Importance of drilling fluid rheology on the continuity of operational activities in drilling a petroleum well.

If drilling fluid is considered important for petroleum well drilling operations, then the study and evaluation of drilling fluid rheology is also very important, especially because drilling fluid parameters such as viscosity, annular velocity, number of reynolds and others must be in a range where it is beneficial to lift the drill cuttings from the bottom to the surface.

Introduction

The part of physics that studies the rheology of fluids is fluid mechanics, however, well drilling is nourished by fluid mechanics and incorporates this knowledge to find the values that best adapt to the rheology of the drilling fluid where the well can be drilled obtaining an effective cleaning of the hole.

There are multiple and striking reasons to learn everything related to the mechanics of fluids, especially understanding that many engineering manage processes where fluid transport is involved, in the oil industry much of the operational principles are based on the transport of fluids, for example the drilling fluid is stored in the mud tanks and are pumped by pumps called mud pumps from the preparation and storage tanks to the bottom of the well, this returns again from the bottom of the well to the tanks.

In order for this displacement to be accomplished satisfactorily without problems in the equipment involved, and for the drilling fluid to effectively clean the hole of the rock cuttings produced by drilling, it is necessary that properties such as viscosity are in accordance with a rheology in accordance with the drilling demand of the well, hence the importance of the rheology of the drilling fluid.

For the case of petroleum engineering, it is very important to study and understand the laws that govern the movement of drilling fluid since it is pumped by the mud pumps from the active tanks until it returns again. In order to enter the world of drilling mud transport behavior, it is necessary to study the rheology of the drilling fluid, the question that arises in this process of understanding the study of drilling fluid transport is to ask ourselves:

What is rheology?

Rheology is a branch of physics that studies the deformation of fluids. Fluids deform just as solids do when they are subjected to certain stresses.

The study of rheology does not exclude the study of the deformation of fluids that are subjected to great efforts to be transported from one part to another. One of the characteristics of rheology as an auxiliary science of physics and fluid mechanics is that it is constantly being evaluated to incorporate new models and equations that can describe the flow and transport behavior of various fluids that are very important nowadays in industrialized processes.

One of the characteristics of rheology as an auxiliary science of physics and fluid mechanics is that it is constantly being evaluated to incorporate new models and equations that can describe the flow and transport behavior of various fluids that are very important nowadays in industrialized processes.

In this case, the oil industry is no exception. Thanks to rheology, it has been possible to develop models that stimulate the production of new chemical additives that are incorporated to the drilling fluid to improve its viscosity properties.

The greatest development achieved by rheology has been obtained in the study of the flow behavior of suspensions in pipes and other conduits, this is a development that has impacted favorably in the drilling of oil wells, since the transport of drilling mud is done through pipes, hoses and fittings that in many cases prevent the proper functioning in terms of its transport.

A drilling engineer who has among its objectives to optimize the process of transporting the drilling fluid, should focus a deep interest in rheology, and thus achieve establish between the pressure exerted by the fluid during transport and the flow rate (flow rate) with which it is being pumped, without neglecting the influence on the flow rate have the flow characteristics of the fluid.

For the above considerations I want to present in this publication a first part of the rheology of drilling fluids dedicated to the study of fluid flow and its relationship in the main activities of the oil industry, for this the following points are presented:

[1] Difference between laminar flow and turbulent flow.

[2] Laminar flow regime.

[3] Laminar flow of a Newtonian fluid.

Difference between laminar flow and turbulent flow

There are several activities within the oil industry that involve fluid transport, however the activity that I will focus on in this post is the drilling of wells. When a hole is drilled, rotary drilling is used in which a drilling mud is used to fulfill certain functions such as transporting the cuttings made by the drill bit from the bottom to the surface. In this transport of the rock cuttings it is not convenient a fluid that moves at low velocities, a drilling mud that circulates at high speeds is needed, so the flow regime that is most applicable to transport these cuttings from the bottom of the hole to the surface is the turbulent flow regime.

Based on several differences that exist between these two regimes, I am going to focus the analysis of why the turbulent regime is the most applicable for the circulation of drilling mud to the bottom of the hole, among the reasons are:

[1] Laminar flow prevails at low flow velocities. The flow is orderly, and the pressure-velocity relationship is a function of the viscous properties of the fluid. This condition of orderly flow at low velocities is what makes it unattractive to apply this transport model for drilling mud circulation, since at low mud velocities there is a lack of ability to carry cuttings from the bottom to the surface.

Another highlight of the laminar flow regime is that viscosity plays a key role, not only to determine the laminar flow regime, but also influences the turbulent flow behavior, all this taking into account that viscosity is the property of fluids that measures the resistance of a fluid to flow.

The fact that the laminar flow regime is not the one commonly used in the circulation of drilling mud does not mean that it is a flow regime that should be ignored, its study and understanding within the oil industry is very important, since other stages such as the transport of oil through pipelines to the tank yard is done through the laminar flow regime.

[2] Turbulent flow prevails at high velocities, a situation that makes its study analysis to be performed based on the inertial properties offered by the drilling mud when it is in circulation. It should be noted that the equations that model this type of flow are of empirical characteristics.

Unlike turbulent flow we find that the laminar flow regime relates the equations for this type of flow to the flow characteristics of the fluid, i.e. laminar flow is based on certain flow models, which we can classify in the following order:

a. Newtonian

b. Bigham's plastic model.

c. Power Law or pseudoplastic.

d. Dilatant.

Of these four laminar flow models, only the first three are of interest in drilling mud technology.

As mentioned above, drilling fluid circulation is not governed by this laminar flow behavior, the other is that most drilling muds fail to form a structure that conforms to any of the laminar flow models, yet the behavior of such fluids can be predicted with sufficient accuracy for practical purposes for one or more of them.

Of the models that govern laminar flow, we can say that its visualization is generally given by means of consistency curves, which in turn can be represented as flow pressure versus flow rate, or shear stress versus strain rate.

That is, when a fluid moves it generates a flow pressure that translates into a shear stress to the fluid, while there is a volume of fluid mass that is moving, which also translates into that volume of fluid that is deforming as a result of the deformation stresses.

It is important to see how the Newtonian, power law and Bingham plastic models behave based on a graph of shear stress versus strain rate.

^{Image Source}

Laminar flow regime.

Laminar flow of Newtonian fluids

Laminar flow is a somewhat abstract flow behavior to understand, the simplest way to understand this behavior is to imagine a real condition, for example a group of rows placed on a flat surface, if there is a force F applied at the upper end, and due to friction, the velocity of each lower row decreases by a constant amount dv, from v to zero, as shown in the following figure:

This behavior can also be explained by the following equation:

From the terms shown in the equation governing the laminar flow behavior of a Newtonian fluid, we have the following descriptions:

F: is the force applied to the swaths so that the fluid can move.

A: is the area of the face of the swaths.

r: is the thickness of the spinneret group.

dv: is the difference in velocity between two adjacent windrows.

dr: is the distance between them.

μ: is the frictional resistance to movement between the spinnerets, also known in rheological terms as viscosity. The unit of viscosity in the metric system is the poise.

τ: is the shear stress.

dv/dr: is the strain rate or velocity gradient defined by the slope of the velocity profile.

The Newtonian model is expressed in the plane by a straight line, which passes through the origin, in turn the slope of the curve defines what the viscosity is, so we could say that the viscosity of a fluid with laminar flow behavior that is Newtonian is expressed as:

Where:

μ: is the viscosity

τ: is the shear stress

γ: is the strain rate

So we could say that:

Viscosity = Shear stress / Strain rate

Since viscosity does not change with strain rate, viscosity represents the only parameter needed to characterize the flow properties of a Newtonian fluid.

The laminar flow of a Newtonian fluid in a tube can be visualized as a telescope of concentric cylinders, the velocity of the cylinders increasing from zero at the tube walls to a maximum at the central axis of the tube, resulting in a parabolic velocity profile.

The strain rate about any point on the radius is given by the slope of the profile at that point. It can be seen that the strain rate is maximum at the pipe walls and zero at the central axis.

The relationship between pressure and flow rate follows the following rule:

If a fluid flows in a pipe of length L and radius R, the force at the end of the cylinder of radius r will be the pressure difference P between the ends of the pipe, multiplied by the straight sectional area of the cylinder, and the shear stress will be:

If we substitute the value of tao in the equation for Newtonian fluid we get that:

The development of this equation leads to the equation commonly known as Poiseuille's equation for laminar flow of Newtonian liquids in pipes:

In the case of well drilling, the drilling fluid circulates through an annular space that may vary between the following annular spaces:

[1] Annular space between drill pipe and hole.

[2] Annular space between drill pipe and casing.

In either of these two annular spaces is considered as a concentric space, which handles two types of diameters: internal and external, for example the external diameter can mean the diameter of the hole and the internal diameter the distance from the outside of the drill pipe and the walls of the hole or casing.

Assuming that the drilling mud circulates through the system as a Newtonian fluid, we could say that to calculate the rate of deformation that the drilling mud can undergo while circulating through the annular space taking into account the circulating pressure and the length of the hole, we have that:

In this case the rate of deformation that the drilling mud will suffer will be equal to the annular space multiplied by the mud circulation pressure, divided by 4 times the length of the existing annular space, however it must be taken into account that the mud circulates at low velocities, that is to say under a Newtonian behavior that will not help to clean the hole, on the other hand the circulation pressure can be calculated taking into account the viscosity of the drilling mud with the following equation:

The viscosity of a Newtonian fluid is determined with a capillary viscometer, in which we can measure the discharge time of a standard volume under a standard hydrostatic head.

The viscosity of the drilling fluid cannot be calculated in this way because the composition of the drilling mud, the mud pumps, do not behave as a Newtonian fluid, however if the circulating fluid had the standard conditions of a Newtonian fluid we could calculate its viscosity by the equations discussed so far.

In conclusion, the pressure exerted by the mud pumps on the drilling mud and the chemical additives that are added to it, make it behave as a non-Newtonian fluid, which is why it is impossible to calculate properties such as viscosity by some of the equations presented.

^{Image source}

In the case of the example shown in the previous image we can see that it is a laminar flow since it simulates a fluid flow that moves smoothly through a pipe.

Conclusions

1] The study of rheology is very important in the oil industry, especially in the application of various drilling fluids used to drill wells. These drilling fluids in the process of circulation from the active tanks to the bottom of the hole, and its subsequent return through the annular space and back to the active tanks, are subjected to a series of stresses that are necessary to reach speeds and pressures needed to transport cuttings from the bottom of the hole to the surface.

Since rheology is the science in charge of studying these deformations, it is necessary to begin its study starting from flow regimes that are not specific to well drilling, to understand why it is necessary that drilling fluids must be modeled according to the turbulent regime.

[2] Under circumstances other than requiring the transport of fluids at high velocities, the Newtonian, Bingham plastic and Power Law flow models can be used within the laminar flow regime, since the main characteristic of this flow regime is that it prevails at low velocities.

[3] A clear and understandable way to understand the unit of measurement of the poise in terms of viscosity is to define the poise as the effort in dynes per square centimeter required to produce a velocity difference of one centimeter per second between two layers separated at a distance of 1 centimeter.

[4] Within what is a graph of shear stress versus strain rate, the only laminar flow model that follows a linear behavior is the Newtonian, and if the slope of the straight line (Newtonian flow) is calculated, the viscosity of the fluid that follows this behavior would be calculated.

[5] There are certain variables that can be easily calculated if the geometry of the pipe through which the fluid is transported is known, which follow the Newtonian fluid behavior, these variables are: shear stress, flow rate, flow pressure and fluid viscosity.

[6] If we take into account that the resistance of a fluid to flow is the viscosity, then the different viscosities at different flow regimes represent a variable of primary importance, taking into account that the higher the viscosity of a fluid, the higher the mud pump pressure capacity will be needed while drilling.

Contributions of this publication to engineering

It is important to be able to mark and define the differences between laminar and turbulent regime fluids, since the differences between these regimes can mark the advantages and disadvantages of using one or the other, not only for the most important activities of the industry that involve the use of fluids, since there are other engineering where fluids are used that must fulfill a certain function, so it is required to adapt these functions to one of the two regimes explained in this article.
In petroleum engineering, the study of rheology seeks to develop models that fit the needs of transporting fluids such as oil, gas, water and drilling fluids.

In this article, the basic principles are presented, starting from the difference between laminar and turbulent regimes, and involving some equations of the Newtonian model to calculate some important variables in fluid transport such as: viscosity, circulation pressure, shear stress, flow rate, among others.

As we advance in the other models such as the Bingham plastic and power law, we can compare the usefulness of these models based on the required needs of transport and that in turn can not be satisfied with the Newtonian model.

Recommended reference

Drilling Fluids Rheology: Basics and Definitions

Determination of drilling fluid rheology under downhole conditions by using real-time distributed pressure data

Measurement of Drilling Fluid Rheology and Modeling of Thixotropic Behavior

Types of Flow and Rheology Models of Drilling Mud