School of Science and Engineering

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1 School of Science and Engineering Capstone Final Report Drilling Fluids: Rheological Properties and Shear Banding Submitted in Spring 2015 By FAYCAL JAALI Supervised by DR. ASMAE KHALDOUN 1

2 AKNOWLEDMENT First of all, I would like to express my deep and sincere feelings of gratitude to my supervisor Dr. Asmae Khaldoun for her tremendous assistance from the very beginning although she was exceptionally busy this semester by having other tasks to handle without her, this work could not be done. Besides, I would like to thank my family and especially my parents for their sensitiveness and patience and their psychological and material support during this tough period. Their love and support were my incentive to move forward toward success. I finally would like to thank all my friends for giving me the opportunity to share this enjoyable opportunity. Special thanks go to Zakaria Tbany, Fatima Zahra Chakir, Ayoub Firkri and Labib Mohamed Yassine. 2

3 TABLE OF CONTENTS: I. INTRODUCTION... 6 II. LITERATURE REVIEW:... 7 II.1 Rheology... 7 II.1.1 Deformation...7 II.1.2 Viscosity...8 II.1.3 Newtonian Fluids...9 II.1.4 Newtonian Fluids...9 II.2 Emulsion II.3 Invert Emulsion III. UNDERSTANDING DRILLING FLUIDS III.1 Overview III.2 Functions of Drilling Fluids III.3 Types of Drilling Fluids III.3.1 Water-Based Mud III.3.2 Oil-Based Mud III.4 STEEPLE Analysis III.4.1 Economical III.4.2 Environmental IV. EXHIBITION OF SHEAR BANDING IV.1 Overview IV.2 how can a material become a shear-banding material? IV.3 how does the transition towards shear-banding occur in time for a given material? IV.4 Materials and procedures IV.5 Experimental results IV.6 Explanation V. ELASTICITY IN INVERT EMULSIONS V.1 Experiment Overview V.2 Experimental results V.3 Explanation VI. THIXOTROPIC BEHAVIOR VI.1 why does thixotropy occur? VI.2 Materials and procedures VI.3 Experimental results

4 VI.4 Explanation VII. SHEAR BANDING VIII. CONCLUSION REFERENCES APPENDIX A APPENDIX B APPENDIX C APPENDIX D

5 ABSTRACT Drilling fluids are generally used to help drilling the wellbore for the extraction of oil and natural gas. These fluids are indispensable for the removal of cuttings generated by the drilling process, cool and lubricate the drillstring, and keep the hydrostatic force in balance. In fact, there are two types of drilling fluids: water based and oil based. In this work, we are particularly focusing on the latter because of the frequency that the anomaly studied appears. Oil based drilling fluids (or muds) are, actually, complex fluids called invert emulsion materials composed of droplets of water dispersed in an oily continuous phase plus clay, emulsifiers and several other components added for specific rheological properties. In fact, these fluids exhibit shear banding when shear stresses are applied to it after a period of rest. Shear bands are actually macroscopic bands of different viscosity that appears in the fluid to overcome a certain shear stress (and shear rate). In this paper, we will try to understand the occurrence of shear banding and what causes them in oil-based drilling fluids. However, before attacking the analysis of shear localization, one should answer two important questions: how can a material become a shear-banding material? And how does the transition towards shear-banding occur in time for a given material? To answer our question and explain the shear localization in oil-based muds, we used the results of simple invert emulsions prepared previously by Dr. Asmae Khaldoune by varying the concentration of clay and emulsifiers. The conducted experiments investigate the elasticity, viscosity and thixotropic behavior of these fluids. From the results of the experiments, we explained the nature and the cause of these shear localizations. As a result, the adhesion caused by the interaction between droplets in invert emulsions, and the aggregation of these clay particles forming a network, add thixotropy to the material. Nonetheless, also the aggregation of surfactant in pure emulsions form a wormlike micelles that gives yield stress to the material. This yield stress makes the material susceptible for shear banding through heterogeneity in the material. 5

6 INTRODUCTION In a world where the primary source of energy is fossil fuel, the optimization of the process of oil drilling from underground became necessary in order to maximize the extraction cost and reduce the expenses on materials. To achieve the latter, an expertise in this area is needed to overcome the recurrent problems that could be faced in the different stages of drilling by conducting extensive studies and researches on the field of chemistry, physics and petroleum engineering. One of the problems that is quite common while drilling in the wellbore is the change in the properties of drilling fluids. These fluids are essential and indispensable in the process, since it is through them that cuttings are removed from the wellbore, the drillstring and bit are kept cool and lubricate and the formation pressure are kept balanced. However, it has been noticed that a certain category of drilling fluids have a tendency to become brittle and break under stress when they stay at rest for a prolonged time. Therefore, this problem can t neglected since its repetitiveness drive the company to huge losses in terms of money and sustainability. Since I am willing to pursue my education in chemical engineering, and after experiencing this field in my internship, I decided to conduct my capstone project with Dr. Khaldoune on drilling fluids and expand my knowledge in this area. In this project, I will try to analyze the rheological behavior of drilling fluids under stress and understand the cause behind the occurrence of shear banding. 6

7 I. LITERATURE REVIEW: 1. Rheology: Rheology is the science that deals with the flow, deformation, and more generally the viscosity of materials under the action of stresses. Rheology is able to integrate the study of all substances that are liquid or solid. But in most cases, the formulator must deal with problems concerning the pasty solids or thick liquids. The terms used here are intentionally ambiguous. Indeed, one must be aware that the term liquid encompasses both very fluid liquids such as water, organic solvents, solutions and dilute dispersions but also much more consistent and viscous substances in pasty appearance, semi-solid or even solid [2]. These differences are often due to the wide range of time scale regarding the flow mechanism. The flow of a fluid such as water occurs instantaneously under the effect of gravity. In some cases, it will take a few hours to observe a significant flow beginning [2]. The viscosity is not the only quantity to be observed, most of the materials also have elastic properties more marked that they have a complex molecular organization. Viscoelasticity examines in concert viscous and elastic properties of materials. Rheometers allow to obtain rheograms called curves that describe the flow properties of the material. To begin, it is necessary to define the shear movement which is the movement type being implemented in rheology. Here are some key terms that should be well understood in order to undergo the rheology of a fluid. 1.1 Deformation: Deformation is defined as the relative displacement of points when a force is applied to it. Deformation can be either reversible or irreversible. The reversible deformation is the product recover its original shape after the removal of the force applied on it. It is said that the product has elastic properties. The irreversible deformation are products that do not show elastic 7

8 properties, they would flow when a force is applied on them. The points will not align with their previous placement before the application of the stress [2] Viscosity: Viscosity is a measure of the resistance of a fluid to change in shape: the viscosity determines the speed of movement of the fluid (for example, the speed of movement of a spoon in a bowl: the higher the liquid viscosity, the more the movement is slow). Let s take for example water and cream. Cream is thicker than water; its shows more resistance to flowing. Hence, cream is more viscous than water [2]. In fact, the addition of a small amount of substance in suspension or solution can greatly increase the viscosity of the liquid. Molecular viscosity is denoted by μ; it is expressed in Pa.s or P (poise). Generally, liquids have a viscosity greater than that of the gas. Because the molecules are closer together in liquids, connections are established between them more frequently which increase the cohesion of the assembly. Of course, the viscosity varies inversely with temperature [2]. Figure1: Viscosity of different fluids [27] 8

9 1.3. Newtonian Fluids: It is called a Newtonian fluid when the viscosity of said fluid is independent of the pressure applied thereto. In fact, the deformations are proportional to the stresses [3]. The water under the prevailing conditions is the perfect example. Actually, water is not more viscous when at rest compared with when turning it slowly or quickly. Perfectly Newtonian fluids do not exist in real life. It is considered that fluids such as water or air are common conditions in Newtonian or approaching (water becomes non- Newtonian in extreme pressure conditions) [3]. The definition of a Newtonian fluid is rather restrictive: the shear stresses are proportional to the velocity gradient, which implies that: - In a simple shear flow, the only constraints are created by the flow shear stress. - The viscosity is independent of shear rate. - The viscosity is independent of time and the stresses vanish immediately when the flow is stopped. Figure2: Graphs showing properties a of Newtonian fluid [28] 1.4.Non-Newtonian Fluids: Unlike Newtonian fluids, non-newtonian fluids are liquids (or any deformable matter) that have their viscosity changing with the change in the applied mechanical stress, or the time 9

10 in which the stress is applied [3]. As we can see in the figures, the non-newtonian fluids have a nonlinear graph when opposing shear stress and shear rate in contrast with the Newtonian fluids. There are actually numerous types of the non-newtonian fluids. We can name Viscoplastic, Pseudoplastic, dilatant and thixotropic fluid [3]. Pseudoplastic fluid occurs when there is an increase in the shear rate resulting in a tendency to become thinner until it reaches a limit of viscosity. The continuous increase in shear rate will cause a deformation at the level of the fluid structure making any further increase in viscosity impossible. However, these fluids are non-memory materials, which means that if the structure is modified due to an application of a force, the fluid will not recover its original structure. An example of the Pseudoplastic fluid is ketchup [3]. Viscoplastic fluids have a certain threshold of stress in order to flow. Once that threshold reached or exceeded, the fluid go from high viscosity to low viscosity. A type of these is Bingham plastic which require a minimum yield stress to flow, once reached, the relationship between the shear stress and the shear rate will find its linearity [3]. Example of Bingham plastic is blood. Dilatant fluid behaves in reverse of Pseudoplastic fluid, which means, it becomes thicker when an increasing shear rate is applied on it. Similar now to Pseudoplastic fluid, it is not affected by the duration of the stress. Hence, once the structure is disturbed or destroyed, the material will recover its original state [3]. Some examples are honey and cement. Thixotropic fluid is generally dispersion, which means that the material thicken and its viscosity increase as fluid remains at rest due to a construction of a system of intermolecular forces [3]. Therefore, to make the fluid flow again, these intermolecular bindings should be overcome by exceeding the yield stress with a strong enough external energy. The viscosity will decrease until reaching the minimum possible with respect to a constant shear rate. 10

11 However, in contrast to Pseudoplastic and dilatant fluids, Thixotropic fluid is time dependent: which means that the fluid will recover its previous structure when it comes to rest [3]. 2. Emulsion: Figure3: Graphs showing properties of non-newtonian fluids [29] Oil generally do not dissolve in water. In fact, when poured in a container filed with water, a two distinct layers of both fluids will form [4]. This is due to the buoyancy effect; the oil is less dense than water which make it float. Therefore, emulsion is when forcing two immiscible fluids to merge and form a mixture [4]. Emulsions are generally more viscous than the two fluids originated from. To achieve this state, an emulsifier is needed to maintain the mixture and avoid the separation again. An example of emulsifier is Lecithin that is found in eggs. Lecithin has a water-loving head and Water-hating tail; the water-loving head dissolves in water and Water-hating tail dissolves in oil, for example, making the mixture unable for separation [4]. 11

12 Figure4: Structure of Lecithin [4] 3. Invert Emulsion: The invert emulsion is when we use the emulsion backward, which means that the normally continuous phase becomes the dispersed and vice versa [5]. For example, we will proceed an invert emulsion if we prepare a water-in-oil emulsion. This technique is generally used in oil drilling. They use an invert emulsion drilling fluids when good wellbore stability and high temperature tolerance are required. Figure5: Image showing Water-in-oil and oil-in-water emulsions [5]. 12

13 II. UNDERSTANDING DRILLING FLUIDS: 1. Overview: The mud or drilling fluids are generally constituted of water, clay and other few chemicals. Sometimes oil is used as the continuous phase instead of water to obtain some specific and desired properties. The purpose of using drilling fluids is to raise the cuttings made by the bit out of the wellbore for disposal or analysis. But equally important, drilling fluids are also used to keep the formation pressure in the well under control. The pressure that mud exerts on the walls of the well depends on the density or weighing of the mud. The heavier it is, the more pressure it exerts. This is why, to increase the pressure that the mud exerts, weighing materials like barite could be added [6]. Figure6: Illustration showing mud circulation [6]. 2. Functions of Drilling Fluids Transport the cuttings out of the well to be remover mechanically before it is recirculated in the wellbore again, and keep the hole clean. Keep the formation pressure balanced and avoid any overwhelm of the hydrostatic forces that could endanger the drilling operation. 13

14 Support the walls of the wellbore until it is cemented or the installation and completion of the equipment Prevents or minimizes damage to the producing formation(s). The drillstring and bit are kept lubricated and cool Transmission of hydraulic horsepower to the bit. Allow the gathering of information concerning the wellbore through the analysis of the cuttings transported outside. 3. Types of drilling fluids: An intensive research was done on the difference between the types of the drilling fluids. Here is a summary of what was collected. There are two main types of drilling fluids, each one used for specific purposes and under specific conditions. 3.1 Water Based Muds: First, the water based muds, is generally constituted of four elements: water, inert solids, active colloidal solids and chemicals [6]. Water represents the continuous phase of any water based mud. The continuous phase are primarily used to provide the initial viscosity, and through addings, these rheological properties could be modified as desired. The continuous phase is also used to suspend the reactive colloidal solids, such as bentonite, inert solids, such as barite [6]. Thirdly, the water serves as medium for the transportation of the horsepower from the surface downhole to the bit. Without forgetting that water also serves as medium for added chemicals in the drilling fluids [6]. To increase the viscosity of the water-based mud, clay is generally used because it increases of the density of mud, gel strength and yield point, and it decreases fluid loss. We can divide the clay used in drilling fluids into three parts: 14

15 Montmorillonites (bentonite) Kaolinites Illites 3.2 Oil Based Muds Second, the oil-based mud, which is any drilling fluid that has as continuous phase any suitable oil. In fact, there are two types of system in which the continuous phase is oil: invert emulsion mud s and true oil muds [6]. The latter consist of the following components: Suitable oil Asphalt Water Emulsifiers Surfactants Calcium hydroxide Weighting materials Other chemical additives Among all these components, only the first two are indispensable for the functioning of oilbased mud. The remaining components are just added in order to enhance some specific rheological properties and plastering characteristics [6]. Even if water is not required among the constituents of oil mud systems, it is generally added with other chemical additives to enhance also some specific rheological properties. Numerous bodying agents are used in oil muds to find to a specific filtration loss characteristics [6]. We can divide these bodying agents into two groups: Colloidal size materials High molecular weight metal soaps 15

16 Asphalt, one the colloidal-size organophilic materials is used in oil muds for its absorption characteristic to limit the fluid loss. It is basically the same concept as clay in water muds. Meanwhile, emulsifiers in the form of Heavy metal soaps of fatty acids are added in the oil muds for the invert emulsion process [6]. The functions of emulsifiers in oil mud s are as follows: Transmit to the oil muds the strength to be able to suspend the cuttings in the gel. Proceed to emulsify any droplet of water in the oil mud during the drilling operation. Control of the tightening of any emulsion of the water resulting from the contamination of the water, therefore, control the loss of fluid. 4. STEEPLE Analysis: 4.1 Economic Drilling fluids are subject to shear banding when a critical shear stresses and shear rates are not attained. Shear banding can damage the drilling fluid through fracture when remaining at rest for a long period of time, make it unusable. By understanding this phenomenon, scientists can prevent huge economic loses to the company. How? First, drilling fluids are highly expensive, and their importance to the drilling operation make the oil company loses money because of this phenomenon. Hence understanding the processes of shear banding will reduce the damages caused by the latter, which will therefore reduce the cost spent on muds in general. Another point in which the company reduces its expenses through this research is time. When fracture occurs in drilling fluids, the process of changing is time consuming making the extraction of oil delayed, and hence huge losses for the company. 16

17 4.2 Environmental: As discussed in previously, drilling fluids make the hydrostatic forces inside the wellbore balanced preventing any overwhelm. A damaged drilling fluids can no longer support these forces endangering the wellbore from collapsing. If this happened, all the drilling apparatus would be under sol polluting all the area countering it and nearby. Therefore, understanding the cause of these fracture will prevent these unbalancing forces to occurs and decrease the chance of any polluting incident. 17

18 III. EXHIBITION OF SHEAR BANDING 1. Overview Systems as foams colloidal suspensions, or as in our example emulsions are constituted of small particles that are subject to soft interaction between them, which means that the distance between them (particles) change progressively. The change in state of these systems from solid to liquid after undergoing on them stress have always created a certain curiosity and interest. Normally, the rheological behavior of systems are described by the mean of the simple yield stress model which provide a velocity profile containing unsheared regions when the stress distribution is heterogeneous. Now, several papers and experiments showed that the flow of these materials exhibits true shear banding, which means two regions with significantly different shear rates in geometries in which the shear stress is homogeneous. The latter behavior is not predicted by the simple model of yield stress since it considers the solid-liquid transition as being smooth. Therefore two questions rises: (1) how can a material become a shearbanding material? and (2) how does the transition towards shear-banding occur in time for a given material? 2. How can a material become a shear-banding material? There are numerous ways by which a fluid can lose its ability to flow; we can cite lowering the temperature, increasing volume fraction or releasing some external stress. This happens to huge variety of materials that extend from polymers and colloids to granular assemblies, also known as soft glassy materials. These systems show different responses depending on the external shear stress. If the shear stress is below the critical value, the system will behave elastically and resist motion, however if it is above, the flow will occur. Hence the importance of acknowledgement of the yield stress. The oscillatory shear experiments is the obvious response for how to extract the yield stress since from this experiment, we can get the 18

19 viscoelastic moduli of the system that procure us with useful information about the yielding behavior. Generally, one can add the dynamic light scattering experiment on the system to determine besides the yield stress, the local arrangement inside the material. To our paper, the question should be asked more specifically in order to be relevant to our analysis. Consequently, the question becomes: how can an invert emulsion becomes a shear-banding material?? Bécu et al, in their experiments showed that the adhesive behavior of the droplets created by their mutual interaction provoke a shear-banding in a simple yielding emulsion [7]. The originality of their work was the control of the short-range attraction between droplets by varying the concentration of surfactant in the emulsion. By this mean, they compared the flow behavior of adhesive emulsion (i.e. attractive glass) with non-adhesive emulsion (i.e. repulsion). The velocity profiles are well described and explained by showing the shear banding expressed on adhesive systems in the contrary of non-adhesive emulsions which shows homogenous flow throughout the yielding transition. Actually, in their experiment, they noticed that free Sodium Dodecyl Sulfate (SDS) forms micelles that do not absorb and are repulsed from the nearby droplets, which creates an excess in osmotic pressure pushing the droplets together[22]. Also, by increasing the SDS concentration therefore the concentration of micelle leads to the depletion forces and later flocculation. As we can notice from the figure below, the first sample constitutes of Brownian droplets meanwhile second is aggregated in one large entity. They concluded from below that low concentration of SDS (1%) leads to non-adhesive emulsion and relatively high SDS concentration (8%) to an adhesive one [Fig.7] [7]. 19

20 Figure 7: a) Emulsion with 1% wt. SDS. b) 8% wt. SDS [7] Also, from the experiment done by varying the velocity profiles on adhesive and nonadhesive emulsions using a Rheometer, Bécu et al found that both emulsion were subject to shear localization in thin lubrication films at the walls and total wall slip was observed: since the velocity was under the critical value, the rotation was that of a solid body [7]. As the velocity increased, both emulsions start to be sheared, yet not in the same way. In the non-adhesive emulsions, the flow stays homogenous (see c-d below) meanwhile in the adhesive emulsions, Bécu et al remarked a huge shear band at the inner wall (fig 8 b and c below) [7]. The band s width continued to grow as the velocity increased until it filled all the gap caused by shear stress, after that the flow recovered its homogeneity (fig 9 d). Figure 8: Velocity profiles in the non-adhesive emulsion for (a) v0 = 0.98, (b) v0 = 1.47, (c) v0 = 1.96, (d) v0 = 2.94 [7]. 20

21 Figure 9: Velocity profiles in the adhesive emulsion for (a) v0 = 0.49, (b) v0 = 0.98 ( ), 1.17 ( ), (c) v0 =1.47 ( ), 1.96 ( ),(d) v0 = 4.78 ( ), 9.78 ( ) [7]. 3. How does the transition towards shear-banding occur in time for a given material? Now, let s focus on question (2) and try to elucidate the origin and the effect of time on shear banding behavior for a given material as the transition from purely solid ( starting from rest) or purely liquid (starting from intense preshear) toward shear banding is a quite complex phenomenon. This phenomenon can be related to thixotropic systems (variation of viscosity over time), and particularly the shear-banding behavior occurring in clay-oil systems. For example, several cases of shear banding or even fractures were reported on latter systems like drilling fluids after undergoing a stress when these systems spent some time at rest. Hence, the specific evolution of shear rate at stoppage agrees with the model predicting the progressive aggregation of droplets with time. To investigate the transition toward thixotropy of emulsions, Ragouilliaux, et al. have compared the behavior of pure emulsions and the loaded emulsions with colloidal particles [8]. In a vision to understand the behavior of these two systems, they analyzed the characteristics 21

22 of their flow over time using the Magnetic Resonance velocimetry (MR). From their analysis, they found that the pure emulsion showed a negligible thixotropic behavior meanwhile the loaded emulsion was significantly thixotropic. At the liquid state, the two fluids share the same behavior, however the aggregation of the colloidal particles that constitutes the loaded emulsions and the links they form in the fluid increases its viscosity making it thixotropic. Therefore, the apparent yield stress of the loaded emulsion will also increase. In our experiment, we investigated also the thixotropic behavior of the loaded emulsions versus the pure emulsion. However, we tried, by varying the concentration of surfactants and clay and analyzing their characteristics to understand how the concentration could affect the behavior of the emulsions. 4. Materials and procedures We started by preparing the pure emulsion by adding progressively water to the oilsurfactant solution under high shear. We used as surfactant Sorbitan monoleates and Vitrea 13 for oil (smells like fuel). For the loaded emulsion, we added progressively the water in an oilsurfactant/clay solution under high shear; the water droplet concentration was 80%. The oil surfactant/clay solution was prepared by mixing the surfactant with the colloidal particles oil soluble clay particles called Bentone 38. Let s keep in mind that oil-clay suspension is a simple solution which means it does not show any yield stress, meanwhile the oil surfactant/clay solution is a more viscous pasty material even at low fraction of water. We can conclude that the clay particles are most likely responsible for this behavior through their aggregation by creating links and even networks inside the material. In fact, we planned to prepare the emulsions by variation of the clay content and surfactant content in the oil solution. The first experimental design given was the variation of the amount of clay from 0 to 5 %clay, and the surfactant from 1 to 10%. However, the 22

23 combination 1% surfactant with clay wasn t enough to prepare stable invert emulsion then we changed the proportion of surfactant to 2%. The 2% surfactant wasn t also enough when we added 5% clay then prepared an emulsion with 3% surfactant and 5%clay. We put the emulsions that we prepared in the Rheometer and let it stabilize during the night. 5. Experimental results After a comparison of ours samples at their solid regime with (frequency1 Hz, strain amplitude 1%), we conducted an Oscillatory measurements by measuring the variation of the elastic modulus G' of the emulsion over time (see figure x). At first, we notice that G of the pure emulsions (10%, 2% of surfactant) increased very briefly, which indicated that their aging is negligible over time. Meanwhile, in the loaded emulsions, G has increased significantly over time which can be explained by aggregation of the clay particles with time forming links and networks, and strengthening the material. Graph 1: Modulus of elasticity versus time for all samples 23

24 6. Explanation That being said, not all pure emulsions exhibit the same behavior. We can notice that the solution with 5.5% concentration of surfactant shows a higher viscosity compared to the other pure emulsions. This can be explained by the network that the surfactant can make throughout the medium by aggregating in wormlike micelles once the critical micelle concentration (CMC) has been crossed. This wormlike micelle can grow and tangle around each other with the increase of concentration forming a complex network. Nonetheless, as we can see in the graph, a very high concentration of the surfactant reduces its viscosity as the repulsive force between the heads prevent those surfactants from aggregating. 24

25 IV. ELASTICITY IN INVERT EMULSIONS 1. Experiment Overview Historically, the normal stress difference was firstly used to prove elasticity in shear flow. Nowadays, other tools are being used for same purpose like getting G using sinusoidal oscillations which shows to be a more convenient measurement. Nonetheless, normal stresses are still widely used in different applications. In fact, when sealing with large strains, using normal stresses is both appropriate and sensible to the microstructures generated by that large strain. In the following experiments, we measure the variation of the Normal stress difference as a function of strain by keeping shear rate constant at 0.01 s Experimental results: As we can see from the graph 2, there are two types of lines. Lines that are, with different slopes, showing increasingly higher negative value of normal stress difference (N1), and lines that are quasi constant at N1 equals 0. Interestingly, the first type is composed of loaded emulsions containing different concentrations of clay, and the second type represent the pure emulsion with only surfactants. As a result, the elasticity is higher in the loaded emulsions compared with the pure emulsion. 25

26 Graph 2: First normal stress difference versus shear strain 3. Explanation: In fact, the negative value of normal stress difference was first extensively explained by Marrucci and Guido who observed at an intermediate shear rate, N1 becomes negative. In their analysis on lyotropic LCPs, they stated that, due the deformation of the ellipsoid shape of domain, the rotation of molecules drive them to become perpendicular to the flow axis at significantly large shear rates. Moreover, taking into consideration the rotational movement of molecules around their axis, these latter rotate from tumbling to wagging state. Therefore, N1 becomes negative at reasonable shear rates. Now we will proceed by isolating the three pure emulsions (2%, 5.5% and 10%) and analyze their behavior before and after adding clay. Indeed, we will examine the change in first normal stress difference with change in strain and compare it with another experiment. In this experiment, we will prepare three pure emulsions with the same concentration of surfactant as our previous graph (2%, 5.5% and 10%) and add a constant amount of clay (concentration 2.5%) in the three solutions. Then we will again measure the first normal stress difference 26

27 versus shear strain, and we will compare it with the graph where pure emulsions results were plotted. Graph 3: First normal stress difference versus shear strain (pure emulsions only) Graph 4: First normal stress difference versus shear strain (keeping clay constant and varying surfactant concentration) From graph 3, we can see that the three concentrations exhibit a slight increase in the first normal stress difference with some exhibition of few peaks or shoulders. These peaks represent the structures being broken and aligning during shear. As discussed earlier, surfactants 27

28 when reaching their critical concentration tend to aggregate and form network throughout the material. So, during the shear, these structure are broken, however for larger concentration (10%) we notice two distinct peaks which indicates that a relaxation time where a new structure was being constructed. In the overall, we deduct a poor elasticity with a few to none resistance to the flow. In graph 4, where we kept the clay constant and varying the concentration of surfactant, we can notice a huge difference in the change of the values of N1. Indeed, the elasticity increases highly with the presence of clay particles. This is due to the change in orientation of surfactants which obstruct the flow. This anomalous orientation of surfactants can be explained by the effect of the clay on them. In fact, the interaction between surfactants and clay particles offsets the force attempting to align the surfactants in the direction of the flow where substantial resistances to deformation were observed at low shear rates. Of course, at higher shear rates these interactions will be overcome and the orientation will follow the flow because the arrangement of the matrix will be disrupted. 28

29 V. THIXOTROPY BEHAVIOR First, one should make a distinction between the two types of yield stress behavior: the simple yield stress fluids and the thixotropic. The non- thixotropic fluids, when the applied stress is removed, they revert back to their original form. That is the upward curve of shear stress versus shear strain will be identical to the downward curve. This behavior is shown in the experiment done by Peder Moller et al. on a 0.1% carbopol under increasing and decreasing shear stresses [7]. This can be explained by the fact that viscosity does not change. On the other hand, if the material is thixotropic, it will gain in liquefaction at high shear stresses, meaning that the decreasing curve will be slightly below the upward curve. An example from 10% bentonite solution under an increasing and then decreasing is stated below. Figure 10: a) 0.1% carbopol and (b) 10% bentonite material behavior [7] 29

30 1. Why does thixotropy occur? Thixotropic materials is a subclass yield stress materials, which means they need a nonzero critical stress to be able to flow as liquid. Several examples of materials show this behavior (yield stress): we can cite colloidal suspensions and emulsions such as oil-surfactant solutions, liquid foods, and mud. However, the particularity of thixotropy is the variation of the value of this yield stress depending on the amount of time the material stayed at rest. K.L. Maki and Y. Renardy explained that once the applied stress is removed, the material tries to recover reaching an apparent equilibrium. After enough time has passed, the microstructures start to reconstitute their original state. Therefore, the waiting time is crucial for the value of the yield because, if a stress is applied before the thixotropic material have fully recovered, the yield stress will be lower. In the same manner, if a constant stress that induces the flow is removed, the microstructure will continue to be built after the fluid will come to rest. 2. Materials and procedures To test the yield stress behavior of our samples and test the change in this behavior when varying the concentration of surfactants and clay, we conducted a thixotropy experiment in which we applied on all our emulsions an increase in shear rate from 0.01s-1 to 1000s-1 then decrease from 1000s-1 to 0.01s-1, then we measured the variation of shear stress versus shear rate. We came out with flow curve (shear stress versus shear rate) for all our sample. 3. Experimental results: We deduct from the results that all our samples show a more or less thixotropic behavior. This can be shown by the difference between the upper and lower curve as it is more or less shifted to the left, depending on the sample. That being said not all the behaviors are the same even between pure emulsions and loaded emulsions. For example, we can notice a degree of 30

31 hysteresis (i.e. the difference between the upward and downward curve) of 10% surfactant that is lower than that of 2% surfactant. Same remark for the loaded emulsions since we can see a lower degree of hysteresis of 2.5% clay 10% surfactant and 5% clay 3% surfactant (See appendix A). 4. Explanation The first differentiation of the thixotropic behavior between our samples is the molecular weight. Products with high molecular weight take longer to recover, and heir degree of hysteresis will hence be larger than systems with low molecular weight particles. However, this could not be the reason since we are using the same type of surfactant and clay in all our samples. The second component that could affect thixotropic behavior is the attractive forces between the components of the material. Let s take for example the bentone in our loaded emulsions, the Van der Walls interactions between its polar particles make them aggregate and form a percolated structure which in turn is the origin of the thixotropy. But also, in the pure emulsions, we cannot neglect the interaction between the surfactant particles forming a wormlike micelles in the material, which also give it a thixotropic behavior. However, the concentration of these two components can affect the forces inside the material increasing or decreasing its thixotropy. As we can see from the 10% surfactant graph, the hysteresis region is lower than the two other concentrations of pure emulsions. However, the 2% and 5% surfactant samples shows a very distinguishable thixotropic behavior, nonetheless we can remark a higher viscosity for 5.5% due to a stronger network created through the wormlike micelles. 31

32 Now, for the loaded emulsions, we can notice some differences between our samples also at the level hysteresis region. As stated by Pham et al., the hard-sphere colloids, in our example bentone clay, when mixed with polymers, surfactant in our example (called living polymers by M.E. Cates) can form attractive glasses, which means the polymers mediate a more strong attractive force between the colloids influencing its rheology [9]. We can see a clear evidence of this analysis by comparing the loaded emulsions and their concentration of clay and surfactant. Of course, we can t neglect that a higher concentration can affect the attraction forces making the network unstable and weaker, hence reducing thixotropy. Another remark can be done concerning systems that ages spontaneously at rest. They are called Brownian in a sense that temperature is important. The best example is the very thixotropic system of bentonite. Peder Moller et al. pointed out that the difference between Brownian and non-brownian particle systems is often considered between 1-5 μm [7]. Smaller particles remains in suspension by Brownian motion, whereas large systems kept immobile. For Brownian systems, we can see an increase in the modulus of elasticity due to ageing as a function of time, which is exactly what we found in our previous experiment, some samples more than others. On the other hand, for systems constituted of large particle, no ageing is observed. 32

33 VI. SHEAR BANDING We can extract an interesting connection from the distinction that we made between the simple and thixotropic yield stress systems, and the occurrence of shear banding or not. Shear banding has always been viewed as being the result of heterogeneity of flow in the system. If one part of the fluid is under yield stress and another part is above, following the logic, we can easily say that the flow will not happen, yet it will. Nonetheless, it is not the whole story since Bonn et al. and Moller et al. put other observations concerning the shear banding of thixotropic yield stress materials after conducting a cone-plate geometry [23]. The observations are as follows: If during an imposed shear rate measurement the shear rate imposed is lower that the critical value, shear banding will occur. The material inside the shear band is sheared exactly at the critical shear rate. The quantity of sheared material can be calculated by deducting the macroscopically imposed shear rate over the critical shear rate. From the observations above, we can say that shear banding cannot only occur due to stress heterogeneity, but also due to having a critical shear rate that is closely linked to the thixotropic behavior of the material. According to Peder Moller et al., this analysis follows exactly their λ- model arguing that if using this model (n>1 corresponding to thixotropic systems) for calculating the steady-state flow curve, it will show a decrease of shear rate which correspond to flow instability [23]. Which means that not only the thixotropic material has a critical shear rate, but also below that value, the flow will be unstable. The instability of the flow is indeed shear banding flow as observed by Bonn et al. and Moller et al [23]. 33

34 In brief, if we applied stresses on thixotropic yield stress material, either the stresses are small which will lead to ageing, or large which will lead to liquefaction. This will affect the viscosity in such a way that at higher stresses, the viscosity is null and at lower stresses the viscosity is infinite. This implied that the values of shear rate between zero and total liquefaction are not accessible by the applied stress. This arise a question: what will happen if a shear rate is imposed in between no flow and total liquefaction flow? Of course shear banding. This implies that the stress versus strain curve exhibit a stress plateau that is only accessible under imposed shear rate. This plateau is observed in all our samples. 34

35 VII. CONCLUSION: The purpose of this study was to prove and explain the shear banding in invert emulsion drilling fluid. We started by answering two important questions concerning shear banding and thixotropy and we tried to bounce from these answers to explain the rheological properties of invert emulsions. From experiments done on 10 samples varying the concentration of clay and surfactant, we tried to investigate their viscosity and elasticity through elastic modulus experiment and normal stress difference. Next, we made distinction between sample and thixotropic yield stress materials. We conducted thixotropic experiments on all our sample and we compared their hysteresis region. From the experiments, we figured out the importance of the aggregation of the particles inside the material and how that affects its rheological properties. The construction of networks, its break up and its assembling again are the major component for the thixotropic behavior. Also, the concentration of the surfactants and/or clay and their interactions through Van der Walls affecting the network making it weaker or stronger. We also discussed shear banding in invert emulsion and how the heterogeneity of the fluids creates shear bands. The difference in yield stress inside the same fluid are a major component of shear banding, but it is not the only cause. The critical shear rate is also a major cause for shear banding. 35

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38 Appendix A: Results of Thixotropy Experiment Pa /s 10 4 Shear Rate Pa /s 10 3 Shear Rate % Clay & 5.5% surfactant 2.5% Clay & 10% surfactant 38

39 Pa Pa /s 10 4 Shear Rate /s 10 4 Shear Rate % Clay & 10% surfactant 10% surfactant 39

40 Pa /s 10 4 Shear Rate % surfactant Pa /s 10 3 Shear Rate. 2.5% Clay & 5.5% surfactant 40

41 Pa /s 10 4 Shear Rate % surfactant Pa /s 10 4 Shear Rate. 2.5% Clay & 2% surfactant 41

42 Pa /s 10 4 Shear Rate. 5% Clay & 3% surfactant 42