Assessing the Reliability of Physical Non-Newtonian Fluid Models for Saline FLOPAAM Polymer Solutions

i FACULTY OF SCIENCE AND TECHNOLOGY

MASTER’S THESIS

Study programme/specialization:

Petroleum Engineering/ D&W

Spring/ Autumn semester, 2020 Open / Confidential Author: Abazar Al-Barakat

Supervisor(s):

Dmitry Shogin

Title of master’s thesis:

Assessing the Reliability of Physical Non-Newtonian Fluid Models for Saline FLOPAAM Polymer Solutions.

Credits: 30 Keywords:

C-FENE-P Salinity Polymer PTT

Material Function Shear-flow

Number of pages: 170 Stavanger, July/2020 date/year

i

Abstract

Experiments were conducted to investigate the impact of salt (NaCl) on rheological properties of specifically FLOPAAM 5115 VHM and FLOPAAM 3630-S polymers. These polymers were dissolved in brines of various salinity levels ranging from 0 to 20 g/l of NaCl. The experiments were comprised of steady shear ramping, start-up and cessation tests using advanced rheometer with a cone and plate tool. Apparent viscosity and shear stresses were recorded at various step shear rates.

The data obtained from these tests were graphically presented and analyzed. Additionally, the scope of this theses was to investigate the reliability of physical non-Newtonian fluid models and their capability to predict the behavior of complex fluids. The models involved in this work are LPTT, EPTT, FENE-P and C-FENE-P. These models were fitted against the experimental data for qualitative and quantitative analysis.

Results of the experiment showed that the salt has a stabilizing effect on the polymers’

viscosity as well as a dampening effect on shear stress growth and a greater decay of shear stress for the cessation test. These effects amplifies with increasing salt content. Furthermore, the data fitting showed interesting results, especially for the C-FENE-P dumbbell model. As it has proven itself capable of predicting viscosity of saline solution very well, something which cannot be said for shear stress, which has shown to be sensitive to the approach used for the applying such models.

ii

Acknowledgement

I would like to express my sincere gratitude and appreciation towards my supervisor Phd.

Dmitry Shogin for being humble and sharing of his extremely valuable knowledge, guidance, and time. Even during this difficult time with the novel Covid-19 virus.

I would also like to offer my appreciation to Kim Andre Vosse Vorland for orienting me on the use of laboratory equipment.

Last but not least, my appreciation is extended to Phd. Mesfin Belayneh Agonafir for being accessible and helping, who kept a positive spirit at the laboratory.

iii

Table of Content

Abstract ...i

Acknowledgement ... ii

List of figures ... vi

List of Tables ... xv

1. Introduction ...1

2. Objectives ...2

3. Polymers ...3

3.1.1 Chemical Nature of Monomers ...3

3.1.2 Molecular Structure of Polymers...3

3.1.3 Polymer Chain Growth Mechanisms ...4

3.2 Polyacrylamide Polymers ...5

3.2.1 Partially Hydrolyzed Polyacrylamide (HPAM) ...5

3.3 Polymeric Flow Phenomena ...7

3.3.1 Shear Dependent Viscosity ...7

3.3.2 Normal Stress Effects ...8

3.3.2.1 Weissenberg Rod Climbing Effect ...8

3.3.2.2 Extrudate Swell Effect ...9

3.3.3 Elastic Recoil/Memory Effects ... 10

4. Mathematical Introduction ... 11

4.1 The Navier-Stokes Equation ... 12

4.1.1 Conservation of Mass ... 13

4.1.2 Conservation of Momentum ... 14

4.2 The Stress tensor and Constitutive Equations ... 15

5. Material Functions ... 18

5.1 Shear Flow ... 18

5.1.1 Stress Tensor for Shear Flow ... 19

5.1.2 Material Functions of Steady Shear Flow ... 20

5.1.3 Material Functions of Unsteady Shear Flow ... 23

5.2 Start-up of Steady Shear Flow ... 24

5.3 Cessation of Steady Shear Flow ... 26

6. Generalized Newtonian Fluid Model ... 28

6.1 The Power-Law Model ... 28

6.2 Carreau-Yasuda Model ... 29

7. Physical Non-Newtonian Fluid Models ... 31

7.1 Hookean Dumbbells Model ... 31

iv

7.2 FENE Dumbbell Model ... 31

7.2.1 FENE-P Dumbbell Model ... 32

7.2.1.1 C-FENE-P Dumbbell Model ... 34

7.3 Concentrated Solutions ... 35

7.3.1 Phan-Thien-Tanner Model ... 35

8. The Experiment ... 37

8.1 Procedure ... 37

8.1.1 Brine Preparation ... 37

8.1.2 Polymer Solution Preparation ... 38

8.1.3 Concentration Determination ... 39

8.1.4 Measurement Procedure ... 41

8.1.4.1 Steady Shear Ramp Measurement ... 42

8.1.4.2 Start-up and Cessation Measurement ... 43

9. Analysis ... 44

9.1 Steady Shear Ramp Data Analysis ... 44

9.1.1 Data/Model Fitting ... 46

9.1.1.1 Full (Non-Affine) Linear PTT... 46

9.1.1.2 Affine Exponential PTT ... 51

9.1.1.3 FENE-P Dumbbells / Affine Linear PTT ... 55

9.1.1.4 C-FENE-P Dumbbells ... 59

9.2 Shear Stress Growth Data Analysis... 63

9.2.1 Data/Model Fitting ... 67

9.2.1.1 Affine Linear PTT ... 67

9.2.1.2 Affine Exponential PTT ... 72

9.2.1.3 FENE-P Dumbbells ... 77

9.2.1.4 C-FENE-P Dumbbells ... 82

9.3 Shear Stress Decay Data Analysis ... 91

9.3.1 Data/Model Fitting ... 95

9.3.1.1 Affine Linear PTT ... 95

9.3.1.2 Affine Exponential PTT ... 99

Conclusions ... 103

Bibliography ... 106

Appendix. A ... 108

Appendix. B ... 117

Appendix. C ... 145

v

vi

List of figures

FIGURE 1(A) ILLUSTRATING THE FINGERING EFFECT OF BY FLOODING WATER WITHOUT POLYMER AND (B)

ILLUSTRATES POLYMER FLOODING (NPD,2020). ... 1

FIGURE 2ILLUSTRATION OF LINEAR(A) AND BRANCHED(B) POLYMERS (BIRD ET AL.,1987). ... 4

FIGURE 3CHEMICAL STRUCTURE OF AN HPAM POLYMER... 6

FIGURE 4AN ILLUSTRATION OF THE TUBE FLOW EXPERIMENT WITH(A) AND WITHOUT(B) THE COVER PLATE (BIRD ET AL.,1987). ... 8

FIGURE 5COMPARISON BETWEEN NEWTONIAN FLUID(N) AND POLYMER FLUID(P) ON ROTATION,N GENERATES VORTEX AND P GENERATES ROD CLIMBING. ... 9

FIGURE 6AN ILLUSTRATION OF THE SWELL EFFECT AS THE FLUID EXITS THE CAPILLARY (YOUSFI ET AL.,2018). . 10

FIGURE 7IMAGES ILLUSTRATING THE MEMORY EFFECTS OF POLYMERS.THE POLYMER FLUID SNAPS BACK IMMEDIATELY AS IT IS CUT USING A SCISSOR (BIRD ET AL.,1987). ... 10

FIGURE 8ARBITRARY CONTROL VOLUME, FIXED IN SPACE, OVER WHICH MASS, MOMENTUM AND ENERGY BALANCES ARE MADE (BIRD ET AL.,1987). ... 12

FIGURE 9SKETCH SHOWING THE COMPONENTS OF STRESS TENSOR PI WITH THEIR RESPECTIVE SIGNS AND INDICES (BIRD ET AL.,1987). ... 17

FIGURE 10AN ILLUSTRATION OF STEADY SHEAR FLOW (BIRD ET AL.,1987). ... 19

FIGURE 11LOGLOGPLOT OF APPARENT VISCOSITY 𝜂 VERSUS SHEAR RATE 𝛾 OF A POLYMER MELT AT SEVERAL TEMPERATURES (BIRD ET AL.,1987). ... 22

FIGURE 12LOGLOG PLOT OF Ψ1VERSUS 𝛾(𝐵𝑖𝑟𝑑𝑒𝑡𝑎𝑙. , 1987). ... 23

FIGURE 13AN ILLUSTRATION OF START-UP OF STEADY SHEAR FLOW (BIRD ET AL.,1987)... 24

FIGURE 14SHEAR STRESS GROWTH PLOT FOR DIFFERENT SHEAR RATES (BIRD ET AL.,1987)... 25

FIGURE 15AN ILLUSTRATION OF RELAXATION OF STEADY SHEAR FLOW (BIRD ET AL.,1987). ... 26

FIGURE 16PLOT SHOWING RELAXATION OF SHEAR STRESS FOR DIFFERENT SHEAR RATES (BIRD ET AL.,1987). .... 27

FIGURE 17AN IDEALIZED FLOW CURVE SHOWING THE POWER LAW REGION, ZERO SHEAR AND INFINITE SHEAR VISCOSITY REGIONS (YAH,2018). ... 29

FIGURE 18SHEAR VISCOSITY CURVE FITTING USING GENERALIZED NEWTONIAN FLUID MODELS (WANG AND SMITH,2018). ... 30

FIGURE 19LODGE–YAMAMOTO NETWORK.THE POLYMER LIQUID CONSISTS OF POLYMER SEGMENTS CONNECTED BY JUNCTIONS, AND CONSTANTLY CHANGES ITS TOPOLOGY (FERRÁS ET AL.,2019). ... 36

FIGURE 20AN ILLUSTRATIVE DIAGRAM OF THE CONE-AND-PLATE SYSTEM (ROTHSTEIN AND MCKINLEY,2001).. 41

FIGURE 21LOGLOG PLOT OF VISCOSITY VERSUS SHEAR RATE FOR FLOPAAM5115VHM POLYMER SOLUTIONS WITH VARIOUS NACL CONCENTRATIONS. ... 45

FIGURE 22LOGLOG PLOT OF VISCOSITY VERSUS SHEAR RATE FOR FLOPAAM3630-S POLYMER SOLUTIONS WITH VARIOUS NACL CONCENTRATIONS. ... 46

FIGURE 23LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION (BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM0 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 121110, 𝜀 = 0.01, 𝜉 = 0.03𝑎𝑛𝑑𝜆 = 60. ... 48

FIGURE 24LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION (BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM5 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 13715, 𝜀 = 0.01, 𝜉 = 0.03𝑎𝑛𝑑𝜆 = 45. ... 49

FIGURE 25LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION (BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM10 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 8728, 𝜀 = 0.01, 𝜉 = 0.03𝑎𝑛𝑑𝜆 = 43. ... 50

FIGURE 26LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION (BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM20 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 5391.6, 𝜀 = 0.01, 𝜉 = 0.03𝑎𝑛𝑑𝜆 = 41. ... 51

FIGURE 27LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION (BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM0 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 121110𝑎𝑛𝑑2𝜖𝜆 = 33.3. ... 52

vii FIGURE 28LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM5 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 13715𝑎𝑛𝑑2𝜖𝜆 = 21. ... 53 FIGURE 29LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM10 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 8728.2𝑎𝑛𝑑2𝜖𝜆 = 18.5. ... 54 FIGURE 30LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM20 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 5391.6𝑎𝑛𝑑2𝜖𝜆 = 17.5. ... 55 FIGURE 31LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM0 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 121110𝑎𝑛𝑑3𝜖2𝜆 = 20. ... 56 FIGURE 32LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM5 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 13715𝑎𝑛𝑑3𝜖2𝜆 = 18. ... 57 FIGURE 33LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM10 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 8728.2𝑎𝑛𝑑3𝜖2𝜆 = 15. ... 58 FIGURE 34LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM0 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 5391.6𝑎𝑛𝑑3𝜖2𝜆 = 12. ... 59 FIGURE 35LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM0 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 121110, 𝜆 = 35, 𝑏 = 50𝑎𝑛𝑑𝐸 = 1000. ... 60 FIGURE 36LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM5 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 13715, 𝜆 = 35, 𝑏 = 50𝑎𝑛𝑑𝐸 = 900. ... 61 FIGURE 37LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM10 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 8728.2, 𝜆 = 35, 𝑏 = 50𝑎𝑛𝑑𝐸 = 90. ... 62 FIGURE 38LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM5115VHM20 G/L NACL POLYMER SOLUTION.FITTED PARAMETERS:𝜂0 = 5391.6, 𝜆 = 35, 𝑏 = 50𝑎𝑛𝑑𝐸 = 20. ... 63 FIGURE 39NORMALIZED SHEAR STRESS GROWTH VERSUS TIME FOR FLOPAAM5115VHM WITH VARIOUS NACL CONCENTRATIONS AT STEP SHEAR RATE 1𝑠 − 1. ... 64 FIGURE 40NORMALIZED SHEAR STRESS GROWTH VERSUS TIME FOR FLOPAAM5115VHM WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 10𝑠 − 1. ... 66 FIGURE 41NORMALIZED SHEAR STRESS GROWTH VERSUS TIME FOR FLOPAAM5115VHM WITH VARIOUS NACL CONCENTRATIONS AT STEP SHEAR RATE 100𝑠 − 1. ... 67 FIGURE 42NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM0 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES (𝑠 − 1)1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED). .... 69 FIGURE 43NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM5 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED). ... 70 FIGURE 44NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM10 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED). ... 71 FIGURE 45NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM20 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED). ... 72 FIGURE 46NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED).

... 74

viii FIGURE 47NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM5 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED).

... 75 FIGURE 48NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM10 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED).

... 76 FIGURE 49NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM20 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1𝑔𝑟𝑒𝑒𝑛, 10(𝑏𝑙𝑢𝑒) AND 100𝑠 − 1(RED). ... 77 FIGURE 50NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

PREDICTION VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATE

1𝑠 − 1. ... 78 FIGURE 51NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATE 10𝑠 − 1. ... 79 FIGURE 52NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

PREDICTION VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATE

100𝑠 − 1. ... 80 FIGURE 53NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM5 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATE 1𝑠 − 1. ... 81 FIGURE 54NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM10 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATE 1𝑠 − 1. ... 82 FIGURE 55NORMALIZED SHEAR STRESS GROWTH (DOTS) AND FENE-P-MODEL PREDICTION (DASHED LINES)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES

1 AND 10 S− 1.FITTED PARAMETERS: B= 1000 AND Λ= 35 ... 84 FIGURE 56NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATE 100 S− 1.FITTED PARAMETERS: B= 1000 AND Λ= 35 ... 85 FIGURE 57NORMALIZED SHEAR STRESS GROWTH (DOTS) AND FENE-P-MODEL PREDICTION (DASHED LINES)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM5 G/L NACL.RED DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES

1 AND 10 S− 1.FITTED PARAMETERS: B= 1000 AND Λ= 35 ... 86 FIGURE 58NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM5 G/L NACL.RED DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATE 100 S− 1.

FITTED PARAMETERS: B= 1000 AND Λ= 35 ... 87 FIGURE 59NORMALIZED SHEAR STRESS GROWTH (DOTS) AND FENE-P-MODEL PREDICTION (DASHED LINES)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM10 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES

1 AND 10 S− 1.FITTED PARAMETERS: B= 1000 AND Λ= 35 ... 88 FIGURE 60NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM10 G/L NACL.RED DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATE 100 S− 1.

FITTED PARAMETERS: B= 1000 AND Λ= 35... 89 FIGURE 61NORMALIZED SHEAR STRESS GROWTH (DOTS) AND FENE-P-MODEL PREDICTION (DASHED LINES)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM20 G/L NACL.DOTTED POINTS REPRESENTING

ix

MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES

1 AND 10 S− 1.FITTED PARAMETERS: B= 1000 AND Λ= 35. ... 90 FIGURE 62NORMALIZED SHEAR STRESS GROWTH (RED DOTS) AND FENE-P-MODEL PREDICTION (BLUE LINE)

VERSUS DIMENSIONLESS TIME, R, FOR FLOPAAM5115VHM20 G/L NACL.RED DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATE 100 S− 1.

FITTED PARAMETERS: B= 1000 AND Λ= 35... 91 FIGURE 63NORMALIZED SHEAR STRESS DECAY VERSUS TIME FOR FLOPAAM5115VHM WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 1 S− 1. ... 93 FIGURE 64NORMALIZED SHEAR STRESS DECAY VERSUS TIME FOR FLOPAAM5115VHM WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 10 S− 1. ... 94 FIGURE 65NORMALIZED SHEAR STRESS DECAY VERSUS TIME FOR FLOPAAM5115VHM WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 100 S− 1. ... 94 FIGURE 66NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM0 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED).

FITTED PARAMETERS: ϵ= 0.01. ... 96 FIGURE 67NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM5 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED).

FITTED PARAMETERS: ϵ= 0.01. ... 97 FIGURE 68NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM10 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED).

FITTED PARAMETERS: ϵ= 0.01. ... 98 FIGURE 69NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM20 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP SHEAR RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED).

FITTED PARAMETERS: ϵ= 0.01. ... 99 FIGURE 70NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM0 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED). ... 100 FIGURE 71NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM5 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED). ... 101 FIGURE 72NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM10 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED). ... 101 FIGURE 73NORMALIZED SHEAR STRESS GROWTH AND EPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM5115VHM20 G/L NACL.DOTTED POINTS REPRESENTING MEASURED DATA AND DASHED LINES REPRESENTING MODEL PREDICTIONS FOR STEP RATES 1 GREEN, 10(BLUE) AND 100 S− 1(RED). ... 102 FIGURE 74POWER-LAW PLOT OF VISCOSITY VERSUS SHEAR RATE FOR FLOPAAM5115VHM WITH VARIOUS

SALINITY LEVEL. ... 108 FIGURE 75POWER-LAW PLOT OF VISCOSITY VERSUS SHEAR RATE FOR FLOPAAM3630-S WITH VARIOUS

SALINITY LEVEL. ... 108 FIGURE 76LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S0 G/L NACL POLYMER SOLUTION. ... 109 FIGURE 77LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S5 G/L NACL POLYMER SOLUTION. ... 109 FIGURE 78LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S10 G/L NACL POLYMER

SOLUTION. ... 110

x FIGURE 79LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND LPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S20 G/L NACL POLYMER

SOLUTION. ... 110 FIGURE 80LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S0 G/L NACL POLYMER SOLUTION. ... 111 FIGURE 81LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S5 G/L NACL POLYMER SOLUTION. ... 111 FIGURE 82LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S10 G/L NACL POLYMER

SOLUTION. ... 112 FIGURE 83LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND EPTT-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S20 G/L NACL POLYMER

SOLUTION. ... 112 FIGURE 84LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S0 G/L NACL POLYMER SOLUTION. ... 113 FIGURE 85LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S5 G/L NACL POLYMER SOLUTION. ... 113 FIGURE 86LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S10 G/L NACL POLYMER

SOLUTION. ... 114 FIGURE 87LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S20 G/L NACL POLYMER

SOLUTION. ... 114 FIGURE 88LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S0 G/L NACL POLYMER SOLUTION. ... 115 FIGURE 89LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S5 G/L NACL POLYMER SOLUTION. ... 115 FIGURE 90LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S10 G/L NACL POLYMER

SOLUTION. ... 116 FIGURE 91LOGLOG PLOT OF NORMALIZED VISCOSITY (RED DOTS) AND C-FENE-P-MODEL VISCOSITY PREDICTION

(BLUE LINE) VERSUS DIMENSIONLESS SHEAR RATE FOR FLOPAAM3630-S20 G/L NACL POLYMER

SOLUTION. ... 116 FIGURE 92NORMALIZED SHEAR STRESS GROWTH VERSUS TIME FOR FLOPAAM3630-S WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 1 S− 1. ... 117 FIGURE 93NORMALIZED SHEAR STRESS GROWTH VERSUS TIME FOR FLOPAAM3630-S WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 10 S− 1. ... 117 FIGURE 94NORMALIZED SHEAR STRESS GROWTH VERSUS TIME FOR FLOPAAM3630-S WITH VARIOUS NACL

CONCENTRATIONS AT STEP SHEAR RATE 100 S− 1. ... 118 FIGURE 95NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM3630-S0 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES

REPRESENTING MODEL PREDICTIONS FOR STEP RATES (S− 1)1 GREEN, 10(BLUE) AND 100 S− 1(RED). .... 118 FIGURE 96NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM3630-S5 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES

REPRESENTING MODEL PREDICTIONS FOR STEP RATES (S− 1)1 GREEN, 10(BLUE) AND 100 S− 1(RED). .... 119 FIGURE 97NORMALIZED SHEAR STRESS GROWTH AND LPTT-MODEL PREDICTION VERSUS DIMENSIONLESS TIME, R,

FOR FLOPAAM3630-S10 G/L NACL.DOTS REPRESENTING MEASURED DATA AND DASHED LINES

REPRESENTING MODEL PREDICTIONS FOR STEP RATES (S− 1)1 GREEN, 10(BLUE) AND 100 S− 1(RED). .... 119