Study of Wax-Solid Deposition and Release-Blockage Effects on SC-CO₂ Displacement Dynamics of High-Pour-Point Oil Through Slim Tube Experiments

Abstract

The quantitative evaluation of the impact of wax-solid deposition on the CO₂ displacement of high-pour-point oil has long been a challenge in gas-flooding experiments. This study employs slim tube experiments to simulate the displacement dynamics, and comprehensively evaluates the productivity/injectivity index formula and the GERG-2008 state equation. The results indicate that the fluctuations in this index remain stable within the 17–20 MPa range and become pronounced within the range of 30–40 MPa. The analysis of seepage velocity reveals an initial increasing trend for supercritical CO₂ under the conditions of 30 MPa, 35 MPa, and 40 MPa, followed by inflection points at different time steps. The observed decline in seepage velocity inflection is associated with the occurrence of wax-solid deposition in high-pour-point oil. Notably, there is a significant surge in CO₂ seepage velocity at 40 MPa during the latter stage of the experiment due to the release-blockage effect of supercritical CO₂. To systematically analyze the influence of wax-solid on the CO₂ displacement in high-pour-point oil, a methodological framework is established in this study. This approach enables precise analysis of displacement dynamic characteristics in the target areas and provides pressure parameters for oilfields.

1. Introduction

High-pour-point oil is a type of crude oil characterized by unique properties, notably its high wax content [1]. In the development of this type of crude oil, cold water displacement was revealed to be generally ineffective. Consequently, segmental displacement [2], supercritical CO₂ displacement [3,4], or CO₂ mixed displacement [5,6,7] emerged as viable alternatives for enhancing displacement efficiency. While CO₂ displacement offers several advantages, such as reducing crude oil viscosity and interfacial tension [8,9], it is not without drawbacks. Wax-solid deposition poses significant challenges during development operations. Once precipitated, wax-solids tend to accumulate on reservoir rock surfaces and downhole equipment, blocking reservoir pores and thereby diminishing well productivity and elevating production and operational costs. From the perspective of flow mechanism analysis, the presence of wax-solids directly affects the fluid flow regime in porous media, which differs from the asphaltene deposition observed in heavy oil separation [10]. It is difficult to directly separate wax-solids, making the assessment of fluid flow states during CO₂ oil displacement even more challenging. The intervention process of carbon dioxide is a complex physical and chemical process, during which changes in temperature and pressure conditions can affect wax precipitation, deposition, and seepage dynamics. In addition, during the occurrence of blockage, due to the high penetration, acidification, expansion, and displacement characteristics of carbon dioxide itself, a release-blockage effect may occur. This study employs slim tubes as carriers and integrates experimental displacement results with various equation-based simulation methods, offering a comprehensive evaluation of the wax-solid displacement process.

For the design and optimization of technologies such as enhanced oil recovery and carbon capture and storage, it is crucial to accurately capture the phase behavior of supercritical CO₂. As the core tool for predicting supercritical carbon dioxide (SC-CO₂) thermophysical properties, the accuracy and applicability of the equation of state directly affect the reliability of engineering solutions [11,12]. Currently, cubic state equations (such as the PR equation [13,14,15] and SRK equation [16,17,18]) are widely used to predict SC-CO₂ density, fugacity coefficients, and phase equilibrium due to their simplicity and computational efficiency. Recently, multi-parameter state equations, such as GERG-2008 [19,20,21], have gained attention in oil and gas reservoir engineering, particularly for calculations involving CO₂ containing impurities, CO₂ in saline layers, multi-component phase equilibrium, and minimum miscibility pressure (MMP). These equations also demonstrate advantages in scenarios requiring high precision in phase transition calculations across varied applications [22,23,24]. This study aims to utilize the state equation to restore the parameters of supercritical CO₂ under formation conditions, contributing to a deeper understanding of the displacement and seepage characteristics of high-pour-point oil.

2. Evaluation Parameters and Experimental Procedures

2.1. Index Calculation Formula

The oil recovery index refers to the daily oil production rate from a single well per unit pressure differential, reflecting well productivity while considering factors such as reservoir properties, fluid characteristics, and completion conditions. Another key parameter for evaluating production efficiency is the injectivity index. Based on displacement experiment data, the index formula of the oilfield site is converted into an index formula suitable for physical experiment environments to assess the displacement effects from the core spatial perspective. The formula is as follows:

I_p = V_p/Δp·t

(1)

I_i = V_i/Δp·t

(2)

In the formula, I is the index, p and i represent productivity and injectivity, respectively, both in cm³/(MPa·min), V_p and V_i are oil mining volume and injection volume, both in cm³, and Δp is pressure difference, MPa; t is time, min.

2.2. Preparation Work and Steps for Slim Tube Experiment

Block JG-2 of the Liaohe Oilfield is a typical high-pour-point oil area, in which the crude oil samples were collected. An active oil sample was prepared considering the composition of associated gas. The injected CO₂ had a purity of 99.999%. Key parameters of the experimental equipment and sand-packed slim tube are listed in Table 1 and Table 2. Some reservoirs, especially special reservoirs, have a certain sensitivity to pressure changes. In the experimental process, for oil products with a certain proportion of medium and heavy components (Table 3), the pressure difference was maintained at around 1 MPa, while ensuring a linear pressure gradient state on the displacement path [25,26].

Table 1. Main parameters of the slim tube experimental equipment.

Elements	Main Parameter Information
Slim tube model	The pressure resistance is 100 MPa, and the temperature resistance is 200 °C.
Back-pressure valve	The pressure resistance is 70 MPa, the temperature resistance is 150 °C, and the pressure control accuracy is less than 0.05 MPa.
Electronic balance	The measuring range is 426 g and the sensing accuracy is 0.0001 g.
Gas meter	The effective volume is 1000 mL + 2000 mL, with an accuracy of 1 mL.

Table 2. Detailed properties and parameters of particle- and sand-packed slim tubes.

Length/cm	Inner Diameter/mm	Porosity/Fraction	Permeability/mD	Sand Grain Composition	Particle Diameter Range/mm
1200	4.00	0.48	5553	Quartz sand	0.15–0.18

Table 3. Properties and thermodynamic parameters of oil samples.

Wax Content/%	Asphaltenes and Resins Content/%	Viscosity (100 °C) /(mPa·s)	Density/(g/cm3)	Wax Precipitation Point/°C	Freezing Point/°C
>35	>15	14.5	0.89	60	>45

The experimental procedure includes the following:

(1)

Cleaning the slim tube with petroleum ether, drying it using high-pressure nitrogen in a high-temperature environment, and then evacuating the tube to a vacuum state.

(2)

Establishing the experimental temperature environment: the slim tube was placed in a constant-temperature oven with a temperature accuracy of 0.1 °C, and the experimental environment temperature was monitored and strictly controlled at 60 °C. The slim tube was saturated with petroleum ether, and the pressure was increased to the experimental level.

(3)

Replacing the petroleum ether with the configured active oil while observing the gas-oil ratio (GOR) at the outlet until it matches standard GOR parameters.

(4)

Conducting the displacement experiments using a constant-pressure method: the inlet and outlet pressures of the slim tube are controlled by a constant-pressure pump, the working pressure ranges of the pump range from 0.00 to 100.00 MPa, with a pressure accuracy of 0.1% FS, and the pressure difference required for displacement can be well stabilized within a certain range. During the experiment, injections were performed at intervals of 0.1 pore volume (PV) to measure produced oil, gas volume, and pump position (when the cumulative injection is 1.2 PV, displacement is halted). The reserve recovery is calculated for different injection volumes, and the relationship curve between reserve recovery and injection volume is plotted.

(5)

Utilizing test data to perform MMP tests via extrapolation, calibrating the PV number at breakthrough by analyzing GOR data, and calculating the oil recovery index and injection index using the relevant data.

3. Slim Tube Experiment Results

During the seven-point testing (Figure 1), it is observed that the minimum miscibility pressure of the crude oil sample was very high, exceeding 60 MPa (pressure-bearing limit of equipment). Therefore, the regression extrapolation on the curve of Formula (3) indicated that the minimum miscibility pressure at a recovery efficiency of 90% was 75 MPa.

y = 0.7814x + 31.3930, R² = 0.9478

(3)

Figure 1. Schematic diagram of minimum miscibility pressure extrapolation curve.

Considering the practical significance of engineering, the fracture pressure of reservoir rocks in the research area does not exceed 40 MPa. Therefore, the upper limit of pressure for subsequent research will be set at this level. According to the flow characteristics, the flow of SC-CO₂ in the slim tube carrier can be divided into two stages: pre-breakthrough and post-breakthrough (associated with transition point and breakthrough point). The frequency and amount of contact between SC-CO₂ and crude oil in space before breakthrough are higher, and this stage before breakthrough has a certain representativeness. Based on the experimental characteristics and gas–oil ratios, CO₂ breakthrough positions were determined for each pressure condition, represented in PV numbers (Table 4).

Table 4. Corresponding relationship table between breakthrough point and displacement pressure.

Displacement Pressure/MPa	17	20	30	35	40
Transition point/PV	0.2	0.2	0.5	0.6	0.6
Breakthrough point/PV	0.3	0.3	0.6	0.7	0.7

Before calibrating breakthrough PVs, test data was used to calculate the productivity index and injectivity index, which were then plotted as shown in Figure 2. Figure 2a illustrates the variation in the recovery index with PV. Higher pressures cause more pronounced fluctuations in this index, which is consistent with the trends in the injection index depicted in Figure 2b. Under the conditions of 17 MPa and 20 MPa, CO₂ breakthrough occurred earlier, reaching 0.3 PV, and both the recovery index and injection index remained relatively stable. Under the condition of 30 MPa, these indices peaked at an injected PV of 0.6. Under the conditions of 35 MPa and 40 MPa, the productivity index and injectivity index also reached the maximum values at 0.7 PV. Based on the characteristics of index changes, pressure conditions are categorized into two distinct ranges: 17–20 MPa is the stable fluctuation pressure range and 30–40 MPa is the vigorous fluctuation pressure range. These two segments exhibit qualitatively different seepage characteristics. In the 17–20 MPa range, seepage is stable and uniform. In the 30–40 MPa range, although not reaching the minimum miscibility pressure, the oil sweep advantage of CO₂ displacement is demonstrated.

Figure 2. Productivity/injectivity index change characteristic chart.

4. Seepage Characteristics

4.1. Equation of State and Darcy’s Law

GERG-2008 (GERG-2008 Wide Range Equation of State) is a high-precision equation of state developed by the European Gas Research Organization (GERG) specifically to calculate the thermodynamic properties of natural gas and multi-component mixed fluids. It has certain advantages in calculating the relevant parameters of supercritical fluids. Through comparison and evaluation with experimental data, the calculation error of this equation of state for pure CO₂ is determined to be less than 0.1% [27,28,29].

The functional form of GERG-2008 based on Helmholtz free energy is as follows:

$$\mathsf{\alpha }\left(\delta ,\tau ,\overrightarrow{x}\right)={\alpha }^0\left(\delta ,\tau ,\overrightarrow{x}\right)+{\alpha }^r\left(\delta ,\tau ,\overrightarrow{x}\right)$$

(4)

The residual part is further divided into pure-component contributions and mixed correction terms, expressed as follows:

$${\alpha }^{\gamma }(\mathsf{\delta },\mathsf{\tau },\overrightarrow{x})={\sum }_{i=1}^N{x}_i{\alpha }_i^r\left(\delta ,\tau \right)+∆{\alpha }^r\left(\delta ,\tau ,\overrightarrow{x}\right)$$

(5)

In the formula, δ represents the contrast density; τ is the reciprocal of the comparison temperature; x is the component mole fraction vector. The expression for the mixed correction term is as follows:

$$∆{\alpha }^r\left(\delta ,\tau ,\overrightarrow{x}\right)={\sum }_{i=1}^{N-1}{\sum }_{j=i+1}^N{x}_i{x}_j{F}_{ij}{\alpha }_{ij}^r(\delta ,\tau )$$

(6)

where F_ij is the binary interaction coefficient, and α_ij^r is the cross-term function.

Key information parameters of supercritical fluids are shown in Table 5.

Table 5. Summary of supercritical fluid-related parameters.

Pressure/MPa	Temperature/°C	Density/(g/cm3)	Deviation Factor/Fraction	Viscosity/(mPa·s)
80	60	1.0511	1.2093	0.1357
70	60	1.0187	1.0917	0.1279
60	60	0.9806	0.9721	0.1194
50	60	0.9344	0.8501	0.1102
40	60	0.8759	0.7255	0.0999
30	60	0.7956	0.5991	0.0876
20	60	0.6641	0.4785	0.0710
10	60	0.2822	0.5629	0.0270

The flow characteristics and flow state of the target fluid in the slim tube can be matched with Darcy’s law. We can use Darcy’s law to correlate the velocity and permeability characteristics of CO₂, and these two parameters show a positive correlation. The permeability calculation formula based on Darcy’s law is as shown in Formula (7). Since this study uses a slim tube carrier instead of a traditional core carrier, the length of the carrier is equivalent to the length of the slim tube.

$$K_{sc-{CO}_2}=\mathrm{Q}\mathsf{\mu }\mathrm{L}/\mathrm{A}∆\mathrm{p}$$

(7)

In the equation, K is the permeability of the supercritical state, D; Q is the flow volume per unit time condition, cm³/s; μ is the phase viscosity, mPa·s; L is the length of the carrier, cm; A is the cross-sectional area of the carrier, cm²; Δp is the pressure difference, 10⁻¹ MPa.

In the displacement process of the slim tube experiment, the pressure difference and pressure gradient along the slim tube path were strictly controlled. Although the properties of the oil are unique, we still controlled the pressure difference at around 1 MPa to ensure the stable progress of the displacement process. Table 6 shows the parameters under the corresponding PVs conditions.

Table 6. Statistical data of pressure difference under different pressure and PVs conditions.

Pressure	30 MPa	35 MPa	40 MPa
PVs
0.1	1.17	1.02	1.41
0.2	1.06	0.81	1.20
0.3	1.06	0.84	0.90
0.4	1.09	0.80	1.04
0.5	1.04	0.78	0.69
0.6	/	0.72	0.55

4.2. Velocity Characteristics of SC-CO₂

At the gas collection location, under the changing conditions of temperature and pressure, the precipitation of dissolved gas is usually inevitable, which also makes the properties of the collected gas usually the properties of a mixed gas—that is to say, under each pressure condition, the gas collected at the outlet contains not only CO₂ but also dissolved gas. We can accurately convert the amount of dissolved gas released through the gas oil ratio, thereby indirectly obtaining the accurate carbon dioxide content. Since measurements occur under atmospheric rather than geological conditions, the GERG-2008 equation of state is applied to convert CO₂ properties to reservoir conditions. Additionally, when utilizing mixed-gas measurement data from the outlet, the dissolved gas portion is subtracted by jointly calculating the specific quantity based on measured data from the oil samples collected at the outlet and dissolved GOR parameters.

The study involves calculations under five pressure conditions: 17 MPa, 20 MPa, 30 MPa, 35 MPa, and 40 MPa. The CO₂ velocity is calculated based on the displacement experiment time. After identifying the breakthrough points for each pressure condition, the corresponding transition point and pre-breakthrough curves are plotted. These plots are divided according to the partition of the stable fluctuation pressure range and relatively severe fluctuation pressure range; in situations with relatively severe fluctuations, the number of inflection points on the curve is greater than or equal to 1. As shown in Figure 3, under the relatively low-pressure conditions of 17 MPa and 20 MPa, CO₂ breakthrough occurs earlier. This is primarily due to the significant difference in viscosity between CO₂ and the oil phase at lower pressures, which results in more pronounced differences between CO₂ flow rate and oil phase flow rate. Consequently, the higher the CO₂ flow rate, the earlier the breakthrough occurs. It is noteworthy that under these relatively low-pressure conditions of 17 MPa and 20 MPa, the seepage velocity of supercritical CO₂ does not increase but decreases directly before the rapid breakthrough. This is mainly because under the relatively low-pressure conditions, the dissolution rate is relatively slow, causing higher velocity values at the initial point. Over time, as the gas approaches breakthrough, its expansion capacity increases, enlarging the interaction volume between the injected CO₂ and crude oil. This accelerates dissolution, causing a sudden rise in crude oil flow rate while the speed of supercritical CO₂ declines.

Figure 3. Velocity characteristics of SC-CO₂ in the stable fluctuation pressure range.

Figure 4 presents the statistical results of seepage velocity under relatively high-pressure conditions (30 MPa, 35 MPa, and 40 MPa). It can be seen that the seepage velocity of supercritical CO₂ initially showed an increasing trend, but the increase was limited. When it reached a certain value, it showed a decreasing trend again, although the time of blockage was different. The decline in seepage velocity is related to the occurrence of wax-solid deposition in high-pour-point oil. Specifically, under these temperature and pressure conditions, wax-solid deposition and pore blockage occurred in the slim tube carrier and flow system. It is particularly noteworthy that the significant upward trend in the CO₂ seepage velocity at the later stage under the 40 MPa condition is mainly due to the release-blockage effect of supercritical CO₂. In other words, under certain temperature and pressure conditions, the CO₂ crude oil flow system exhibits both blockage and release-blockage effects simultaneously.

Figure 4. Velocity characteristics of SC-CO₂ in the range of intense pressure fluctuations.

Figure 3 and Figure 4 illustrate two distinct types of seepage velocity performance, consistent with the pressure range classification results of the slim tube experiment. The results indicate that under different pressure conditions, the flow system displays two distinct fluctuation states: stable fluctuation and relatively severe fluctuation.

4.3. Permeability Characteristics

Based on the velocity characteristics of SC-CO₂, three pressure points with more obvious variation features were selected to participate in the calculation of permeability characteristics, namely the pressure points in the range of relatively severe fluctuation pressure. By combining Darcy’s law with the calculation results of the GERG-2008 equation of state, the permeability of SC-CO₂ under different pressures was simulated, and the results were plotted with PV numbers in Figure 5. The simulation results show that the permeability showed a trend of first increasing and then decreasing at 30 MPa and 35 MPa. At 40 MPa, the permeability showed a sudden upward trend after 0.4 PV, which aligns with the pattern exhibited by the seepage velocity.

Figure 5. Characteristics of simulated permeability changes in SC-CO₂.

5. Discussions

Usually, when testing the basic physical properties and wax precipitation characteristics of high-pour-point oil samples, there are many types of equipment and many different methods available for us to choose from, such as the density meter method, the vacuum cutting distillation method, DSC testing, and the rheological method. These methods have their own advantages in exploring the composition, wax precipitation characteristics, and thermal properties of oil samples. However, many methods cannot capture the dynamic characteristics of wax during complex dynamic displacement processes. As in the reservoir conditions, the CO₂ displacement of high-pour-point oil by carbon dioxide occurs in porous media. When temperature and pressure reach critical levels, wax-solids precipitate and deposit, affecting fluid flow behavior. Given the similarities in thermodynamic properties and precipitation mechanisms between wax-solids and asphaltenes, their deposition processes are often interconnected. However, due to fundamental differences in material composition, the methods for evaluating their impact on fluid flow behavior differ significantly. Asphaltenes are soluble in toluene but insoluble in n-heptane, making it relatively easy to study their solubility characteristics and identify suitable solvents for extraction and separation analysis. In contrast, in wax-solids, it is difficult to find stripping solvents. It is very difficult to independently study the effect of wax-solids, which lack easily identifiable stripping solvents, making it challenging to independently assess their impact on the permeability behavior of porous media. To address this, innovative indirect detection methods are employed. For instance, the index formula on the oilfield site is converted into an index formula suitable for physical experimental environments, enabling the indirect detection and analysis of observed trends.

In addition, the heterogeneity of long rock cores and the combined effects of bound water can also interfere with research. Figure 6 highlights the differences between the long core and slim tube. As shown in Figure 6a, the results of this displacement experiment reflect not only wax deposition but also the combined effects of multiple elements, such as core skeleton and bound water. In the literature, papers by Yu (2023) [30] and Xu (2019) [31] studied the blockage during the CO₂ displacement of high-pour-point oil, but did not focus on the separate detachment of wax-solid deposits. In contrast, this study employs a slim tube as a carrier, with a controllable sand filling environment inside (Figure 6b). Then, the injection of pure oil, the index calculation formula, and the state equation are further combined to evaluate the entire seepage process from multiple angles, effectively mitigating interference from heterogeneity, residual oil, and bound water. We focused more on the transition point and pre-breakthrough stage, precisely because carbon dioxide has not yet exerted its maximum extraction effect at this stage, and the relatively small extraction and integration effects offset each other. At the same time, observing the viscosity–temperature curve (Figure 7), the viscosity change in crude oil around 60 °C is not sensitive. Therefore, we believe that at approximately this stage, the seepage velocity is less affected by phase behavior and viscosity changes. We strictly followed the preset step sequence, strictly followed the standard operation in the experiment, and closely associated the seepage velocity with wax deposition at this stage. A relevant design is required before conducting CO₂ displacement experiments with high-pour-point oil. This study establishes a rapid and accurate testing method system, providing crucial support for determining optimal experimental pressure conditions.

Figure 6. Comparison diagram of elements between the long core carrier and slim tube carrier.

Figure 7. Viscosity–temperature curve of test sample.

6. Conclusions

(1)

Based on the fluctuation characteristics of oil production index and injection index, the range of 17–20 MPa belongs to the stable fluctuation pressure range, while the range of 30–40 MPa belongs to the relatively severe fluctuation pressure range.

(2)

This experiment was conducted using homogeneous and waterless slim tubes as carriers. Throughout the entire process, we strictly followed industry standards to ensure the reliability of every step and link and tried to eliminate the influence of other factors (such as viscosity changes, phase behavior, experimental artifacts, etc.) to explore the flow characteristics. The flow velocity trend lines of supercritical CO₂ under the conditions of 30 MPa, 35 MPa, and 40 MPa exhibit inflection points, indicating the occurrence of wax-solid deposition in the displacement system.

(3)

Under the condition of 40 MPa, the CO₂ seepage velocity shows a significant upward trend in the later stage of the experiment, mainly due to the release-blockage effect of supercritical CO₂. According to its strong penetrability and displacement expansion characteristics, CO₂ can also undergo release-blockage under certain temperature and pressure conditions. It is certain that, at certain points, blockage and release-blockage phenomena occur together.

(4)

In the calculation of permeability, the flow of CO₂ is related to Darcy’s law, and there is a positive correlation between the two corresponding parameters. The simulation of the permeability of supercritical CO₂ under different pressure conditions shows a sudden upward trend after 0.4 PV at 40 MPa, indicating that the release-blockage effect impacts not only the flow velocity of CO₂, but also the overall fluid flow capacity of the system.

(5)

With a slim tube as a carrier, the comprehensive evaluation model integrating the index formula and state equation achieves efficient and accurate data processing; based on slim tube testing, the test data is organically combined with state equations, index formulas, and Darcy’s law to fully understand the wax-solid deposition and release-blockage effect and propose optimization strategies, providing valuable guidance for oilfield gas-flooding production.