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  1. PETE 203DRILLING ENGINEERING Drilling Hydraulics

  2. Drilling Hydraulics • Energy Balance • Flow Through Nozzles • Hydraulic Horsepower • Hydraulic Impact Force • Rheological Models • Optimum Bit Hydraulics

  3. Nonstatic Well Conditions • Physical Laws: • Conservation ofMass • Conservation ofenergy • Conservation ofmomentum • Rheological Models • Newtonian • Bingham Plastic • Power – Law • API Power-Law • Equations of State • Incompressible fluid • Slightly compressible fluid • Ideal gas • Real gas

  4. Average Fluid VelocityPipe Flow Annular Flow WHERE v = average velocity, ft/s q = flow rate, gal/min d = internal diameter of pipe, in. d2 = internal diameter of outer pipe or borehole, in. d1=external diameter of inner pipe, in.

  5. Law of Conservation of Energy States that as a fluid flows from point 1 to point 2: { In the wellbore, in many cases Q = 0 (heat) r = constant

  6. In practical field unitsthis equation simplifies to: p1andp2 are pressures in psi ris density in lbm/gal. v1 and v2 are velocities in ft/sec. Dpp is pressure added by pump between points 1 and 2 in psi Dpf is frictional pressure loss in psi D1 and D2 are depths in ft. where

  7. Determine the pressure at the bottom of the drill collars, if (bottom of drill collars) (mud pits)

  8. Velocity in drill collars Velocity in mud pits, v1

  9. Pressure at bottom of drill collars = 7,833 psig NOTE: KE in collars May be ignored in many cases

  10. Fluid Flow Through Nozzle Assume:

  11. If This accounts for all the losses in the nozzle. Example:

  12. For multiple nozzles in // Vn is the same for each nozzle even if the dn varies! This follows since Dp is the same across each nozzle. &

  13. Hydraulic Horsepower HHP of pump putting out 400 gpm at 3,000 psi = ? Power In field units:

  14. Hydraulic Impact Force What is the HHP Developed by bit? Consider:

  15. Impact = rate of change of momentum

  16. Newtonian Fluid Model Shear stress = viscosity * shear rate

  17. Laminar Flow of Newtonian Fluids

  18. Newtonian Fluid Model . In a Newtonian fluid the shear stress is directly proportional to the shear rate (in laminar flow): i.e., The constant of proportionality, is the viscosity of the fluid and is independent of shear rate.

  19. Newtonian Fluid Model . Viscosity may be expressed in poise or centipoise.

  20. Shear Stress vs. Shear Rate for a Newtonian Fluid . Slope of line = m

  21. Example - Newtonian Fluid

  22. Example 4.16 Area of upper plate = 20 cm2 Distance between plates = 1 cm Force req’d to move upper plate at 10 cm/s = 100 dynes. What is fluid viscosity?

  23. Example 4.16

  24. Bingham Plastic Model

  25. Bingham Plastic Model tand tyare often expressed inlbf/100 sq.ft

  26. Power-Law Model

  27. Power-Law Model n = flow behavior index K = consistency index

  28. Rheological Models 1. Newtonian Fluid: 2. Bingham Plastic Fluid: What ifty = 0?

  29. Rheological Models K = consistency index n = flow behavior index 3. Power Law Fluid: When n = 1, fluid is Newtonian and K = m We shall use power-law model(s) to calculate pressure losses (mostly).

  30. Velocity Profiles(laminar flow) Fig. 4-26. Velocity profiles for laminar flow: (a) pipe flow and (b) annular flow

  31. 3D View of Laminar Flow in a pipe - Newtonian Fluid “It looks like concentric rings of fluid telescoping down the pipe at different velocities”

  32. Summary of Laminar Flow Equations for Pipes and Annuli

  33. Fig 4.33: Critical Reynolds number for Bingham plastic fluids.

  34. Fig 4.34: Fraction Factors for Power-law fluid model.

  35. Total Pump Pressure Pressure loss in surf. equipment Pressure loss in drill pipe Pressure loss in drill collars Pressure drop across the bit nozzles Pressure loss in the annulus between the drill collars and the hole wall Pressure loss in the annulus between the drill pipe and the hole wall Hydrostatic pressure difference (r varies)

  36. Total Pump Pressure

  37. Types of Flow Laminar Flow Flow pattern is linear (no radial flow) Velocity at wall is ZERO Produces minimal hole erosion

  38. Types of Flow - Laminar Mud properties strongly affect pressure losses Is preferred flow type for annulus (in vertical wells) Laminar flow is sometimes referred to as sheet flow, or layered flow: * As the flow velocity increases, the flow type changes from laminar to turbulent.

  39. Types of Flow Turbulent Flow Flow pattern is random (flow in all directions) Tends to produce hole erosion Results in higher pressure losses (takes more energy) Provides excellent hole cleaning…but…

  40. Types of flow Turbulent flow, cont’d • Mud properties have little effect on pressure losses • Is the usual flow type inside the drill pipe and collars • Thin laminar boundary layer at the wall Fig. 4-30. Laminar and turbulent flow patterns in a circular pipe: (a) laminar flow, (b) transition between laminar and turbulent flow and (c) turbulent flow

  41. Turbulent Flow - Newtonian Fluid The onset of turbulence in pipe flow is characterized by the dimensionless group known as the Reynolds number In field units,

  42. Turbulent Flow - Newtonian Fluid We often assume that fluid flow is turbulent ifNre > 2,100

  43. Pressure Drop Calculations PPUMP Q = 280 gal/min r = 12.5 lb/gal PPUMP = DPDP + DPDC + DPBIT NOZZLES + DPDC/ANN + DPDP/ANN + DPHYD