Accurate Pressure Gradient Research Articles

A fully Lagrangian mixed discrete least squares meshfree method for simulating the free surface flow problems

This paper presents a fully Lagrangian mixed discrete least squares meshfree (MDLSM) method for simulating the free surface problems. In the proposed method, the mass and momentum conservation equations are first discretized in time using the projection method. The resulting pressure Poisson equation is then re-written in the form of three first-order equations in terms of the pressure field and its first-order derivatives. The mixed discrete least squares meshless method is then used to solve this system of equations and simultaneously calculate the pressure field and its gradients. The advantage of the proposed Lagrangian MDLSM is twofold. First, the pressure gradients are directly computed and, therefore, they enjoy higher accuracy than those calculated in the conventional DLSM via a post-processing method. The more accurate pressure gradient will in turn lead to more accurate velocity field when used in the momentum equations. Second, the proposed Lagrangian MDLSM method can be more efficient than the corresponding original Lagrangian DLSM method, for the specific number of nodes, since the costly calculation of the shape function second derivatives required for solving the pressure Poison equation are avoided in each time step of the simulation. Several free surface problems are solved and the results are presented and compared to those of DLSM method. The results indicate the superior efficiency and accuracy of the proposed Lagrangian MDLSM method compared to those of the existing Lagrangian DLSM method in the literature.

A unit cell model for gas-liquid pseudo-slug flow in pipes

Pseudo-slug flow is a subset of intermittent flow which has not been properly understood and modeled. However, this flow pattern is widely encountered in oil and gas production and transportation, driving the needs for proper modeling efforts. A new pseudo-slug unit cell model is proposed in this paper. The proposed model modifies the existing slug unit cell model by accounting the continuous gas passage, slippage, and interfacial momentum exchange in the pseudo-slug body. Pseudo-slug characteristics (length, velocity, and body holdup) reported in literature are incorporated through ad-hoc closure relationships. These closures remain to be improved in the future. Overall, the proposed model produces more accurate pressure gradient and film holdup (HLF) predictions compared to two state-of-the-art models which generally treat pseudo-slug as slug flow (TUFFP Unified model and OLGAS 7.3.5®).

Adverse Hemodynamic Conditions Associated with Mechanical Heart Valve Leaflet Immobility.

Artificial heart valves may dysfunction, leading to thrombus and/or pannus formations. Computational fluid dynamics is a promising tool for improved understanding of heart valve hemodynamics that quantify detailed flow velocities and turbulent stresses to complement Doppler measurements. This combined information can assist in choosing optimal prosthesis for individual patients, aiding in the development of improved valve designs, and illuminating subtle changes to help guide more timely early intervention of valve dysfunction. In this computational study, flow characteristics around a bileaflet mechanical heart valve were investigated. The study focused on the hemodynamic effects of leaflet immobility, specifically, where one leaflet does not fully open. Results showed that leaflet immobility increased the principal turbulent stresses (up to 400%), and increased forces and moments on both leaflets (up to 600% and 4000%, respectively). These unfavorable conditions elevate the risk of blood cell damage and platelet activation, which are known to cascade to more severe leaflet dysfunction. Leaflet immobility appeared to cause maximal velocity within the lateral orifices. This points to the possible importance of measuring maximal velocity at the lateral orifices by Doppler ultrasound (in addition to the central orifice, which is current practice) to determine accurate pressure gradients as markers of valve dysfunction.

Empirical modeling of plasma sheet pressure and three‐dimensional force‐balanced magnetospheric magnetic field structure: 1. Observation

AbstractA three‐dimensional (3‐D) magnetic field configuration in force balance with a realistic plasma pressure distribution can provide more accurate evaluation of the role of magnetic field on plasma sheet dynamics and M‐I coupling. We used Geotail and Time History of Events and Macroscale Interactions During Substorms (THEMIS) data to establish an empirical model for nightside equatorial isotropic plasma pressure to r = 30 RE for Kp = 0–5 and for solar wind dynamic pressure (PSW) = 1.5 and 3 nPa. The model pressure is used in the companion paper for modeling a 3‐D force‐balanced pressure and magnetic field equilibrium. Larger convection during higher Kp drives the plasma sheet further earthward, resulting in larger increase of pressure and pressure gradient at smaller radial distance. On the other hand, magnetosphere compression by increasing PSW enhances pressure and pressure gradient mainly in the tail plasma sheet. While both pressure and radial gradients are enhanced with increasing Kp or PSW, there is no significant azimuthal pressure variation statistically under all Kp and PSW conditions. The empirical pressures well reproduce these statistical profiles with very high correlation coefficients. Additionally, comparisons with pressure gradients computed using two simultaneous measurements from two THEMIS spacecraft show reasonable agreement. Furthermore, our model provides more accurate pressure gradients than previous empirical models. The model magnetic field distributions obtained in the companion paper from requiring force balance with these empirical pressure profiles are also found to be consistent with the magnetic field observations, indicating that our equilibria well represent realistic 3‐D pressure and magnetic field configurations.

Three-Phase Compositional Modeling With Capillarity in Heterogeneous and Fractured Media

SummaryWe model for the first time capillarity in fully compositional three-phase flow, with higher-order finite-element (FE) methods. Capillary pressure gradients may be an important driving force, particularly in layered or fractured porous media, which exhibit sharp discontinuities in permeability. We introduce a simple local computation of the capillary pressure gradients, propose a fractional-flow formulation in terms of the total flux, and resolve complications arising from gravity and capillarity in the upwinding of phase fluxes. Fractures are modeled with the crossflow equilibrium concept, which allows large timesteps and includes all physical interactions between fractures and matrix blocks. The pressure and flux fields are discretized by the mixed hybrid finite-element method, and mass transport is approximated by a higher-order local discontinuous Galerkin (DG) method. Numerical-dispersion and grid-orientation effects are significantly reduced, which allows computations on coarser grids and with larger timesteps. The main advantages in the context of this work are the accurate pressure gradients and fluxes at the interface between regions of different permeabilities. The phase compositions are computed with state-of-the-art phase-splitting algorithms and stability analyses to guarantee the global minimum of Gibbs free energy. Accurate compositional simulation motivates the use of an implicit-pressure/explicit-composition (IMPEC) scheme, and we discuss the associated Courant-Friedrichs-Lewy (CFL) condition on the time-steps. We present various numerical examples on both core- and large-scale, illustrating the capillary end effect, capillary-driven crossflow in layered media, and the importance of capillarity in fractured media for three-phase flow.

Large Eddy Simulation of Laminar and Turbulent Flow on Collocated and Staggered Grids

Momentum and Continuity are the basic equations for fluid flow modeling. The momentum equations in their final form are known as Navier-Stokes equations and can be solved using different numerical methods. There are several approaches such as SIMPLE, PISO, and Fractional Step for solving these equations. In solution procedure, it needs to decide where to store the velocity components. Staggered and Collocated grids can be used to evaluate this problem. On Staggered grids, the velocity components are stored at the cell face, and the scalar variables such as pressure are stored at the central nodes. However, on Collocated grids, all parameters are defined at the same location at the central nodes. The Staggered grids method gives more accurate pressure gradient estimation. However, Collocated grids method is simpler for solving the equations. In this paper, for solving Navier-Stokes equations, Collocated and Staggered grids are employed. Comparison of horizontal and vertical velocities and stream lines at various Reynolds numbers was performed. The results were validated using standard tests such as lid-driven cavity, channel and backward facing step. Discussion is made on accuracy of these methods to estimate horizontal and vertical velocity profiles.

Static Bottom-Hole Pressures in Wells

A compote procedure is presented in this article for estimating static pressure gradient. The procedure integrates reservoir properties; temperature, pressure, depth, and density to calculate pressure drop in wellbore. The procedure constraints are intended to ensure that an accurate pressure gradient is obtained.

Acoustic analysis with absorbing finite elements and far-field computations using free-space Green's functions

A family of absorbing-boundary finite elements (FEs) is recently developed for the acoustic time-harmonic, transient and modal analyses of problems having fluid domains of infinite extent. These elements can be easily ‘glued’ to the truncated exterior surface of an underlying FE mesh. The desirable characteristics of the absorbing elements are that they are local and produce banded symmetric element matrices. Since the use of the absorbing FEs reduces the size of the FE model through the premature truncation of the mesh, a post-processing procedure must be employed to obtain solutions far away from FE domain in the case of transient and time-harmonic analyses. In this paper free-space Green's functions are utilized, in the context of time-harmonic analysis, in association with the computed solutions at the exterior boundary where absorbing-boundary FEs are placed in order to compute pressure distribution outside the FE computational domain. The paper demonstrates that the computation of accurate pressure gradients at the absorbing-boundary element nodes plays a crucial role in obtaining accurate pressure solutions outside the FE computational domain.

A General Pressure Gradient Formulation for Ocean Models. Part I: Scheme Design and Diagnostic Analysis

Abstract A Jacobian formulation of the pressure gradient force for use in models with topography-following coordinates is proposed. It can be used in conjunction with any vertical coordinate system and is easily implemented. Vertical variations in the pressure gradient are expressed in terms of a vertical integral of the Jacobian of density and depth with respect to the vertical computational coordinate. Finite difference approximations are made on the density field, consistent with piecewise linear and continuous fields, and accurate pressure gradients are obtained by vertically integrating the discrete Jacobian from sea surface. Two discrete schemes are derived and examined in detail: the first using standard centered differencing in the generalized vertical coordinate and the second using a vertical weighting such that the finite differences are centered with respect to the Cartesian z coordinate. Both schemes achieve second-order accuracy for any vertical coordinate system and are significantly more a...

Accurate pressure gradient calculations in hydrostatic atmospheric models

Most models of atmospheric flow which use the primitive equations require a diagnostic equation to determine local total pressure. In hydrostatic models, this equation is the vertically integrated hydrostatic equation. A frequently used approximation to this integration is to hold the temperature constant within model layers yielding a linear proportionality between Op or Mir (Exner’s function) and Az. This procedure yields static pressures with errors on the order of 10−3mb.

Galerkin Methods for the Numerical Solution of Boundary Value Problems

Abstract This paper presents a new technique for solving some of the partial differential equations that are commonly used in simulating reservoir performance. The results of applying this technique to a simple problem show that one obtains accurate pressure problem show that one obtains accurate pressure values near wells, as well as accurate pressure gradients, which can be explicitly calculated. The method is completely rigorous in that convergence of the discrete numerical solution to the continuous solution for both pressure and pressure gradient is established. High-order, piecewise-polynomial approximations are used near the wells where pressure gradients are steep, while low-order, pressure gradients are steep, while low-order, piecewise-polynomial approximations are used piecewise-polynomial approximations are used elsewhere to reduce greatly the calculation time. This combination is shown to give a uniformly good approximation to the solution. These approximations, obtained by using a Galerkin process with suitable Hermite subs paces, are shown to be theoretically and numerically superior to the usual approximations obtained from standard finite-difference techniques. Not only are much greater accuracies obtained, but computer times are also greatly reduced. The application of this technique to multiphase flow problems (e.g., single well coning problems) would have considerable practical interest, but such extensions of this technique with full mathematical rigor have not been made as yet. However, the numerical methods presented here are general, and in principle extend to multidimensional, multiphase flow. Moreover, the preliminary results given in this paper are sufficiently encouraging that we feel the effort in attempting these extensions is justified. Introduction The problem of obtaining accurate pressure distributions and pressure gradients around wells is of considerable importance in the numerical simulation of reservoir performance. The most common approach to solving this problem is to use finite difference techniques (see McCarty and Barfield or Peaceman and Rachford). This approach, however, has many disadvantages, the major one being that many grid points are generally necessary for accurately describing the pressure distribution and the pressure gradient around wells. This need for a fine grid results in large computer times and often in prohibitively high costs. Besides investigating the method of finite differences, some authors, such as Welge and Weber and Roper, Merchant and Duvall, have considered a combination of analytical and numerical techniques with some success. These approaches, however, are all nonrigorous and quite -often cannot even be applied. In this paper, we present a numerical formulation of high-order present a numerical formulation of high-order accuracy, based on the Galerkin method, for solving this problem. We treat here only the partial differential equation that describes steady-state, single-phase flow. However, the methods presented are general and in principle extend to multidimensional, multiphase principle extend to multidimensional, multiphase flow. Specifically we treat special cases of the problem in two dimensions described by: problem in two dimensions described by: (1) (2) where G is a rectangle (with sides parallel to the coordinate axis) with boundary G, / n denotes the outward normal, and and beta are non-negative constants such that + beta greater than 0. SPEJ p. 204