Lesson 12 Laminar Flow - Slot Flow PETE 411 Well Drilling Lesson 12 Laminar Flow - Slot Flow

Lesson 12 - Laminar Flow - Slot Flow The Slot Flow Approximation Shear Rate Determination Pressure Drop Calculations Laminar Flow Turbulent Flow Transition Flow - Critical Velocity

Read: Applied Drilling Engineering Ch.4 to p. 145 Homework #6 On the Web Due Friday, October 4, 2002

Representing the Circular Annulus as a Slot Equal Area and Height Simpler Equations-yet accurate { slot approximation is OK if (d1/d2 > 0.3 }

Free body diagram for fluid element in a narrow slot

Representing the Annulus as a Slot Consider: - pressure forces - viscous forces

Representing the Annulus as a Slot Summing forces along flow:

Representing the Annulus as a Slot Evaluate t0 at wall where y = 0 But,

Representing the Annulus as a Slot

Representing the Annulus as a Slot Hence, substituting for v0 and t0 :

Representing the Annulus as a Slot The total flow rate:

Representing the Annulus as a Slot In field units, psi/ft, cp., ft/sec, in

Example 4.22 Compute the frictional pressure loss for a 7” x 5” annulus, 10,000 ft long, using the slot flow representation in the annulus. The flow rate is 80 gal/min. The viscosity is 15 cp. Assume the flow pattern is laminar. 6 p 1” 7” 5”

The average velocity in the annulus, Example 4.22 The average velocity in the annulus,

Example 4.22 A somewhat more accurate answer, using an exact equation for a circular annulus, results in a value of 50.9792 psi. Difference = 0.0958 psi i.e., within 0.2%

Determination of Shear Rate...(why?) If shear rate in well is known: 1. Fluid can be evaluated in viscometer at the proper shear rate. 2. Newtonian equations can sometimes give good accuracy even if fluid is non-Newtonian.

Determination of Shear Rate The maximum value of shear rate will occur at the pipe walls. For circular pipe, at the pipe wall, from (Eq. 4.51)

Determination of Shear Rate From Eq. 4.54b, (at the wall)

Determination of Shear Rate (why?) Using the Newtonian Model, Changing to field units, (circular pipe) sec-1, ft/sec, in

From the slot flow approximation, Annulus: From the slot flow approximation, But, Eq. 4.60 c

Shear Rate in Annulus In field units: (annulus) Where,

Power - Law: Example 4.24 A cement slurry has a flow behavior index of 0.3 and a consistency index of 9,400 eq. cp. The slurry is being pumped in an 8.097 * 4.5 - inch annulus at 200 gal/min. (i) Assuming the flow pattern is laminar, compute the frictional pressure loss per 1,000 ft of annulus. (ii) What is the shear rate at the wall? n = 0.3 K = 9,400

Example 4.24

Example 4.24

(ii) Shear rate at pipe wall, Example 4.24 cont’d (ii) Shear rate at pipe wall, = 75 RPM

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 PUMP

Types of 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 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…

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

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