Francisco Marcondes

Investigation of Several Interpolation Functions for Unstructured Meshes in Conjunction with Compositional Reservoir Simulation

One of the key parameters in numerical simulation of fluid flow problems is the interpolation function used for adjusting the numerical value from the position where it is evaluated to the interface of the control volumes; for instance, if the finite-volume method is employed. In this article, we present an investigation of several interpolation functions in conjunction with the element based finite-volume method (EbFVM) using unstructured triangular meshes. We investigate the mass weighted upwind (MWU) and a modified version of this method, the upwind scheme, a streamline based upwind scheme, and a limited second order upwind scheme. These interpolation functions are implemented in a compositional simulator using vertex cell unstructured grids. The accuracy of these interpolation functions are evaluated for several case studies. For some of them, we also compare the results with the available analytical solutions.

The Influence of Baffles on the Natural Convection in Trapezoidal Cavities

This article presents an investigation into natural convection in trapezoidal cavities. It examines a cavity whose floor and upper inclined walls are both adiabatic, while the vertical walls are isothermal. For these isothermal walls, we consider two thermal boundary conditions. Under the first condition, the short wall on the left side is heated as the tall one on the right side is cooled. The second condition is the reverse of the first—the short wall is cooled as the tall one is heated. Considering laminar conditions and a two-dimensional system, steady-state computations are carried out to assess the effects of one and two baffles, the baffles height (H b ), Rayleigh number, 103 ≤ Ra ≤ 106, and three Prandtl number values. To demonstrate the various effects, the results from several designed case studies are shown in terms of isotherms, streamlines, and local and average Nusselt numbers in order. Predictions reveal that the second baffle decreases the cavitys fluid flow and heat transfer. As the height of the baffle rises, the heat transfer drops drastically. Also, two baffles produce more pronounced thermal stratification than only one.

Numerical analysis of natural convection in parallel, convergent, and divergent open‐ended channels

Purpose – To investigate the natural convection in open‐ended parallel, convergent, and divergent channels using a fully elliptic procedure without extending the domain outside the channel for the application of the boundary conditions at the inlet and outlet of the channels.Design/methodology/approach – The model is two‐dimensional and fully elliptic in x and y directions, and the equations are solved only inside the channel by the finite volume method using a co‐located arrangement with a segregated procedure and boundary fitted coordinates. The pressure‐velocity coupling is solved by the PRIME algorithm.Findings – The results are shown in terms of velocity vectors, streamlines, isotherms, and the local and the average Nusselt number for all fluids and configurations investigated. For high values of the Rayleigh number, a recirculation region in the outlet of all investigated configurations and Prandtl numbers was observed. Based on the results, a single correlation is proposed to evaluate the average N...

A 3D Total Variation Diminishing Scheme for Compositional Reservoir Simulation Using the Element-Based Finite-Volume Method

Interpolation function is a key parameter for numerical simulation using finite-difference, finite-element, and finite-volume methods, especially when the advective terms of the conservation equations are considered. Due to the flow orientation, a first-order interpolation scheme such as upwind introduces a considerable degree of numerical diffusion in the numerical solution. In this work, we present a second-order total variation diminishing scheme in conjunction with 3D compositional reservoir simulation using the element-based finite-volume method (EbFVM). The results of several case studies using the hexahedron element are shown in terms of oil, water, and gas production, as well as saturation field.