A Review of Drag Coefficient Models in Gas‐Liquid Two‐Phase Flow

Chen, Yanling; Wang, Liang; Chang, Haijun; Zhang, Qunwei

doi:10.1002/cben.202200034

Cited by 11 publications

(8 citation statements)

References 84 publications

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“…The modified annular velocity (

), as defined in Equation (9), depends on the weight and flow rate of the drilling fluid, the size of the drilled hole, the outer diameter of the drill pipe, the rate of penetration, the rotation of the drill string, the plastic viscosity, the yield point, the viscometer readings at 600, 300, 3, and 6 rpm, the wellbore inclination, and the azimuthal directions [ 63 ].

where

is the cutting density, which can be obtained as

according to [ 47 , 64 ]; α is the borehole angle (degrees); β is the azimuth angle (degrees);

is the modified cutting diameter, which can be obtained as follows:

, in accordance with [ 60 ], where the specification of the mud motor, such as the revolution per gallon ratio ( x ) and GPM of the mud pump flow rate, can be calculated while determining

; and

is the annular velocity across the drill pipe and can be calculated as follows:

, in accordance with [ 5 , 8 , 60 ].…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A Developed Robust Model and Artificial Intelligence Techniques to Predict Drilling Fluid Density and Equivalent Circulation Density in Real Time

Al-Rubaii,

Al-Shargabi,

Aldahlawi

et al. 2023

Sensors

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When drilling deep wells, it is important to regulate the formation pressure and prevent kicks. This is achieved by controlling the equivalent circulation density (ECD), which becomes crucial in high-pressure and high-temperature wells. ECD is particularly important in formations where the pore pressure and fracture pressure are close to each other (narrow windows). However, the current methods for measuring ECD using downhole sensors can be expensive and limited by operational constraints such as high pressure and temperature. Therefore, to overcome this challenge, two novel models named ECDeffc.m and MWeffc.m were developed to predict ECD and mud weight (MW) from surface-drilling parameters, including standpipe pressure, rate of penetration, drill string rotation, and mud properties. In addition, by utilizing an artificial neural network (ANN) and a support vector machine (SVM), ECD was estimated with a correlation coefficient of 0.9947 and an average absolute percentage error of 0.23%. Meanwhile, a decision tree (DT) was employed to estimate MW with a correlation coefficient of 0.9353 and an average absolute percentage error of 1.66%. The two novel models were compared with artificial intelligence (AI) techniques to evaluate the developed models. The results proved that the two novel models were more accurate with the value obtained from pressure-while-drilling (PWD) tools. These models can be utilized during well design and while drilling operations are in progress to evaluate and monitor the appropriate mud weight and equivalent circulation density to save time and money, by eliminating the need for expensive downhole equipment and commercial software.

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“…The modified annular velocity (

where

is the cutting density, which can be obtained as

according to [ 47 , 64 ]; α is the borehole angle (degrees); β is the azimuth angle (degrees);

is the modified cutting diameter, which can be obtained as follows:

, in accordance with [ 60 ], where the specification of the mud motor, such as the revolution per gallon ratio ( x ) and GPM of the mud pump flow rate, can be calculated while determining

; and

is the annular velocity across the drill pipe and can be calculated as follows:

, in accordance with [ 5 , 8 , 60 ].…”

Section: Methodsmentioning

confidence: 99%

“…where Wc is the cutting density, which can be obtained as Wc = MW e f f CCA + MW e f f + (1 − CCA)MW e f f according to [47,64]; α is the borehole angle (degrees); β is the azimuth angle (degrees); d cm is the modified cutting diameter, which can be obtained as follows:…”

Section: Mathematical Development Of the Model For The Ecd Effcm And ...mentioning

confidence: 99%

A Developed Robust Model and Artificial Intelligence Techniques to Predict Drilling Fluid Density and Equivalent Circulation Density in Real Time

Al-Rubaii,

Al-Shargabi,

Aldahlawi

et al. 2023

Sensors

View full text Add to dashboard Cite

show abstract

“…In Equations ( 19) and ( 20), d cm is the modified cutting diameter (inches), Wc is the cuttings density (lb/cf) according to [17,48], M e f f is the effective viscosity of the drilling fluid (cP), and Mapp is the apparent viscosity of the drilling fluid (cP), which can be obtained from Equations ( 22)-( 25), respectively.…”

Section: Ti = 𝑅𝐹 • 𝐴𝐹 • 𝑀𝑊mentioning

confidence: 99%

A Novel Efficient Borehole Cleaning Model for Optimizing Drilling Performance in Real Time

et al. 2023

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The drilling industry has evolved significantly over the years, with new technologies making the process more efficient and effective. One of the most crucial issues of drilling is borehole cleaning, which entails removing drill cuttings and keeping the borehole clean. Inadequate borehole cleaning can lead to drilling problems such as stuck pipes, poor cementing, and formation damage. Real-time drilling evaluation has seen significant improvements, allowing drilling engineers to monitor the drilling process and make adjustments accordingly. This paper introduces a novel real-time borehole cleaning performance evaluation model based on the transport index (TIm). The novel TIm model offers a real-time indication of borehole cleaning efficiency. The novel model was field-tested and validated for three wells, demonstrating its ability to determine borehole cleaning efficiency in typical drilling operations. Using TIm in Well-A led to a 56% increase in the rate of penetration (ROP) and a 44% reduction in torque. Moreover, the efficient borehole cleaning obtained through the use of TIm played a significant role in improving drilling efficiency and preventing stuck pipes incidents. The TIm model was also able to identify borehole cleaning efficiency during a stuck pipe issue, highlighting its potential use as a tool for optimizing drilling performance.

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“…and transportation using fluidized beds [8][9][10][11][12]. Scientific researchers have also investigated the flotation [13] and sedimentation of particles immersed in non-Newtonian fluids using relative experimental and/or numerical studies of their terminal velocities [14,15]. For particles of sand and other mineral aggregates found during sedimentation, terminal velocity was recently measured and studied by the authors of [16,17]; for larger particles, the recent determination of terminal velocity by the authors of [18] is also worthy of note.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Particle Terminal Velocity for Improved Design of Clarifiers, Thickeners and Flotation Devices for Wastewater Treatment

Friso

2023

Clean Technol.

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The prediction of the terminal velocity of a single spherical particle is essential to realize mathematical modeling useful for the design and adjustment of separators used in wastewater treatment. For non-spherical and non-single particles, terminal velocity can be traced back to that of single spheres using coefficients and Kynch’s theory, respectively. Because separation processes can involve small or large particles and can be carried out using gravity, as with clarifiers/thickeners, or by centrifugation in centrifuges where the acceleration can exceed 10,000× g, the Reynolds number of the particle can be highly variable, ranging from 0.1 to 200,000. The terminal velocity depends on the drag coefficient, which depends, in turn, on the Reynolds number containing the terminal velocity. Because of this, to find the terminal velocity formula, it is preferable to look first for a relationship between the drag coefficient and the Archimedes number which does not contain the terminal velocity. Formulas already exist expressing the relationship between the drag coefficient and the Archimedes number, from which the relationship between the terminal velocity and the Archimedes number may be derived. To improve the accuracy obtained by these formulas, a new relationship was developed in this study, using dimensional analysis, which is valid for Reynolds number values between 0.1 and 200,000. The resulting mean relative difference, compared to the experimental standard drag curve, was only 1.44%. This formula was developed using the logarithms of dimensionless numbers, and the unprecedented accuracy obtained with this method suggested that an equally accurate formula for the drag coefficient could also be obtained with respect to the Reynolds number. Again, the resulting level of accuracy was unprecedentedly high, with a mean relative difference of 1.77% for Reynolds number values between 0.1 and 200,000.

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A Review of Drag Coefficient Models in Gas‐Liquid Two‐Phase Flow

Cited by 11 publications

References 84 publications

A Developed Robust Model and Artificial Intelligence Techniques to Predict Drilling Fluid Density and Equivalent Circulation Density in Real Time

A Developed Robust Model and Artificial Intelligence Techniques to Predict Drilling Fluid Density and Equivalent Circulation Density in Real Time

A Novel Efficient Borehole Cleaning Model for Optimizing Drilling Performance in Real Time

Mathematical Modeling of Particle Terminal Velocity for Improved Design of Clarifiers, Thickeners and Flotation Devices for Wastewater Treatment

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