Bingham Plastic Research Articles

Simulation of grout diffusion in fractured rock mass by equivalent seepage lattice elements

There are a large number of discontinuities in underground rock masses with different geometric properties, inducing complex grout diffusion processes. Classical discrete models commonly necessitate fine meshes to explicitly model these discontinuities and result into great computing efforts. In this work, a seepage lattice element model is proposed, which models the fissure seepage by pore seepage in equivalent pipes. We use the new model to study the horizontal grouting cases, considering diffusion as well as solidification processes of Bingham fluid. Some patterns are found: (i) The lattice elements do not need complex discretization which properly capture the grout diffusions processes; (ii) The diffusion of grout will become steady after reaching a specific distance from the injection point where the rock domain full of grout is the diffusion range; (iii) Crack openings, injection pressure and shear strength significantly influence this diffusion range. The proposed method and revealed rules can assist engineers to control the diffusion range and optimize the designs.

Similarity relations for laminar pipe flows of Bingham fluids in friction coordinates

Similarity relations for laminar pipe flows of Bingham fluids in friction coordinates

Physics-Based Swab and Surge Simulations and the Machine Learning Modeling of Field Telemetry Swab Datasets

Drilling operations are the major cost factor for the oil industry. Appropriately designed operations are essential for successful drilling. Optimized drilling operations also enhance drilling performance and reduce drilling costs. This is achieved by increasing the bit life (minimizing premature bit wear), drilling more quickly, which reduces drilling time, and also reducing tripping operations. This paper is presented in two parts. The first part compares the parametric physics-based swab and surge simulation results obtained from the Bingham plastic, power law, and Robertson–Stiff models. The aim is to show how the model’s predictions deviate from each other. Two 80:20 oil/water ratio (OWR) oil-based drilling fluids and two 90:10 OWR oil-based drilling fluids, 1.96 sg and 2.0 sg, were considered in vertical and deviated wells. Analysis of the simulation results revealed that the deviations depend on the drilling fluid’s physical and rheological parameters as well as the well trajectory. Moreover, the model’s predictions were inconsistent. Data-driven machine learning (ML) modeling is the focus of the second section. Data-driven modeling was performed using both software-generated datasets and field datasets. The results show that the random forest regressor (RF), artificial neural network (ANN), long short-term memory (LSTM), LightGBM, XGBoost, and multivariate regression models predicted the training and test datasets with higher R-squared and minimum mean square error values. Deploying the ML model in real-time applications and the planning phase would lead to potential applications of artificial intelligence for well planning and optimization processes.

Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Submarine sediment flows is one of the main means for transporting sediment to the deep sea, often traveling long-distance and transporting significant volumes of sediment for tens or even hundreds of kilometers. Its strong destructive force often causes serious damage to submarine utilities on its course of movement. The sediment concentration of the sediment flow determines its density difference with the ambient seawater, and this density difference determines the flow ability of the sediment flow, and thus affects the final deposition locations of the transported sediment. In this paper, sediment flows of different sediment concentration with various silt and clay weight ratios (referred to as silt/clay ratio) are studied using flume tests. Our test results indicate that there is a critical sediment concentration at which sediment flows travel the fastest for a specific sediment composition. The critical sediment concentrations and their corresponding maximum velocities for each of the four silt/clay ratios are obtained. The results further indicate that the clay content is linearly negatively correlated with the critical sediment concentration. As the sediment concentration increases, the flow behaviors of sediment flows transform from the flow state to the collapsed state, and the fluid properties of the two turbid suspensions with changing flow behaviors are both Bingham fluids. Additionally, this paper also provides a microscopic explanation of the above-mentioned results by analyzing the arrangement of particles within the sediment flow.

The analytical solution for the flow of a Papanastasiou fluid in ducts with variable geometry

We solve the isothermal, steady and creeping flow of the regularized Papanastasiou model in ducts, such as symmetric channels and axisymmetric pipes, with varying rigid walls. The classic lubrication approximation is invoked to simplify the governing equations and to produce an exact analytical solution for the flow field with the aid of the Lambert W function. For specific suitable values of the parameters of the Papanastasiou model, the solution reduces to the corresponding exact analytical solutions for the ideal yield-stress Bingham and Newtonian fluids. The analytical solutions derived here are used to calculate the average pressure drop required to maintain the constant volumetric flowrate through the duct. Results are provided for symmetric undulating or linearly varying channels with the emphasis put on the effects of the Bingham and regularization numbers, and the amplitude of the undulation or the wall variation, respectively. For Bn→0 the yield surface approaches the axis of symmetry, σ(z)→0, i.e., no unyielded region appears in the flow. In this case, the last term in the formula for v is well-defined at y=0 provided that the numerator is zero. This implies that p′=c/h4 where c is constant. With the aid of the total mass balance, we find that c=−16, and thus p′→−16/h4 as Bn→0. Thus, Eqs. (34) and (37) reduce to the corresponding formulas for a Newtonian fluid given in Eq. (25). Noting that f(y,z)>0, and substituting the solution for γ˙ into inequality (52) gives the trivial W(f(y,z))≥0 which holds for any value of y and z because of the properties of the Lambert function. Eq. (53) is used in conjunction with Eq. (8) to find the unknown pressure gradient, p′(z). First, we integrate by parts Eq. (8) and apply the no-slip condition at the upper wall to find ∫0h(z)y2γ˙dy=2. Then, by substituting Eq. (53) into the latter, and performing the integration with respect to y from the axis of symmetry (y=0) to the wall (y=h(z)), gives: Using properties of the Lambert function and denoting with w=w(z) the value of W function at f(y=h(z),z), i.e.: we find the integral I(z) in Eq. (54) in terms of W and w. Then, we set Φ(z)≡−p′(z)h(z)/2>0, rearrange the resulting equation and upon simplification, we derive the strongly non-linear algebraic equation for Φ: The axial velocity component, u=u(y,z), can be found by integrating Eq. (53) with respect to y between y and h(z) and applying the no-slip condition at the wall:

Pressure drop in converging flows in three-dimensional printing of concrete

The additive manufacturing technology of extrusion of concrete mixtures through a nozzle and deposition layer-by-layer is commonly called three-dimensional concrete printing (3DCP). Such materials are rheologically characterized by yield stress and viscosity. The Bingham model is a good approximation of their rheological behavior. We have developed approximate expressions for determination of pressure for flow through slightly tapered tubes and wedge-shaped extrusion dies, starting from the Buckingham–Reiner equation for flow of a Bingham fluid in a straight tube. The predictions are compared to numerical simulations for convergence half-angles (taper) from 0° to 30° and to analytical solutions available in the literature. Good comparison has been obtained for taper angles up to 15° but the agreement deteriorates as the angle increases. Some experimental data available in the literature have been analyzed, and the challenges for prediction of pressure drop in flow of concrete mixtures through tubes and dies, including entry flow losses, are discussed.

Investigation of proteinaceous algal biomass as a drilling fluid component

This study represents the first investigation into the potential of Spirulina algae proteins as drilling fluid constituents to address the problems of the environmental impacts of the petroleum industry. Algae protein is a common waste product from many bioprocessing operations including biofuel production, so this work also presents a solution to a waste utilization problem for bioprocessing industries. As such, this technology could create an important coproduct for bioprocessing industries while providing more sustainable and environmentally-benign drilling fluids for the petroleum industry. Algae biomass was hypothesized to serve as a bentonite replacement or as an additive that could improve drilling fluid performance by reducing fluid loss via permeation, and/or improvement of lubricity via reduction in coefficient of friction. Measurements were taken in accordance with API RP 13B-1 using an OFITE viscometer, OFITE 4-Unit HTHP Filter Press, and OFITE extreme pressure and lubricity tester. The rheological tests include viscosity, yield stress, and gel strength. Key findings include a friction reduction of up to 27% and a standard fluid loss as low as 13.5 mL. The biomass was able to increase the viscosity of the drilling fluids and exhibited a shear-thinning rheology with yield points exceeding 40 lbf/ft2. The rheology was fitted to the Bingham plastic model and the Herschel-Bulkley model. These findings have potential impacts in the fields of petroleum, chemical, environmental, and material engineering. It is concluded that Spirulina biomass is a good potential additive for decreasing fluid loss and improving the lubricity of drilling fluids, but it will not suffice as a bentonite replacement.

Oil-based drilling mud comprising biosurfactant and hydrophobic zinc nano-powders with excellent H2S scavenging performance

Hydrogen sulfide (H2S) could be released during the drilling operations of oil and gas wells. The release of this lethal gas to the surface will expose the working personnel to high safety and health risks. Additionally, the contact of this very corrosive gas with handling and processing equipment will result in severe economic losses. Despite such serious issues, formulating and testing oil-based muds (OBMs) with H2S scavenging capability is still lacking in the literature. Thus, the key aim of this study is to formulate invert emulsion diesel-based drilling mud (abbreviated as IEDBM) that is capable of effectively scavenge H2S in-situ once it is encountered. This aim is realized through the addition of a small quantity of potassium permanganate to the formulated IEDBM. According to the obtained results, the inclusion of a small amount of potassium permanganate (i.e., 1 wt.%) can scavenge up to 0.43 and 0.71 kg H2S per barrel of the formulated mud at the breakthrough (i.e., 29.8 h) and saturation (i.e., 86.2 h) times, respectively. The IEDBM was stabilized using Span 80 (a non-ionic surfactant) and rhamnolipid anionic biosurfactant. The IEDBM also comprised hydrophobic zinc nano-powders (contact angle with water ∼105⁰) as weighting agent. The application of rhamnolipid biosurfactant and hydrophobic zinc nano-powders in drilling formulations is another novel aspect of the work reported herein. The shear rate-shear stress data were well fitted using the Bingham plastic, Casson, and Herschel–Bulkley models. The apparent viscosity of the IEDBM was investigated under different shear rates and the obtained results showed a sharp drop in the mud apparent viscosity with increasing the shear rate up to 40 s−1, followed by a slower decrease upon the further increase in the applied shear rate; which is in line with those of OBMs reported in the literature. The effect of temperature on the apparent viscosity of the IEDBM was also investigated; the change in the mud viscosity was found to be inversely proportional to temperature in almost a linear fashion. The results presented in this work reveal the high potential of formulating OBMs with effective H2S scavenging performance and appropriate flow properties.

Numerical investigation on flow and heat transfer performance of non-Newtonian Bingham fluid in novel spiral wound tube heat exchangers

Based on the field of the coal chemical industry, exploring the applicability of high-performance heat exchangers for coal water slurry and their flow and heat transfer mechanism is of great significance for promoting the development of clean coal technology. In this paper, the flow pattern and forced convection heat transfer of a pair of tandem heated cylinders with different distances were discussed using the bi-viscous Bingham model by numerical simulation. And a novel spiral wound heat exchanger with variable diameter tubes was proposed. The results illustrate that the heat transfer coefficient under unit pressure drop h/△P of the heat exchanger decreases with the increase of the diameter of the variable tubes. When the diameter of variable tubes is 12 mm, h/△P is 19.83% larger than that of the original structure with uniform tube diameter. The empirical correlation between operating and structural parameters and heat exchanger performance is obtained. The research results provide guidance for the design of coal water slurry preheaters and the structural optimization of spiral wound tube heat exchangers.

Effect of the rotation and inclined magnetic field on peristaltic slip flow of a Bingham fluid with heat transfer in asymmetric channel and porous medium

Effect of the rotation and inclined magnetic field on peristaltic slip flow of a Bingham fluid with heat transfer in asymmetric channel and porous medium

Rheological behavior of activated bentonite suspensions and estimation of flow models using least squares method

In this study, bentonite samples were obtained from Wyoming-USA (WB), Eldivan-Çankırı (EB), Reşadiye-Tokat (RB), Niksar-Tokat (NB) and Ünye-Ordu (UB) regions. Then, these were evaluated in two main sections as raw and activated. Raw samples were obtained by reducing the samples obtained from the quarry to less than 75 μm particle size as a result of grinding and sieving processes. On the other hand, activated bentonites were obtained as a result of the activation process with 2.5%wt Na2CO3 and 0.5%wt MgO by dry activation method. After the sample preparation procedures, for the characterization X-ray fluorescence spectroscopy (XRF), X-ray diffraction spectroscopy (XRD), scanning electron microscopy (SEM), brunauer-emmett-teller (BET) surface area and cation exchange capacity (CEC) analyzes were performed. With the suspensions prepared according to American Petroleum Institute (API) 13A standard with bentonite samples and shear stress measurements were performed at different shear rates. According to measured shear stress values, rheological evaluations with Bingham Plastic (BPM), Power Law (PLM), Casson (CM) and Robertson-Stiff (RSM) models were done by using least squared method (LSM) by MatLab. Also, results were validated statistically. When BPM was evaluated, it showed the R-EB coded suspension as the best with 0.9960 R2. R–NB for PLM was expressed as 0.9927 R2. For CM, the sample coded A-WB with 0.9975 R2 was best expressed. When the results were evaluated in general, it was determined that RSM expressed the shear stresses of the samples with higher accuracy compared to the others. Despite the high accuracy in all of the samples for RSM, the A-UB coded suspension stood out with 0.9987 R2.

Microbiological, Physicochemical, Organoleptic, and Rheological Properties of Bulgarian Probiotic Yoghurts Produced by Ultrafiltered Goat’s Milk

In this experimental work, the microbiological, physicochemical, organoleptic, and rheological properties of yoghurts produced by ultrafiltered goat’s milk using two volume-reduction ratios and three probiotic starters were studied. It was established that the dry matter, fats, proteins, count of lactic acid bacteria, titratable acidity, and dynamic viscosity increased and the pH decreased with the rise of the volume-reduction ratio during ultrafiltration. All yoghurts exhibited Bingham plastic flow behaviour. We recommend using a volume-reduction ratio of 3 and MZ2f + Bifidobacterium bifidum BB-87 to produce probiotic Bulgarian yoghurts with the highest dry matter contents (23.02%), protein contents (10.20%), fat contents (9.80%), number of viable lactic acid cells (9.34 logN), viscosity (4.99 Pa·s at shear rate of 1.22 s−1), and organoleptic properties and the highest score (15) in the range of this experiment.

Physics-Informed Neural Networks for Bingham Fluid Flow Simulation Coupled with an Augmented Lagrange Method

As a class of non-Newtonian fluids with yield stresses, Bingham fluids possess both solid and liquid phases separated by implicitly defined non-physical yield surfaces, which makes the standard numerical discretization challenging. The variational reformulation established by Duvaut and Lions, coupled with an augmented Lagrange method (ALM), brings about a finite element approach, whereas the inevitable local mesh refinement and preconditioning of the resulting large-scaled ill-conditioned linear system can be involved. Inspired by the mesh-free feature and architecture flexibility of physics-informed neural networks (PINNs), an ALM-PINN approach to steady-state Bingham fluid flow simulation, with dynamically adaptable weights, is developed and analyzed in this work. The PINN setting enables not only a pointwise ALM formulation but also the learning of families of (physical) parameter-dependent numerical solutions through one training process, and the incorporation of ALM into a PINN induces a more feasible loss function for deep learning. Numerical results obtained via the ALM-PINN training on one- and two-dimensional benchmark models are presented to validate the proposed scheme. The efficacy and limitations of the relevant loss formulation and optimization algorithms are also discussed to motivate some directions for future research.

Rheological Study of Formate (Nacl) and Ethylene Glycol Based Drilling Fluid Using MATLAB

Non-Newtonian models are used in describing the rheology of drilling fluids. Models, such as Power Law, Bingham Plastic, and the Hershel-Buckley model are used to predict drilling fluid behaviour. Selection of the best rheological model that accurately represents the shear stress-shear rate data is optimal in determining fluid use and predicting realistic rheological behaviour. This research is aimed at studying the best rheology model to fit collected data from sodium chloride (NaCl) and ethylene glycol (EG) based drilling fluid. The assessment utilized a total of ten sets of experimental viscometry data from laboratory-formulated drilling fluid samples A to J with the varying volume of formate sodium chloride (NaCl) and ethylene glycol (EG). Using Equations relating shear rates to shear stress, MATLAB non-linear regression approach was used to determine the best of the three rheological models to fit the experimental. The Root square (R2), Adjusted Root square (Adj R2), and Root Mean Square Error (RMSE) were used in determining the goodness of fit and degree of deviation of the experimental data. data. High concentrations of both NaCl and ethylene glycols in the formulation provide a better shear rate shear stress fit. Although the ethylene glycol presence may have account for the improved fit, as Sample E, F and G despite containing high volume of the formate NaCl, the data where not effectively fitted by the models. From the results, the power law model was the least suitable with an R2 value of 0.881-0.956, Adj R2 83-96%, and a poor RSME in the range 2-9. The Herschel-Bulkley model showed an improved fit for the fluids with an R2 0.897-0.973, Adj R287- 98%, and a better RSME <3. this model also shows a good shear thinning behaviour from its three parameter consistency (n) index values. The Bingham plastic model best fits the rheology of the drilling fluid data R2 0.93-0.99, Adj R2 93-98%, and RSME of <2.

Rheology of granular rafts.

Rheology of macroscopic particle-laden interfaces, called "granular rafts," has been experimentally studied in the simple shear configuration. The shear-stress relation obtained from a classical rheometer exhibits the same behavior as a Bingham fluid, and the viscosity diverges with the surface fraction according to evolutions similar to 2D suspensions. The velocity field of the particles that constitute the granular raft has been measured in the stationary state. These measurements reveal nonlocal rheology similar to dry granular materials. Close to the walls of the rheometer cell, one can observe regions of large local shear rate while in the middle of the cell a quasistatic zone exists. This flowing region, characteristic of granular matter, is described in the framework of an extended kinetic theory showing the evolution of the velocity profile with the imposed shear stress. Measuring the probability density functions of the instantaneous local shear rate, we provide evidence of a balance between positive and negative instantaneous local shear rate. This behavior is the signature of a quasistatic region inside the granular raft.

Effect of Silica Flour and Potasium Chloride as Additives in the Rhelogical Properties of High Temperature High Pressure Gas Well Cement Slurry

This study explores the effects of silica flour and potassium chloride on the rheological properties of high temperature and pressure gas wells. Seven different materials were used as additives which includes: fresh water, dyckerhoff, silica flour, antifoam, extender, fluid loss, dispersant, retarder, anti-settling agent, gas control agent, dry viscosifier, potassium chloride and accelerator. Four recipes were prepared using these additives in different mixtures. Recipe four has all the additives including silica flour and potassium chloride. A series of flow tests was performed using an advanced shear-stress/shear strain controlled rheometer. Rheological properties of cement slurries were calculated from the resulting flow curves using the Bingham plastic model and the Herschel–Bulkley’s model. Changes in shear stress–shear rate relationships, yield stress, plastic viscosity, and shear thinning/thickening behavior were found to be related to temperature and the type and dosage of supplementary cementitious material. The four recipes were applied in 10 cases.Among the four different recipes tested for all the 10 cases, Recipe 4 has the best regression values for both temperature vs transit time and pressure vs transit time this can be attributed to the presence of silica flour and potassium chloride.

Exploring the periodic behavior of the lid-driven cavity flow filled with a Bingham fluid

Exploring the periodic behavior of the lid-driven cavity flow filled with a Bingham fluid

The viscoplastic circular hydraulic jump

We examine theoretically the spread of a jet impacting on a circular disk and the hydraulic jump of a viscoplastic fluid of the Herschel–Bulkley type. The depth-averaging approach is employed in the supercritical region, and the subcritical flow is assumed to be inertialess of the lubrication type. The jump is treated as a shock, where the balance of mass and momentum is established in the radial direction, including the effect of surface tension across the jump. We show that, in contrast to the Newtonian jet, which requires separate formulations in the developing-boundary layer and fully viscous layers, the supercritical formulation for the fully yielded and pseudo-plug layers is uniformly valid between the impingement zone and the jump. Consequently, a viscoplastic jet does not experience the discontinuity in the film height, pseudo-plug layer velocity gradient, and shear stress, exhibited by a Newtonian film at the transition location. The jump is found to occur closer to impingement, with growing height, as the yield stress increases; the subcritical region becomes invaded by the pseudo-plug layer. The viscosity does not influence sensibly the jump location and height except for small yield stress; only the yielded-layer is found to remain sensitive to the power-law rheology for any yield stress. In particular, shear thickening can cause the fully yielded layer to drop in height despite the jump in the film surface. We also find that the jump would not occur if the disk was smaller than a critical size, but the yield stress tends to enhance the formation of the jump compared to a Newtonian jet. We show that an almost constant local downstream Froude number also exists for a viscoplastic fluid. Finally, our results reduce to the limiting cases of Bingham, power-law, and Newtonian fluids.

Numerical modelling of planned corner deposition in 3D concrete printing

Analysis of different path planning strategies and the effects of changing printhead direction in the geometrical conformity and the process precision around 90 corner in order to enable a simple and cost-effective way of facilitating the determination of an optimal printing mode for fast and accurate print corners in 3D concrete printing.The material flow is characterized by a viscoplastic Bingham fluid. The printhead moves according to a prescribed speed to print the trajectory. The model solves the Navier-Stokes equations and uses the volume of fluid (VOF) technique. The acceleration steps and jerk (j) carry out the direction change. A smoothing factor is provided to smooth the toolpath. Several simulations were performed by varying the smoothing factor and jerk.Overfilling at the sharp corner was found when the printhead velocity was kept constant while extruding mortar at a fixed extrusion velocity; however, proportional extrusion velocity with the printhead motion has improved the quality of the corner. Otherwise, a slight improvement in the corner shape related to applying a jerk was found.The Computational Fluid Dynamics (CFD) model could take an important amount of computing time to solve the problem; however, it serves as an efficient tool for accelerating different costly and time-consuming path planning processes for 3D concrete printing. Smaller angles and tilted printhead positions should be numerically and experimentally investigated in future research.The developed CFD model is suited for executing parametric studies in parallel to determine the appropriate printing motion strategy for each trajectory with corners.Computational Fluid Dynamics investigation of the path planning strategy for printing trajectory with a right-angle corner in 3D concrete printing.

A Bingham Plastic Fluid Solver for Turbulent Flow of Dense Muddy Sediment Mixtures

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1×10−4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results.