scholarly journals Viscous fingering in a radial elastic-walled Hele-Shaw cell

2018 ◽  
Vol 849 ◽  
pp. 163-191 ◽  
Author(s):  
Draga Pihler-Puzović ◽  
Gunnar G. Peng ◽  
John R. Lister ◽  
Matthias Heil ◽  
Anne Juel
Keyword(s):  
Stability Analysis ◽  
Flow Rate ◽  
Small Amplitude ◽  
Viscous Fingering ◽  
Flow Rates ◽  
Injection Flow ◽  
Fingering Instability ◽  
Air Liquid Interface ◽  
Hele Shaw Cell ◽  
Axisymmetric Perturbations

We study the viscous-fingering instability in a radial Hele-Shaw cell in which the top boundary has been replaced by a thin elastic sheet. The introduction of wall elasticity delays the onset of the fingering instability to much larger values of the injection flow rate. Furthermore, when the instability develops, the fingers that form on the expanding air–liquid interface are short and stubby, in contrast with the highly branched patterns observed in rigid-walled cells (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108, 2012, 074502). We report the outcome of a comprehensive experimental study of this problem and compare the experimental observations to the predictions from a theoretical model that is based on the solution of the Reynolds lubrication equations, coupled to the Föppl–von-Kármán equations which describe the deformation of the elastic sheet. We perform a linear stability analysis to study the evolution of small-amplitude non-axisymmetric perturbations to the time-evolving base flow. We then derive a simplified model by exploiting the observations (i) that the non-axisymmetric perturbations to the sheet are very small and (ii) that perturbations to the flow occur predominantly in a small wedge-shaped region ahead of the air–liquid interface. This allows us to identify the various physical mechanisms by which viscous fingering is weakened (or even suppressed) by the presence of wall elasticity. We show that the theoretical predictions for the growth rate of small-amplitude perturbations are in good agreement with experimental observations for injection flow rates that are slightly larger than the critical flow rate required for the onset of the instability. We also characterize the large-amplitude fingering patterns that develop at larger injection flow rates. We show that the wavenumber of these patterns is still well predicted by the linear stability analysis, and that the length of the fingers is set by the local geometry of the compliant cell.

Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells

2013 ◽  
Vol 731 ◽  
pp. 162-183 ◽  
Author(s):  
Draga Pihler-Puzović ◽  
Raphaël Périllat ◽  
Matthew Russell ◽  
Anne Juel ◽  
Matthias Heil
Keyword(s):  
Viscous Fingering ◽  
Base Flow ◽  
Elastic Membrane ◽  
Minor Role ◽  
Viscous Effects ◽  
Flow Rates ◽  
Air Bubble ◽  
Lubrication Equation ◽  
Fingering Instability ◽  
Air Liquid Interface

AbstractRecent experiments by Pihler-Puzovic et al. (Phys. Rev. Lett., vol. 108, 2012, article 074502) have shown that the onset of viscous fingering in circular Hele-Shaw cells in which an air bubble displaces a viscous fluid is delayed considerably when the top boundary of the cell is replaced by an elastic membrane. Non-axisymmetric instabilities are only observed at much larger flow rates, and the large-amplitude fingers that develop are fundamentally different from the highly branched fingers in rigid-walled cells. We explain the mechanism for the suppression of the instability using a combination of linear stability analysis and direct numerical simulations, based on a theoretical model that couples a depth-averaged lubrication equation for the fluid flow to the Föppl–von Kármán equations, which describe the deformation of the elastic membrane. We show that fluid–structure interaction affects the instability primarily via two changes to the axisymmetric base flow: the axisymmetric inflation of the membrane prior to the onset of any instabilities slows down the expansion of the air bubble and forces the air–liquid interface to propagate into a converging fluid-filled gap. Both of these changes reduce the destabilizing viscous effects that drive the fingering instability in a rigid-walled cell. In contrast, capillary effects only play a very minor role in the suppression of the instability.

Viscous fingering with a single fluid

2005 ◽  
Vol 83 (5) ◽  
pp. 551-564 ◽  
Author(s):  
Kristi E Holloway ◽  
John R de Bruyn
Keyword(s):  
Numerical Simulations ◽  
Viscous Fingering ◽  
High Flow ◽  
Cell Width ◽  
Flow Rates ◽  
Viscosity Contrast ◽  
Fingering Instability ◽  
Hele Shaw Cell ◽  
Initial Viscosity

We study fingering that occurs when hot glycerine displaces cooler, more viscous glycerine in a radial Hele-Shaw cell. We find that fingering occurs for a sufficiently large initial viscosity contrast and for sufficiently high flow rates of the displacing fluid. The wavelength of the fingering instability is proportional to the cell width for thin cells, but the ratio of wavelength to cell width decreases for our thickest cell. Similar fingering is seen in numerical simulations of this system.PACS Nos.: 47.54.+r, 68.15.+e, 47.20.–k

scholarly journals Viscous-fingering mechanisms under a peeling elastic sheet

2019 ◽  
Vol 864 ◽  
pp. 1177-1207
Author(s):  
Gunnar G. Peng ◽  
John R. Lister
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Cell Walls ◽  
Viscous Fingering ◽  
Base Flow ◽  
Fingering Instability ◽  
Linear Perturbations ◽  
The Stability ◽  
Rigid Walls ◽  
Hele Shaw Cell

We study the mechanisms affecting the viscous-fingering instability in an elastic-walled Hele-Shaw cell by considering the stability of steady states of unidirectional peeling-by-pulling and peeling-by-bending. We demonstrate that the elasticity of the wall influences the steady base state but has a negligible direct effect on the behaviour of linear perturbations, which thus behave like in the ‘printer’s instability’ with rigid walls. Moreover, the geometry of the cell can be very well approximated as a triangular wedge in the stability analysis. We identify four distinct mechanisms – surface tension acting on the horizontal and the vertical interfacial curvatures, kinematic compression in the longitudinal base flow, and the films deposited on the cell walls – that each contribute to stabilizing the system. The vertical curvature is the dominant stabilizing mechanism for small capillary numbers, but all four mechanisms have a significant effect in a large region of parameter space.

scholarly journals Influence of mineralization and injection flow rate on flow patterns in three-dimensional porous media

2019 ◽  
Vol 21 (27) ◽  
pp. 14605-14611 ◽  
Author(s):  
R. Moosavi ◽  
A. Kumar ◽  
A. De Wit ◽  
M. Schröter
Keyword(s):  
Porous Media ◽  
Flow Field ◽  
Flow Rate ◽  
Three Dimensional ◽  
Flow Patterns ◽  
Low Flow ◽  
Flow Rates ◽  
Injection Flow Rate ◽  
Injection Flow

At low flow rates, the precipitate forming at the miscible interface between two reactive solutions guides the evolution of the flow field.

scholarly journals Improved Gas Chromatographic Analysisof Organophosphorus Pesticides with Pulsed Splitless Injectiony

1996 ◽  
Vol 79 (2) ◽  
pp. 571-578 ◽  
Author(s):  
Philip Wylie ◽  
Katsura Uchiyama
Keyword(s):  
Flow Rate ◽  
Active Sites ◽  
Organophosphorus Pesticides ◽  
Green Bean ◽  
Flow Rates ◽  
Mass Spectral ◽  
Injection Flow ◽  
Splitless Injection ◽  
Peak Areas ◽  
Column Flow Rate

Abstract Gas chromatographic (GC) analysis of 6 organo-phosphorus pesticides (methamidophos, acephate, omethoate, diazinon, dimethoate, and chlorpyrifos) was performed with cool on-column, splitless, and pulsed splitless injections and with nitrogen–phos phorus or mass-selective detection. The pulsed splitless technique uses a high column flow rate during injection to sweep the sample out of the inlet rapidly, reducing analyte loss due to adsorption or thermal decomposition. After injection, the column flow rate is automatically reduced to normal values for chromatographic analysis. Pesticide recoveries for splitless and pulsed splitless injections were determined by comparison of GC peak areas with those obtained with cool on-column injection. With conventional splitless injection at a column flow rate of 5 mL/min, recoveries of acephate, omethoate, and methamidophos were only 57, 63, and 71 %, respectively. Pulsed splitless methods with very fast injection flow rates dramatically improved recoveries, with all 6 pesticides falling in the 97–102% range. Because column flow rates are much less for GC with mass spectral detection (GC/MS), recoveries with splitless injection were lower and improvements with pulsed splitless injection were less dramatic for GC/MS. When splitless injection was used, recoveries of the 6 pesticides spiked into a green bean matrix were better than those of pesticides dissolved in pure solvent, presumably because matrix compounds compete with pesticides for active sites in the inlet. By using pulsed splitless injection of solvent standards with very fast initial column flow rates, systematic analyte losses in the inlet were eliminated, making recoveries of pesticides from solvent and green bean matrix very similar.

Methodology to Investigate the Hydraulic Characteristics of a Water-Powered Piston-Type Proportional Injector Used for Agricultural Chemigation

2018 ◽  
Vol 34 (3) ◽  
pp. 545-553 ◽  
Author(s):  
Pan Tang ◽  
Hong Li ◽  
Zakaria Issaka ◽  
Chao Chen
Keyword(s):  
Flow Rate ◽  
Calculation Model ◽  
Differential Pressure ◽  
Coefficient Of Determination ◽  
Inlet Flow ◽  
Flow Rates ◽  
Injection Flow Rate ◽  
Injection Flow ◽  
Inlet Flow Rate ◽  
Injection Ratio

Abstract. The proportional injector is commonly used in agricultural chemigation due to its relatively high injection ratio. A major challenge with the proportional injector is related to its dependence on differential pressure, which is significantly influenced by changes in the viscosity, and setting injection ratio. A series of experiments were conducted to investigate the influence of differential pressures, solution viscosities, and setting injection ratios on the inlet and injection flow rates of a D25RE2 proportional injector. A mathematical model was developed to represent the hydraulic performance of this proportional injector. Finally, the mathematical model was verified using four different kinds of chemicals (humic acid, urea ammonium nitrate 32% N, fosthiazate, and colza oil). The inlet flow rate increased significantly with increasing differential pressure and decreased with increasing setting injection ratio. Results showed that the highest operating differential pressure should not be greater than 0.15 MPa for the D25RE2 proportional injector. The inlet flow rate gradually decreased with increasing viscosity, and a quadratic function relationship was derived between the inlet flow rate and the viscosity. The injection flow rate decreased with increasing viscosity. However, the viscosity had a slight influence on the injection flow rate when it was lower than 20 mPa·s. Mathematical models for calculating the inlet and injection flow rates with the influence of viscosity were developed, respectively. The coefficient of determination and the root mean square error (RMSE) for inlet flow rate calculation model were 0.8316 and 143.36 kg h-1, respectively. The coefficient of determination and the RMSE for the injection flow rate calculation model were 0.9706 and 0.9520 kg h-1, respectively. The calculating formula of inlet flow rate had a satisfactory accuracy under low differential pressure and high setting injection ratio. The calculating formula of the injection flow rate had a good accuracy, which is useful for calculating the injection flow rate when injected with different kinds of solutions. The average deviations between calculated and experimental injection flow rates with injection ratios of 0.2%, 1.2%, and 2% were obtained as 4.96%, 4.66%, and 4.1% respectively, which indicated that the average deviations decreased with increasing setting injection ratio. Results from this study are useful for both designers and users to effectively manage agricultural chemigation system with the proportional injector. Keywords: Agriculture, Chemigation, Proportional injector, Hydraulic performance.

Flow Rate-Dependent Skin in Water Disposal Injection Well

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Ibrahim M. Mohamed ◽  
Gareth I. Block ◽  
Omar A. Abou-Sayed ◽  
Salaheldin M. Elkatatny ◽  
Ahmed S. Abou-Sayed
Keyword(s):  
Flow Rate ◽  
Hydraulic Fracture ◽  
Produced Water ◽  
Gas Production ◽  
Gas Content ◽  
Well Test ◽  
Drilling Mud ◽  
Flow Rates ◽  
Skin Factor ◽  
Injection Flow

Reinjection is one of the most important methods to dispose fluid associated with oil and natural gas production. Disposed fluids include produced water, hydraulic fracture flow back fluids, and drilling mud fluids. Several formation damage mechanisms are associated with the injection including damage due to filter cake formed at the formation face, bacteria activity, fluid incompatibility, free gas content, and clay activation. Fractured injection is typically preferred over matrix injection because a hydraulic fracture will enhance the well injectivity and extend the well life. In a given formation, the fracture dimensions change with different injection flow rates due to the change in injection pressures. Also, for a given flow rate, the skin factor varies with time due to the fracture propagation. In this study, well test and injection history data of a class II disposal well in south Texas were used to develop an equation that correlates the skin factor to the injection flow rate and injection time. The results show that the skin factor decreases with time logarithmically as the fracture propagates. At higher injection flow rates, the skin factor achieved is lower due to the larger fracture dimensions that are developed at higher injection flow rates. The equations developed in this study can be applied for any water injector after calibrating the required coefficients using injection step rate test (SRT) data.

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