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A General Discussion on Fluid Rheology

Writer's picture: Sri KrishnaSri Krishna

Introduction.

Before going into the details of rheology and what it is, let’s consider the effects on external force on a purely solid body such as a block of metal and a fluid body like water. The normal intuition or anyone with a high school level understanding of physics would know that the force required to move any object is directly proportional to its mass. So that means, heavier the object the larger the force required to move it.


The same principle applies to fluids as well. Since fluids move more freely than solids, fluids are generally considered as a continuum and the force required to move a fluid body is directly proportional to its mass.


Now what happens when the fluid contains suspensions of minute solids particles? Is the force required to move the fluid suspended with solids particles proportional to its mass? The answer is yes of course, but it is no longer directly dependent. Fluids with suspended particles in it are called Particulate Fluids. The force required to move such fluids alters depending on the current velocity of the fluid. The required external force to increase fluid velocity either increases or decreases depending on the composition of the fluid.


Due to these behaviors, the fluids are categorized in to two types. Fluids that have the direct proportional relationship between force and mass are called Newtonian Fluids while those that don’t are called Non-Newtonian Fluids.



Types of Non-Newtonian Fluids.

As explained before, some fluids need progressively lesser force to increase velocity while some need progressively more force. They are respectively termed Shear Thinning & Shear Thickening fluids.


The word is ‘Shear’ because the fluid moves by shearing against the surface it moves on.

 

Shear Thinning.

The exact cause is not yet clear, but the binding theory is that it occurs due to small structural changes within the fluid. For example, if the fluid is a colloidal system, phase separation occurs during fluid flow. This reduces the internal friction in the fluid (commonly called viscosity) thereby leading to Shear Thinning behavior. In polymer systems, shear thinning is caused by disentanglement of polymer chains during flow.


So, in general, when the fluid is static some interconnected network of bonds are present in the fluid structure due two which the initial force required to move the fluid is high. When the fluid starts to move, these bonds are sheared off and internal resistance is reduced.

This is the most commonly observed Non Newtonian fluid behavior.


Shear Thickening.

In this type of fluid, the force required to increase the velocity of the fluid increases. This behavior is expressed only in concentrated suspensions such as food slurries in food processing industries.


The theory behind this behavior is that when the fluid is stationary, voidage is minimum and the liquid present is sufficient to fill the void space. At low fluid velocities, liquid lubricates the motion of each particle, resulting in small stress. At high fluid velocities, the material expands so that there is no longer sufficient liquid to fill the increased void. Therefore, there is nothing to prevent solid-solid contact which increases resistance.



Drilling Fluids.

Drilling fluids are a suspension of weighting agents and other chemicals due to which they have Non-Newtonian behavior. Drilling fluids are generally Shear Thinning. So far there haven’t been any Shear Thickening drilling fluids.


Now why is this behavior of the fluid important? By characterizing the behavior, we can evaluate the resistance offered by the fluid at various flow velocities.


There are many reasons for circulating drilling fluids, one of which is to transport drilled cuttings to the surface. In order to transport them a minimum threshold fluid velocity is needed which can lift the cuttings by counteracting its weight. This minimum velocity is determined using various methods. Now after the required velocity is determined, the next step is to evaluate the force required to achieve this fluid velocity.


Fluids are pumped from the surface into the drill string out of which the fluid exits the bit nozzles and are returned to the surface along the annulus. The pumps at the surface provide the force for the fluid to move. For fluids this force is evaluated as the pressure for fluid movement. From the fluid velocity we can determine the fluid resistance and from which we determine the pressure required for the fluid to move.



Rheological Models.

The resistance of the fluid that has been discussed for so long is termed the Viscosity of the fluid. For evaluating viscosity, multiple mathematical models have been developed over the years which accurately determines the fluid resistance.


The commonly used models in the field are:

  1. The Power Law Model and

  2. The Hershel Bulkley Model.


The viscosity profile for Power Law and Hershel Bulkley fluids are the same. The difference is that Hershel Bulkley fluids have another characteristic property called the Yield Point. The Yield Point is basically the threshold force required to make the fluid move from rest. Consider it like inertia for a liquid body. Not all fluids have this property (like water) but there are many lab studies conducted that show the presence of a Yield Point in Non-Newtonian fluids. Mathematically, the equations for both have the following form:



This clearly looks pretty complex for those not familiar with mathematical models. To make it simple, the shear stress is equivalent to the external force and the shear rate is equivalent to fluid velocity. The ‘K’ is termed Consistency Index which is the value of fluid resistance or Viscosity. The ‘n’ or ‘m’ basically tells us the extent of Non-Newtonian behaviour. If they are less than 1, then the fluid is Shear Thinning and if they are greater than 1, the fluid has Shear Thickening behaviour. If it is equal to 1, then the fluid behaves in a Newtonian manner i.e., the viscosity does not change with increasing fluid velocity.


There are many other rheology models beyond these two models but are more complicated with multiple parameters in it. The details of these models are not discussed here. There are excellent sources available for a detailed explanation of these models.



Model Fitting.

So now we have various models defined. How do we choose the right model? Normally, when there is a lack of adequate information drilling engineers generally choose the model which they are comfortable with. The commonly chosen models are either Bingham Plastic (not discussed as it is outdated) or Power Law. The engineer simply decides the PV and YP values he/she desires and then calculates the chosen rheology parameters.


In the field however, we have rheological data obtained from the rheogram readings to determine the rheology that fits drilling fluid that has been prepared. The workings of the equipment are not discussed here but in a simplistic manner, the equipment determines the force needed to move the fluid at various speeds.


So, these values are converted to a chart as shown below..

Note:

'RPM' on the x-axis is the shear rate or the speed and the 'Dial' on the y-axis is the shear stress or the force required to move the fluid from a stationary position.


As you can observe, the data are just points and not a continuous line. With this data a curve fitting algorithm is performed which would identify the model that best fits the data. The end result would be something that looks like the chart shown below (called a Rheogram)..

For the example above the best fit rheology model was Power Law and the parameters are

  • K – 5.87.

  • n – 0.39.


Now with these parameters, we can determine the viscosity of the fluid under study at any fluid velocity; which is ultimately what we need.

 

Final Remarks.

In summary, all drilling fluids are generally 'Shear Thinning' in nature. It is preferable to have a rheology that has a yield point so that the fluid has suspension characteristics to suspend any cuttings and other solids binding the fluid when the fluid becomes stationary. With the rheological model determined, the pressure required to circulate the fluid can be determined. The critical area to focus on is the annulus (the section where the fluid returns to the surface). If the pressure required in the annulus is too high, then the formation may fracture which leads to many other complications such as loss circulation and well control.


Evaluating such requirements can provide the engineer with the limitations of the system during the design stage which allows them to put forth contingencies and consider other design options for the fluid.

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Mageshwari K
2024年11月02日

Good

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