Pore Scale Numerical Modelling of Geological Carbon Storage Through Mineral Trapping Using True Pore Geometries

Mineral trapping (MT)is the most secure method of sequestering carbon for geologically significant periods of time. The processes behind MT fundamentally occur at the pore scale, therefore understanding which factors control MT at this scale is crucial. We present a finite elements advection–diffusion–reaction numerical model which uses true pore geometry model domains generated from $$\upmu$$ μ CT imaging. Using this model, we investigate the impact of pore geometry features such as branching, tortuosity and throat radii on the distribution and occurrence of carbonate precipitation in different pore networks over 2000 year simulated periods. We find evidence that a greater tortuosity, greater degree of branching of a pore network and narrower pore throats are detrimental to MT and contribute to the risk of clogging and reduction of connected porosity. We suggest that a tortuosity of less than 2 is critical in promoting greater precipitation per unit volume and should be considered alongside porosity and permeability when assessing reservoirs for geological carbon storage (GCS). We also show that the dominant influence on precipitated mass is the Damköhler number, or reaction rate, rather than the availability of reactive minerals, suggesting that this should be the focus when engineering effective subsurface carbon storage reservoirs for long term security. Article Highlights The rate of reaction has a stronger influence on mineral precipitation than the amount of available reactant. In a fully connected pore network preferential flow pathways still form which results in uneven precipitate distribution. A pore network tortuosity of <2 is recommended to facilitate greater carbon mineralisation.

Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

Microstructure and Mechanical properties of transition zone in laser additive manufacturing of TC4/AlSi12 bimetal structure

Ti/Al bimetallic structure (BS) has a good development prospect and broader application potential in aerospace engineering. Considering the limitation that dissimilar welding is only applicable to the thin plate, it is necessary to explore a new manufacturing process for Ti/Al BS. In this study, a TC4/AlSi12 BS was prepared by laser additive manufacturing (LAM). TC4 zone, AlSi12 zone and transition zone were formed in the LAM process. Due to the sufficient diffusion reaction, the transition zone with a width of about 0.8mm was obtained. At the same time, a few micro-cracks were found in the transition zone. The microstructure and phase composition of the transition zone had been emphatically studied. Research results showed that the presence of Si element made the phase composition of the transition zone more complicated. The structure evolution from TC4 to AlSi12 was: α-Ti → Ti3Al → TiAl+(TiAl+Si) → Ti5Si3 → TiAl3+(α-Al+Si) → α-Al+ Si +TiAl3 +(α-Al+Si) → α-Al+Si+(α-Al+Si). The hardness distribution of BS was uneven, with the highest value reaching 524HV. The tensile strength of the TC4/AlSi12 BS was about 110Mpa, and the fracture location was located in the transition zone.

An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion

In this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary differential equation. The unknowns represent concentrations or densities that cannot be negative. Widely used approximations, such as difference schemes, can produce negative solutions because of truncation errors and can become unstable. We propose a new difference scheme that guarantees the positivity of the numerical solution for arbitrary mesh step sizes. It has explicit and fast performance even for nonlinear reaction terms that consist of sums of positive and negative functions. The numerical examples illustrate the simplicity and efficiency of the method. A numerical simulation of a model of cancer migration is also discussed.

Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations

Background: solute transport in highly heterogeneous media and even neutron diffusion in nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that solute concentration profiles exhibit anomalous non-Fickian growth rates and so-called “heavy tails”. Methods: a nonlinear-coupled 3D fractional hydro-mechanical model accounting for anomalous diffusion (FD) and advection–dispersion (FAD) for solute flux is described, accounting for a Riesz derivative treated through the Grünwald–Letnikow definition. Results: a long-tailed solute contaminant distribution is displayed due to the variation of flow velocity in both time and distance. Conclusions: a finite difference approximation is proposed to solve the problem in 1D domains, and subsequently, two scenarios are considered for numerical computations.