In this paper, we present a numerical study of the effect of the bulk sorbent particle packing on the break-through time. In our experiments, we fix the physical and chemical properties of the sorbent particles but vary the packing density (macroporosity) and the CO2 volume fraction at the inlet. After that, the gas flow through the reactor is simulated, and CO2 volume fraction as a function of time at the outlet is measured. We show that, in the case of high macroporosity, the recorded CO2 concentration strongly depends on the macroporosity. On the contrary, if the macroporosity is low, we observe almost no difference in the break-through curves for the models with macroporosity less than 45%.

The paper presents an approach for reconstructing the properties of two-dimensional viscoelastic medium with defined geometry using the simulated annealing algorithm. The inverse problem solution requires a lot of computational resources because the direct seismic modeling is performed at each iteration. The staggered grid finite-difference scheme is implemented using CUDA technology to speed up the solution of the direct problem by parallelization. The choice of the simulated annealing method for solving inverse problem is due to the method's ability to avoid local minima of the target functional. However, the simulated annealing method needs a good coverage of the model space by realizations of random probing vectors. It leads to enormous computation time in the case of a four-layer medium with elliptical inclusion in the third layer, which has 37 parameters. Therefore, the sequential reconstruction of model parameters, where the simulated annealing algorithm searches for the parameters in 1 or 2-D subspace, is introduced. Nevertheless, the attenuation properties of medium were not reconstructed by simulated annealing. For their study, the deep convolutional neural network is used.

Yttrium oxide has promising characteristics such as chemical stability and a porous structure for various high-temperature applications in catalysis and chemical engineering. The prediction of the structural properties of Y2O3 presents a computational challenge. In this study, we implemented a phase-field approach to obtain a precise description of the Y2O3 sintering process over a wide range of temperatures. In the phase-field method, the microstructure is described by a system of continuous variables that model Y2O3 crystallites, where the microstructure interfaces have a finite width over which the material transfers. The experiments on stepwise sintering process were carried out and the obtained data on the textural and morphological properties of Y2O3 particles were used to calibrate and validate the numerical model. The evolution of the specific surface area and pore volume for the pores ranging from 3 to 70 nm and the rate of growth of Y2O3 crystallites during sintering of Y2O3 grains were effectively predicted. The obtained model indicates that a stepwise increase in the calcination temperature from 600 to 900 and 1200 degrees C decreases the surface area of the materials from 54 to 15 and 5 m(2)/g, respectively. This study can be used to predict the textural properties of yttrium oxide during the sintering of porous ceramics and for the exploitation of catalyst systems.

Прохоров 1 *, Я. В. Базайкин 2 , В. В. Лисица 2 Применение метода фазового поля для оценки изменения геометрических свойств пористых сред в процессе высокотемпературных воздействий 1 Институт математики СО РАН, г.Новосибирск, Российская Федерация 2 Институт нефтегазовой геологии и геофизики СО РАН, г.Новосибирск, Российская Федерация

The sintering process is widely used in modern industry because it allows for obtaining materials with predefined properties. Chemical or physical techniques can measure these properties. Besides the cost of such methods, it is worth noting that some techniques destroy samples, which causes difficulties in measuring the parameters’ evolution. Computer simulation of the sintering process allows for overcoming these difficulties. The sintering models based on the system of Cahn-Hilliard and Allen-Cahn equations require optimization if the number of grains is large. However, optimizations affect the solution; thus, a detailed quality assessment is required. The article presents such a study for our optimization: the Allen-Cahn equations are solved in small subdomains of the whole computational domain, which change over time. We provide comparative tests between solutions obtained by our algorithm and solutions obtained by solving the system in the whole domain. Besides common approaches, we use powerful tools of topology: Hausdorff distance and Betti numbers. The choice of the algorithm parameters is justified by obtained accuracy and efficiency.

The sintering simulation is an actual problem in computational mathematics since computer simulation allows performing much more experiments than can be performed using chemical or physical techniques, especially in the case of studying the material’s intrinsic structure. The most perspective approach for the sintering simulation is a phase-field method. Usually, this approach requires solving the system of the Cahn-Hilliard and Allen-Cahn equation. The main difficulty is that number of Allen-Cahn equations is equal to the number of different grains in the sample. It causes requirements in computational resources to increase not only with increasing the grid size but with increasing the number of grains in the sample; if finite differences are used for solving the system. The paper presents the sintering simulation algorithm, which tracks the individual grains. This feature allows solving each of the Allen-Cahn equations only in a small subdomain corresponding to the current grain. The algorithm is implemented using Graphic Processor Units.

В работе представлен алгоритм решения системы уравнений Аллена–Кана и Кана–Хиллиарда, которая описывает процесс спекания. Алгоритм не требует значительных по мощности вычислительных ресурсов и позволяет выполнить моделирование процесса спекания большого количества отдельных частиц на вычислительном узле с процессором Intel Xeon E5 2697 v3 и графическим ускорителем NVIDIA K40 за приемлемое время. Проведены эксперименты по моделированию спекания сорбентоподобных структур — упаковок сферических частиц, и на них показана эффективность алгоритма. In this work, we present an algorithm for solving the system of Allen–Cahn and Cahn–Hilliard equations, which describes the process of sintering. The algorithm does not require significant computational resources and makes possible the sintering simulating of a large number of grains using a computation node with an Intel Xeon E5 2697 v3 CPU and an NVIDIA K40 GPU in a reasonable time. Experiments were carried out to simulate the sintering of sorbent-like structures (packings of spherical particles), for which the efficiency of the algorithm was shown.

Computer simulation of the sintering process makes it possible to study the internal properties of the sample, the measurement of which by chemical or physical methods can be difficult and expensive. The interest in studying the properties of yttrium oxide is caused by the fact that it can be used to deactivate sorbents from calcium oxide, which are used to absorb carbon dioxide. The most promising approach to sintering modeling is the phase-field method. However, when using this method, with an increase in the number of grains in the sample, the requirements for computing resources significantly increase. Therefore, when studying the properties of large samples of yttrium oxide, a special approach to the implementation of the phase-field method is necessary. The paper describes an algorithm that allows tracking individual grains to reduce computational effort and shows the possibility of modeling the sintering of samples consisting of 8000 grains.

The paper presents a numerical algorithm for simulation of the reactive transport at the pore scale. The algorithm allows simulating pore space evolution, porosity, absolute permeability, and form factor changes due to core matrix dissolution or precipitation. We also, introduce the topological measure; the persistence diagrams of independent cycles in pore space to classify different dissolution scenarios. Using derived classification, we constructed the statistically reliable porosity-permeability relations for different dissolution scenarios.

We present an algorithm for the pore-scale simulation of the reactive transport in a 3D case. The algorithm is designed to facilitate the observation of pore space changes caused by chemical fluid-solid interaction. Additionally, the algorithm allows estimation of the main macroscopic properties evolution of the porous material, such as permeability, hydraulic tortuosity, and formation factor. Also, we develop an algorithm to compute the persistence diagrams for the independent cycles in the pore space, which quantitatively characterizes the changes in the pore space topology. Moreover, we speed up this algorithm by using the original digital image reduction approach. Applying the clustering technique to the persistence diagrams, we show that different matrix dissolution scenarios can be distinguished based on the persistence homology. These scenarios depend on the flow rate, reaction rate, and species concentration at the inlet. At the same time, the samples from the different clusters illustrate utterly different behavior of the cross-property (porosity-permeability) relations. This is extended version of our conference paper [1].

The paper presents an original algorithm for reducing three-dimensional digital images to improve the computing performance of persistence diagrams. These diagrams represent changes in pore space topology during essential or artificial changes in the structure of porous materials. The algorithm has linear complexity because during reduction, each voxel is checked not more than seven times. This check, as well as the removal of voxels, takes a constant number of operations. We illustrate that the algorithm's efficiency depends on the complexity of the original pore space and the size of filtration steps. The application of the reduction algorithm allows the computation of one-dimensional persistence Betti numbers for models of up to 5003 voxels by using a single computational node. Thus, it can be used for routine topological analysis and the topological optimization of porous materials.

The paper presents an original algorithm for reducing three-dimensional digital images to improve persistence diagrams computing performance. These diagrams represent topology changes in digital rocks pore space. The algorithm has linear complexity because removing the voxel is based on the structure of its neighborhood. We illustrate that the algorithm's efficiency depends heavily on the pore space's complexity and the size of the filtration steps.

The article describes the application of the digital image reduction algorithm to speed up the calculation of persistent diagrams that describe changes in the topology of the pore space of the rock matrix during the dissolution process. The dependence of the efficiency of the reduction algorithm on the properties of the rock sample and the value of the discrete time step is shown.

A new algorithm for the reduction of three-dimensional digital images is proposed to improve the performance of persistence diagrams computing. These diagrams represent changes in topology of the pore space in the rock matrix. The algorithm has a linear complexity, since the removal of the voxel is based on the structure of its neighborhood. It is shown that the efficiency of the algorithm depends heavily on the complexity of the pore space and the size of filtering steps.

In the current study, the volume-sintering model was implemented for the simulation of sorption/desorption and textural evolution of the set of CaO-based sorbents with broad differences in porous structure. The porous structure of the materials was modeled with the dense random packing of spheres using the Lubachevsky-Stillinger compression algorithm. The simulated packages were fitted to the parameters of the porous structure of real templated and non-templated CaO-based sorbents. The sintering of the packages during sorption/regeneration cycles was carried out based on the assumptions of the lattice diffusion mechanism and the sintering rate of CaCO3 being higher than that of CaO in the proposed model. The obtained model predicts well the dependence of textural changes and the recarbonation extent on the number of the sorption/regeneration cycles for the sorbents with different porosity and grain size.