Abstract
A severe problem to flow assurance occurs when subsea flowlines become blocked with gelled waxy crudes. To design proper surface pump facilities, it is essential to know the minimum pressure required to restart the flow. Simulating and predicting this minimum pressure require the understanding of several physical phenomena, including compressibility, shrinkage, and rheological behavior. This study aims to characterize and simulate the rheological behavior of two commercial waxy crude oils. Based on its survey of the literature, we select the de Souza Mendes and Thompson (2013) model to fit the oil’s behavior and then conduct, using a rheometer, a considerable number of experiments with the selected oils. To verify the solution of our algorithm, we compared our theoretical solutions with some results of the literature. When comparing the simulation with experiments, the model was unable to predict the data perfectly; hence, we propose a modified version without changing the physical meaning of the equations, to improve its predictions. Once any of the empirical parameters were able to influence the elastic behavior in such a way that the shear stress decreased with time, the structural elastic modulus function was modified, which means that the relation of the structure parameter and the storage modulus was modified. One of the interesting results of the analysis is when relating the storage modulus and a new parameter added in the modification, a value was found to be, regardless of the aging time or the oil used, constant.
Similar content being viewed by others
Abbreviations
- a, b, m :
-
Empirical parameters
- C:
-
Atom of carbon
- H:
-
Atom of hydrogen
- t eq :
-
Equilibrium time (s)
- n :
-
Herschel-Bulkley exponential term
- k :
-
Herschel-Bulkley apparent viscosity (Pa. s)
- G 0 :
-
Storage modulus of the completely structured material (Pa)
- G s :
-
Structural elastic modulus (Pa)
- G′:
-
Storage modulus (Pa)
- G″:
-
Loss modulus (Pa)
- λ :
-
Structure parameter
- λ 0 :
-
Initial value of the structure parameter
- λ eq :
-
Structure parameter at equilibrium
- γ :
-
Strain (m)
- γ e :
-
Elastic strain (m)
- γ v :
-
Viscous strain (m)
- τ :
-
Shear stress (Pa)
- τ y :
-
Static limit of the shear stress (Pa)
- τ yd :
-
Dynamic shear stress (Pa)
- \( \dot{\gamma} \) :
-
Shear rate (s − 1)
- \( {\dot{\gamma}}_1 \) :
-
Transition shear rate from static to viscous (s − 1)
- η :
-
Apparent viscosity (Pa. s)
- η ∞ :
-
Purely viscous (Pa. s)
- η s :
-
Structural viscosity (Pa. s)
- η v :
-
Addition of η ∞ and η s (Pa. s)
- η 0 :
-
Initial viscosity (Pa. s)
- η eq :
-
Viscosity at equilibrium (Pa. s)
- θ 1 :
-
Relaxation time (s)
- θ 2 :
-
Retardation time (s)
References
Ajienka JA, Ikoku CU (1991) The effect of temperature on the rheology of waxy crude oils
Barnes HA (1997) Thixotropy—a review. J Non-Newtonian Fluid Mech 70(1):1–33
Barnes HA (1999) The yield stress—a review or ‘παντα ρει’—everything flows? J Non-Newtonian Fluid Mech 81(1):133–178
Barnes HA, Walters K (1985) The yield stress myth? Rheol Acta 24(4):323–326
Chang C, Boger DV, Nguyen QD (1998) The yielding of waxy crude oils. Ind Eng Chem Res 37(4):1551–1559
Chang C, Nguyen QD, Rønningsen HP (1999) Isothermal start-up of pipeline transporting waxy crude oil. J Non-Newtonian Fluid Mech 87(2):127–154
da Silva JAL, Coutinho JA (2004) Dynamic rheological analysis of the gelation behaviour of waxy crude oils. Rheol Acta 43(5):433–441
Davidson MR, Dzuy Nguyen Q, Chang C, Rønningsen HP (2004) A model for restart of a pipeline with compressible gelled waxy crude oil. J Non-Newtonian Fluid Mech 123(2):269–280
de Souza Mendes PR (2009) Modeling the thixotropic behavior of structured fluids. J Non-Newtonian Fluid Mech 164(1):66–75
de Souza Mendes PR (2011) Thixotropic elasto-viscoplastic model for structured fluids. Soft Matter 7(6):2471–2483
de Souza Mendes PR, Thompson RL (2012) A critical overview of elasto-viscoplastic thixotropic modeling. J Non-Newtonian Fluid Mech 187:8–15
de Souza Mendes PR, Thompson RL (2013) A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids. Rheol Acta 52(7):673–694
Dullaert K, Mewis J (2005) A model system for thixotropy studies. Rheol Acta 45(1):23–32
Dullaert K, Mewis J (2006) A structural kinetics model for thixotropy. J Non-Newtonian Fluid Mech 139(1):21–30
Herschel WH, Bulkley R (1926) Konsistenzmessungen von Gummi-Benzollösungen. Kolloid Z 39:291–300
Lee HS (2008). Computational and rheological study of wax deposition and gelation in subsea pipelines. ProQuest
Luthi IF (2013). Rheological characterization of a waxy crude oil and experimental study of the restart of a line blocked with gelled waxy crude. Campinas: Faculty of Mechanical Engineering, State University of Campinas, 124 p. Master Thesis
Mewis J (1979) Thixotropy—a general review. J Non-Newtonian Fluid Mech 6(1):1–20
Mewis J, Wagner NJ (2009) Thixotropy. Adv Colloid Interf Sci 147:214–227
Mujumdar A, Beris AN, Metzner AB (2002) Transient phenomena in thixotropic systems. J Non-Newtonian Fluid Mech 102(2):157–178
Phillips DA, Forsdyke IN, McCracken IR, Ravenscroft PD (2011a) Novel approaches to waxy crude restart: part 1: thermal shrinkage of waxy crude oil and the impact for pipeline restart. J Pet Sci Eng 77(3):237–253
Phillips DA, Forsdyke IN, McCracken IR, Ravenscroft PD (2011b) Novel approaches to waxy crude restart: part 2: an investigation of flow events following shut down. J Pet Sci Eng 77(3):286–304
Slibar A, Paslay PR (1963) Steady-state flow of a gelling material between rotating concentric cylinders. J Appl Mech 30(3):453–460
Srivastava SP, Handoo J, Agrawal KM, Joshi GC (1993) Phase-transition studies in alkanes and petroleum-related waxes—a review. J Phys Chem Solids 54(6):639–670
Thewlis J (1962) Oxford encyclopedia dictionary of physics
Tiu C, Boger DV (1974) Complete rheological characterization of time‐dependent food products. J Texture Stud 5(3):329–338
Toorman EA (1997) Modelling the thixotropic behaviour of dense cohesive sediment suspensions. Rheol Acta 36(1):56–65
Vinay G, Wachs A, Frigaard I (2009) Start-up of gelled waxy crude oil pipelines: a new analytical relation to predict the restart pressure. In: Asia Pacific Oil and Gas Conference & Exhibition. Society of Petroleum Engineers
Acknowledgments
The authors would like to thank PRH-ANP and Repsol-Sinopec-Brazil, for the financial support to this work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Van Der Geest, C., Guersoni, V.C.B., Merino-Garcia, D. et al. A modified elasto-viscoplastic thixotropic model for two commercial gelled waxy crude oils. Rheol Acta 54, 545–561 (2015). https://doi.org/10.1007/s00397-015-0849-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-015-0849-8