COMPARISON OF VARIOUS FRACTIONAL BASIS FUNCTIONS FOR SOLVING FRACTIONAL-ORDER LOGISTIC POPULATION MODEL

Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value problem arising in population growth models. The method reduces the given problem to a set of algebraic equations consist of polynomial coefficients. Our main goal is to present a comparative study of these polynomials and to asses their performances and accuracies applied to the logistic population equation. Numerical applications are given to demonstrate the validity and applicability of the method. Comparisons are also made between the present method based on different basis functions and other existing approximation algorithms

Supercritical CO2 Foam Enhanced Oil Recovery: From Mechanistic Model Fit to Lab Experiments to Field-Scale Evaluation

This study investigates how a mechanistic foam modeling approach based on bubble population balance is applied to a series of laboratory experimental data of a supercritical CO2 foam in reservoir conditions to extract model parameters (topic 1). The model with model parameters determined from the fit is then used to estimate how far fine-textured strong foam can propagate into the reservoir, before turning into coarse-textured weak foam and before being segregated by gravity (topic 2). With the help of mechanistic model, a possible range of gas mobility for supercritical CO2 foam is calculated and the resulting gas-phase mobility reduction factor (MRF) are applied to the field-scale EOR reservoir simulations (topic 3). A mechanistic foam model that honors three different foam states and two steady-state strong-foam flow regimes is used to fit coreflood experimental data from Yin (2007). The results show why supercritical CO2 foams are fundamentally different compared to other gaseous foams. The role of mobilization pressure gradient is shown to be the key to this difference – the pressure gradient required for supercritical CO2 foam is much lower, and thus the attainment of strong foam in the reservoir is easier. This study shows how far strong foams injected into the injection well can propagate at different injection foam qualities and velocities, which is one of the most important questions in actual field applications. Two main mechanisms that limit field foam propagation, such as “conversion from strong foam to weak foam” and “gravity segregation”, are examined. The results show that foam propagation distance increases with increasing injection pressure or rate and increases with decreasing foam quality down to a certain threshold foam quality below which the distance is not sensitive to foam quality any longer. CMG STARS simulations for a sector with an inverted 5-spot pattern are performed to evaluate how oil recovery changes at different injection foam qualities and velocities. The pre-determined values of gas mobility required for the simulation are guided by the mechanistic model. The use of sweep-efficiency contour plots is shown to be a convenient graphical method to determine the optimum injection foam quality that changes at different injection rates

A hybrid approximation scheme for 1-D singularly perturbed parabolic convection-diffusion problems

Our study is concerned with a hybrid spectral collocation approach to solving singularly perturbed 1-D parabolic convection-diffusion problems. In this approach, discretization in time is carried out with the help of Taylor series expansions before the spectral based on novel special polynomials is applied to the spatial operator in the time step. A detailed error analysis of the presented technique is conducted with regard to the space variable. The advantages of this attempt are presented through comparison of our results in the model problems obtained by this technique and other existing schemes

A Predictor-Corrector Scheme for Conservation Equations with Discontinuous Coefficients

In this paper we propose an explicit predictor-corrector finite difference scheme to numerically solve one-dimensional conservation laws with discontinuous flux function appearing in various physical model problems, such as traffic flow and two-phase flow in porous media. The proposed method is based on the second-order MacCormack finite difference scheme and the solution is obtained by correcting first-order schemes. It is shown that the order of convergence is quadratic in the grid spacing for uniform grids when applied to problems with discontinuity. To illustrate some properties of the proposed scheme, numerical results applied to linear as well as non-linear problems are presented

Energy efficiency in virtual machines allocation for cloud data centers with lottery algorithm

Energy usage of data centers is a challenging and complex issue because computing applications and data are growing so quickly that increasingly larger servers and disks are needed to process them fast enough within the required time period. In the past few years, many approaches to virtual machine placement have been proposed. This study proposes a new approach for virtual machine allocation to physical hosts. Either minimizes the physical hosts and avoids the SLA violation. The proposed method in comparison to the other algorithms achieves better results