Analytical Solutions for Steady‐State Gas Flow in Layered Soils with Field Applications

The presented research demonstrates the results of a series of numerical simulations of gas flow through a single-stage centrifugal compressor with a vaneless diffuser. Numerical results were validated with experiments consisting of eight regimes with different mass flow rates. The steady-state and unsteady simulations were done in ANSYS FLUENT 13.0 and NUMECA FINE/TURBO 8.9.1 for one-period geometry due to periodicity of the problem. First-order discretization is insufficient due to strong dissipation effects. Results obtained with second-order discretization agree with the experiments for the steady-state case in the region of high mass flow rates. In the area of low mass flow rates, nonstationary effects significantly influence the flow leading stationary model to poor prediction. Therefore, the unsteady simulations were performed in the region of low mass flow rates. Results of calculation were compared with experimental data. The numerical simulation method in this paper can be used to predict compressor performance.

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Experimental, Numerical, and Statistical Investigation of Two Phase Flow in a Cylindrical Perforation Tunnel

10.1115/omae2021-62956 ◽

2021 ◽

Author(s):

Ekhwaiter Abobaker ◽

Abadelhalim Elsanoose ◽

Mohammad Azizur Rahman ◽

Faisal Khan ◽

Amer Aborig ◽

...

Keyword(s):

Numerical Simulation ◽

Steady State ◽

Statistical Analysis ◽

Flow Rate ◽

Gas Flow ◽

Two Phase Flow ◽

Phase Flow ◽

Gas Flow Rate ◽

Two Phase ◽

Flow Through

Abstract Perforation is the final stage in well completion that helps to connect reservoir formations to wellbores during hydrocarbon production. The drilling perforation technique maximizes the reservoir productivity index by minimizing damage. This can be best accomplished by attaining a better understanding of fluid flows that occur in the near-wellbore region during oil and gas operations. The present work aims to enhance oil recovery by modelling a two-phase flow through the near-wellbore region, thereby expanding industry knowledge about well performance. An experimental procedure was conducted to investigate the behavior of two-phase flow through a cylindrical perforation tunnel. Statistical analysis was coupled with numerical simulation to expand the investigation of fluid flow in the near-wellbore region that cannot be obtained experimentally. The statistical analysis investigated the effect of several parameters, including the liquid and gas flow rate, liquid viscosity, permeability, and porosity, on the injection build-up pressure and the time needed to reach a steady-state flow condition. Design-Expert® Design of Experiments (DoE) software was used to determine the numerical simulation runs using the ANOVA analysis with a Box-Behnken Design (BBD) model and ANSYS-FLUENT was used to analyses the numerical simulation of the porous media tunnel by applying the volume of fluid method (VOF). The experimental data were validated to the numerical results, and the comparison of results was in good agreement. The numerical and statistical analysis demonstrated each investigated parameter’s effect. The permeability, flow rate, and viscosity of the liquid significantly affect the injection pressure build-up profile, and porosity and gas flow rate substantially affect the time required to attain steady-state conditions. In addition, two correlations obtained from the statistical analysis can be used to predict the injection build-up pressure and the required time to reach steady state for different scenarios. This work will contribute to the clarification and understanding of the behavior of multiphase flow in the near-wellbore region.

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Steady-state thermal uniformity and gas flow patterns in a rapid thermal processing chamber

IEEE Transactions on Semiconductor Manufacturing ◽

10.1109/66.75859 ◽

1991 ◽

Vol 4 (1) ◽

pp. 14-20 ◽

Cited By ~ 62

Author(s):

S.A. Campbell ◽

K.-H. Ahn ◽

K.L. Knutson ◽

B.Y.H. Liu ◽

J.D. Leighton

Keyword(s):

Steady State ◽

Thermal Processing ◽

Gas Flow ◽

Rapid Thermal Processing ◽

Flow Patterns

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A Hybrid Coupling Scheme and Stability Analysis for Coupled Solid/Fluid Turbine Blade Temperature Calculations

Volume 4: Heat Transfer; Electric Power; Industrial and Cogeneration ◽

10.1115/98-gt-088 ◽

1998 ◽

Cited By ~ 5

Author(s):

Andreas Heselhaus

Keyword(s):

Heat Conduction ◽

Steady State ◽

Turbine Blade ◽

Gas Flow ◽

Guide Vane ◽

Thermal Design ◽

Navier Stokes ◽

Coupling Scheme ◽

Flow Solver ◽

Turbine Blade Cooling

Efficient thermal design of turbine blade cooling needs to take wall temperature effects on heat transfer into account. This can only be achieved by a coupled calculation of hot gas flow and blade heat conduction. In this paper principle and stability proof of an algorithm are presented that allows to couple a steady state finite element heat conduction solver with a blockstructured steady state finite volume (FV) Navier-Stokes time marching flow solver. The stability of the developed coupling procedure as well as the instability of an alternative algorithm is shown analytically and numerically. The benefits of coupled calculating are shown for a convectively cooled turbine guide vane blade. In the example treated, temperature differences of more than 100 K arise compared to the same calculation performed in an uncoupled way.

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An Approximate Method for Non -Darcy Radial Gas Flow

Society of Petroleum Engineers Journal ◽

10.2118/687-pa ◽

1964 ◽

Vol 4 (02) ◽

pp. 96-114 ◽

Cited By ~ 3

Author(s):

G. Rowan ◽

M.W. Clegg

Keyword(s):

Linear Equation ◽

Flow Rate ◽

Analytical Solutions ◽

Gas Flow ◽

Darcy’S Law ◽

Darcy's Law ◽

Non Linear Equation ◽

Approximate Analytical Solutions ◽

Non Linear ◽

Flow Law

Abstract Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is shown to be very good. Some observations on the interpretation of gas well tests are made. Introduction The flow of gases in porous media is a problem that has been the subject of much study in recent years, and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law (1) leads to a non-linear equation of the form (2) in a homogeneous medium, assuming an equation of state(3) It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form (4) This form of equation was first suggested by Forchheimer and, later, Katz and Cornell, and Irmay, developed a similar equation. Houpeurt derived this form of equation using the concept of an idealized pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type, for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al., and Aronofsky and Jenkins, but the latter solutions, apart from the simple linearization of equation [2] to yield a diffusion equation in p2, are not so well-known. SPEJ P. 96ˆ

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SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL

The ANZIAM Journal ◽

10.1017/s1446181117000311 ◽

2017 ◽

Vol 59 (2) ◽

pp. 167-182 ◽

Cited By ~ 1

Author(s):

H. Y. ALFIFI

Keyword(s):

Steady State ◽

Hopf Bifurcation ◽

Partial Differential Equations ◽

Differential Equations ◽

Analytical Solutions ◽

Numerical Solutions ◽

Partial Differential ◽

Analytical Results ◽

Transient Solutions ◽

The Impact

Semi-analytical solutions are derived for the Brusselator system in one- and two-dimensional domains. The Galerkin method is processed to approximate the governing partial differential equations via a system of ordinary differential equations. Both steady-state concentrations and transient solutions are obtained. Semi-analytical results for the stability of the model are presented for the identified critical parameter value at which a Hopf bifurcation occurs. The impact of the diffusion coefficients on the system is also considered. The results show that diffusion acts to stabilize the systems better than the equivalent nondiffusive systems with the increasing critical value of the Hopf bifurcation. Comparison between the semi-analytical and numerical solutions shows an excellent agreement with the steady-state transient solutions and the parameter values at which the Hopf bifurcations occur. Examples of stable and unstable limit cycles are given, and Hopf bifurcation points are shown to confirm the results previously calculated in the Hopf bifurcation map. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.

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