PETE 203 DRILLING ENGINEERING Drilling Hydraulics

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

Nonstatic Well Conditions Physical Laws: Conservation of Mass Conservation of energy Conservation of momentum Rheological Models Newtonian Bingham Plastic Power – Law API Power-Law Equations of State Incompressible fluid Slightly compressible fluid Ideal gas Real gas

Average Fluid Velocity Pipe 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.

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

In practical field units this equation simplifies to: where p1 and p2 are pressures in psi r is 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.

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

Velocity in drill collars Velocity in mud pits, v1

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

Fluid Flow Through Nozzle Assume:

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

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. &

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

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

Impact = rate of change of momentum

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

Laminar Flow of Newtonian Fluids

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. .

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

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

Example - Newtonian Fluid

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?

Example 4.16

Bingham Plastic Model

t and ty are often expressed in lbf/100 sq.ft Bingham Plastic Model t and ty are often expressed in lbf/100 sq.ft

Power-Law Model

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

1. Newtonian Fluid: 2. Bingham Plastic Fluid: Rheological Models 1. Newtonian Fluid: 2. Bingham Plastic Fluid: What if ty = 0?

Rheological Models 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). K = consistency index n = flow behavior index

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

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

Summary of Laminar Flow Equations for Pipes and Annuli

Fig 4.33: Critical Reynolds number for Bingham plastic fluids.

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

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)

Total Pump Pressure

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

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.

Types of Flow Flow pattern is random (flow in all directions) 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…

Turbulent flow, cont’d Types of flow 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

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,

Turbulent Flow - Newtonian Fluid We often assume that fluid flow is turbulent if Nre > 2,100

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

DRILLPIPE DRILL COLLARS BIT NOZZLES ANNULUS 2103 DRILL COLLARS BIT NOZZLES ANNULUS

Optimum Bit Hydraulics Under what conditions do we get the best hydraulic cleaning at the bit? Maximum hydraulic horsepower? Maximum impact force? Both these items increase when the circulation rate increases. However, when the circulation rate increases, so does the frictional pressure drop.

Jet Bit Nozzle Size Selection Nozzle Size Selection for Optimum Bit Hydraulics: Max. Nozzle Velocity Max. Bit Hydraulic Horsepower Max. Jet Impact Force

Jet Bit Nozzle Size Selection Proper bottom-hole cleaning Will eliminate excessive regrinding of drilled solids, and Will result in improved penetration rates Bottom-hole cleaning efficiency Is achieved through proper selection of bit nozzle sizes

Jet Bit Nozzle Size Selection - Optimization - Through nozzle size selection, optimization may be based on maximizing one of the following: Bit Nozzle Velocity Bit Hydraulic Horsepower Jet impact force There is no general agreement on which of these three parameters should be maximized.

Maximum Nozzle Velocity From Eq. (4.31) i.e. so the bit pressure drop should be maximized in order to obtain the maximum nozzle velocity

Maximum Nozzle Velocity This (maximization) will be achieved when the surface pressure is maximized and the frictional pressure loss everywhere is minimized, i.e., when the flow rate is minimized.

Maximum Bit Hydraulic Horsepower The hydraulic horsepower at the bit is maximized when is maximized. where may be called the parasitic pressure loss in the system (friction).

Maximum Bit Hydraulic Horsepower The parasitic pressure loss in the system, In general, where

Maximum Bit Hydraulic Horsepower

Maximum Bit Hydraulic Horsepower

Maximum Jet Impact Force The jet impact force is given by Eq. 4.37:

Maximum Jet Impact Force But parasitic pressure drop,

Maximum Jet Impact Force Upon differentiating, setting the first derivative to zero, and solving the resulting quadratic equation, it may be seen that the impact force is maximized when,