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- 1. Drilling Engineering 2 Course (1st Ed.)
- 2. 1. Mud Weight Planning 2. drilling hydraulics: A. the hydrostatic pressure
- 3. 1. drilling hydraulics: A. types & criteria of fluid flow B. fluid Rheology and models a. Bingham plastic & Power-law models
- 4. Parameters influence rheological properties of drilling fluid Since multiple aspects of drilling and completion operations require the understanding of how fluid moves through pipes, fittings and annulus, the knowledge of basic fluid flow patterns is essential. Generally, fluid movement can be described as laminar, turbulent or in transition between laminar and turbulent. It should be understood that rotation and vibrations influence the rheological properties of drilling fluids. Also the pulsing of the mud pumps cause variations in the flow rates as well as the mean flow rates. Furthermore changing solid content influences the actual mud density and its plastic viscosity. Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 5
- 5. Laminar vs. turbulent flow Fluid movement, when laminar flow is present, can be described as in layers or “laminae”. Here at all times the direction of fluid particle movement is parallel to each other and along the direction of flow. In this way no mixture or interchange of fluid particles from one layer to another takes place. At turbulent flow behavior, which develops at higher average flow velocities, secondary irregularities such as vortices and eddys are imposed to the flow. This causes a chaotic particle movement and thus no orderly shear between fluid layers is present. Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 6
- 6. Ideal laminar flow (animation) Ideal laminar flow in a tube (note that the particles to the center of the tube move faster, as affected to a lesser extent dissipative effect of the walls) Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 7
- 7. Laminar, transitional, and turbulent flow Laminar vs. turbulent flow Fall 13 H. AlamiNia Laminar, transitional, and turbulent flow from a faucet Drilling Engineering 2 Course (1st Ed.) 8
- 8. Laminar vs. turbulent flow Laminar and turbulent water flow Fall 13 H. AlamiNia Laminar vs. turbulent flow of smoke Drilling Engineering 2 Course (1st Ed.) 9
- 9. Reynolds number The so called “Reynolds number” is often used to distinguish the different flow patterns. After defining the current flow pattern, different equations are applied to calculate the respective pressure drops. For the flow through pipes, the Reynolds number is determined with: and for the flow through annuli: Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 10
- 10. Reynolds number range The different flow patterns are then characterized considering the Reynolds number. Normally the Reynolds number 2,320 distinguishes the laminar and turbulent flow behavior, for drilling purposes a value of 2,000 is applied instead. Furthermore it is assumed that turbulent flow is fully developed at Reynolds numbers of 4,000 and above, thus the range of 2,000 to 4,000 is named transition flow: Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 11
- 11. Rheological Classification of Fluids All fluids encountered in drilling and production operations can be characterized as either “Newtonian” fluids or “Non-Newtonian” ones. Newtonian fluids, like water, gases and thin oils (high API gravity) show a direct proportional relationship between the shear stress and the shear rate, assuming pressure and temperature are kept constant. They are mathematically defined by: • 𝜏 [dyne/cm2] ... shear stress • 𝛾[1/sec] ... shear rate for laminar flow within circular pipe • μ [p] ... absolute viscosity [poise] Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 14
- 12. Newtonian flow model A plot of −𝑑𝑣 𝑟 𝜏 vs. 𝑑𝑟 produces a straight line that passes through the origin and has a slop of μ. Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 15
- 13. Non-Newtonian fluids Most fluids encountered at drilling operations like drilling muds, cement slurries, heavy oil and gelled fracturing fluids do not show this direct relationship between shear stress and shear rate. They are characterized as Non-Newtonian fluids. To describe the behavior of Non-Newtonian fluids, various models like “Time-independent fluid model” including the “Bingham plastic fluid model”, the “Power law fluid model” and “Time-dependent fluid models” were developed Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 16
- 14. Non-Newtonian fluids time depended models The time dependence mentioned here concerns the change of viscosity by the duration of shear. It is common to subdivide the time depended models into “Thixotropic fluid models” and The “Rheopectic fluid models”. It shall be understood that all the models mentioned above are based on different assumptions that are hardly valid for all drilling operations, thus they are valid to a certain extend only. Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 17
- 15. Bingham plastic fluid model Bingham plastic fluid model 𝜏y [lbf/100 ft2] yield point μp [cp] plastic viscosity Sketch of Bingham fluid model Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 19
- 16. Bingham fluids In contrary to Newtonian fluids, Bingham fluids do have a yield point 𝜏 𝑦 and it takes a defined shear stress (𝜏 𝑡 ) to initiate flow. Above 𝜏 𝑦 , 𝜏 and 𝛾 are proportional defined by the viscosity, re-named to plastic viscosity μp Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 20
- 17. Power-law fluid model Power-law fluid model n [1] flow behavior index K [1] consistency index Sketch of Power-law fluid model Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 21
- 18. Power-law fluid model When the characteristics of the Power-law fluid model is done on a log-log scale, the results is in a straight line. Here the slope determines the flow behavior index n and the intercept with the vertical, the value of the consistency index (logK). The flow behavior index (n), that ranges from 0 to 1.0 declares the degree of Non-Newtonian behavior, where n = 1.0 indicates a Newtonian fluid. The consistency index K on the other hand gives the thickness (viscosity) of the fluid where, the larger K, the thicker (more viscous) the fluid is. Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 22
- 19. rheological properties determination To determine the rheological properties of a particular fluid, a rotational viscometer with six standard speeds and variable speed settings is used commonly. In field applications, out of these speeds just two are normally used (300 and 600 [rpm]) since they are sufficient to determine the required properties. rotational Viscometer Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 23
- 20. individual fluid parameters determination Newtonian fluid model Bingham plastic fluid model Power-law fluid model r2 [in] rotor radius, r1 [in] bob radius, r [in] any radius between r1 and r2, θN [1] dial reading of the viscometer at speed N, N [rpm] speed of rotation of the outer cylinder Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 24
- 21. 1. Dipl.-Ing. Wolfgang F. Prassl. “Drilling Engineering.” Master of Petroleum Engineering. Curtin University of Technology, 2001. Chapter 4

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