Herschel–Bulkley fluid

About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.

Viscoplastic flow around a cylinder in an infinite medium

Abstract: The purpose of the numerical simulations carried out in this study is to determine the flow characteristics of a Herschel–Bulkley viscoplastic fluid around a cylinder in an infinite medium. Inertia is assumed to be negligible. Two types of boundary conditions are considered: the fluid adheres or slips (zero tangential stress) on the cylinder wall. Finite-element modelling involves regularising the Herschel–Bulkley model, as proposed by Papanastasiou [J. Rheol. 31 (1987) 385]. The effect of the yield stress value and shear-thinning index on the kinematic field and drag exerted on the cylinder were explored systematically. The location, dimension and kinematics of the rigid zones were determined. The results are compared with available theoretical data.

Numerical investigation of the hydromechanical response of a natural fracture during fluid injection using an efficient sequential coupling model

Abstract: Hydraulic fracturing is a complicated hydromechanical coupled process, especially in shale gas and deep geothermal reservoirs, in which natural fractures exist. Due to the geological complexity caused by invisibility, and the challenge and high cost in field investigations, numerical modeling becomes an alternative. In this paper, an integrated numerical model is developed to investigate the hydromechanical behavior of a natural fracture during the fluid injection. In the developed model, the mechanical behavior of the fracture including fracture opening, closure, shear dilation, and shear failure is described by proposed constitutive equations; meanwhile, the hydraulic process is simplified as the fluid flows through two parallel planes. The coupled mechanical and hydraulic equations are sequentially formulated in an implicit schema by combining the finite different method and the finite volume method. The advantage of this numerical schema is that the two coupled processes are solved separately and only one sub-iteration is needed. Thus, the solution is efficient and stable than that formulated in a monolithic coupling. Besides, the implicit formulation of the flow equation makes it possible to set a relative large time step. The developed model is verified through three numerical examples. Then, it is used to investigate the hydromechanical behavior of a natural fracture during the fluid injection with a fictive reservoir. Sensitivity studies with variations in the stress state, the fluid injection rate, the fluid viscosity, and the injection form are conducted. The simulation results show that the mechanism in the far field is mainly dominated by shear dilation in contact condition, whereas the mechanism near the injection could be mixed shear–tension in either the contact or the separation conditions. With the increase in the shear stress and the injection length, decrease in the injection rate and the fluid viscosity, the fracture state near the injection will change from separation to contact, the injection pressure will decline below the primary normal stress, and the dominated mechanism is shear dilation. The findings in this study give a better understanding of the mechanical mechanism and the pressure response of a natural fracture during the fluid injection.

Transition from a simple yield-stress fluid to a thixotropic material

Abstract: From magnetic resonance imaging rheometry we show that a pure emulsion can be turned from a simple yield stress fluid to a thixotropic material by adding a small fraction of colloidal particles. The two fluids have the same behavior in the liquid regime but the loaded emulsion exhibits a critical shear rate below which no steady flows can be observed. For a stress below the yield stress, the pure emulsion abruptly stops flowing, whereas the viscosity of the loaded emulsion continuously increases in time, which leads to an apparent flow stoppage. This phenomenon can be very well represented by a model assuming a progressive increase of the number of droplet links via colloidal particles.

Experimental study of the very slow flow of a yield stress fluid around a circular cylinder

Abstract: The slow flow of a yield stress fluid around a circular cylinder was studied by Particle Image Velocimetry (PIV) technique and drag measurement. The fluid used was a Carbopol® 940 gel with shear-thinning elastoviscoplastic behaviour. The case of significant yield stress effects was examined. Special attention was paid to preparing the fluid, controlling slip and the initial stress state in the fluid. In addition to the overall field extending beyond the sheared zone, the field very near to the cylinder was examined in greater detail. Asymmetry was observed between the upstream flow and downstream flow. Examination of the very near field revealed the existence of a recirculation zone upstream of the cylinder. These effects were not predicted numerically with the Herschel–Bulkley viscoplastic model usually used. The sheared zone obtained experimentally is more extensive than that obtained numerically with the Herschel–Bulkley viscoplastic model. A static rigid zone was observed at the downstream stagnation point. Detailed analysis of the results showed that normal stresses could be the cause of this upstream recirculation.