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A modified elasto-viscoplastic thixotropic model for two commercial gelled waxy crude oils

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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.

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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)

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Acknowledgments

The authors would like to thank PRH-ANP and Repsol-Sinopec-Brazil, for the financial support to this work.

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Authors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, 13083-860, Brazil

    Charlie Van Der Geest & Antonio C. Bannwart

  2. Center for Petroleum Studies, University of Campinas, UNICAMP, Campinas, 13083-970, Brazil

    Vanessa C. Bizotto Guersoni

  3. Repsol Sinopec Brazil, Rio de Janeiro, 22250-040, Brazil

    Daniel Merino-Garcia

Authors
  1. Charlie Van Der Geest
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  2. Vanessa C. Bizotto Guersoni
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  3. Daniel Merino-Garcia
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  4. Antonio C. Bannwart
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Correspondence to Charlie Van Der Geest.

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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

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  • DOI: https://doi.org/10.1007/s00397-015-0849-8

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