Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 2962-2983 ◽  
Author(s):  
Zhengming Xu ◽  
Xianzhi Song ◽  
Zhaopeng Zhu
Keyword(s):  
Drag Force ◽  
Shear Viscosity ◽  
Settling Velocity ◽  
Particle Diameter ◽  
Viscoelastic Fluids ◽  
Proppant Transport ◽  
Fluid Elasticity ◽  
Fracturing Fluids ◽  
Proposed Model ◽  
Velocity Equation

Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an elastic drag force. Based on the experimental data from the available literature, it is concluded that the elastic drag force is a function of the fluid elasticity, particle diameter, particle terminal settling velocity, and density difference between the fluid and particle. The formula for the elastic drag force is determined on the basis of the force analysis, and a relationship between the elastic drag coefficient and particle Reynolds number (Re) is developed. An explicit equation that directly predicts the terminal settling velocity in viscoelastic fluids is determined by correlating the dimensionless particle diameter and Re. To validate the proposed model, a total of 108 settling experiments in viscoelastic fluids are conducted. The absolute percentage error (APE) between the predicted and measured terminal settling velocities is 15.26%, which indicates that the proposed explicit terminal settling velocity equation can provide satisfactory prediction accuracy of the terminal settling velocity for particles in viscoelastic fluids. Furthermore, an illustrative example is provided to show that the proposed model can be used to calculate the required fluid elasticity to obtain the desired terminal settling velocity when the fluid shear viscosity is fixed. The proposed models are valid with a consistency index range of approximately 0.16 to 1.2 Pa⋅sn, flow behavior index range of approximately 0.282 to 0.579, an Re range of approximately 0.005 to 30, and a fluid relaxation time range of approximately 0.183 to 110 seconds. This study can help operators choose proper drilling/fracturing fluids to enhance the cuttings/proppant transport and maximize drilling/fracturing performance.

Settling Velocity of Particles in Viscoelastic Fluids: A Comparison of the Shear-Viscosity and Elasticity Effects

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1689-1705 ◽  
Author(s):  
Sumanth Kumar Arnipally ◽  
Ergun Kuru
Keyword(s):  
Elastic Properties ◽  
Shear Viscosity ◽  
Settling Velocity ◽  
Particle Diameter ◽  
Viscoelastic Fluids ◽  
Spherical Particles ◽  
High Shear ◽  
Fluid Shear ◽  
Particle Settling ◽  
Fluid Elasticity

Summary The objective of this paper is to determine how fluid shear viscosity and elasticity might influence the particle-settling velocity, and even more so to answer the question of which one of these two rheological properties is more dominant in controlling the particle-settling velocity when viscoelastic drilling fluids are used. The settling velocities of spherical particles (diameters: 1.18, 1.5, 2, and 3 mm) in partially hydrolyzed polyacrylamide (HPAM) polymer fluids were measured using the particle-image-shadow graph (PIS) technique. Two sets of test fluids were formulated by mixing three different grades of HPAM (molecular weights of 500,000, 8 million, and 20 million g/g mol) at polymer concentrations of 0.09, 0.05, and 0.03 wt%. The shear-viscosity and elasticity characteristics of test fluids were determined by performing shear-viscosity and frequency-sweep oscillatory measurements, respectively. The first set of fluids had almost identical shear-viscosity characteristics while showing significantly different elastic properties (quantified in terms of relaxation time). The second set of fluids had similar elastic properties but different shear-viscosity characteristics. In addition, the effect of the particle size on the settling velocities in these test fluids was also investigated. The experimentally measured settling velocities were compared with the values calculated from the Shah et al. (2007) model developed for predicting the settling velocity of spherical particles in power-law (viscoinelastic) fluids as well as the values calculated from the Malhotra and Sharma (2012) correlation developed for settling velocity in shear-thinning viscoelastic fluids in unconfined media. Experimental results showed the following: When the fluids with similar shear-viscosity profiles were used, the settling velocity of spherical particles decreased significantly with the increasing fluid elasticity. The settling-velocity values can be 14 to 50 times overestimated if the effect of the elasticity is not considered. At constant elasticity, the settling velocity of spherical particles also decreased significantly when the fluid shear viscosity was increased. The spherical particle-settling velocity increased pronouncedly as particle diameter increased from 1.18 to 3 mm. However, the magnitude of the increase in settling velocity with the increasing particle diameter is less for the samples with higher elasticity and similar shear-viscosity characteristics. The fluid shear viscosity and the elasticity both seem to have significant effect on the particle-settling velocity. However, from the field operational point of view, fluids with high shear-viscosity values are not always practical to use because the high shear viscosity increases parasitic pressure losses and potentially has a negative effect on the drilling rate. Hence, in such cases increasing the fluid elasticity can help to reduce the particle-settling velocity even at lower shear-viscosity values. By conducting experiments under controlled conditions, we were able to quantify the individual effects of fluid shear viscosity and elasticity on the particle-settling velocity for the first time in drilling literature.

Experimental Investigation of Flow Field Past a Spherical Particle Settling in Viscoelastic Fluids Using Particle Image Velocimetry Technique

2018 ◽  
Author(s):  
Sumanth Kumar Arnipally ◽  
Majid Bizhani ◽  
Ergun Kuru
Keyword(s):  
Flow Field ◽  
Shear Viscosity ◽  
Particle Image ◽  
Settling Velocity ◽  
Viscoelastic Fluids ◽  
Particle Settling ◽  
Settling Particle ◽  
Fluid Elasticity ◽  
Piv Technique ◽  
Direction Opposite

Experimental investigation of flow field past a spherical particle settling in viscoelastic fluids using particle image shadowgraphy techniques studies have shown that the settling velocity of particles in viscoelastic fluids decreased significantly with the increasing elasticity of the fluids. However, our understanding of how and why the change in fluid elasticity influences the particle settling velocity are not yet fully developed. An experimental study, therefore, has been conducted to understand the reasons behind why the settling velocity of the particles decrease with the increasing fluid elasticity. The main objectives were: (i) to investigate the fluid flow field behind the settling particle by using particle image velocity (PIV) technique; (ii) to understand the changes caused by the elasticity of the fluid on the flow field past the settling particle; (iii) more specifically, to determine how the fluid velocity profile and the resultant drag forces acting on the settling particle change with the increasing fluid elasticity. Two different viscoelastic fluids were formulated by mixing 3 grades of HPAM polymer (MWs: 500,000; 8,000,000; 20,000,000; concentrations: 0.09% and 0.1%wt). The fluids were designed to have almost identical shear viscosity but significantly different elastic properties. The shear viscosity and elasticity of the fluids were determined by performing shear viscosity and frequency sweep oscillatory measurements, respectively. The settling velocities of the spherical particles in viscoelastic polymer fluids were measured by using particle image shadowgraph technique. The fluid flow field behind the settling particle was determined by using the PIV technique. Results of the PIV measurements demonstrated that negative wakes were present in viscoelastic fluids. The stagnation point (i.e. the point where the velocity becomes zero and above that the fluid starts moving in the direction opposite to the particle movement) was closer to the particle settling in the higher elasticity fluid than that in the lower elasticity fluid. The velocity of the fluid in the recirculation region was higher for the flow of the fluid with higher elasticity. The presence of negative wakes having fast moving fluid in the reverse direction near the settling particle possibly creates an additional drag force (acting on the particle in the direction opposite the particle movement), which would eventually slow down the settling particle. Knowledge of the settling behavior of particles is indispensable to design and optimize numerous industrial operations such as cuttings transport in oil and gas well drilling and proppant transport in hydraulic fracturing. In this study, by conducting experiments under controlled conditions, we were able to show how the change in fluid elasticity influenced the particle settling velocity. The results from this fundamental study can be used for development of optimum drilling and fracturing fluid formulations for effective transport of cuttings and proppants.

Proppant Settling Correlations for Non-Newtonian Fluids Under Static and Dynamic Conditions

1982 ◽  
Vol 22 (02) ◽  
pp. 164-170 ◽  
Author(s):  
Subhash N. Shah
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Particle Motion ◽  
Settling Velocity ◽  
Fluid Model ◽  
Reynolds Numbers ◽  
Newtonian Fluids ◽  
Velocity Data ◽  
Proppant Transport ◽  
Fracturing Fluids

Abstract This paper presents a new approach for analysis of proppant sealing data in non-Newtonian pseudoplastic fracturing fluids and develops drag coefficient correlations as a function of fluid model parameter n', Results of experiments with these fluids under static as well as dynamic conditions are discussed. A wide range of n' and particle Reynolds number is investigated. It is shown that at low-particle Reynolds numbers the fluid model parameter n' has a significant effect on proppant settling velocity. This effect diminishes at higher particle Reynolds numbers. The dynamic settling velocity data agree reasonably well with the correlations developed from static velocity data. Further, experimental results of earlier investigations agree well with the correlations of this study. Introduction Many examples of flow around submerged objects appear in engineering work. In the oilfield industry, one example is particle or proppant transport in a fracture during hydraulic fracturing. Hydraulic fracturing has been in use commercially for 30 years. The formations are fractured hydraulically by pumping a slurry of viscous fracturing fluid and proppant at high pressures. The purpose of the proppant is to hold the fracture open at the end of the treatment. The production increase resulting from the treatment depends on fracture conductivity and final proppant distribution. Knowledge of settling velocity of a single particle in the fracture and streamlines around the particle is of great value in understanding the complex transport process leading to a particular proppant distribution in the fracture. A thorough understanding of proppant transpose would help design better fracturing treatments. The purpose of this investigation is two fold:to gather experimental data of proppant settling velocity in several non-Newtonian fracturing fluids, andto develop correlations between drag coefficient and particle Reynolds number. These correlations later can be used to predict the settling velocity of a particular particle in a non-Newtonian fracturing fluid of known rheological properties. Experience has shown that most fracturing fluids exhibit highly non-Newtonian fluid characteristics. They may possess completely different properties under shear than when at rest. For simplicity, most of the studies reported in the literature are undertaken by dropping proppant in a stagnant fluid. In the actual fracturing process, however, the proppant is settling while fluid is moving in the fracture. Thus, to validate the correlations derived from the settling velocity data in a stagnant fluid, some dynamic experiments also are conducted. Literature Review The subject of particle motion in Newtonian fluids has been studied extensively by many investigators. In contrast, very little has been accomplished in the case of particle motion in non-Newtonian fluids, particularly on proppant transport in the fracture. Most recently, a preliminary work on dynamic proppant transport in fracturing gels has been reported by Hannah and Harrington. Experiments were conducted with a concentric cylinder tester to measure the fall rate of proppant in non-Newtonian fracturing gels. The test device used was similar to one reported previously by Novotny. Their experimental data did not agree with the theoretical predictions, and no explanation has been given for the discrepancy. Later, using a similar tester, Harrington et al. measured the settling rate of proppant in cross-linked fracturing gels. SPEJ P. 164^

Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development

2021 ◽  
Author(s):  
Silin Jing ◽  
Xianzhi Song ◽  
Zhaopeng Zhu ◽  
Buwen Yu ◽  
Shiming Duan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Volume Concentration ◽  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Newtonian Fluids ◽  
Spherical Particles ◽  
Bubble Volume ◽  
Particle Reynolds Number

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

A visualization study of proppant transport in foam fracturing fluids

2018 ◽  
Vol 52 ◽  
pp. 235-247 ◽  
Author(s):  
Songyang Tong ◽  
Robin Singh ◽  
Kishore K. Mohanty
Keyword(s):  
Proppant Transport ◽  
Fracturing Fluids

A Study of Particle Settling in Non-Newtonian Fluids—Part I: A New Method for the Study of Particle Settling in Drilling and Fracturing Fluids

1994 ◽  
Vol 116 (1) ◽  
pp. 10-15 ◽  
Author(s):  
L. Jin ◽  
M. E. Chenevert
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Force Measurement ◽  
Newtonian Fluids ◽  
Particle Settling ◽  
Number Range ◽  
Fracturing Fluids ◽  
Wide Range ◽  
Good Set ◽  
Settling Of Particles

A drag force measurement method is presented which makes it possible to study the settling of particles in transparent and opaque fluids. A dimensionless treatment that takes into account the shear thinning effects of fluids was applied to normalize the measured drag force data. A wide range of particle Reynolds numbers can be covered by this method and a profile of friction factor versus Reynolds number can be established by the proposed dimensionless treatment. An algorithm for the prediction of settling of particles in non-Newtonian fluids was introduced. It can be executed by a computer program. With a good set of experimental data, the settling velocities predicted by the computer model are very close to the measured ones in the fluids tested. This method can be used to study the suspension properties of drilling and fracturing fluids, transparent or opaque. The wide coverage of Reynolds number range simplifies the experiment.

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