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Thixotropy is a great rheological behavior of waxy crudes oils and is of great importance for hydraulic characteristics and security of oil pipeline restart. In this paper, through the experiment of four waxy crudes, three kinds of thixotropic rheology characteristics in the conditions that shear stress decays under a constant shear rate, shear stress decays after shear rate steps up and hysteresis loop of shear rate cycle changes are studied . For eight thixotropic models, experimental data are fitted in the method of least-squares and average deviation is taken as a statistical indicator to evaluate the thixotropic models. It shows that the model with the idea of Cheng that completely reversible and totally irreversible structures both exist in waxy oil products and based on Houska model can describe thixotropic behaviors of waxy crudes most well.

Thixotropy is a great rheological behavior of many materials including waxy crude oils and is of great importance for hydraulic characteristics and security of oil pipeline restart. It can be described that due to the difference between failure rate and recovery rate of internal structure of the fluid system, under the effect of shear stress, the apparent viscosity continuously decreases with time and recovers gradually over time after stress relieving [

Domestic and foreign scholars had a wide range of studies for thixotropic fluid including crude and made a number of mathematical models used to describe the characteristics of thixotropic fluid [

Through experiments in the paper, three thixotropic rheological characteristics above of waxy crude are studied and eight thixotropic models in the literature are evaluated.

A stress-controlled rheometer (HAAKE RS150H) was used as an experimental apparatus.

The pretreated oil sample was heated to a heat-treating temperature as shown in

In this paper, experiment of four crude oils is done for each measurement temperature under the constant shear rate loaded including 1 s^{−}^{1}, 2 s^{−}^{1}, 4 s^{−}^{1}, 8 s^{−}^{1}, 16 s^{−}^{1}, 32 s^{−}^{1} and the shear rate loaded that steps up. Each shear rate experiment adopts new sample and shear time is 10 min. Record data points per second.

During the hysteresis loop measurement, shear rate is changing linearly according to the following methods.

R is rate of change of the shear rate (for constant in an experiment), s^{−}^{1}/s; t_{1} is the time for shear rate rising, s.

Experimental temperature is near the pour point temperature of oils, and rate of change of shear rate is 1.5625 s^{−}^{1}/s, 1.0 s^{−}^{1}/s, 0.5 s^{−}^{1}/s, 0.2 s^{−}^{1}/s, 0.05 s^{−}^{1}/s and 0.025 s^{−}^{1}/s. The time for shear rate rising is 16 s, 25 s, 50 s, 125 s, 500 s and 1000 s.

The thixotropic models in the literature that put forward for studying waxy crude oils, widely applied in the waxy crude oil at present and put forward for blood and being applicable to description of blood hysteresis loop are object of study.

Model 1: This model was originally developed for slurry by Houska but currently widely used for hydraulic analysis of oil pipeline restart [

Oil | Properties | |||
---|---|---|---|---|

Wax content [ | WAT [ | Gel point @ heating-up temperature [ | Density at 20˚C [^{−}^{3} | |

Daqing | 24.37 | 42 | 32 (45) | 863.11 |

Zhongyuan | 21.51 | 51 | 33 (53) | 856.09 |

Daqing-Nanpu mixed | 14.20 | 44 | 29 (50) | 866.18 |

Sudan | 18.78 | 63 | 38 (65) | 892.20 |

where ^{−1}; t is the shear time, s. τ_{y}_{0} represents the permanent yield stress and τ_{y}_{1} is the thixotropic part of yield stress, which can decay with time. The symbol of a is structure buildup rate constant, while b is structure breakdown rate constant. k, Δk, m, n are all model parameters, unit of the first two is Pa∙s_{n}, the last two are dimensionless.

In general, all the parameters in the model are determined by fitting experimental data (as well as other models below). Houska model does not consider that structure in limited time is not completely reversible.

Model 2: This model was proposed by Zhao Xiaodong inspired by Cheng’s hypothesis of existence of reversible and irreversible structures in waxy oils [

where _{y}_{2} is the thixotropic part of yield stress of recoverable structure, Pa. τ_{y}_{3} is the thixotropic part of yield stress of unrecoverable structure, Pa. a_{1 }is the building rate constant of recoverable structure, s^{−1}; b_{1} is the cracking rate constant of recoverable structure, s^{m}^{−}^{1}; b_{2} is the cracking rate constant of unrecoverable structure, s^{m}^{−}^{1}; k, Δk_{1}, Δk_{2}, m_{1}, m_{2}, n are all model parameters, unit of the first three is Pa・s^{n}, the last three are dimensionless.

Model 3: This model was by Chen Hongjian based on Houska model and the characteristic is that it uses separate structure parameters for the yield stress and the consistency cracking down [

where _{1}, a_{2}, b_{1}, b_{2}, m_{1}, m_{2} are all model parameters. The units are the same as the former ones.

Model 4: This model is proposed by Huang based on statistical mechanics and irreversible thermodynamics principle of state variables entropy. It is derived by introducing a structural arrangement parameter to describe system entropy increase rate caused by structural changes due to the shearing and has been used to describe the hysteresis loop feature of human body blood [

where _{1} is the aggregate dissociation rate constant, s^{n−1};

Under the experimental condition of hysteresis loop, the expression of the model is shown below.

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Model 5: Fang Bo developed this model to describe the hysteresis loop feature of viscoelastic-thixotropic behavior of blood [

where G is the elastic modulus, Pa.

Under the condition of constant shear rate and after integral, the equation is shown below.

For the loading mode of hysteresis loop and after integral, the equation is shown below.

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Model 6: This model is proposed by Fang Bo based on the model 5 and has been used to describe hysteresis loop characteristics that reflect viscoelasticity, thixotropy and shear thinning feature of blood [

where K_{0} is the dissociation rate constant of elastomer, s^{m}^{−}^{1}; m is the parameter of the impact on elastomer dissociation rate of

Under the condition of constant shear rate and after integral, the equation is shown below.

For the loading mode of hysteresis loop and after integral, the equation is shown below.

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Model 7: The model proposed by Hou Lei for viscoelastic mechanics analysis of waxy crude oils, has been used to describe the stress attenuation characteristics of Daqing crude oil and Zhongyuan crude oil with the pour-point depressants under the constant shear rate [

where _{eq }is the structural parameter when the shear reaches a balance, dimensionless. k_{1} is cracking rate constant of structure, s^{1}^{−}^{q}; k_{2} is the recovery rate constant of structure, s^{−}^{q}; a and c are parameters, unit is Pa×s^{b} and Pa×s^{d} respectively.

Model 8: The model ia proposed by Liu Gang with mechanical analogy principle, which is a viscoelastic- thixotropic mathematical model that liken the gelled crude oil to the physical model that Maxwell body and thixotropic components parallel. It is used to describe the stress attenuation characteristics of the waxy crude oils under constant shear rate [

where B is the characteristic parameter associated with the size of wax crystal flocculation body in crude oil, Pa×s; n is the parameter related to structural damage, dimensionless; D is the cracking rate constant of structure, s^{n}^{−}^{1}.

Under the condition of constant shear rate and after integral, the equation is

Among them,

where t_{1} is the time as the shear rate increases from 0 to a set value, s; k is the linear increase rate as the shear rate increases from 0 to a set value, s^{−}^{2}.

For the loading mode of hysteresis loop and after integral according to the relationship between the shear rate and the time, the equation is shown below.

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For three kinds of loading modes, the mathematical models above are respectively integrate and dispersed,and experimental data are fitted with the least-squares principle through the computer program, then the model parameter values can be obtained respectively. At the same time the average deviation is used as a statistical index that evaluates the goodness fit of the fitting curve and the experimental data. Here the average deviation is defined as the average value of deviation absolute value between experimental and fitting value.

4 oil samples described in

The result shows that fitting effect of model 2 is the best for four kinds of waxy crude oils under three kinds of loading modes, which is obviously superior to other models. Fitting effect of model 4 - 6 put forward for thixotropy of human body blood is not good when used to describe hysteresis loop of thixotropy of waxy crude oils. And under the other two loading modes, their fitting effect is also inferior to other models, so they are not suitable for waxy crude oils.

With the thixotropy test data of four kinds of waxy crude oils under three kinds of loading modes, feasibility of eight thixotropic models that describe the thixotropy of waxy crude oils in the literature has been evaluated. The

Loading Mode | Oil | AADs of Various Model, /% | |||||||
---|---|---|---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Model 7 | Model 8 | ||

Hysteretic loop | Zhongyuan | 10.363 | 5.360 | 10.475 | 19.312 | 21.025 | 19.049 | 11.955 | 24.144 |

Daqing | 14.257 | 7.611 | 14.501 | 42.601 | 45.602 | 41.610 | 22.217 | 54.451 | |

Daqing-Nanpu mixed | 16.894 | 7.113 | 18.376 | 48.685 | 45.259 | 45.592 | 26.071 | 57.876 | |

Sudan | 10.136 | 5.428 | 10.793 | 29.182 | 27.927 | 28.508 | 14.839 | 39.069 | |

Shear rate step up | Zhongyuan | 4.547 | 2.134 | 4.136 | - | 8.208 | 8.508 | 3.502 | 7.369 |

Daqing | 5.074 | 3.171 | 4.410 | - | 8.268 | 11.556 | 3.839 | 6.092 | |

Daqing-Nanpu mixed | 6.640 | 2.405 | 6.060 | - | 7.934 | 8.909 | 5.098 | 8.039 | |

Sudan | 2.441 | 1.265 | 2.250 | - | 3.681 | 3.396 | 2.099 | 4.110 | |

Constant shear rate | Zhongyuan | 9.821 | 3.255 | 5.904 | - | 14.395 | 13.600 | 8.144 | 10.000 |

Daqing | 9.262 | 2.815 | 6.728 | - | 14.779 | 15.124 | 7.490 | 9.205 | |

Daqing-Nanpu mixed | 10.053 | 3.499 | 4.204 | - | 14.753 | 13.878 | 8.364 | 10.342 | |

Sudan | 9.226 | 3.192 | 4.853 | - | 16.674 | 12.313 | 6.438 | 10.263 |

a. For model 4, only test data of hysteresis loop were fitted.

result shows that:

1) Model 2 with the idea of Cheng that completely reversible and totally irreversible structures both exist in waxy oil products, based on the Houska model and with two structure parameters can well describe three thixotropic behaviors of waxy crudes.

2) Models 4 - 6 put forward for the human body blood thixotropy are not suitable for waxy crudes.

National Natural Science Foundation of China (No. 51404072).