Three-Dimensional and Nonisotropic Effects in the Analysis of Interference Test Data

1976 ◽  
Vol 16 (05) ◽  
pp. 231-234
Author(s):  
R. Rodriguez-Nieto ◽  
R.D. Carter
Keyword(s):  
Gas Flow ◽  
Three Dimensional ◽  
Observation Point ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Pulse Testing ◽  
Two Dimensional Flow ◽  
Interference Test ◽  
Flow Through ◽  
Interference Tests

Abstract A three-dimensional analytical model is presented for predicting the performance of pressure and flow rate in anisotropic gas reservoirs. The model considers interference effects and restricted flow entry and uses the point-source solution to the equation that describes unsteady-state real-gas flow through porous media. Introduction The assumption of two-dimensional flow through isotropic porous media is frequently found in reservoir studies. Observed pressure behavior often can be matched using a two-dimensional flow model. However, there are some reservoirs for which matching would not be achieved, when reasonable values of the matching parameter are used, if three-dimensional and nonisotropic effects are not accounted for. THEORY It has been found that results obtained for linear or radial gas flow, regarding the gcg product fixed at its initial value, are good approximations to certain solutions that consider the pressure dependence of this product. To extend this treatment to problems of flow in three dimensions, the following development is presented. The pseudopressure drop occurring at any point in a finite, uniform, anisotropic reservoir resulting from a constant real-gas flow rate at a point source is approximated by 24,865 q sc p sc T res m (x, y, z, t) = ------------------------ F......(1) Tsc kh This equation is derived in Appendix A. The fundamental assumption made in the derivation of Eq. 1 is that the viscosity-compressibility product is a constant. Generally, this is not true. However, for some reservoir problems where small changes in pressure are involved, such as those taking place in pressure are involved, such as those taking place in pulse testing and interference tests, this assumption pulse testing and interference tests, this assumption is reasonable. The corresponding pressure drop is given by the following equation, which is derived in Appendix B: iZi m p = ...................................(2) 2pi EXAMPLE Interference data from a hypothetical test are analyzed by a procedure similar to that proposed for two-dimensional flow in oil reservoirs. From these data, a representative value of the porosity in the region between the production well and the observation point is obtained. Three possible observation-point locations are considered to emphasize the influence of three-dimensional and nonisotropic effects. These locations are characterized by their vertical separation with respect to the midpoint of the well-completion interval. The information needed is given in Fig. 1 and Table 1; y (ft) 9840 --------------------------------------------- 4920 ---- - ------ - ------ - -----* PRODUCING WELL 4592 ---- - ------ - ------ - --* OBSERVATION POINTS 0 ---------------------------------------------------->X (ft) 0 7544 8200 16400 Z(ft) -------------------------------------------------- CASE 3 574 ---------------------------* CASE 2 328 ---------------------------* CASE 1 82 ---------------------------* * MIDDLE POINT OF THE COMPLETION INTERVAL 0 -------------------------------------------------- FIG. 1 LOCATION OF THE PRODUCING WELL AND THE OBSERVATION POINTS; INTERFERENCE-TEST EXAMPLE. SPEJ P. 231

Wake behaviour and instability of flow through a partially blocked channel

2007 ◽  
Vol 582 ◽  
pp. 319-340 ◽  
Author(s):  
M. D. GRIFFITH ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN ◽  
W. P. ANDERSON
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
Recirculation Bubble ◽  
Dimensional Flow ◽  
Starting Point ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
The Stability

The two-dimensional flow through a constricted channel is studied. A semi-circular bump is located on one side of the channel and the extent of blockage is varied by adjusting the radius of the bump. The blockage is varied between 0.05 and 0.9 of the channel width and the upstream Reynolds number between 25 and 3000. The geometry presents a simplified blockage specified by a single parameter, serving as a starting point for investigations of other more complex blockage geometries. For blockage ratios in excess of 0.4, the variation of reattachment length with Reynolds number collapses to within approximately 15%, while at lower ratios the behaviour differs. For the constrained two-dimensional flow, various phenomena are identified, such as multiple mini-recirculations contained within the main recirculation bubble and vortex shedding at higher Reynolds numbers. The stability of the flow to three-dimensional perturbations is analysed, revealing a transition to a three-dimensional state at a critical Reynolds number which decreases with higher blockage ratios. Separation lengths and the onset and structure of three-dimensional instability observed from the geometry of blockage ratio 0.5 resemble results taken from backward-facing step investigations. The question of the underlying mechanism behind the instability being either centrifugal or elliptic in nature and operating within the initial recirculation zone is analytically tested.

Effect of Axial Velocity Variation in Aerofoil Cascades

1971 ◽  
Vol 13 (2) ◽  
pp. 92-99 ◽  
Author(s):  
S. Soundranayagam
Keyword(s):  
Wind Tunnel ◽  
Incompressible Flow ◽  
Axial Velocity ◽  
Three Dimensional ◽  
Velocity Variation ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Wind Tunnel Data ◽  
Flow Through

The effect of the variation of axial velocity in the incompressible flow through a cascade of aerofoils is discussed and it is shown that changes take place in the flow angles and in the blade circulation. A method is proposed by which the effect of axial velocity variation on a known two-dimensional flow or alternatively the two-dimensional equivalent of a flow with axial velocity variation can be calculated. The method is very easy to apply. The deviation may increase or decrease depending on the change in blade circulation and the stagger. An increase in apparent deflection through the cascade can be accompanied by a reduction in the blade force. The method would be particularly useful for the interpretation of cascade wind tunnel data and in the design of impeller stages where three-dimensional flows occur.

Choking Effects in the Blade Rows of Turbomachines

1980 ◽  
Vol 22 (4) ◽  
pp. 161-173 ◽  
Author(s):  
J. H. Horlock
Keyword(s):  
Shear Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Entry And Exit ◽  
Transonic Compressor ◽  
Dimensional Flow ◽  
Blade Row ◽  
Two Dimensional Flow ◽  
Flow Through

Three-dimensional flows through cascades of blades are studied, the blading being fully choked internally. Initially the two-dimensional flow through a ‘zero stagger, zero camber’ blade row, with subsonic entry and exit flow, is described. The radial flows are produced by radial variations in throat area, or by a variety of entry shear flows. Subsequently, the analysis is developed to describe similar fully choked flows through staggered blade rows, particularly the first rotating row of a transonic compressor.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Two-Dimensional Flow With Standing Vortexes in Ducts and Diffusers

1960 ◽  
Vol 82 (4) ◽  
pp. 921-927 ◽  
Author(s):  
Friedrich O. Ringleb
Keyword(s):  
Wind Tunnel ◽  
Potential Flow ◽  
Separation Control ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Princeton University ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
Trapping Devices

The conditions for the equilibrium of two vortexes in a two-dimensional flow through a duct or diffuser are derived. Potential-flow considerations and a few basic results from viscous-flow theory are used for the discussion of the role of cusps as separation control and trapping devices for standing vortexes. The investigations are applied to cusp diffusers especially with regard to the wind tunnel of the James Forrestal Research Center of Princeton University.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Steady small-disturbance transonic dense gas flow past two-dimensional compression/expansion ramps

2018 ◽  
Vol 848 ◽  
pp. 756-787 ◽  
Author(s):  
A. Kluwick ◽  
E. A. Cox
Keyword(s):  
Gas Dynamics ◽  
Gas Flow ◽  
External Forcing ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Dense Gas ◽  
Dimensional Flow ◽  
Flow Past ◽  
Two Dimensional Flow ◽  
Dimensional Parameters

The behaviour of steady transonic dense gas flow is essentially governed by two non-dimensional parameters characterising the magnitude and sign of the fundamental derivative of gas dynamics ($\unicode[STIX]{x1D6E4}$) and its derivative with respect to the density at constant entropy ($\unicode[STIX]{x1D6EC}$) in the small-disturbance limit. The resulting response to external forcing is surprisingly rich and studied in detail for the canonical problem of two-dimensional flow past compression/expansion ramps.

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