Bài giảng Well drilling engineering - Chapter 5: Rheology models & Viscometer (Part 3) - Đỗ Quang Khánh

1 Well Drilling Engineering  Rheology models & Viscometer Dr. DO QUANG KHANH 2 Rheological Models Newtonian Bingham Plastic Power-Law Rotational Viscometer 3 Read  ADE Ch. 4 HW #  ADE 4.24, 4.29, 4.31 4 Rheological Models 1. Newtonian Fluid Bingham Plastic Fluid Power Law Fluid 5 Newtonian Fluid Model Shear stress = viscosity * shear rate 6 Laminar Flow of Newtonian Fluids 7 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. . 8 Newtonian Fluid Model Viscosity may be expressed in poise or centipoise . . 9 Shear Stress vs. Shear Rate for a Newtonian Fluid Slope of line = m . 10 Example - Newtonian Fluid 11 Example 4.16 Area of upper plate = 20 cm 2 Distance between plates = 1 cm Force req’d to move upper plate at 10 cm/s = 100 dynes. What is fluid viscosity? 12 Example 4.16 13 Bingham Plastic Model 14 Bingham Plastic Model t and t y are often expressed in lbf/100 sq.ft 15 Bingham Plastic Model (p .134) 1 dyne is the force that, if applied to a standard 1 gram body, would give that body an acceleration of 1 cm/sec 2 16 Example 4.17{parallel plates again!} Bingham Plastic Fluid Area of upper plate = 20 cm 2 Distance between plates = 1 cm 1. Min. force to cause plate to move = 200 dynes 2. Force req’d to move plate at 10 cm/s = 400 dynes Calculate yield point and plastic viscosity 17 Example 4.17 Yield point, 18 Example 4.17 Plastic viscosity, 19 Power-Law Model 20 Power-Law Model n = flow behavior index K = consistency index 21 Power-Law Model 22 Example 4.18 Power-Law Fluid Area of upper plate = 20 cm 2 Distance between plates = 1 cm Force on upper plate = 50 dyne if v = 4 cm/s Force on upper plate = 100 dyne if v = 10 cm/s Calculate consistency index (K) and flow behavior index (n) 23 Example 4.18 v = 4 cm/s Area of upper plate = 20 cm 2 Distance between plates = 1 cm Force on upper plate = 50 dyne if v = 4 cm/s ( i ) 24 Example 4.18 v = 10 cm/s Area of upper plate = 20 cm 2 Distance between plates = 1 cm Force on upper plate = 100 dyne if v = 10 cm/s ( ii ) 25 Example 4.18 Combining Eqs. (i) & (ii): ( i ) ( ii ) 26 Example 4.18 From Eq. (ii): ( ii ) 27 Apparent Viscosity Apparent viscosity = ( t / g ) is the slope at each shear rate, 28 Apparent Viscosity Is not constant for a pseudoplastic fluid The apparent viscosity decreases with increasing shear rate (for a power-law fluid) (and also for a Bingham Plastic fluid) 29 Typical Drilling Fluid Vs. Newtonian, Bingham and Power Law Fluids 0 (Plotted on linear paper) 30 Summary: Rheological Models 1. Newtonian Fluid: 2. Bingham Plastic Fluid: What if t y = 0? 31 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 Summary: Rheological Models 32 Rotational Viscometer Rheological Models Newtonian Bingham Plastic Power-Law Rotational Viscometer Laminar Flow in Wellbore Fluid Flow in Pipes Fluid Flow in Annuli 33 Figure 3.6 Rotating Viscometer Rheometer We determine rheological properties of drilling fluids in this device Infinite parallel plates 34 Rheometer (Rotational Viscometer) Shear Stress = f (Dial Reading) Shear Rate = f (Sleeve RPM) Shear Stress = f (Shear Rate) 35 Rheometer - base case RPM sec -1 3 5.11 6 10.22 100 170 200 340 300 511 600 1022 RPM * 1.703 = sec -1 36 Example A rotational viscometer containing a Bingham plastic fluid gives a dial reading of 12 at a rotor speed of 300 RPM and a dial reading of 20 at a rotor speed of 600 RPM Compute plastic viscosity and yield point q 600 = 20 q 300 = 12 See Appendix A 37 Example q 600 = 20 q 300 = 12 (See Appendix A) 38 Rotational Viscometer, Power-Law Model Example: A rotational viscometer containing a non-Newtonian fluid gives a dial reading of 12 at 300 RPM and 20 at 600 RPM. Assuming power-law fluid , calculate the flow behavior index and the consistency index. 39 Example q 600 = 20 q 300 = 12 40 Gel Strength 41 Gel Strength  = shear stress at which fluid movement begins The yield strength, extrapolated from the 300 and 600 RPM readings is not a good representation of the gel strength of the fluid Gel strength may be measured by turning the rotor at a low speed and noting the dial reading at which the gel structure is broken (usually at 3 RPM) 42 Gel Strength In field units, In practice, this is often approximated to The gel strength is the maximum dial reading when the viscometer is started at 3 rpm. t g = q max,3 43 Table 4.3 - Summary of Equations for Rotational Viscometer Newtonian Model or 44 Table 4.3 - Summary of Equations for Rotational Viscometer Bingham Plastic Model or or 45 Table 4.3 - Summary of Equations for Rotational Viscometer Power-Law Model or or or