A mathematical study on the viability of the geochemical flow for an enhanced oil recovery: A simplified model

In the oil recovery process, it is well-known that adding some types of chemical species (for instance water-soluble polymer or solvents) into the water injected into porous media can enhance the oil recovery factor for the water flood recovery method. However, the use of such chemical species in the injection process increases the overall cost; not only in regard to the cost of chemical species, but also by increasing the time to reach water breakthrough. To study this behavior, we use a system of partial differential equations that models the flow of water, oil and chemical species (soluble in water or oil) into one-directional porous media filled with oil. For the case that the chemical species is soluble only in water and for suitable initial conditions (of the Riemann type), we prove that the system’s solution projects to a single scalar equation. We use the solution of the scalar equation to define a functional called the profit functional, which allows study of the economic viability of chemical injection. This study presents a simple way to deal with this class of problems in which we dynamically obtain regions to optimize the functional solution that we defined.     

On the conditional increments of degradation processes

Recently, Wang and Xu (2010) developed an efficient EM algorithm for the semiparametric inference of the inverse Gaussian (IG) process. In the presence of missing degradation data, the algorithm needs to compute the mean of the IG increment during some time interval [_s1,_s2]$[s_1,s_2]$ conditional on that the process is tied down on two points before _s1$s_1$ and after _s2$s_2$, respectively. This study derives the conditional distribution of this increment and gives the expectation of the increment and of the reciprocal of the increment. The results simplify the implementation of the EM algorithm for the IG process. In a similar vein, we further derive distributions for the conditional increments of the Wiener process and the Gamma process, respectively.     

Method of thermomechanical characteristics as a means of studying crosslinking and degradation processes in multicomponent polymer systems

A method of obtaining and interpreting thermomechanical curves has been developed to facilitate the study of crosslinking and degradation processes in multicomponent polymer systems. The method is highly sensitive and makes it possible to study on small specimens a variety of structural changes governed by the nature of the polymer, by the macrostructure of the test pieces, by the mixture composition, and by the action of various external factors. It is also shown that the thermomechanical characteristics can conveniently be used as a criterion for evaluating working properties (e.g., heat resistance, etc.).Mekhanika Polimerov. Vol. 3, No. 3, pp. 387–391, 1967     

三维强化采油渗流耦合系统隐式迎风分数步差分方法的收敛性分析

对强化(化学)采油数值模拟中的渗流耦合系统问题,本文提出隐式迎风分数步差分格式,利用变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到最佳阶l2模误差估计.该方法已成功应用到强化采油数值模拟的生产实践中,并且得到了很好的数值模拟效果.     

Minimization of grid orientation effects in simulation of oil recovery processes through use of an unsplit higher order scheme

We present an unsplit second-order finite difference algorithm for hyperbolic conservation laws in several variables. Although the method can be directly implemented for general hyperbolic systems, we focus in this article on reducing grid orientation effects in porous media flow. In particular, we consider miscible and immiscible displacement processes. Our main concern is to develop a scheme that can easily be implemented into existing standard finite-difference-based reservoir simulators as an option to be used if grid orientation effects occur. The principle of the scheme is to build a higher order scheme to reduce numerical dispersion and that does not split the spatial operator to reduce the effect of the grid orientation. Numerical results are presented, which show that the method presented here reduces the effect of the numerical dispersion to a level that minimizes the grid orientation effects in a computationally efficient manner. © 1996 John Wiley & Sons, Inc.     

Nonparametric evaluation of the first passage time of degradation processes

This paper discusses a nonparametric method to approximate the first passage time (FPT) distribution of the degradation processes incorporating random effects if the process type is unknown. The FPT of a degradation process is unnecessarily observed since its density function can be approximated by inverting the empirical Laplace transform using the empirical saddlepoint method. The empirical Laplace transform is composed of the measured increments of the degradation processes. To evaluate the performance of the proposed method, the approximated FPT is compared with the theoretical FPT assuming a true underlying process. The nonparametric method discussed in this paper is shown to possess the comparatively small relative errors in the simulation study and performs well to capture the heterogeneity in the practical data analysis. To justify the fitting results, the goodness‐of‐fit tests including Kolmogorov‐Smirnov test and Cramér‐von Mises test are conducted, and subsequently, a bootstrap confidence interval is constructed in terms of the 90th percentile of the FPT distribution.     

Simulation of the processes of deformation of orthotropic viscoelastic polymer materials

The similarity and simulation of the processes of deformation of orthotropic linear heredity materials are investigated by the similarity method. Systems of determining parameters are given. The possibility of modeling in particular cases of different and identical materials is demonstrated. Modeling of the buckling process is considered as an example.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp 603–606, July–August 1968.     

Influence of temperature and humidity on the creep of polymer materials

Conclusions By analyzing the results of the original creep tests under shear and tensile conditions subject to various temperatures and humidities, and also analyzing some control experiments involving simultaneous shear and tensile strain, we have shown that the displacement function of the relaxation spectrum expressing the maintenance of the temperature-humidity-time analogy is independent of the form of the stressed state in the range of linear viscoelasticity for a Poisson coefficient close to 0.5.For Communication 2 see [2].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 627–632, July–August, 1976.     

Simulation of crystallization processes in viscoelastic polymer melt flows

A simplified model for plate extrusion is presented. Calculations for the exponential form of the Phan-Thien Tannner fluid combined with a nonisothermal crystallization model are performed. A Study for the Deborah- and Péclet-number is carried out to investigate if stress is transported in regions of crystallization. It is shown that for the presented model, this is only the case for regions close to walls. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of elevated hydrostatic pressure on the diffusion constants of polymer materials

The authors give experimental results showing how the diffusion constants of various polymer materials depend on the (elevated) hydrostatic pressure.A. A. Zhdanov Leningrad State University. Translated from Mekhanika Polimerov, No. 2, pp. 344–346, March–April, 1974.     

A discrete model for the recovery of oil from a reservoir

We simulate oil recovery by means of a molecular approach: we consider the solid and liquid materials to be composed of a finite number of particles, which are approximants for molecules. Porous flow is studied qualitatively under the assumption that particles of rock, oil, and the flooding flow interact with each other locally by means of a compensating Lennard-Jones potential and are also under the influence of gravity. Extensive computations are described and discussed in which initial data and parameters are varied. A comparison is made with actual physical experiments.     

Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes

It is still a challenge to study the degradation mechanisms of complex systems with multiple performance characteristics. This paper develops a two-stage stochastic degradation model. The degeneration processes of two correlated performance characteristics are described by a correlated bivariate Wiener process in the first stage, in which neither of the degradation levels of performance characteristics reaches their thresholds. When one of the degradation levels of performance characteristics reaches its threshold, the system operates defectively in the second stage, and the system degradation process is described by the other performance characteristic which is modeled by a univariate Wiener process. The system fails completely when both the degradation levels of performance characteristics reach their thresholds. Explicit expressions of the system reliability and availabilities are given based on different inspection and maintenance policies. Simulation is also presented, and it shows that the analytical results and the simulation results are in good agreement. Finally, a detailed case study of the rail track geometry degradation is given to demonstrate the results obtained in the paper.     

Instability in Runge-Kutta schemes for simulation of oil recovery

Runge-Kutta timestep schemes have been used recently in an attempt to increase the maximum stable timestep for IMPES (implicit pressure, explicit saturation) simulation of oil recovery. It has been claimed that anm-stage method will increase the real stability boundary bym ². A rigorous stability analysis for a Buckley-Leverett problem shows that this claim is false, and that previous stabilized IMPES schemes are never more efficient than ordinary IMPES. Test calculations support these results.     

Modelling and Simulation of solidification processes in polymer melt flows

This work deals with the modelling and simulation of solidification processes in polymer melt flows. Two models describing the latent heat and the rheological behaviour were implemented in a finite volume code. The models are empirical and their parameters are identified using experimental results obtained from investigations with a rotational rheometer and a differential scanning calorimetry. First results of the simulation of a solidifying channel flow are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

FE-Analysis of concentration dependent healing processes in a polymer matrix

In this contribution, a macroscopic four-phase model, based on the Theory of Porous Media, is presented to simulate healing processes in a polymer matrix which depend on the amount (concentration) of catalysts. Therefore, the healing process is described by the phase transition from liquid like healing agents to solid like healed material. This phase transition is a function depending on the concentration. To show the applicability of the developed model, a numerical example will be presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-isothermal,compressible gas flow for the simulation of an enhanced gas recovery application

In this work, we present a framework for numerical modeling of CO₂ injection into porous media for enhanced gas recovery (EGR) from depleted reservoirs. Physically, we have to deal with non-isothermal, compressible gas flows resulting in a system of coupled non-linear PDEs. We describe the mathematical framework for the underlying balance equations as well as the equations of state for mixing gases. We use an object-oriented finite element method implemented in C++. The numerical model has been tested against an analytical solution for a simplified problem and then applied to CO₂ injection into a real reservoir. Numerical modeling allows to investigate physical phenomena and to predict reservoir pressures as well as temperatures depending on injection scenarios and is therefore a useful tool for applied numerical analysis.