Numerical Simulation of Barite Sag in Pipe and Annular Flow

With the ever increasing global energy demand and diminishing petroleum reserves, current advances in drilling technology have resulted in numerous directional wells being drilled as operators strive to offset the ever-rising operating costs. In as much as deviated-well drilling allows drillers to exploit reservoir potential by penetrating the pay zone in a horizontal, rather than vertical, fashion, it also presents conditions under which the weighting agents can settle out of suspension. The present work is categorized into two parts. In the first part, governing equations were built inside a two-dimensional horizontal pipe geometry and the finite element method utilized to solve the equation-sets. In the second part, governing equations were built inside a three-dimensional horizontal annular geometry and the finite volume method utilized to solve the equation-sets. The results of the first part of the simulation are the solid concentration, mixture viscosity, and a prediction of the barite bed characteristics. For the second part, simulation results show that the highest occurrence of barite sag is at low annular velocities, nonrotating drill pipe, and eccentric drill pipe. The CFD approach in this study can be utilized as a research study tool in understanding and managing the barite sag problem.

Numerical Analysis on Flow Behavior of Molten Iron and Slag in Main Trough of Blast Furnace during Tapping Process

The three-dimensional model was developed according to number 4 of the main trough of blast furnace at China Steel Co. (CSC BF4). The k-ε equations and volume of fluid (VOF) were used for describing the turbulent flow at the impinging zone of trough, indicating fluids of liquid iron, molten slag, and air in the governing equation, respectively, in this paper. The pressure field and velocity profile were then obtained by the finite volume method (FVM) and the pressure implicit with splitting of operators (PISO), respectively, followed by calculating the wall shear stress through Newton’s law of viscosity for validation. Then, the operation conditions and the main trough geometry were numerically examined for the separation efficiency of iron from slag stream. As shown in the results, the molten iron losses associated with the slag can be reduced by increasing the height difference between the slag and iron ports, reducing the tapping rate, and increasing the height of the opening under the skimmer.

The Convergence of a Class of Parallel Newton-Type Iterative Methods

A general iterative process is proposed, from which a class of parallel Newton-type iterative methods can be derived. A unified convergence theorem for the general iterative process is established. The convergence of these Newton-type iterative methods is obtained from the unified convergence theorem. The results of efficiency analyses and numerical example are satisfactory.

Analysis of Tensegrity Structures with Redundancies, by Implementing a Comprehensive Equilibrium Equations Method with Force Densities

A general approach is presented to analyze tensegrity structures by examining their equilibrium. It belongs to the class of equilibrium equations methods with force densities. The redundancies are treated by employing Castigliano’s second theorem, which gives the additional required equations. The partial derivatives, which appear in the additional equations, are numerically replaced by statically acceptable internal forces which are applied on the structure. For both statically determinate and indeterminate tensegrity structures, the properties of the resulting linear system of equations give an indication about structural stability. This method requires a relatively small number of computations, it is direct (there is no iteration procedure and calculation of auxiliary parameters) and is characterized by its simplicity. It is tested on both 2D and 3D tensegrity structures. Results obtained with the method compare favorably with those obtained by the Dynamic Relaxation Method or the Adaptive Force Density Method.

Revisited Optimal Error Bounds for Interpolatory Integration Rules

We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor’s expansion. These bounds depend on the regularity of the integrand. The method of integration by parts “backwards” to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.

Analysis of Subgrid Stabilization Method for Stokes-Darcy Problems

A number of techniques, used as remedy to the instability of the Galerkin finite element formulation for Stokes like problems, are found in the literature. In this work we consider a coupled Stokes-Darcy problem, where in one part of the domain the fluid motion is described by Stokes equations and for the other part the fluid is in a porous medium and described by Darcy law and the conservation of mass. Such systems can be discretized by heterogeneous mixed finite elements in the two parts. A better method, from a computational point of view, consists in using a unified approach on both subdomains. Here, the coupled Stokes-Darcy problem is analyzed using equal-order velocity and pressure approximation combined with subgrid stabilization. We prove that the obtained finite element solution is stable and converges to the classical solution with optimal rates for both velocity and pressure.

Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

Lebesgue Constant Using Sinc Points

Lebesgue constant for Lagrange approximation at Sinc points will be examined. We introduce a new barycentric form for Lagrange approximation at Sinc points. Using Thiele’s algorithm we show that the Lebesgue constant grows logarithmically as the number of interpolation Sinc points increases. A comparison between the obtained upper bound of Lebesgue constant using Sinc points and other upper bounds for different set of points, like equidistant and Chebyshev points, is introduced.

A Finite Volume-Complete Flux Scheme for a Polluted Groundwater Site

We present a model of a polluted groundwater site. The model consists of a coupled system of advection-diffusion-reaction equations for the groundwater level and the concentration of the pollutant. We use the complete flux scheme for the space discretization in combination with the ϑ-method for time integration and we prove a new stability result for the scheme. Numerical results are computed for the Guarani Aquifer in South America and they show good agreement with results in literature.

Selection of an Interval for Variable Shape Parameter in Approximation by Radial Basis Functions

In radial basis function approximation, the shape parameter can be variable. The values of the variable shape parameter strategies are selected from an interval which is usually determined by trial and error. As yet there is not any algorithm for determining an appropriate interval, although there are some recipes for optimal values. In this paper, a novel algorithm for determining an interval is proposed. Different variable shape parameter strategies are examined. The results show that the determined interval significantly improved the accuracy and is suitable enough to count on in variable shape parameter strategies.