Derivation of an Enhanced Pressure Differential Expression, for a Penetration Injection with Back Pressure

Prashant Unnikrishnan Nair

In real-world water injection applications, an in-line injection facilitates a pressure differential that boosts the current flow. A pressure differential created by the injection of a pressurized flow into the mainline of flow is derived from the momentum transfer equation. Heat loss is disregarded, and such empirical equations provide a ballpark value to these pressure differentials during the injection. In industrial applications, injection of the fluid is done on the surface, due to weld and other constraints where losses due to friction and eddy current formation are imminent. On the other hand, penetration injection provides a far more augmented pressure differential that has a polynomial impact based on the mainline flow rate and the injection flow rate. This paper aims to derive an accurate representation of the pressure differential values obtained from a penetration injection through experimentation and compare it against a surface injection or empirical calculation. The paper concludes by indicating that the penetration injection augments the pressure differential with a new empirical formula for the derived pressure differential as a polynomial equation for this apparatus and can be extended across different sizes of the mainline and injection line diameters. This work provides a precise formula that can be used to derive pressure differential and estimate the flow and pressure rates. The formula also provides a platform for further utility in the fracturing operations where fracture flow from the well upstream presents multiple injection fractures to the mainline through fracture pores.

1999 ◽  
Vol 121 (4) ◽  
pp. 751-755 ◽  
E. de Villiers ◽  
D. G. Kro¨ger

The rate of heat, mass, and momentum transfer in the rain zone of three counterflow cooling tower geometries is analyzed using simplifying assumptions and numerical integration. The objective of the analysis is to generate equations for use in a one-dimensional mathematical cooling tower performance evaluations. Droplet deformation is taken into account and momentum transfer is calculated from the air flow’s mechanical energy loss, caused by air-droplet interaction. A comparison of dimensionless semi-empirical equations and experimental data demonstrates the method’s capability to predict the pressure drop in a counterflow rain zone.

2009 ◽  
Vol 1243 ◽  
J. Solórzano-López ◽  
R. Zenit ◽  
C. González-Rivera ◽  
M. A. Ramírez-Argáez

ABSTRACTGas jets play a key role in several steelmaking processes as in the Basic Oxygen Furnace (BOF) or in the Electric Arc Furnace (EAF). They improve heat, mass and momentum transfer in the liquid bath, improve mixing of chemical species and govern the formation of foaming slag in EAF. In this work experimental measurements are performed to determine the dimensions of the cavity formed at the liquid free surface when a gas jet impinges on it as well as liquid velocity vector maps measured in the zone affected by the gas jet. Cavities are measured using a high speed camera while the vector maps are determined using a Particle Image Velocimetry (PIV) technique. Both velocities and cavities are determined as a function of the main process variables: gas flow rate, distance from the nozzle to the free surface and lance angle. Cavity dimensions (depth and diameter) are statistically treated as a function of the process variables and also as a function of the adequate dimensionless numbers that govern these phenomena. It is found that Froude number and Weber number control the depression geometry.

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Yohan Cha ◽  
Tae-Min Oh ◽  
Gye-Chun Cho

Abrasive waterjets are being increasingly used in civil engineering for rock and concrete cutting, particularly for the demolition or repair of old structures. The energy of an abrasive waterjet is primarily provided by the accelerated abrasive. The momentum transfer during mixing and acceleration determines the abrasive velocity, which affects the cutting performance. Meanwhile, the geometry of the focus at which mixing occurs influences the momentum transfer efficiency. In this study, the effects of the focus geometry on the optimum abrasive flow rate (AFR) and momentum transfer characteristics in hard rock cutting were investigated. Experiments were conducted using granite specimens to test the AFR under different focus geometry conditions such as diameter and length. The results show that the focus geometry significantly affects the maximum cutting depth and optimum AFR. The maximum cutting energy was analyzed based on the cutting efficiency of a single abrasive particle. In addition, the momentum transfer parameter (MTP) was evaluated from the empirical relationship between the maximum energy and the cutting depth for granitic rocks. Accordingly, a model for estimating the MTP based on the AFR was developed. It is expected that the results of this study can be employed for the optimization of waterjet rock cutting.

2017 ◽  
Vol 11 (1) ◽  
pp. 38-46 ◽  
Czesław Janusz Jermak

Abstract In the paper, the flow-through phenomena in the air gauge are under discussion form the thermodynamic and gasodynamic perspective. The main elements of the cascade are considered the inlet nozzle (restriction), measuring chamber and the measuring nozzle with the measuring slot (displacement between the nozzle head and measured surface). The purpose of the analysis was to point out the impact on the metrological characteristics of the air gauge. In particular, attention was paid to the airflow through the measuring slot. Here, the complex phenomena take place, among others the supersonic areas and a “bubble ring,” which cause discontinuity and hysteresis in the static characteristic. On the other hand, the air stream expansion after the restriction (inlet nozzle) is observed in the measuring chamber. The point of the above discussion was to work out some recommendation on the nozzles geometry and the localization of the back-pressure measuring point in the chamber.

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
I. I. Esen

Hydraulic performance of an airlift pump having a rectangular cross-section 20 mm × 80 mm was investigated through an experimental program. The pump was operated at six different submergence ratios and the liquid flow rate was measured at various flowrates of air injected. The effectiveness of the pump, defined as the ratio of the mass of liquid pumped to the mass of air injected, was determined as a function of the mass of air injected for different submergence ratios. Results obtained were compared with those for circular airlift pumps using an analytical model for circular pumps. Effectiveness of the rectangular airlift pump was observed to be comparable to that of the circular pumps. Hydraulic performance of the rectangular airlift pump investigated was then described by a set of semilogarithmic empirical equations.

Hanseup Kim ◽  
Aaron A. Astle ◽  
Luis P. Bernal ◽  
Khalil Najafi ◽  
Peter D. Washabaugh

This paper reports experimental characterization of directional gas pumping generated by MEMS-fabricated checkerboard-type electrostatic microvalves. It is found that the oscillatory motion of the checkerboard microvalve membrane provides both the pumping and valve functions of a pump, namely: 1) to cause the volume displacement and, thus, compression and transfer of gas, and 2) to direct gas flow in one direction by closing and opening air paths in the proper sequence. Here, we describe the microvalve-only design, and report the pumping performance producing a maximum flow rate of 1.8 sccm and a maximum pressure differential of 3.0 kPa for five microvalves driven simultaneously with a sinusoidal signal of ± 100V amplitude at 5.5 kHz.

Yumin Xiao ◽  
R. S. Amano

In this paper the study of the flows over shrouded turbine blades with staggered-seals is presented by computing the three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations along with a compressible non-linear k-ε turbulence model. The swirl of the blade is coupled into the calculation. A multi-zone technique is used to generate the grids in the complex flow channel. The calculation results show that the leakage flow rate in the seal-channel is dominated by the pressure difference. It was also observed that the circumferential momentum transfer in the channel is very slow in the region in front of the seal tooth. The major effect of the rotating blade is the increase of local pressure distribution along the shrouded tip clearance path. However, the swirl motion of the blade tip does not significantly change the flow pattern in the axial-radial plane.

Tomiichi Hasegawa ◽  
Akiomi Ushida ◽  
Hiroshige Uchiyama ◽  
Takatsne Narumi

Flow rates under some pressure differentials were measured for the flow of water through micro-orifices. It was found that the flow rate decreases as the time has elapsed after inception of the flow under a constant pressure differential and that the decrease in flow rates is larger for city water than for pure water, and the gold orifice provides a less decrease with time in flow rates than the nickel orifice, although the flow rate at the incipient stage of the experimental run is lower in the gold orifice than in the nickel orifice.

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