Bài giảng Well drilling engineering - Chapter 5: Flow Patterns & Frictional Pressure Losses (Part 4) - Đỗ Quang Khánh

1 Well Drilling Engineering  Flow Patterns & Frictional Pressure Losses Dr. DO QUANG KHANH 2 Laminar Flow in Wellbore Fluid Flow in Pipes & Annuli The Slot Flow Approximation Shear Rate Determination Frictional Pressure Loss Turbulent Flow in Wellbore Turbulent Criteria Frictional Pressure Loss Pump Pressure 3 Read:  Applied Drilling Engineering Ch.4 HW #  ADE 4.40, 4.41, 4.42 4 Laminar Flow in Wellbore Fig. 4-26. Velocity profiles for laminar flow: (a) pipe flow and (b) annular flow 5 Laminar Flow in Wellbore Laminar Flow Flow pattern is linear (no radial flow) Velocity at wall is ZERO Produces minimal hole erosion 6 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 . 7 Table 4.4 - Summary of Laminar Flow Equations for Pipes and Annuli Fictional Pressure Loss Shear Rate at Pipe Well Newtonian Pipe Pipe Annulus Annulus 8 Table 4.4 - Summary of Laminar Flow Equations for Pipes and Annuli Fictional Pressure Loss Shear Rate at Pipe Wall Bingham Plastic Pipe Pipe Annulus Annulus 9 Table 4.4 - Summary of Laminar Flow Equations for Pipes and Annuli Fictional Pressure Loss Shear Rate at Pipe Well Power-Law Pipe Pipe Annulus Annulus 10 Representing the Circular Annulus as a Slot { slot approximation is OK if (d 1 /d 2 > 0.3 } Equal Area and Height Simpler Equations-yet accurate 11 Free body diagram for fluid element in a narrow slot 12 Representing the Annulus as a Slot Consider: - pressure forces - viscous forces 13 Representing the Annulus as a Slot Summing forces along flow: 14 Representing the Annulus as a Slot Evaluate t 0 at wall where y = 0 But, So, 15 Representing the Annulus as a Slot 16 Representing the Annulus as a Slot Hence, substituting for v 0 and t 0 : 17 Representing the Annulus as a Slot The total flow rate: 18 Representing the Annulus as a Slot In field units , psi/ft, cp., ft/sec, in 19 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. 7” 5” 1” 6 p 20 Example 4.22 The average velocity in the annulus, 21 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% 22 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. 23 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) 24 Determination of Shear Rate From Eq. 4.54b, (at the wall) 25 Determination of Shear Rate (why?) Using the Newtonian Model, Changing to field units, (circular pipe) sec -1 , ft/sec, in 26 Annulus: From the slot flow approximation, But, Eq. 4.60 c 27 Shear Rate in Annulus In field units: (annulus) Where, 28 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 29 Example 4.24 30 Example 4.24 31 Example 4.24 cont’d (ii) Shear rate at pipe wall, = 75 RPM 32 Turbulent Flow in Wellbore 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 cleaningbut 33 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 Turbulent flow, cont’d 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 34 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, 35 Turbulent Flow - Newtonian Fluid We often assume that fluid flow is turbulent if N re > 2,100 D p f = 11.41 v 1.75 turbulent flow D p f = 9.11 v laminar flow Use max. D p f value 37 Turbulent Flow - Bingham Fluid We often assume that fluid flow is turbulent if N Re > N Rec = f(N He ) 38 Turbulent Flow - Bingham Fluid We often assume that fluid flow is turbulent if N Re > N Rec = f(N He ) Turbulent Flow - Power Law Fluid n = 1.0 41 Summary of Turbulence Criteria 42 Summary of Frictional Pressure Loss in Turbulent Flow 43 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) 44 Total Pump Pressure PUMP