scholarly journals Analytical solutions of model equations for two phase gas mixtures: Transverse velocity perturbations

1984 ◽  
Vol 27 (5) ◽  
pp. 1114 ◽  
Author(s):  
J. Frederick Cavalier ◽  
William Greenberg
Keyword(s):  
Analytical Solutions ◽  
Transverse Velocity ◽  
Gas Mixtures ◽  
Two Phase ◽  
Model Equations

Modeling Gas-Liquid Head Performance of Electrical Submersible Pumps

2004 ◽  
Author(s):  
Datong Sun ◽  
Mauricio Prado
Keyword(s):  
Petroleum Industry ◽  
Nuclear Industry ◽  
Two Phase ◽  
Liquid Model ◽  
Electrical Submersible Pumps ◽  
Pump Head ◽  
Fluid Properties ◽  
Interfacial Characteristic ◽  
Model Equations ◽  
Shock Loss

This study presents a new gas-liquid model to predict Electrical Submersible Pumps (ESP) head performance. The newly derived approach based on gas-liquid momentum equations along pump channels has improved the Sachdeva model [1, 2] in the petroleum industry and generalized the Minemura model [3] in the nuclear industry. The new two-phase model includes novel approaches for wall frictional losses for each phase using a gas-liquid stratified assumption and existing correlations, a new shock loss model incorporating rotational speeds, a new correlation for drag coefficient and interfacial characteristic length effects by fitting the model results with experimental data, and an algorithm to solve the model equations. The model can predict pressure and void fraction distributions along impellers and diffusers in addition to the pump head performance curve under different fluid properties, pump intake conditions, and rotational speeds.

Steady one-dimensional nozzle flow solutions of liquid–gas mixtures

2013 ◽  
Vol 737 ◽  
pp. 146-175 ◽  
Author(s):  
S. LeMartelot ◽  
R. Saurel ◽  
O. Le Métayer
Keyword(s):  
Two Phase Flow ◽  
Gas Mixtures ◽  
Ideal Gas ◽  
Nozzle Flow ◽  
Pure Liquid ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Flow Models ◽  
Relaxation Effects

AbstractExact compressible one-dimensional nozzle flow solutions at steady state are determined in various limit situations of two-phase liquid–gas mixtures. First, the exact solution for a pure liquid nozzle flow is determined in the context of fluids governed by the compressible Euler equations and the ‘stiffened gas’ equation of state. It is an extension of the well-known ideal-gas steady nozzle flow solution. Various two-phase flow models are then addressed, all corresponding to limit situations of partial equilibrium among the phases. The first limit situation corresponds to the two-phase flow model of Kapila et al. (Phys. Fluids, vol. 13, 2001, pp. 3002–3024), where both phases evolve in mechanical equilibrium only. This model contains two entropies, two temperatures and non-conventional shock relations. The second one corresponds to a two-phase model where the phases evolve in both mechanical and thermal equilibrium. The last one corresponds to a model describing a liquid–vapour mixture in thermodynamic equilibrium. They all correspond to two-phase mixtures where the various relaxation effects are either stiff or absent. In all instances, the various flow regimes (subsonic, subsonic–supersonic, and supersonic with shock) are unambiguously determined, as well as various nozzle solution profiles.

scholarly journals Iterative Analytical Solutions for Nonlinear Two-Phase Flow with Gas Solubility in Shale Gas Reservoirs

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaoji Shang ◽  
J. G. Wang ◽  
Zhizhen Zhang
Keyword(s):  
Capillary Pressure ◽  
Analytical Solutions ◽  
Shale Gas ◽  
Nonlinear Term ◽  
Two Phase Flow ◽  
Gas Production ◽  
Phase Flow ◽  
Gas Solubility ◽  
Production Rates ◽  
Two Phase

The governing equations of a two-phase flow have a strong nonlinear term due to the interactions between gas and water such as capillary pressure, water saturation, and gas solubility. This nonlinearity is usually ignored or approximated in order to obtain analytical solutions. The impact of such ignorance on the accuracy of solutions has not been clear so far. This study seeks analytical solutions without ignoring this nonlinear term. Firstly, a nonlinear mathematical model is developed for the two-phase flow of gas and water during shale gas production. This model also considers the effects of gas solubility in water. Then, iterative analytical solutions for pore pressures and production rates of gas and water are derived by the combination of travelling wave and variational iteration methods. Thirdly, the convergence and accuracy of the solutions are checked through history matching of two sets of gas production data: a China shale gas reservoir and a horizontal Barnett shale well. Finally, the effects of the nonlinear term, shale gas solubility, and entry capillary pressure on the shale gas production rate are investigated. It is found that these iterative analytical solutions can be convergent within 2-3 iterations. The solutions can well describe the production rates of both gas and water. The nonlinear term can significantly affect the forecast of shale gas production in both the short term and the long term. Entry capillary pressure and shale gas solubility in water can also affect shale gas production rates of shale gas and water. These analytical solutions can be used for the fast calculation of the production rates of both shale gas and water in the two-phase flow stage.

scholarly journals Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987490
Author(s):  
Muhammad Rehan Saleem ◽  
Ubaid Ahmed Nisar ◽  
Shamsul Qamar
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Scheme ◽  
Flow Model ◽  
Numerical Study ◽  
Momentum Exchange ◽  
Two Phase ◽  
Runge Kutta ◽  
Model Equations

This article deals with the numerical study of two-phase shallow flow model describing the mixture of fluid and solid granular particles. The model under investigation consists of coupled mass and momentum equations for solid granular material and fluid particles through non-conservative momentum exchange terms. The non-conservativity of model equations poses major challenges for any numerical scheme, such as well balancing, positivity preservation, accurate approximation of non-conservative terms, and achievement of steady-state conditions. Thus, in order to approximate the present model an accurate, well-balanced, robust, and efficient numerical scheme is required. For this purpose, in this article, Runge–Kutta discontinuous Galerkin method is applied successfully for the first time to solve the model equations. Several test problems are also carried out to check the performance and accuracy of our proposed numerical method. To compare the results, the same model is solved by staggered central Nessyahu–Tadmor scheme. A good comparison is found between two schemes, but the results obtained by Runge–Kutta discontinuous Galerkin scheme are found superior over the central Nessyahu–Tadmor scheme.

scholarly journals Analytical solutions of compacting flow past a sphere

2014 ◽  
Vol 746 ◽  
pp. 466-497 ◽  
Author(s):  
John F. Rudge
Keyword(s):  
Analytical Solutions ◽  
Stokes Flow ◽  
Solid Matrix ◽  
Rigid Sphere ◽  
Deformable Solid ◽  
Two Phase ◽  
Low Viscosity ◽  
Flow Past ◽  
Phase Medium ◽  
Flow Past A Sphere

AbstractA series of analytical solutions are presented for viscous compacting flow past a rigid impermeable sphere. The sphere is surrounded by a two-phase medium consisting of a viscously deformable solid matrix skeleton through which a low-viscosity liquid melt can percolate. The flow of the two-phase medium is described by McKenzie’s compaction equations, which combine Darcy flow of the liquid melt with Stokes flow of the solid matrix. The analytical solutions are found using an extension of the Papkovich–Neuber technique for Stokes flow. Solutions are presented for the three components of linear flow past a sphere: translation, rotation and straining flow. Faxén laws for the force, torque and stresslet on a rigid sphere in an arbitrary compacting flow are derived. The analytical solutions provide instantaneous solutions to the compaction equations in a uniform medium, but can also be used to numerically calculate an approximate evolution of the porosity over time whilst the porosity variations remain small. These solutions will be useful for interpreting the results of deformation experiments on partially molten rocks.

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