Research on the Effect of Static Pressure on the Rheological Properties of Waxy Crude Oil

Abstract

In this paper, with the application of a MARS 60 high-pressure rheometer, experimental tests are conducted on Shengli crude oil to test its gel point, viscosity and thixotropy under different static pressures. Consequently, the effect of static pressure on the rheological parameters of waxy crude oil is revealed. It is proven that with the increase in the static pressure, the gel point of Shengli crude oil increases linearly, and the viscosity also gradually increases. The power law equation is employed to describe the relationship between the apparent viscosity and shear rate of Shengli crude oil under different static pressures. With the increase in the static pressure, the consistency coefficient (K) increases linearly, and the rheological index (n) decreases linearly. The relationship between the viscosity of Shengli crude oil and the static pressure and shear rate can be obtained. The Cross thixotropic model is used to describe the thixotropic curve of Shengli crude oil under different static pressures. With the increase in the static pressure, the thixotropic coefficient of consistency (ΔK) and the structure fracture constant (b) increase linearly. This is because a high pressure results in high structure strength and strong non-Newton rheological behavior in gelled crude oil and also causes remarkable structure fracture in crude oil. The results in this paper can provide an important theoretical basis for crude oil production and transportation.

1. Introduction

Due to the high gel point and high viscosity components of waxy crude oil, such as wax, resin and asphaltene, waxy crude oil has complicated rheological properties, which cause difficulties in its exploitation and transportation. The rheological properties of waxy crude oil are affected by many factors [1,2,3]. References [4,5,6,7] mainly focus on the influence of crude oil’s composition, thermal history, shear history, gas dissolution and other factors on the rheological properties of crude oil, while the influence of static pressure on the rheological properties of crude oil is rarely involved.

The effects of pressure on the viscosity and wax appearance point of Bohai crude oil were studied [8]. The results show that the viscosity of crude oil increased exponentially with the increase in pressure, and a lower test temperature can cause more sensitive changes in the apparent viscosity of crude oil when the pressure changes. The wax appearance point increased linearly with the increase in pressure, and the wax appearance point increased by nearly 0.1 °C with a 0.1 MPa rise in pressure. The effects of pressure on the viscosity and structure recovery characteristics of Maya crude oil were studied by Mortazavi-Manesh et al. [9]. The results show that the viscosity of crude oil increased with the increase in pressure. In the recovery process of the gel structure, the storage modulus and loss modulus under high pressure were higher than those under normal pressure, and it can be summarized that pressure accelerates the establishment of the microstructure in crude oil. The viscosity–temperature characteristics of heavy crude oil under given temperature and pressure values were studied by Macdonald et al. [10]. The results show that the viscosity of heavy crude oil decreased gradually with the increase in temperature and the decrease in pressure. Referring to the research by Behzadfar et al. [11], the effects of temperature, pressure, CO₂ dissolution and shear rate on the rheological properties of asphaltene were studied using a high-pressure rheometer. It can be concluded that within the test temperature range of −10~180 °C, the viscosity of asphaltene decreases when the temperature increases, and within the test pressure range of 0–15 MPa, an increase in pressure could cause an increase in asphaltene viscosity. It can also be summarized that changes in pressure and CO₂ dissolution can cause more sensitive changes in asphaltene viscosity at a low temperature. Yangi et al. [7] studied the effects of different light hydrocarbons (C1–C4) on the solubility and rheological properties of crude oil under saturated gas dissolution pressure. The solubility of crude oil increases gradually with the increase in the saturated gas dissolution pressure, but the gel point, viscosity and yield stress of crude oil decrease gradually. As for the property improvement results, liquefied petroleum gas was the best, C₂H₄ was the second best and natural gas was the worst. Sun et al. [5] studied the rheological properties of crude oil with different saturation pressures and water contents. The results show that a crude oil emulsion shows non-Newtonian fluid characteristics at a low temperature. Before the water content reaches 70%, the viscosity of the emulsion increases gradually with the increase in the water content; on the contrary, when the water content is over 70%, the viscosity of crude oil increases if the water content increases. With the increase in the water content, the viscosity of the emulsion gradually decreases. In addition, an increase in the CH₄ partial pressure will cause a decrease in emulsion viscosity.

As mentioned above, current studies mainly study the effects of static pressure and saturated gas dissolution pressure on crude oil viscosity, but there are a few studies which focus on the gel point and thixotropic characteristics of crude oil under different static pressure conditions [12,13]. Therefore, it is necessary to study the effects of static pressure on the rheological properties of waxy crude oil. In this paper, a high-pressure test system, a MARS 60 rheometer, is used to carry out experiments on the gel point, viscosity and thixotropy of crude oil under different static pressure conditions. The influence of static pressure on the rheological properties of waxy crude oil is studied, and the relationship between the static pressure and crude oil gel point, viscosity and thixotropy is quantified.

2. Method

2.1. Experimental Instruments and Samples

A MARS60 high-pressure rheometer (Thermo Electron (Karlsruhe) GmbH, made in Karlsruhe, Germany) is used in this research, equipped with a coaxial cylinder sealed pressure unit with a PZ38 measuring rotor, air compressor, temperature control system and software system. As shown in Figure 1, the sealed pressure unit consists of an external magnetic ring, internal magnetic ring, measuring rotor and a sealed system cup. It is necessary to optimize the distance of the magnetic coupling measurement before starting experiments. The optimum distance is 1.3 mm (measured by 1035 standard viscosity liquid). Before the test, the sealed system with a rotor is placed on the main body of the rheometer, and once the test starts to run, the outer magnetic ring is driven by measuring the axis; then, the rotation motion of the rotor is realized under the influence of magnetic coupling. In the test process, the temperature and pressure are measured by the control system. N₂ is used as a pressure medium to study the effect of static pressure on the rheological properties of gelled crude oil, and because N₂ shows poor solubility in crude oil, the effect of N₂ can be neglected [9].

The tested oil sample is Shengli crude oil, and the basic physical properties of Shengli crude oil (20 °C; 0.1 MPa) are shown in

Table 1. Basic physical properties of Shengli crude oil.

Density (20 °C, kg/m3)	Wax Content (%)	Asphaltene Content (%)	Resin Content (%)	Gel Point (°C)
884.0	34.67	0.68	4.88	24.4

. To ensure the repeatability of the measurement results, oil samples need to be pre-treated at 70 °C to eliminate the effects of shear and thermal history of crude oil. The oil sample density is measured by standard GB/T1884-2000 [14], and the gel point of the oil sample is measured using the method of crude oil rheology [15].

2.2. Experimental Program

2.2.1. Modulus and Loss Factor

In viscoelasticity, modulus parameters are commonly used to characterize the viscoelasticity of materials. Among them, the storage modulus reflects the elasticity of materials, and the loss factor represents the relative elasticity and viscosity of materials. A small-amplitude oscillatory measurement is used to obtain the variation in the storage modulus and loss factor of Shengli crude oil with the changes in temperature under different static pressures. Therefore, the gelling point can be calculated. The experimental process is as follows: the pre-treated oil sample is added into the sealed pressure unit, the sealed pressure unit is scavenged and pressurized, the pressure range is 0–5 MPa, the oil sample is heated at a constant temperature of 70 °C for 20 min, the sample is cooled to 15 °C with a cooling rate of 0.5 °C/min, and during the cooling process, a small-amplitude oscillating shear test with a 0.1 Hz oscillating frequency is carried out.

2.2.2. Viscosity

The dynamic cooling test is applied for the measurement of Shengli crude oil viscosities under the conditions of different static pressures, shear rates and temperatures. The pre-treated oil sample is added into the sealed pressure unit, the sealed pressure unit is scavenged and pressurized, the pressure range is 0–5 MPa and the oil sample is heated at a constant temperature of 70 °C for 20 min and then cooled to 15 °C with a cooling rate of 0.5 °C/min. During the cooling process, different shear rates are applied for the dynamic cooling test.

2.2.3. Thixotropy

The thixotropic curves of Shengli crude oil under different static pressures are measured using a MARS60 high-pressure rheometer. The pre-treated oil sample is added into the sealed pressure unit, the sealed pressure unit is scavenged and pressurized, and the pressure range is 0–5 MPa. Firstly, the oil sample is heated at a constant temperature of 70 °C for 20 min; secondly, the sample is cooled to 45 °C with a cooling rate of 2 °C/min and sheared for 10 s⁻¹ at a constant temperature for 20 min; then, the oil sample is cooled to the measured temperatures (22–24 °C) at a cooling rate of 0.5 °C/min and kept at a constant temperature for 50 min to ensure the gelled structure of the crude oil is fully formed. At last, constant shear rate tests (5 s⁻¹, 10 s⁻¹ and 15 s⁻¹) are carried out to obtain the thixotropic curves of gelled crude oil.

3. Results and Discussion

3.1. Gel Point of Waxy Crude Oil

A small-amplitude oscillatory measurement is carried out to obtain the variation in the storage modulus and loss factor of waxy crude oil with the changes in temperature under different static pressures. Therefore, the gel point can be calculated. As shown in Figure 1, when the temperature drops to about 30 °C, the wax molecules in crude oil gradually precipitate and form a spatial network structure; thus, waxy crude oil gradually changes from a Newtonian fluid to a non-Newtonian fluid. With the further decrease in temperature, the storage modulus increases sharply. This is because of the structural strength enhancement of crude oil, which occurs with the increase in static pressure, as when the density of crude oil increases, the internal structure of crude oil becomes more compact and the effective distance between wax crystals decreases gradually; thus, a greater Van der Waals attraction can accelerate the establishment of the internal microstructure in crude oil, so the storage modulus of crude oil increases gradually with the increase in static pressure.

When the temperature decreases, the wax molecules in crude oil crystallize gradually, and the intercrystalline space between wax crystals form a space network structure which can trap liquid crude oil inside; therefore, crude oil gradually changes from a sol state to gel state. Referring to former research [14], based on the results of the small-amplitude oscillatory measurement, when (the loss factor) δ = 45°, the corresponding temperature is the gel point of crude oil. The gel points of Shengli crude oil under the test pressure are 24.4 °C, 24.8 °C, 25.1 °C, 25.4 °C, 25.7 °C and 26.0 °C, respectively. With an increase in the static pressure, the gel point of Shengli crude oil increases gradually by about 0.3 °C with a rise of 1 MPa in pressure. Moreover, the relationship between the gel point (T_n) and pressure (p) can be described through linear fitting (T_n = 24.448 + 0.314·p, R² = 0.997).

3.2. Viscosity of Waxy Crude Oil

Dynamic cooling experiments are used to test the viscosity of Shengli crude oil under different static pressures, and the fitting results and relationship between the shear rate and temperature are shown in Figure 2. Obviously, under the same temperature and shear rate, the crude oil viscosity increases gradually with the increase in static pressure, and the effect of an increasing pressure on the oil viscosity is similar to that of the decrease in temperature on crude oil viscosity. Moreover, under the same temperature and pressure, the viscosity of crude oil decreases with the increase in the shear rate. An increasing pressure is conducive to the establishment of crude oil’s internal microstructure, forming a three-dimensional network structure, adsorbing surrounding liquid crude oil and trapping it in the space network structure to form a solvation layer [16], thus resulting in an increase in viscosity. However, with the increase in shear rate, cross-linking between wax crystals is inhibited, while the solvation layer in crude oil is destroyed, resulting in a decrease in the viscosity of the crude oil system.

The power law equation [15] is used to describe the relationship between the apparent viscosity (μ) and shear rate ($\dot{\gamma }$) of waxy crude oil under different static pressures, and the fitting parameters are shown in

Table 2. Parameters (K and n) of power law equation under different static pressures.

Temperature	Parameter	0.1 MPa	1 MPa	2 MPa	3 MPa	4 MPa	5 MPa
18 °C	K	21.44	23.94	25.50	27.68	29.86	32.42
	n	0.31	0.295	0.285	0.273	0.258	0.233
20 °C	K	14.39	16.67	19.88	21.49	22.59	24.15
	n	0.350	0.332	0.312	0.287	0.277	0.257
22 °C	K	8.59	10.28	12.32	14.73	15.89	17.07
	n	0.372	0.350	0.319	0.306	0.292	0.286
24 °C	K	4.68	6.07	7.06	9.39	10.15	11.21
	n	0.403	0.394	0.354	0.342	0.323	0.313

.

$$\mu =K{\dot{\gamma }}^{n-1}$$

(1)

where K is the consistency coefficient in Pa·sⁿ, and n is the rheological index.

Based on the above analysis, it can be seen that under the same temperature, with the increase in the static pressure, the consistency coefficient increases and the rheological index decreases gradually; under the same static pressure, with the increase in temperature, the consistency coefficient decreases gradually and the rheological index decreases gradually. The results show that the non-Newton rheological behavior of gelled crude oil increases and the shear thinning behavior is weakened by the increases in static pressure and temperature. On the contrary, the non-Newton rheological behavior of gelled crude oil decreases and the shear thinning behavior is strengthened with the decrease in static pressure and the increase in temperature.

With reference to the experimental data, studies have been carried out on the variation in the consistency coefficient and rheological index with static pressure in the power law equation. As shown in Figure 3, which presents the corresponding fitting curves, the parameters in the power law equation vary with the static pressure. The consistency coefficient (K) and rheological index (n) are conditional parameters, which depend greatly on the static pressure, as shown in

Table 3. Values of consistency coefficient (K) and rheological index (n) under different static pressures (p).

Temperature	Fitted Equation	R2	Fitted Equation	R2
18 °C	K = 21.46 + 2.14p	0.995	n = 0.312 − 0.015p	0.969
20 °C	K = 14.99 + 1.95p	0.959	n = 0.349 − 0.019p	0.990
22 °C	K = 8.74 + 1.76p	0.982	n = 0.365 − 0.018p	0.935
24 °C	K = 4.72 + 1.35p	0.977	n = 0.403 − 0.019p	0.950

[9,11]. The increase in static pressure is beneficial to the formation of a solvation layer, which results in the increase in viscosity and consistency coefficient. With the increase in the static pressure, the internal structure of crude oil becomes more compact, and the effective distance between wax crystals decreases gradually; thus, the wax intercrystalline force increases, which weakens the shear thinning behavior and rheological index. Therefore, linear fitting can be used to describe the relationship between parameters (K, n) and static pressure.

3.3. Thixotropy of Waxy Crude Oil

The thixotropic behavior of Shengli crude oil under different static pressures was tested using the constant shear rate test, and the thixotropic curves of Shengli crude oil under different static pressures are shown in Figure 4. Within the range of the test static pressures, the thixotropic curves of crude oil under different static pressures are similar to those of crude oil under an atmospheric pressure, and the wax crystal network structure of crude oil is destroyed by a constant shear rate, while the shear stress (τ) gradually decreases until a dynamic equilibrium state is reached. In the test results, with the increase in static pressure, the maximum shear stress and equilibrium shear stress increase, and the structural fracture of gelled crude oil becomes more significant. The thixotropic behavior of gelled crude oil is closely related to the size and dispersion of the wax crystal. Compared with crude oil under an atmospheric pressure, the density of crude oil under high pressure increases, the effective distance between wax crystals decreases and the internal structure of crude oil becomes more compact under high pressure, which causes an increase in the Van der Waals attraction between wax crystals, and smaller wax crystals form a large wax crystal floc through mutual adsorption. This kind of formation promotes the establishment of the internal microstructure in crude oil and enhances the internal structure of crude oil. Higher pressure gives rise to higher wax crystal size, dispersion degree, speed of shear stress attenuation and speed of structural fracture in gelled crude oil.

In order to describe the thixotropic curves of Shengli crude oil under different static pressure conditions, the Cross model [15] is used to fit the relationship, and the model is shown as follows:

$$\tau =(K+\lambda \mathrm{\Delta }K){\dot{\gamma }}^n$$

(2)

$${\displaystyle \frac{d\lambda }{dt}}=a(1-\lambda )-b\lambda {\dot{\gamma }}^m$$

(3)

where τ (Pa) is the shear stress, τ_y0 (Pa) is the residual yield stress, τ_y1 (Pa) is the thixotropic yield stress, ΔK (Pa·sⁿ) is the thixotropic coefficient of consistency, a is the structuring constant and b and m are the structure fracture constants, respectively.

According to the reduction in the former literature [17], rate equations can be converted into the following equation:

$$\lambda ={\lambda }_e+({\lambda }_0-{\lambda }_e)\exp [-(a+b{\dot{\gamma }}^m)t]$$

(4)

where λ₀ is the structure parameter when the shear time is 0, λ₀ = 1 and ${\lambda }_e={\displaystyle \frac{a}{a+b{\stackrel{·}{\gamma }}^m}}$ is the equilibrium shear stress.

A thixotropic model of crude oil can be drawn as follows:

$$\tau =\left\{K+\left[{\displaystyle \frac{a}{a+b{\dot{\gamma }}^m}}+(1-{\displaystyle \frac{a}{a+b{\dot{\gamma }}^m}})\exp \left[-(a+b{\dot{\gamma }}^m)t\right]\mathrm{\Delta }K\right]\right\}{\dot{\gamma }}^n$$

(5)

With the help of the curve fitting tool in MATLAB (R2017b), Equation (5) is used to fit the thixotropic curves of Shengli crude oil under different shear rate conditions, the fitted curve is shown in Figure 5 and the corresponding parameters are shown in

Table 4. Parameters of Cross model.

Temperature	Pressure (MPa)	K	ΔK	a	b	m	n	R2
22 °C	0.1	40.71	99.01	0.00483	0.0225	0.407	0.353	0.978
	1	49.32	109.6	0.00331	0.0230	0.355	0.329	0.966
	2	64.13	123.7	0.00158	0.0307	0.258	0.252	0.980
	3	69.52	133.4	0.00587	0.0316	0.0220	0.219	0.980
	4	76.27	162.8	0.00841	0.0430	0.0300	0.210	0.969
	5	88.46	173.3	0.00341	0.0476	0.207	0.200	0.967
24 °C	0.1	24.17	88.5	0.01627	0.0243	0.369	0.282	0.960
	1	32.58	101.6	0.00833	0.0281	0.106	0.252	0.984
	2	40.75	115.3	0.00989	0.0304	0.1	0.231	0.973
	3	52.49	124.0	0.00891	0.0341	0.082	0.212	0.965
	4	61.44	135.1	0.00915	0.0435	0.07	0.209	0.957
	5	73.05	149.2	0.00665	0.0450	0.01	0.199	0.964

. In the fitting tool, the x-axis is the shear rate, the y-axis is time and the z-axis is shear stress.

In Figure 5, it can be seen that the Cross model can well describe the fracture curve of Shengli crude oil under different static pressures. According to the data in

Table 5. Relationship between variation in model parameters and static pressure under different temperatures and shear rates.

Temperature	Fitted Equation	R2	Temperature	Formula	R2
22 °C	K = 41.05 + 9.41p	0.978	24 °C	K = 22.40 + 9.94p	0.997
	ΔK = 94.15 + 15.69p	0.968		ΔK = 88.87 + 11.95p	0.993
	b = 0.019 + 0.0054p	0.926		b = 0.023 + 0.0045p	0.944
	n = 0.345 − 0.033p	0.867		n = 0.272 − 0.016p	0.893

, it is obvious that the parameters including K, ΔK and b all increase with the increase in static pressure, the relationship between these three factors and the static pressure is linear, the specific relationship is shown in Figure 6 and the corresponding relationship is shown in Table 5. The value of a changes a little, while the value of n decreases linearly with the increase in static pressure, which shows that with the increase in static pressure, the structure of gelled crude oil shows stronger strength, and crude oil shows an evident non-Newton rheological behavior, and similarly, the structure fracture of crude oil can be strengthened when the static pressure rises.

4. Conclusions

Taking Shengli crude oil as example, this paper analyses the effects of different static pressures on the rheological properties of waxy crude oil. The following conclusions can be drawn:

(1) Static pressure decreases the effective distance between wax crystals, increases the Van der Waals attraction between wax crystals and enhances the strength of the gel structure, which brings out strong non-Newtonian fluid characteristics in Shengli crude oil. With the increase in static pressure, the gel point and viscosity of gelled crude oil increase gradually, and the structural fracture of gelled crude oil becomes more significant.

(2) A linear relationship can well describe the relationship between the gel point of Shengli crude oil and static pressure.

(3) The power law equation is used to describe the relationship between the apparent viscosity and shear rate of Shengli crude oil under different static pressures; with the increase in static pressure, parameter K increases linearly and parameter n decreases linearly. The relationship between the viscosity of Shengli crude oil and the static pressure and shear rate can be obtained.

(4) The Cross thixotropic model is used to describe the thixotropic curve of Shengli crude oil under different static pressures; with the increase in static pressure, parameters K, ΔK and b all increase linearly, while parameter n decreases linearly.