Miscible porous media displacements in the quarter five-spot configuration. Part 2. Effect of heterogeneities

1998 ◽  
Vol 371 ◽  
pp. 269-299 ◽  
Author(s):  
CHING-YAO CHEN ◽  
ECKART MEIBURG
Keyword(s):  
Correlation Length ◽  
Viscous Fingering ◽  
Length Scale ◽  
Correlation Lengths ◽  
Miscible Displacements ◽  
Fingering Instability ◽  
Entire Flow ◽  
Flow Domain ◽  
Selection Mechanisms ◽  
Nonlinear Nature

Direct numerical simulations are employed to investigate the coupling between the viscous fingering instability and permeability heterogeneities for miscible displacements in quarter five-spot flows. Even moderate inhomogeneities are seen to have a strong effect on the flow, which can result in a complete bypass of the linear growth phase of the viscous fingering instability. In contrast to their homogeneous counterparts (cf. Part 1, Chen & Meiburg 1998), heterogeneous quarter five-spot flows are seen to exhibit a more uniform dominant length scale throughout the entire flow domain. In line with earlier findings for unidirectional displacements, an optimal interaction of the mobility and permeability related vorticity modes can occur when the viscous length scale is of the same order as the correlation length of the heterogeneities. This resonance mechanism results in a minimal breakthrough recovery for intermediate correlation lengths, at fixed dimensionless flow rates in the form of a Péclet number Pe. However, for a constant correlation length, the recovery does not show a minimum as Pe is varied.Confirming earlier observations, the simulations show a more rapid breakthrough as the variance of the permeability variations increases. However, this tendency is far more noticeable in some parameter regimes than in others. It is furthermore observed that relatively low variances usually cannot change the tendency for a dominant finger to evolve along the inherently preferred diagonal direction, especially for relatively small correlation lengths. Only for higher variances, and for larger correlation lengths, are situations observed in which an off-diagonal finger can become dominant. Due to the nonlinear nature of the selection mechanisms at work, a change in the variance of the heterogeneities can result in the formation of dominant fingers along entirely different channels.

scholarly journals A new exponentially-decaying error correlation model for assimilating OCO-2 column-average CO<sub>2</sub> data, using a length scale computed from airborne lidar measurements

2021 ◽  
Author(s):  
David F. Baker ◽  
Emily Bell ◽  
Kenneth J. Davis ◽  
Joel F. Campbell ◽  
Bing Lin ◽  
...  
Keyword(s):  
Correlation Length ◽  
Error Model ◽  
Airborne Lidar ◽  
Length Scale ◽  
Correlation Model ◽  
Correlation Lengths ◽  
New Model ◽  
The Mean ◽  
Error Correlation ◽  
Along Track

Abstract. To check the accuracy of column-average dry air CO2 mole fractions (XCO2) retrieved from Orbiting Carbon Overvatory (OCO-2) data, a similar quantity has been measured from the Multi-functional Fiber Laser Lidar (MFLL) aboard aircraft flying underneath OCO-2 as part of the Atmospheric Carbon and Transport (ACT)-America flight campaigns. Here we do a lagged correlation analysis of these MFLL-OCO-2 column CO2 differences and find that their correlation spectrum falls off rapidly at along-track separation distances of under 10 km, with a correlation length scale of about 10 km, and less rapidly at longer separation distances, with a correlation length scale of about 20 km. The OCO-2 satellite takes many CO2 measurements with small (~3 km2) fields of view (FOVs) in a thin (<10 km wide) swath running parallel to its orbit: up to 24 separate FOVs may be obtained per second (across a ~6.75 km distance on the ground), though clouds, aerosols, and other factors cause considerable data dropout. Errors in the CO2 retrieval method have long been thought to be correlated at these fine scales, and methods to account for these when assimilating these data into top-down atmospheric CO2 flux inversions have been developed. A common approach has been to average the data at coarser scales (e.g., in 10-second-long bins) along-track, then assign an uncertainty to the averaged value that accounts for the error correlations. Here we outline the methods used up to now for computing these 10-second averages and their uncertainties, including the constant-correlation-with-distance error model currently being used to summarize the OCO-2 version 9 XCO2 retrievals as part of the OCO-2 flux inversion model intercomparison project. We then derive a new one-dimensional error model using correlations that decay exponentially with separation distance, apply this model to the OCO-2 data using the correlation length scales derived from the MFLL-OCO-2 differences, and compare the results (for both the average and its uncertainty) to those given by the current constant-correlation error model. To implement this new model, the data are averaged first across 2-second spans, to collapse the cross-track distribution of the real data onto the 1-D path assumed by the new model. A small percentage of the data that cause nonphysical negative averaging weights in the model are thrown out. The correlation lengths over the ocean, which the land-based MFLL data do not clarify, are assumed to be twice those over the land. The new correlation model gives 10-second XCO2 averages that are only a few tenths of a ppm different from the constant-correlation model. Over land, the uncertainties in the mean are also similar, suggesting that the +0.3 constant correlation coefficient currently used in the model there is accurate. Over the oceans, the twice-the-land correlation lengths that we assume here result in a significantly lower uncertainty on the mean than the +0.6 constant correlation currently gives – measurements similar to the MFLL ones are needed over the oceans to do better. Finally, we show how our 1-D exponential error correlation model may be used to account for correlations in those inversion methods that choose to assimilate each XCO2 retrieval individually, and to account for correlations between separate 10-second averages when these are assimilated instead.

Stability Considerations in Downward Miscible Displacements

1964 ◽  
Vol 4 (04) ◽  
pp. 356-362 ◽  
Author(s):  
J.M. Dumore
Keyword(s):  
Transition Zone ◽  
Viscous Fingering ◽  
Favorable Effect ◽  
Homogeneous Layer ◽  
Oil Viscosity ◽  
Critical Rate ◽  
Miscible Displacements ◽  
Viscous Fingers ◽  
The Stability ◽  
Definition Of

Abstract If, in a vertical, downward miscible displacement, the transition zone between the displacing and displaced fluids is neglected, a criterion for stable displacement can be obtained by considering a small hypothetical protrusion of one of the fluids into the other. This criterion leads to the definition of the well-known critical rate, uc = kg ??/?µ. The consideration is further extended by taking into account the transition zone that develops as a result of diffusion and mixing. A generalization of the previous criterion leads to the definition of another characteristic rate, the stable rate, which in actual miscible drives will be less than the critical rate. In such drives, the entire transition zone is stable at rates less than the stable rate. At rates between the stable and critical rates, the displacement is only partly stable, i.e. part of the transition zone adjacent to the displaced fluid is in an unstable position. From that part of the transition zone viscous fingers will develop. At rates greater than the critical rate the entire displacement is unstable and viscous fingers will develop more strongly. Results of laboratory experiments are in agreement with the expected behavior based on the theoretically deduced stability of the displacement. INTRODUCTION The simplest form of miscible drive in an oil-bearing formation is the injection of a fluid that is completely miscible* with the oil under reservoir conditions. In general, such a fluid, a solvent for example, is less dense and less viscous than the oil present in the formation. If it is injected into a horizontal homogeneous layer, gravitational forces will lead to the formation of a gravity tongue of solvent in the upper part of the layer and the adverse solvent-oil viscosity ratio will cause viscous fingers to develop. If, however, the solvent is injected up-structure into a dipping layer, gravity has a favorable effect, because it tends to keep the less dense solvent up-structure. Tongue formation and viscous fingering are consequently reduced and it is even possible that they will be suppressed completely. Viscous fingering and gravity tonguing are the consequences of the instability of the displacement. A stable displacement cannot result in growing viscous fingers and/or growing gravity tongues. Since large amounts of oil can be bypassed if there is viscous fingering and/or gravity tonguing, the stability of a miscible drive is very important with respect to the recovery efficiency of the drive. The stability is of particular importance in miscible-slug drives, as it determines how quickly the miscible slug between the displaced and displacing fluids will be distorted and broken up, after which the drive is no longer completely miscible. Stability is thus a most important factor in determining the success of a miscible drive, and it is considered that the aspects of stability considered in this paper will make a useful contribution to existing theories. Consideration is given only to vertical downward displacements, in which no gravity tongues can develop and which are therefore simpler than downward displacements in sloping layers.

NUMERICAL ANALYSIS OF VISCOUS FINGERING INSTABILITY DUE TO MISCIBLE DISPLACEMENT

2020 ◽  
Vol 61 (4) ◽  
pp. 539-545
Author(s):  
A. Nemati ◽  
H. Saffari ◽  
B. Z. Vamerzani ◽  
R. Azizi ◽  
S. M. Hosseinalipoor ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Viscous Fingering ◽  
Miscible Displacement ◽  
Fingering Instability

A comparison of the correlation structure in GPR images of deltaic and barrier‐spit depositional environments

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1142-1153 ◽  
Author(s):  
Paulette Tercier ◽  
Rosemary Knight ◽  
Harry Jol
Keyword(s):  
Correlation Length ◽  
Ground Penetrating Radar ◽  
Depositional Environments ◽  
Geostatistical Analysis ◽  
Maximum Correlation ◽  
Correlation Lengths ◽  
Correlation Structures ◽  
Geostatistical Models ◽  
Ground Penetrating ◽  
Radar Facies

We have used geostatistical analysis of radar reflections to quantify the correlation structures found in 2-D ground‐penetrating radar (GPR) images. We find that the experimental semivariogram, the product of the geostatistical analysis of the GPR data, is well‐defined and can be modeled using standard geostatistical models to obtain an estimate of the range or correlation length, and the maximum correlation direction, in the 2-D GPR image. When we compare the results from geostatistical analysis of GPR data from selected deltaic and barrier‐spit depositional environments we find different correlation structures in GPR images from different depositional environments. GPR images from braid deltas have near‐horizontal correlation directions and correlation lengths on the order of a few meters. In contrast, the GPR image of a fan‐foreset delta has a very long (>24 m) correlation length and a maximum correlation direction plunging 20°. In the GPR images from barrier spits, we find maximum correlation directions that are horizontal or plunging a few degrees. The correlation lengths range from 7 to 43 m, depending on the orientation of the GPR image relative to spit end growth, and on the specific radar facies that is analyzed.

Spatial correlation length of normalized cone data in sand: case study in the north of Denmark

2014 ◽  
Vol 51 (8) ◽  
pp. 844-857 ◽  
Author(s):  
S. Firouzianbandpey ◽  
D.V. Griffiths ◽  
L.B. Ibsen ◽  
L.V. Andersen
Keyword(s):  
Spatial Correlation ◽  
Correlation Length ◽  
Vertical Direction ◽  
Cone Penetration ◽  
Correlation Lengths ◽  
Cone Penetration Testing ◽  
The North ◽  
Site Investigations ◽  
Depositional Process ◽  
Spatial Correlation Length

The main topic of this study is to assess the anisotropic spatial correlation lengths of a sand layer deposit based on cone penetration testing with pore pressure measurement (CPTu) data. Spatial correlation length can be an important factor in reliability analysis of geotechnical systems, yet it is rarely estimated during routine site investigations. Results from two different sites in the north of Denmark are reported in this paper, indicating quite strong anisotropy due to the depositional process, with significantly shorter spatial correlation lengths in the vertical direction. It is observed that the normalized cone resistance is a better estimator of spatial trends than the normalized friction ratio.

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