Ethan Clarke
The Bingham Plastic model is a linear model that describes the flow behaviour of Bingham plastic fluids. It is a common rheological model used in the drilling industry to monitor drilling fluids. The Bingham Plastic model is also used to describe the behaviour of fluids that do not exhibit a direct proportionality between shear stress and shear rate, which are classified as non-Newtonian fluids. To employ this model, users must have values for the Bingham Plastic constants, μ∞ and τo, or have rheological test data.
| Characteristics | Values |
|---|---|
| Type of fluids | Non-Newtonian fluids |
| Fluid behaviour | Viscoplastic |
| Fluid properties | Requires a finite yield stress to start flowing |
| Fluid properties | Has a linear stress-strain relationship |
| Fluid examples | Drilling fluids, toothpaste |
| Modelling | Requires two parameters: yield stress and plastic viscosity |
| Modelling | Does not describe flow behaviour in the low-shear rate region |
| Modelling | Can be used with rheological test data |
| Modelling | Can be used for hydraulic analysis |
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What You'll Learn
- The Bingham plastic model is a linear model
- It is used to describe the flow behaviour of Bingham plastic fluids
- It is a common viscosity model used in hydraulic analysis
- It is used to describe the behaviour of fluids that do not exhibit a direct proportionality between shear stress and shear rate
- It is used to monitor drilling fluids
The Bingham plastic model is a linear model
Bingham plastic fluids are defined as fluids with a linear stress-strain relationship and which require a finite yield stress before they start to flow. An example of this is toothpaste, which requires a certain pressure to be applied to the tube before it will extrude. In this scenario, the toothpaste behaves as a Bingham plastic fluid, and the pressure applied to the tube is analogous to the yield stress of the fluid.
The Bingham plastic model is a two-parameter model that includes yield stress and plastic viscosity. The yield stress is the value of shear stress at which the fluid begins to flow, and the plastic viscosity describes the linear relationship between shear stress and shear rate once the fluid is flowing.
While the Bingham plastic model is a useful tool for describing the flow behaviour of Bingham plastic fluids, it is important to note that it does not accurately describe this behaviour in the low-shear rate region. In this region, the model overestimates the gel strength of the fluid, leading to a discrepancy between the predicted and actual flow behaviour. This limitation of the Bingham plastic model has prompted the development of alternative models, such as the Power Law model, to better describe the behaviour of pseudo-plastic and dilatant fluids.
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It is used to describe the flow behaviour of Bingham plastic fluids
The Bingham plastic model is used to describe the flow behaviour of Bingham plastic fluids. Bingham plastics are viscoplastic materials that behave as rigid bodies at low stresses but flow as viscous fluids at high stresses. They are named after Eugene C. Bingham, who proposed their mathematical form in 1916.
The Bingham plastic model is a linear model that describes the flow behaviour of Bingham plastic fluids. It is a two-parameter model that includes yield stress and plastic viscosity. The yield stress is the minimum stress required for the fluid to flow, and the plastic viscosity indicates the liquid phase viscosity and the size, shape, and number of particles in the fluid.
The Bingham plastic model is commonly used in the drilling industry to describe the flow of drilling fluids, which are often non-Newtonian fluids. These fluids do not exhibit a direct proportionality between shear stress and shear rate. The Bingham plastic model can also be used to describe the flow of MR fluids in the presence of a magnetic field, which causes the fluid to behave as a non-Newtonian fluid.
To employ the Bingham plastic model, users must have values for the Bingham Plastic constants, μ∞ and τo, or have rheological test data. The model can be used to determine dial readings at different RPMs and to calculate the pressure drop in a piping network. However, it is important to note that the Bingham plastic model does not describe the flow behaviour of Bingham plastic fluids in the low-shear rate region.
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It is a common viscosity model used in hydraulic analysis
The Bingham Plastic model is one of the most common viscosity models used in hydraulic analysis. It is used to describe the flow behaviour of non-Newtonian fluids, which are widely used in the drilling industry. These fluids are too complex to be characterised by the Newtonian model as they do not exhibit a direct proportionality between shear stress and shear rate.
The Bingham Plastic model is a linear model that describes the flow behaviour of Bingham plastic fluids. It is a two-parameter model that includes yield stress and plastic viscosity. The fluid initially resists flowing until the shear stress exceeds a certain value, after which there is a linear relationship between shear stress and shear rate. This model is useful for treating drilling fluids and indicating the nature of contamination. For instance, an increase in plastic viscosity may indicate solid contamination, while an increase in yield point may suggest chemical contamination.
To employ this model, users must have values for the Bingham Plastic constants, μ∞ and τo, or have rheological test data. The apparent viscosity of the fluid can be described using these values. The Bingham Plastic model uses a constant value for plastic viscosity, and a value for μ∞ of 0 would result in a Newtonian fluid.
The Bingham Plastic model is also useful in the oil and gas industry, where yield stress fluids are common in processes such as reservoir flows of heavy oil, drilling fluids, hydraulic fracturing, and sealing operations. The model can aid in understanding the leading-order effects of parameters such as yield stress, shear-thinning, and viscosity.
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It is used to describe the behaviour of fluids that do not exhibit a direct proportionality between shear stress and shear rate
The Bingham plastic model is a linear model that is used to describe the behaviour of fluids that do not exhibit a direct proportionality between shear stress and shear rate, also known as non-Newtonian fluids. These fluids are widely used in the drilling industry and include plastic and pseudo-plastic fluids.
The Bingham plastic model is a two-parameter model that includes yield stress and plastic viscosity. It states that a finite yield stress is required for the fluid to start flowing, and once it starts to flow, there is a linear relationship between shear stress and shear rate. This is in contrast to Newtonian fluids, which exhibit a direct proportionality between shear stress and shear rate.
The Bingham plastic model is useful for treating drilling fluids and can be used to indicate the nature of contamination of the drilling fluid and the required treatment. It is also used to describe the behaviour of fluids with a gelation bonding property, such as drilling fluids that can suspend drilling cuttings and solids when circulation stops.
To employ the Bingham plastic model, users must have values for the yield stress (τo) and plastic viscosity (μ∞), or rheological test data. The model can then be used to calculate the pressure drop in a piping network and evaluate pumping costs or find the flow rate for a given pressure drop. However, it is not suitable for calculating pressure losses or matching viscosities of the fluid over a large range of shear rates.
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It is used to monitor drilling fluids
The Bingham Plastic Model is a useful tool for monitoring and treating drilling fluids. It is a two-parameter rheological model that is commonly used in the drilling industry to describe the flow characteristics of many types of muds. The model is particularly useful for fluids that do not exhibit a direct proportionality between shear stress and shear rate, which are classified as non-Newtonian fluids.
The Bingham Plastic Model is based on the concept that a finite stress must be applied to initiate the flow of a fluid, and that at greater stresses, the flow will be Newtonian. This is often referred to as the yield stress or yield point (τy or YP), which is the threshold stress that must be exceeded for the fluid to start flowing. In the context of drilling fluids, this behaviour enables the fluid to suspend the drilling cuttings and solids within when the circulation stops. Additionally, the model can indicate the nature of contamination of the drilling fluid and the required treatment. For instance, an increase in plastic viscosity (PV) of the fluid may indicate solid contamination, as it suggests that the solids are becoming smaller and requiring more liquid phase. On the other hand, an increase in the yield point could suggest chemical contamination or degradation.
The Bingham Plastic Model is also useful for understanding the flow behaviour of drilling fluids. It is a linear model that describes a linear relationship between shear stress and shear rate after the initial yield stress threshold has been reached. However, it is important to note that the model does not accurately describe the flow behaviour of Bingham plastic fluids in the low-shear rate region, as the model parameter yield point tends to overestimate the gel strength of the fluid.
To employ the Bingham Plastic Model, users must have values for the Bingham Plastic constants, μ∞ and τo, or have rheological test data. These values can be used to determine dial readings at different RPMs using specific equations. Additionally, the direct-indicating rotational rheometer was specifically designed to apply the Bingham plastic fluid model.
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Frequently asked questions
The Bingham Plastic Model is used to describe the flow behaviour of Bingham plastic fluids. It is a linear model that does not describe the flow behaviour of Bingham plastic fluid in the low-shear-rate region.
Bingham plastic fluids are fluids that have a linear stress-strain relationship and require a finite yield stress before they start to flow. They are non-Newtonian fluids, meaning they do not exhibit a direct proportionality between shear stress and shear rate.
To employ the Bingham Plastic Model, users must have values for the Bingham Plastic constants, μ∞ and τo, or have rheological test data. The model is expressed as:
τ = τo + μ∞ * γ
The Bingham Plastic Model is commonly used in hydraulic analysis and in the drilling industry to describe the behaviour of drilling fluids. It is also used in the handling of slurries and in 3D printing.
