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Schematic representation of general behaviour of jet flow with miscible fluids. The blue region indicates the trapped ambient fluid during the vortex roll up process
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In this work, we perform a series of experiments to study a buoyant miscible jet flow wherein a heavy fluid is injected vertically downward into a more viscous light ambient fluid. The injection flow occurs in a large rectangular tank, representing an unbounded environment. Using non-intrusive experimental methods, including high-speed camera imagi...
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Citations
... After the breakdown position, the jet mixes with the ambient fluid and the jet diameter progressively grows, by moving away from the source. The distance between the nozzle exit and the breakdown position is known as the laminar length [11,21]. By approaching the end-wall, i.e. the impingement region, the jet flow direction gradually is changed where it decelerates and accelerates in the longitudinal and radial directions, respectively. ...
... Injection of a fluid into an ambient fluid of different density typically leads to the formation of a buoyant jet [1]. A positively (negatively) buoyant jet is typically generated when the momentum and buoyancy fluxes act in the same (opposite) direction [2,3]. Buoyant jets are a frequent occurrence both in the natural world and in industry. ...
... To understand buoyant jet behaviours, it is essential to examine jet characteristics, which as described in recent studies [13][14][15][16], can be classified into two categories based on their temporal behaviour: unsteady and quasi-steady. As an example, the jet penetration length, representing the distance that the jet has traveled at a given moment in time, serves as a model for the unsteady and quasi-steady characteristics in positively and negatively buoyant jets, respectively [2,16,17]. ...
... In the current study, we investigate the dynamics of our buoyant jets for a wide range of dimensionless numbers, i.e., 8 × 10 2 ≲ Re ≲ 14 × 10 3 and 10 2 ≲ Ar ≲ 6 × 10 5 . Furthermore, to extend the applicability of our results across diverse conditions and scales, we make all lengths, times, and velocities dimensionless using characteristic parameters obtained by balancing the source momentum and volume fluxes [2]. We achieve this by employingD n ,D n V0 , andV 0 to make lengths, times, and velocities dimensionless, respectively. ...
We study positively buoyant miscible jets through high-speed imaging and planar laser-induced fluorescence methods, and we rely on supervised machine learning techniques to predict jet characteristics. These include, in particular, predictions to the laminar length and spread angle, over a wide range of Reynolds and Archimedes numbers. To make these predictions, we use linear regression, support vector regression, random forests, K-nearest neighbour, and artificial neural network algorithms. We evaluate the performance of the aforementioned models using various standard metrics, finding that the random forest algorithm is the best for predicting our jet characteristics. We also discover that this algorithm outperforms a recent empirical correlation, resulting in a significant increase in accuracy, especially for predicting the laminar length.
... In addition to the above-mentioned studies, there exists also a range of relevant studies on the effects of a viscosity ratio on injections and displacement flows. [28][29][30][31][32][33][34][35][36][37] When a more-viscous fluid is injected into a less-viscous fluid in narrow channels, a well-known interfacial instability, called the viscous fingering or Saffman-Taylor instability, occurs, with different fingering patterns depending on the flow, fluids, and geometry parameters. [38][39][40] The finger formation is primarily driven by the viscosity contrast between two fluids and its growth, resulting in an unstable flow. ...
... Among possible approaches to quantify the quality of mixing between the fluids in different conditions, let us rely on a mixing index criterion (using 2D camera images) defined as follows: 30,108 ...
This paper studies the buoyant miscible injection of a high-viscosity fluid in a pipe filled with a low-viscosity fluid. The injection is carried out via an eccentric inner pipe inside an inclined closed-end outer pipe. A heavy fluid is injected into a light fluid at a constant density difference. Although the density difference is small, the buoyancy force, quantified via the Archimedes number ( Ar), remains large. Our research relies on non-intrusive experimental methods, via a mix of high-speed camera imaging, ultrasound Doppler velocimetry, planar laser induced fluorescence, and particle image velocimetry techniques, accompanied by complementary numerical simulations. The effects of the viscosity ratio ( M), the Reynolds number ( Re) and the inclination angle ( β) are analyzed on the injection/placement flow dynamics. Accordingly, a detailed description of the flow is presented, in terms of the concentration and velocity fields, the average front velocity of the heavy fluid ( Vf), the mixing index, and the flow regimes. The findings reveal that V f is mainly governed by an inertial-buoyant balance, allowing us to develop a correlation for V f versus Ar, M, Re and β. The results also show that a heavy fluid front separation occurs when M is small, β is large ( i.e. near-vertical inclinations), and Re is large. This observation permits us to classify the flows into separation and non-separation regimes, in a dimensionless group plane based on a combination of the aforementioned dimensionless numbers.
... Hassanzadeh et al. conducted an experimental investigation of a buoyant, vertical, miscible jet flow, analyzing various quasi-steady features including laminar length, jet radius, spread angle, virtual origin, velocity profiles, and energy dissipation [6]. In a separate study of vertical jets, they identified three flow regimes -a jellyfish regime, a funnel regime, and a cone regime -and examined the impact of a viscosity ratio (m) on the flow behaviors of their buoyant jets [16]. ...
... In addition to the above-mentioned studies, there exists also a range of relevant studies on the effects of a viscosity ratio on injections and displacement flows. [28][29][30][31][32][33][34][35][36][37] When a more-viscous fluid is injected into a less-viscous fluid in narrow channels, a well-known interfacial instability, called the viscous fingering or Saffman-Taylor instability, occurs, with different fingering patterns depending on the flow, fluids, and geometry parameters. [38][39][40] The finger formation is primarily driven by the viscosity contrast between two fluids and its growth, resulting in an unstable flow. ...
... Among possible approaches to quantify the quality of mixing between the fluids in different conditions, let us rely on a mixing index criterion (using 2D camera images) defined as follows: 30,108 ...
We report experimental results on the injection of a heavy fluid into a light one in a closed-end pipe, inclined at intermediate angles. The injection of the heavy fluid is made using an inner duct with a smaller diameter than that of the pipe in which the light fluid is placed. The fluids used are miscible and Newtonian, and they have the same viscosity. Our observation shows that, during the removal/replacement of the light fluid by the heavy fluid, at least four distinct flow stages can be identified: (i) initial buoyant jet of the heavy fluid, (ii) development of a mixing region, (iii) slumping flow of the heavy fluid, and (iv) heavy fluid front reaching the pipe end and returning toward the mixing region. Using high-speed camera images along with the ultrasound Doppler velocimetry and laser induced fluorescence data, the flow characteristics in these flow stages are quantified, and they are described in detail vs the dimensionless groups that govern the flow dynamics, namely, the Froude number (Fr), the Reynolds number (Re), the Archimedes number (Ar), and the pipe inclination angle (β). While our findings are of fundamental importance, they can also be used to provide a fluid mechanics understanding of the dump bailing method in the plug and abandonment (P&A) of oil and gas wells.
We study the injection flow of a heavy viscoplastic fluid into a light Newtonian fluid, via modelling and experiments. The injection is carried out downward, via an eccentric inner pipe inside a vertical closed-end outer pipe. This configuration results in a core viscoplastic fluid surrounded by an annular Newtonian fluid. The flow is structured and mixing is negligible. As the injection rate increases in a typical experiment, we observe three distinct flow regimes, associated with the core fluid behaviour, namely the breakup, coiling and buckling (bulging) regimes. In the breakup regime, the core fluid is yielded due to the extension caused by buoyancy, while in the buckling regime the yielding occurs due to the compression promoted by the pressure and the interfacial shear stress applied by the upward flow of the annular fluid. For the coiling regime, the core fluid remains largely unyielded until it exhibits a coiling behaviour. We develop a lubrication approximation model, using the Herschel–Bulkley constitutive equation, with dimensionless flow parameters including the Bingham number, the power-law index, the buoyancy number, the viscosity ratio, the diameter ratio, the eccentricity and the aspect ratio. Based on a reasonable prediction to the yielding onset, the model allows us to classify the flow regimes versus an elegant combination of the dimensionless numbers.
We present an experimental study of buoyant displacement flows in vertical narrow centric/eccentric annular configurations, representing the oilfield primary cementing process, from a fluid mechanics perspective. In this study, we consider the reverse circulation cementing case, i.e. the case in which the cementing fluids are pumped down from the surface into the annulus and the in-situ fluids are taken through the casing or tubing. The fluid proxies used to represent the industrial fluids are miscible, with different rheological behaviours, i.e. salt-water (Newtonian), Xanthan (shear-thinning) and Carbopol (viscoplastic) solutions, and they have various density contrasts. Our dimensional analysis and systematic simplifications allow us to describe the flow using five dimensionless numbers: m (viscosity ratio), Fr (densimetric Froude number, quantifying effects of the density difference or buoyancy), Re (Reynolds number, quantifying the effects of the imposed flow rate), e (eccentricity) and f (reciprocation frequency). We examine the effects of the aforementioned parameters in stationary and moving annuli, wherein we change the frequency of the inner pipe reciprocation motion, over a fixed amplitude. Using mainly high-speed camera imaging techniques, we analyze displacement flow patterns and mixing between the fluids. We show that the density-stable or density-unstable configurations, the non-Newtonian effects, and the annulus eccentricity exert a significant impact on the displacement flow features, which we explain through a detailed comparison between Newtonian and non-Newtonian displacements. In addition, we demonstrate that an interplay between the yield stress and the annulus motion can remarkably change the displacement flow behaviour, particularly the wall residual layer thicknesses of the displaced fluid. Finally, we quantify the effects of different flow parameters on the leading front velocity, representing the displacement efficiency in the reverse circulation cementing.
