constant of these reactions. The obtained results demonstrated that both catalysts are able to reduce the activation energies and shift oxidation regions to lower temperatures, with Cu-SFO showing superior performance. Kinetic predictions further supported these findings and revealed that the selected catalysts contributed significantly to decreasing oxidation times across all conversion ranges. Additionally, thermodynamic analyses indicated that Cu-SFO facilitated a more ordered and energetically favorable oxidation process, as demonstrated by increasingly negative entropy values and consistently lower Gibbs free energy. The research highlights the Cu-SFO catalyst exceptional ability to accelerate the transition from low-temperature to high-temperature oxidation while maintaining high catalytic activity. Taken together all these results, this research work contributes to provide comprehensive insights from the kinetic and thermodynamic analysis that reveal unique catalytic effects and reaction mechanisms, presenting an approach to stabilize combustion front and improve heavy oil recovery efficiency, addressing a critical challenge in the field of in-situ combustion.

Combustion behavior and effluent liquid properties in extra-heavy crude oil reservoirs developed by steam huff and puff

In recent years, interest in in-situ combustion (ISC) as an alternative technique for extra-heavy crude oil reservoirs subjected to steam huff and puff has grown significantly; however, the ISC behavior and effluent liquid properties in such oil reservoirs remain under-explored. In this work, the combustion tube (CT) was used to investigate the combustion behavior of extra-heavy crude oil. Also, the effluent liquid properties during ISC were analyzed comprehensively. The results revealed that when the secondary water bodies (SWB) were present at the injection end of CT, a stable combustion front advanced, causing a gradual temperature rise and a CO2 concentration above 12 % in the effluent gas. This suggested that steam injection wells in these reservoirs were suitable candidates for subsequent air injection after steam huff and puff. Conversely, when the SWB was located at the production end of CT, the peak temperature of combustion decreased, indicating a transition to medium-temperature combustion and unstable combustion front advancement, making steam injection wells unsuitable for ISC as production ones. Three key criteria for evaluating ISC effectiveness in extra-heavy crude oil were: (1) the intensity of –CH2 and –CH3 peaks, (2) the C-O absorption peak between 1100 and 1000 cm−1, and (3) the distribution of characteristic peaks around 750 cm−1. A significant decrease in these peaks indicated high-temperature combustion and substantial oil upgrading. Also, the presence of alkynes suggested extensive thermal cracking and a stable combustion front. The anion concentration of effluent water increased compared to crude water, but the relationship between water ion concentration and combustion state was weak, without a discernible pattern.

Spatiotemporal variability of satellite-derived abundance of Karenia spp. during 2021 in shelf waters along the Pacific coast of Hokkaido, Japan

Unprecedented catastrophic damage to coastal fisheries attributable to harmful Karenia outbreaks were reported in Pacific coastal shelf waters off the southern coast of Hokkaido from late summer to autumn in 2021. To understand the spatiotemporal variability of the Karenia blooms, we analyzed Sentinel 3-derived abundances of Karenia spp. together with marine environmental variables. Karenia spp. were very widely distributed over a maximum of more than 400 km along the shelf from the easternmost Pacific coast of Hokkaido to Cape Erimo, where there was a nearly stable water-mass front, to the west, where pure subtropical water inhibited the westward expansion of Karenia spp. blooms. The duration of the appearance of Karenia spp. at a fixed point was very long—about 45 days—in the middle part of the shelf. East of the Tokachi River, the time-averaged abundances of Karenia spp. were robustly correlated with the time-averaged alongshore velocity and stability of the Coastal Oyashio, a coastal boundary current; more intense and stable alongshore currents were associated with less developed Karenia spp. blooms. Time-averaged abundances of Karenia spp. were the highest in the middle part of the shelf, west of the Tokachi River, where low-salinity water from the river suppressed the development of the surface winter mixed layer and might have fostered favorable growth conditions and supplied nutrients of land origin. During the period of Karenia spp. blooms, abundances changed rapidly on a small scale (typically, ≤2 days and ≤50 km) in association with physical-biochemical coupled submesoscale variations. Subsampling of these variations of Karenia spp. abundances at 1-day intervals showed that the maxima and center of gravity of Karenia spp. abundances moved slowly westward along the coast at a typical velocity of 4 cm s−1. This velocity was one-third that of the time-averaged alongshore velocity of the Coastal Oyashio. Particle-tracking experiments implied that horizontal advection by the Coastal Oyashio, which supplied Karenia spp. eliminated from the upstream shelf to the downstream shelf, contributed to the long duration of Karenia spp. blooms on the middle part of the shelf.

On the Origin of the Ancient, Large-scale Cold Front in the Perseus Cluster of Galaxies

The intracluster medium of the Perseus Cluster exhibits spiral-shaped X-ray surface brightness discontinuities known as “cold fronts,” which simulations indicate are caused by the sloshing motion of the gas after the passage of a subcluster. Recent observations of Perseus have shown that these fronts extend to large radii. In this work, we present simulations of the formation of sloshing cold fronts in Perseus using the AREPO magnetohydrodynamics code, to produce a plausible scenario for the formation of the large front at a radius of 700 kpc. Our simulations explore a range of subcluster masses and impact parameters. We find that low-mass subclusters cannot generate a cold front that can propagate to such a large radius, and that small impact parameters create too much turbulence, which leads to the disruption of the cold front before it reaches such a large distance. Subclusters that make only one core passage produce a stable initial front that expands to large radii, but without a second core passage of the subcluster, other fronts are not created at a later time in the core region. We find a small range of simulations with subclusters with mass ratios of R ∼ 1:5 and an initial impact parameter of θ ∼ 20°–25° that not only produce the large cold front but a second set in the core region at later times. These simulations indicate that the “ancient” cold front is ∼6–8.5 Gyr old. For the simulations providing the closest match with observations, the subcluster has completely merged into the main cluster.

Non-thermal recovery of a viscous oil with a surfactant-polymer process

The goal of this work is to improve recovery of a viscous oil reservoir at 70 °C using a non-thermal process. Polymer floods can improve sweep efficiency, but leave behind a residual oil saturation. A surfactant-polymer flood has the potential to improve both the sweep as well as the displacement efficiency. Phase behavior experiments with the viscous oil, water and surfactants were conducted to identify surfactants. 1D and 2D sandpack displacements were conducted to evaluate the efficacy of the process. Phase behavior experiments showed Winsor type I behavior with a low interfacial tension using a single surfactant, but not ultralow tension. Water flood recovered about 50% OOIP and reduced the oil saturation to about 45% in 1D floods. The subsequent SP flood increased the cumulative oil recovery to 99% in sandpacks when the viscosity of chemical slugs exceeded the oil viscosity. When the permeability decreased (as in a Bentheimer core), the oil recovery decreased to about 86%. Secondary SP floods also recovered most of the oil and faster than tertiary floods. Reduction of polymer concentration (and viscosity to about 1/4th of the oil viscosity) reduced the oil recovery, especially in 2D sandpack floods. Decrease in interfacial tension increased the requirement of polymer concentration to maintain flood front stability. This flood demonstrates the effectiveness of Winsor type I SP formulation for viscous oil, high permeability reservoirs. Such a SP process would reduce the carbon footprint of viscous oil recovery compared to that of thermal processes.

Existence of global weak solutions and simulations to a Dirichlet problem for a generalized Swift–Hohenberg equation

In this paper, we shall investigate an initial–boundary value problem of a generalized Swift–Hohenberg model subject to homogeneous Dirichlet boundary conditions in two spatial dimensions. The model consists of a nonlinear term of the form ψ2Δ2ψ2 in the free energy functional, which is used to model the stability of fronts between hexagons and squares in pinning effect. We first prove the global-in-time existence and uniqueness of weak solutions to this initial–boundary value problem in the case with the parameter β<0, where we employ the energy method and make use of various techniques to derive delicate a priori estimates. At the end, a few numerical experiments of the model are also performed to study the competition between hexagons and squares.

Air Injection into Condensate Reservoirs in the Middle and Late Stages Increases Recovery with Thermal Miscible Mechanism

Summary Condensate gas reservoirs in the middle and late stages of development are faced with problems such as formation pressure reduction, serious retrograde condensation, and oil and gas seepage channel plugging, which make it difficult to further improve oil and gas recovery by conventional development methods. For this kind of condensate gas reservoir, in this paper we put forward air injection technology as a development means, taking the K condensate gas reservoir in the Tarim Oilfield as the research object. We explored the thermal oxidation characteristics and displacement efficiency of condensate oil/volatile oil by air injection through the thermal oxidation displacement experiment. In addition, we determined quantitatively the minimum miscibility pressure (MMP) of oil samples at high temperature and the correlation between MMP and temperature through a high-temperature, high-pressure slimtube experiment, and clarified the mechanism of “thermally assisted miscible” through fine full-component numerical simulations under high-temperature and high-pressure conditions, which indoor experiments could not achieve. The results showed that condensate oil/volatile oil can form a stable thermal front by injecting air, and the oil displacement efficiency is more than 90%. The MMP of flue gas produced by condensate oil and oxidation reaction decreases gradually with temperature increase, and the MMP is only 11 MPa at 260°C. The high temperature formed by oxidation heat release forces the oil phase into the gas phase, and the extraction of flue gas makes C2-C4 in the oil phase increase continuously, both of which promote the realization of heat-assisted evaporation miscible phase. This thermal-assisted miscible-phase mechanism makes air injection displacement technology an innovative replacement technology for greatly improving the recovery efficiency of condensate gas reservoirs in the middle and late development stages.

Radiative heat recuperation in combustion of layered solid fuel

In this work, we investigate the properties and stability of the combustion waves propagating in a system of layered solid fuel material in which the neighbouring fuel sheets can recuperate heat via thermal electromagnetic radiation. The analysis is undertaken within the flame sheet model, which allows to determine the combustion wave speed and structure and derive the dispersion relation characterising the stability of the reaction front. The proper choice of parameters leads to superadiabatic combustion temperature and significant increase of the combustion wave speed. In addition, the stable steady regimes of combustion can be substantially extended in the space of parameters. Such an enhancement of stability and ability to control the characteristics of the combustion wave propagation can be very attractive for the combustion synthesis of new layered materials, similarly to the chemical furnace technology proposed earlier.

Stability of fronts in the diffusive Rosenzweig–MacArthur model

AbstractWe consider a diffusive Rosenzweig–MacArthur predator–prey model in the situation when the prey diffuses at a rate much smaller than that of the predator. In a certain parameter regime, the existence of fronts in the system is known: the underlying dynamical system in a singular limit is reduced to a scalar Fisher–KPP (Kolmogorov–Petrovski–Piskunov) equation and the fronts supported by the full system are small perturbations of the Fisher–KPP fronts. The existence proof is based on the application of the Geometric Singular Perturbation Theory with respect to two small parameters. This paper is focused on the stability of the fronts. We show that, for some parameter regime, the fronts are spectrally and asymptotically stable using energy estimates, exponential dichotomies, the Evans function calculation, and a technique that involves constructing unstable augmented bundles. The energy estimates provide bounds on the unstable spectrum which depend on the small parameters of the system; the bounds are inversely proportional to these parameters. We further improve these estimates by showing that the eigenvalue problem is a small perturbation of some limiting (as the modulus of the eigenvalue parameter goes to infinity) system and that the limiting system has exponential dichotomies. Persistence of the exponential dichotomies then leads to bounds uniform in the small parameters. The main novelty of this approach is related to the fact that the limit of the eigenvalue problem is not autonomous. We then use the concept of the unstable augmented bundles and by treating these as multiscale topological structures with respect to the same two small parameters consequently as in the existence proof, we show that the stability of the fronts is also governed by the scalar Fisher–KPP equation. Furthermore, we perform numerical computations of the Evans function to explicitly identify regions in the parameter space where the fronts are spectrally stable.

Bifurcations and Stability of Phase Transition Fronts in Geothermal Reservoirs

Bifurcations and Stability of Phase Transition Fronts in Geothermal Reservoirs

Novel THAI well arrangements for improving heavy oil recovery rate in comparison to that achievable in the conventional THAI in situ combustion technology

The toe-to-heel air injection (THAI) method is an environmentally friendly process for in situ upgrading of heavy oils and bitumen via in situ combustion (ISC). Unlike the conventional ISC that uses a vertical producer, the THAI process uses a horizontal producer (HP) well to produce the upgraded oil to the surface. Recent field data has shown that the THAI process is a relatively low-oil-production-rate technology. These considerations call for innovative solutions so that the oil production rate is improved, whilst propagating a stable, efficient, and safe combustion front. Consequently, this work has provided those solutions. Through numerical reservoir simulations, using CMG STARS, five completely new THAI well configurations, which have been labeled A01, A02, A03, A04, and A05, have been developed and studied, and their performances are compared against that of the conventional THAI process which has wells arranged in a classic SLD pattern (i.e. the best-performing conventional THAI process) and against each other. The THAI arrangements A02-A04, however, assume a horizontal air injection well, which currently is not used in field practice but may be developed in the future. In field practice, THAI is applied in a line drive configuration starting up-dip and going down on the structure whilst taking advantage of the contribution provided by the drainage due to gravity; the expansion is made one way only (by drilling new patterns in one direction only). For this reason, the classic SLD pattern refers to the case where the dip of the reservoir is significant (>2–3°). However, when the dip of the reservoir is not significant (“flat” reservoirs) there is a possibility to expand the process in both opposing directions. This is the case dealt with in this work. All configurations A01-A05 assume expansion of the THAI commercial operation in both directions. Selection criteria have been developed and used to determine the two best performing processes. For example, in terms of long-term stability, safety, and efficiency of the combustion process, a process named model A01 is the best, as it achieved 99.8% oxygen utilisation when compared with any other model. It also achieves oil recovery, due to two years of combustion only, of 30.78% OOIP, which is greater than that in the base case model. Overall, based on the weighted selection criteria, which are developed from the deepest analyses of the quantitative 1-dimensional time-dependent parameters and from thorough analyses of the qualitative 2-dimensional profiles of temperature, the combustion zone in the form of oxygen mole fraction, and the oil-flow dynamics inside the reservoir in the form of oil saturation, then model A01 is the best and is followed by model A03. The overall performance of each of these two novel methods outweighs that of the conventional THAI process. However, model A03 uses a horizontal well for injection, which is not current field practice. Therefore, future developmental work should concentrate on the novel method A01 for upgrading and recovery of heavy oils and bitumen, especially since this is low-carbon, efficient, wastewater-free, and provides upgrading inside the reservoir and hence it has a low surface footprint.

Front stability of infinitely steep travelling waves in population biology

Reaction–diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many reaction–diffusion models of biological invasion are extensions of the well–known Fisher–Kolmogorov–Petrovskii–Piskunov model that describes the spatiotemporal evolution of a 1D population density, u(x,t) , as a result of linear diffusion with flux J=−∂u/∂x , and logistic growth source term, S=u(1−u) . In 2020 Fadai introduced a new reaction–diffusion model of biological invasion with a nonlinear degenerate diffusive flux, J=−u∂u/∂x , and the model was formulated as a moving boundary problem on 0<x<L(t) , with u(L(t),t)=0 and dL(t)/dt=−κu∂u/∂x at x=L(t) (Fadai and Simpson 2020 J. Phys. A: Math. Theor. 53 095601). Fadai’s model leads to travelling wave solutions with infinitely steep, well–defined fronts at the moving boundary, and the model has the mathematical advantage of being analytically tractable in certain parameter limits. In this work we consider the stability of the travelling wave solutions presented by Fadai. We provide general insight by first presenting two key extensions of Fadai’s model by considering: (i) generalised nonlinear degenerate diffusion with flux J=−um∂u/∂x for some constant m > 0; and, (ii) solutions describing both biological invasion with dL(t)/dt>0 , and biological recession with dL(t)/dt<0 . After establishing the existence of travelling wave solutions for these two extensions, our main contribution is to consider stability of the travelling wave solutions by introducing a lateral perturbation of the travelling wavefront. Full 2D time–dependent level–set numerical solutions indicate that invasive travelling waves are stable to small amplitude lateral perturbations, whereas receding travelling waves are unstable. These preliminary numerical observations are corroborated through a linear stability analysis that gives more formal insight into short time growth/decay of wavefront perturbation amplitude. Julia–based software, including level–set algorithms, is available on Github to replicate all results in this study.

Biopolymer-enhanced delivery of reactive sulfide reagents for in-situ mercury remediation of heterogeneous contaminated soils

Mercury pollution from natural and anthropogenic sources demands effective remediation. This study focuses on optimizing a chemical stabilization approach using sulfur-containing compounds to create stable mercury sulfide (HgS) and immobilize elemental mercury in polluted soils. We propose using xanthan gum biopolymer to enhance the in-situ delivery of sulfide microparticles, overcoming soil heterogeneities due to its non-Newtonian behavior. Stability tests indicated that increased biopolymer concentration enhances particle stability due to the viscous and shear-thinning behavior of the polymer solutions. Various combinations (12 solutions) of xanthan polymer, pyrite microparticles, and sulfide-containing reagents were tested in batch experiments. Pyrite microparticles slightly reduced the xanthan solution's viscosity while retaining its non-Newtonian character. All solutions effectively transformed liquid mercury droplets into cinnabar, demonstrating successful mercury stabilization. Notably, solutions containing PIAX and SIPX, xanthate organosulfur compounds, significantly reduced the dissolved concentration of elemental mercury. Column experiments demonstrated xanthan gum's superior performance for in-situ injection of pyrite microparticles and sulfide mixtures into the soil compared to conventional water injection. At a polymer concentration of 4 g/L, a stable displacement front and an 88 % recovery of the initially injected particle-suspension density were achieved. The combined effects of xanthate's floating behavior and xanthan gum's shear-thinning nature substantially enhanced the delivery of pyrite microparticles in porous media for soil mercury remediation. This combination reduced the aqueous elemental mercury concentration in artificially polluted sand by up to 97 %, particularly with the xanthate organosulfur compound, PIAX. Xanthate has a higher potential to react with elemental mercury to form cinnabar compared to sodium thiosulfate. Additionally, the pyrite microparticles, rendered hydrophobic in xanthate solutions, integrated into the mercury droplets, forming a black paste. This study introduces a promising approach for efficient elemental mercury stabilization in contaminated soils by integrating biopolymers, reactive soluble compounds, and pyrite microparticles for sustainable decontamination.