Modeling and simulation of non-Newtonian fluid flows and heat transfer in a non-isothermal coiled tubing to oil well operations

Oliveira, Bruno Rodrigues de; Borges, R.F.O.; Filho, Leônidas Pereira; Villares, P.; Paraiso, E. C. H.; Oechsler, Bruno Francisco; Rocha, José Marcelo; Calçada, Luís Américo; Scheid, C. M.

doi:10.1016/j.geoen.2023.211980

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…converging-diverging tubes respectively, where 2 F 1 is the hypergeometric function, Im ( 2 F 1 ) is the imaginary part of the hypergeometric function and F 1 is the imaginary part of the Appell hypergeometric function in equations ( 13)- (16). It is worth mentioning that all these relationships maintain dimensional consistency and validated for a Newtonian fluid flow [36].…”

Section: ∆P − Q Relation For Rectangular Channelmentioning

confidence: 82%

“…These complex fluid properties combined with the structured geometry of corrugated channels benefit various applications. In flexographic printing, they control ink thickness [10,11]; in food processing, they ensure uniform coating [12,13]; in polymer processing, corrugated channels are used in extrusion and injection molding processes where they optimize flow [14,15]; in oil and gas, they enhance transportation efficiency [16]. They are also crucial in biomedical drug delivery systems [17] and wastewater treatment [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Scaling Laws for Optimal Power-Law Fluid Flow within Converging-Diverging Dendritic Networks of Tubes and Rectangular Channels

Garg

2024

Preprint

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Power-law fluid flows in the converging-diverging tubes and rectangular channel are prevalent in engineered microfluidic devices, many industrial processes and heat transfer applications. We analyzed optimal flow conditions and network structures for power-law fluids in linear, parabolic, hyperbolic, hyperbolic cosine and sinusoidal converging-diverging dendritic networks of tubes and rectangular channels, and aiming to maximize flow conductance under volume and surface-area constraints. This model shed light on strategies to achieve efficient fluid transport within these complex dendritic networks. Our study focused on steady, incompressible, 2D planar and axisymmetric laminar flow without considering network losses. We found that the flow conductance is highly sensitive to network geometry. The maximum conductance occurs when a specific radius/channel-height ratio $\beta$ is achieved. This value depends on the constraint as well as on the vessel geometry such as tube or rectangular channel. However independent of the kind of the converging-diverging profile along the length of the vessel. We found that the scaling, i.e., $\beta_{\max}^* = \beta_{\min}^* = N^{-1/3}$ for constrained tube volume and $\beta_{\max}^* = \beta_{\min}^*= N^{-(n+1)/(3n+2)}$ for constrained surface area for all converging-diverging tube-networks profile remains the same as found by \citet{garg2024scaling} for the power-law fluid flow in a uniform tube. Here, $\beta_{\max}^*,~ \beta_{\min}^*$ are the radius ratios of daughter-parent pair at the maximum divergent part or minimum convergent part of the vessel. $N$ represents the number of branches splitting at each junction, and $n$ is the power-law index of the fluid. Further, we found that the optimal flow scaling for the height ratio in the rectangular channel, i.e., $\beta_{\max}^* = \beta_{\min}^* = N^{-1/2} \alpha^{-1/2}$ for constrained tube volume and $\beta_{\max}^* = \beta_{\min}^*= N^{-1/2} \alpha^{-n/(2n+2)}$ for constrained surface area for all converging-diverging channel-networks, respectively, where $\alpha$ is the channel-width ratio between parent and daughter branches. We validated our results with experiments, existing theory for limiting conditions, and extended Hess-Murray's law to encompass shear-thinning and shear-thickening fluids for any branching number $N$.

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Section: ∆P − Q Relation For Rectangular Channelmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Scaling Laws for Optimal Power-Law Fluid Flow within Converging-Diverging Dendritic Networks of Tubes and Rectangular Channels

Garg

2024

Preprint

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Evaluation of fatigue life prediction models and investigation of fracture mechanisms of mild steel

Hu,

Zhong,

et al. 2024

Engineering Failure Analysis

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Scaling laws for optimized power-law fluid flow in self-similar tree-like branching networks

Garg,

Mishra,

Pattanayek

2024

Journal of Applied Physics

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The power-law fluid flow in tree-like self-similar branching networks is prevalent throughout the natural world and also finds numerous applications in technology such as oil recovery and microfluidic devices. We investigate analysis of optimal power-law fluid flow conditions and the optimal structures within tree-like branching networks, focusing on maximizing flow conductance under the constraint of the network tube’s volume and the surface area. The study considered fully developed laminar power-law fluid flow regimes without considering any losses in the network system. A key observation was the sensitivity of the dimensionless effective flow conductance to the network’s geometrical parameters. We found that the maximum flow conductance occurs when a dimensionless radius ratio β∗ satisfies the equation β∗=N−1/3 and β∗=N−(n+1)/(3n+2) under constrained tube-volume and surface-area, respectively. Here, N represents the bifurcation number of branches splitting at each junction, and n is the fluid power-law index. We further find that this optimal condition occurs when pressure drops are equipartition across each branching level. We validated our results with various experimental results and theories under limiting conditions. Further, Hess–Murray’s law is justified and extended for the shear-thinning and shear-thickening fluid flows for an arbitrary number of branches N. Further, in this study, we also derive the relationships between the geometrical and flow characteristics of the parent and daughter tubes as well as the generalized scaling laws at the optimal conditions for the other essential parameters such as tube-wall stresses, length ratios, mean velocities, tube-volume, and surface-area of the tube distributing within the networks. We find that the fluid power-law index n does not influence the constrained tube-volume scaling at the optimal conditions; however, the scaling laws vary with n under the constrained tube’s surface area. These findings offer valuable design principles for developing efficient transport and flow systems.

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Modeling and simulation of non-Newtonian fluid flows and heat transfer in a non-isothermal coiled tubing to oil well operations

Cited by 5 publications

References 24 publications

Scaling Laws for Optimal Power-Law Fluid Flow within Converging-Diverging Dendritic Networks of Tubes and Rectangular Channels

Scaling Laws for Optimal Power-Law Fluid Flow within Converging-Diverging Dendritic Networks of Tubes and Rectangular Channels

Evaluation of fatigue life prediction models and investigation of fracture mechanisms of mild steel

Scaling laws for optimized power-law fluid flow in self-similar tree-like branching networks

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