Computational investigation for endocytosis of CoVID-19 virus SARS-CoV-2 in cell membrane

CoVID-19 virus SARS-CoV-2 follows the endocytosis process to enter inside a cell to infect it. It is important to study the endocytosis of SARS-CoV-2 in cell membrane to prevent the pandemic of CoVID-19. In this paper we develop a finite element based computational model for endocytosis of SARS-CoV-2 in cell membrane and determine curvature generation on it during the process. The virus SARS-CoV-2 is modeled as a rigid spherical particle and cell membrane as an anisotropic elastic material, while its fluidic nature due to lipid exchange with infinite reservoir is preserved using suitable conditions. With the help of a contact pair created between the virus particle and cell membrane, endocytosis process is computationally studied and the curvature of membrane is evaluated as the time progresses during the endocytosis process. At the tip of the virus particle and half-radius distance from it, the membrane follows the curvature of virus very quickly. However, it takes more time for the membrane point located at a distance equal to the radius of the virus particle. This is compensated by the cytoplasmic peripheral proteins binding onto the inside surface of the cell membrane. The role of cytoplasmic peripheral BAR proteins is investigated by using a linear curvature-coupling model with protein concentrations. It is observed that F-BAR protein is more sensitive to the curvature of virus particle in comparison to the other BAR proteins. The sensitiveness deteriorates as the curvature is increased.

Analytical Solution of Unsteady-state Forchheimer Flow Problem in an Infinite Reservoir: The Boltzmann Transform Approach

For several decades, attempts had been made by several authors to develop models suitable for predicting the effects of Forchheimer flow on pressure transient in porous media. However, due to the complexity of the problem, they employed numerical and/or semi-analytical approach, which greatly affected the accuracy and range of applicability of their results. Therefore, in order to increase accuracy and range of applicability, a purely analytical approach to solving this problem is introduced and applied. Therefore, the objective of this paper is to develop a mathematical model suitable for quantifying the effects of turbulence on pressure transient in porous media by employing a purely analytical approach. The partial differential equation (PDE) that governs the unsteady-state flow in porous media under turbulent condition is obtained by combining the Forchheimer equation with the continuity equation and equations of state. The obtained partial differential equation (PDE) is then presented in dimensionless form (by defining appropriate dimensionless variables) in order to enhance more generalization in application and the method of Boltzmann Transform is employed to obtain an exact analytical solution of the dimensionless equation. Finally, the logarithms approximation (for larger times) of the analytical solution is derived. Moreover, after a rigorous mathematical modeling and analysis, a novel mathematical relationship between dimensionless time, dimensionless pressure, and dimensionless radius was obtained for an infinite reservoir dominated by turbulent flow. It was observed that this mathematical relationship bears some similarities with that of unsteady-state flow under laminar conditions. Their logarithm approximations also share some similarities. In addition, the results obtained show the efficiency and accuracy of the Boltzmann Transform approach in solving this kind of complex problem. Doi: 10.28991/HEF-2021-02-03-04 Full Text: PDF

Numerical Modelling of Radiogenic Ingrowth and Diffusion of Pb in Apatite Inclusions with Variable Shape and U-Th Zonation

The fundamental premise of apatite U-Th-Pb thermochronology is that radiogenic Pb is redistributed by volume diffusion. In practice, it is often additionally assumed that crystals (1) lose radiogenic Pb to an infinite reservoir, (2) have a simple geometry and (3) are chemically homogeneous. Here we explore the significance of the latter three assumptions by numerical modelling of Pb radiogenic ingrowth and diffusion in apatite inclusions within other minerals. Our results indicate that the host minerals are likely to hamper diffusive Pb loss from the apatite inclusions by limiting the Pb flux across their boundaries, and thus the thermal histories that are reconstructed assuming a fully open boundary may be significantly inaccurate, precluding a meaningful interpretation. We also find that when apatite boundaries are flux-limited, heterogeneities in U and Th concertation within apatite have subordinate effect on bulk-grain U-Th-Pb dates and can cause intra-grain U-Th-Pb dates to increase towards the boundaries. Finally, we show that it is important to correctly account for crystal geometry when modelling intra-grain U-Th-Pb dates. We suggest that the effect of surrounding minerals on diffusive Pb loss from apatite (and loss of other radiogenic isotopes from other minerals) should be examined more closely in future research.

Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative

The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system; where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type; the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdiffusive phenomena. Synthetic results highlight the effect of anomalous flows throughout the entire transient behavior considering a significant permeability in the matrix and it is contrasted with the effect of an almost negligible matrix permeability. The model is solved analytically in the Laplace space, incorporating the Tartaglia–Cardano equations.

Using Well Interference CRM-Models to Estimate Filtration-Capacitive Properties of the Layer According to Development Data

В работе предложены две CRM-модели, описывающие интерференцию скважин. Модели получены путем комбинации уравнения материального баланса и уравнения притока. В первой модели рассматривается общий для всех скважин поровый объем пласта. Во второй модели все скважины имеют индивидуальные поровые объемы, между которыми происходят перетоки. На синтетических примерах показано, что для бесконечного пласта можно применять первую модель, а для ограниченного пласта лучшие результаты дает вторая модель. The article dwells upon two CRM-models describing well interference. The models are obtained by means of combination of material balance and flow equation. The first model describes reservoir space, which is common for all wells. In the second model all wells have individual reservoir space with cross-border flows. Synthetic examples gives evidence, that the first model is more suitable for infinite reservoir, and the second model is more suitable for finite reservoir.

Applicability of heat-exchanger theory to estimate heat losses to surrounding formations in a thermal flood

Heat losses to cap and base rocks undermine the performance of a thermal flood. As a contribution to this subject, this paper investigates the applicability of the principles of heat exchanger to characterise heat losses between a petroleum reservoir and the adjacent geologic systems. The reservoir-boundary interface is conceptualised as a conductive wall through which the reservoir and adjacent formations exchange heat, but not mass. For a conduction-dominated process, the heat-transport equations are formulated and solved for both adiabatic and non-adiabatic conditions. Simulations performed on a field-scale example show that the rate of heating a petroleum reservoir is sensitive to the type of fluids saturating the adjoining geologic systems, as well as the characteristics of the cap and base rocks of the subject reservoir. Adiabatic and semi-infinite reservoir assumptions are found to be poor approximations for the examples presented. Validation of the proposed model against an existing model was satisfactory; however, remaining differences in performances are rationalised. Besides demonstrating the applicability of heat-exchanger theory to describe thermal losses in petroleum reservoirs, a novelty of this work is that it explicitly accounts for the effects of the reservoir-overburden and reservoir-underburden interfaces, as well as the characteristics of the fluid in the adjacent strata on reservoir heating. These and other findings should aid the design and management of thermal floods.